The Marginal Productivity Theory of Distribution: A Critical History 9781134010899, 1134010893

Table of contents :
Routledge Advances in Heterodox Economics
Contents
Acknowledgements
Introduction
The main criticisms
1 Basic concepts
2 Forerunners and founders
W. Petty (1623–1687), T.R. Malthus (1766–1834), M. Longfield (1802–1884) and I. Butt (1813–1879)
J.H. von Thünen (1783–1850)
C. Menger (1840–1921)
F. von Wieser (1851–1926)
A. Marshall (1842–1924)
P. Wicksteed (1844–1927)
A.W. Flux (1867–1942)
V. Pareto (1848–1923)
L. Walras (1834–1910)
K. Wicksell (1851–1926)
S. Webb (1859–1947)
J.B. Clark (1847–1938)
3 Followers and critics, 1900–1920
J.A. Hobson (1858–1940)
T.N. Carver (1865–1961)
F.Y. Edgeworth (1845–1926)
S.J. Chapman (1871–1951)
H.J. Davenport (1861–1931)
F.W. Taussig (1859–1940)
W.M. Adriance (1878–1957)
4 Followers and critics, 1920 to 1940
G. Cassel (1866–1945)
F.M. Taylor (1855–1932)
F. Knight (1885–1972)
J.M. Clark (1884–1963)
P. Sraffa (1898–1983)
M.H. Dobb (1900–1976)
D.H. Robertson (1890–1963)
J.R. Hicks (1904–1989)
P.H. Douglas (1892–1976)
J.M. Keynes (1883–1946)
R.A. Lester (1908–1997) and F. Machlup (1928–1983)
E.H. Chamberlin (1899–1967)
L.M. Fraser (d. 1963)
5 Followers and critics after 1940
N. Kaldor (1908–1986)
M. Bronfenbrenner (1914–1997)
Joan Robinson (1903–1983)
Y-K. Ng (b. 1942)
S. Weintraub (1914–1983)
E.J. Nell (b. 1935)
H.G. Johnson (1923–1977)
M. Blaug (b. 1925)
6 Summary of the main themes
Monocausality, multicausality and disentanglement
Imputation of factor rewards by means of simultaneous equations
The adding-up (or exhaustion-of-product) problem and the use of Euler’s theorem
Circularity and the measurement of capital
Social and political implications
7 Miscellaneous considerations
The Clarkian and the positivist meanings of MPL
Calculation of fully net marginal products: the allocation of fixed or overhead costs
The MPTD and exploitation
An equitable-by-chance outcome
The MPTD, the labour theory of value and the law of diminishing returns
The MPTD and the indivisibility of inputs
The MPTD and supply-side considerations
The MPTD, the MC = MR rule and the true marginal cost
8 The normative language of the non-normative MPTD
9 General conclusion: neither normative nor positive
Appendix A W.S. Jevons (1835–1882) and the MPTD
Appendix B Marshall’s concept of net marginal product: fully net or partially net?
Appendix C Wicksteed’s recantation
Notes
References
Index

Citation preview

The Marginal Productivity Theory of Distribution The Marginal Productivity Theory of Distribution (MPTD) claims that in a free-market economy the demand for a factor of production will depend upon its marginal product – where ‘marginal product’ is defined as the change in total product that is caused by, or that follows, the addition or subtraction of the marginal unit of the factor used in the production process, with all other inputs held constant. From its inception in the early nineteenth century the MPTD has been claimed by some economists to be a solution to the ethical problem of distributive justice, i.e. to be a means of determining fairness in wages, profits, interest and rent. Other economists have rejected this ethical claim, but have seen the MPTD as a valid demand-side criterion in the determination of equilibrium and efficiency. This book argues that the MPTD is valid, neither as a normative theory of social justice, nor as a positive law of economics. It suggests that economics is yet to develop a satisfactory theory of distribution that is scientific in the quantitative or mathematical sense. Through a survey of the origin and subsequent evolution of the MPTD in the writings of over 50 contributors over 150 years, John Pullen presents a critical history of the concept. The book begins by examining the conceptual tools that have been deployed to facilitate this analysis of past contributions to the MPTD and then looks at various economists and their contribution to the debate including its supporters such as Wicksteed, Marshall, Wicksell and Stigler, and its critics such as Pareto, Hobson, Edgeworth, Adriance and Cassel. This book will be of interest to students and researchers in microeconomics, macroeconomics and the history of economics. John Pullen was previously Associate Professor in the Department of Business, Economics and Public Policy at the University of New England, Australia, before being appointed as an Honorary Fellow in 2006.

Routledge Advances in Heterodox Economics Edited by Frederic S. Lee University of Missouri-Kansas City Over the past two decades, the intellectual agendas of heterodox economists have taken a decidedly pluralist turn. Leading thinkers have begun to move beyond the established paradigms of Austrian, feminist, Institutionalevolutionary, Marxian, Post Keynesian, radical, social, and Sraffian economics – opening up new lines of analysis, criticism, and dialogue among dissenting schools of thought. This cross-fertilization of ideas is creating a new generation of scholarship in which novel combinations of heterodox ideas are being brought to bear on important contemporary and historical problems. Routledge Advances in Heterodox Economics aims to promote this new scholarship by publishing innovative books in heterodox economic theory, policy, philosophy, intellectual history, institutional history, and pedagogy. Syntheses or critical engagement of two or more heterodox traditions are especially encouraged. 1 Ontology and Economics Tony Lawson and his critics Edited by Edward Fullbrook 2 Currencies, Capital Flows and Crises A Post Keynesian analysis of exchange rate determination John T. Harvey 3 Radical Economics and Labor Frederic Lee and Jon Bekken 4 A History of Heterodox Economics Challenging the mainstream in the twentieth century Frederic Lee

5 The Marginal Productivity Theory of Distribution A critical history John Pullen This series was previously published by The University of Michigan Press and the following books are available (please contact UMP for more information): Economics in Real Time A theoretical reconstruction John McDermott Liberating Economics Feminist perspectives on families, work, and globalization Drucilla K. Barker and Susan F. Feiner Socialism After Hayek Theodore A. Burczak Future Directions for Heterodox Economics Edited by John T. Harvey and Robert F. Garnett, Jr. Heterodox Macroeconomics Edited by Jonathan P. Goldstein and Michael G. Hillard

The Marginal Productivity Theory of Distribution A critical history John Pullen

LONDON AND NEW YORK

First published 2010 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN Simultaneously published in the USA and Canada by Routledge 270 Madison Ave, New York, NY 10016 Routledge is an imprint of the Taylor & Francis Group, an informa business This edition published in the Taylor & Francis e-Library, 2009.

To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk. © 2010 John Pullen All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data Pullen, John, 1933– The marginal productivity theory of distribution : a critical history / John Pullen. p. cm. Includes bibliographical references and index. 1. Marginal productivity. 2. Distribution (Economic theory) 3. Production (Economic theory) I. Title. HB523.P85 2009 331.2′101—dc22 2008054170 ISBN13: 978-1-134-01088-2 ePub ISBN ISBN10: 0–415–48712–9 (hbk) ISBN10: 0–203–87576–1 (ebk)

ISBN13: 978–0–415–48712–2 (hbk) ISBN13: 978–0–203–87576–6 (ebk)

Contents Acknowledgements xi

Introduction 1 1 Basic concepts 8 2 Forerunners and founders 11 W. Petty (1623–1687), T.R Malthus (1766–1834), M. Longfield (1802–1884) and I. Butt (1813–1879) 11 J.H. von Thünen (1783–1850) 14 C. Menger (1840–1921) 15 F. von Wieser (1851–1926) 17 A. Marshall (1842–1924) 19 P. Wicksteed (1844–1927) 27 A. W. Flux (1867–1942) 30 V. Pareto (1848–1923) 35 L. Walras (1834–1910) 39

K. Wicksell (1851–1926) 42 S. Webb (1859–1947) 50 J.B. Clark (1847–1938) 51 3 Followers and critics, 1900 to 1920: from Hobson to Adriance 61 J.A. Hobson (1858–1940) 61 T.N. Carver (1865–1961) 68 F.Y. Edgeworth (1845–1926) 71 S.J. Chapman (1871–1951) 74 H.J. Davenport (1861–1931) 76 F.W. Taussig (1859–1940) 78 W.M. Adriance (1878–1957) 81 4 Followers and critics, 1920 to 1940: from Cassel to Fraser 83 G. Cassel (1866–1945) 83 F.M. Taylor (1855–1932) 88 F. Knight (1885–1972) 90

J.M. Clark (1884–1963) 94 P. Sraffa (1898–1983) 96 M.H. Dobb (1900–1976) 99 D.H. Robertson (1890–1963) 101 J.R. Hicks (1904–1989) 102 P.H. Douglas (1892–1976) 107 J.M Keynes (1883–1946) 108 R.A. Lester (1908–1997) and F. Machlup (1928–1983) 109 E.H. Chamberlin (1899–1967) 112 L.M. Fraser (d. 1963) 113 5 Followers and critics after 1940: from Kaldor to Blaug 116 N. Kaldor (1908–1986) 116 M. Bronfenbrenner (1914–1997) 117 Joan Robinson (1903–1983) 118 Y-K. Ng (b. 1942) 123

S. Weintraub (1914–1983) 124 E.J. Nell (b. 1935) 124 H.G. Johnson (1923–1977) 125 M. Blaug (b. 1925) 128 6 Summary of the main themes 134 Monocausality, multicausality and disentanglement 134 Imputation of factor rewards by means of simultaneous equations 135 The adding-up (or exhaustion-of-product) problem and the use of Euler’s theorem 135 Circularity and the measurment of capital 136 Social and political implications 137 7 Miscellaneous considerations 138 The Clarkian and the positivist meanings of MPL 138 Calculation of fully-net marginal products: the allocation of fixed or overhead costs 139 The MPTD and exploitation 141

An equitable-by-chance outcome 142 The MPTD, the labour theory of value, and the law of diminishing returns 142 The MPTD and the indivisibility of inputs 143 The MPTD and supply-side considerations 144 The MPTD, the MC = MR rule, and the true marginal cost 144 8 The normative language of the non-normative MPTD 148 9 General conclusion: neither normative nor positive 152

Appendix W.S. Jevons (1835–1882) and the MPTD 155 A Appendix Marshall’s concept of net marginal product: fully net or B partially net? 158 Appendix Wicksteed’s recantation 162 C Notes 167 References 191 Index 203

Acknowledgements I am particularly grateful to Geoff Harcourt, Fred Lee, John King, and two anonymous readers for their extremely detailed and valuable assistance. The first version of this study was presented as a paper at the thirteenth conference of the History of Economic Thought Society of Australia, at Sydney University, July 2000, and received many useful comments from conference participants. Additional helpful advice has been generously given over the years by Mike Canfell, Peter Cribbett, Paul Flatau, Hitoshi Hashimoto, Michael McClure, Paul Oslington, Robert Prasch, Greg Smith, Malcolm Treadgold and Michael White. None of the above, however, should be held responsible for any remaining errors and omissions.

Introduction The history of the Marginal Productivity Theory of Distribution (MPTD) is characterized by vigorous debate. In the writings of J.B. Clark the MPTD was accorded the status of a scientific law and a moral imperative – a status that it seems to have retained in many modern textbooks. But early twentiethcentury critics, such as J.A. Hobson, accused it of ‘false separatism’, and argued that the impossibility of disentangling the specific products of the various factors of production destroyed both its intellectual respectability and its practical usefulness. By the mid-twentieth century the MPTD was developed as a purely positive theorem, purporting to be an essential element in explaining the path to profit maximization and equilibrium, claiming to be devoid of normative implications, and enjoying the status of one of the fundamental truths of neoclassical economics. D.H. Robertson said of it: ‘the statement that ‘wages tend to measure the marginal productivity of labour’ is at once the most illuminating analytically and the most important practically for the consideration of wage policy’ (1950, 221). More recently, it has been said: It is difficult to exaggerate the importance of marginal productivity. Without a general theory of production and distribution, neoclassical economics would never have displaced classical thinking … marginal productivity offered a clear rationale for why factor prices are determinate, a problem that had vexed late nineteenth-century economists. (Mandler 1999, 19–20) However, beginning in the 1950s, during the Cambridge capital theory controversy, arguments came from the side of Cambridge (UK) that challenged its status even as a positive theorem. As the name suggests, the MPTD claims that in a free-market economy the demand for a factor of production will depend upon its marginal product – where ‘marginal product’ is defined as the change in total product that is caused by, or that follows, the addition or subtraction of the marginal unit of the factor used in the production process, with all other inputs held constant. Those who support the MPTD claim that a distribution system based on the principle of marginal productivity will be economically efficient and will move each firm toward a situation of maximum profits. They see the MPTD as a fundamental positive law of neoclassical economics. However, some exponents of the MPTD – notably J.B. Clark (1899) – introduced normative implications into the MPTD, arguing that distribution according to marginal productivities is not only economically but also

morally correct. For Clark and other like-minded exponents a distribution system based on the MPTD conforms to the principles of natural justice and, if the MPTD is allowed to prevail, all exploitation would be removed from the economic system and all allegations of class conflict will be effectively answered. The vigour with which the MPTD controversy has been waged is thus explained by the fact that as well as being an intriguing intellectual exercise, it has aroused political and ideological conflicts. Some see it as the ultimate answer to the radical critiques of writers such as Karl Marx, Henry George and Major Douglas. If the distribution of factor incomes on the basis of the MPTD is both economically efficient and morally justified there are no grounds for class conflict, no case for government interference in income distribution, no reason to overthrow capitalism, no need to make land common property or to redistribute land values through taxation, and no need to socialise bank credit. Others see the MPTD as a surreptitious and questionable attempt to justify the existing social class structure and existing distribution of wealth, to show the futility of trade union attempts to raise wages and, in short, to discredit all socialist or redistributionist policies. However, attitudes toward the MPTD do not fall neatly into the two categories – labour versus capital, or socialist versus capitalist. It receives support from economists of a conservative political disposition as well as from economists of a radical or reformist disposition. The former see it as an iron law of wages; as a scientific answer to the socialist argument that labour is always exploited and persecuted under capitalism; as a theoretical counter to trade union pressure for higher wages; and as a defence of laissez-faire. They argue that it is neither economically nor morally justified for wages to be higher than the marginal product of labour. Employers find ready consolation in the MPTD because it appears to exonerate them from charges of exploitation, and to place the onus for higher wages on the employees themselves. If wages are affected by the marginal product of labour, then (it is argued) the way to increase wages is for employees to work harder and to improve their marginal productivity. Modern textbooks often claim that the MPTD is a purely positive theorem, devoid of any revolutionary, reformist or reactionary politics; but, as will be seen below, some of the most prominent advocates of the MPTD have clearly been motivated by a desire to defend capitalism against socialist critiques. But some economists of a redistributionist or egalitarian tendency also support and invoke the MPTD. They see the MPTD as a welcome theoretical justification for higher wages and for the reform of capitalism, arguing that

when workers do not receive as wages the full value of their marginal product, they are being exploited. This study of the MPTD comprises nine chapters. Chapter 1 introduces the basic conceptual tools that have been deployed to facilitate this analysis of past contributions to the MPTD. In particular, it defines and seeks to justify the following concepts and terms: the specific marginal product of labour (SMPL); the marginal product after labour (MPAL); the fully net marginal product of labour and the partially net marginal product of labour; the notion of the proprietorial ‘of’; monocausal and multicausal marginal products; and the difference between ceteris paribus and ceteris inefficacibus. Chapter 2 considers those early contributors who may be regarded as the forerunners or founders of the MPTD. Chapters 3, 4 and 5 present and discuss a wide selection of contributions from followers and critics. Because of the importance and influence of George Stigler (1911–1991) in the history of the MPTD, his views are quoted and discussed in many sections throughout this study, rather than in one specific section. His discussion of the MPTD was, however, rather selective, concentrating mainly on likeminded defenders of the MPTD and suggesting a progressive line of development. This study attempts to supplement Stigler’s by introducing a discussion of some of the critics of the MPTD – for example, Hobson, Davenport and Adriance, who were not considered in Stigler’s Production and Distribution Theories (1941) – and to give as much attention to its criticisms as to its defenders. The four chapters – 2, 3, 4 and 5 – are arranged in (roughly) chronological rather than thematic order, so that each contribution can be explored in detail and located in its historical setting. The views of each contributor are considered in turn, and compared and contrasted with those of predecessors and successors. The aim has been to re-create the debate as it progressed and to emphasise its continuity. The grouping of this material into four chapters is somewhat arbitrary, and is not meant to convey any significant intellectual categorisation. Although writers such as Wicksteed, Marshall, Wicksell and Stigler were in general agreement in supporting the MPTD, their reasons for doing so often differed from one another, and the degree of their support often varied over time, leading in at least one case (Wicksteed) to an arguable recantation. Likewise, among those who opposed the MPTD, or opposed certain aspects of it, such as Pareto, Hobson, Edgeworth, Adriance and Cassel, there was no unanimity on the nature and reasons for their opposition. To give a full and fair account of the content of each contribution, and to cope with the particularities and complexities of the arguments on both sides, it became obvious that each of the contributors would have to be treated in the first instance in a one-by-one chronological sequence, even though that

has meant some unavoidable repetition when each contribution is weighed against the basic concepts and major themes of this critique. Chronological presentation allows the ideas of each author on various aspects of the MPTD to be brought together in one particular subsection, instead of being dispersed under thematic headings, thus facilitating an overall appreciation of the content and interconnections of each author’s position. There are, however, instances where a particular author – especially a more influential one – is referred to in locations other than the subsection bearing his or her name. The Index will enable these dispersed references to be located. The survey of contributions is a selection only, and does not pretend to be comprehensive.1 One of its regrettable limitations is that it is mainly restricted to works written in English or translated into English – a limitation that hopefully does not cause offence and that can be at least partially justified on the principle of division of labour. The selection will be sufficiently justified if it succeeds in conveying an impression of the extent and intensity of the debate. Whereas Chapters 2 to 5 present the individual contributions in (roughly) chronological order, Chapter 4 collates them in thematic order. For example, the question of whether or how capital can be measured was discussed by a number of authors covered in Chapters 2 to 5, notably Wicksell, Sraffa and Joan Robinson, whose individual views are presented in detail. In Chapter 6 their individual views are brought together in summary form under the theme ‘Circularity and the measurement of capital’, and compared and contrasted, together with comments from the secondary literature where appropriate. The five main themes thus summarised in Chapter 6 are: • Monocausality, multicausality and disentanglement This theme concerns the causality of the marginal product, i.e. the question of whether the marginal product is a monocausal or a multicausal phenomenon, and involves the disentanglement problem, i.e. the question of whether, if more than one factor is involved in the production of the marginal product, their particular contributions can be disentangled. If the marginal product of labour is the product of the marginal unit of labour alone there is no disentanglement problem, and it would be appropriate from both an economic and an ethical perspective to allocate the marginal product to the marginal unit. Similarly, no disentanglement problem is involved in allocating the marginal product of capital to the marginal unit of capital, and the marginal product of land to the marginal unit of land.

Although advocates of the MPTD have recognised the multicausality of the total product and the impossibility of disentangling the separate contributions of the various factors to the total product, they have usually regarded the marginal product as monocausal, and have therefore maintained that, where marginal products are concerned, there is no disentanglement problem; the marginal product of each factor can be identified and separately measured. • Imputation of factor rewards by means of simultaneous equations Running parallel with the development of the MPTD, there has been an alternative approach that attempts to solve the problem of distribution by means of simultaneous equations. • The adding-up (or exhaustion-of-product) problem and the use of Euler’s theorem The amount of attention given over the years to the adding-up (or exhaustionof-product) problem is indicative of the major role it has played in attempts to prove the validity of the MPTD. If the sum of the revenues of the factors does not equal the total output, a marginal productivity theory of distribution cannot be valid. It is therefore imperative for supporters of the MPTD to prove that the adding-up theorem is correct. A coherent summary of the adding-up arguments is rendered difficult by the fact that some of the contributors appear to have begun by supporting it but to have later changed their minds, thus presenting us with the problems of reconciling their altered views and defining the precise nature of and reason for their recantation. • Circularity and the measurement of capital A recurring objection to the MPTD has been the idea that it involves circular reasoning, and is therefore incapable of reaching a determinate solution. There are a number of versions of the circularity problem. One states that circularity arises from the fact that, in order to determine the rate of wages, the MPTD requires calculation of the marginal product of labour, but before that can be calculated, the cost of the additional other variables that need to be employed along with the marginal unit of labour have to be deducted, but their cost depends on the prevailing rate of profit, and this can be known only if the rate of wages is already known. It has been argued that the principal problem for the MPTD is not the adding-up problem but the circularity involved in the measurement of capital. • Social and political implications

The MPTD is frequently surrounded by an odour of sanctity. If the marginal product of labour is monocausally attributed to the marginal unit of labour then, on the basis of a Lockean theory of property rights, a short logical step will lead to the conclusion that the marginal unit of labour has an exclusive right to the marginal product of labour, and that for labour to receive either more or less than its marginal product would be an injustice, an exploitation, and a contravention of natural and moral law. This normative interpretation of the MPTD has been described as ‘naïve productivity ethics’, and the MPTD has been declared a positive theorem devoid of moralistic implications, but as shown in Chapter 8, a moralistic tone nevertheless pervades many modern accounts of the MPTD. Although the MPTD is often put forward as a purely positive theorem, a number of prominent exponents have made no secret of the fact that their motivation in developing the MPTD was to promote certain political, ethical and ideological goals. Some have welcomed the MPTD as a theoretical refutation of a socialistic redistribution of wealth, and have regarded it as a means of preserving the existing order and preventing the onset of social chaos and anarchy. Chapter 7 expands and clarifies the critique of the MPTD by discussing in more detail some of the issues touched upon by the writers considered in the preceding chapters. Chapter 8 shows that, although many modern presentations of the MPTD profess to be theorems of positive science, they contain vestiges of the language of normative judgements. In the light of the arguments of this study, Chapter 9 draws a number of conclusions about the status of the MPTD as a normative and as a positive law of distribution. It argues that the MPTD lacks both normative and positive credibility. Its inadequacies render it ineffectual and unconvincing as an explanation of the distribution process, and unsatisfactory as a substitute for the bargaining power theory of distribution. The popularity, persistence and prestige of the MPTD could be attributed, at least in part, to its association with differential calculus and Euler’s theorem, which have bestowed upon it an aura of ‘scientific’ respectability. They may also be attributed, at least in part, to a fear that the theoretical vacuum created by abandoning the MPTD might be filled by politically unacceptable heterodox alternatives. This study suggests that although the bargaining power theory of distribution might lack the mathematical apparatus usually associated with the MPTD, it is markedly superior as an expression of marketplace realism. If the scientific status of a theory is judged by its success in explaining reality, then a simple bargaining or supply-and-demand

theory of distribution can claim to be more truly scientific than the MPTD pretender. Popular textbooks sometimes refer to limitations on the real-world applicability of the MPTD, but rarely if ever present any serious challenges to its essential validity or usefulness. They see the MPTD as the orthodox theory of distribution, and imply that any challenges are regrettable deviations – whereas, from the perspective of critics of the MPTD, it is the MPTD that has been a long-standing regrettable deviation. This study sets out to redress the balance of the debate, and to show that the critics have made a significant and convincing contribution to a more acceptable and realistic theory of distribution.

The main criticisms The following are the main criticisms of the MPTD presented in this study. They are stated briefly and bluntly at this point, and are developed in detail below. • Formulations of the MPTD do not generally recognise that the marginal product of a variable factor is a multicausal phenomenon, even though the other factors are held constant. This means that the MPTD does not provide a satisfactory answer to the disentanglement problem. It does not explain what portion of the marginal product is attributable to the variable factor and what portion to the fixed factors. Failure to resolve the disentanglement problem undermines the normative or distributive justice claims sometimes made for the MPTD, and means that the MPTD cannot provide a sound basis for the distribution of factor rewards. Even if the marginal product that occurs after the employment of the last unit of labour is equal to almost nothing, that ‘almost nothing’ is not produced by the last unit of labour alone. If the last unit of labour receives a wage equal to the marginal product that occurs after the employment of the last unit of labour, the last unit of labour is receiving a reward for something it has not produced. • The use of simultaneous equations to solve the distribution problem presents considerable practical difficulties in establishing the equations and, more fundamentally, provides only a description of what is actually happening, rather than a theory of distribution. • The use of Euler’s theorem to solve the adding-up or exhaustion-of-product problem is not appropriate, because it refers to a situation where the variables change simultaneously, whereas the situation considered by the MPTD is one

where, because of the ceteris paribus assumption, changes to the factors occur sequentially. • The application of the MPTD to real-world situations requires the allocation of fixed costs among the various factors of production, but neither economic theory nor accountancy theory appears capable of providing a rational principle of allocation. • Repeated assertions are made that the MPTD in its modern version is a positive theorem, devoid of normative implications, but the language of many modern presentations retains distinct vestiges of ethical and ideological judgements. Whether intentionally or not, advocates of the MPTD continue to convey the impression that it remains an ethical theory of distribution.

1 Basic concepts A major theme in this attempt to trace and interpret the volatile history of the MPTD is the distinction between two possible meanings of the expression ‘the marginal product’ of a factor of production. On the one hand, the expression can mean the portion of the product that has been actually produced by the marginal unit of the factor. On the other hand, it can mean the change (in the total output) that occurs after the addition or subtraction of the marginal unit of the factor. Both meanings have been used, and are still being used, in the MPTD literature, often without being clearly distinguished. Given the centrality of the distinction in the following study of the history of the MPTD, it is essential that it be explained and justified in some detail. To simplify the explanation the following definitions and acronyms are deployed: • SMPL, or the specific marginal product of labour. When labour (the variable factor) is combined with other (fixed) factors in a productive process, the SMPL is the portion of the product that has been physically produced or caused by the marginal unit of labour, as distinct from the portions causally attributable either to the fixed factors or to previous, intra-marginal units of labour. Similarly, SMPK and SMPN are the specific marginal products of capital and of land (or natural resources). • MPAL, or the marginal product after labour, is the increase in the total product that occurs after the employment of the marginal unit of labour. Similarly, MPAK and MPAN. • MPL is the marginal product of labour, without specifying whether it be SMPL or MPAL. The distinction between the SMPL and the MPAL appears to be fundamental to any attempt to understand and evaluate the arguments and counterarguments surrounding the MPTD. It derives from the obvious fact that the MPAL is a multicausal phenomenon. Every production process obviously requires more than one factor. Capital produces nothing without labour. Even the simplest form of labour produces nothing without material resources. Every unit of output, even a marginal unit, is therefore a multicausal or joint product, composed of the specific products causally contributed by the different factors. The MPTD proceeds on the assumption that while one factor varies, the other factors are held constant. From this it might appear that the change in total

product is caused by the marginal unit of the variable factor alone. But this appearance of monocausality would be deceptive, since the marginal unit of the variable factor does not act alone. It acts in combination with the factors that are held constant or assumed to be constant. These constant factors contribute causally to the change in the total product, even when they are being held constant. Holding them constant does not eliminate their effectuality. It would be an illusion to conceive of an unchanged factor as being incapable of producing changes; or to claim that, when labour is the only thing that changes, labour is the only cause and the only cost. Ceteris paribus is not the same as ceteris inefficacibus. An active, causal factor is not magically transformed into a passive, non-causal factor simply by intoning ceteris paribus. The factories and machines that perform causative and productive functions in cooperation with labour are not suddenly rendered impotent by the incantation of the ceteris paribus clause. In calculating the marginal product of labour, ceteris paribus eliminates the effect of any changes to capital, but does not eliminate the ongoing causal influence of existing capital.1 To regard the marginal product of labour as being caused by the marginal unit of labour alone is to argue post hoc ergo propter hoc, and to interpret a correlation as a causation. The longevity and popularity of the MPTD may be seen as a tribute to the awesome ubiquity and influence of that fallacy in economics. The change in the total product that occurs after the application of a marginal unit of labour is not caused by that marginal unit of labour alone. The MPAL is produced by the other factors as well as by labour, even if the other factors remain unchanged when an extra unit of labour is employed. The MPAL involves specific contributions caused by capital and land as well as the specific contribution caused by labour. The causative role of the fixed factors, as well as that of the variable factor, may be illustrated by applying Alfred Marshall’s famous metaphor of the two blades of a pair of scissors to explain the dual roles of demand and supply in the determination of value. One blade acting alone will not be sufficient; a pair of scissors requires a second blade, even if it is held in a fixed position. Applying this metaphor to the MPTD, the marginal unit of the variable factor, acting alone, will not produce any change in the product. To be productive, it requires also a causative input exercised by the fixed factors, even though they are held fixed. This distinction between the MPAL and the SMPL may also be described as a distinction between the proprietorial and non-proprietorial uses of the preposition ‘of’. Previous studies of the MPTD (e.g. Machlup ([1936] 1950) have discussed some of its main concepts such as marginal product, marginal physical product, marginal value product, and so on. This study extends the

linguistic analysis to the meaning of ‘of’, and highlights the ambiguities that occur in the use of ‘of’ in the concept ‘marginal product of a factor’. The word ‘of’ is one of the shortest and most frequently used in the English language, but one of the most difficult to define. The Oxford English Dictionary gives no fewer than 63 senses in 16 categories. This paper will be concerned with the fourteenth category: ‘In the sense of belonging or pertaining to; expressing possession and its converse: ‘the owner of the house’, ‘the house of the owner’’, and in particular with sense no. 49a conveying the notion of proprietorship: ‘Belonging to a person (etc.) as something that he (etc.) has or possesses.’ Discussion of the proprietorial ‘of’ is also extended to other words connoting a proprietorial relationship, such as pronouns in the possessive case (his, hers, its, their); nouns in the genitive case (labour’s, capital’s); and words such as ‘from’, ‘by’ and ‘to’ (as used in the phrases ‘arising from’, ‘created by’, ‘due to’) that suggest a causative and hence a proprietorial connection. The language of the pioneers of the MPTD – their frequent use of the proprietorial ‘of’; the possessive adjectives ‘his’, ‘its’, ‘their’; and verbs such as ‘results from’ and ‘occasions’ – provides undeniable textual evidence of a concern with causal connections. The view that the MPTD is concerned only with costs and not with causes is a later development in the history of the MPTD. The use of the proprietorial sense of ‘of’ in the expression ‘marginal product of labour’ might conceivably be justified by arguing that, in saying the marginal product is the product ‘of’ labour, we are not saying it is the marginal product of labour alone in an exclusionary sense. But that qualification is rarely mentioned in the literature. Readers are rarely warned against interpreting the use of ‘of’ in a sole proprietor sense. In the absence of such warning, the implication is that those who use ‘of’ in the expression ‘marginal product of labour’ intend to use it, and intend it to be interpreted, in an exclusive, monocausal, sole-proprietor sense. An appropriate subtitle for this study would be ‘The use and abuse of the proprietorial ‘of’’. Another important element of the conceptual apparatus deployed in the following critique of the MPTD is the distinction between gross marginal product and net marginal product – or ‘marginal net product’, to use Alfred Marshall’s term. Marshall emphasised this distinction in recognition of the fact that when a marginal unit of labour is employed, it is often necessary, for technical reasons, to employ extra units of non-labour factors to assist the marginal unit of labour. In Marshall’s example, the extra shepherd requires an extra crook. The cost of the extra non-labour factors is deducted from the gross MPAL to arrive at the net MPAL.

Marshall’s concept of net marginal product is further elaborated in what follows by distinguishing between the ‘partially net marginal product of labour’ and the ‘fully net marginal product of labour’ – with apologies to readers for the unavoidable cumbersomeness of the terms. This distinction occupies a key position in assessing the validity of the MPTD as a principle of positive economics. It is developed in detail below, but in simple introductory terms the concept of the partially net MPAL is arrived at by deducting from the gross MPAL the cost of the extra units of other variable factors that need to be employed along with the marginal unit of labour; whereas the concept of the fully net MPAL requires that a portion of the costs of the fixed factor(s) be also deducted.2

2 Forerunners and founders This chapter deals with 15 authors who contributed to the early development of the MPTD. Some of the contributions could only be described as vague intimations or approximations that were not recognised by the contributors themselves or by their contemporaries as formal statements of the MPTD. Other contributions in this chapter, however, have come to be regarded as the seminal foundations of the MPTD to which future scholars continually return.

W. Petty (1623–1687), T.R. Malthus (1766–1834), M. Longfield (1802–1884) and I. Butt (1813–1879) There are a number of possible claimants to the title of founder of the MPTD. According to Routh (1975, 40), one such is William Petty who in his Political Anatomy of Ireland (1672) calculated what each factor could produce in the absence of the others, and so enunciated the essence of the MPTD. Thomas Robert Malthus could also be considered as an early contributor when he said in his Principles of Political Economy (1820): ‘[Profits] are only a fair remuneration for that part of the production contributed by capitalists, estimated exactly in the same way as the contribution of the labour’ (1989, I, 81). On the basis of this statement, Schumpeter (1954, 114) heralded Malthus as a pioneer of ‘the productivity theory of distribution’. Malthus’ pioneer status could also be seen in his concept of the rent of land as the product of the ‘quality of the earth, by which it can be made to yield a greater portion of the necessaries of life than is required for the maintenance of the persons employed on the land’ and as ‘a boon most important to the happiness of mankind’ (1989, I, 139, 239). His concept of rent in this absolute sense, as distinct from differential rent, could be regarded as a precursor of the notion of the specific product of a factor, as explained above. The classical theory of differential rent is another possible precursor. As Steedman (1997, 48) notes, ‘it is not difficult to present the logic of the Anderson-Malthus-West-Ricardo theory of (intensive) rent as a marginal productivity theory, applied to at least one input’; and this view appears to be shared by Kurz (1999, 145), who interprets marginalism as ‘an offspring of the theory of differential rent as it had been developed by authors such as Thomas Robert Malthus’, and as a ‘generalisation of the principle of

intensive diminishing returns to the treatment of all sorts of economic phenomena’. Schumpeter claimed that Mountifort Longfield, in lectures delivered at Trinity College, Dublin, in 1833, and published in 1834, presented ‘a reasonably complete and reasonably correct theory of distribution based upon the marginal productivity principle, not only the marginal cost principle’ (Schumpeter 1954, 465). Longfield ‘explained both profits … and wages in terms of the contributions to total product that result from the addition to the productive set-up of the last element of capital (tools) or labor’ (Schumpeter 1954, 465; cited by Black (1971), who notes that Bowley (1937, 185) also attributed a marginal productivity theory of wages to Longfield). The strongest evidence for the claim that Longfield was a pioneer of the MPTD appears to be the following: If a spade makes a man’s labour twenty times as efficacious as it would be if unassisted by any instrument, only of his work is performed by himself, and the remaining must be attributed to the capital. And this is the measure of the intensity of the demand for such an instrument. A labourer working for himself would find it for his interest to give of the produce of his labour to the person who would lend him one, if the alternative was that he should turn up the earth with his naked hands; or if he worked for another, his employer might pay a similar sum for the purpose of supplying him with an instrument. (Longfield [1834] 1931, 195; quoted in Moss 1973, 327) As Moss (1973, 327) shows, if a worker is willing to rent a machine for of the joint product of his labour and the machine, then that rental value is the marginal product of the machine, for it is the difference between what the worker can produce with and without the machine. In his own words, Longfield was in effect saying that the demand for capital will be determined by the value of its marginal product. Black agrees that Longfield applied a marginal productivity theory to capital and profits, but rejects the view that Longfield also had a marginal productivity theory of labour and wages. According to Black, Longfield regarded wages as being determined by each labourer’s specific input, not by the marginal product increment.1 He describes Longfield’s theory of wages as a productivity theory, rather than as a marginal productivity theory, but does not belittle Longfield’s achievement. He regards Longfield’s ideas on distribution as ‘[p]erhaps his most original contribution’ (Black 1987, 237): ‘it remains undeniable that to present the essence of a marginal productivity

theory of capital returns and a productivity theory of wages was a massive achievement of original thought in 1833.’2 The weakness of Longfield’s argument is that it involves what J.A. Hobson later described as a ‘false separatism’ (see below). Although the argument has an air of superficial plausibility in a situation where a unit of capital is added to labour, it loses symmetry and plausibility in a situation where a unit of labour is added to capital. Capital by itself can produce nothing. If a unit of labour is added, the joint product is, say, 20 units. A strict application of the MPTD must then lead to the absurd conclusion that the MPL is 20 units and that there can be no return to capital, i.e. that wages equal 20 units and profits equal zero. Although Longfield’s argument could be described as a marginal productivity theory of capital, it cannot readily be interpreted as a marginal productivity theory of labour. Moss also argues that Longfield’s views on the determination of the profits of capital were extended by Isaac Butt – Longfield’s successor at Trinity College, Dublin – to the determination of the rent of land, and to ‘a general principle for explaining all factor payments’ (Moss 1973, 335). When Butt said that ‘the proportion in which their joint product is divided between the capitalist and the labourer’ is given by ‘the relation in exchange between the product of the powers of capital and the product of unassisted labour’ (Butt 1838, 20), he seems in effect to have been saying that returns to factors are determined by the respective outputs of the factors, and was thus presenting a productivity theory of distribution. But he came close to presenting a marginal productivity theory of distribution when he illustrated his argument by an example in which he supposed that ‘a machine which cost £10,000 would make 100 men do the work of 120, and that it were possible, by expending an additional £10,000 in improving it, to make them do the work of 130 men’. He concluded: it is quite evident that the owner of the machine will not expend the money until the relative value of the power of labour and capital has reached the point at which £10,000 worth of capital will be equal to the value of the labour of ten men. (Butt 1838, 23) In this cumbersome but quite effective example, Butt was saying that a marginal expenditure of £10,000 on capital equipment will increase output by 20 per cent (from the output of 100 men to the output of 120 men), and a further expenditure of £10,000 on capital equipment will increase output by 81/3 per cent (from the output of 120 men to the output of 130 men); and that the additional expenditures on capital equipment will occur only if they are

equal to the additional revenue. Although he did not express the idea as a formal statement, he thus seems to have argued that (1) investment in capital equipment will occur up to the point where marginal revenue equals marginal cost; (2) the return to a factor of production will be determined by the value of its marginal product; and (3) the returns to successive amounts of investment in capital equipment will tend to diminish. There were of course a number of loopholes and unanswered questions in Butt’s exposition – for example, can the product of ‘unassisted labour’ be more than extremely small or even zero; and, given that the product of capital and labour is a joint product, how can their separate outputs be disentangled? However, these deficiencies do not detract from the fact that Butt’s writings contain clear intimations of the MPTD.3

J.H. von Thünen (1783–1850) The first truly marginal productivity theory of distribution appears to have come from J.H. von Thünen. In Part II (first published 1850), Section I of The Isolated State, in a chapter entitled ‘The wage is equal to the extra product of the last labourer who is employed in a large enterprise’, von Thünen presented an example of how the production of potatoes increases when more people are employed to gather them, and argued that ‘the rational farmer … who wishes to obtain the maximum net product’ will employ extra labourers until ‘the value of the extra output is in balance with the labour cost of its production’. A table used in the example contains a column headed ‘The last person hired therefore produces an increment of’. He concludes that ‘as long as he continues to derive a profit it is in the entrepreneur’s interest – be he manufacturer or farmer – to go on raising the number of his labourers’ and that ‘the wage equals the additional product created by the last man hired’ (Thünen 1966, 235, 254–6; emphases added). Thünen provided the basis for the standard exposition of the MPTD but, at the same time, his ideas contained themes that were later to give rise to a strong current of criticism and dissent. Although Thünen has been rightly credited with being the founder, or one of the founders, of the MPTD, he could also be debited with being the founder, or one of the founders, of the failure to distinguish between the marginal product that occurs after the employment of an additional unit of labour, and the marginal product that can be causally attributed to that unit of labour; or in the terminology used in Chapter 1, the failure to distinguish between the specific marginal product of labour (SMPL) and the non-specific or multicausal marginal product after labour (MPAL). The italicized words in the above quotations from The Isolated State – namely ‘of’, ‘labour cost’, ‘produces’, ‘credited by’ –

suggest that Thünen believed that the increase in the total product following the employment of an extra unit of labour is attributable in an exclusive causal sense to that unit of labour. Later critics argued that the use of ‘of’ in a proprietorial sense in the phrase ‘the extra product of the last labourer’ is justifiable only if the last labourer could produce without the aid of the land and equipment. It would not be justifiable to say that the last person ‘produces’ an increment of produce, or that the additional product is ‘created by’ the last person, if (as Thünen obviously intended in the context of this potato-gathering example) these words are used in an exclusive causal sense. If the criticisms of the MPTD outlined later in this study carry any weight, then Thünen’s ‘rational farmer’ who tried to balance ‘the value of the extra output … with the labour cost of its production’ (Thünen 1966, 255) would in fact be acting most irrationally. He would have failed to recognise the causative role played by the non-labour factors (even if they are held constant) when the extra unit of labour is employed. He would have failed to make a proper calculation of the full or true cost of the marginal product. Far from maximising profit, he would be incurring a loss if he paid the last unit of labour a wage equal to the value of the marginal product. That Thünen did not take account of the non-wage costs in his example is all the more curious, given the frequent emphasis throughout The Isolated State on the costs of materials, equipment, depreciation, insurance and so on. If he had given consideration to the productive contributions made by these cooperating factors, he would have had to address what became known as the disentanglement problem – i.e. the problem of identifying, separating or disentangling the specific marginal products of the various factors.

C. Menger (1840–1921) A significant role has been claimed for Carl Menger in the development of the MPTD: ‘Prior to Menger no satisfactory theory of distribution had emerged … Menger was the first economist to raise this question, and, moreover, to suggest the proper manner of answering it’ (Stigler 1941, 152). Menger (1871) argued that the value of higher order goods (i.e. factors of production) is derived from the (anticipated) value of the goods of a lower order (i.e. consumer goods) that are being produced by the higher order goods: ‘The value of goods of higher order is always and without exception determined by the anticipated value of the goods of lower order in whose production they serve’ (quoted in Stigler 1941, 152). This theory of value has become known as the theory of imputation – the term being attributed to

Wieser. Schumpeter (1954, 915) described the theory of imputation as ‘marginal productivity with a difference’. Menger has also been credited with developing the idea that the factors of production are substitutable for one another and may be combined in variable proportions. Hayek (1934, 401) noted that Menger ‘distinguishes clearly between the case where the proportions in which two or more factors can be used in the production of any commodity are variable and the case where they are fixed’. And Stigler argued that Menger’s recognition of the variation of proportions was one of his greatest achievements. This formulation of the principle of variation of proportions as a general rule governing all resources is one of Menger’s greatest achievements … [In classical theory] the proportion between labor and capital was generally assumed to be fixed; certainly variations in this proportion played no part in accepted classical theory. (Stigler 1941, 150; emphasis in original) Hayek interpreted Menger as saying that, in the case of variable proportions, ‘such quantities of the different factors as can be substituted for each other in order to get the same additional quantity of the produce must have equal value’; and, in the case of fixed proportions, ‘the value of the different factors is determined by their utility in alternative uses’. In Hayek’s view, this shows that Menger had a ‘fairly developed theory of marginal productivity’ (Hayek 1934, 401–2). Stigler also held that Menger’s principle of variation of proportions ‘leads directly to the marginal productivity theory of distribution’, a view supported by Hutchison: [Menger] contends … that there is generally a very wide field for varying the combinations in which complementary production goods are employed, and that chemically fixed proportions are not the rule, an aperçu which is the necessary starting-point for a marginal productivity analysis of distribution. (Hutchison 1953, 142) This view was also supported by Schumpeter (1954, 917), who stated: The idea of substitutability was, of course, familiar to Thünen. But Menger was the first to formulate it explicitly … To say the least, this foreshadowed the ‘law of variable proportions’. However, not all commentators share this esteem for Menger’s contribution to the MPTD.4

Stigler regarded Menger’s explanation of the determination of the value of productive agents as ‘unquestionably superior to any preceding explanations … with the possible exception of that of von Thünen’ (Stigler 1941, 150, 153),5 and quoted the following (rather tortuous) statement from Menger as evidence that Menger was a founder of the MPTD: The value [of a quantity of a good of higher order] is equal to the difference between the significance of that want-satisfaction which would result if we had disposal over the quantity of the good of higher order whose value is in question and the significance, in the contrary case, of that satisfaction which would follow from the most economic application of the totality of goods of higher order in our possession [i.e., the remaining resources of this and other kinds]. (quoted in Stigler 1941, 152–3) Stigler concluded from the context of this statement that Menger was referring to the effect on the total product of a withdrawal of a unit of a factor of production, and that Menger was in effect asserting that ‘This marginal product fixes the value of the resource’. But Stigler admitted that, although Menger’s meaning is ‘fairly clear’, it is ‘not as clear as could be desired’ – surely a major understatement. Stigler recognised that there are some inadequacies in Menger’s theory: Menger has failed to develop the indispensable postulate of diminishing returns; it is not clearly brought out that the units withdrawn must be small; and the question whether this method of valuation of agents exactly exhausts the product is not raised. (Stigler 1941, 153) He nevertheless claimed that the theory ‘is essentially correct. The only criticism is to be leveled at its inadequacy.’6 Menger accepted the impossibility of separating the full contribution of each factor, but believed that it was possible to separate their marginal contributions – by withdrawing small quantities of each successively (see Schumpeter 1954, 914). The view advanced in this study is that separability is as impossible for the marginal contribution as for the full contribution of each factor – owing to the ongoing contribution from the fixed factors, even though they are fixed, and even in the short period.

F. von Wieser (1851–1926) Friedrich von Wieser recognised that every product is a multicausal product: ‘No productive instrument, be it ever so efficient, yields a return by its unaided agency; it always requires the assistance of others. … the result is the joint product of all its factors and causes’ (Wieser [1888] 1956, 72, 74), and he recognised that physical disentanglement is impossible, i.e. that it is impossible ‘to discover which portion of the joint product, physically considered, each factor has produced, or of which part of the result each factor is the physical cause’.7 However, he argued that, because the productive elements can be combined in different ways, a series of simultaneous equations can be established which ‘makes it possible for us to distinguish the specific effect of each single element, just as though it alone were active’, and ‘not only to separate these effects approximately, but to put them into exact figures’ (1956, 87). Wieser defined the ‘productive contribution’ of each factor as ‘that portion of return in which is contained the work of the individual productive element in the total returns of production’. He also confidently proclaimed the adding-up or the exhaustion-of-the-product theorem, asserting that the ‘sum of all the productive contributions exactly exhausts the value of the total return’ (Wieser 1956, 88). According to Streissler (1987, 921–2; 1990, 175), Wieser ‘did advance marginal productivity theory’, and was the first to pose the problem of whether the total of the marginal productivity remunerations of the factors of production would exactly exhaust the full product,8 but was not able to prove the theorem, despite many attempts and despite his assertions that the theorem was correct. Even if Wieser’s imputation theory is theoretically sound, the difficulty of establishing the simultaneous equations would appear to render it impracticable. Wieser recognised the complexity of the task. He noted that ‘The value of labour is not to be calculated as one thing; there must be separate calculations for every kind and quality of labour between which one can distinguish’. The same would apply to all the different types of land, and to the ‘incalculable variety of forms’ of capital.9 He also conceded that ‘the stating of the equations is frequently made with only a trifling degree of exactitude’ and that in practice ‘instead of calculating directly, we try to attain our end, in a somewhat circumstantial way, by a method of testing’ (1956, 88–9). The precise meaning of ‘a method of testing’ was not, however, satisfactorily explained. If by ‘a method of testing’ Wieser meant observing the different values of output associated with different values of inputs, then we are faced with the problem, not recognised

or addressed by Wieser, of disentangling the extra value produced by a marginal unit of (say) labour, from the extra value produced by the marginal units of other factors that (for technological reasons) have to be employed along with the marginal unit of labour.10 In addition, there is the problem, again not recognised or addressed by Wieser, of disentangling the extra value produced by the marginal unit of labour from the productive contributions of the factors that are held constant.11 It is doubtful, therefore, whether Wieser’s method of imputation by the use of simultaneous equations can provide a practicable solution to the problem of distribution. It may also be argued that the use of simultaneous equations does not constitute a theory of distribution. Each equation is merely a mathematical statement of the way in which, for any given productive situation, the value of the output is equal to the sum of the values of the various inputs. The equations do not explain why the values of the various inputs are what they are. Thus, Wicksell argued: [from Wieser’s simultaneous equations,] we shall learn nothing more than we know already, namely that when competition is free the remuneration for, or the share in the proceeds of, one and the same ‘means of production’ must be approximately the same in all transactions. The … equations tell us this and nothing more. (1970, 24) According to Wicksell, if by ‘productive contribution’ Wieser meant merely the rewards actually received by the different factors, then ‘he has stated a true, but self-evident rule’; but that if Wieser meant something else, then ‘his ‘solution’ must a priori be declared false’ (1970, 24). According to Uhr, Wicksell also criticised Wieser for lack of consistency in treating the coefficients in his simultaneous equations – sometimes treating them as unknowns to be determined, and sometimes as predetermined knowns. [Wicksell] found that Wieser had assumed the technical coefficients of production to be variable and to be among the unknowns of the problem to be determined in the earlier part of his textual discussion. But later when Wieser set up his simultaneous equations, he assumed, rather inconsistently, that these coefficients were predetermined or were among the known rather than the unknown factors of the problem.12

Another criticism that could be made of Wieser’s idea (that the problem of distribution can be solved by the method of simultaneous equations) is that, when we attempt to substitute real-world numerical values for the coefficients of the variables in the equations, the values would presumably be the values that exist in a given real-world market situation. Each simultaneous equation would therefore merely record what happens to exist at a given time and place, and the solution of the system of equations would not necessarily describe an equilibrium situation. This is what Wicksell probably meant when he said that if the simultaneous equations merely record the rewards actually received by the different factors, the equations ‘tell us this and nothing more’. If the system when solved is to convey an equilibrium situation, it would need to define the characteristics of equilibrium and to incorporate the equilibrium condition. A theory of distribution is supposed to discover and define equilibrium, not to presume it. There would be no need for a theory of distribution if a particular system is known to be in equilibrium. It should also be noted that when Wieser spoke of distinguishing the ‘specific’ effect of each factor, he was using ‘specific’ not as J.B. Clark later used it, namely the portion of the joint product actually caused by each factor, but in the sense of the increase in value that can be imputed to each factor. Thus, Wieser’s approach avoided J.B. Clark’s disentanglement problem. It did not provide, and did not aim to provide, a means of distinguishing between the specific product of the variable factor and the specific products of the constant factors, which, even though unchanged, continue to exert a productive influence. It is interesting to note that, in seeking to develop a theory of distribution, Wieser was motivated by a desire to find an alternative to the arbitrariness and uncertainty that would prevail if the process of distribution were determined simply by the struggle of market forces. It is of great importance that we should try to formulate theoretically the rules for the imputation of productive returns … If we do not succeed in doing so, the valuation of production goods will remain an enigma; and the existing order of things … will lie under the accusation of arbitrariness, if not the worse accusation of force and injustice. (1956, 78) His aim was to provide a ‘rule by which to adjust the quarrel between owners and workers’ (1956, 78). His theory of imputation thus appears to have been driven by a political and ideological attempt to justify the ‘existing order of things’ and by market agoraphobia.

A. Marshall (1842–1924) Alfred Marshall acknowledged Thünen’s influence. He said, ‘I loved von Thünen above all my other masters’ (Marshall [1890] 1925, 360); Thünen’s book was ‘the one book which really guided me’ (cited in Whitaker 1975, I, 38); and ‘My own obligations to [Thünen] are greater than to any other writer excepting only Adam Smith and Ricardo’ (cited in Whitaker 1975, II, 249). Initially he had adopted a wages fund theory of wages, but later developed a marginal productivity theory similar to Thünen’s, and remained ‘absolutely fixed ever since’ to that theory. He had read Thünen ‘probably in 1869 or 70’, but thought that he had developed, ‘partially at least’, a similar theory before reading Thünen. I cannot recollect whether I formulated the doctrine ‘normal wages’ = ‘terminal’ (I got ‘marginal’ from von Thünen’s Grenze) productivity of labour before I read von Thünen or not. I think I did so partially at least.13 Whitaker places Marshall’s conversion to Thünen’s approach after 1870. He argues that Marshall’s Economics of Industry (1879) presents ‘what is essentially a marginal-productivity doctrine’, a view shared by Stigler, who argued that, in the Economics of Industry, ‘Marshall advanced the marginal productivity theory in England for probably the first time since Longfield and Butt wrote’.14 In the first edition of the Principles, in the example of a sheep farmer who employs an additional shepherd without any extra expenditure on plant or interest or management, the MPTD was expressed as: ‘the shepherd who is on the margin of not being employed – the marginal shepherd, as we may call him – adds to the total produce a net value just equal to his own wages’. More generally, the MPTD was expressed as: ‘the wages of every class of labour tend to be equal to the produce due to the additional labour of the marginal labourer of that class’.15 But Whitaker believes that it was only in the 1880s that Marshall ‘clearly adopted an analysis of distribution involving explicitly the partial derivatives of the production function’ (Whitaker 1975, 47–8, 178n). Marshall also appears to have accepted the validity of the adding-up theorem. Stigler saw evidence in the first two editions of the Principles that Marshall believed that the distributive shares exhaust the national dividend, and quoted the following statement from the third edition which appears to confirm that view: ‘the national dividend is thus completely absorbed in remunerating the owner of each agent of production at its marginal rate’ (Marshall, Principles, 3rd edn, 605; cited in Stigler 1941, 353). The fact that this quoted statement was omitted from later editions may possibly be interpreted as a change of mind on the adding-up theorem, but that interpretation would be unlikely.

The strongest evidence that Marshall continued to support the adding-up theorem is the negative evidence that he did not attempt a refutation – which he surely would have done if he had disagreed with the adding-up theorem, given the importance attached to it by Wicksteed, Flux and other contemporaries. Stigler (1941, 353) also cited the fourth edition of the Principles, p. 609, as evidence that Marshall retained ‘the theory of exhaustion of product by marginal imputation’. Stigler concluded: ‘Marshall accepts the exhaustion-of-product argument of Wicksteed, although in the fifth and later editions he ignores its author, and never passes judgment on the use of Euler’s theorem.’16 However, Marshall made a significant addition to Thünen’s views on distribution by introducing the concept of net marginal product.17 Stigler (1941, 345) acknowledged that the ‘difficulty in isolating the net product of a productive service … plays a crucial role in [Marshall’s] Principles’. Marshall defined net marginal product as the ‘net addition to the value of his total product … caused by a certain extra use of any one agent; net that is after deducting for any extra expenses that may be indirectly caused by the change, and adding for any incidental savings’.18 He recognised that when a firm employs an additional unit of labour, it will usually need to employ additional units of other variable factors – such as materials, power, supervision – to work with the additional unit of labour, and that the cost of these extra non-labour variable factors would have to be deducted from the value of the marginal product in order to calculate the net marginal product of labour. He argued that the profit-maximising and equilibrium position is one where this net marginal product equals wages: ‘[every business man] endeavours to employ each agent up to that margin at which its net product would no longer exceed the price he would have to pay for it’ (Marshall 1949, 337). Whitaker (1988, 107) argues that Marshall used the concept of net product rather than marginal product, not because he perceived any conflicting theoretical differences between the two concepts, but because of ‘his desire to make his discussion realistic and palatable to men of business and affairs’. The distinction between ‘marginal product’ and ‘net product’ is expressed thus by Whitaker (1988, 196): Unlike the marginal product concept, which varies the amount of only one input, holding the quantities of all others constant, the net product admits simultaneous variation of the quantities of all inputs. The precise meaning that Marshall intended to attach to ‘net product’ is not, however, clear. Textual evidence may be used to support (at least) two

different interpretations:19 (1) The net product of labour is calculated by deducting (from the value of the marginal product) the costs of all the other factors used in conjunction with the marginal unit of labour – including not only other variable factors such as extra fuel and power, extra supervision and extra tools, but also a proportionate part of the costs of the fixed capital, such as land, buildings and existing equipment, and a return on loan capital and owner capital. This could be described as the fully net marginal product; (2) The net product of labour is calculated by deducting (from the value of the marginal product) only the costs of the extra variables used in conjunction with the marginal unit of labour. This could be called the partially net marginal product. Whether, when Marshall referred to the marginal net product, he meant fully net or partially net, is unclear. The textual evidence is ambiguous.20 If Marshall intended interpretation (2), his argument would suffer from the same defect as that of his master Thünen, namely that it would fail to recognise the causative role, and the cost, of the fixed factors. If ‘net product’ is interpreted as only partially net, i.e. net only of variable costs, then (as argued above) the equality of the net product of labour and the wages of labour would not be a profit-maximising condition. It would make no commercial sense for any businessman to employ additional units of an agent of production up to the point where the reward of the last unit equals the agent’s partially net product. To do so would be to reward the variable agent not only for the contribution made by itself, but also for the contribution made by the fixed capital towards the production of the marginal product. It would in effect be saying that the contribution of the fixed capital to the production of the marginal product is costless; or that no part of the revenue from the marginal product needs to be allocated to offset the cost of the fixed capital. As argued above, a tendency for wages to equal the net product of labour would not occur, and would make no commercial sense, unless ‘net product’ is defined so as to incorporate, even in the short period,21 a deduction of a portion of the costs of the fixed capital as well as a deduction of any extra non-labour variable costs. On the balance of the textual evidence it would seem more likely that Marshall’s ‘net product’ was intended as a ‘partially net marginal product’; it does not eliminate the contribution made by the constant non-labour factors to the marginal product of labour. The question is therefore: In calculating the net marginal product of labour, should there be a deduction for a portion of the profits that are being made – or are expected or planned to be made – on fixed capital? Should the net marginal product of labour be fully net or partially net? Arguments could be advanced on both sides. Against the use of the concept of fully net, it may be said that profits are a residual, and cannot be regarded as a cost deduction,

because they cannot be known until after the production process is completed and the sale of the product has been effected. Arguments in favour of using a fully net concept include: 1 If normal profits are defined as the level of profits that a firm must achieve if it is to stay in business, then normal profits are in effect a cost that has to be covered, just like wages, electricity, raw materials and other costs that have to be met if the firm is to stay in business. 2 It would be normal and sensible business practice for firms to incorporate an allowance for their expected normal profits into the price structure for their products and services, in the same way as they would incorporate all their expected outgoings. 3 The fact that profits are often declared and paid to shareholders at the end of the financial year and therefore appear to be a residue does not in reality mean that they are a residue rather than an ongoing cost. When a firm is functioning profitably, profits, whether normal or above normal, are being generated day by day throughout the financial year, and the firm is meeting day by day on average its profits target just as it is meeting its wages target or its materials target. 4 If interest paid to creditors on loan capital is regarded as a cost that should be deducted in calculating the net marginal product of labour, surely the profit paid to owners/shareholders on equity capital should likewise be regarded as a cost, and should be deducted in calculating the net marginal product of labour. Even if the law gives priority to loan capital over equity capital in the distribution of income and assets, it is just as important for a firm to meet market expectations in its returns on equity capital as it is for it to meet the contractual returns on loan capital. The returns paid on loan capital are known in advance, whereas the returns available on owner capital are not known before operations proceed, but the expected or desired returns on owner capital would presumably enter into the firm’s policy-making decisions when setting the prices of its products and the payments for its factors of production. Equity capital is not a free good. In using the terms ‘fixed (or constant) factors’ and ‘variable factors’, it is of course not being suggested that some factors will be forever fixed. They are called ‘fixed’ only with reference to a particular time and place. Over time, or in a different productive situation, the factors once described as fixed may become variable. The point being made here is that an appropriate portion of the cost of the fixed factor should be included in calculating marginal cost, not just because at some different time and place the fixed factors may become variable, but because the fixed factors are physically contributing to the productive process and are imposing ongoing costs on the productive

process, even when they remain fixed. These ongoing costs of the fixed factors cannot be ignored in calculating the cost of the marginal product that follows the addition of a marginal unit of a variable factor; and therefore cannot be ignored in defining the equilibrium and profit-maximising situation. These ongoing costs of the fixed factors will affect the size of the fully net MPAL, which is one of the determinants of the wage of the marginal unit of labour. The argument can be reinforced by considering a situation where labour is the fixed factor and capital is variable. It would be inconceivable that a business-person would deliberately decide not to take the periodical wage bill into consideration in calculating marginal cost, simply because labour is, in that situation, the fixed factor. If the ongoing costs of the fixed factors are taken into account in calculating the MPAK (marginal product after capital) when labour is the fixed factor, why should they not be taken into account in calculating the MPAL (marginal product after labour) when capital is the fixed factor? It has been argued that the profit-maximisation rule under the MPTD should be, not the equality of wages and the marginal product of labour, but the equality between the marginal product of labour and wages plus interest: The equality in fact should be between the marginal product of labour, on the one hand, and the wage plus the interest on the additional finance required to advance the wage of the additional wage-earner, on the other. (Harcourt 1979, 924) To the right-hand side of this equality could be added the cost of items of variable capital (raw materials, power) used by the extra unit of labour, and if the concept of ‘fully net marginal product’ is being applied, a further addition would be an appropriate portion of the cost of the fixed capital, which, even though fixed, contributes to the marginal product. Another argument for the inclusion of a fixed-cost component is that, to take an extreme case, if revenue is distributed in strict accordance with the MPTD, the value of the initial output from a new, fully equipped factory would have to be allocated entirely to the first unit of labour employed; and each subsequent increase in output would have to be allocated entirely to each subsequent employee. C.J. Bliss (1975) defined net productivity as follows: ‘net value-product of labour … consists of the value of the product of labour less the value of the inputs co-operating with labour when the levels of these inputs are chosen optimally so as to maximize profit’ (96; emphasis in original); and he argued

that this definition of net value product corresponds to Marshall’s definition of the marginal productivity of labour. By the expression ‘inputs co-operating with labour’ Bliss appears to have meant the extra amounts of the other factors that are employed in conjunction with the marginal unit of labour. In an example where horses, labour and land are used to produce wheat, and where extra horses are taken on with the extra labour, Bliss stated: ‘the marginal net value product of labour will be the value of the extra output produced less the extra cost of horse time consequent upon the change in the employment of labour’ (96). In this example, the calculation of the net product involves a deduction of the cost of the extra variable capital, but not of a proportionate part of the cost of the capital that remains constant. Thus it would appear that Bliss has interpreted Marshall’s net marginal product as partially net rather than fully net. Despite the convincing textual evidence that Marshall made a clear distinction between marginal product and net marginal product, Stigler (1941, 356) suggested that ‘in general Marshall’s net and marginal products are identical, and that his distribution theory is, in spite of contrary admonitions, a marginal productivity theory’. He believed that Marshall’s statement – ‘In each case the income tends to equal the value of the marginal net product’ (Marshall 1949, 535) – is ‘an outright acceptance of the marginal productivity theory’ (Stigler 1941, 356). Schumpeter endorsed Stigler’s interpretation: ‘Professor Stigler … has shown very well how Marshall … ended up by accepting eventually the whole of the marginal productivity apparatus’, adding that Marshall’s Principles contains ‘a very complete and properly qualified marginal productivity theory of the firm and of distribution’ (Schumpeter 1954, 1032). However, the claim of Schumpeter that Marshall accepted the MPTD is rendered less convincing when he added that Marshall’s net marginal product was a ‘dangerous concept’, because marginal productivity in that sense ‘is no longer properly expressed by a partial differential coefficient’ (1954, 1043). It is difficult to understand how Marshall could be said to have accepted the MPTD when it is also said that one of his key concepts – the net marginal product – severely compromised the attempted proof (based on Euler’s theorem) of the adding-up theorem, and hence destroyed the validity of the MPTD. Although Stigler and Schumpeter held the view that Marshall in fact fully subscribed to the MPTD, they argued that he was not prepared to admit that he fully subscribed to it. Stigler, for example, said that, although the first edition of Marshall’s Principles (1890) contains ‘the essence of the theory’ (Stigler 1941, 346), and although Marshall’s text suggests ‘an outright capitulation to the marginal productivity theory’ (Stigler 1941, 354),

Marshall showed ‘reluctance to accept the marginal productivity theory’ (Stigler 1941, 354), and his position in the eighth edition (1920) was ‘at least as far from an open or complete acceptance of the marginal productivity theory as it had been thirty years before’; and Schumpeter argued (1954, 1032) that Marshall ‘would never admit the full extent to which he actually ‘accepted the marginal productivity analysis’. Stigler and Schumpeter were in effect saying that Marshall was mistaken in thinking that he had not fully subscribed to the MPTD. Schumpeter attributed this reluctance to (among other things) Marshall’s ‘justifiable aversion to assigning a ‘causal’ role to the partial coefficients of the production function’ (1954, 1033); whereas Stigler believed (1941, 348) that the fundamental reason for Marshall’s reluctance to accept an ‘outright’ marginal productivity theory was ‘the difficulty of measuring the marginal productivity of a productive service’. Stigler also believed that Marshall’s desire to emphasise supply considerations played an important part in his reluctance to accept the MPTD, even though, according to Stigler, supply considerations are ‘analytically irrelevant’ to this problem (Stigler 1941, 354).22 It should be noted that the fully net marginal product is not the same as the specific marginal product of labour (SMPL), as defined above. The fully net marginal product of labour removes the non-labour costs from the MPAL, but the SMPL is the product specifically caused by the marginal unit of labour. The domain of costs is not necessarily the same as the domain of causes. The fully net MPL therefore does not provide a basis (in conjunction with a Lockean theory of property rights) for normative conclusions. The net MPL (whether fully net or partially net) is as much a multicausal phenomenon as the gross MPL, by contrast with the monocausal SMPL. Even though the costs of the other cooperating factors are removed in calculating the net MPL, their causal influences remain. The causal contributions of the various factors that contribute collectively to the production of the MPL are as unidentifiable and as inextricable in the case of the net MPL as they are in the case of the gross MPL. It is not clear whether Marshall believed that his concept of net marginal product of labour, found by deducting from the marginal product the costs of the extra factors used in conjunction with the marginal unit of labour, was in fact identical with the SMPL, i.e. with that part of the marginal product specifically attributable to the marginal unit of labour. Specific causality is implicit in the following statement: ‘the wages of every class of labour tend to be equal to the net product due to the additional labour of the marginal labourer of that class’ (Marshall 1949, 429). Whether or not Marshall intended it, the phrase ‘due to’ suggests that the marginal shepherd is monocausally responsible for the net product. But as Marshall did not

explicitly address the question of specific causality in J.B. Clark’s sense, his precise position on the matter remains unclear. Marshall insisted that the ‘doctrine that the earnings of a worker tend to be equal to the net product of his work’ (Marshall 1949, 429–30) does not of itself constitute a theory of wages: ‘This doctrine has sometimes been put forward as a theory of wages. But there is no valid ground for any such pretension’ (Marshall 1949, 429). However, he held that the doctrine ‘throws into clear light the action of one of the causes that govern wages’ (Marshall 1949, 430). In other words, he appears to have been saying that the MPTD does not provide a complete and determinate theory of wages because it is an explanation of only the demand for labour, and does not take account of the conditions affecting the supply of labour.23 The thesis being offered in this study of the MPTD is that it does not even provide an adequate explanation of the demand for labour. Marshall qualified his statements on the MPTD by arguing, not that wages equal the net product of labour, but that they ‘tend’ to equal it, or are ‘about equal’ to it (Marshall 1949, 446–7). A further qualification or complication occurred when he said that the cost of each agent is ‘proportionate to the additional net product resulting from its use’ (Marshall 1949, 427), without indicating whether he intended any significant difference between ‘proportionate to’ and ‘equal to’. It should also be noted that Marshall distinguished between ‘equal to’ and ‘governed by’. In saying that wages tend to be equal to the net product of labour, he did not mean that wages are governed by it, ‘for net products like all other incidents of marginal uses, are governed together with value by the general relations of demand and supply’. A further important qualification occurred when he recognised that ‘of course the net product of an individual cannot be separated mechanically from that of others who are working together with him’ (Marshall 1949, 446–7).24 The concept of net marginal product introduces into the MPTD the problem of a circular chain of causation. It is argued here that the cost of capital items (variable or fixed) has to be deducted from the marginal product of labour (MPAL) in order to arrive at the fully net marginal product of labour. But the cost of capital items can be calculated only if the rate of profit is already known, and the rate of profit can be found only if the rate of wages is known; or, in other words, only if the distribution of income between profits and wages is known. The MPTD sets out to determine the level of wages, but seems to require that the level of wages be already known. It sets out to solve the problem of distribution via the calculation of net products, but the calculation of net products seems to be possible only if the problem of

distribution is already solved. Some critics of the MPTD argue therefore that, since the net marginal products of the factors are interdependent and cannot be derived independently of one another, the MPTD by itself cannot provide a determinate solution in practice to the problem of what determines the distribution of the product, and therefore does not provide an acceptable alternative to a solution in terms of bargaining power and market conflict.25 Marshall does not appear to have explicitly or systematically addressed this issue. His emphasis on the interdependence of economic phenomena is well known, especially through his metaphors of balls in bowls and the movement of the planets. But in his discussion of the MPTD he was engaged in partial equilibrium analysis. In that context therefore the concept of general interdependence was not relevant. Marshall’s concept of net marginal product receives scant attention in the modern secondary literature. There could be several reasons for this neglect: 1 Textbook writers might be assuming that everyone – even a beginner who has never heard of the MPTD – is aware that the costs of any additional nonlabour variable factors that need to be employed to support the employment of the marginal unit of labour have to be deducted from the value of the marginal product in order to identify the marginal product of labour. 2 The use of the first partial derivative of output with respect to labour (∂Q/ ∂L) as a definition of the marginal product of labour removes the problem of extra units of non-labour variables. The partial derivative assumes that only one variable is changing; it eliminates (at least at the theoretical level) the problem of simultaneous movements of labour and non-labour variables. The process of calculating a partial derivative of output with respect to one variable does not therefore require any deductions for changes in output associated with changes in other variables – because, by definition, other variables are being held unchanged. 3 As Bliss (1975) has argued, if units of labour have to be combined with units of capital in fixed proportions (because of the technical demands of the production process) – i.e. if in the real world it is not technically feasible for additional units of labour to be added while the capital remains unchanged – then the resulting production function for the ‘net product’ of labour may not be smooth and differentiable. Such a production function cannot easily be accommodated within a conventional economics curriculum based on models requiring differentiable functions. A major reason why the notion of marginal net product has not played a very central role in economic theory, particularly as it is taught to students, is the stress laid on the traditional mathematical formulation of equilibrium models

under which every function in sight is assumed differentiable, there are no corners, all diagrams display only smooth curves. (Bliss 1975, 100)

P. Wicksteed (1844–1927) If, as the MPTD states, factors of production are paid in equilibrium according to their marginal products, it becomes necessary to ask whether the amount of product thus distributed to the factors is exactly equal to the total amount produced. The MPTD could not claim to be a valid explanation of the distribution process either if the total of the returns distributed to the factors is less than the total product, i.e. if there is an undistributed residue, or if the total returns required for the factors proved to be theoretically greater than the total product available for distribution. If this adding-up problem, or exhaustion-of-product problem, cannot be solved, the MPTD becomes logically untenable. Writing in 1930, Lionel Robbins said that ‘even at the present day’ the adding-up theorem ‘remains the subject of lively controversy’ (Robbins 1930, 248); and in 1934, Joan Robinson stated that ‘after forty years, economists are still debating the adding up problem’ (1934, 414). Even today, not everyone agrees that the problem has been solved or is capable of solution. Philip Wicksteed’s support for the MPTD was clearly stated in An Essay on the Co-ordination of the Laws of Distribution (1894): The (marginal) significance of each factor is determined by the effect upon the product of a small increment of that factor. (Wicksteed [1894] 1992, 56; emphasis in original) The individual entrepreneur, if he contemplates taking on or discharging a workman, will ask himself whether that workman will be worth his wage or not, i.e., whether he will increase the product, other factors remaining constant, at least to the extent of his wage … The man, on his side, can insist on having as much as the marginal significance of his work, i.e., as much as the difference to the product which the withdrawal of his work would make. (Wicksteed [1894] 1992, 60) The law of distribution which we are to examine is too obvious and selfevident not to be constantly assumed by economic writers. (Wicksteed [1894] 1992, 59)26

The criticisms of the MPTD that have been raised above could be raised also in relation to Wicksteed. In asking whether the extra workman ‘will increase’ the product, and in referring to that increase as ‘his’ work, Wicksteed appears to have attributed the increase of the product solely to the efforts of the marginal unit of labour, without giving any consideration to the productive impact of the constant factors that assist the marginal unit of labour. It implies that the fixed factors play no part in producing the increase in output that occurs after the employment of a small increment of a variable factor. This is brought out even more clearly in the statement: ‘Each factor is … treated as having its independent influence, at the margin, on the increment or decrement of the product’ (Wicksteed [1894] 1992, 61; emphasis added). In addition, in defining the marginal cost of employing an extra unit of labour as merely the wage of that extra unit, Wicksteed did not consider the view that the ongoing costs of the fixed factors (e.g. interest on loan capital, rent on leased capital) are accruing on a daily basis, and must therefore be part of the marginal cost of employing the marginal unit of labour. In causal terms, his attempt to calculate the specific marginal product of a variable factor omitted the ongoing productive influence of the fixed factors. In value terms, his attempt to calculate the value of the marginal cost of employing the marginal unit of a variable factor omitted the ongoing costs of the fixed factors. The thesis being advanced in this study is that when Wicksteed referred to ‘the product of a small increment of that factor’, he failed to distinguish between the extra product that occurred after the small increment and the product that occurred because of the small increment; and that when he referred to the cost of that extra product he included only the cost of the marginal unit of the factor and did not include also a portion of the cost of the fixed factors that cooperate with the variable factor. Wicksteed’s most famous contribution to the MPTD debate was his attempt to solve the adding-up problem. He believed in 1894 that he had shown that: under conditions usually regarded as normal, the marginal distribution exhausts the product, and … where every factor has taken a share regulated by its marginal efficiency, there is nothing left.27 Stigler described Wicksteed’s Co-ordination as ‘magnificent’. He claimed that ‘its daring and its originality command the highest respect’ and that it ‘is enough alone to insure him a place of lasting importance in the history of economic thought’. According to Stigler, previous theories of distribution had either asserted that one factor receives the residual share – thus eliminating

any adding-up problem – or assumed that the distributive shares exhaust the product, but Wicksteed was the first to raise the question explicitly.28 Wicksteed’s proof of the adding-up theorem was based on the assumption that the firm’s production function is a homogeneous function of the first degree, i.e. that the firm is operating in a situation of constant returns to scale, although, as Steedman notes (1992, 12), Wicksteed did not use the technical term ‘homogeneous of the first degree’. From that assumption, Wicksteed proceeded to a mathematical demonstration of the adding-up theorem – a demonstration of over six pages that he himself described as ‘long and perhaps tedious’ (Wicksteed [1894] 1992, 80); and that A.W. Flux, in his 1894 review of the Co-ordination, showed to be unnecessary, as it amounted to nothing more than a proof of the ‘so-well known’ Euler’s theorem (Flux 1894a, 311; cited in Steedman 1992, 13). Wicksteed wrote to Flux, thanking him for this invaluable suggestion and confessing: ‘I have had no mathematical education, and am deplorably ignorant of mathematical literature.’29 Although the MPTD has been used to support both the ideology of free market capitalism and the ideology of socialism and redistributionism, the question of whether Wicksteed himself in developing the MPTD was motivated by ideological or apologetic concerns is debatable. Was his development of the MPTD an internalist exercise in value-free price theory, or was it conceived of as a contribution to the political and ethical debate on the ideal nature of society? Wicksteed’s biographer, C.H. Herford, said that the application to economics of Jevonian calculus became a burning controversy between the advocates and enemies of socialism (cited in Routh 1975, 257); and Bernard Shaw30 wrote in 1886 that ‘the most successful attack so far on the value theory of Karl Marx has come from Mr Philip Wicksteed, a well-known Unitarian minister, who is an able follower of Jevons in economics’ (Shaw 1991, 144). And in 1888, in a favourable review of Wicksteed’s The Alphabet of Economic Science, he said that this ‘remarkable little text book’ provides ‘a demonstration, helped out by the most captivating curve diagrams, of a theory of value which has already left the Ricardian dogma as dead as the Doges – a theory worked out in England by Stanley Jevons, and first appreciated at anything like its full importance by Mr Wicksteed’. He credited Wicksteed with being the first to point out ‘that Marx’s theory of value was out of date, and the term ‘SURPLUS VALUE’ A MISNOMER’. He saw in the Alphabet ‘an exposition of the sounder analysis of value, which is quite the best and cheapest in the language’.31 But Steedman argues persuasively that ‘[Wicksteed’s] move towards marginal theory was probably not motivated by a desire to combat Marx’s

‘surplus theory’ and was certainly not motivated by hostility to the Labour movement generally or by an ‘apologetic’ intent’ (Steedman 1992, 42–3). According to Steedman, Marx’s surplus theory had only limited influence in Britain, and Wicksteed believed he had already adequately refuted Marx in his article ‘Das Kapital: A Criticism’ in 1881. Wicksteed’s support for the Labour movement and the Labour Church, and his indictment of the present organisation of industry for its failures and defects, show that he was not an apologist for capitalism in its contemporary form. Steedman concludes: ‘It would be difficult seriously to consider either Wicksteed himself, or his view of marginal productivity theory as “apologetic”.’32 His character and the tenor of his writings suggest that his theoretical work in developing the MPTD was not undertaken for the sake of pure science, but was motivated by a desire to promote social reform. He seems not to have realised that the MPTD might also be used as an argument against reform.

A.W. Flux (1867–1942) In a review of Wicksteed’s Co-ordination, Alfred William Flux attempted a proof of the adding-up theorem – which he defined as the theorem that ‘when each of the factors of production has received remuneration at the rate measured by its marginal productivity, the whole produce is exactly distributed’ (Flux 1894a, 309). According to Flux, the ‘chief merit’ of Wicksteed’s work was ‘the attention which he directs to the problem, even more than the form of his solution’ (1894a, 309). Flux’s solution involved the use of Euler’s theorem, namely: If P = f(a, b, c, …) is a homogeneous function of the first degree, i.e., mP = f(ma, mb, mc, …), then

Joan Robinson expressed the economic significance of this theorem as follows: Translated into economic language, this proposition states that the total product is equal to the sum of the amounts of the factors, each multiplied by its marginal product, provided that conditions of constant returns prevail, in

the sense that a given proportional increase in the amount of every factor of production would lead to the same proportional increase in the product. (Robinson 1934, 399) Flux also referred to the use of Euler’s theorem to prove the adding-up theorem in his Economic Principles (1904), where he stated that, if the production function is homogeneous, then ‘the assignment, to each of the factors of production, of payment at the marginal rate of its contribution to the product, exhausts the total product’ (314–15). He acknowledged that this ‘striking proposition’ had been expressed by Wicksteed in his discussion of the problem of distribution. Flux went on to say that this argument remains important even if the production function is not homogeneous: ‘Where increase of production proceeds by the increase of different factors of production in differing proportions, the above proposition does not cease to have importance’ (Flux 1904, 315), but the context appears merely to make the obvious point that increases by differing proportions will not have the same effect as increases by constant proportions. He did not argue that the adding-up problem can be solved without the assumption of a homogeneous production function. However, it is not universally accepted that Flux’s application of Euler’s theorem provides a convincing proof of the adding-up theorem.33 One area of contention is that Flux’s solution is based on the supposition of a linear homogeneous production function, i.e. on the assumption of constant returns to scale. This assumption, it is argued, constitutes a major limitation that renders the MPTD of little relevance to the real world, where constant returns to scale rarely prevail. If the validity of the MPTD depends on the solution of the adding-up problem, and if the solution of the adding-up problem requires the assumption of linear homogeneity and constant returns to scale, then these validity conditions are so restrictive that they amount to a virtual rejection of the general applicability of the MPTD. Its applicability becomes a rare exception rather than a general rule. Thus, if the Wicksteed-Flux method solves the adding-up problem, it does so at the cost of demonstrating the MPTD’s lack of relevance to the real world. Instead of saying ‘the adding-up problem can be solved when constant returns to scale prevail’, it would be more correct to say ‘the adding-up problem cannot be solved unless constant returns to scale prevail’. The negative expression ‘cannot … unless’ embodies this criticism of the adding-up problem more accurately than the positive expression ‘can … if’. The unreality of Wicksteed’s solution was noted by Edgeworth. Wicksteed had claimed that his solution to the distribution problem was of universal

applicability: [it] would hold equally in Robinson Crusoe’s island, in an American religious commune, in an Indian village ruled by custom, and in the competitive centres of the typical modern industries. (Wicksteed [1894] 1932, 42) Edgeworth described Wicksteed as ‘a distinguished mathematical economist’, but, in a tone of gentle mockery, commented: There is a magnificence in this generalisation which recalls the youth of philosophy. Justice is a perfect cube, said the ancient sage; and rational conduct is a homogenous function, adds the modern savant. A theory which points to conclusions so paradoxical ought surely to be enunciated with caution. (Edgeworth 1904, 181, 182; [1925] 1970, 31; cited in Creedy 1986, 16) Stigler, defending Wicksteed and the use of Euler’s theorem, rejected these criticisms by Edgeworth. He interpreted the above 1904 statement by Edgeworth not as gentle mockery but as ‘vehement comment’34 and responded with some vehemence of his own: Edgeworth’s role in the controversy is neither important nor praiseworthy. Some of his arguments are nothing more than ridicule; the remainder are based upon rather obvious misapprehensions. (Stigler 1941, 340) Stigler regarded Edgeworth’s comments as ‘highly misrepresentative’ of Wicksteed’s position (1941, 342). It should be noted that, in his 1894 review of Wicksteed, Flux accepted, without questioning it or defending it, the fundamental principle of the MPTD – namely that ‘the payment for the use of land is measured by its marginal productivity, exactly as in the case of other industrial agents’ (Flux 1894a, 309) – and he accepted that the marginal productivity of a factor can be isolated and can be measured by the first partial derivative of output with respect to that factor. This may be seen also in a later publication where he argued that the marginal product of a factor could be disentangled from the joint product of a number of factors: ‘the contribution of labour, or of a special grade of labour,

can be, for practical purposes separated from the joint product’ (Flux 1904, 118). In the case of a group of labourers performing similar tasks, he saw a causal connection between the change in output and the change in the quantity of labour. If their numbers can be increased or decreased slightly, without a change in the rest of the apparatus of production, with which they are associated, the consequent change in the product can be directly attributed to the change in their numbers. (Flux 1904, 118) However, in an entry in the Economic Journal (1894), Flux appears to have acknowledged the multicausal nature of a factor’s marginal product, thereby raising doubts about the possibility of disentanglement. He was responding to an objection made by Joseph Shield Nicholson to the importance assigned to the last portion added. Nicholson described this as the fallacy of ‘the tail wags the dog, and the tip of the tail wags the tail’. Flux responded to this ridicule by comparing it to the proverb ‘It is the last straw that breaks the camel’s back’; and by arguing: ‘It would, of course, be evidently absurd to maintain that this violent result is due to the last straw alone, and does not depend on the presence of all those which precede the last’ (Flux 1894b, 341–2). Flux appears to have seen no economic or ethical problem in paying the same wage to each member of a group of labourers even though, in a situation of diminishing returns, the marginal product of the last unit would be less than the marginal product of earlier units. He approved of Jevons’ statement that ‘the whole capital employed can only be paid at the same rate as the last portion added; hence it is the increase of produce or advantage which this last addition gives, that determines the interest of the whole’ (quoted in Flux 1894b, 340–1); and in his own words stated: If the addition of one to the group add a certain amount to its total product, and it is indifferent which of the group, thus enlarged, does the work of the added man, then each in turn may be regarded as the last added, and none can be assigned an importance superior to any other. (Flux 1904, 120) Applying the terminology of this present study, Flux did not distinguish between the specific marginal product of labour (SMPL) and the marginal product after labour (MPAL). Nor did he distinguish between the gross

MPAL and the net MPAL, or refer to the circularity involved in measuring the net MPAL. The distinction (set out above) between the monocausal SMPL and the multicausal MPAL leads to the following three observations, offered here as contributions to the debate over the validity of the adding-up theorem and the MPTD.35 First, there is the obvious point that the adding-up problem becomes a problem only when the marginal products under discussion are multicausal or non-specific, i.e. the marginal product after labour, the marginal product after capital and so on. There is no adding-up problem – or, to put it another way, the adding-up problem is solved – if the marginal products under discussion are monocausal or specific, i.e. in the sense used by J.B. Clark. If there are three factors of production – land, labour and capital – the sum of their three specific marginal products, multiplied by their respective quantities, must equal the total product. Even if these three specific products cannot be disentangled and are therefore unknowable quantities, it is absolutely certain that the sum of the three specific products, each multiplied by the respective quantities of the factors, will exactly equal the total product. The total product is made up of these three components, and of nothing else. Therefore, if each factor receives a reward equal to the value of its specific marginal product, the sum of the rewards must exactly equal the total product. Second, if the marginal product of a factor is understood as the first partial differential of output with respect to the factor, then it would appear that the adding-up theorem is disproved. The first partial derivative of output with respect to labour is the marginal product after labour (MPAL), not the specific marginal product of labour (SMPL). It is a measure of the nonspecific, multicausal increase in output that occurs after the addition of an extra unit of a factor, but it is caused, not solely by that extra unit, but by the action of that unit in cooperation with the units of the factors that are held constant. Ceteris paribus is not ceteris inefficacibus. The first partial derivative includes not only the specific marginal product of labour (SMPL), but also a productive contribution from the fixed factors; i.e.∂P/∂L = MPAL, and MPAL > SMPL. Similarly, ∂P/∂K = MPAK, and MPAK > SMPK ∂P/∂N = MPAN, and MPAN > SMPN. If, as argued above, the total product (P) must be equal to the quantity of the factors multiplied by their specific marginal products,

i.e. L.(SMPL) + K.(SMPK) + N.(SMPN) = P then L.(MPAL) + K.(MPAK) + N.(MPAN) > P or L.(∂P/∂L) + K.(∂P/∂K) + N.(∂P/∂N) > P. Thus, if the returns to the factors are equal to their partial differentials, the result is that the sum of the returns must exceed the total product – a result that is obviously impossible. Third, there is another, and more fundamental, limit to the usefulness of Flux’s solution – a limit that appears not to have received due recognition in the extensive literature on the adding-up theorem. Flux attempted a static, timeless solution to a process that, by definition, takes place over time. The MPTD refers to a situation where one factor is changed while the others are assumed to remain constant. The ceteris paribus assumption means that the changes occur sequentially, not simultaneously. Thus, if marginal units of labour (L), capital (K) and land (N) are added in that sequence, the marginal product of labour will be ∂P/∂L, but the marginal product of capital will be, not ∂P/∂L, but ∂P1/∂K, where P1 > P (because of the increment to P following the application of the marginal unit of labour); and the marginal product of land (N) will be, not ∂P/∂N, but ∂P2/∂N, where P2 >P1 (because of the increment to P1 following the application of the marginal unit of capital). This means that the use of Euler’s theorem as the basis for the proof of the adding-up problem is not appropriate – because Euler’s theorem assumes that P remains constant in the calculation of ∂P/∂K, ∂P/∂L, and ∂P/∂N. A theorem based on a constant level of P will therefore not be relevant to the MPTD.36 If factors receive rewards equal to their marginal products, then the total payments to the factors will be L.∂P/∂L+K.∂P1/∂K+N.∂P2/∂N

(1)

According to the Flux solution based on Euler’s theorem, the total product will be equal to L.∂P/∂L+K.∂P/∂K +N.∂P/∂N But since P2 >P1 > P, expression (1) must exceed expression (2).

(2)

In other words, we are faced with an absurd situation where the sum of the rewards paid to the factors exceeds the amount of product available for distribution, thus confirming that Euler’s theorem is not applicable to a situation where the changes in the various factors occur sequentially, not simultaneously.37 Euler’s theorem may or may not have a useful application elsewhere in economics, but because it lacks a time dimension and because its relevance is limited to a situation where P remains constant during successive differentiations, it would appear to have no useful or meaningful relevance to the MPTD, where P will usually alter after every change in factor inputs. Flux’s attempt to apply Euler’s theorem to the MPTD did not recognise the essentially sequential nature of the processes that the MPTD seeks to explain.38 It would seem therefore that if there is a proof of the adding-up theory, it must be found elsewhere. The static or timeless nature of attempts to prove the adding-up theorem using Euler’s theorem is evident in Flux’s statement: We shall suppose the conditions of industry to remain steady for a sufficient time to enable the entire round of productive operations to be completed, i.e., take no account of change in progress; time will not be one of the variables with which we are concerned. In fact we shall deal with the produce per unit of time or in any given time. (Flux 1894a, 309) Here Flux assumes conditions that are confusing and mutually exclusive. He did not clearly explain what he meant by ‘the entire round of productive operations’; and he did not explain how the conditions of industry may be said to ‘remain steady’, even though changes are being made to the variables. To summarise the above three observations: (1) If by ‘marginal product’ of a factor is meant ‘specific marginal product’ (where ‘specific’ is understood in the sense used by J.B. Clark), then there is no adding-up problem. (2) If marginal products are defined (in the conventional manner) as first differentials, the adding-up theorem is disproved, because the sum of the marginal products must exceed the total product. (3) The use of Euler’s theorem to prove the adding-up theorem is inappropriate because it takes output as constant, whereas, in the logic of the MPTD, output should increase with successive applications of the marginal units of the factors.39 The support that the Wicksteed-Euler theorem continues to receive could perhaps be explained (at least in part) by the fact that the scientific

pretensions and aspirations of economics are considerably enhanced if it can be shown that the central economic problem of distribution is once-and-forall resolved by the application of a rigorous and indisputable mathematical theorem.

V. Pareto (1848–1923) Vilfredo Pareto has been credited with being one of the discoverers of the MPTD,40 because of his article in the Giornale degli economisti, published in 1894, the same year as Wicksteed’s Co-ordination. In his Cours d’économie politique (1897) and his Manual of Political Economy (original Italian edition, 1906; first French edition, 1906; English edition, 1971), Pareto raised a number of objections to the MPTD, but Tarascio (1973) has argued that these objections should not be allowed to deny Pareto the recognition he deserves as a co-discoverer.41 Pareto’s objections to the MPTD included the following: 1 Fixed-factor proportions. The MPTD may be applied only if the proportions in which the factors are combined can be varied, i.e. only if the technical conditions of the production process are such that the amount of one factor can be varied while the other factors are fixed. This became known as the ‘variability of factor proportions’ condition.42 Hicks argued that Pareto’s reasons for this objection to the MPTD were ‘merely silly’ (Hicks 1932b, 86; cited in Tarascio 1973, 401), but Tarascio provided quotations from the Manual which suggest that Pareto, while noting the existence of fixed coefficients in some cases, was not denying the possibility of variable coefficients; he was merely asserting that there are limits to their variability. Stigler did not regard the possibility of fixed-factor proportions as a serious restriction on the applicability of the MPTD. He believed that there would not be a significant number of production processes in which, for technical reasons, the factors had to be combined in strictly fixed proportions.43 He regarded this objection by Pareto to the use of Euler’s theorem44 as ‘intellectually quite respectable, but of questionable importance’ (Stigler 1941, 364). For practical purposes, it may be asserted, factors are never so related; there is always some variability in their proportions at the margin … There may be obscure cases of factors functionally related to each other, but these unimportant cases are not important enough to justify rejecting the Euler

theorem approach. Similarly, there is always some variability in the product that can be secured from any one factor. (Stigler 1941, 367) Stigler believed that Pareto, in objecting to the MPTD on the grounds of nonvariability of factor proportions, had shown a ‘fundamental misconception of scientific law in general and economic theory in particular’. Stigler argued that ‘Generalizations cannot fit every case’ and that the assumption of variability of factor proportions ‘would have ample methodological defense if it fitted the facts only a third of the time’. His conclusion was that this assumption ‘seems, empirically, to be well-nigh impregnable’. He added that this assumption does less violence to the facts than the assumption (used by Pareto) that indifference curves and demand curves are continuous (Stigler 1941, 368). However, if Pareto’s fixed-factor-proportions objection refers only to the practical applicability of the MPTD, merely limiting the MPTD to situations where factor proportions may be varied, and is not an objection to the MPTD as such, it is not relevant to the principal theme of this study. If, as argued here, there are grounds for rejecting the claim of the MPTD to be a valid theory of distribution, then debates about the extent to which the MPTD is applicable would appear to be redundant. 2 Constant returns to scale. Another objection raised by Pareto against the use of Euler’s theorem to solve the adding-up problem45 was concerned with the assumption of constant returns to scale. Some authors assume that if all the factors of production are doubled, the product will also double. This may be approximately true in certain cases, but not rigorously or in general. … But this assumption is not, in general, admissible. (Pareto 1897, 712; quoted in Stigler (1941, 364), who regarded this objection by Pareto as ‘utterly unconvincing’) To support his objection, Pareto gave an example in which the factors involved in the transport system of Paris were doubled, but the result would not be a doubling of the output. Stigler argued that if Pareto had considered an industry that is fully competitive rather than a monopoly, like the Paris transport system, he would have realised that output could be doubled (Stigler 1941, 364). However, as is argued above, the assumption that firms exist in a state of competitive equilibrium could be seen as unrealistic as, or even more unrealistic than, the

assumption of constant returns to scale, and would therefore constitute a major restriction on the usefulness of the MPTD. As with the first objection (i.e. invariability of factor proportions), this second objection by Pareto relates only to the applicability of the MPTD. It restricts the range of real-world situations to which the MPTD may be applied, but is not an objection to the MPTD itself. 3 Factor interdependence. A third argument employed by Pareto against the MPTD concerned the interdependence of the factors of production and the use of Euler’s theorem to solve the adding-up problem. He argued that Euler’s theorem cannot be validly used in that context – because Euler’s theorem involves the calculation of partial differentials of the various factors of production, and partial differentials can be calculated only if the various factors are independent of one another, but the factors of production are not independent of one another.46 Pareto made use of this interdependence criticism in a 1902 review of Essai sur la théorie générale de la monnaie (1901) by Albert Aupetit, who presented a mathematical expression to show how maximum output could be ascertained for a given expenditure on the various factors of production. Pareto argued that the theory was wrong, because the variables (i.e. the quantities and prices of the inputs) are not independent. He recognised that Aupetit had not asserted that the variables are independent, but had assumed their independence as a simplified point of departure. Pareto believed that such a simplification departed too far from reality – ‘Nous croyons qu’ici il va trop loin et que cette simplification nous éloigne trop de la réalité’.47 Some factors (for example, one coach-driver for one coach) have an almost constant relationship to the product, but other factors (for example, the number and strength of the horses for a coach, or the frequency of the relays) can vary independently (Pareto 1902, 92). Pareto was very polite in this criticism of Aupetit, whose work he described as ‘une remarquable contribution’. He tended to minimise the force of his criticism, saying that ‘si nous signalons ainsi de petits défauts de l’ouvrage, c’est précisément parce que nous n’en trouvons pas de grands’,48 but in fact the criticism presents a major impediment in any attempt to justify the adding-up theorem by making use of partial differentiation. Stigler gave two replies to Pareto’s criticism on the grounds of the interdependence of the factors. The first – which appears to accept the criticism – was:

If two resources must be used together in some functional relationship, then the pair form a technical datum. As such they must be treated as a single factor of production, and economic theory has neither the power of nor interest in separating their returns. (Stigler 1941, 367). In saying that economic theory does not have the power to separate the returns of the two factors, Stigler appears to have accepted the disentanglement objection raised by Hobson and others (see below), and we can only wonder at what Stigler had in mind in saying that economic theory has no interest in separating the returns of the two factors. Such an admission appears to abandon the essential aim of a theory of distribution. Stigler’s second response to the problem of interdependent factors was to assert that, if two factors are used in different proportions in different industries, then ‘the problem must be solved by simultaneous equations of the type developed by Walras and Wieser’ (Stigler 1941, 367). This second response by Stigler to the problem of interdependent factors is not entirely convincing. Its merit is that, by invoking the use of simultaneous equations, it does away with the need for partial differentials, and therefore renders redundant the objection of Pareto that the interdependence of the factors makes the calculation of partial differentials impossible. But the effectiveness of Stigler’s response to Pareto’s objection then relies on the effectiveness of the Walras-Wieser simultaneous equations approach – an approach that some critics have considered to be neither theoretically sound nor practically useful (see, for example, Wicksell, as noted above), and to be incapable of providing a determinate answer to the problem of optimum factor returns in any particular real-world instance. Tarascio has described Pareto’s criticisms as ‘some reservations about the generality of the marginal productivity theory as a theory of production’ (1973, 401; emphasis in original). Tarascio was here referring to Pareto’s argument that many concrete examples may be found where the factor proportions are fixed rather than variable – as in the first criticism discussed above. However, it seems to me that although the first and second criticisms stress the limited applicability of the MPTD and may therefore be properly described ‘as reservations about the generality’ of the MPTD, the third criticism is much more serious, and provides valid grounds for rejecting any use of differential calculus in justifying the MPTD or in proving the addingup theorem. If the adding-up theorem cannot be proved, the MPTD itself must of course be rejected.

Schultz (1932, 292–3) held the view that ‘Pareto’s theory, as developed in the Cours, is not a complete rejection of the marginal productivity theory, but only a correction of it’. He supported that view with quotations from Pareto’s Cours (Section 717): ‘the consideration of marginal productivity cannot be applied without correction … One must not therefore make use of the theory of marginal production without taking these corrections into account.’ But the question of whether Pareto merely corrected the MPTD or actually abandoned it is left somewhat unclear in the following statement by Schultz in response to criticisms of Pareto by Hicks (1932b): ‘By the time Pareto came to write his Manuel he definitely bade adieu to the marginal productivity theory, for (in his judgment) he had a better and more general theory.’49 4 Calculation of coefficients of production. A fourth criticism of the MPTD from Pareto concerns the complexity of the task of calculating the coefficients of production. It must be clearly understood that the determination of the coefficients of production is not only a technical problem, but that it depends on prices, the state of the market, and in general on all the circumstances of economic equilibrium. It is a system of equations which must be solved; it is not a set of isolated, independent equations.50 He was critical of those economists who ‘make desperate efforts to substitute for this system of simultaneous equations a system of equations which can be solved individually’ (Pareto 1971, 466–7).

L. Walras (1834–1910) The first published attempt by Léon Walras to discuss the marginal productivity theory appears to have been his ‘Note sur la réfutation de la théorie anglaise de fermage de M. Wicksteed’ (‘Note on Mr. Wicksteed’s Refutation of the English Theory of Rent’), published in Recueil publié par la Faculté de Droit de l’Université de Lausanne (1896). Walras said he had written the ‘Note’ in 1894, after the publication of, and in response to, Wicksteed’s Co-ordination of 1894. The ‘Note’ was republished later that year as an appendix in the third edition of Walras’ Eléments d’économie pure, 485–92. In Stigler’s words (1941, 368), it was ‘essentially a claim that Walras first discovered and formulated the general productivity theory in his chapter on the Ricardian rent theory’. Walras’ claim to priority was based on his belief that Wicksteed’s equation

is identical to one he had written in his ‘Note’ of September 1894. According to Walras, the equation written by Wicksteed ‘differs from mine (if it really differs at all) only by being a more general form’. Walras virtually accused Wicksteed of plagiarism – ‘Mr. Wicksteed … would have been better guided if he had not been obliged to appear ignorant of the works of his predecessors’ (Walras 1954a, 495; quoted in Stigler 1941, 369). Stigler argued that Walras’ claim to priority (over Wicksteed’s Co-ordination of 1894) in the formulation of the general marginal productivity theory was ‘completely unfounded’, and attributable to ‘self-confusion’. He described Walras’ accusation of plagiarism as ‘a gross impertinence’. According to Stigler, ‘Walras did not have a marginal productivity theory before Wicksteed’s brochure appeared’.51 Walras said that Wicksteed had demonstrated that ‘the rate of remuneration of each factor is the differential coefficient of the product with respect to the quantity of that factor’, but added that ‘It is not my purpose to evaluate this part of Mr. Wicksteed’s work’ (Walras 1954b, 493). We are left to wonder why he did not choose to offer an evaluation of this part. He had no hesitation in offering evaluations of other parts, and it is clear that he considered Wicksteed’s theory of distribution unsatisfactory. He concluded this 1894 note by saying that he doubted whether Wicksteed was ‘justified in proffering his little treatise to fill the gap [between the new theory and the old theory of distribution]’ (1954b, 493). Walras’ ‘Note’ of September 1894 on Wicksteed was extended by a postscript written in October 1895 in which he argued that Enrico Barone52 had provided a more general proof. According to Walras, Wicksteed’s proof was applicable only to the case where the production function is linear and homogeneous, but Barone had provided a proof applicable to the general case where the production function is neither linear nor homogeneous. Walras therefore concluded that, when free competition exists, the following propositions will always be valid, namely: ‘the rate of remuneration for each service is equal to the partial derivative of the production function, i.e. to its marginal productivity’, and ‘the total quantity of the output is distributed among the productive services’ (1954b, 495; emphasis in original). A peculiar feature of Walras’ position was his argument in the 1895 postscript that ‘the consideration of marginal productivity is relevant to the determination of the coefficients of production [i.e. the quantities of the various factor services], but is not relevant to the determination of the prices

of services’ (1954b, 495). A similar statement had occurred earlier in his Elements: The marginal productivities are taken into account, not, in the inept and incorrect way of the English School, for the determination of the prices of land-services, but for the determination of the coefficients of production, just as costs of production are taken into account for the determination, not of the prices of products as the English School would have it, but of the quantities of output. (1954a, 417–18) Walras’ denial that the marginal productivity is relevant to the pricing of productive services appears to be inconsistent with his statement that ‘under the rule of competition, the rate of remuneration for each service is equal to the partial derivative of the production function, i.e. to its marginal production’ (1954b, 495; emphasis in original). Throughout its history, the MPTD has been interpreted mainly as a theory that is relevant to the pricing of the factors of production. Walras’ interpretation as a theory relevant to the determination of quantities rather than prices suggests that he cannot strictly be regarded as a proponent of the MPTD in its more commonly accepted sense. It may be relevant to note that Walras used the expression ‘Theory of Marginal Productivity’ (1954b, 495), but did not include the term ‘Distribution’ in that title.53 An even more peculiar feature of Walras’ ‘Note on Mr. Wicksteed’s Refutation of the English Theory of Rent’ is that, after being first published in the Recueil of the Faculty of Law of the University of Lausanne, and republished as an appendix in the third edition (1896) of the Eléments, it was omitted from the fourth edition of 1900 and from the ‘Edition Définitive’ of 1926.54 William Jaffé believed that, despite its withdrawal from subsequent editions of Walras’ Elements, the Note ‘still constitutes a noteworthy event in the history of marginal productivity theory, if for no other reason, for the controversy it has stirred up’.55 Its withdrawal could also be regarded as a noteworthy event, although in the literature of the MPTD its appearance is more noted than its withdrawal. Pareto had criticised Walras’ marginal productivity theory owing to the interdependence of the variables in the production function: ‘On y traite comme des variables indépendantes des quantités qui ne le sont pas, et les équations que l’on écrit pour déterminer le minimum ne sont pas admissibles.’56

In a letter written to Barone on 10 December, 1901,57 Walras responded to this criticism by Pareto, asserting that ‘Contrairement à l’opinion de M. Pareto’, he persists in believing that his equations are ‘parfaitement admissibles’ (Schultz 1929, 548). Schultz regarded Walras’ response as ‘not convincing’. He believed that Walras was ‘troubled’ by Pareto’s criticism, and noted that when Walras revised his Eléments in 1902, he omitted a crucial equation referring to Euler’s theorem, without advising the reader of the omission (Schultz 1929, 551). Schultz (1929, 547) also noted that Pareto had published his criticisms of the MPTD in his Cours d’économie politique (1897), and had advised Walras of his criticisms before publishing them in his Cours, but that Walras had not referred to the criticisms in the third edition (1900) of his Eléments d’économie politique pure. Walras’ Elements was not only a contribution to the development of mathematical economics, but also an earnest expression of faith and hope in the future achievements of mathematical economics.58 In the Preface to the fourth edition of the Elements (1900), Walras argued that ‘those economists who do not know any mathematics, who do not even know what is meant by mathematics and yet have taken the stand that mathematics cannot possibly elucidate economic principles … will always have to face the alternative either of steering clear of this discipline … or of tackling the problem of pure economics without the necessary equipment’. He looked forward to the day when ‘mathematical economics will rank with the mathematical sciences of astronomy and mechanics’ (Walras 1954a, 47–8). It will be argued below that the MPTD has been put forward by its supporters as evidence of the fruitfulness of the mathematical approach to economics, but that detractors say that its deficiencies have been glossed over for fear of undermining the scientific status of economics.

K. Wicksell (1851–1926) It was claimed by Lionel Robbins that Knut Wicksell, in his discussion of the theory of distribution in Value, Capital and Rent (first German edition, 1893), must be looked upon as ‘one of the founders of the marginal productivity theory’ (Robbins 1934, xii). The claim was strongly endorsed by Stigler, who also regarded Wicksell as ‘one of the founders of the general marginal productivity theory of distribution’. Although Wicksell did not give an ‘explicit mathematical

statement’ of the general theorem, his work ‘suggests’ the general theorem; it contains ‘implicitly the general marginal productivity theory’, and ‘contains all the essentials’ of the general theorem (Stigler 1941, 294–5, 373). The claim was expressed in even stronger terms when Stigler declared that Wicksell, in his Value, Capital and Rent, presented ‘the first complete mathematical formulation of the marginal productivity theory of distribution’ (Stigler 1941, 293; cited in Uhr 1960, 70).59 In an article in Ekonomisk Tidskrift in 1900 Wicksell said that he had developed his version of the MPTD after reading Wicksteed’s Co-ordination (1894). He added that he had not at first found anything new in what Wicksteed had said, and that it was only after developing his own ideas that he realised that Wicksteed had anticipated him. However, Stigler (1941, 374) believed that the MPTD was ‘thoroughly embedded’ in Wicksell’s Value, Capital and Rent (1893), although Wicksell was unaware of it.60 In Value, Capital and Rent, Wicksell said: thrift requires that each factor shall be employed in such quantities that the falling out of a small portion of this quantity would diminish the result by an amount equal to the share in the proceeds which belongs to this quantity.61 In addition, in 1893, he referred approvingly to Thünen’s law that the average wage depends on the yield of the last worker, and that the level of the rate of interest depends on the productiveness of the last invested particle of capital.62 In his journal article in 1900, Wicksell defined the MPTD in the following terms: ‘the increase in the product due to the worker last employed determines both his wage and that of the other workers, assuming that all the workers are equally strong and skilful’ ([1900] 1958a, 94). He argued that, under free competition, distribution will logically follow this law of wages63 and he declared that ‘this remarkable law may be regarded theoretically as infallible’. He recognised that the extent to which it corresponds with reality depends on the extent to which the assumption of free competition is realised, but added in a footnote that ‘Experience seems to indicate that the sphere of validity of the law is not small, even when competition is not completely free’ ([1900] 1958a, 95). The argument he put forward in support of this ‘infallible’ law of wages is therefore of sufficient importance to merit being quoted in full: For as long as a worker is content with a smaller wage than that which corresponds to the increase in the total product which he brings about if employed, it must be advantageous for the landowner to increase his labour

force by one, and competition between the employers then raises the level of wages. On the other hand, as soon as an employed worker demands a wage higher than his additional product, that is, than that part of the total product which would disappear if he were dismissed, it is more advantageous for the landowner to decrease his labour force, and competition between the workers leads to a decline in wages everywhere. The remainder of the product, whether it is thought of as rent or as rent and entrepreneurial profit combined, goes to the landowner; or, in modern terminology, wages are determined by the marginal productivity of labour, and the landowner-employer is the residual claimant. (Wicksell [1900] 1958a, 94–5)64 One interesting feature of Wicksell’s argument is his use of the expressions ‘due to’ and ‘brings about’, and the possessive pronoun ‘his’, in the phrases ‘the increase in the product due to the worker last employed’, ‘the increase in the total product which he brings about’, and ‘his additional product’. These expressions imply that Wicksell perceived the marginal product of labour to be a monocausal phenomenon, i.e. one that is produced by labour, and labour alone. Another interesting feature is that, although the argument attempts to justify paying to the marginal unit of labour a wage equal to that labourer’s marginal product, it does not provide any convincing proof that all the workers in that operation would be paid a wage equal to the wage of the marginal worker. It is important for such a proof to be spelt out, because if each successively employed worker is to receive (in accordance with the MPTD) a wage equal to his or her marginal product, rather than a wage equal to the marginal product of the last worker, there would be no remainder or surplus available as rent or profit for the landowner or entrepreneur, i.e. there would be no ‘residual claimant’. Conversely, if the marginal products of the previously employed workers are different from the marginal product of the last employed worker, but if all the workers receive a wage equal to the marginal product of the last employed worker, then the wages of the previously employed workers will not be equal to their marginal products; in other words, the distribution of income under these circumstances will be contrary to the MPTD and will constitute a refutation of the MPTD. Wicksell did not address this issue in the context of this 1900 article. Like J.B. Clark and many others, Wicksell argued that ‘the productivity of labour’ cannot be determined for production as a whole – he went so far as to assert that the expression is meaningless in reference to the total product – but that the marginal productivity of labour is a meaningful and determinable quantity. Wicksell seems to have believed, unlike Hobson and others, that

there would be no problem in disentangling the marginal products of the various factors. He considered the objection that in a clothing factory employing 100 machinists and 100 sewing-machines, if one machinist were dismissed, one machine would stand idle; or if one machine broke down, one machinist would be idle; and it would be impossible to separate the marginal productivity of labour from that of capital, and impossible to decide what is labour’s share and what is capital’s share. He replied to this objection by arguing that ‘by a slight adjustment of production’, a slight surplus of machines or a slight surplus of machinists could be accommodated. He confidently concluded that the ‘change in total product which would follow an increase or decrease in one factor would be quite distinct from that resulting from a change in the other factor’ (1958b, 128). But he did not show how a ‘slight adjustment of production’ could be logically consistent with the ceteris paribus clause upon which the MPTD is based. In his Lectures on Political Economy Wicksell repeated his endorsement of the MPTD as a general principle: ‘the share of the product going to any particular factor of production is determined by its marginal productivity’ (1934, I, 147). Once again he did not question the feasibility of separating and measuring either the specific marginal product or the net marginal product of each factor. Wicksell also argued that marginal products can be found by calculating partial derivatives: Mathematically expressed, this means that the share in the proceeds of the different factors of production must be proportional to the partial derivative of the above-mentioned [production] function in respect of the factor in question as variable. (Wicksell [1893] 1970, 25) He concluded that the ‘true solution’ of the problem of distribution lies in this ‘simple formula’. However, Wicksell argued that the MPTD could not be applied to the determination of the rate of return on aggregate capital. In his Value, Capital and Rent (1893) he stated that the MPTD theorem ‘can by no means be applied to the increase in the national capital itself and to the surplus returns brought about thereby’ (Wicksell [1893] 1970, 142). He described the MPTD as the ‘true solution of the problem of distribution’, but added the caution: ‘provided that at the same time the special position of capital as an element in production is sufficiently considered’ ([1893] 1970, 25).65 He described this as a ‘curious divergence’, and added the explanation:

Whereas labour and land are measured each in terms of its own technical unit (e.g. working days or months, acres per annum) capital, on the other hand, as we have already shown, is reckoned, in common parlance, as a sum of exchange value – whether in money or as an average of products. In other words, each particular capital-good is measured by a unit extraneous to itself. However good the practical reasons for this may be, it is a theoretical anomaly which disturbs the correspondence which would otherwise exist between all the factors of production. (Wicksell [1901] 1934, 149; emphasis in original) Wicksell regarded this explanation as ‘quite simple’, but it is neither clear nor convincing. Measures of labour in working days or months and of land in acres per annum are hardly satisfactory, given the enormous variety in the quality, productivity and exchange value of individual units of labour and land. They must surely be also measured in units extraneous to themselves. The only meaningful way of obtaining a measure of the quantity of labour, when labour consists of disparate units such as brain surgeons and gravediggers, is to measure each unit in some non-labour numéraire, such as market value.66 If Wicksell’s measurement argument is used to conclude that the MPTD does not apply to capital, then it could equally be used to conclude that the MPTD does not apply to labour and land. Writing to Marshall in 1905, Wicksell said: So long as capital is defined as a sum of commodities (or of value) the doctrine of the marginal productivity of capital as determining the rate of interest is never quite true and often not true at all – it is true individually but not in respect of the whole capital of society.67 He noted that a characteristic feature of capital goods is that they ‘are not always entirely used up in one year’s (direct) production … but often give many years of service, so that the productive power embodied in them may be expended over a succession of years’.68 From this he concluded that, in the case of capital, ‘In general, it is impossible to say how much, and which part, of it is used each year’ ([1900] 1958a, 116–17). If, as Wicksell argued, it is not possible to identify how much capital is involved in the production process in any particular time period, it is also not possible to give a numerical value to the coefficient of the marginal product of capital. This particular objection to the applicability of the MPTD constitutes a major critique of the credibility of the MPTD as a general theory of distribution.

Were Wicksell’s objection to be accepted, the credibility of the MPTD would be further restricted if land is regarded as a form of capital; and would be nullified completely if labour is also regarded as a form of capital, i.e. if Wicksell’s objection is applicable to human capital as well as to non-human capital. It could be argued that labour, like capital, is not ‘used up in one year’s (direct) production … but often gives many years of service’. Another limitation to the MPTD is implicit in Wicksell’s (1893) statement that, in equating the rate of interest with the last unit of capital, ‘the wage can and must be assumed to be given’; and that in determining the wage, ‘it must be assumed that the rate of interest is given’ (Wicksell [1893] 1970, 141–2 and 142 n.). In other words, Wicksell was specifying the standard assumption required for partial differentiation of one variable, namely that the other variables are assumed given, or independent, or held constant. In the context of Value, Capital and Rent (1893), he does not appear to have considered Pareto’s objection that, in determining the distribution of the product, the factor rewards are necessarily interdependent and that therefore partial differentiation is not legitimate. Wicksell is credited (by Stigler, Uhr and others69) with having demonstrated the product-exhaustion problem (or the adding-up theorem). But neither Stigler nor Uhr appears to have given adequate weight to Pareto’s objection. The question of whether the validity of the adding-up theorem is essentially dependent on the assumption that the production function is linear and homogeneous was vigorously discussed by Edgeworth, Pareto, Walras, Barone and Wicksell. In his article in 1900 Wicksell argued that the validity of the adding-up theorem depends on the assumption that ‘the scale of production is immaterial for the result’,70 i.e. ‘that production on a small scale and production on a large scale yield the same relative return’ (1958a, 98; emphasis in original). A similar defence of the assumption of a linear homogeneous production function was made by Wicksell in a letter to Walras on 28 October 1900 in which he thanked Walras for his gift of a copy of the fourth edition (1900) of his Eléments, and complimented him on having removed from the fourth edition a note critical of Wicksteed’s use of that assumption. J’ai vu avec satisfaction que vous avez supprimé la note concernant M. Wicksteed. En effet, la critique de M. Barone, que vous y aviez rendue ne m’a pas paru tout à fait juste. La restriction du théorème de la productivité marginale aux cas où la productivité totale est une fonction homogène et du premier degré des facteurs productifs (de la terre, du travail, etc.) qu’a introduit M. Wicksteed, et qui a paru si superflue à M. Barone, n’est en réalité autre chose que votre proper supposition d’une concurrence illimitée

parmi les entrepreneurs, car cette concurrence évidemment ne peut avoir lieu qu’à la condition que la production à une petite échelle est proportionellement aussi lucrative que celle à une grande échelle, et voilà précisement le sens de la restriction de M. Wicksteed.71 In a letter replying to Wicksell’s of 28 October 1900, Walras gave the following reason for his omission of the critical note of Wicksteed: Votre observation relative aux productivités marginales mérite un sérieux examen. Je ne m’engage finalement pas dans cette controverse pour la même raison qui m’a fait supprimer l’appendice sur Wicksteed: J’avoue que, n’ayant pas fait une étude approfondie de la question, je préfère me borner à l’indiquer, en la maintenant au dehors de ma théorie.72 In mathematical terms, using Wicksell’s notation, if a is the number of workers, b is the number of acres of land, and P is the product, Wicksell expressed the adding-up theorem in the form:

where ∂P/∂a and ∂P/∂b are the marginal products of labour and land. This follows from the assumption that P is a homogeneous and linear function of a and b, so that any increase in a and b will yield the same proportionate increase in P. In other words, there are constant returns to scale, and the relative returns remain the same, irrespective of the scale of production ([1900] 1958a, 98). Wicksell recognised that this assumption places severe restrictions on the validity and/or reality of the adding-up theorem: This assumption is far from obvious or generally valid; on the contrary, it may be questioned whether it is ever strictly fulfilled, since the advantage of combining and dividing work must always appear to some extent when production is on a larger scale. ([1900] 1958a, 98) Wicksell acknowledged that Wicksteed73 had forestalled him in recognising the importance of this restrictive assumption. In his article in 1900, Wicksell acknowledged Walras’ claim to priority, over himself and over Wicksteed, in formulating a general marginal productivity theory; but he argued that Walras’ version was no more general than his own.

Wicksell argued that Walras’ version remained dependent on the limiting assumption of a linear and homogeneous production function (as it was for Wicksteed). Wicksell said that Walras was ‘mistaken’ in thinking that his version was independent of that assumption, and he defended Wicksteed against Walras’ accusation of plagiarism. Wicksell concluded (in 1900) that ‘Wicksteed’s treatment of the problem is particularly commendable, and not at all deserving of the scornful dismissal accorded to it by Walras’ (Wicksell 1900, 313; 1902, 425; 1958a, 100; see Stigler 1941, 374–5). But in an article published in 1902 Wicksell withdrew this criticism of Walras and confessed that he had done him an injustice. Wicksell argued in his 1902 article that the adding-up theorem did not depend on the restrictive assumption that the production function is linear and homogeneous; for the adding-up theorem to be valid, it is sufficient to assume that average costs are constant.74 He argued that under free competition a firm will be tending towards its most advantageous or maximum position, which will be one where average costs are constant.75 He therefore claimed that when the theory is based on an assumption of constant average costs, it gains in ‘general validity and completeness’ (Wicksell 1958b, 121). To support this new argument, Wicksell advanced the following attempt at an algebraic proof. If w = average wage; r = rent per acre; a = number of workers; b = number of acres; Q = quantity produced; k = average cost per unit of product, then k = (aw + br)/Q

(1)

If the number of workers increases by one man (from a to a+1), total wage costs will increase from aw to (a+1)w,76 and the product will increase by an amount qa, which he described as the marginal product of labour. Wicksell then stated that whether k increases or decreases ‘clearly depends on whether w/qa is greater or smaller than k’, and that when w/qa = k, k will be at a minimum value, i.e. the firm will be at its optimum or equilibrium point.77 Similarly, if the number of acres is increased by one (from b to b+1), and output increases by qb (i.e. the marginal productivity of land), Wicksell concluded that k will be at a minimum value, and the firm will be at its optimum or equilibrium point, when r/qb =k. By substituting w = kqa and r = kqb in equation (1), we obtain

k = (akqa + bkqb)/Q

(2)

or Q=aqa +bqb Wicksell ([1902] 1958b, 127)concluded: In other words, when production is arranged in the most advantageous manner possible, the whole product is equal to the sum of the marginal productivity of labour multiplied by the number of workers and the marginal productivity of land multiplied by the number of acres. Wicksell added that in the special case of constant returns to scale (i.e. where large-scale and small-scale production give the same return), the above equation is identically satisfied, i.e. it is valid for all values of a and b; but in the general case, it is valid only as a maximum condition, i.e. only for values of a and b that correspond to the most advantageous production arrangement ([1902] 1958b, 127). Several comments could be made on this 1902 attempt by Wicksell to prove the adding-up theorem. It does not require, and does not permit, the use of differential calculus. Wicksell conceived the marginal product (qa) of labour as the extra product resulting from the employment of an extra unit of labour (i.e. an extra workman) – not as an extra infinitesimal unit of labour, as required by differential calculus. His attempted proof thus avoids Pareto’s objection (see above) to the Wicksteed-Flux solution, namely that the use of differential calculus in proving the adding-up theorem is illegitimate, because the variables (wages, profits, rent) are not independent of one another. The attempt is notable for its simplicity. With some elementary manipulation of equations, it claims to have delivered a solution to a problem that has occupied and continues to occupy the minds of many leading members of the profession. If Wicksell’s solution is correct, it must be hailed not only for its simplicity but also for its brilliant ingenuity. However, the profession seems not to have accorded serious recognition to Wicksell’s solution, at least at the textbook level. It is not mentioned in any of the textbook accounts of the MPTD presented in Chapter 8. The legitimacy of Wicksell’s interpretation of his equation (2), namely Q = aqa +bqb, is open to question. He interprets it to mean that ‘the whole product is equal to the sum of the marginal productivity of labour multiplied by the number of workers and the marginal productivity of land multiplied by the

number of acres’. If equation (2) is valid and if this interpretation of it is correct, then Wicksell would have satisfactorily proved the adding-up theorem. But is this a logical and legitimate interpretation of equation (2)? Wicksell appears to have read more into equation (2) than is there. Equation (2) merely says that the original output (Q) that exists before the introduction of an extra unit of labour and an extra unit of land is equal to the sum of the marginal productivity (qa) of the extra unit of labour multiplied by the original number (a) of workers, and the marginal productivity (qb) of land multiplied by the original number (b) of acres of land. This would appear to be the only interpretation that can be logically and legitimately drawn from equation (2), and it is difficult to understand how Wicksell or anyone else could have interpreted equation (2) otherwise. This alternative interpretation of equation (2) does not in any way provide a proof of the adding-up theorem. It could also be noted that, if in equilibrium the average product of labour equals the marginal product of labour (qa), and the average product of land equals the marginal product of land (qb), and if ‘of’ in the preceding lines means the specific products of the factors – where ‘specific’ is defined in the sense used by J.B. Clark – then the equation Q=aqa +bqb merely says that the total product equals the sum of what is specifically produced by labour and what is specifically produced by land. Another objection to Wicksell’s attempted algebraic proof is that, like Flux’s attempted proof of the adding-up theorem, it lacks a time dimension, and overlooks the essentially sequential nature of the processes that the MPTD seeks to explain. Wicksell showed that, when an extra unit of labour is employed, and when average costs are constant (k′ = k), then w = kqa. By a similar process, he argued that when an extra unit of land is employed, and when average costs are stable, then r = kqb. The value of w, namely w = kqa, is obtained by assuming the quantity of labour increases while the quantity of land remains unchanged. The value of r, namely r =kqb, is obtained by assuming the quantity of land increases while the quantity of labour remains unchanged. In Wicksell’s algebraic proof, no formal recognition is given to the fact that the two processes occur over time.78 But if the two processes are viewed sequentially and cumulatively, then when the extra unit of labour is first applied, the new level of output will be Q + qa, as Wicksell stated; but when the extra unit of land is later applied, the new level of output will be,

not Q + qb as Wicksell stated, but Q + qa +qb. The average cost (k′) following the application of the extra unit of labour will be, as Wicksell stated: k′ = [(a + 1)w + br] / (Q + qa)

(3)

but the average cost following the subsequent application of the extra unit of land will be not k′ = [(b + 1)r + aw] / (Q + qb)

(4)

but k′ = [(a + 1)w + (b + 1)r] / (Q + qa +qb)

(5)

If average costs remain constant, i.e. k = k′, then [(a + 1)w + (b + 1)r] / (Q + qa +qb) = (aw + br) / Q

(6)

which leads to Q = (aw + br)(qa +qb) / (r + w)

(7)

Even if Wicksell were correct in thinking that equation (2) can be interpreted in a way that provides a proof of the adding-up theorem, no such interpretation can be given to equation (7). It is interesting to note Wicksell’s awareness of the political and ideological significance of the MPTD. He was staunchly anti-socialist – see, for example, his references to ‘’Hegelian’ darkness’ and the ‘conceit of Karl Marx’ (1970, 17) – and he regarded the theory of value of the socialists as ‘a terrible weapon against the existing order’ (1934, I, 28). He believed that the MPTD provided a theoretical refutation of the socialist theory of value. This

probably explains why he maintained his support for the MPTD, even though he had significantly undermined it by excluding capital.

S. Webb (1859–1947) There are statements in the writings of Sidney Webb which suggest that he accepted the MPTD. The basic principle that factor returns are equal to, or determined by, or influenced by, the output of the marginal factor unit is implicit in statements such as: the return to the last increment of capital is the most that a lender of capital can normally obtain for its use. (Webb 1888, 207)79 The amount of produce obtained by the labor of the man at the margin of cultivation, with the minimum capital and ability, sets the standard of normal wages throughout the community. (Webb 1888, 208) The relations between the factors are defined by their respective ‘marginal effectiveness’. (Webb [1889] 1964, 69) However, it is also clear that, for Webb, there are forces other than ‘marginal effectiveness’ that influence the size of factor returns, and that, despite the hints contained in the above three quotations, he did not support the MPTD.80 On the contrary, he stated that a ‘scientific analysis’ of wages does not depend on ‘any claptrap as to the product of labour’ (Webb [1889] 1964, 69), and he expressed in his own words the disentanglement objection later stressed by Hobson: The aggregate produce is universally resultant from a combination of the factors of production … and no part of it can be ascribed to any particular one of those factors, just as in an advanced industrial community, no man can ascertain or estimate the actual amount of his own contribution to the aggregate … the total varies according to the aggregate effectiveness of the combination of the factors, but the classification of the total into its different categories varies independently of its amount, according to the relations of these factors. (Webb [1889] 1964, 69)

Class conflict appears to have played a far greater role than ‘marginal effectiveness’ in Webb’s views on distribution: ‘under a system of unrestrained private ownership of the instruments of production, the earth may be the Lord’s, but the fullness thereof will inevitably be the landlord’s’ (Webb [1889] 1964, 73). He described the distinction commonly made between land and capital as a ‘queer artificial distinction’ and as ‘merely an illogical physiocratic survival’. He argued that the capitalist would possess exploitative powers equivalent to those of the landlord: Complete private property in capital, whether immovable or movable, necessarily involves the power to extract as mere ‘rent’, and without rendering any return, the equivalent of the whole economic advantage of all instruments of production exceeding in effectiveness the worst in use. (Webb [1889] 1964, 72) It is also interesting to note that in 1888 Webb recognised the circularity problem in the definition and measurement of capital. In dividing the aggregate output, the amount paid in interest will depend on the rate of interest and on the value of capital; but ‘the pecuniary valuation of the capital stock … itself depends upon the current rate of interest’.81

J.B. Clark (1847–1938) The idea that the MPTD provides a solution to the problem of an equitable distribution of the product between profits and wages is to be found most prominently in the writings of J.B. Clark. In his Distribution of Wealth (1899), Clark argued that the distribution process is just, and economic exploitation is non-existent, if each factor receives what it produces. He believed that ‘to each what he creates’ is the ‘natural law of distribution’: ‘Give to a man the wealth that he creates, neither more nor less. Every one owns what he brings into existence; let not society wrest or filch from him any part of it’ (1963a, 598). If society does not ensure that wages are equal to the whole product of labour, there is ‘institutional robbery’ and a ‘legally established violation’ of the rights of property, and ‘every right-minded man should become a socialist’ (J.B. Clark 1956, 4, 9). The MPTD was thus interpreted by J.B. Clark as a natural law of distribution which, if implemented, would safeguard the property rights of all the factors and abolish exploitation. In his view, it explains not only how distribution occurs, but also how it ought to occur. Clark’s awareness of the political

implications of the MPTD,82 and of the role it could play in preventing political revolution, is clearly evident in his statements: If it were a general conviction that social evolution is in the direction of iniquity, – that distribution already robs the workers and will rob them more hereafter, no force could prevent a violent overturning of the social order. (J.B. Clark 1963a, 596) This thesis we have to prove; and more hinges on the truth of it than any introductory words can state. The right of society to exist in its present form, and the probability that it will continue so to exist, are at stake. These facts lend to this problem of distribution its measureless importance. (J.B. Clark 1956, 3) The fact that J.B. Clark’s MPTD was developed not as an a-political, internalist exercise – or a development of theory for the sake of theory – but as a tool in a political and ideological controversy is also apparent in the following statements of his son, J.M. Clark: The marginal theories of distribution were developed after Marx; their bearing on the doctrines of Marxian socialism is so striking as to suggest that the challenge of Marxism acted as a stimulus to the search for more satisfactory explanations. (J.M. Clark [1931], 1950, 64–5) [J.B. Clark’s MPTD] is probably best construed as an emphatic rebuttal to the exploitation theories of Henry George and Karl Marx, in which rent and profits are, inherently, robbery. (J.M. Clark 1968, 506) [J.B. Clark’s] statements are oriented at Marx, and are best construed as an earnest, and not meticulously-qualified, rebuttal of Marxian exploitation theory. (J.M. Clark 1952, 411; cited in Harcourt 1975, 352) J.B. Clark recognised that the principle of ‘to each what he creates’ might not be universally acceptable as a principle of distributional justice. Some might prefer, for example, the principle of ‘work according to ability and pay according to need’ (1956, 8). But if one accepts a labour theory of property

rights, then, according to J.B. Clark, the MPTD is the ‘natural law of distribution’. He defined the specific product of labour as the ‘product that can be traced to the last unit of labor’ (1956, 160), and believed that it is equal to the reduction or enlargement in the total product that results from taking one man from the labour force or adding one man to it. J.B. Clark’s ‘final productivity rule’ was: ‘the law of wages and interest is: These incomes are fixed by the final productivity of labor and of capital’ (1956, 160–1). That J.B. Clark’s concept of specific product bears an exclusive, causal relationship to the marginal unit of the variable factor is confirmed by J.M. Clark’s statement: [J.B.] Clark used the term ‘specific productivity’ to emphasize the idea that the increment of product due to a marginal unit of a factor is the product causally attributable to any and every unit of this factor, the units being interchangeable … This causal concept, and especially the ethical conclusions, have been subject perhaps to more criticism than any other features of Clark’s system; yet he would appear to have regarded them as his most basically-important contribution. ( J.M. Clark 1952, 411; see also 1968, 306) With this concept of monocausal or specific productivity, J.B. Clark linked morality with causality, and deduced the ethical implications of the MPTD. If the marginal product is produced by the marginal unit of labour, the marginal product ought to be the exclusive property of the marginal unit of labour. If the whole product is distributed among the various factors according to the marginal productivity law, the distribution system is fair and just, because each factor receives what it produces. If each man gets what employers would lose by his absence, he gets what he is effectively worth … Each pound or dollar tends, under natural law, to secure for its owner what, in production, it is separately worth. (J.B. Clark 1963b, 602) According to J.B. Clark, the specific marginal product of labour sets an upper ethical limit to wages – ‘No man can get more than his presence adds to the product that the land and the labor could create without him’ (1956, 160); and it also sets a lower ethical limit. A wage that is greater or less than the marginal product of labour is morally indefensible. Social justice requires distribution according to marginal productivities.

Thus, in J.B. Clark’s version of the MPTD, ‘of’ in the phrase ‘marginal product of labour’ carries a proprietorial significance. Proprietorship of the marginal product is derived from two sources: (1) the belief or assumption that the marginal product of labour is produced by the marginal unit of labour; and (2) an implicit or explicit invoking of a Lockean or contributor theory83 of property rights according to which property rights in an object are said to belong to the person who has produced it. In Clarkian-style expositions of the MPTD it is either argued or implied that since the marginal unit of labour produces the marginal product, the marginal unit of labour has a moral right to be the exclusive proprietor of the marginal product. J.B. Clark did not deny that labour cooperates with other factors to create the product, but he believed that the ‘specific’ product of the marginal unit of labour could be disentangled, and separately identified and measured, by observing the change in the total product that occurs after adding an additional unit of labour while holding all other factors constant. This idea had been expressed by J.B. Clark in an earlier article. In the Yale Review (1892–3) he stated: ‘Let the capital of an establishment remain exactly as large as it is, introduce a small supply of extra labor, and whatever of product is created by the addition is virtually due to labor only.’84 However, J.M. Clark was not so convinced of the validity of this ethical implication. He argued that it is unwarranted to say either that J.B. Clark’s MPTD satisfies all ethical standards or that it is completely devoid of ethical significance (J.M. Clark 1952, 411). He also said of his father: ‘the ethical approval he attached to his marginal productivity theory left many loose ends’ (J.M. Clark 1968, 506). The validity of J.B. Clark’s argument depends on (among other things) whether the specific product of each factor can be disentangled and identified. He believed that the increase in the product that occurs when the last unit of labour is employed can be traced monocausally to the last unit of labour, and is therefore the specific product of labour. In other words, he believed that the marginal product after labour (MPAL) is the same as the specific marginal product of labour (SMPL), and that therefore the wage of the marginal unit of labour should be determined by the MPAL. If it is technically possible to identify the specific product of labour in this way, then J.B. Clark’s claim to have enunciated the natural and normative law of distribution would carry conviction, assuming a Lockean labourcreated theory of property rights. But J.B. Clark’s claim to have identified the specific marginal product of labour was soon subjected to criticism85 and is difficult to sustain. It depends on a monocausal, as opposed to a multicausal, concept of the marginal product of labour. It is based on the view that, by

holding or assuming other factors constant, the increase in total product that occurs after an extra unit of labour is employed occurs solely because of that extra unit of labour, i.e. it is created by labour and by labour only. A fundamental criticism that could be directed at Clark’s marginal productivity theory of distribution is that his use of ‘of’ in an exclusive soleproprietor sense in the expression ‘marginal product of labour’ is neither logically, nor linguistically, nor ethically justified. The marginal product that occurs after the employment of an extra unit of labour (with other factors held constant) does not occur solely because of that extra unit of labour. It occurs because of the combined effect of the extra unit of labour acting together with the factor or factors held constant. It is a multicausal phenomenon rather than a monocausal phenomenon. And since the MPAL is not created by the marginal unit of labour alone, the marginal unit of labour cannot logically claim (on a Lockean theory of property rights) to have exclusive ownership rights over the MPAL. If the value of the MPAL goes wholly to labour, then the other (constant) factors that have contributed along with labour to the creation of the MPAL will receive no reward for their contributions. Such a situation not only contravenes the Lockean theory of property rights according to which each factor that has contributed to the production of a commodity has a moral right to what it has produced – but also defies commercial sense, because it means that the other factors are being expected to supply their services without reward. Such a situation cannot be expected to persist, and cannot conceivably be regarded as a situation of equilibrium.86 If the MPAL could be separated into the part specifically created by the marginal unit of labour (i.e. the SMPL) and the part created by the nonvariable factors acting in cooperation with the marginal unit of labour, then a valid equilibrium condition would be ‘wage = SMPL’. But neither J.B. Clark nor any subsequent supporter of the MPTD has been able to show how the specific product of the marginal unit of labour can be distinguished from the specific products of the other factors that act in conjunction with the marginal unit of labour. Unless and until this distinction can be made, the MPTD must remain devoid of any normative relevance within the context of a contributor theory of property rights. If we recognise the causal contribution of the nonvariable factors to the marginal product that occurs with the employment of the marginal unit of the variable factor, then a profit-maximising firm should cease employing labour not when the wage equals the MPAL, but at a point where the wage is somewhat less than the MPAL, so that part of the MPAL can be apportioned to the non-variable factors that causally cooperate with the marginal unit of labour.

The disentanglement problem is exacerbated by the fact that the things that are held constant (but which continue to exert a causal influence) can consist not only of physical capital but also of human capital in the form of existing units of employed labour. By their presence the production process can take advantage of the division and cooperation of labour, thus increasing productivity, but the MPTD does not explain how the specific contribution of the marginal unit of labour can be separated from the specific contributions of the earlier units of labour. For example, suppose a man is employed to roll a log, unaided by capital equipment, and is to receive a wage of $10 for every 20 metres it rolls. By himself, he rolls it 20 metres in one hour, and since his marginal product is 20 metres, his wage (if the MPTD principle is adhered to) is $10. But when a second (homogeneous) unit of labour is added, they succeed in pushing it 60 metres in an hour. The marginal product of the second man is 40 metres, and, according to the MPTD, his wages should be $20. In this situation the MPTD appears not to have established a distribution of rewards that satisfies the requirements of distributive justice, contrary to J.B. Clark’s belief. He recognised that under free competition ‘all men must accept what the last men get who enter the market’ (J.B. Clark 1889, 49), but did not see that this free competition rule contradicts the MPTD rule. J.B. Clark sought to answer the criticisms that (1) if an intra-marginal unit has a higher productivity than a marginal unit, it is being exploited if it does not receive more than the marginal unit; and (2) if a marginal unit has a lower productivity than an intra-marginal unit, it is being exploited if it receives less than the intra-marginal unit, given that all the units are assumed to be homogeneous. The higher productivity of the intra-marginal unit, he argued, is due to its combination with a larger portion of the fixed factor. The lower productivity of the marginal unit is due to the fact that, when more and more units of the variable factor are employed, they each benefit less and less from the cooperative contribution of the fixed factor (see Spiegel 1991, 619). Clark’s reply to the argument that the MPTD involves exploitation is summarised thus by Hutchison (1953, 258): [Clark argued (1899, 319–33) that the] wage given by marginal productivity does not involve any exploitation of the ‘intra-marginal’ workers as had seemed to be suggested in Thünen’s analysis. As successive workers are employed with a fixed total quantity of equipment, the average equipment that each works with declines. The apparently higher productivity of the ‘intra-marginal’ workers is due not to the workers themselves, who are assumed to be homogeneous, but to the larger amount of equipment per head that the ‘intra-marginal’ workers would be working with. J.B. Clark returned to this issue in his Essentials of Economic Theory (1907). He argued that, in a firm employing ten equally productive units of labour

with each using one-tenth of the firm’s capital, each unit would produce onetenth of the product; but this is ‘more than the amount which is added to the product by the advent of the tenth unit of labor. Though one of ten units creates, with the aid of a tenth of the capital, a tenth of the product, of itself it creates less.’ In other words, assuming a situation of diminishing returns, he argued that the average product of the ten units will exceed the marginal product of the tenth unit. He defined the latter as ‘the difference between the product of all the capital and nine units of labor and that of all the capital and ten units of labor’. He claimed that this extra product of the tenth unit is ‘its own product’. It is ‘what it adds to the product that was creating before it arrived on the scene’ and ‘can be attributed entirely to the increment of labor’ (J.M. Clark 1968, 137–8; emphasis in original). As noted above, J.B. Clark argued that, owing to the pressure of competition, each of the ten units of labour would have to accept a wage equal to the marginal product of the tenth unit. The difference between the average product and the marginal product would leave a surplus for the other factors. It would thus provide an answer to the objection that if each additional unit receives a wage equal to its marginal product, there would be nothing left over for profits or rents. But J.B. Clark’s position on this issue appears to involve contradictions. It states that the productivity of each unit of labour, whether marginal or intramarginal, is affected by the amount of the fixed factor acting in cooperation with labour, whereas elsewhere he appears to have argued that the increased production that follows the employment of an extra unit of labour is the specific marginal product of labour which, by his definition, excludes a causative role for the fixed factors. Distinguishing between the average product of labour and the marginal product of labour does not prove that the marginal product is a monocausal product that can be attributed entirely to the last increment of labour. He argued that all ten units of labour contribute equally to production, so that each unit contributes one-tenth of the total product; but he also argued that the tenth unit produces less than the average! On the basis of a labour theory of property rights, he claimed that the marginal unit of labour is entitled only to the marginal product; and, because of competition, all the other units would have the same entitlement as the marginal unit. He did not apply the same labour theory of property rights to the average product of each of the ten units. Furthermore, if diminishing returns persist, and the marginal product of labour continues to decline, J.B. Clark’s argument would justify an everdecreasing level of average wages and an ever-increasing surplus for capital –

a situation which would encourage critics to argue that the MPTD is a theoretical device concocted to exploit labour. However, J.M. Clark argued that the worker’s pay would be ‘indefinitely larger’ than it could be if he lived alone, or in a wilderness or a savage state. He appears to have condoned the level of wages resulting from the application of the MPTD by comparing it with what would result under an alternative system of distribution: ‘It would be a losing bargain for the worker to surrender the product of mere labor in a state of civilization in exchange for what both labor and capital create in a state of savagery’ (J.M. Clark 1968, 145). Another strange feature of J.B. Clark’s theory was his belief that the specific products of labour and capital cannot be disentangled in a primitive society but can be disentangled in an exchange economy – by varying one factor while holding the other factors constant.87 Although J.B. Clark’s arguments for the MPTD occur in their most complete form in his Distribution of Wealth (1899), versions may be found in a number of previous publications. Henry has argued that Clark’s Distribution of Wealth is ‘largely a restatement of his argument as developed over the previous decade’ (Henry 1995, 71), and he has noted, for example, that J.B. Clark’s presidential address in 1894 to the American Economic Association stated that the new theory of distribution ‘serves as a scientific repellent to anarchism and socialism’ (Henry 1994, 73). In his paper ‘The Possibility of a Scientific Law of Eages’, read at the third annual meeting of the American Economic Association, in Philadelphia, on 27 December 1888, and published in Publications of the American Economic Association (1889),88 J.B. Clark attempted to show that the marginal product of labour is created solely by the marginal unit of labour, by making use of the concept of ‘no-rent instruments’, or what might be called ‘no-profit capital’, by analogy with norent land. They consist of ‘machines that have outlived their usefulness to their owners, and that still do their work, and give their entire product to the men who operate them’. The labourers will be ‘virtually empty-handed’. He believed that such ‘no-rent instruments’ occur everywhere ‘in indefinite variety and extent’, and that ‘if labour uses them it gets the entire product of the operation’. This will also occur, he argued, at the ‘intensive margin of cultivation’. The standard of pay for all the men will be set by the wages received at the margin, whether extensive or intensive, because under free competition ‘all men must accept what the last men get who enter the market’ and ‘competition will compel other men to accept the same amount’ (1889, 46, 47, 49, 58). He summed up the argument in the following ‘formula’: General wages tend to equal the actual product created by the last labor that is added to the social working force.

(1889, 49; emphasis in original) Under perfect competition the reward of each [i.e. of capital and of labour] is virtually its own actual product. (1889, 62; emphasis in original) J.B. Clark’s concept of ‘no-rent instruments’ was an ingenious attempt to prove that the marginal product is created solely by the marginal unit of the variable factor, but it could be criticised on grounds of realism. How realistic is it to say that ‘everywhere’ there are owners of unprofitable mills, furnaces and machines who allow them to remain in operation solely for the benefit of the supervisors and workmen who operate them?89 Other early developments of J.B. Clark’s version of the MPTD occurred in articles in the Quarterly Journal of Economics (1890–1) and the Yale Review (1892–3). In the former, entitled ‘Distribution as determined by a law of rent’, he stated: If natural conditions could completely have their way, the final man would get as a wage what he actually produces. It is the final productivity of labor that fixes its pay … He tends … to get as wages what his presence in the working system is worth.90 More generally, he stated that ‘what a social class gets is, under natural law, what it contributes to the general output of industry’.91 The same idea may be seen in his article in Yale Review (1892–3): Let the capital of an establishment remain exactly as large as it is, introduce a small supply of extra labor, and whatever of product is created by the addition is virtually due to labor only.92 The term ‘virtually’ suggests that at least some of the additional output is created by a factor or factors other than labour. However, in a re-statement of the proposition later in the same article, ‘virtually’ was omitted. We have attributed products to marginal labor by supposing a case in which the capital in any industry remained unchanged, and new labor was introduced into it. The addition thus made to the product was seen to be due to labor only. (1892–3, 273)

This idea that the marginal unit of a factor is the sole cause of the marginal product that occurs after the application of the marginal unit of the factor was also applied by J.B. Clark to capital. Now we can isolate the product that is due to capital in exactly the same way. We can leave the labor in an industry unchanged in amount, introduce new capital, and measure the increase in the output. The extra product is the outcome of the use of capital. (1892–3, 273–4) Following the publication of The Distribution of Wealth in 1899, J.B. Clark, in an article in the Political Science Quarterly of 1902, reaffirmed his belief in the possibility of separating and disentangling the specific marginal product of labour, and reasserted the claim that, if labour is mobile and competition is free, wages would tend to equal the marginal product of labour: If a shop representing a hundred thousand dollars’ worth of capital and a hundred men produces a hundred cases of goods in a week, and if the same shop with ninety men produces ninety-three cases per week, then seven cases are attributable to the labor of ten men, and the weekly pay of each man should be the value of seven-tenths of a case. (J.B. Clark 1902, 559–60) He attributed a quasi-metaphysical significance to his MPTD when he argued that under ‘normal conditions’, and under the influence of nature and ‘cosmic forces’, the natural and fair rate of pay will tend to prevail: We may accept the fact that in the adjusting of wages nature, in the main, has its way and that cosmic forces, which we are beginning to understand, assign to labor a general rate of pay. This rate of pay depends on the productive contribution which labor makes to the income of society. The men in a mill do not get what they and the mill together produce, but under normal conditions they tend to get something approximating the part of that joint product which they may fairly regard as solely the fruit of their own labor. (J.B. Clark 1902, 558) It should be noted that, according to J.B. Clark, it is only under competition that workers receive as wages the value of what they produce. He stated that, under competition:

Where many manufacturers are seeking labor as well as many laborers seeking employment, there is a play of forces which gives to a man approximately what he is worth to an employer – that is, what his presence adds to the output of a mill. (J.B. Clark 1904, 6–7) On the other hand, if a monopolist charges a price beyond the competitive level, the value of the worker’s output increases, but the worker’s wage usually remains at the market rate. If a monopolist voluntarily adopts a liberal policy towards his workers, or if he is compelled to do so by a strong trade union, wages might increase somewhat beyond the competitive level, i.e. the monopolists ‘share gains, in some degree, with their men’. Clark acknowledged that it is ‘probably true in the history of a considerable number of trusts that they have paid their workmen just a shade more than such workers could elsewhere get’. But, apart from those circumstances where some labourers are paid ‘a little more in the way of wages than others can get’, a monopolist pays ‘less than the men are worth to him’ (1904, 7). In other words, under monopoly, labour receives less than the value of what it produces, and the MPTD does not apply. J.B. Clark argued that, when monopoly exists, conflicts between employers and organised labour will be resolved only by recourse to some system of arbitration. Resolution of industrial conflict hinges on the question whether the demands of strikers are or are not just. The decision cannot be left to the parties: ‘Neither of the contending parties is impartial enough to tell us or to ascertain for himself’; and consequently ‘the first thing that is needed is a disinterested judgment’ (1904, 74–5). It would not be necessary for the arbitration to be compulsory in the full sense, but it should be arbitration that ‘has authority behind it’ and ‘could be introduced only by the agency of the state’ (1904, 84–5). It is clear that, when production departs from competition, J.B. Clark no longer relied on market forces to effect a fair distribution. From this extensive review of J.B. Clark, it is obvious that his arguments and the counter-arguments involve considerable complexity. In a review of J.B. Clark’s Essentials of Economic Theory, Thorstein Veblen acknowledged the ‘undue tenuity’ of his criticisms of Clark, but in extenuation stated: ‘The manner of argument required to meet this theory of the “natural law of final productivity” on its own ground is itself a sufficiently tedious proof of the futility of the whole matter in dispute’ (Veblen 1907–8, 176).

3 Followers and critics, 1900–1920 From Hobson to Adriance The early years of the twentieth century saw the emergence of a number of strong critics of the MPTD. It continued to receive support from other sources, but now had to contend with a body of opinion that questioned either its validity or its usefulness or both.

J.A. Hobson (1858–1940) One of the earliest and most vigorous opponents of the belief that the productivity of the marginal unit of a factor can be separately identified and measured was John Atkinson Hobson. In The Economics of Distribution ([1900] 1972), he described this belief as ‘a false separatism … which ignores the organic unity in a business’. The productivity of the last unit of labour ‘cannot be rightly separated’ either from the productivity of the earlier units of labour, or from the productivity of the land and the capital. It is a fallacy, he argued, to assign ‘a particular amount of productivity’ to a particular dose of a factor (1972, 144). Against the view that the productivity of the last dose of labour could be measured by the reduction in aggregate product which would have ‘attended’1 the withdrawal of the last dose, Hobson argued that this reduction is not wholly due to the withdrawal of the last dose of labour, but is partly due to the fact that the withdrawal of a unit of labour results in an adjustment of the proportion in which the other factors are combined. This dislocation of the production process will lead to diminished productivity of the other units of labour and of the units of capital and land (1972, 145). This ‘dislocation’ argument implies, although Hobson did not state it in the context, that the increased production that attends the introduction of a further dose of labour is not entirely due to that dose, but is also due to the productiveness of the land and the capital and the previous doses of labour; in other words, MPAL > SMPL. His argument was succinctly summarised in the statement: Where it is essential to productivity that land, capital, and labor shall all cooperate, it is impossible to assign to any one of them a product based on the supposition of a separate productivity. Similarly, where there exists a necessary organic quantitative relation between the factors, no separate product can be put down to any single dose of each.2

In another variation of the same anti-MPTD argument, Hobson considered an extreme case where only one dose of each of the three factors (land, labour and capital) was involved in the production process. He argued that if the one dose of (say) labour were removed, ‘the whole service of capital and land disappears’; and he asked: ‘Is the destruction of the whole product a right measure of the productivity of the labour-dose alone?’ (Hobson 1972, 147). He thus aimed to show that the three factors cooperate in the production process and that no one factor can be regarded as the sole cause of the joint product. The argument, however, did not convince Edgeworth, who regarded it as equivalent to ‘substituting x wherever a mathematician had used dx or x!’, and suggested that the error would have been corrected if Hobson had acquired an ‘elementary discipline in the differential calculus’.3 Stigler claimed that Marshall ‘refuted’ Hobson’s dislocation argument. It might be more correct to say that Marshall attempted to refute it. Whether his attempt was successful is not as clear-cut as Stigler seems to have thought. Marshall admitted that the removal of one unit of labour will decrease the efficiency of the non-variable factors, but claimed that this loss of efficiency would only be temporary, because forces are at work that will readjust the factor proportions and restore efficiency. The implication was that the readjustment would occur quickly, and that therefore the dislocation would be temporary, and its effects could be ignored; but no evidence was provided to support that implication. Hobson’s Economics of Distribution (1900) thus appears to have contained an unambiguous rejection of the MPTD and a clear statement of the reasons for the rejection. However, his position on the MPTD was rendered less clear in his article ‘Marginal Units in the Theory of Distribution’ in the Journal of Political Economy (1903–4). This long and involved article, described later by Hobson himself as ‘somewhat elaborate’ (1904–5, 587), began with what appears to have been a complete reversal of his 1900 position. Referring to Marshall’s example where the employment of a tenth shepherd enables 20 more sheep to be marketed, he appears to have conceded to Marshall that the 20 sheep are ‘the specific product’ of the marginal shepherd. He argued that no consideration needs to be given to the contribution of the fixed factors – the land and capital – to the marginal product of 20 sheep, because ‘any assistance the marginal shepherd receives from capital and land is attended by a corresponding shrinkage in the assistance rendered to the other nine [shepherds]’ (1903–4, 450). He concluded that the wages of the marginal labour will be ‘virtually the whole addition to the productivity of the business which follows its employment’ (1903–4, 449).4

However, this apparent recantation appears to be itself recanted later in the second part of the same article when, turning from ‘an illusory static to a real dynamic society’, he argued that if the farmer employs a tenth shepherd, it is because by employing him ‘he will make a slightly better use of the other given factors’, but that ‘it is not possible to discriminate how much of what is added to the total product can rightly be attributed to the specific productivity of the tenth shepherd and how much to the better functioning of the other factors’ (1903–4, 460). Hobson’s explanation for this second reversal would appear to be that in the first part of the article he was considering ‘an illusory static’ society, but in the second part he turned to ‘a real dynamic society’ (1903–4, 460) – but the precise difference that he intended to establish between the static and dynamic states of society was not made clear.5 The intended difference may possibly have been that in ‘an illusory static’ society, extra doses of labour could be added without any change in the other factors; whereas, in ‘a real dynamic’ society, the extra doses would be ‘composite doses of farmingpower, composed in varying proportions of the several factors, and no dose will be considered to have a separate productive value apart from the others with which it will co-operate’ (1903–4, 461). This criticism by Hobson could be called his ‘composite dose’ criticism. It states that in the real world a marginal dose of one factor usually needs to be accompanied by additional cooperating doses of other factors, to form a ‘composite dose’, and that the separate productivity of the various marginal doses cannot be separated. It has been described by Blaug as ‘probably the oldest and most persistent objection advanced against marginal-productivity theory’, and one that ‘has since been echoed by many other gifted amateurs in economic theory’ (Blaug 1968, 442). In a second reply to Hobson’s ‘dislocation argument’ – in what Blaug (1968, 442) has described as a ‘long unsatisfactory footnote’ designed to give Hobson ‘a lesson in differential calculus’ – Marshall argued (1961, I, 409) that if a change in one factor requires a change in other factors, the contributions of the changes in the other factors can be neglected. This view was endorsed by Stigler: ‘the change of productivity of the non-variable resources involves only higher order differentials, and must be neglected’. Stigler regarded this point as ‘conclusive’ (Stigler 1941, 355). A similar defence of Marshall on this point has been advanced by Blaug. He believes that Marshall introduced the concept of net marginal product ‘in an effort to overcome Hobson’s objection that a single factor cannot be varied in amount without altering the amounts employed of all other factors’. Blaug continues: in mathematical terms, this reduces to the argument that a change in any one of the first partial derivatives of the production function involves significant

changes in all the other first-order differentials. Marshall points out correctly that the marginal product of a variable factor is defined on the basis of an optimum combination of all factors, in which case the change in the productivity of the fixed factors consequent on a change in the variable factor involves only negligible variations in higher-order differentials. However, in that case the marginal net product of a factor will equal its marginal gross product, and the terminological concession to Hobson becomes pointless and even misleading. (Blaug 1985, 410) However, it is doubtful whether Marshall’s ‘second order of smalls’ argument based on calculus was an adequate reply to Hobson’s criticism. Although the use of calculus provides a useful and convenient way of formulating the MPTD, the validity of the MPTD is not essentially dependent upon the use of calculus.6 It was conceived and formulated in the past – even by Marshall himself – and is frequently formulated today, in non-calculus terms.7 The method of calculus is based on infinitesimal changes in the variable factor; but the validity (such as it is) of the MPTD is not affected by expressing the marginal unit of the variable factor in more realistic units – such as one whole shepherd, or one whole spade. Marshall’s reply to Hobson would have been more convincing if it had been expressed in real-life units as well as in calculus. Another unsatisfactory aspect of Marshall’s ‘second order of smalls’ argument is that it is based on a particular interpretation of Hobson’s ‘dislocation’ argument. He appears to have interpreted Hobson’s argument as a two-stage process, namely (1) a small reduction in labour causes a small dislocation in the balance of the factors, and (2) the small dislocation in the balance of the factors causes a further reduction in output, in addition to the reduction represented by the output that was previously being produced by the unit of labour that is now withdrawn. Expressed in calculus terms, in the first stage, the balance of factors is differentiated with respect to the small change in labour; and in the second stage, output is differentiated with respect to the change in the balance of factors. The resulting change in output is therefore of the ‘second order of smalls’, and therefore ‘can’ (Marshall), or ‘must’ (Stigler), be ignored. But this interpretation of Hobson’s argument as a two-stage process requiring two-stage differentiation is somewhat tendentious.8 An alternative and plausible interpretation is that the removal of the marginal unit of the variable factor not only reduces the output (i.e. the specific marginal product) of that marginal unit, but also reduces the output of the non-variable factors owing to the dislocation of the balance of the factors. The two reductions are not

successive events requiring successive differentiations. They are two effects of the one cause. There is no reason for the second reduction – resulting from the dislocation of the balance of factors – to be regarded as being of ‘the second order of smalls’. Marshall, in fact, appears to have been not entirely convinced by his ‘second order of smalls’ reply to Hobson, and to have introduced his concept of marginal net product to cater for Hobson’s objection. The value of the marginal unit of the variable factor would be calculated by deducting from the value of the marginal product the cost of the extra units of the other factors employed in conjunction with the marginal unit of the variable factor. Blaug has argued that Marshall’s introduction of the concept of marginal net product was in fact a capitulation to Hobson; and furthermore that the concept is ‘illegitimate’, because it assumes prior knowledge of ‘the cost of the cooperating factor to the industry as a whole’ (Blaug 1968, 443). The circularity argument, in this or in other forms, was to figure prominently in the Cambridge capital theory controversy. Hobson later (1904–5, 587) declared that in his 1903–4 article he had ‘set forth a number of reasons for rejecting’ the MPTD. His ‘composite dose’ criticism of the MPTD was an attempt to prove that the specific marginal product of the variable factor cannot be identified because the variable factor usually requires an accompanying change in other factors. He did not explicitly note the further objection that the fixed factors exert a causative and productive influence, even though they do not change. The inseparability of the productive contributions of the various factors arises, not merely (as Hobson argued) because a change in one variable factor usually requires a change in other variable factors (e.g. an extra shepherd requires an extra crook) but also, and more fundamentally, because the constant factors have a productive effect on output (along with the productive effect of the factor that is being varied), even though they are being held constant. In The Industrial System ([1909, revised 1910] 1969), Hobson again accused the MPTD of ‘using the language of a false separatism’: Our analytic method has tacitly assumed a separate productivity attributable to each part of each factor employed in a business, whereas no such separate productivity exists … So intimate is the interdependence of the factors upon one another, and of the several parts of each factor upon the other parts of its own factor and upon all the parts of the other factors, that no separate productivity can rightly be attributed to any factor, still less to any part of a factor. (1969, 106)

He accused J.B. Clark of viewing the industrial system as a mechanical process, whereas it is one of ‘organic cooperation’ in which the identification of the separate contributions of the various factors is as impossible as the identification of the separate contribution of a hand or a foot to the activity of the human body (1969, 107). The idea that the marginal product can be causally traced to the marginal unit of the variable factor alone is very clearly rejected in the statement: [W]hat is added to the product by the entrance of the tenth unit of labour, and what is lost by its exit, is not the measure of the ‘bare productivity’ of that unit, but of the difference in the aggregate productivity of the whole complex of units of capital and labour. In other words, the separatist treatment of productivity breaks down. (Hobson 1969, 114) With reference to the example of the tenth shepherd and the 20 extra sheep, he argued: [I]t cannot be maintained that twenty sheep form the separate product of the tenth shepherd, but only that a ten group is more productive by twenty sheep than a nine group. (1969, 115) He concluded that the impossibility of disentangling the specific marginal products renders the MPTD useless as a theory of distribution: It is thus quite evident that adding doses of labour and noting the increase of the aggregate product throws no serviceable light upon the determination of wages … no separate dose has any separate product.9 Hobson’s rejection of the MPTD could not have been more categorical: Regarded as a theory of distribution of the product, the marginal productivity theory is a misapplication of an unsound and unprofitable assumption. (Hobson 1969, 118) According to Hobson, distribution of the products of every industry is determined, not by the MPTD, but by ‘pulls’ and ‘squeezes’. Chapter 7 of The Industrial System was entitled ‘Distribution of the Surplus by Pulls’.10 Factors that have a relative scarcity, either natural or contrived, exert ‘pulls’ that enable them to ‘extort a piece of ‘surplus’ payment over and above that

payment for which its owners would consent to apply it in production, if they could not get this surplus’ (1969, 137). Hobson regarded scarcities and pulls as a normal part of the distribution process: the exchange of goods and the distribution of wealth are normally and largely directed by these pulls in which a surplus is divided according to the degree of scarcity attaching to the several factors of production. (1969, 137) The existence of these pulls, also described as ‘squeezes’ (1969, 167), means that ‘in most market prices as well as in most ‘normal prices’ there is an element of unearned and unnecessary payment, which represents, not a genuine cost of production, but a superior power of bargaining’ (1969, 167). In these very forceful terms, Hobson thus rejected the MPTD, and substituted bargaining or scarcity as the determinant of distribution. The anti-disentanglement argument was taken up again by Hobson in 1910 in a journal article entitled ‘The Marginal Productivity Theory. A Reply to Criticism’. Exponents of the MPTD had argued that although disentanglement of the products of the various factors is not possible in the case of the total product, it is possible in the case of the marginal product. S.J. Chapman had argued: In a complicated community in which there is group production, it is impossible to assign to each factor the commodities that it produces, since it always produces in collaboration with other factors. But it is possible to impute to each factor the product contributed at the margin to the total quantity produced. (Chapman 1904–14, II, 14, quoted in Hobson 1910, 302) Chapman concluded that ‘each person will tend to receive as a wage his value – that is, the value of this marginal product – no more and no less’, from which it follows that In order to get more than he actually does get, he must become more valuable – work harder, for instance – that is, he must add more to the product in which he participated. (Chapman 1904–14, II, 14, quoted in Hobson 1910, 302) Hobson rejected ‘the legitimacy of attributing a separate and measurable product’ to the marginal labourer.

If the complexity of an organic co-operation of the factors renders it impossible to assign to each factor its special share of the product, it should be equally impossible, and for the same reason to assign a special product to one portion of a factor, viz. the marginal labourer.11 According to Hobson, the statement that the marginal unit of a factor gets ‘what it is worth’ simply means that it gets ‘what, under the existing conditions of scarcity and utility (operating by supply and demand) it can get … a not particularly illuminating statement, and certainly not one that furnishes a basis for a theory of distribution’ (1910, 308; emphasis in original). Hobson’s verdict on the law of ‘Separate Productivity’ was: ‘Nothing can be learnt of the theory or the art of distribution … by falsely attributing a separate productivity to a single factor or to a single unit of a factor’ (1910, 309). Hobson did not believe that free competition could be relied upon to produce an equitable distribution of factor rewards, arguing that, to be strictly free, competition would require that everyone should have ‘an equal abundance of all the various sorts and qualities of land, labour, capital and managing ability’.12 Homan ([1928] 1968, 327) agreed that Hobson ‘has a case against the justice of current distribution’ and that competition theory is inapplicable to a system in which ‘special advantage plays so large a part’, but ridiculed Hobson’s argument on the grounds that an ‘equal abundance’ of factors is ‘simply a meaningless phrase’, because there is no common denominator to quantify the various factors. Homan said that Hobson’s views on this point were ‘most obvious nonsense’, and that Hobson ‘occasionally goes to the untoward length of complete unintelligibility’. Perhaps Hobson’s most memorable contribution to the anti-MPTD argument was his forceful statement of the political, ideological and social class implications of the MPTD. In his Work and Wealth ([1914] 1968) he stated that, if the MPTD is valid, it provides a theoretical defence for employers against workers’ demands, and demonstrates ‘the final futility of all attempts of the labouring classes … to get higher wages’ (1968, 174–5): [The proponents of marginalism] are able to deduce from it practical precepts very acceptable to those politicians and business men who wish to show the injustice, the damage and the final futility of all attempts of the labouring classes, by the organized pressure of trade unionism or by politics, to get higher wages or other expensive improvements of the conditions of their employment …it has evidently re-created the defences against the attacks of the workers upon the fortresses of capital which were formerly supplied by the wage-fund theory in its most rigorous form. If wages can only rise on condition of the workers working harder or better, no injustice is done to any

class of labour … and no remedy exists for poverty except through improved efficiency of the workers.13 He returned to this ideological theme in his Free-thought in the Social Sciences (1926). He believed that the acceptance of the MPTD was due not merely to ‘the craving of scientific men for exactitude’, but also to vested interests.14 They look with favour on the MPTD because ‘it serves to dispose of the charge against capitalists of exploiting labour’, and provides a defence against socialist propaganda and attacks on property. If, according to the MPTD, each factor receives just as much as it produces, then justice is done to each factor, and there is ‘no unearned surplus to fight over’ (Hobson 1926, 108–9). The moral and political message of the MPTD is that we are living in the best of all possible economic worlds, and anyone who, by agitation and wilful misrepresentation, tries to incite envy or stir up discontent is as foolish as he is wicked. The charge of profiteering is meaningless, and combination can get nothing solid for the workers. (Hobson 1926, 110) In Hobson’s interpretation, the MPTD emerged because it is ‘accommodated to the requirements of the influential classes for the defence of their economic interests’, and is ‘admirably adapted for the re-establishment of confidence in the natural equity and efficiency of the economic system as it stands’. With scathing satire, he declared that the MPTD ‘beautifully … fills the requirements of conservatism’. It is ‘a rebuke alike to the envy and class hatred of the workers’, and ‘a sedative to the foolish compunction astir in the minds of many men of great possessions when they survey the condition of the poorer classes!’ (Hobson 1926, 110–11).

T.N. Carver (1865–1961) J.B. Clark’s The Distribution of Wealth (1899) was enthusiastically reviewed by Thomas Nixon Carver (1901): So far as the strictly constructive part of the work is concerned, it is practically above criticism … Professor Clark’s central thesis as to the shares in distribution will stand the test of criticism. (1901, 580, 602) Carver believed that Clark’s discussion of the method of distinguishing the product of the various factors of production was ‘a model of clearness and conclusiveness’ (1901, 581). Carver claimed that this ‘method of difference’

was ‘the only method adequate to the task of distinguishing between the products of labor and of capital’. It involves observation of the ‘variation in the product which follows a variation in the factors of production’. Carver concluded: ‘Under any rational theory of causation the variation in the product must then be attributed to the variation in the factor’.15 He used the metaphor of the millstones to illustrate the point: Without some such method as this it would be as unpracticable to try to distinguish the product of labor from that of capital as it would to distinguish the product of the upper from that of the nether millstone.16 The ‘method of difference’ was explained in more detail: If the total product of a certain community, or of a certain industry, is x, and the addition of another unit of labor to the force already at work makes the product x + y, or the subtraction of one unit from the force makes the product x–y, the product of one unit of labor is y. With that unit, y is; without that unit, y is not: therefore, that unit is the cause of y. This amount is all that a unit of labor is worth on the market: it is the maximum amount which any employer can afford to pay … and under perfect competition the employer will have to pay so much. (Carver 1901, 582–3) It is clear then that, in his 1901 review of Clark, Carver firmly believed that what we have called the MPAL was in fact the same as the SMPL, and that the ‘method of difference’ succeeded in isolating the marginal product that was specifically caused by labour. He unhesitatingly translated a correlation into a causation. This support for the MPTD was repeated, even more strongly, by Carver in The Distribution of Wealth (1904). While not explicitly endorsing the moral dimensions of J.B. Clark’s MPTD, he firmly endorsed the principle that factors of production will tend to be rewarded according to their marginal productivities. Carver argued that the principle applied to agricultural labour: The normal tendency, therefore, is for wages in agriculture to proximate pretty closely to the marginal productivity of labor … each individual laborer gets as wages approximately the equivalent of the amount which he individually can add to the product of the group to which he belongs, or of the amount which he can subtract from the product of the group by withdrawing himself from it. Find out what the group could produce without his help, and then find out what it can produce with his help, and the difference between these two amounts is the measure of his worth to the group.

(1904, 157) However, its application was not restricted to agricultural labour. Carver conceived of it as a ‘general law’ applicable also to all ‘industrial establishments’ and to ‘society at large’: This law is that a given unit of labor of any kind is valued in industry according to the amount which it can add to the total product of industry, or the amount which can be produced with this unit over and above what can be produced without it … In other words, the wages of any particular kind of labor are determined by its marginal product.17 [T]he rule that a laborer generally gets the equivalent of the marginal product of his kind of labor is of universal application. (1904, 179) The marginal productivity of labor of any class determines the rate of wages of that class. (1904, 181) He also extended the application of ‘the law of marginal productivity’ (1904, 223) to capital – ‘The productivity of capital is, like that of land and labor, subject to the principle of marginal productivity’ (1904, 220) – and to management: The law of marginal productivity can be applied to the earnings of business management as well as to the wages of other labor. The amount which any individual business man can get by means of his superior management (not through his superior bargaining capacity) depends upon the amount which he can add to the product of the community over and above the amount which it could produce without his help. That determines how much his help is wanted.18 From a hypothetical table showing the effect on agricultural output of successive increases in the number of laborers, it is once again clear that when Carver referred to the ‘marginal product of labor’ he meant what in this study is called the MPAL, not the SMPL. In his table, when the number of labourers is increased from one to two, output increases from 500 bushels to 900 bushels, and this difference of 400 bushels is said to be ‘the marginal product of labor’. When a fifth laborer is employed, output increases by a further 100 bushels. The statement ‘the fifth laborer adds only 100 bushels to the total crop over and above what four could produce’ (1904, 158–9; emphasis added) implies that the fifth labourer is the sole cause of the extra

100 bushels, and that ‘of’ in the phrase ‘marginal product of labor’ is being used in a sole-cause and sole-proprietor sense. No recognition is given to the causative role of the constant factors that cooperate with the fifth labourer. The productivity of capital is defined in a similar manner: Find out how much can be produced without any particular tool or machine, and then how much can be produced with it, and in the difference you have the measure of its productiveness … this is the only way in which the productiveness of labor or any other factor can be determined. (1904, 216) From this it is clear that Carver believed that the marginal product that occurs after the application of an extra unit of capital (i.e. MPAK) is the marginal product that is specifically caused by the extra unit of capital (i.e. SMPK); and that the value of this MPAK could be paid as a reward to the marginal unit of capital, without any recognition of the role of labour in causally contributing to the productivity of the marginal unit of capital. This failure to recognise the multicausal nature of the marginal product of a factor is also evident when, in replying to the criticisms of Hobson and Davenport in their reviews of his Distribution of Wealth, he argued that when a tenth man is employed on a farm: Whatever the tenth man adds would represent his value to the farmer. There may be objections to calling this amount the ‘specific product’ of the tenth man – that is a matter of words; but there can be no objection to saying that this amount is the maximum amount which the farmer, as an ‘economic man’, can afford to pay for the labor of the tenth man. (Carver 1904–5, 266) This statement presupposes that ‘whatever the tenth man adds’ can be disentangled and distinguished from the contribution made by the fixed factors that assist the tenth man. The failure to make the distinction between the MPAL and the SMPL is more than ‘a matter of words’, since it leads to the erroneous conclusion that the farmer can afford to pay to the tenth man the full MPAL. As argued above, such a procedure makes no commercial sense, as well as being ethically questionable, because it means that no portion of the MPAL would be available as a reward for, or to cover the cost of, the productive contribution made by the fixed factors to the production of the MPAL.

However, Carver recognised that the marginal product of labour affects only the demand for labour, and that the ‘wages of any particular kind of labor depend … quite as much upon its supply as upon its demand’ (1904, 165). He discussed at some length the factors that will influence the supply of labour – in particular, ‘the standard of living and the painfulness of labor’, and ‘the marginal cost of acquiring proficiency in the skilled occupations’ (1904, 184). This point was reasserted when replying to critics: [T]he wages of labor are determined by an equilibrium of forces – the productivity of labor, on the one hand, creating the demand for it, and the standard of living of laborers, on the other hand, restricting the supply of it. (1904–5, 263)

F.Y. Edgeworth (1845–1926) Francis Ysidro Edgeworth appears in some statements to have been in no doubt about the validity of the view that factor returns tend to be equal to their marginal products: ‘in a state of equilibrium the increment of value produced by the last increment of a factor is just equal to its price.’19 However, as noted above, Edgeworth cast doubt on the validity of the adding-up theorem.20 He expressed further doubts in a 1925 review of J.M. Clark’s Studies in the Economics of Overhead Costs (1923) where he stated that the proposition that ‘the relation between product and factors may be represented by the mathematical expression known as a ‘homogeneous function,’ seems ‘contrary to common sense based on experience of physical and human nature’, and ‘implies that throughout the arts of production the relation between means and end can be represented by one and the same simple mathematical formula’.21 The review also included a criticism of J.M. Clark’s proposition that ‘the sum of the marginal products of the factors equals the whole income of the business’ (1923, 474) described by Edgeworth as ‘paradoxical’ (1925, 250) and, like the assumption of a homogeneous function, as ‘contrary to common sense based on experience of physical and human nature’ (1925, 249).22 Edgeworth argued that, if the price of a factor is set by the MPTD rule – i.e. ‘in perfect competition the increment to income obtained by taking on the marginal increment of a variable factor is just equal to the cost of that marginal increment’ – then the total income ‘may not cover the total cost, that of the variable factors and the overhead, not to speak of profits’ (Edgeworth 1925, 250). He added that in industries with overhead costs, ‘it is quite conceivable that a workman is not paid as much as by his work he adds

to the income of the concern’.23 To pay workers less than their marginal product is, according to Edgeworth, a deliberate and justifiable policy for a firm’s entrepreneurs or ‘directing minds’: [T]he total cost of all the factors [excluding the entrepreneurial factor] is intended by directing minds, and so tends, to be less than the whole income of the business. (Edgeworth 1925, 250) Edgeworth concluded the review with a neat juxtaposition of the views of the two Clarks: While Professor John Bates Clark teaches that the ideal remuneration of labour is its marginal product, Professor John Maurice Clark finds that wages are commonly below that marginal product. (Edgeworth 1925, 251) Edgeworth would appear to be saying that payment of the variable factors according to the value of their marginal products is commercially impracticable or impossible because some portion of the value of the marginal products must be held back to meet the costs of the fixed factors. In other words, in equating marginal revenue and marginal cost in order to achieve maximum profit, the firm, in calculating the marginal cost of employing a marginal unit of (say) labour, should include not only the wage of that unit of labour but also a contribution to its overhead or fixed-factor costs. As argued above, the fixed factors continue to exert a causative function, and need to be continually funded and rewarded, even though they are fixed. Ceteris paribus does not mean ceteris inefficacibus. Further reservations by Edgeworth on the MPTD – both on its validity and on its importance – may be seen in his comments on an article by S.J. Chapman (1906). The latter had accepted the MPTD principle that the wage of an employee would be equal to the extra output made by taking on an extra employee, and had asked whether the same principle applied to the remuneration of employers or entrepreneurs. He concluded that the principle does apply to employers, provided we assume that the extra employer makes no difference to the organisation of industry. Edgeworth argued that the principle would apply to employers as well as to employees only if the average amount of work performed by the employees remains constant when an extra employer is added. Edgeworth believed that there is ‘some ground for assuming’ that the work performed by the employees would increase, with the result that the remuneration of the extra employer would be proportionately less than the marginal product of the extra employer.

Edgeworth concluded that the qualifications expressed by Chapman and himself introduce some uncertainty into the usefulness of the MPTD as an explanation for the remuneration of employers.24 Even though he admitted that the MPTD remains the ‘most probable’ explanation, these qualifications detract from the universality of its theoretical validity. Furthermore, he expressed doubts about the importance of the MPTD. Even if the MPTD is valid (i.e. even if, in accordance with J.B. Clark’s dictum, every workman gets the product of his work), the workman ‘is not thereby deterred from desiring more than what is his product’. Edgeworth concluded: ‘On the whole I see no reason to modify the opinion that the theorem in question is neither true nor important’ (Edgeworth 1907, 524–31). Edgeworth also expressed misgivings about the MPTD as a principle of distributive justice. In a review of J.B. Clark’s Distribution of Wealth he said: However terms are defined, the doctrine as we interpret comes to the old doctrine – as old at least as Burke’s Thoughts on Scarcity, in which he invokes ‘the laws of commerce’ against the claims of the ‘labouring poor’ – that the division of the total produce effected by the play of the labour market, or which would be effected if the market played freely, constitutes the best possible distribution. Doubtless it is difficult to find a better. Yet there are those who doubt whether a fair wage may not be defined by some other criterion than the produce added by the marginal labourer, whether our author has not too slightly dismissed the aspirations embodied in other definitions. (Edgeworth {1925] 1970, Vol. III, 101). He noted (1907, 531; quoting, with a slight inaccuracy, Cannan 1905, 363) that, ‘as Mr. Cannan happily observes’, socialists would say ‘You may call it what you please provided you hand it over’; and he quoted J.S. Mill’s statement that it is no consolation to those who complain that their share of the product is too small to be told that ‘this principle of remuneration is in itself an injustice’ (J.S. Mill [1848] 1909, Book II, ch. i, art. 4; quoted in Edgeworth 1907, 531). Despite these strong criticisms by Edgeworth of the MPTD, Stigler (1941, 131–3) argued that Edgeworth in some of his earliest writings had outlined ‘the kernel of the general marginal productivity theory’, and, referring to the summary of the general equilibrium theory presented by Edgeworth in his Collected Papers Relating to Political Economy (Edgeworth [1925] 1970, III, 54), Stigler argued that Edgeworth’s equations state ‘the equality of marginal products and prices of the factors of production’, and that therefore they include the marginal productivity theory. Stigler concluded the section on

Edgeworth in his 1941 chapter on Euler’s theorem with the assertion: ‘In Edgeworth’s positive formulation of the theory of distribution, we have seen, he virtually accepts the marginal productivity theory’.’25 Stigler’s interpretation of Edgeworth’s views on the MPTD was rather selective. He appears to have been concerned to add Edgeworth’s name and prestige to the list of MPTD followers, but does not appear to have given adequate emphasis to the strength of Edgeworth’s criticisms of the MPTD.

S.J. Chapman (1871–1951) Sydney J. Chapman defined the MPTD as the theory that ‘declares that each person will tend to receive as a wage his value – that is, the value of this marginal product – no more and no less’.26 He accepted that the separation of the total product into the contributions of each factor is impossible: ‘it is impossible to assign to each factor the commodities that it produces, since it always produces in collaboration with other factors’ (1904–14, II, 14). However, like J.B. Clark, he believed that disentanglement is possible for marginal products: [I]t is possible to impute to each factor the product contributed at the margin to the total quantity produced – that is, to discover what would be lost if the factor in question were withdrawn and all things else remained the same. (1904–14, II, 14) The role of the MPTD was explained more fully in another work: [T]he modern doctrine of distribution affirms that payment for the employed agents in production is settled by the forces of demand and supply. The demand for a factor is supposed to measure the marginal worth of that factor to employers, in view of the existing supplies of other factors. (Chapman 1912, 219) [A]n employer will not pay labour more than its marginal worth. (1912, 234) [T]his theory in its bearing on employed factors does not declare that each agent gets what it makes, but merely that each agent gets the difference that it makes to the total output of a productive group which is organized to work as a whole.

(1912, 220) Chapman described this as ‘the beautiful theory of distribution’ (1912, 229). Unfortunately, its beauty is not apparent to the eye of every beholder. We can agree with Chapman that the MPTD does not declare that each agent ‘gets what it makes’ in the literal or physical sense. If a factory worker makes a part that is 1/10,000th of the product, it is unlikely that his wage will be that very 1/10,000th part. But in asserting that the ‘marginal worth’ of a factor is equal to ‘the difference that it makes to the total output of a productive group’, Chapman did not indicate how to calculate ‘the difference that it makes’. The expression ‘it makes’ begs the question. The difference to the total output occurs after the employment of the marginal unit of the variable factor but does not occur solely because of it. Chapman recognised that the total output is multicausal – it is the output of ‘a productive group’ – but he appears not to have recognised that the marginal output (or ‘the difference … to the total output’) is also a multicausal phenomenon. He made no reference to Hobson’s argument that the disentanglement of marginal products is just as impossible as the disentanglement of the total product. Chapman noted that one of the popular objections to the theory is that it implies ‘a certain inevitableness about each person’s income, which makes it repellent to the reformer, who is rightly dissatisfied with the great difference between incomes to-day and, perhaps, is inclined to appeal against economic distribution to ethics’ (1904–14, II, 13–14). But he argued that no such rigid restriction or inevitableness applies to a worker’s wages: ‘In order to get more than he actually does get, he must become more valuable – work harder, for instance – that is, he must add more to the product in which he participates’ (1904–14, II, 14). Chapman stated that the ‘immense inequalities of wealth to-day and the low level of wages in too many cases must be regretfully recognized’ (1904–14, III, 10), and that enormous differences between the incomes of ‘equally deserving persons’ can be the result of social arrangements (1904–14, II, 16). He believed that ‘improved distribution must form a large part of the ultimate object of reform’ (1904–14, III, 10). The remedy, he argued, lies not in radical reforms, but in the spread of education and other opportunities: ‘The chief line of reform that morals entail upon us is … to spread more evenly education and other opportunities throughout the community. If this be done, unreasonable inequalities in income will right themselves’ (1904–14, II, 16). He did not specify what was involved in these ‘other opportunities’. He did not advocate policies such as property redistribution, or land value taxes, or public works to create employment. On the contrary, he objected to ‘complete reconstruction of the machinery of distribution’ and warned that

‘Violent interference with distribution might easily result in ultimate loss to those whom it was intended to benefit’ (1904–14, III, 10). He did, however, advocate ‘ethical guidance in consumption’, on the grounds that a ‘large portion of our present ills is caused by foolish and unworthy desires, and unwise and even deleterious consumption’ (1904–14, II, 16). Chapman considered the objection that if each worker receives a wage equal to the wage of the marginal worker, then the earlier workers are being exploited because their marginal productivity is greater than that of the marginal worker. He believed that this objection was ‘wholly illusory’, that it was a dangerous misinterpretation of the theory of wages, and one that could be ‘used mischievously’. His reply was that the same argument could be applied to every factor of production – for example, it could be argued on similar grounds that employers are being exploited by operatives. He concluded: it follows in consequence that all the factors in production taken together are worth something enormously greater than the value of their total product. As this conclusion is absurd, the line of demonstration pursued must be fallacious. (1904–14, II, 20) Chapman’s argument is not entirely convincing. Instead of proving that exploitation does not occur, it suggests that the workplace is characterised by mutual exploitation – with labour exploiting capital and capital exploiting labour – and implies that the ensuing balance of benefits will be left indeterminate. Chapman’s admission that ‘no factor can retain for itself all the wealth due to its existence’27 (1904–14, II, 20) reinforces this indeterminacy, and could even be interpreted as a rejection of the validity and/or usefulness of the MPTD. Nevertheless, he reasserted his allegiance to the MPTD – ‘Sharing according to the marginal worth of the factors is the general principle of division’ (1904–14, II, 21) – and he concluded, somewhat ineffectually and unconvincingly, that ‘we know that the benefit is spread throughout the community’ – which could be seen as an act of faith in the trickle-down effect. But he was forced to admit: ‘How the benefit from progress gets shared out actually, cannot be reckoned, because the requisite measurements are wanting and the terms in the problem are a multitude’ (1904–14, II, 21). Chapman made a further contribution to the MPTD debate in an article entitled ‘The Remuneration of Employers’, published in the Economic Journal in 1906. Stigler (1941, 337) regarded this as ‘a most elegant diagrammatic proof that the residual share is equal to the marginal product of

the factor receiving the residual’. Chapman’s argument is reproduced by Stigler, and does not need to be reproduced again here. A full evaluation would require a detailed analysis; but, in brief, there is at least one aspect that appears to be less than satisfying. At the penultimate step of the argument, the residual share is shown to be not equal to the marginal product of the factor receiving the residue; but in the ultimate step, the difference between the two is conveniently eliminated by changing the discrete variables to infinitesimal variables, so that the magnitude of the difference approaches zero and can be neglected. When the change in the number of labour units employed becomes so small as to be neglected, the diagrams representing the before-and-after situations coalesce, and the area representing the marginal product becomes tautologically identified with the area representing the residual share. As a geometrical exercise, Chapman’s argument is indeed ‘most elegant’, but whether it succeeds in being a ‘proof’ of the MPTD is questionable.

H.J. Davenport (1861–1931) Herbert Joseph Davenport in his Value and Distribution ([1908] 1964) adopted an argument similar to that of Hobson in opposing the possibility of disentangling the marginal products. He rejected J.B. Clark’s view that, when an extra item of a factor is added, the resulting change in output is entirely attributable in a causal sense to that extra item. For Davenport, part of the increase in output is due to the ‘together-ness’ of the co-operating factors: ‘is it safe to attribute all of the increase in product to the new item? Is not this increase due rather to the mere ‘togetherness’ of all of the co-operating facts?’ (Davenport 1964, 472). Against the MPTD, Davenport concluded that the compensation paid to the different cooperating productive factors cannot, either ‘actually or logically’, be declared to be the ‘precise equivalent of the productivity contribution’ – owing to the impossibility of determining the ‘separate and specific productivity’ of each factor (Davenport 1964, 471): With complementary production goods, no separate and specific significance, like that attached to consumption goods, can be ascribed to any one item … In the competitive economy all possibility of ascription of a single productive significance to any productive item disappears … There can, therefore, be no one degree of productivity assignable as the specific productivity of any particular item. (Davenport 1964, 476) Davenport realised that if it is impossible to assign to each factor its specific productive contribution, then it is also impossible to use a Lockean theory of property rights to attach moral or religious sanction to what each factor

happens to receive ‘under the ordinances of competition’: ‘What under the ordinances of competition one gets, gives no safe report of what under the ordinances of God he deserves’ (Davenport 1918–19, 283; cited in Valk 1928, 27). These criticisms by Davenport of the MPTD were reasserted and strengthened in his Economics of Enterprise ([1913] 1929). Against J.B. Clark’s view that the specific product of each factor can be identified and measured, Davenport argued: [T]he factors do not function separately but together, the productivity of each depending therefore upon the presence of the others … therefore the productivity is never the separable and specific productivity of each, but only the joint and inseparable productivity of all together. (1929, 156) The point was illustrated by analogy with a horse and wagon: One buys … a horse, to go with a wagon which otherwise would be useless. But this is not to attribute to the horse all of the result from both horse and wagon. The horse would be equally useless without the wagon. (1929, 147) The interdependence and productive inseparability of the three factors of production was also illustrated by analogy with a three-legged stool: ‘Which leg of a three-legged stool supports the stool?’ (1929, 147). Against the view that the return received by a factor is determined by, or is a measure of, its productivity, he argued that factor returns are determined by market forces, and that ‘the market price of each productive efficiency cannot express the quantum of that efficiency, is not equal to it, is not determined by it, does not measure it, and is not measured by it’ (1929, 136). He repeated his 1908 concept of the ‘togetherness’ of the productive process, and argued that, although the entrepreneur can estimate how much benefit he will get by employing an extra unit of a factor, he cannot calculate ‘its separate productivity’; he can only calculate ‘what it would signify to have it there to go with whatever else is there’ (1929, 149).

F.W. Taussig (1859–1940) Doubts about the validity and/or usefulness of J.B. Clark’s MPTD were also expressed by Frank William Taussig in a paper presented at the Twenty-

second Annual Meeting of the American Economic Association, New York City, 27–31 December 1909 (published in 1910), and in his Principles of Economics (1911). He recognised that J.B. Clark’s MPTD ‘makes its appearance in most of the textbooks that are now in fashion’, but predicted: ‘It will be remembered as a promising attempt to grapple with an intricate problem, a step forward in our slow and uncertain progress toward the truth; but it will not be accepted as a definitive advance’ (Taussig 1910, 137). Referring to J.B. Clark’s theory that wages and interest are the specific products of labour and capital, he said that, although ‘to some economists it seems conclusive … I find myself unable to accept the reasoning’ (Taussig 1911, II, 257). The basis of Taussig’s criticism was that ‘there is no separate product of the capital. Nor is there any separate product of the labor. There is one product, all produced by labor, and indistinguishable as to its source.’ Likewise, ‘there is no product of the labor distinct from the product of the tools … in concrete reality, we cannot make out any separable product of either’ (Taussig 1910, 139, 141). The anti-separation argument was repeated in his Distribution of Wealth (1911): Capital as such is not an independent factor in production, and there is no separate productiveness of capital. (Taussig 1911, II, 8) [C]apital is itself made by labor … there is no separate product of the tool on the one hand, or of the labor using the tool on the other … We can disengage no concretely separable product of labor and capital. (Taussig 1911, II, 197–8) Taussig argued that capital is not an independent factor of production; it is simply a different way of applying labour.28 His objection to the MPTD was therefore not exactly the same as Hobson’s. They reached the same conclusion, namely the inseparability of the products of labour and capital, but, whereas Hobson accepted that the two factors are distinct, Taussig saw capital as a form of labour, adding that ‘If there be a factor in production separate from labor, it is not capital, but ‘abstinence’ or ‘waiting’ or ‘preference for present goods’ or ‘time preference,’ (Taussig 1910, 140). However, in a statement that is difficult to reconcile with the foregoing, Taussig seems to have accepted the validity of the MPTD for the determination of the rate of interest on capital: ‘interest is determined proximately by the increase of product resulting from the last or marginal application of capital’, while at the same time asserting that ‘it does not also point to the cause determining wages’ (Taussig 1910, 138).

Foreshadowing the circularity argument that was to play such a prominent role in the Cambridge capital theory controversy, Taussig added: ‘In the application of the principle to both wages and capital, and in the attempt to reach an independent law for each, there is reasoning in a circle.’29 As an alternative to the MPTD, Taussig proposed a ‘discounted marginal product of labor’ theory: [W]ages are determined, under competitive conditions, by the discounted marginal product of labor. (1910, 142) The simplest and clearest mode of stating the theory of general wages is, in my judgment, to say that wages are determined by the discounted marginal product of labor. (1911, II, 198) Current wages, he believed, will be determined by the future utilities yielded by labour, discounted at the current rate of interest. He compared this discounting process for wages with the discounting that is involved in the determination of the rate of interest. He argued that interest is a reward for waiting, or sacrifice, and is the present value of a future good that has been discounted at the current rate of interest. Taussig concluded that the ‘theory of wages is thus strictly consistent with the theory of interest’ (1911, II, 199). It may conceivably be argued, against Taussig’s discounted marginal product theory, that although he rejected J.B. Clark’s MPTD because it presupposed the separability of the products of labour and capital, his ‘discounted’ theory rests on the same presupposition. Before we can discount the future product of labour, we must first be able to disentangle the future product of labour from the future products of other factors. But that particular criticism of Taussig would not be justified. In his ‘discounted’ approach, he was in effect abandoning J.B. Clark’s notion of specific causal contributions, and substituting a residual-accounting approach that defines labour’s product, not in terms of labour’s causal contribution, but as the residue left over after deducting the interest paid to capital. However, Taussig admitted that this discounting approach can lead to a determinate explanation of wages and to a ‘consistent conclusion on the apportionment of returns between laborers and capital-owners’ only if there is ‘a basic and independently determined rate of interest’ (1911, II, 201), or if there is a known ‘margin’ that is ‘necessary to induce the investment and

management of capital’ (1911, II, 202). In other words, Taussig appears to have been arguing that if this rate of interest, or this ‘margin’, is exogenously determined, then the current rate of wages can be found as a residual by subtracting interest payments from the value of the future product, and then by discounting labour’s expected future share. In the absence of an agreed ‘margin’ there can be no determinate theory of wages. If there be no such margin, there is no ground for distinguishing between interest and the other returns to the owners of capital and land. And if there be no such margin, there is no ground for saying that wages are in any determinate relation to the product of labor. If the return to the owners of capital is only a matter of accident, or the result merely of power in their hands, the amount which they will advance to laborers is subject to no controlling tendency. The most that can then be said is that the general rate of wages will depend on the relation between the number of the laborers and the amounts which the capitalists choose to advance. (1911, II, 202) Taussig noted (1910, 151–2) that the rate of interest had remained comparatively steady over the previous 200 years, and wondered whether there might not be an independent force regulating the rate of interest. Taussig’s discounted marginal product theory has not been generally adopted in subsequent discussions of the theory of wages, perhaps because interest rates have not subsequently been so stable, and perhaps because there has been little evidence that they are exogenously determined. Taussig was well aware that, if economics is incapable of developing a satisfactory theory of wages, the process of wage determination will become ‘a game of grab’ in which each side ‘tries to get as much as possible, and there is no telling what will be the outcome’ (Taussig 1910, 148). If it be all a matter of monopoly or non-competitive return, then the laborers may secure more or less in the way of wages according as they fight more or less vigorously for their share. The better they are organized, the more they have aid from legal enactment, the more they use or threaten physical violence, the more they will succeed in getting. Conversely, the better the capitalists are organized, and the more they have at their command the law, or physical coercion, or the threat of starvation, the more will they in their turn succeed in getting. Perhaps we are in a fool’s paradise in supposing there is anything normal or regular in the return to capital owners; their doings may be after all, as the socialists say, only a process of wringing as much as possible from the poor and oppressed. This is a pessimist view.

(Taussig 1910, 149) There is in these comments an underlying fear of the social and political unrest consequent upon a failure to find a determinate theory of wages. This fear is also evident in the writings of other advocates of the MPTD, and perhaps explains why, in their desperation to avoid economic conflict, they have been led to propose ideas, such as the exogenous determination of the rate of interest, that now appear to be quite fanciful.

W.M. Adriance (1878–1957)30 One of the clearest and strongest critiques of J.B. Clark’s concept of specific productivity is to be found in an article by Walter Maxwell Adriance in the Quarterly Journal of Economics (1914–15). Adriance argued that ‘when labor and capital cooperate to produce a result that result is their joint product. It is a verbal absurdity to ascribe it to either factor alone’ (157; original italics). He continued: [I]f a man cuts down a tree it is vain to speculate as to what fraction of the work is done by the man and what fraction by the ax. Let two men plow a field with the aid of a team and a plow, the one driving and the other holding the plow handles. It would puzzle the greatest mathematician in the land to say just how much of the plowing is done by the team, plow, and the men respectively. (Adriance 1914–15, 157–8) In general, he concluded: [T]here is no such thing as empty handed or unaided labor. Some material instrument is always employed, and as long as this is true, we are left without any method of disentangling the specific product of labor. (Adriance 1914–15, 157) Adriance quoted with approval Hobson’s remark in his Industrial System ([1910] 1969, 115) that ‘No separate dose [of labour] has any separate product’, and cited Hobson’s comment that if the employment of one extra shepherd means that 20 more sheep can be cared for, the 20 extra sheep are the product, not of the extra shepherd, but of the entire group of shepherds. Referring to fish caught by a group of fishermen, Adriance argued that the ‘mathematical error’ of the MPTD lies in ‘not attributing to the cooperation of the rest of the group [of fishermen] any part of the so-called ‘marginal product’’. The entire catch, including the marginal catch, is the product of the

entire group and their equipment;31 and ‘cannot by any necromancy be fractionally ascribed’ (Adriance 1914–15, 159–60; emphasis in original). Adriance concluded that ‘Clark’s method of disentangling the product of labor from the product of capital has … no reality’ (152) and ‘there is no such thing as specific productivity’ (157). He stated: There is a difference, however, between the mere cooperation of a factor in a productive process, and the specific creation by that factor of a distinguishable product. The fact that the services of a factor are desirable in the process of value creation does not mean that a particular part of the value created can be ascribed to the independent agency of the factor. (1914–15, 165–6) Adriance also made some interesting sociological observations, which might be just as true now as then, on why the MPTD has gained and kept such a vogue. [W]ith its parade of scientific accuracy, [the MPTD] is after all but a precise formulation of a widespread and deep-seated belief that, to a reasonable degree of approximation, a man gets out of his productive activities what he deserves. (1914–15, 169) He added that the MPTD ‘seemed to give a scientific sanction to a popular notion’; established a ‘soothing correlation between reward and productive contribution’; and ‘has tended to make us, as economists, more conservative than we have any right to be’ (Adriance 1914–15, 174–6). The last quotation hints at an ideological motive for accepting and propagating the MPTD. Adriance cited, with apparent approval, the statement by Professor Wicker that Clark’s Distribution of Wealth is ‘the apologia of an unwarranted conservatism’ (Adriance 1914–15, 175–6). One puzzling feature of Adriance’s article is that, despite recognising the multicausal nature of the marginal product of labour and despite rejecting therefore the moral implications of specific productivity, he stated that: ‘it may be a correct business judgment to justify the employment of the extra man on the ground that the extra product warrants the expense’ (Adriance 1914–15, 158). He did not argue that, in calculating the expense of employing the extra man, the businessman should include not just the wage of the extra man and the cost of other items of variable capital needed by the extra man, but also a proportionate share of the cost of the constant capital.

4 Followers and critics, 1920 to 1940 From Cassel to Fraser Among the contributors selected for inclusion in this chapter, followers happen to be more numerous than critics, but whether the arguments for the defence are more compelling than the arguments for the prosecution is another matter. As will be seen, while some of the followers introduced reservations and qualifications, others remained totally and unflinchingly committed to the MPTD.

G. Cassel (1866–1945) An important contribution to the MPTD debate was made by Gustav Cassel in The Theory of Social Economy ([1918] 1932). When two or more individuals cooperate in production, how should the product be divided? Cassel called this ‘the problem of imputation or attribution’. It would be solved if an ‘objective standard for a just distribution’ of the product could be found, i.e. if there were ‘a kind of technical relation of cause and effect between activity and product’, or ‘a causal link between work and produce’. He recognised that the idea of an objective principle which distributes products on the basis of causality is very popular, and that such distribution would be in accord with, and would satisfy, a ‘primitive feeling of justice’ (Cassel 1932, 177–8). But, unfortunately, according to Cassel, ‘there is no such key to the problem’, and therefore ‘there can be no just distribution in this objective sense’ (Cassel 1932, 181). The impossibility of this kind of imputation is obvious, he said, when we consider the heterogeneous nature of labour: ‘There is no common measure for the work of the thinker, the artist, the manager of a business, and the manual worker. Their common product can never be shared according to the work done by each’ (Cassel 1932, 178). The impossibility is even clearer when other factors of production – capital and land – are added to labour. The distribution problem thus develops into the ‘most bitter controversy’ (Cassel 1932, 178–9): Each party is naturally inclined to emphasise the importance of its own share of the work, to claim as large a portion as possible of the returns, and, consequently, to denounce the actual apportionment as unfair. As a rule, the so-called proof of this is to imagine one’s own share of the work withdrawn and then ask what the other factors of production would do without it.

Unfortunately, this argument suffers from the weakness that it can be used with the same striking effect with regard to each factor of production that is indispensable. Taking away that particular factor of production always reduces the result of the activity of the others to zero. (Cassel 1932, 178–9). Having denied the possibility of dividing the total product by means of the causal contributions of the factors, Cassel then considered the possibility of dividing the product according to marginal productivity, i.e. by measuring the effect upon the total product of withdrawing a small part of each factor. He recognised that there are some qualifications or reservations to the use of marginal productivity as a principle of distribution: (1) the method breaks down ‘when the factor of production is indivisible’; (2) it also breaks down ‘when one part of it cannot be withdrawn without throwing other factors of production out of work’;1 (3) the marginal productivity of a factor, or ‘the increase in the product due to a small increase in the factor’,2 would be zero if the marginal unit of the factor has no effect; and (4) the marginal productivity principle can be applied only when ‘the factors of production can co-operate effectively, within certain limits, in any proportion we care to choose, and when, therefore, the factor of production in question can be steadily substituted for the other factors without altering the final product’. Notwithstanding these reservations and qualifications, Cassel seems to have admitted the validity of the MPTD, arguing that the marginal productivity of a factor is ‘a measure of the share of that factor of production in the results of production’, and that the price of the factor must clearly, in a state of equilibrium, be equal to its marginal productivity, ‘otherwise it would be more economical to use more or less of the factor in question’ (Cassel 1932, 179–80). Cassel immediately went on to assert that, although the MPTD is applicable to ‘the manufacture of one single product’, it cannot be extended to the distribution of ‘the entire social product’. In denying its extension from the micro to the macro level, he gave the following arguments, which are neither clear nor compelling. The marginal productivity of a factor of production cannot, however, be defined in the social productive process as a whole as long as the prices of the products are indeterminate, and, consequently, a definite measure of the total product is lacking. In any case, the proposition that the price of a factor of production is equal to its marginal productivity in the productive process as a whole can have no other meaning than that its price is the same in every one of its uses in the different branches of production, and that the prices of the products can be determined in accordance with the principle of cost on

the basis of this pricing of the factors of production. But this condition merely brings the pricing of the factor of production back to the general pricing process which is examined in the preceding Book. (Cassel 1932, 180–1) Cassel’s position on the MPTD, even at the micro level, became somewhat obscure when he attempted to integrate it with the principle of scarcity – which he regarded as the ‘paramount principle’ in the pricing process. In linking the principle of marginal productivity to the principle of scarcity, he relegated the former to a subordinate or supplementary position. He believed that the ‘apportionment of the common proceeds of production’ is ‘mainly governed’ by the principle of scarcity, and that the ‘shares of the various factors of production’ are ‘substantially determined by supply and demand’. He argued that the principle of scarcity is ‘modified in certain cases’ by the marginal productivity (or imputation) principle, but that the scarcity principle retains its ‘fundamental importance’. The distribution of the ‘total outcome of social production’ is ‘primarily determined’ by the relative scarcity of the factors.3 This interesting attempt to integrate the marginal productivity principle and the scarcity principle, as determinants of the values of the factors of production, adds a new dimension to the MPTD, but leaves many questions unanswered. Does it signify, and was it intended by Cassel to signify, a weakening of support for the MPTD, and a movement away from the MPTD towards a simpler, non-marginalist, scarcity principle of distribution? Or does it constitute a more sophisticated and improved version of the MPTD? The exact nature of the modification that the marginal productivity principle makes to the scarcity principle, and the reasons for this modification to occur ‘in certain cases’ but not in others, are left somewhat vague. One possible interpretation is that Cassel saw marginal productivity as a micro principle applicable to the individual firm, and scarcity as a macro principle applicable to the economy as a whole, but the text remains inconclusive on such a possibility. It does not establish a clear-cut demarcation between the marginal productivity principle at the micro level, and the scarcity principle at the macro level. It suggests that the marginal productivity principle retains a role (even though a subordinate one) in the distribution process at the macro level. On the basis of his Theory of Social Economy (1932) it is difficult therefore to place Cassel squarely in the pro-MPTD school or in the anti-MPTD school. In a later publication, On Quantitative Thinking in Economics (1935), Cassel appears to have given increased emphasis to the principle of scarcity and less to the principle of marginal productivity in the distribution process, reducing

the latter principle to an even more subordinate role. He was particularly critical of mathematical attempts to prove the validity of the MPTD. Referring to Joan Robinson’s use of Euler’s theorem (Robinson 1934), he said: Here we have a striking example of the incredible degree to which economic theory has allowed itself to be entangled in difficulties which in fact it has itself created by adopting more or less arbitrary mathematical formulae, connected with doubtful quasi-mathematical calculations, and by not giving sufficient attention to the economic realities that should be represented by such mathematical symbols. (Cassel 1935, 122–3) Cassel noted that the following formula had been used to express the dependence of the product on the factors of production: p=xuyvzw

(1)

where p is the total product; x, y, z are the factors of production; and the exponents u, v, w represent the contributions made by the factors. It had been assumed that u+v+w=1

(2)

and that u, v and w are constants – an assumption that Cassel regarded as ‘very arbitrary’. From this it was argued that (3) ̉ Equation (3) had been interpreted as saying that ‘the total product is equal to the sum of the quantities of the factors of production, each multiplied by its marginal product’, and that ‘Every factor receives its share of the total product according to a compensation determined by its marginal productivity’. The MPTD, so formulated, had been presented as ‘a very simple and fine solution of the problem of distribution’. It was asserted to be ‘the natural basis of the theory of distribution’ (Cassel 1935, 120–2).

Cassel noted (1935, 122) that ‘Generations of students have been brought up to believe in the general correctness of the theory of marginal productivity and of the solution of the problem of distribution based upon that theory’, but he referred disparagingly to the uncritical adoption of this belief: [E]conomists brought up to believe uncritically in the theory of marginal productivity regarded this doctrine as a fundamental and almost self-evident truth from which all further investigation of social distribution had to start.4 In this 1935 publication Cassel repeated and expanded some of the criticisms of the MPTD he had mentioned in his Theory of Social Economy. 1 The MPTD is applicable ‘only in those cases where the amount of a factor can be varied continually, and where the product itself may be regarded as a continuous function of this variable factor’. As this is not generally the case, the MPTD cannot claim to be a general theory of distribution (Cassel 1935, 123). 2 The MPTD is of no use in explaining the entrepreneur’s profit. As the entrepreneur’s contribution is particularly indivisible, the marginal productivity of the entrepreneur cannot be calculated (Cassel 1935, 123). 3 A more basic criticism is that, in the theory of prices and hence in the theory of distribution, the ‘Principle of Scarcity’ is the fundamental principle: ‘Distribution, therefore, fundamentally depends upon the relative scarcity of the different factors of production’ (Cassel 1935, 124). The marginal productivity principle has ‘only a secondary position as one of the supplementary principles’ in determining distribution; it merely modifies the scarcity principle ‘to a certain degree’ (Cassel 1935, 124). 4 With regard to equation (2) above, he argued that the sum of the exponents will not necessarily equal one. Equations (1) and (2) mean that when each factor is doubled, the product will double, i.e. equation (1) will be a linear homogeneous function; but he argued that, because of the advantages associated with large scales of production, a doubling of the factors will usually result in the product increasing by more than double. Moreover, experience has shown that the various factors do not grow in the same proportion. Equation (3) is therefore not a pure mathematical derivation from equation (1) (Cassel 1935, 126–7, 130). Cassel argued that the marginal-productivity principle of distribution ‘is theoretically defective and has no support in observations of actual economic life’ (Cassel 1935, 130), and he concluded with a scathing comment on the MPTD and its advocates:

It is difficult, then, to understand why intelligent men, having to face the great responsibilities of the modern economist, should waste their time in discussing such a purely hypothetical solution of the problems of economic growth and of social distribution. (Cassel 1935, 130) According to Cassel, the solution to the problem of distribution lies not with the MPTD, but with an approach similar to that of Marshall, Wieser, and/or Walras. He believed that the distribution problem, like the problem of prices in general, can only be represented by a system of simultaneous equations.5 This distinction between the marginal productivity principle and the scarcity principle was developed further, with ever greater emphasis given to the scarcity principle, in Cassel’s Fundamental Thoughts in Economics ([1925] 1929), which consisted of a series of lectures on ‘Advanced Economics’ that he had been invited to give by the University of London. He said of his Principle of Scarcity that it was ‘the core of the theory of prices which I have developed in my different writings, and which in fact forms the basis of my whole economic work’ (Cassel 1929, 77–8). He admitted that in ‘a certain sense’ the Principle of Scarcity is ‘nothing else than the old familiar theory of demand and supply’, but he argued that scarcity should be given ‘its due central position in our economic theory’. He argued that, when the prices of the factors of production are being considered, the Principle of Scarcity ‘is forced into the background, and indeed in most cases entirely disappears’ (Cassel 1929, 100–1), but he insisted that the Principle of Scarcity is the ‘fundamental principle’ that determines the prices of the factors of production: ‘Essentially, prices are paid for elementary factors of production because they are supplied in a certain scarcity … the fundamental fact [is] that a price is paid primarily because of the scarcity of the thing’ (Cassel 1929, 111, 114). Other principles – namely the marginal productivity principle, the Differential Principle and the Principle of Substitution – are required ‘to make the problem determinable’ but are ‘supplementary principles’ (Cassel 1929, 91, 95, 115). His Fundamental Thoughts (1929) also emphasised the concepts of general interdependence and simultaneous equations discussed in his Social Economy.He argued that there is a ‘mutual interdependence’ of prices: ‘all prices are determined at once’, and he again asserted that the Principle of Scarcity is ‘intimately connected’ with the solution of the distribution problem by the use of a system of simultaneous equations.6 He believed, or hoped, that such a solution by means of simultaneous equations would apply not only to the prices of consumer goods and the prices of the elementary factors of production, but also to ‘the income of all the members of the

society, and therewith the entire social distribution of income’ – i.e. it would be a solution to the distribution problem at the aggregate or macro level, as well as at the individual or micro level – but he warned that ‘much unclearness and much traditional doctrinarianism have still to be removed’ before such a solution becomes ‘a definite achievement of economic science’ (Cassel 1929, 86–7, 93, 95, 116). Cassel’s views on distribution were taken up by the Dutch economist, Dr Willem L. Valk, in his book The Principles of Wages (1928), a comprehensive analysis and critique of the MPTD.7 Valk’s conclusion was that there does exist an economic law that determines distribution, and that therefore there is ‘no need to examine the Bargain Theory of Wages’. He argued that this law of distribution is to be found not in the MPTD, but by combining the theories of J.B. Clark and Gustav Cassel. However, the difference between the ‘Bargain Theory of Wages’ and Cassel’s scarcity principle was left unclear. Valk’s objection to the MPTD was based on a rejection of the adding-up theorem. He argued that ‘when the prices of the means of production are equal to marginal productivity, the sum of these prices would exceed the sum available for distribution’ (1928, 134). An important practical implication of Valk’s Cassel-Clark law of distribution was that no ‘artificial change’ in distribution could be successful, by which he apparently meant no change imposed by political policy; but that social improvement can be achieved by a change in circumstances – such as the supply and education of labour – and above all by increasing the total amount of produce available for distribution.

F.M. Taylor (1855–1932) In his Principles of Economics (first edition, 1921), ch. 36, ‘The Present System of Distribution’, Fred Taylor questioned the linguistic propriety of the term ‘marginal product of a factor’. If the total output increases following an increase in one of the variable factors, Taylor said that ‘With some show of reason’ this increase in output ‘is frequently designated the marginal product’ of the variable factor (1925, 131; emphasis in original), but in ‘Note 2’ in his ‘Appendix – Explanatory Notes’ he argued that the ‘propriety of this designation for the addition to output consequent upon the addition of a unit of the changing factor is questionable’ (1925, 565), although he admitted that it ‘conforms to the common usage of current economic writing’ (1925, 565– 6). He argued that it would be ‘absurd’ to contend that the increase in the number of units of the variable factor is ‘alone responsible for bringing into existence’ the extra units of output (1925, 366).

When each of several factors must necessarily be present, if a given result is to be brought about, no one of them taken by itself can be physically or technically credited with the production of that result, or any assigned part of it. (1925, 566) Taylor argued that the productive cooperation of the fixed and variable factors, and the impossibility of disentangling their respective contributions, is as necessary in the case of the marginal unit of the variable factor as in the case of the total output of all the fixed and variable factors. For the production of the marginal product, the fixed factors are ‘just as necessary’ as the marginal unit of the variable factor. The marginal unit of the variable ‘could produce nothing’ if the fixed factors were not present (1925, 566; emphasis in original). In short, it cannot be too much emphasized that there is no possibility of isolating any portion of the product and saying that it was produced by any particular unit or units of any of the factors in any physical sense. (1925, 566; emphasis in original) Although Taylor did not refer in this context to J.B. Clark in person, this would appear to be a clear refutation of J.B. Clark’s view that, although disentanglement of the total product is not possible, it is possible to identify and disentangle the marginal product of the marginal unit of each factor. However, in a surprising turnaround, Taylor then proceeded to argue the converse. He said that ‘in view of all the circumstances, it is reasonable to act as if [the marginal unit of the variable factor] were alone responsible for the added units of product’ (1925, 560; emphasis in original). He proposed two situations in which it would be justified to credit a particular portion of the output to a particular marginal unit of a variable factor. The first situation is one where units of the fixed factor are ‘so numerous that they can be ignored in economic reckoning’, i.e. they are ‘in effect free goods’ or ‘non-economic factors’. Whatever such units produce can therefore be credited entirely to the variable factor. The second proposed situation is one where one of the factors ‘is conceived by the producer as fixed in amount’. Taylor argued that it would then be legitimate to ignore the productive contribution of that fixed factor, and to treat the increased output as ‘due exclusively to the other factor’. For example, if a farmer owned land the quantity of which he could not or would not change, then if his output of wheat increased by 200 bushels following the employment of an extra farm-hand, the farmer ‘might reasonably act as if

the laborer were alone the producer of these 200 bushels, though of course this would not be true in any literal sense – those 200 bushels would be, like all the other bushels, the joint product of the several factors involved’. In this situation, Taylor seems to have been in effect endorsing the MPTD, arguing that ‘the farmer could afford to treat [the labourer’s] services as worth substantially 200 bushels of wheat’ (1925, 535; emphasis in original). By establishing this somewhat questionable distinction between, on the one hand, what is literally true, and, on the other hand, how an employer ‘might reasonably act’, Taylor appears to have reached the contradictory conclusion that the MPTD is neither literally nor logically valid, but that we are justified in acting in practice as if it were valid. It is difficult to reconcile this latter conclusion with his previous cogent argument that the productive contribution of a marginal unit of a factor cannot be disentangled. On the textual evidence of his Principles, Taylor’s position on the MPTD remains, to say the least, ambiguous – harsher critics might even say selfcontradictory. Was it his intention to support or to reject the MPTD? He cited two situations in which he believed the contribution of the fixed factors could be ignored and hence the marginal product could ‘reasonably’ be regarded as the sole product of the marginal unit of the variable factor. As neither of these two situations is likely to be a common occurrence in the real world, they could perhaps be interpreted as exceptions that do not negate the general antidisentanglement rule. On whether or not Taylor intended this interpretation, the textual evidence in the Principles is inconclusive.

F. Knight (1885–1972) The strong attachment of some orthodox economists to the MPTD appears to be based on the belief that, by providing us with a law of distribution, the MPTD establishes the basis for a social system, and removes the possibility of the social disorder and chaos that could occur if the process of distribution were effected by a lawless conflict between bargaining powers. This appears to have been the motivation behind Frank Knight’s attachment to the MPTD. In Risk, Uncertainty and Profit ([1921] 1965) he stated: ‘In the absence of a law connecting distributive share with effective contribution our social system would be no system, but chaos’ (p. 103). This fear that society will disintegrate into anarchy if the MPTD is denied has introduced an element of ethical fervour into the defence of a theorem claimed by defenders to be purely positive. Knight even went so far as to argue that the validity of the MPTD is beyond dispute, and should no longer be subjected to argument among economists.

It is, therefore, inappropriate for economists to argue as to whether the separation of contributions to a joint product can or cannot be made; it is made; it is our business to explain the mechanism by which it is accomplished.8 He was perfectly correct of course in saying that the ‘separation of contributions’ is made. In countless situations every day, revenue is distributed among factors of production. However, in his earnest hope of finding a scientific law of distribution, it seems that Knight was prepared to close off debate on the possibility that there is no scientific law of distribution – or that the only law of distribution is the law of superior bargaining power – and that the ‘separation of contributions’ is in fact achieved not by a law of economics but by the rough-and-tumble of the market place. As the following quotations show, Knight was firmly convinced that, in a competitive situation, contributions to the productive process are separated and rewarded according to their marginal productivities. [T]he separate contributions of separate agencies to a joint product can be identified. … [A system of] free contract under competition … tends to give to the owner of each agency the separate contribution of that agency. (1921, 103) [R]emunerations will rapidly be readjusted towards the values which the individuals contribute to the output of the groups with which they work. (1921, 106) The standard of what a group could afford to pay for a man is clearly the amount which he enables it to produce more than it would produce without him. (1921,107) [In a competitive organisation] the total produce would be divided among all claimants by giving each his added product. (1921, 108)

[P]roductive resources receive (through ‘imputation’) product increments equal (in price) to the productive increments they contribute at the margin. (1935, 175) To the argument that the marginal product of labour is a joint product that cannot be separated into specific contributions, Knight replied that ‘it involves a confusion between mechanical and economic productivity’ (1921, 112), but his failure to elaborate on the significance of this distinction left his response unconvincing. He also believed that the adding-up problem can be solved: ‘it is demonstrable that when the units are sufficiently small the sum of the separate, specific contribution of all the agencies exhausts the total joint product’ (1921, 103). Knight’s belief that the adding-up problem is not a problem appears to have been based on Wicksteed’s arguments. He referred the reader to Wicksteed’s works for ‘a full discussion and demonstration of the theoretical exhaustiveness of the distributive process’ (1921, 108). As noted above, other commentators have not been entirely persuaded by Wicksteed’s arguments; and there is strong evidence (see Appendix C below) that even Wicksteed himself abandoned them. In asserting the ‘very separable effects of separate agencies’ (1921, 113), Knight conformed to the thesis of J.B. Clark, but he rejected the ‘sweeping moral and social dogmas’ that Clark had deduced from it (1921, 109). He did not, in Risk, Uncertainty and Profit, give reasons for the rejection, merely referring readers to the writings of Carver and J.M. Clark, by whom the ‘illegitimacy of these ethical deductions has been well argued’ (1921, 109). Knight defended the adding-up theorem against the ‘dislocation’ criticism of Hobson. As noted above, the latter had argued that the sum of the marginal products, as defined by the MPTD, would be greater than the total product – because the marginal product lost by the withdrawal of one unit of a factor would be greater than the specific product of that unit, owing to the dislocation caused by the withdrawal. Knight’s reply was that Hobson had considered only a situation where the organisation is small, and the unit, or block of units, is large. According to Knight, the dislocation would be negligible when the factor unit is small by comparison with the size of the organisation (1921, 110–11). Knight’s support for the MPTD appears to have been based ultimately on what he described as an ‘appeal … to fact’: [T]he final appeal is to fact. It is the value to the producer as an addition to his organization as a whole which determines the amount which he will bid

in the market for the use of any unit of labor, land, or capital, or the amount of any one which he will purchase at an established price. Hence it is this ‘specific product’ which rules the apportionment of income at large among productive agencies at large. (1921, 113) However, as is argued above, this alleged ‘fact’ is not a logically sustainable fact of commercial life. If any producer pays to an extra unit of labour a wage equal to the value added to the organisation after the employment of that unit of labour (i.e. if the wage is equal to the MPAL) the organisation would be heading for bankruptcy, because the producer (misguided by the MPTD) would have failed to make adequate provision and provide adequate returns for the services of the constant factors that cooperate with the extra unit of labour. Knight believed that disagreements about the validity of the MPTD have arisen because of different meanings attached to the words ‘production’, ‘product’, ‘cause’ and ‘effect’. In referring to the specific or separate product of a factor, Knight explained that he was not claiming that the factor in question was the sole cause of the product. He argued that no event is ever the result of one single cause, and that every effect has an infinite number of causes. Which one of these multiple causes is singled out and described as ‘the’ cause depends on particular circumstances. This linguistic analysis of the nature of causation provides the key to an understanding of Knight’s support of the MPTD, and therefore deserves to be given in full: We wish now to point out that in calling the addition made by any agency to the total output of a large organization its specific or separate product, we are using the word ‘product’ in the same meaning and the only meaning which the words ‘cause’ and ‘effect’ or equivalent terms ever have. It is never true in an absolute sense that one event is the cause of another. The whole state of the universe at one moment may perhaps be said to cause its whole state at the next moment, but when we say that ‘A’ is the ‘cause’ of ‘B’ we always assume that other things are equal; we never mean that if the rest of the universe were removed ‘A’ alone would produce ‘B’. And the imputation of any single event to another as cause or effect is always largely arbitrary. Every event has an infinite number of causes, and it depends upon circumstances, the point of view, the problem in hand, which of these we single out for designation as ‘The’ cause. ‘The’ cause of a phenomenon is merely that one of its necessary conditions which is for some practical reason crucial, generally from the standpoint of control. It is the one about which we must concern ourselves, the circumstances enabling us to take the others for

granted. It may be quite correct to name a dozen different antecedents as ‘the’ cause of a particular occurrence, according to the point of view. The fact that other agencies, even the whole social system, may be concerned in the production of a certain good does not therefore argue against its being the (specific) product of the particular agency upon whose activity its creation actually hinges under the actual circumstances of the case. (1921, 114; emphases in original) This is a perceptive and important comment on the linguistic conventions governing the use of ‘cause’. If in a conversation about modes of transport you say ‘I travel to work by train’, meaning that you travel by train rather than by taxi or tram or bus, you are obviously not intending to say that the train itself is the sole cause of your arrival at work, and that the train driver, the train track, the signalling system and so on were not also causally responsible. The train is singled out for specific mention, because, of the many contributing causes, it is the one that you wish to emphasise in the context of your present conversation. Unlike some later commentators, Knight believed that the MPTD was concerned with causal relationships, not with mere correlations.9 He declared that there is the ‘tendency under competition for any laborer and the owner of any piece of property to get as income his (its) causal contribution to production (or things equal to the same value)’, but he rejected the idea that this causal relationship has ethical implications; it ‘does not mean that they tend to get what they ought to have’. He referred to the ‘fallacy of attributing ethical significance to distribution based on what the individual puts into the social total’ (Knight [1928] 1956, 95; emphasis added). However, Knight’s views on causation raise two important difficulties in relation to the MPTD. In the first place, his claim that the meaning he gives to the words ‘cause’ and ‘effect’ is the ‘only meaning’ that the words ‘ever have’ could be questioned. Irrespective of whether his meaning is the correct one or not, there would appear to be no doubt that J.B. Clark and many other disputants (both supporters and critics) in the MPTD debate have used the term ‘cause’ in the sense of ‘sole cause’ when discussing a factor’s marginal product. Second, in adopting this multicausal concept of causality, Knight appears to have undermined his case for the MPTD. If the marginal product (MPAL) is caused, not by the marginal unit of labour alone, but by a multiplicity of causes, then equating the value of the marginal product with the wage of the marginal unit of labour cannot claim to have commercial justification and cannot be an equilibrium condition.

Knight was of the opinion that hostility to the MPTD is due mainly to the (mistaken) ‘popular dogma’ that remuneration according to productivity represents ‘moral desert’ and ‘ideal justice’. He regarded this as ‘a confusion of the most egregious sort’. He believed, on the contrary, that ‘inequalities in inherited property and opportunity’ and ‘natural differences in personal capacity’ mean that remuneration according to productivity does not constitute a valid moral claim; and he concluded: ‘there is almost no case at all for an identification or close assimilation of causal contribution to production with moral desert in distribution’ (1921, 114–115n.). In contrast to Knight’s view, the thesis being advanced here is that, even if there are no differences in inherited property and natural talents, remuneration of factors according to the MPTD cannot be either morally or commercially justified because of inherent weaknesses in the MPTD – namely its failure to recognise the causal role of the non-variable factors in creating the marginal product of the variable factor; the impossibility of disentangling the causal contributions of the non-variable factors from the causal contribution of the variable factor; and the absence of any acceptable criterion (other than bargaining-determined market values) for deciding what would be an appropriate portion of the ongoing costs of the fixed capital to deduct from the MPAL in order to arrive at the fully net MPAL.

J.M. Clark (1884–1963) John Maurice Clark, in his Studies in the Economics of Overhead Costs (1923), appears to give a firm endorsement to the adding-up theorem: [I]f all costs were variable … the sum of the marginal products of the different factors (each multiplied by the amount of the factor) would always equal the whole product. (1923, 472) The truth is that the marginal products of land and labour … are so related that the sum of the marginal products must equal the whole. (1923, 473)10 As noted above, J.M. Clark wrote to Wicksteed in 1915 saying that he believed he had developed a geometric proof of the adding-up theorem, and he continued in that belief even though Wicksteed replied that ‘it cannot be done’. In 1952 J.M. Clark wrote that J.B. Clark ‘was correct in concluding that, under static conditions, the sum of the marginally-imputed shares would absorb the whole product’, but added that it was left for others – Wicksteed

and Flux – to produce a ‘mathematically-satisfying demonstration’ (J.M. Clark 1952, 611). However, he also expressed some observations and reservations which, although not explicitly directed at his father’s MPTD, effectively cast some serious doubts on its validity. For example, having defined the ‘marginal contribution to production’ as ‘the difference in the product caused by allowing industry one unit more (or one unit less) of a given factor of production, to work with’, he argued that if additional labourers are paid what their marginal product is worth, ‘the whole value of the product would be absorbed before all the operating expenses were covered, leaving nothing for the owners but a deficit’ (1923, 468–9). J.M. Clark was here using the term ‘marginal product’, not in the sense of the specific marginal product of labour (SMPL) which was the sense used by J.B. Clark – but in the sense of the marginal product after labour (MPAL). As argued above and as the above quotation from J.M. Clark emphasises, to equate wages with MPAL is a formula, not for equilibrium and profit maximisation, but for commercial disaster. The same theme recurs in J.M. Clark’s following statements: [I]ndustry cannot afford at all times to pay labor its full short-run marginal product, because this would leave nothing to cover the long-run marginal product of capital; the two between them absorbing more than the whole product of industry. … Those factors of production which are responsible for the variable expenses behave in such a way that, in general, the sum of their marginal contributions tends to absorb the whole product of the industry, and other factors can get their rewards only as a deduction from the marginal products of the variable factors. Capital is a variable cost in the long run … Capital has marginal productive importance. (1923, 470) If a concern striving to enlarge its output bids for the variable factors of production up to their full immediate marginal worth, it will end up paying them all its gross income, and having nothing left to pay for its constant factors. (1923, 474)

J.M. Clark thus emphasised that the allocation of fixed or overhead costs raises a serious difficulty for the MPTD. The firm must cover its overhead costs; it cannot stay in business if its returns cover only the marginal costs.11 The significance of J.M. Clark’s statements on overhead costs is that they appear to recognise that the marginal product after labour (MPAL) is a multicausal phenomenon and consists not only of what labour has specifically produced (the SMPL) but also of what has been produced by capital; and that if capital is to receive a reward (or if the cost of the capital is to be covered), it must be deducted from the MPAL. No business could survive if it allowed the entire MPAL to be paid to labour, leaving nothing for capital. In J.M. Clark’s words: ‘wages must nearly always be less than marginal product so long as business is run on old-fashioned business principles’ (1923, 474). The thesis advanced in this study differs from that of J.M. Clark. He appears to argue (1) that capital can have a marginal product only when it is variable, and (2) capital warrants a reward only when it has a marginal product. Proposition (1) is valid, by definition, because ‘marginal product’ is defined as the variation in the product associated with a variation in a factor. But proposition (2) does not appear to be valid. Capital exerts a causative and productive role, both when it is unchanged – when (by definition) it does not have a marginal product – as well as when it is variable and hence has a marginal product. The marginal product after labour (MPAL) is greater than the specific marginal product of labour (SMPL), because capital makes a productive contribution to the MPAL, even when capital is constant. To express this distinction more formally: All cases where a factor has a marginal product are cases where the factor can claim (on economic and ethical grounds) a reward. But not all cases where a factor can claim a reward are cases where the factor has a marginal product. ‘All x are y’ does not necessarily mean ‘All y are x’. When capital is held constant while labour varies, capital will not (by definition) have a marginal product, but it will nevertheless have a product. If that product is to be rewarded, or in other words if the cost of capital is to be covered, it is logically impossible for labour to receive in wages the full amount of the MPAL. These comments by J.M. Clark would appear to provide cogent grounds for concluding that the MPTD as formulated by J.B. Clark is untenable, but J.M. Clark – perhaps constrained by filial respect – did not draw that conclusion. None the less, his comments represent a serious indictment of the MPTD – as serious as any that were later expressed during the Cambridge capital theory controversy.

P. Sraffa (1898–1983) An article published in 1925 by Piero Sraffa contained the following footnote: The expression ‘productivity of a factor’ can be misleading. It is therefore useful to clarify that by average product of a factor we mean the total quantity of the product divided by the number of units of that factor which, together with others, it is necessary to use in the production of that quantity; and by marginal product of a factor we mean the increment of product that is obtained by adding to a given quantity of factors a ‘dose’ of the factor being considered. It is a question of an analytical expedient, which does not in the least imply that the factor under consideration contributes more or less to the product than the factors with which it is combined. Given these definitions, the propositions that follow are not exposed to the criticisms that Loria directs at this expression (I fondamenti scientifici della riforma economica, Turin, 1922, Chapter 1). (Sraffa [1925] 1998, 331) Unfortunately, the precise meaning of this footnote is somewhat unclear. One possible (monocausal) interpretation of the statement ‘the increment of product … is obtained by adding to a given quantity of factors a ‘dose’ of the factor being considered’ is that the marginal product of a variable factor is the product of the marginal unit of the variable factor alone (i.e. the adding of the marginal unit of the variable factor is the sole and sufficient cause of the marginal product); and, therefore, if labour is the variable factor, we are logically entitled to describe the marginal product as the marginal product of labour. Another possible (multicausal) interpretation is that the marginal product is the joint product of the marginal unit of the variable factor together with unchanged previous units of the variable factor and of other factors. The former being so nonsensical, it is surely the latter interpretation that Sraffa intended. But, in that case, for what reason and on whose authority did he declare that, when we use the phrase ‘marginal product of labour’ to refer to the joint product of the marginal unit of labour acting together with the other factors, we are utilising an ‘analytical expedient’? It was not an analytical expedient that was known and accepted by Hobson, Davenport, Adriance and so on, who argued that the expression ‘marginal product of labour’ falsely suggests that the marginal unit of labour is the sole cause of, and has sole proprietorial rights over, the increment in the product that occurs after the application of the marginal unit of labour. It is regrettable that Sraffa did not have the opportunity to develop his analytical expedient argument more fully.

The subsequent and ongoing controversy surrounding the MPTD suggests that if indeed Sraffa’s analytical expedient has been generally adopted by the academic community, its adoption has turned out to be most inexpedient. The expression ‘marginal product of labour’ is rarely accompanied by a warning that ‘of’ is not being used in a proprietorial sense. It continues to convey the idea (even if the users do not intend it) that the increment in the product is produced solely by the marginal unit of the variable factor, and hence gives rise (falsely) to the idea that, by equating the reward of the marginal unit of the factor with the value of the increment in the product, both justice and equilibrium are being achieved. However, it should be remembered that Sraffa refused permission for this 1925 article (or an English translation of it) to be republished in his lifetime, stating that ‘it seems to me impossible to present to a new public in one’s lifetime an article without implying that one still agrees with all that it contains or else pointing out which are the points or aspects on which he has changed his mind’.12 The clear implication is that there were certain aspects of this article on which Sraffa later changed his mind. In the absence of further evidence we therefore do not know whether this particular footnote would have been reaffirmed, modified or rejected if Sraffa had revised the 1925 article at a later stage. It is possible that Sraffa’s 1925 footnote was in fact not concerned with the question of whether the marginal product is monocausal or multicausal. It is possible that, in replying to Loria, Sraffa’s intention was to argue that the marginal unit of labour is no more and no less productive than the previous units of labour. The ‘academic expedient’ he was referring to might have been the assumption that the units of labour are homogeneous and are all equally productive. Again, it is regrettable that he did not have the opportunity to provide further clarification. In addition to these earlier (1925) concerns about the meaning of ‘the marginal product of a factor’, Sraffa in 1936 was undermining the credibility of the MPTD by stressing the problems involved in the measurement of capital. In a letter to Joan Robinson in October 1936, he wrote: If one measures labour and land by heads or acres the result has a definite meaning, subject to a margin of error: the margin is wide, but it is a question of degree. On the other hand if you measure capital in tons the result is purely and simply nonsense. How many tons is, e.g., a railway tunnel? If you are not convinced, try it on someone who has not been entirely debauched by economics. Tell your gardener that a farmer has 200 acres or employs 10 men – will he not have a pretty accurate idea of the quantities of

land & labour? Now tell him that he employs 500 tons of capital, & he will think you are dotty – (not more so, however, than Sidgwick or Marshall). (Joan Robinson Papers, vii/Sraffa, King’s College, Cambridge, cited in Bradford and Harcourt 1997, 131; and King 2002, 80–1) The margin is indeed ‘wide’, and does not become less so by being described as ‘a question of degree’. It could be argued that, when the varieties of human strength, skill, intelligence, energy, motivation and so on are taken into account, units of labour are as diverse as units of capital; and that units of land are no less diverse when one considers not only their physical characteristics but also their commercial and residential qualities, such as visual amenity and proximity to urban services. Measurements of labour by heads or person hours, and measurements of land by square metres, are not therefore very meaningful. Criticisms of the MPTD frequently refer to the difficulty or impossibility of measuring capital, but could be directed with equal force to the measurement of labour and land. The main purpose of Sraffa’s Production of Commodities by Means of Commodities. Prelude to a Critique of Economic Theory (1960) has been described as: ‘to present the foundation for a critique of the marginal theory of value and distribution’, even though ‘the relevance of Sraffa’s results for this purpose is not made explicit’ (Harcourt and Massaro 1964, 442). On the other hand, Blaug is of the view that Sraffa’s Production of Commodities by Means of Commodities does not show that there is no determinate solution to the distribution problem. The notion that the functional distribution of income is indeterminate, depending rather on the ‘class struggle’, has now become an article of faith in all Cambridge models … It is difficult to see, however, why anyone would be persuaded by Sraffa’s treatise to believe in the theoretical indeterminacy of income distribution and hence in the importance of power bargaining. (Blaug 1975, 28) Blaug argues that Sraffa’s analysis ‘is entirely independent of and compatible with any particular theory of the distribution process’ and that ‘Cambridge theories of distribution must get along without Sraffa’s support’.13 However, Sraffa’s treatment of fixed capital in Production of Commodities by Means of Commodities could be interpreted in a way that, at least implicitly, supports the case against the MPTD. He stated:

We shall regard durable instruments of production as part of the annual intake of a process, on the same footing as such means of production (e.g. raw materials) as are entirely used up in the course of a year.14 This suggests that the cost of producing extra output should include a certain portion of the cost of the fixed capital, namely the portion used up in the process. Such an interpretation would lend support to the view being developed in this study that the true marginal cost of production involves not only the cost of the marginal unit of the variable factor, and the cost of additional units of other variable factors required to support the marginal unit of the variable factor, but also some portion of the cost of the fixed factors.

M.H. Dobb (1900–1976) In his Wages (1928), Maurice Dobb explained the MPTD thus: [G]iven a certain supply of labour, its price was determined by the extra product which was yielded by the additional labour of the marginal man. To the employer labour was a commodity the worth of which to him was simply the product it yielded. (Dobb 1928, 82) He argued that, according to the MPTD, the wage that could be commanded would not be greater than the ‘net product’ of the marginal worker. The term ‘net product’ was not further defined in this context in the 1928 edition. He did not indicate whether ‘net’ was intended to mean fully net or partially net (as these terms are defined above). But in a revised edition, ‘net product’ was described as ‘after allowing for any incidental expenses, such as extra raw materials involved in employing [the marginal labour]’ (1959, 104), thus implying that he meant partially net rather than fully net. Dobb criticised economists who regarded the statement ‘Wages = the Marginal Net Product of Labour’ as ‘a unique discovery which furnished a complete theory of wages capable of taking the place of all the earlier, cruder explanations’ (Dobb 1928, 83), and ‘as a discovery that furnished a complete and final theory, not only of wages, but of the distribution of income in general’ (Dobb 1959, 105). He criticised J.B. Clark for declaring the MPTD to be a natural law which held ‘independently of time and place’; and said that Jevons had spoken ‘ambiguously’ and with ‘a hint of a profound meaning of the words’ when he said that the worker received ‘the due value of his produce’ (Dobb 1959, 105). Quoting Marshall’s statement: ‘This doctrine has sometimes been put forward as a theory of wages. But there is no valid ground for any such pretension’ (as quoted in full above) (Dobb

1928, 84; 1959, 106), Dobb agreed that ‘Wages = the Marginal Net Product of Labour’ does not constitute a complete theory of wages. That equation ‘might be one of the equations in such a theory, and an important one; but it is only one equation, which by itself told one nothing’ (Dobb 1928, 83; emphases in original). Following Marshall, Dobb argued that the ‘Marginal Net Product of Labour’ is ‘a variable quantity depending on a complicated set of factors’ (1928, 83) and ‘depends, not only on the supply of labour, but also on the supply of all the other factors of production … as well as upon the intrinsic efficiency of labour itself’ (1959, 106–7). These other factors of production that affect the ‘product yielded by labour’ include ‘the state of natural resources … the efficiency of organisation … the amount and quality of the machinery that is used’ (Dobb 1928, 85). He therefore argued that the equation ‘Wages = the Marginal Net Product of Labour’ needs to be supplemented with the explanatory statement that the Marginal Net Product of Labour ‘varies, not only with the efficiency of each ‘man-hour’, but also with the supply of fixed capital relatively to the supply of labour’ (Dobb 1928, 85). He concluded that ‘when all this has been said, the theory is robbed of much of its apparent simplicity and finality’ (Dobb 1959, 106). Although the expression ‘the extra product which was yielded by the additional labour of the marginal man’ (1928, 82) suggests monocausality, Dobb’s references to the role of other factors indicate that his was a multicausal concept of the marginal product. And although his explanation of ‘net product’ referred only to ‘incidental expenses, such as extra raw materials’, thus implying a partially net concept, his recognition of ‘fixed capital’ as a cause of the marginal net product could be interpreted as an intimation of a fully net concept. However, he did not proceed to consider how or whether the contributions of these other factors could be disentangled from that of labour. The fact that he did not allude to this problem suggests that he did not regard it as a serious defect of the MPTD. In a further development, Dobb appeared to remove the notion of causality – both mono and multi – from his version of the MPTD, asserting that to equate profit with the marginal product of capital ‘is to say nothing about how profit or ‘rate of return’ is determined’ ([1970] 1988, 16).15 Whereas the notion of factor causality had been an explicit part of the MPTD for J.B. Clark and other early contributors, and had been at least an implicit unstated part for others, this explicit 1970 rejection by Dobb indicates the extent to which attitudes on this key issue have changed. The reasons for the change and the principal agents responsible for the change are matters worthy of further research. One possible conjecture is that supporters of the MPTD had come to realise that a causality-based version of the MPTD could not logically withstand the ‘false separatism’ accusation of Hobson and that, if

the MPTD was to survive, it had to find an alternative non-causal justification requiring only the temporal juxtaposition or correlation of an input increase with an output increase.16 By removing causation, the new MPTD could no longer be accused of ‘false [causal] separatism’. As argued below, it must now place its trust in the separability and allocation, not of causal influences, but of fixed or overhead costs. In the same 1970 publication, Dobb presented two objections to the MPTD: (1) the circular reasoning involved in the measurement of capital, and (2) the possibility of the reswitching of techniques. The latter, he argued, gives ‘the coup de grace to the whole notion of a production function, and hence to the very idea of marginal productivity as a determinant of profit’.17 As noted below, counter-arguments have been made to both of these criticisms. Circular reasoning, it is said, is a common occurrence in economics, and merely reflects the interdependence and reciprocity of economic forces. And it is argued that, although the reswitching of techniques prevents the formation of a production function that is smooth and differentiable over its entire length, it does not preclude differentiation over the range where one particular technique is operative between two successive switch points; the reswitching phenomenon reduces the applicability of the MPTD, but does not affect its essential validity.

D.H. Robertson (1890–1963) In his chapter on ‘Wage Grumbles’ in Economic Fragments (1931), Dennis Robertson defended the MPTD against a number of criticisms. In particular, he attacked those who asserted the impossibility of disentangling specific products, even at the margin. He referred to Bernard Shaw’s statement that, when a farmer and his labourers produce a crop of wheat, ‘nobody on earth can say how much of the wheat each of them has grown’; and to Bertrand Russell’s question: When a railway employee shunts goods trains, ‘what proportion of the goods carried can be said to represent the produce of his labour?’ Robertson accused such ‘popular writers’ of ‘ignorance of the elements of mathematical economics’ and ‘sheer ignorance of the existence of the weapons forged by economic science for performing the process of disentanglement’ ([1931] 1950, 224–5). It is true that ‘popular writers’ often expressed their anti-disentanglement arguments in terms of total products rather than marginal products, and thus left themselves open to the criticism that they were ignorant of marginalist economics; but their arguments would be equally telling if applied to marginal outputs. The contention of this study is that Robertson attributed too much power to the ‘weapons forged by economic science’. They can isolate

the marginal product after labour (MPAL), but not the specific marginal product of labour (SMPL). In addition, the armoury of economics does not include a weapon capable of determining the value of the fully net MPAL independently of the value determined by the contest of bargaining forces in any particular market, and does not include a weapon capable of providing a theoretically sound criterion for the allocation of overhead costs between the different factors of production.

J.R. Hicks (1904–1989) Support for the marginal productivity principle also came from John Hicks, particularly in his Theory of Wages (1932a). He emphasised ‘the extremely abstract assumptions on which alone it is rigorously true to say that wages equal the marginal product of labour’ (1932a, 9–10), but did not question the fundamental validity of the MPTD. The validity and importance of this principle we shall see no reason to question. (1932a, vi) This ‘Law of Marginal Productivity’ is regarded by most modern economists as the most fundamental principle of the theory of wages. Nothing will be said here to contradict that view. (1932a, 9) Clearly it is most consonant with the conditions of equilibrium that each factor should be remunerated according to its marginal product (1932a, 233) [T]he most ordinary non-mathematical analysis shows that every factor must get its marginal product. (1932a, 234) every … factor must get its marginal product, since otherwise the demand for it would expand or contract … This is a perfectly satisfactory line of argument. (1932a, 234–5) [T]he [marginal productivity] theory seems both simple and impossible to controvert. It is an absolutely necessary foundation for sound economic reasoning about wages.

(Hicks 1932b, 88) The importance of marginal productivity in Hicks’ Theory of Wages (1932a) has been stressed by Kurt Rothschild, according to whom marginal productivity ‘obtained a pivotal role and provides a background throughout the entire book’; it was the ‘central factor’ in Hicks’ explanation of labour demand, even though Hicks also admitted18 that there is a gap between the abstract assumptions of theory and the practical applications in reality (Rothschild 1994, 64–5). It is clear that in these quotations Hicks was using ‘marginal product’ to mean not the specific product of a factor (SMPL, SMPK), but the change in total product that occurs after the employment of a marginal unit of a factor (MPAL, MPAK). It is also clear that Hicks had rejected the disentanglement objection of Hobson and others, and was unconcerned about the question of identifying the fully net marginal product, i.e. the question of determining an appropriate deduction for the productive contribution that comes from the other variable factors that need to be employed and from the fixed factors.19 Although Hicks agreed with earlier writers on the general principle of marginal productivity, he differed on the role of the assumption of constant returns to scale20 in the proof of the adding-up theorem. He believed that the theorem could be solved without recourse to that assumption and without the use of Euler’s theorem. Consequently, his view was that ‘it is not true, as most English and American economists seem to imagine, that the [adding-up] problem remained unsolved’ (Hicks 1932a, 233); the adding-up difficulty is a ‘delusion’ (Hicks 1932a, 235).21 Referring to Edgeworth’s ‘scathing’ comment22 on the assumption of constant returns to scale upon which the Wicksteed-Flux solution of the adding-up theorem is based, he argued that the assumption ‘appears much less startling’ and ‘much less ridiculous than it seems to have appeared to Edgeworth’ (Hicks 1932a, 236). It means simply that there will be no residue, positive or negative, if the commodity in question is produced under conditions [in which] a proportional increase in all the quantities of factors employed will increase the quantity of product in the same proportion in which the factors were increased. (Hicks 1935, 236) Hicks nevertheless doubted whether the condition of constant returns to scale could be considered to be ‘generally satisfied’ (1932a, 236); it rules out the possibility of increasing returns23 due to economies of specialisation and cooperation.

In presenting his alternative solution, Hicks acknowledged the contribution of Walras and Wicksell. He thought that Walras’ solution, although ‘altogether free from the objections to which Wicksteed’s own solution is liable’, was not clearly expressed;24 but that Wicksell’s solution was ‘perfectly intelligible’. Hicks said that his own solution was presented ‘with Wicksell’s aid’ (Hicks 1932a, 234). Hicks’ 1932 solution to the adding-up theorem was as follows:25 Let x = units of output a, b, … = units of factors of production [proportions assumed constant] pa,pb, … = prices of factors [assumed constant] πx = cost of production per unit px = selling price per unit. The production function is: x = f(a,b,c …)

(1)

Total cost of production = apa +bpb +…

(2)

(3) In equilibrium, the unit cost of production must equal the selling price of the product, ‘since otherwise the owners of that factor would be receiving a return either higher or lower than was being earned by similar services elsewhere in the market, and someone would therefore have an incentive to act differently’ (Hicks 1932a, 237). i.e. πx = px

(4)

In equilibrium, the unit cost of production (πx) must be a minimum. In order that πx should be a minimum

(5)

(6)

(7)

(8)

(9)

Then, since

and similarly for the other factors

This is the marginal productivity law [i.e. the price (or reward) of factor a equals its marginal product multiplied product]. Substituting πx, pa and pb in (3), we have

by the unit selling price of the

[which is the adding-up theorem; it shows that if each factor receives a payment equal to its marginal product multiplied by the number of units of the factor, then the total payments to the factors will be exactly equal to the number of units of output that have been produced by the factors]. A commentary on Hicks’ solution could include the following. First, Robinson (1933b, 301–4) defended Wicksteed against Hicks’ criticism on the grounds that Wicksteed’s assumption of constant returns to scale is merely a corollary of his assumption that there is perfect competition and that firms are of optimum size.26 Second, according to Hicks (1932a, 238), Wicksteed incorrectly believed that the proof of the adding-up theorem required the cost curve to be a horizontal line; whereas Walras and Wicksell correctly showed that it was only necessary for the curve to have a minimum point, and for equilibrium to occur at that point. It is significant, however, that in his mathematical proof Hicks made use of the firstorder condition for a straight line (first partial differential equals zero), but did not use the second-order condition for a minimum point (the second partial differential is positive). This means that, despite his assertion to the contrary, Hicks’ 1932 mathematical solution is concerned only with a situation where the cost curve is a horizontal line, not with a situation where costs are at a minimum point.27 His mathematical solution does not require that the second-order condition be satisfied, and therefore appears to substantiate Wicksteed’s view – a view that Hicks described as ‘untenable’ (Hicks 1932a, 238). Third, Hicks’ 1932 solution showed that the adding-up theorem does not require the assumption of constant returns to scale.28 However, that solution does require an assumption of constant costs. The distinction between constant returns to scale and constant costs is therefore important. Hicks noted the potential for terminological confusion when he referred to ‘constant returns’ as ‘that ill-treated expression’, and when in speaking of ‘increasing returns’ he noted that he was using that term ‘in a special sense’ (Hicks 1932a, 236). Hicks believed that the condition of minimum cost29 is preferable to Wicksteed’s ‘untenable’ condition of constant returns to scale. He supported this belief by the rather vague assertion that the assumption of minimum cost ‘appears, on the surface at least, more in keeping with the fundamental assumptions on which it is reasonable to base an equilibrium theory’ (Hicks 1932a, 238–9) – by which he presumably meant that an

assumption of minimum cost is more realistic than an assumption of constant returns to scale. However, he also admitted that an assumption of minimum cost is ‘not without its difficulties’ (Hicks 1932a, 239), citing Sraffa (1926). It has the unrealistic implication that there is no tendency to diminishing returns and that increasing returns could ‘upset the marginal productivity theory’ (Hicks 1932a, 236, 239). A critic might well argue that both assumptions involve high levels of abstraction and are equally unrealistic. To say that the adding-up theorem is valid only if a firm is operating under conditions of minimum cost or constant cost or constant returns to scale is to say that the adding-up theorem is a mere curiosum, valid only in an extreme situation, and invalid in every other situation. In a revised version of some aspects of his Theory of Wages (1932a), Hicks (1936–37) presented a solution (of the adding-up problem) based on the assumption of constant returns to scale, even though in The Theory of Wages, he had argued that that assumption was not necessary. He defined ‘constant returns to scale’ as ‘that technical condition in which an increase in all factors in the same proportion will leave the marginal product of every factor unchanged’, adding that ‘Thus non-proportional returns can arise only from a change in the proportions in which the factors are employed, not from a change in the scale of production’ (Hicks 1936–37, 2). He then concluded: ‘But if marginal returns are constant throughout, marginal returns equal average returns. Thus if each factor is paid according to its marginal product, total product will be exactly exhausted’ (Hicks 1936–37, 2). It is significant that, in this 1936–37 version, the adding-up theorem is proved without the use of Euler’s theorem, without the use of calculus, and with virtually no mathematical concepts apart from the elementary concept that if marginal product is constant, marginal product equals average product.30 Hicks did not say that he intended the 1936–37 comments to contradict or replace the 1932 version. The 1932 version aimed to show that the adding-up theorem could be proved without the assumption of constant returns to scale, but with the assumption of minimum cost. The 1936–37 article showed that the theorem can be proved with the assumption of constant returns to scale, because constant returns to scale imply constant average costs, and constant average costs imply that marginal costs are equal to average costs.31 Hicks later modified his views on the MPTD. His second edition (1963) of The Theory of Wages was very critical of the first. He relates that, on an occasion when he was being entertained to dinner by a small group of very eminent American economists (including Schumpeter),

we spent the evening, I trying to persuade them that my Theory of Wages was a thoroughly bad book, they trying to persuade me that it was a good one. They did not persuade me of that, but they certainly did persuade me that it was still alive. (Hicks 1963; cited in Hamouda 1993, 27) His dissatisfaction with the first edition began soon after its publication.32 He became particularly dissatisfied with its first chapter, ‘Marginal Productivity and the Demand for Labour’, which he described in 1963 as ‘that terrible first chapter’ (321). At a late stage in writing the 1932 version, he had realised, having got it from Wicksell, that adding-up occurs only ‘if the output which is being produced by the firm is that which it can produce at minimum cost’ (Hicks 1963, 322).33 But in 1932 he had not realised ‘that minimum cost, in this sense, is not a condition of maximum profit, except in the case of a perfect market’ (Hicks 1963, 322). In reaching this new realisation he paid tribute to the review by Gerald Shove (1933) of the first edition of The Theory of Wages. According to Hamouda, Hicks remained convinced that the demand for labour would be determined by the marginal product of labour (not by the marginal net product of labour as Marshall had said). Hicks repeatedly acknowledged that throughout his life he outgrew some of the ideas he had developed at earlier stages, and wanted most of the outgrown ideas to be forgotten; he was frustrated when others held on to them (Hamouda 1993, 41, 124). However, there is no indication that Hicks ever relinquished his adherence to the marginal productivity theory of wages. He was no less convinced in his later publications of the validity of the MPTD than in his earlier works.

P.H. Douglas (1892–1976) In The Theory of Wages (first published in 1934) Paul Douglas outlined the MPTD and offered answers to some of the criticisms that had been raised against it, particularly those of Hobson, despite describing Hobson as ‘one of the finest spirits in modern life’ (1957, 61). As noted above, one of Hobson’s main criticisms was that all products – even those at the margin – are the joint products of the factors involved, and that it is impossible to distinguish the specific amount produced by each factor. In answering that disentanglement criticism Douglas first of all considered a response involving J.B. Clark’s notion of a ‘zone of indifference’, i.e. the idea that many factories and machines are so antiquated that they are in fact norent instruments, they no longer earn any return for their owners, and the

entire output they help to create goes to labour, thus solving the problem of distinguishing the separate contributions of labour and capital. Douglas did not regard the ‘no-rent machines’ argument of J.B. Clark as an adequate response to Hobson: ‘it is difficult to conceive businesses or machines perpetuated, which over any reasonable space of time yield absolutely no returns to their owners’ (Douglas 1957, 64). For that and other reasons, Douglas concluded: Consequently, Clark’s attempt to escape from the problem of the joint creation of product by both labor and capital and to establish an absolute separate identity for the product of labor as distinguished from that of capital has largely failed. (1957, 64) Nevertheless, Douglas believed that Hobson’s criticism of the MPTD could be effectively answered by arguing that the validity of the MPTD is not dependent upon being able to identify the specific products of the various factors. Quoting the authority of Carver, Wieser and ‘the mathematical school’, Douglas argued that the MPTD requires only that the extra product which has resulted from the last unit of labour be ‘imputed’ to labour, and similarly for capital. However, Douglas did not explain how the imputation process was to be conducted. As he had referred approvingly to Wieser, he presumably believed that imputation could be achieved by Wieser’s method of simultaneous equations. He was apparently either not aware of Wicksell’s objections to that method – as outlined above – or not convinced by them. The disentanglement of Wieser’s imputed returns would appear to be as difficult as the disentanglement of J.B. Clark’s specific products. Hobson had also criticised the MPTD on the grounds that it is not usually feasible to change the quantity of an input by an individual unit; in practice, workers (for example) are usually engaged in groups. Douglas’ response was to adopt a rather strange, relativist concept of individuality, arguing that ‘even if workers are engaged in groups, such a group would be only an infinitesimal increment for a corporation such as the United States Steel Company and certainly would be only such in all society as a whole’ (1957, 61). A more pertinent response might have been to distinguish between the MPTD itself and its mode of presentation by calculus. The latter requires very small changes in inputs; but the validity (such as it is) of the MPTD itself is not dependent on small changes. The argument that, in equilibrium,

wages equal the marginal product is just as applicable (or just as inapplicable) to a change of one worker as to a change of one thousand workers. Another objection levelled by Hobson at the MPTD was: If the factor inputs consist of one dose each of labour, capital and land, and if the dose of labour is withdrawn, production would entirely cease. Does this mean that the entire output is the product of labour alone? ‘Is the destruction of the whole product a right measure of the separate productivity of the labour-dose alone?’34 Douglas replied by arguing that the amount to be imputed to a factor was ‘not the amount by which the total product would be decreased if all of the units of the factor in question were entirely withdrawn, but only the quantity which would be lost if a given increment were withdrawn’. He claimed that ‘This error lies behind much of Hobson’s criticism of the theory’, and to support his case quoted Edgeworth’s comment that Hobson had confused x and ̉∂x (Douglas 1957, 65). The replies of Douglas and Edgeworth appear, however, not to have weakened the force of Hobson’s argument. If the formula ‘wage = marginal product’ applies to the last unit employed, it also applies to the first. Hobson was therefore perfectly correct in pointing out that, if only one unit of labour is involved with capital and land in the production process, and if that first and only unit is removed so that production ceases entirely, the logic of the MPTD leads to the absurd conclusion that the entire product was the marginal product of labour and should go as wages to labour, leaving nothing for capital and land.

J.M. Keynes (1883–1946) The concept of user cost,35 employed by John Maynard Keynes in The General Theory of Employment Interest and Money (1936), adds weight to the argument that the calculation of marginal cost should include not only the cost of the marginal unit of the variable factor but also some of the cost of fixed capital, even in the short period. Keynes criticised the ‘modern theory of value’ for including only ‘marginal factor cost’ in the short period supply price of a commodity: Now in the modern theory of value it has been a usual practice to equate the short-period supply price to the marginal factor cost alone … this procedure deprives our analysis of all reality … since it divorces the ‘supply price’ of an article from any ordinary sense of its ‘price’. (Keynes 1936, 67)

He argued that user cost should also be included – for ‘the short-period supply price is the sum of the marginal factor cost and the marginal user cost’ (Keynes 1936, 67). An entrepreneur’s user cost was defined as ‘the amounts which he pays out to other entrepreneurs for what he has to purchase from them together with the sacrifice which he incurs by employing the equipment instead of leaving it idle’ (Keynes 1936, 23). Marginal user cost therefore includes, in addition to purchases from other firms of items required to produce and sell the additional output, an allowance for ‘the marginal disinvestment of the firm’s own equipment involved in producing the marginal output’ (Keynes 1936, 67). It was Keynes’ view that current economic theory generally ignored disinvestment in equipment – ‘the notion that the disinvestment in equipment is zero at the margin of production runs through a good deal of recent economic theory’ (Keynes 1936, 72) – and he criticised Pigou for assuming that in general disinvestment in equipment is ‘of secondary importance’ and can be ignored (Pigou 1933, 42; cited in Keynes 1936, 72). In Keynes’ view the assumption that the cost of raw materials must be allowed for, but that disinvestment due to using raw materials and fixed capital can be safely neglected, ‘does not correspond to the facts’.36 The concept of fully net marginal product being developed in this study of the MPTD involves a deduction (from the gross MPAL) of an amount greater than Keynes’ user cost. The latter involves, in addition to the cost of purchases from other entrepreneurs, the cost of disinvestment in equipment. However, the calculation of the fully net marginal product (as defined in this study) involves deductions not only for the depreciation of fixed capital, but also for the ongoing cost of fixed capital as measured by the interest on loan capital37 and/or by the profits and dividends on equity capital. When equating marginal cost with marginal revenue as an equilibrium condition, the costs associated with the use of fixed capital may be seen either as costs that should be deducted from the gross MPAL in calculating the fully net MPAL, or as costs that should be included in calculating the true marginal cost.

R.A. Lester (1908–1997) and F. Machlup (1928–1983) In 1946 Richard Lester published a famous attack on the MPTD, inciting an equally famous response from Fritz Machlup. Their articles in the American Economic Review represented the two sides of the full cost versus marginalist theories of pricing. Although the arguments applied to the problem of the determination of the prices of products in general, they are applicable to the problem of the determination of the prices of factors, i.e. to the problem of distribution.

The central theme of Lester’s article38 was that the empirical evidence is inconsistent with the MPTD. After extensive interviews with businesspeople, he argued that the application of the MPTD is operationally impractical, especially in large-scale, multi-process, multi-product businesses, and that businesspeople do not in fact use the marginalist approach in determining the prices of their products. The heads of manufacturing concerns hiring 50 or more workers said they would have extreme difficulty in calculating the marginal variable costs and the marginal productivity of factors. Citing the work of W.J. Eiteman,39 Lester concluded that there is no doubt that it would be utterly impractical under present conditions for the manager of a multi-process plant to attempt, by means of repeated variation in the number of men employed, to work out and equate marginal costs and marginal returns for each productive factor. (Lester 1946, 75) Continuing the debate the following year, Lester (1947, 147–8) argued that the wage policies of many firms simply do not conform to the marginalist principle that ‘each worker receives the value of his marginal product under competition’ and that, in practice, wages may increase for a variety of ‘nonmarket reasons’ – such as ‘notions of ‘fairness’ and ‘rightness’, increases in the cost of living, customs and tradition, maintenance of historic relationships, desire for the security from criticism provided by conformance to an industry pattern, public sentiment, etc.’. The result, according to Lester, is that ‘a wide diversity of wage rates may exist and persist in the same locality for workers of equal skill, ability, and effectiveness’, but that such facts ‘seem to be largely overlooked by theorists of the marginalist faith’. He concluded that ‘Wage–employment relationships for individual firms cannot be adequately explained if we confine our thinking within the mental ruts of the marginalists’. In answering Lester, Machlup argued that the alleged inapplicability of marginal analysis is ‘often due to a failure to understand it, to faulty research techniques, or to mistaken interpretations of ‘findings’’ (Machlup 1946, 520). The fact that businesspeople are incapable of measuring marginal productivity in a true or objective sense, as judged by an economist, but rely on ‘subjective estimates, guesses and hunches’, does not invalidate the MPTD and does not prove that the MPTD is not used in business; nor is it relevant that businesspeople do not always act as the result of ‘a conscious decision, made after careful calculations of differential revenue and cost’ (Machlup 1946, 524). Their knowledge of their business enables them to act by routine, and to

size up a situation without reducing its dimensions to definite numerical values … such exactness is not necessary in everyday life … [the businessman] need not engage in higher mathematics, geometry, or clairvoyance … On the basis of hundreds of previous experiences of a similar nature the business man would ‘just know,’ in a vague and rough way, whether or not it would pay him to hire more men. (Machlup 1946, 525, 535) Machlup sought to cast further doubt on Lester’s argument by disparaging the interview processes used by Lester to gather his empirical evidence: [O]ne should realize the dangers of attempts to use utterances of business men as evidence against the correctness of marginal analysis. Business men’s answers to direct questions about the reasons for charging the prices they are charging are almost certainly worthless. Every single fact or act has probably hundreds of ‘reasons’; the selection of a few of them for presentation to the inquirer is influenced by the prejudices or old theories which the informant had impressed upon him by school, radio, newspapers, etc.40 In concluding his defence of the MPTD against Lester’s criticisms, Machlup asserted that ‘the marginal theory of business conduct of the firm has not been shaken, discredited or disproved’ by the empirical findings of Lester and others, and that ‘no substitute theory has been forthcoming from those who decried marginal productivity theory’ (Machlup 1946, 547, 553). In a 1967 review of the outcome of the 1946 debate, Machlup said that the prime target of the 1946 attack by Lester and others was ‘the marginalproductivity principle in the explanation of the demand for labor on the part of the individual firm’, and that the chief aim of the attack was ‘to force the abandonment or subversion of marginalism’. His verdict on the outcome of ‘the war of 1946’ was that it ended in a draw, with marginalism continuing to dominate in the microeconomic textbooks, but with alternative approaches to the theory of the firm featured in the journals and monographs with the implication that ‘a superior theory may eventually replace marginalism’ (Machlup 1967, 3–4). Machlup’s counter to the full-cost or average-cost theory of Lester and others takes the position that businesspeople are in fact marginal productivity theorists even though they may not be consciously aware of it and even though they may consciously deny it. It extols the mind of the (marginalist) economist over that of the businessperson, and suggests that the businessperson who claims to be using the full-cost principle is in fact using

the MPTD. But if ‘marginal cost’ is understood in the sense of ‘true marginal cost’, as defined below, then the economist who claims to be using the MPTD is in fact using the full-cost principle, because true marginal costs are calculated by comparing before-and-after total costs. Machlup disparagingly suggested that the businessman was influenced by ‘prejudices or old theories’ which had been ‘impressed upon him’, but did not consider the possibility that marginalist economics might be one of those ‘prejudices and old theories’. Although the Lester–Machlup exchange stimulated a vigorous debate, the issues it raised concerned the extent to which the MPTD could be used, and was in practice being used in practical business. These issues remain seriously important, but the issues being raised in this study are of a different nature, concerned as they are with the logical consistency and the normative implications of the disentanglement of factor inputs.41

E.H. Chamberlin (1899–1967) A paper written in 1933 by Edward Chamberlin, and first published in Viner (1936), contains the following statement that appears, at first glance, to limit the MPTD to situations of pure competition, and to deny its applicability to all other situations – by claiming that in all other situations the adding-up principle is false and therefore the MPTD is invalid. [In situations other than pure competition] the sum of the incomes computed on the basis of marginal products is greater than the total product. The two will be equal only when the productivity function is a homogeneous function of the first degree, i.e. when a small proportionate change in all the factors together will yield a proportionate change in product.42 [The rule that] factors are paid according to the value of their marginal products … applies only to competition. As has been shown above, there is no tendency whatever for factors to be paid in this way when monopoly elements are present. (Chamberlin 1967, 247) A further statement of this same idea was given in the American Economic Review in 1934: ‘There is no escaping the conclusion that even a slight element of monopoly necessarily reduces the remuneration of all factors below their marginal productivity’ (Chamberlin 1934, Supplement, 24). Chamberlin supported his argument by the use of a diagram (1967, 239). As is the case with most diagrams in economics, his diagram gives an artificial

air of precision, but is quite unnecessary. It appeals to those whose education has led them to believe that analytical economics requires diagrams, and that ‘nondiagrammatic economics’ is a contradiction in terms; but his argument can be expressed just as clearly in words, and gains nothing by being recast in pictures. Furthermore, the following attempt at a verbal restatement seems to reveal an aspect of Chamberlin’s argument that deprives it of its radical appearance. Chamberlin’s conclusion followed directly from the assumption (or definition) that, because of a downward-sloping demand curve, the value of the marginal product, and the marginal revenue, will be lower under monopolistic competition than under pure competition. In referring to the value of the marginal product under monopolistic competition, Chamberlin introduced the term ‘marginal revenue product’, while retaining the term ‘value of the marginal product’ when referring to pure competition.43 His statement that the sum of the marginal products is greater than the total product except under pure competition appears to be a radical limitation on the applicability of the MPTD – restricting it to the rarely realised state of pure competition, and depriving it of virtually all relevance to the real world. However, this radical appearance dissipates when Chamberlin’s terminology is understood. If, instead of employing the contrasting terms ‘value of the marginal product’ when referring to pure competition and ‘marginal revenue product’ when referring to monopolistic competition, he had used the terms ‘value of the marginal product under pure competition’ and ‘value of the marginal product under monopolistic competition’, there would have been no appearance of a radical limitation of the MPTD. His argument would amount merely to the statement that under pure competition the value of the total product would equal the sum of the values of the various marginal products under pure competition; and under monopolistic competition the value of the total product would equal the sum of the values of the various marginal products under monopolistic competition. In Chamberlin’s article, the appearance of a rejection of the MPTD under monopolistic competition was therefore purely terminological. Its radical appearance arose because he took the term ‘value of the marginal product’ (which he had used to refer to pure competition) and applied it also to monopolistic competition where, by assumption or definition, the value of the marginal product would be less (because of the lower price of the product) than under pure competition. Since the total value of the marginal products under pure competition is equal to the value of the total product under pure competition, then the total value of the marginal products under pure

competition must exceed the value of the total product under monopolistic competition, because, by the definition of monopolistic competition, the price per unit of marginal product under monopolistic competition is less than the price per unit of product under pure competition. It should also be noted that Chamberlin’s use of the possessive case (‘their’) of the personal pronoun in the statement ‘factors are paid according to the value of their marginal products’ (1942, 188) implies the presence of a solecause and soleproprietor relationship between the MPAL and the marginal unit of labour. No reference is made to the problems involved in disentangling the SMPL and the net MPAL.

L.M. Fraser (d. 1963) Whereas early critics of J.B. Clark denied the possibility of disentanglement and therefore rejected the MPTD, another group of critics later emerged who also opposed J.B. Clark’s belief in the possibility of disentanglement, but nevertheless continued to accept the MPTD, arguing that its validity does not depend on the ability to identify each factor’s contribution. This point was made, for example, by Lindley M. Fraser in his Economic Thought and Language (1947), with the help of culinary and musical metaphors: All we mean by the marginal product of a given factor class is the difference made to the total product by the addition (or subtraction) of a small quantity of that factor class, the amounts of all other factor classes in use remaining unchanged. And to say that the value of the factor in question tends to equal the value of its marginal product, as so defined, implies nothing whatever as to the amount which it as a whole has contributed to the productive process. The theory does not in the least require us to ‘unscramble eggs’. (1947, 352–3; emphasis in original) [I]t is of the essence of modern industrial methods of production that they are co-operative … And we are no more in a position to identify that part of the total product which is due to any one participating agent than, for example, to decide how much of the beauty of a Beethoven symphony is due to the violins and how much to the trumpets or the flutes. (1947, 352) As noted above, the normative implications attached by J.B. Clark to the MPTD were derived, using a Lockean theory of property rights, from the assumption that the causative or specific marginal product of each factor could be separately identified. By redefining the MPTD in a way that

removes the need to identify specific causal contributions, Fraser believed that he had effectively answered the ‘false separatism’ criticism of Hobson and others, and that the MPTD was thus converted from a normative to a purely positive theorem. On Lockean principles, no normative conclusions are possible if the scrambled eggs cannot be unscrambled. According to Fraser, anyone who draws ethical implications from the MPTD has misunderstood it, and he held J.B. Clark largely responsible for the misunderstanding. J.B. Clark was himself largely to blame for this misunderstanding. His language undoubtedly implies that he believed himself to have shewn that the labourer receives as wages exactly what he has put into the productive process – if it does not also imply that he considered this to be a ‘just’ state of affairs. (Fraser 1947, 353n.) Fraser concluded that the MPTD is ‘essentially positive, not normative, in its assertions. It makes no claim to establish that if any factor class is paid according to its marginal productivity it is therefore getting its ‘fair share’ of the national dividend, or is drawing out of the productive process exactly what it has put into it’ (Fraser 1947, 352; emphasis in original). It will be argued below that, although many modern writers on the MPTD support Fraser’s view that the MPTD is a positive, non-normative theorem (i.e. as a theorem that explains how factor rewards are determined, irrespective of whether they are just) their language continues to suggest that specific marginal products can be identified, and that the equality of wages and the MPAL is an ethical imperative. In this modern version the validity and usefulness of the MPTD do not depend on our ability to identify the specific marginal product of each factor. However, as argued in this study, the claim of the MPTD to be a positive theorem that provides a plausible and practical alternative to the bargaining theory of distribution is undermined by the multicausality of the marginal product and by the problem of allocating overhead costs and identifying the fully net marginal product of each factor.

5 Followers and critics after 1940 From Kaldor to Blaug This set of contributions contains some of the most prominent critics of the MPTD, as well as some very ardent advocates. By comparison with earlier contributions, the arguments here are less concerned with ethical considerations – although, as noted in Chapter 8, an ethical undercurrent is frequently perceptible – and more concerned with technical controversies, such as circularity and the measurement of capital.

N. Kaldor (1908–1986) In a necessarily brief but succinct and valuable statement, Nicholas Kaldor (1950) enumerated the following five problems associated with the MPTD: 1 The adding-up problem. He appears to have accepted Wicksteed’s proof that the problem is solved under conditions of constant returns to scale;1 the problem is that the ‘proposition could not therefore be valid in situations of increasing returns to scale’ (1950, 556). 2 The definition of ‘factors of production’. Kaldor argued that intermediate products (e.g. steel, machinery, electric power) cannot be regarded as factors in the MPTD, because ‘their supply is not independently given to the economic system but depends on the prices paid for them. In order to find the independent variables the intermediate products must be resolved to their ultimate constituents.’ He concluded: ‘Serious and yet unresolved difficulties however confront any attempt to find a quantitative measure of capital in terms of the production period’ (Kaldor 1950, 556).2 3 The divisibility of factors. Kaldor noted that the MPTD is applicable only if marginal products are determinate quantities, and this requires that the factors be divisible, i.e. capable of variation by small increments (Kaldor 1950, 556). 4 The variability of coefficients. The MPTD assumes that ‘the different factors of production can be substituted for another at the margin, so that the same product could be obtained by a number of alternative combinations of factors. If factors are required in fixed proportions (so many men per machine, etc.), there is no marginal productivity attaching to any one factor taken separately’ (Kaldor 1950, 556).3

5 The assumption of perfect competition. The MPTD is valid only under conditions of perfect competition. Under conditions of monopoly the prices of factors will depend on ‘the degree of ‘monopolistic exploitation’ (Pigou) of factors, as well as their marginal productivity’ (Kaldor 1950, 556). Kaldor’s entry in Chambers Encyclopedia concludes with the pessimistic statement: ‘Thus the problem posed by Ricardo, the discovery of ‘the laws which regulate distribution’, still eludes the grasp of economists’ (Kaldor 1950, 556). Kaldor disagreed with Wicksteed on the role of the assumption of constant returns to scale. According to Kaldor, Wicksteed had regarded the assumption as ‘little more than a tautology’ (Kaldor 1960, 220) – because of the way in which he (Wicksteed) had defined the factors of production. Since, in order to differentiate the production function, it is necessary for the factors to be divisible and variable, Wicksteed had argued that ‘We must regard every kind and quality of labour that can be distinguished from other kinds and qualities as a separate factor; and in the same way, every kind of land will be taken as a separate factor’ (Wicksteed 1932, 33; quoted in Kaldor 1960, 220). Kaldor argued that when the factors of production are defined in that way, the assumption of constant returns to scale is not a tautology, but a restrictive assumption similar to other restrictive assumptions implied by the MPTD, i.e. ‘the universal role of perfect competition, and the absence of external economies and diseconomies’ (Kaldor 1960, 220). On the difficulty of measuring capital – a difficulty that featured prominently in the Cambridge capital theory controversy – Kaldor argued that in order to calculate the marginal product of capital, it is necessary to establish ‘precise numerical relationships’ between different quantities of capital, but ‘whilst land can be measured in acres-per-year and labour in man-hours, capital (as distinct from ‘capital-goods’) cannot be measured in terms of physical units’, and it cannot be measured in monetary units without assuming, or without foreknowledge of, the rate of interest. Measurement in terms of value (as so many £’s of ‘capital’) already assumes a certain rate of interest, on the basis of which services accruing in different periods in the future or costs incurred at different dates in the past, are brought to a measure of equilibrium. (Kaldor 1960, 220) Other critics have also regarded the measurement of capital as a major stumbling block to the MPTD.

M. Bronfenbrenner (1914–1997) In discussing the MPTD, Martin Bronfenbrenner identified what he considered to be a number of ‘ambiguities and misunderstandings’ that have enjoyed ‘long if subterranean lives in backlash literature’ (1971, 183). He believed that one of the oldest ambiguities has been the confusion of marginal product and specific product. He defined the marginal products of the inputs a, b, c, … as the first partial derivatives of the production function X = F(a, b, c, …), and defined specific products as the ‘specific units of output produced solely by one or another input’ (1971, 122, 183). According to Bronfenbrenner, critics who, by denying the possibility of isolating specific products, believed they had refuted the MPTD were wrongheaded, because they had confused specific products with marginal products. As examples of such wrongheaded and confused critics, he cited (from Robertson [1931] 1950) Bernard Shaw’s argument about the respective contributions of the farmer and his labourers, and Bertrand Russell’s argument about the respective contributions of the porter and the railway. Bronfenbrenner added that ‘no qualified economist has maintained a specificproductivity theory of either input demand or input prices’.4 Bronfenbrenner’s comments did not advert to the fact – he did not assert it or deny it – that, since the MPAL (or ̉∂P/̉∂L) is not produced by the marginal unit of labour alone, the payment to the marginal unit of labour of a wage equal to the MPAL cannot constitute either commercial sense or profitmaximising equilibrium. Nor did Bronfenbrenner explain whether or how the net MPAL can be calculated without first knowing the level of wages. These features deserve to be included in any list of ‘ambiguities and misunderstandings’ connected with the MPTD.

Joan Robinson (1903–1983) Joan Robinson said that one of the aims of her work on the theory of imperfect competition in the 1930s (see Robinson 1933a) was to refute the MPTD, and that her refutation was inspired by Sraffa’s (1926) article on ‘The Laws of Returns Under Competitive Conditions’: My aim was to attack the internal logic of the theory of static equilibrium and to refute, by means of its own arguments, the doctrine that wages are determined by the marginal productivity of labour.5 Her article on Euler’s theorem had implied support for the MPTD (see Robinson 1934), but between then and the Cambridge capital theory

controversy of the 1960s she moved from supporter to opponent. In 1970 she argued: When competition prevails … the wage is equivalent to what Marshall called the marginal net product of labour – that is the value of average output per head minus a gross profit sufficient to pay for replacement and net profit at the going rate on the value of capital per man employed, when all inputs are reckoned at the prices appropriate to the given rate of profit. The wage is determined by technical conditions and the rate of profit … The question then comes up, what determines the rate of profit?6 She concluded that this argument ‘destroys the doctrine that wages are regulated by marginal productivity’ (Robinson 1970, 310). In 1975 she asserted that there is no room for a theory of profits based on marginal productivity of capital (Robinson 1975, 398; cited in Harcourt 1996, 325). In 1980 the rejection of the MPTD was expressed even more forcefully: In principle, a given technical situation is compatible with any proportion of relative shares. This rules out the notion of earnings determined by productivity. The share of wages in net output … depends upon commercial, social and political influences and the fortunes of the class war. The share of wages in the value of net output is affected by monopoly power and the pricing policy of corporations, by particular scarcities, by effective demand, by bargaining power and the social and political climate in which it operates. (Bhadhuri and Robinson 1980, 111) Her opposition to the MPTD appears to have been based on three main arguments: (1) the difficulty of aggregating and defining capital; (2) the circularity involved in measuring the value of capital; and (3) the reswitching problem. She has been interpreted by some writers7 as arguing that capital is either difficult or impossible to measure, owing to the problem of aggregating the vast array of heterogeneous items that are included in the concept of capital. If it is difficult to measure capital, then it is also difficult to measure the marginal productivity of capital. The MPTD must therefore be either invalid, or non-operational, or both. This aggregation argument has been criticised by, for example, Ng (1974b), who argues that the problem of aggregation applies to every commodity.

[T]he complications due to aggregation apply to consumer goods too, not just capital equipment. If we insist on methodological ‘purity’ and reject the concept of aggregate capital, we must also reject the usage of such aggregate terms as apples, tables, and in fact every common noun in our dictionaries. (Ng 1974b, 129) Ng also argues that the validity of the MPTD is not dependent on the aggregation of capital. There is no need to aggregate the heterogeneous types of capital equipment, because a rate of return can be calculated for each type (1974b, 128). This particular argument by Ng would be relevant if the aim is merely to address the problem of determining the rate of return on each type of capital, but it would not of course be relevant, and presumably was not intended to be relevant, if the aim is to address the wider problem of determining the rate of return on aggregate (or social, or overall) capital. Del Punta, another critic of Joan Robinson, has said (1971, 216) that the unmeasurability of capital is ‘the pivot of her criticism of the marginal productivity theory’. However, she recognised that the problem of aggregating and measuring capital also applied to labour: There is no point in trying to define a unit of abstract labour to apply over the whole world. There are problems even within one capitalist economy of the proper weighting, for instance, of skilled and professional work in terms of a unit of ‘ordinary’ labour; when the difference between one kind of production and another is strongly influenced by natural conditions it is impossible to give such weighting any practical meaning. (Robinson 1979, 64) It has been argued that her intention was to show – not that capital is incapable of measurement8 – but that, owing to its heterogeneity, there can be no measure of capital other than by means of its exchange value. Length can be measured by metres and weight by kilograms, but capital can be measured only by its exchange value – which means, in practice, by its monetary value. From this, Robinson concluded that the MPTD involves an inescapable circularity.9 The circularity argument is found expressed in various versions in the MPTD literature. One version runs as follows. The level of wages is a function of the net marginal product of labour; the net marginal product of labour is a function of the capital used in conjunction with the marginal unit of labour; the value of the capital is a function of the rate of profit; the rate of profit is a function of the level of wages. From this, Robinson and others conclude that, to determine the rate of wages, we must first of all know the rate of wages.10

Critics of the MPTD say that, owing to the circularity phenomenon, the measurement of capital becomes an unsolvable problem11 and the MPTD becomes indeterminate and operationally unclear. The MPTD aims to provide an explanation of the distribution of income between wages and profits, but can do so only if that distribution is already known. It provides a theoretical solution of the distribution problem only if the distribution problem is already solved, or only if some of the variables are assumed to be exogenous. It requires foreknowledge of the very distribution it purports to determine. Critics conclude that, because the MPTD does not provide a determinate theory of the distribution of income between profits and wages, it fails to provide a credible explanation of the distribution process,12 and the only credible explanation is the one that the MPTD claims to supplant, namely a bargaining power explanation that invokes the interaction of conflicting market forces, or a Marxist explanation that involves class war. Several arguments could be advanced in support of the MPTD against the circularity objection. Although the circularity of the factor valuation process means that it will often be difficult or even impossible to predict in advance what the precise value of a factor will be, the indisputable fact remains that the formation of factor values is constantly occurring in the marketplace, despite the circularity process and through the circularity process. If the circularity argument is taken as proof that the value of capital is unmeasurable (and hence that the MPTD is useless), then it proves too much. It leads to the nihilistic and absurd position that the values of all economic variables are unmeasurable. Circular and reciprocal causation is not restricted to the case of capital, but occurs regularly throughout the economy as part of the normal process of value formation.13 If the phenomenon of circular causation in the value formation process is widespread or even universal, and applicable to the values of factor inputs as well as to commodities and other services, then circular causation per se does not invalidate the MPTD. If the MPTD is to be invalidated as a distribution theory that explains the values of factor inputs, it must be shown to involve one or more features (other than circular causation) that invalidate it, but that are not present in the theory that explains the values of commodities and other services. The circularity argument has also been criticised on the grounds that it exhibits a misunderstanding of the nature of simultaneous equations. I really fear that Joan Robinson … has not really understood the basic principle of a system of simultaneously solvable equations and therefore worries about the derivation of the rate of interest from the capital stock, while the definition of the capital stock presumes the knowledge of the interest rate. Where does the puzzle come in all this if one has really understood what a system of interdependent variables is about?14

Perhaps the critical issue here is not whether a circular chain of causation exists, but whether it is possible to establish a sufficient number of simultaneous equations, and whether it is possible to substitute real-world, empirical values for the coefficients of the variables that make up the simultaneous equations. Even if Weizsäcker and Ng are correct in saying that the circularity involved in the MPTD can be handled by a set of simultaneous equations, there remains the problem of finding appropriate values for the coefficients in any real-world situation. Unless that problem can be resolved, the MPTD will remain a theoretically interesting but practically nonoperational and indeterminate concept.15 The appropriate values are of course not necessarily those that happen to exist here and now, but those that will exist in a looked-for equilibrium outcome where all the variables are endogenous and interdependent. This circularity and interdependence controversy that figured in the course of the Cambridge capital theory controversy of the 1950s to 1970s would appear to be a revival of the separability and disentanglement controversy which, as we have seen, was so vigorously debated in the early years of the MPTD. If Hobson et al. had been participants in the Cambridge capital theory controversy, they would probably have argued that the MPTD lacks practical applicability because the fully net marginal products of the various factors cannot be disentangled. Attitudes towards the disentanglement problem have followed a cyclical path through the normative and the positive phases of the MPTD. In J.B. Clark’s formulation, the MPTD claimed normative (as well as positive) implications. The validity of the normative MPTD was challenged by Hobson and others on the grounds that the causal contributions of the various factors cannot be disentangled. But when the MPTD was interpreted as a positive theorem, concerned with costs rather than with causes, the problem of causal disentanglement was declared to be irrelevant. However, if, as argued above, the validity of the positive MPTD requires identification of the fully net MPAL, then a new version of the disentanglement objection emerges. If labour is the changed variable, calculation of the fully net marginal product of labour requires that an appropriate portion of the ongoing costs of the unchanged factors16 be deducted from the gross MPAL. But what criterion can be used to determine the appropriate portion? Likewise, if capital is the changed variable, the calculation of the fully net marginal product of capital requires that an appropriate portion of the ongoing costs of the unchanged factors be deducted from the gross MPAK. But, again, what criterion can be used to determine the appropriate portion?

The disentanglement problem cannot be made to disappear simply by declaring that the MPTD is not concerned with causes and is not a normative theorem. It reemerges, in a different form, but with equal force, in the positive version of the MPTD. The fundamental and apparently insuperable problem for the MPTD is not the interdependence of the factors and the circularity of their relationships – both of which are normal features of economic processes – but the inseparability of the costs and products of the various factors. Unless the MPTD can provide an acceptable formula for disentangling the appropriate portions, it cannot claim to be a viable alternative to the bargaining theory of distribution. The attack on the MPTD by Robinson and others in the course of the Cambridge capital theory controversy did not depend entirely on arguments about the definition and measurement of capital, and the circularity of the factor valuation process. It also involved the reswitching and capital reversing17 debate. According to Harcourt (1977, 353), the Cambridge capital theory controversy was started by an article published by Robinson in the Review of Economic Studies in 1953 to 1954.18 The article, described by Robert Dorfman (1987, III, 324) as a ‘disturbing paper’, maintained that the reswitching of technological methods presents a major objection to the MPTD. Reswitching can occur when a change in interest rates makes it more profitable for a firm to bring back a technique that had been previously abandoned. At first, this phenomenon was regarded as a curiosum, but is now thought by some commentators to be of a general nature and a normal outcome when production processes involve different proportions of labour and capital. If reswitching and capital reversing occur, the relationship between the productivity of capital and the rate of interest (or the rate of profit on capital) is more complex than the MPTD suggests. It means there is no monotonic relationship between the capital–labour ratio (or the output–labour ratio) and the rate of interest.19 The production function will not be smoothly differentiable along its entire length, and there will be no unique value for the marginal product of labour (defined as ∂Q/∂L). The first partial derivative will have different values on different sides of each switch point. There will therefore be multiple equilibrium points for wages, and the MPTD will be incapable of providing a unique solution to the determination of factor rewards. The phenomenon of reswitching has therefore been thought to undermine the credibility of the MPTD as a theory of income distribution (see Hatta 1987;Scazzieri 1987).

However, some commentators have said that the importance of the reswitching phenomenon has been exaggerated.20 They argue that reswitching does not undermine the validity of the MPTD, because an equilibrium condition can be established over the intervals between any successive switch points. It merely results in different values for the partial derivative, and hence different equilibrium conditions, at different stages of production. If that is correct, then reswitching, if it occurs, does not have any significance for the validity of the MPTD as such; it merely challenges the ability of the MPTD to provide a unique solution, applicable at all levels of the production process for a particular product, to the question of the equilibrium levels of factor rewards.21 By contrast, the issues addressed in this study challenge the ability of the MPTD to provide any determinate solution, let alone a unique solution, to the distribution problem.

Y-K. Ng (b. 1942) Yew-Kwang Ng has defended the neoclassical MPTD against the attacks of ‘neoMarxist Keynesians’. He states that he has ‘great difficulty understanding why the neo-Marxist Keynesians deny the working of the marginal productivity principle for a competitive market economy’, and that he ‘cannot see how one can reasonably deny the influence of marginal productivity in determining factor rewards’ (Ng 1974a, 124, 125). He defends the MPTD against the circularity objection, arguing that circularity may seem to occur if viewed within a partial equilibrium framework: For example, the marginal productivity of capital depends on the prices of various commodities which depend on consumers’ demand which depends on income distribution which, in turn, depends on the rate of interest. (Ng 1974b, 128) But he argues: This is no more circular than the determination of a price by the supply of and demand for a commodity, since the supply and demand depend on prices of other commodities which depend also on the price of this particular commodity. (Ng 1974b, 128)22 A response might be that the case against the MPTD does not ‘deny the influence of marginal productivity in determining factor rewards’. Rather, the case against the MPTD lies in its over-simplified and reductionist assertion

that the marginal productivity of any one factor can be disentangled and identified. It is Ng’s view that ‘if profit maximization and competition are assumed, factor price must equal its marginal productivity’.23 The use of the possessive case of the personal pronoun in the statement ‘factor price must equal its marginal productivity’ raises the question of monocausality versus multicausality. Elsewhere, Ng recognises the multicausal nature of the marginal product: ‘it is the physical capital stock … that determines with other variables the marginal productivity’ (Ng 1974b, 128; emphasis added). Is it a legitimate use of words therefore to refer to the marginal product of a factor as ‘its’, without providing an explanation of how its productive input can be segregated from the inputs of the other variables?

S. Weintraub (1914–1983) Criticism of the MPTD, and support for Joan Robinson and the Cambridge (UK) attack on the MPTD, have come from Sidney Weintraub, for whom marginal productivity theory faces ‘some formidable obstacles’ (1972, 45). These include: (1) Joan Robinson’s argument that, whereas the MPTD asserts that productivity affects wages, the reverse is in fact the case – because higher wages will encourage capital intensification, which will increase productivity; (2) For a large part of the labour force, it is impossible to identify a tangible product. What is the marginal productivity of an economist, a college president, a baseball player, a soldier and so on?; (3) The capital reversing phenomenon (i.e. the fact that a lower rate of interest can either promote or retard capital intensification) shows that ‘anything can happen’ to marginal productivity. Weintraub describes this as ‘a scientifically nihilistic insight’ (Weintraub 1972, 50); (4) With increasing technological complexity, ‘the more hopeless it becomes to impute separable productivities to each element’ (Weintraub 1972, 51). To these formidable obstacles could be added the difficulty or impossibility of deciding what portion of the fixed costs to include in the calculation of the true marginal cost, along with the cost of the marginal unit of the variable factor.

E.J. Nell (b. 1935) The case against the MPTD has also been persuasively presented by Edward Nell who stressed, among other things, the multicausal nature of the marginal product, the impossibility of disentanglement, and the role played by property

rights and bargaining power in the distribution process. In a brief but challenging article, he questions the view – ‘deeply ingrained in our culture’ – that ‘the incomes of individual factors will be proportional to their separate and individual contributions’, and that ‘in competition each unit of a factor will receive the value of the extra product the employment of an extra unit of the factor brings as reward’ (Nell 1973, 103, 105). Pursuing arguments similar to those of earlier critics of the MPTD, he maintains the multicausality principle of production – ‘a productive system turns out a surplus which is the joint product of all the contributing elements’ (1973, 110) – and supports the bargaining power principle of distribution, arguing that this surplus is distributed not according to productive contributions, but according to ‘the rules of property, the respective manipulative skills of the parties involved and the effect of the price mechanism through the pressures of effective demand’. Irrespective of movements in marginal products, the returns to labour and to capital can move ‘in a capricious and haphazard way as the relative scarcity of labor to capital varies’. According to Nell, our ‘faith that our works will be duly and proportionally rewarded’ must be abjured (1973, 108, 110, 111) – which reinforces Adriance’s (1914–15) comment on the ‘soothing correlation of reward and productive effort’ (cited above), and Hobson’s reference to ‘emollient doctrines’ designed ‘to allay the passions of the economic struggle’ (Hobson 1910, 308–9).

H.G. Johnson (1923–1977) Harry Johnson regarded the MPTD as a positive, non-normative theorem, and appears to have been firmly convinced that its validity could be proved.24 However, at the same time, he recognised that the MPTD by itself does not provide the ultimate answer to the distribution problem, and that issues of a wider, normative nature – such as the ownership of capital – need to be addressed and resolved. [T]he positive theory that factors derive their incomes from their contributions to the productivity process should be sharply distinguished from the question of whether the owners of the factors are ethically entitled to own them … The focal point of social criticism should be the justice of ownership of capital by those who own it or of the processes by which they have acquired and retain it.25 Johnson (1973, 20) provided several proofs of the adding-up theorem. The first begins with the assumption of constant returns to scale: i.e. λX = f (λL, λC)

where X, L and C are the quantities of product, labour and capital respectively. Applying Euler’s theorem, Let Then

λ = 1/L X/L = f (1, C / L)

=g(C / L) since 1 is a constant Hence

X = L.g(C / L)

The marginal products are:

And the proof of the adding-up theorem then follows:26

As already stated, any proof of the adding-up theorem based on Euler’s theorem presents two difficulties. First, it does not address the interdependence objection (raised, for example, by Pareto) that it is illegitimate to take partial derivatives of a production function where the variables are not independent of one another. Second, it does not consider the objection (raised above) that, since the factors are varied sequentially (not instantaneously), as required by the ceteris paribus assumption of the MPTD, then X does not remain constant when the factors are successively varied.27 An objection raised in the past to the above proof of the adding-up theorem is that it requires the assumption of constant returns to scale, and that such an assumption is not empirically realistic. As Johnson said: The ‘adding-up problem’ then became the question of whether it is reasonable or not to assume that there are constant returns to scale in

production, since this is an empirical question not intuitively obvious in the affirmative.28 However, according to Johnson, the issue of constant returns to scale is ‘spurious’, because, in his view, the validity of the adding-up theory does not depend on an assumption of constant returns to scale. It can be proved by merely assuming perfect competition. This alternative proof was presented by Johnson (1973, 21–2) in three simple steps: 1 Under perfect competition, the value of the product must equal the cost of production (i.e. zero profits). Thus:

where p = price of product X = quantity of product wi = factor prices qi = factor quantities 2 The marginal productivity principle states that factors are paid according to the value of their marginal product:

(3) Substituting for wi in (1):

Johnson concluded (1973, 22) that this proves that ‘marginal productivity payments must exhaust the product under perfect competition’. This alternative proof does not invoke the assumption of constant returns to scale and does not use Euler’s theorem. It thus avoids the two difficulties mentioned above – the interdependence objection and the sequential

objection. However, it raises a new difficulty. If statements (1) and (2) are true, then statement (3) must follow. Statement (1) is true by definition; but Johnson’s use of statement (2) in the context of this attempted proof of the adding-up theorem is of questionable validity. His aim in this attempt is to prove the adding-up theorem. The attempt assumes in statement (2) that the marginal productivity principle is true. But, as argued above, the marginal productivity theorem cannot be true unless the addingup theorem is true. The attempted proof formulated by Johnson (1973, 21–3) thus appears to involve a process of circular reasoning that must seriously compromise its validity. Although Johnson based this attempted proof of the adding-up theorem on the assumption of perfect (or zero-profit) competition, he then discarded this assumption and extended the argument to conditions of imperfect or monopolistic competition: [T]he conclusion that marginal productivity payments to factors will exactly exhaust the product under conditions of zero-profit competition can readily be extended to conditions of imperfect or monopolistic competition provided that competition among the firms eliminates monopoly profits. (Johnson 1973, 193, 23) However, this extension would appear to be merely linguistic. The statement ‘provided that competition among the firms eliminates monopoly profits’ implies that imperfect or monopolistic competition would in fact not exist. It might exist in one sense – namely if there are few sellers or only one seller – but if the sellers are not enjoying monopoly profits, then their profit situation is effectively the same as if they were in perfect competition. It would of course be possible to abandon the restrictive assumption of perfect competition and to extend the argument to include imperfect and monopolistic competition by defining monopoly profits as a cost – for example, as the salary paid to an entrepreneur or manager who has successfully manoeuvred the company into a monopoly position by, say, mergers or patents. In that sense of ‘costs’, it would then be as true under monopoly as under perfect competition that the value of the total product must equal the cost of production, as in statement (1) above, but this extension of premise (1) of the argument would not obviate the difficulty associated with premise (2).

M. Blaug (b. 1925) A comprehensive account of the MPTD has been provided by Mark Blaug in his Economic Theory in Retrospect (1962; and four further editions, 1968,

1978, 1985, 1996). He defended the theory in the following terms: Marginal productivity theory states that each productive agent will be rewarded in equilibrium according to its marginal productivity as measured by the effect on the total product of the addition or withdrawal of a unit of that agent, the quantity of the other agents being held constant.29 Blaug states (1962, 418) that, although proper allowance must be made for the recognised shortcomings of the MPTD, no alternative theory threatens it. The implication is that Blaug himself accepts the MPTD in principle (with the qualifications that he lists) but, by leaving open the possibility of an alternative theory, he refrains from declaring it absolutely unassailable. This view is retained throughout the five editions of Economic Theory in Retrospect, with some minor but interesting variations. In the first edition (1962), the ‘shortcomings’ of the MPTD were listed as follows: [I]t is static, it is of little practical use in production problems, it neglects the supply side in factor markets, it cannot be applied to factor markets as a whole because of the interdependence of demand and supply, and it sheds no direct light on the problem of relative shares because it fails to analyze the nature of technical change. Nevertheless, contemporary distribution theory is a marginal productivity theory, properly qualified to make allowance for these objections. It is as secure from attack as any theory can be, for no alternative theory is in sight. (Blaug 1962, 418) The statement ‘contemporary distribution theory is a marginal productivity theory’ was altered in the second edition to ‘in the eyes of most economists, contemporary distribution theory is a marginal productivity theory’ (Blaug 1968, 446), thus recognising that support for the MPTD is not universal among contemporary economists, and implying that it is legitimate to claim to be an economist even if you reject the MPTD. In addition, the statement ‘It is as secure from attack as any theory can be, for no alternative theory is in sight’ (Blaug 1962, 418) was altered in the second edition to a more modified: ‘so long as no satisfactory alternative theory is in sight it will remain secure from attack’ (Blaug 1968, 446). Both versions imply that, for Blaug, a bargaining power theory of distribution is not a satisfactory alternative threat to the MPTD. A distinctive feature of Blaug’s account of the MPTD is that the MPTD has a ‘microeconomic bias’, and that it fails ‘to throw light on the determination of

relative shares’ (1962, 416); in other words, it provides an explanation (on the demand side) for the prices of factors at the level of the individual firm, but not for the relative shares of the factors or classes (land, labour, capital) at the aggregate level. Blaug appears to give more emphasis to this feature of the MPTD than do most other commentators.30 This distinction between ‘factor pricing’ and ‘relative shares’ was expressed more forcefully in the following statement, added to the third edition of Economic Theory in Retrospect, in which Blaug argues that it is misleading to describe marginal productivity theory as a theory of distribution: A theory of distribution might be expected to tell us something about personal income distribution, or at any rate the distribution of incomes between wages, profits and rents. But marginal productivity theory is a theory of factor pricing, not a theory of the distribution of relative shares. (Blaug 1978, 449; emphasis in original) It is significant that the title of the marginal productivity chapter (Chapter 11) in Economic Theory in Retrospect was ‘Marginal Productivity Theory of Distribution’ in the first and second editions, but became ‘Marginal Productivity and Factor Prices’ in the third (1978) and later editions. The MPTD is described in the Preface to the third edition as the ‘so-called’ MPTD (Blaug 1978). Given this distinction between factor prices and relative shares, Blaug endorses the MPTD as a theory of microdistribution, but rejects it as a theory of macrodistribution: ‘As I have argued passionately it [i.e. the MPTD] says nothing about shares … The theory of income distribution in neoclassical economics is about the theory of factor pricing’ (Blaug, in Caravale 1983, 128).31 He argues that marginal productivity is only one of many elements of a general equilibrium solution to the problem of distributive shares, and that attempts to test it empirically have been inconclusive. To the question: ‘Is there a neoclassical theory of distribution based on marginal productivity, which is logically coherent?’, Blaug replied: ‘The answer is yes’ (in Caravale 1983, 134); and added: ‘There is a logically coherent theory which generates the prices of every kind of labour, and of every kind of capital good in the market’ (in Caravale 1983, 136).32 In this respect, Blaug sees an essential difference between the theory of distribution of classical economics and the theory of distribution (developed in the 1890s) based on marginal productivity. The former, he argues, was

concerned with the relative shares of land, labour and capital, while the latter is concerned with the more limited problem of factor prices. When economics turned back in the 1890s to the classical problems of factor pricing, it took some time to realize that the new theory of distribution33 dealt with a much more restricted range of questions. The relative shares of land, labor, and capital, which had been at the heart of classical distribution theory, disappear as a problem in marginal productivity theory. The microeconomic focus of the new theory precluded conclusions about the tripartite division of revenues à la Adam Smith. With the demise of the wages fund theory, not only that theory but all the macroeconomic problems of distribution with which it was concerned were abandoned. It took a long time, however, before economists became fully aware of the limited content of marginal productivity theory. Right up to the 1920s it was not uncommon for economists to discuss such issues as the level of wages and of employment as a whole in terms of the operation of the entire economy conceived as a giant firm. But, obviously, the interdependence of aggregate demand and supply renders the theory inapplicable to such problems. Indeed, it is easy to show that marginal productivity analysis is necessarily based on the assumption of a given level of income in the economy as a whole. (Blaug 1962, 414–15) Blaug believes that, among nineteenth-century neoclassical economists, it was only J.B Clark, and possibly Böhm-Bawerk, who applied the marginal productivity principle to the economy as a whole; and in the twentieth century, John Hicks, in his Theory of Wages (1932a) was the first to attempt to explain the functional distribution of income by applying the marginal productivity principle to an aggregate production function. According to Blaug, when nineteenth-century writers like Wicksteed, Wicksell, Walras and Marshall applied the marginal productivity principle they were concerned with factor pricing,34 not relative shares (Blaug 1978, 487). The distinction between factor pricing and relative shares might, however, be questioned. If the MPTD is valid as an explanation (even if only partial) of the demand for an individual unit of labour at the micro level, and if the aggregate or macro demand for labour is a summation of the demands for individual units of labour, why does not the MPTD also provide an explanation of the aggregate demand for labour? In addition, in what sense is a factor price different from a relative share? The wage of an individual man is both the factor price of his labour and his relative share of the revenue from the production process in which he is engaged. Conversely, the relative share of labour in the aggregate is merely a summation of the factor prices received by the individual labourers. Is ‘relative share’ just another name for

‘factor price’, with the only difference being that, owing to a verbal convention, the former is used at the macro or aggregate level and the latter at the micro or individual level?35 Blaug states that the variables in the production function at the aggregate level are interdependent, and implies that the variables at the individual level are independent. If this is correct, then Pareto’s interdependence objection would rule out the use of Euler’s theorem at the aggregate or macro level but not at the individual or micro level;36 and, consequently, if the validity of the MPTD depends on the use of Euler’s theorem, the MPTD could not be proved valid at the macro level. However, the view that the variables in the production function are independent at the micro level is debatable. An alternative view is that the amount of labour that a firm employs will depend on the amount of land and capital that it employs; and vice versa. In the later editions of Economic Theory in Retrospect, Blaug further questions the significance, importance and relevance of the MPTD, considered as a theory of distributive shares. The section entitled ‘Marginal Productivity Once Again’ is enhanced in the third and subsequent editions by a lengthy segment in which (among other things) Blaug doubts whether the MPTD (at the macro level) merits the title ‘theory’. He considers it to have ‘few practical implications’ (Blaug 1978, 510); he wonders at the amount of attention given to it in conventional textbooks; and he argues that it leaves aside the many sociological determinants of distribution: [I]t relegates to ‘sociology’ such forces as unions, the corporate power structure, the monetary system, the state of aggregate demand, and government policies toward incomes and prices, all of which seem to be very relevant to problems of income distribution. (Blaug 1978, 510–11, and later editions) He notes that the MPTD does not assert, but does not deny, that the class struggle ‘has a lot to do with the determination of distributive shares’ (Blaug 1978, 511). In the same vein, he adds: ‘Actually, the great mystery of the modern theory of distribution is why anyone regards the share of wages and profits in total income as an interesting problem. It has after all little practical relevance.’37 Furthermore, he doubts whether distributive shares are interesting as a theoretical problem. He argues that distributive shares are the outcome of many forces, including ‘the initial distribution of resources among households, the preferences of households, the production functions of firms, and the behavioral assumptions of economic agents, such as utility and profit maximization’. He concludes: In short, the neoclassical theory of functional income distribution, call it the marginal productivity theory or what you will, is a much more modest theory than many of its enemies would have us believe. (Blaug 1978, 512) Blaug takes issue with those who argue that capital cannot be measured in its own technical units, but labour and land can. He argues that ‘labour and land also cannot be successfully measured in their own technical units’; that ‘the problem of measuring ‘labour’ is on all

fours with the problem of measuring ‘capital’’; and that ‘heterogeneous capital is no more difficult to measure than heterogeneous labour or heterogeneous output’, noting as an example that ‘from the standpoint of the output to which they contribute, a graduate engineer is as different from an errand boy as a turret lathe is from a screwdriver’ (Blaug 1975, 10, 80). He concludes that ‘there is no such thing as the marginal product of the total stock of capital in the economy, just as there is no such thing as the marginal product of the labour force’ (Blaug 1975, 9; emphases in original). If I understand it correctly, Blaug’s position thus appears to be that the MPTD cannot be applied at the aggregated or macro level owing to the impossibility of measuring aggregated quantities of the various factors, but is applicable at the disaggregated or micro level; and, furthermore, at the micro level, marginal productivity is only one of many elements of an equilibrium solution. The equality of factor prices and marginal products is an equilibrium solution of a set of simultaneous equations and it seems pointless to select ‘marginal productivity’ as a sort of prime mover. (Blaug 1975, 7) It could, however, be argued that the measurability problem, which precludes macro application of the MPTD, also precludes its micro application. Each individual firm will usually employ a number of different kinds of capital, ranging perhaps from screwdrivers to turret lathes, and a number of different kinds of labour, ranging perhaps from errand boys to graduate engineers. In its attempts to establish an equilibrium level for its employment of capital, it must find some way of aggregating these different kinds of capital; and likewise for labour and land. If they are aggregated in their own technical units – so many screwdrivers, so many errand boys and so on – the resulting set of simultaneous equations (for all but the smallest enterprises) would become totally impractical. If they are aggregated in monetary units, the petitio principii problem re-emerges. The only available source of information for the monetary value of errand boys and engineers is current market values, which are set by bargaining forces; but the essential aim of a theory of marginal productivity is to arrive at equilibrium levels of factor prices without recourse to the bargaining process. If the measurability problem is relevant at both micro and macro levels, then a ‘simultaneous equations’ solution of the MPTD will have little or no practical use, even though it might appear to be theoretically satisfying. It would be yet another case of ‘theory without measurement’. The proposition being advanced in this study is that, even as a theory of microdistribution, the coherence of the MPTD is questionable, because (1)

the MPTD ignores the causative function of the constant factors (i.e. it assumes that ceteris paribus means ceteris inefficacibus); (2) it provides no solution to the disentanglement of specific contributions, and no solution to the disentanglement of fully net marginal products and to the allocation of overhead costs; and (3) it cannot provide a determinate solution to the problem of distribution unless it invokes a bargaining power theory of distribution – a theory which the MPTD pretends to supplant. Blaug has also expressed the view that a ‘wholesale denial of marginal productivity theory would mean that, among other things, we could never raise questions about the contributions of individual workers to output’ (1972, 296n.). Such a wholesale denial was what the early critics of the MPTD were in effect putting forward when they argued that the SMPL is unknowable and cannot be disentangled from the MPAL. They would have agreed therefore that there is no point in raising questions about it – if that means trying to formulate a universal theory or law of distribution that is more sophisticated and more scientific than a basic bargaining power theory. In a world where factor prices are determined by sheer bargaining power, the only questions are: Who has the greater bargaining power and how did they get it?

6 Summary of the main themes Chapters 2 to 5 have presented a detailed chronological account of contributions either for or against the MPTD. In Chapter 6 an attempt is made to collate and summarise those parts of the individual contributions that relate to the five main themes of this study.

Monocausality, multicausality and disentanglement Throughout the history of the MPTD, the most recurring and disputed theme has probably been the causality of the marginal product, i.e. the question of whether the marginal product is a monocausal or a multicausal phenomenon. It is universally acknowledged that the total product is the result of the actions of many factors or causes, but it has been either asserted or implied by some contributors, and denied by others, that the marginal product can be causally attributed to the marginal unit of the factor, and that if more than one factor is involved in the production of the marginal product, their particular contributions can be disentangled. Thünen appears to have been the first to regard the marginal product of labour as the product of labour alone, and to have stated or assumed that the marginal product of each factor can be separately identified and measured. Other early advocates of the MPTD adopted the same view. Menger and Wieser believed that marginal contributors are identifiable – in the latter case, by employing simultaneous equations. Marshall, Wicksteed, Flux and many subsequent contributors argued or implied that a partial differential coefficient of the production function defines and isolates the marginal product. Edgeworth accepted the possibility of disentanglement, but argued that a worker’s wage must be less than the marginal product – not equal to it as the MPTD claims – because otherwise there would be nothing left for profits. Cassel accepted the separability of the marginal product, but insisted on the limited applicability of the MPTD and gave more prominence to the principle of scarcity. The most prominent critic of the monocausality of the marginal product was Hobson. Those who asserted or implied its monocausality were accused by Hobson of a ‘false separatism’. Others who shared his criticism included Davenport – who spoke of the ‘togetherness’ of the productive factors – and also Taylor, Taussig and Adriance. But Taylor then argued, somewhat paradoxically, that it would be appropriate to proceed as if the marginal unit of a factor is solely responsible for the marginal product; and Taussig

introduced an alternative version of the MPTD based on the concept of a discounted marginal product. Adriance, an undeservedly neglected critic of the MPTD, argued that it is a verbal absurdity and a mathematical error to attribute the marginal product to a particular factor. More recently, it has been argued that the question of causality is irrelevant to the MPTD, and that the validity of the MPTD does not depend on the ability to disentangle the specific product of each factor. In Fraser’s expression, the MPTD does not require us to unscramble eggs. Bronfenbrenner argued that specific products should not be confused with marginal products, and the inability to identify specific products does not constitute a refutation of the MPTD. In this interpretation, the MPTD is a positive theorem, not a normative theorem, and does not warrant any ethical judgements about the distribution of factor rewards.

Imputation of factor rewards by means of simultaneous equations This approach may be seen, for example, in the writings of Wieser, Cassel, Douglas and Stigler. It avoids the attribution of causes, but the practical difficulties involved in establishing the equations have been recognised by both supporters and critics. More radically, it was criticised – notably by Wicksell – as merely providing a description of current exchange relationships, not a theory of distribution.

The adding-up (or exhaustion-of-product) problem and the use of Euler’s theorem The first attempt at a formal proof of the adding-up theorem seems to have been made by Wicksteed. It has been debated ever since. The debate is complicated by the fact that there is some evidence that Wicksteed recanted. Arguments about whether or not he recanted have become as involved and as controversial as the Wicksteed-Flux solution itself. One view (for example, Hutchison) is that he did recant but didn’t need to. Another view (for example, Robbins and Stigler) is that the recantation was more verbal than real. But evidence from Wicksteed’s correspondence suggests that a recantation was explicit and real, not merely verbal. Other writers have put forward variations on Wicksteed’s attempt to prove the adding-up theorem. Flux appears to have been the first person to make use of Euler’s theorem in the adding-up theorem. Subsequently, Euler’s theorem has figured prominently in the MPTD debate. Stigler’s Production and Distribution Theories (1941) devoted 68 of its 392 pages to ‘Euler’s

theorem and the marginal productivity theory’. However, doubts about the applicability of Euler’s theorem to the MPTD were raised, for example, by Edgeworth and Pareto. A major objection to the Wicksteed-Flux attempt came from Pareto, who argued that the interdependence of the factors in a production function means that the calculation of partial differentials, as in the Wicksteed-Flux approach, is mathematically illegitimate. The application of Euler’s theorem to the MPTD requires the assumption of constant returns to scale or a linear homogeneous production function. Edgeworth ridiculed that assumption, arguing that it is contrary to common sense; and Walras claimed that Barone had provided a proof of the adding-up theorem that did not depend on an assumption of constant returns to scale, but required only the assumption of free competition. Wicksell at first defended Wicksteed and disagreed with Walras’ claim, but later apologised to Walras and conceded that his claim was correct. Wicksell developed a proof of the adding-up theorem which he believed does not require an assumption of either constant returns to scale or minimum cost, is not based on Euler’s theorem, and does not require the use of differential calculus. Hicks also argued that the adding-up theorem does not require an assumption of constant returns to scale, but can be proved by assuming that the firm is in equilibrium and is operating at minimum cost. However, he acknowledged that the assumption of minimum cost also presents difficulties. Robinson’s reply to Hicks was that constant returns to scale are a corollary of equilibrium and optimum size. In reply to both Robinson and Hicks, it has been argued that the assumption of equilibrium and optimum size is as unrealistic as the assumption of constant returns to scale. A similar view was expressed in more recent times by Johnson, who argued that an assumption of either constant returns to scale or minimum cost is not necessary, and that an assumption of perfect competition is sufficient in order to prove the addingup theorem. Yet another variation – as suggested in this study – is that Euler’s theorem cannot be used to prove the MPTD, because the events pertaining to the MPTD are essentially sequential, not simultaneous.

Circularity and the measurement of capital If the MPTD is to have a useful, practical application, the factors of production must be capable of measurement. A number of critics have argued that, although labour and land can be measured in their respective technical units (e.g. the numbers of persons or hectares), the measurement of capital

presents an insurmountable difficulty which renders the MPTD ineffectual. Capital, it is argued, has no meaningful technical unit of measurement, and aggregations of capital can only be measured by means of value, but to do so involves an inescapable process of circular reasoning. This circularity objection may be seen in the writings of, for example, Wicksell, Webb, Sraffa, Dobb, Robinson and Kaldor. According to Kaldor, the principal problem for the MPTD is not the adding-up problem but the circularity involved in the measurement of capital. But the circularity objection has been dismissed by critics, such as Weizsäcker and Ng, who argue that economic relationships frequently involve causal circularity, especially in a general equilibrium framework, and circularity, if represented by a system of simultaneous equations, does not involve self-contradiction or indeterminacy. And Blaug argues that capital is no more difficult to measure and involves no greater circularity of argument than land and labour.

Social and political implications Although it is often claimed that the MPTD is a positive theorem of economics, the textual evidence shows that some of the leading contributors to the debate were aware of its political implications, and were motivated by a desire to influence political events. Wieser feared that unless a rule could be found to resolve the conflict between owners and workers, the existing order of things would be threatened by accusations of arbitrariness, force and injustice. Wicksell hoped that the MPTD would dispel ‘Hegelian darkness’ and refute the socialist theory of value, which he regarded as ‘a terrible weapon against the existing order’ (cited above). J.B. Clark was even more explicit in asserting the role of the MPTD in current political and ideological controversy. He believed that, unless the question of distribution can be resolved, ‘the right of society to exist in its present form’ would be threatened and ‘no force could prevent a violent overturning of the social order’. His MPTD has been described as a ‘rebuttal of the exploitation theory of Henry George and Karl Marx’ (cited above). Taussig’s comments on the MPTD also reveal a concern with the civil unrest that might occur if there is no law of economics to forestall the conflict between capitalists and labourers; and if the distribution process involves the owners of capital ‘wringing as much as possible from the poor and oppressed’. In this ‘game of grab’, with each side trying to get as much as possible, ‘there is no telling what will be the outcome’ (cited above). Knight had similar concerns for social order. He rejected the ethical dogmas that J.B. Clark had deduced from the MPTD, but when he said that there

would be social chaos unless there is an economic law connecting productive contributions with rewards, he appears to have implicitly acknowledged an ethical significance for the MPTD. Opponents of the MPTD have also been inspired, in some cases, by its political ramifications. Hobson argued that, if the MPTD is valid, it provides employers with a theoretical demonstration of the futility of attempts by labourers and trade unions to increase wages and improve working conditions. It is an ‘emollient’ doctrine designed to ‘allay the passions of the economic struggle’ (cited above). Adriance said that the MPTD provides a ‘soothing correlation between rewards and productive contributions’, and encourages among economists an ‘unwarranted conservatism’ (cited above). Nell, likewise, casts doubt on the deeply ingrained faith that work will be duly rewarded.

7 Miscellaneous considerations This chapter develops some of the points mentioned earlier, and considers other aspects of the MPTD debate.

The Clarkian and the positivist meanings of MPL In the history of the MPTD, the expression ‘marginal product of labour’ (MPL) and the preposition ‘of’ have been used in two different senses. For J.B. Clark, MPL meant the portion (of the joint product) that is specifically produced by labour. The ‘of’ is given proprietorial significance, and allows normative conclusions to be drawn. When other writers used a non-normative version of the MPTD, and defined MPL as the change in total product that occurs after a change in the amount of labour employed, they were using ‘of’ in a sense quite different from J.B. Clark’s. Their ‘of’ has no proprietorial significance, and does not lead to Lockean-based normative conclusions. If they were aware of their different meaning of ‘of’, they rarely drew their readers’ attention to it. The normative version of the MPTD and the positive version of the MPTD both say that the criterion of profit maximisation is: MPL = wages, but the meaning of MPL has changed. In the Clarkian version it meant SMPL; in other versions it means MPAL.1

Calculation of fully net marginal products: the allocation of fixed or overhead costs According to the MPTD, profit-maximising equilibrium occurs when MPAL = wages, where MPAL is the change in total output that follows the application of an extra unit of labour, with other factors held constant. But in real life, calculation of the MPAL is made difficult by the fact that ceteris paribus does not always prevail. When an extra unit of labour is employed, it will often be necessary to employ extra units of capital also. Marshall (1949, 336–7) addressed this issue by introducing the concept of net marginal product (or marginal net product), which is calculated by subtracting from the (gross) MPAL the costs of the additional units of other factors that need to be employed to support the marginal unit of labour.2 The profit-maximising equilibrium condition in value terms would thus be, not ‘MPAL = wage’, but ‘net MPAL = wage’. It was argued above that it is not clear from Marshall’s texts whether his concept of net marginal product was intended to be fully net

or partially net, i.e. whether the deductions that are made in order to calculate the net MPAL would include only extra items of variable capital (such as power and materials); or whether they would also include a proportionate charge for the use of fixed capital (such as land and buildings). It was further argued above that, since fixed capital continues to exert a causative influence in the production process, even though it is held constant, then a contribution for the maintenance and depreciation of fixed capital should3 also be deducted from the gross MPAL in calculating the net MPAL, even in the short term. Equality between the partially net MPAL and wages would not be a profit-maximising equilibrium position, because the costs of the constant factors would remain uncovered (i.e. the constant factors that act in combination with labour would receive no revenue). Their services would be withdrawn, resulting in disequilibrium. Common sense and proper accounting practice suggest that a portion of the cost of the constant factors should be taken into account, even in the short term,4 when estimating the costs incurred in employing the marginal unit of labour; and that a portion of the MPAL be reserved as a reward for the contributions made by the constant capital. It would be commercial folly to maintain that, as a condition of profit maximisation and equilibrium, the partially net MPAL should be paid entirely as wages to labour. It makes no commercial sense to give to labour the entire value of something that has been produced by both labour and (constant) capital. Such a procedure would be a criterion, not of profit maximisation and equilibrium, but of imminent bankruptcy and disequilibrium. Any business operators who had been beguiled by the MPTD into thinking that they would achieve maximum profits and equilibrium by equating the gross MPAL and wages, or even the partially net MPAL and wages, would soon come to regard their studies of neoclassical economics as regrettable. If you cannot climb a ladder without the help of the ladder, then it would seem obvious that a portion of the cost of the ladder should be taken into account, along with the cost of your labour, in estimating the marginal cost of the process. If the ladder contributes to the climber’s upward progress, if capital (though held constant) contributes to the marginal product (MPAL) that occurs after the employment of the marginal unit of labour, then it would seem to be economically inappropriate (as well as being morally inappropriate in Lockean terms) to allocate the entire MPAL to wages, and not to reserve some portion of the MPAL as a contribution towards the return for, or towards the costs of, the constant capital. If each successive marginal unit of labour were to be awarded a wage equal to the value of the gross MPAL, then in due course the total product, being a

summation of the products of the successive marginal units of labour, will go entirely to labour, with no return for the constant factors. The equality ‘MPL = wages’ is generally said in standard accounts of the MPTD to be a profit-maximising and equilibrium condition. But this criterion would appear to be valid only if MPAL is understood as the fully net MPAL. Expositions of the MPTD rarely refer to this limitation and, of those that do, few give due recognition to the feasibility of calculating the fully net MPAL without having recourse to the bargaining theory of distribution that the MPTD seeks to supplant. It should however be noted that the partially net MPAL (and even the fully net MPAL) is not the same as the SMPL; ‘after’ is not the same as ‘solely because of’. The fully net marginal product that occurs after the employment of the marginal unit of labour is still a multicausal phenomenon; it is not the monocausal specific product of the marginal unit of labour. The deduction of other costs associated with the employment of the marginal unit of labour does not lead to the identification of the specific product of labour. The domain of costs is not the domain of causes. The relative costs of capital and labour are not necessarily a measure of their relative causal contributions to the production process. In the case of a ditch being dug by one man using one spade, the relative costs of the man and the spade may vary over time according to the market’s estimation of their relative scarcities, even though their relative causal contributions remain the same. In this regard, it is important to distinguish between the approach of the businessman and the approach of the theoretician. The businessman can, if he wishes, apply the equality ‘wage = fully net MPAL’ as a commercial rule, because for him the calculation of the fully net MPAL is not impossible, nor even particularly difficult. He simply deducts from the gross MPAL the current market-determined costs of the extra variable factors that need to be employed along with the marginal unit of labour, together with an appropriate portion of the costs of the fixed capital, using the prevailing market rate of interest on his borrowed capital, and the customary or target rate of profit on his equity capital. But the task of the theoretician, seeking to develop a determinate model of distribution, is not so simple. If the theory or model is to be complete, it cannot take the prevailing rates of interest and profit as exogenously given. It needs to explain what determines the current levels of interest and profit. The accountant and the economic theorist will also differ on the method of allocating the costs of fixed capital. The former is concerned with the problem of allocating indirect or overhead costs to products and departments in order to make decisions about what products to produce and what prices to

set, and to value inventories. The latter is concerned with developing economic principles for allocating the firm’s revenue between the factors of production. Indirect or overhead costs are the costs that cannot be traced, or cannot easily be traced, to the individual products of a multi-product firm or to the individual factor units of a multi-factor operation. They include: the cost of premises; the cost of equipment; insurance; depreciation; upstream costs such as research, development and design; downstream costs such as distribution, advertising, transport and customer servicing. In allocating their overhead costs, accountants of particular firms may choose one of a wide variety of accounting methods – or a combination of methods – to suit their needs or preferences. The method adopted could be applied across an entire production plant, or varied according to each department or each type of activity within the plant. The allocation could be either volume-based or nonvolume-based (involving items such as set-up costs), and could be proportioned to measurable inputs such as direct labour hours, or direct labour costs, or machine hours, or direct material quantities or costs. Standard texts on cost accounting show the great variety and complexity of the options available to accountants in allocating overhead costs. Although particular firms, or accountants, or bodies of accountants may be quite satisfied with the rules they adopt for the allocation of overheads, the rules appear to be very flexible and even arbitrary when viewed from the perspective of economics. As Hicks argued, ‘there is no firm economic solution’ to the problem of the allocation of overheads.5 The accounting texts also indicate that the term ‘marginal cost’ when used by MPTD economists is very different from the term when used by accountants. For example, in Australian accounting standards, ‘marginal costing’ (also called ‘variable costing’ or ‘direct costing’) refers to a system that excludes fixed manufacturing overheads from product cost, as distinct from a system called ‘absorption costing’ which includes fixed manufacturing overheads as part of product cost, but ‘marginal costing’ includes some variable manufacturing overheads. Surveys have shown that there is a wide variety in the costing systems that Australian firms choose to adopt (see Langfield-Smith et al. 1998, 7.5, 7.9; Joye and Blayney 1990). As argued throughout this study, the MPTD is incapable of providing a determinate solution to the distribution problem unless fully net marginal products can be disentangled. The calculation of the fully net marginal products of the factor inputs requires that fixed costs be allocated among the various factors, but the fact that both cost accountancy and economic theory do not claim to have established an agreed and universal principle for solving this allocation problem suggests that it remains a theoretically insurmountable problem, notwithstanding that particular firms and their accountants make allocation decisions to suit their pragmatic convenience.

The MPTD and exploitation The payment of a wage equal to the MPAL in accordance with the MPTD creates paradoxically a situation where capital is being exploited by labour. Exploitation of capital by labour could be defined (utilising a Lockean theory of property rights) as a situation where wages exceed the value of the product that is specifically caused by labour, i.e. where wages exceed SMPL.6 If this definition of exploitation is adopted, and if the arguments presented above are valid, it follows that when labour receives as wages the full value of the gross MPAL, then labour is in fact being overpaid and is exploiting capital, because the gross MPAL must exceed the SMPL. Labour alone is not causally responsible for creating the whole of the multicausal gross MPAL. If its wage equals the gross MPAL, it is being paid for something it has not produced. Its wage exceeds its causative contribution.7 For any given production process, assuming that each unit of labour is equally productive (i.e. the SMPL is constant), the overall degree of exploitation of capital by labour would be the same whether each unit of labour receives an identical wage (i.e. the average wage); or whether earlier units with higher marginal productivity receive more than later units whose marginal productivity declines because of diminishing returns. The only difference is that under the latter system the excess of the wage over the SMPL would be greater for labourers employed earlier in the production process than for those employed later, i.e. the degree of exploitation of capital by labour would decline as more labourers were employed. Under the former system, the excess of the wage over the SMPL (i.e. the degree of exploitation of capital by labour) would be constant for all units of labour. The overall amount of exploitation would be the same under both systems of payment.

An equitable-by-chance outcome If the gross MPAL is paid to labour as wages, then wages will include not only a reward for labour, but also a reward for the use of the capital that works with the labour to produce the gross MPAL. If the gross MPAK is paid to capital as profit, then profit will include not only a reward for the use of capital but also a reward for the labour that works with the capital to produce the gross MPAK. Using a Lockean theory of property rights, it follows that, in the former case, labour is depriving capital of some of the reward that ought to go to capital; and, in the latter case, capital is depriving labour of some of the reward that ought to go to labour.

There is therefore the possibility that these mutual deprivations will balance out, and that labour and capital will each receive rewards commensurate with their specific products. But as the specific products are unknowable, such an equitable balancing would be entirely a matter of chance.

The MPTD, the labour theory of value and the law of diminishing returns Ambiguity in the use of ‘of’ is not confined to the MPTD. It has precedents, for example, in the labour theory of value and the law of diminishing returns, both of which do not distinguish between ‘the product of labour’ and ‘the product of labour alone’, i.e. between the MPAL and the SMPL. The MPTD was considered by J.B. Clark and some other writers to have provided a scientific rebuttal of socialist claims (based on a labour theory of value and a labour theory of property) that labour is exploited under the capitalist system. It is paradoxical, therefore, that in attributing a monocausal and sole-proprietor significance to the marginal product of labour, Clark’s MPTD, which was deemed to answer and supersede the labour theory of value, perpetuates the linguistic usages found in those versions of the labour theory of value according to which, since the whole product is created by labour, labour has a moral right to the whole product, and is subject to exploitation if some of that product is paid to factors other than labour. In those versions of the labour theory of value, the use of the proprietorial ‘of’ implies that the products of labour are the products of labour alone. Like the MPTD, they fail to admit the multicausal nature of the product; they fail to distinguish between ‘of labour’ and ‘of labour only’. This misuse of the proprietorial ‘of’ also occurs in expositions of the Law of Diminishing Returns, where the change in total output that occurs after the employment of an extra unit of a variable factor is described as the product of that factor. It thus implies a monocausal relationship between the extra unit of the variable factor and the change in total product, and fails to state explicitly that the change in total product is produced by the extra unit of the variable factor acting in combination with the factors held constant. The latter do not cease to exert a causative impact by being held constant. This inaccurate use of language, endemic in earlier economic discourse, has been unquestioningly absorbed into the MPTD. The connection between the MPTD and the Law of Diminishing Returns was forcefully emphasised by Hobson (1910, 308–9):8 the marginal reasoning is simply a belated application of the ‘dosing’ hypothesis which led to the adoption of a preposterous law of Diminishing Returns … Is there any other

‘science,’ which for the best part of a century has sought to rear an intellectual edifice on such silliness? … to erect this folly into a corner-stone of a theory of distribution is a piece of extravagance which can only be explained by the desire to find emollient doctrines to allay the passions of the economic struggle … With the Law of Diminishing Returns and of Separate Productivity disappears whatever speciousness attached to marginal significance regarded as a theory of distribution.

The MPTD and the indivisibility of inputs A common criticism of the MPTD is that it is often impossible or impracticable for technical reasons to add or subtract the variable factor in minute quantities, as required by the infinitesimal calculus. Wicksteed recognised that indivisible inputs introduce a ‘serious indeterminateness’ into marginal products, but Steedman questions whether the adjective ‘serious’ is really called for, and adds: ‘It is, of course, an elementary error to suppose that input indivisibilities are fatal to the very concept of “marginal product”’ (Steedman 1992, 26). Indivisibility of inputs touches only the practicability of the MPTD, and is not a substantial issue, either for supporters of the MPTD or for opponents. For the latter, the main weakness of the MPTD is not that inputs are lumpy. Even if minute divisibility of capital, for example, were possible – the case of a single seed being sown in a field is often cited as an example of minute divisibility – the MPTD would not provide a satisfactory theory of distribution. There remains the more fundamental difficulty of disentanglement. The extra output that occurs after the addition of an extra unit of capital, however small that extra unit might be, cannot be monocausally attributed to that extra unit. It is impossible to disentangle the specific contributions of the marginal units of the various factors, whether those marginal units be large or small. When a plant grows after the sowing of a seed, how is it possible to distinguish the portion of that product that is causally attributable to the seed from the portions that are causally attributable to the other forces that have cooperated with the seed? What part of the plant is caused by the seed, and what parts are caused by the soil, the sunlight, the air, the water, and the farmer’s labour and capital? The specific contribution made by the seed to the final product would be nil without the productive contributions of the other factors.

The MPTD and supply-side considerations Various writers (for example, Alfred Marshall) have noted that the MPTD is not a complete theory of distribution. It refers only to demand-side

considerations (i.e. to the forces that affect what an employer is willing to pay for factor services) and at best can only claim to be a demand-side theory of wages.9 To be a complete theory of distribution it would need to be supplemented by supply-side considerations – such as the hereditary distribution of wealth, the ownership of natural resources, the standards of education and health of the labour supply – all of which will affect the quantity and quality of labour supplied, and the resulting levels of wages. The marginal productivity of a factor will set the upper limit to what an employer is prepared to pay, but an abundant supply of the factor could mean that the resulting level of wages will be less than the upper limit. These supply-side considerations would also have to be taken into account in assessing the fairness of the outcome.10 But can it be argued that the only, or the major, reason for the inadequacy of the MPTD as a theory of distribution is the absence of these supply-side considerations? Is it true that, if supply-side considerations are incorporated, the MPTD would become a complete and adequate theory of distribution? It is the contention of this study that the failure of the MPTD to recognise the productive role of the constant factors means that the MPTD is inadequate, even as a theory purporting to explain only the demand-side determinants of distribution. This inadequacy would not be overcome by incorporating supply-side considerations.

The MPTD, the MC = MR rule and the true marginal cost One possible contributory reason for the elevated status, popularity and longevity of the MPTD may be that a proposition such as ‘maximum profits from the employment of labour occur where the marginal product of labour equals the wage of the marginal unit of labour’ appears, at first sight, to be a consequence, or a particular application, of the more general proposition that, if marginal revenue and marginal cost can be calculated – a disputable proposition at the aggregate level11 – then ‘maximum profits occur where marginal revenue equals marginal cost’. If the marginal product of labour (MPL) is the marginal revenue (MR), and the wage (W) is the marginal cost (MC), the ‘MR = MC’ principle becomes (in the context of the MPTD) the ‘MPL = W’ principle. However, this argument does not distinguish between the cost of the marginal unit of the variable factor, and the cost of producing the marginal product that follows the employment of the marginal unit of the variable factor. If output increases following the employment of a marginal unit of labour, the cost of

producing the marginal output is not the same as the cost of the marginal unit of labour. The former would have to include not only the wage of the marginal unit of labour, but also the cost of any additional factors needed to assist the marginal unit of labour (e.g. extra materials, fuel, supervision), and a portion of the cost of the fixed factors that add their causal contributions to that of the marginal unit of labour. It is a contention of this study that the validity of the MPTD is damaged by the fact of multicausality (i.e. by the causative role of the constant factors), even when the MPTD refrains from identifying causal inputs and attributing proprietorial rights, and is considered in purely positive terms of revenues and costs. The reason for this contention is that, if the marginal product that occurs after the employment of the marginal unit of labour is not produced by that unit of labour alone and contains more than the specific product of that unit of labour (i.e. if the SMPL is not the sole component of the MPAL) then it follows that the cost of that marginal unit of labour is not the only cost of the marginal product. Multiple causes imply multiple costs. In a productive process requiring more factors than labour (i.e. if the causes of the MPAL are multiple) then the costs of production will also be multiple. Economic theory usually excludes the costs of fixed factors, often described as sunk or fixed costs, from the calculation of marginal costs, because marginal costs are thought to include only the costs associated with changes in the employment of factors. Since fixed costs are, by definition, not changed when the variable factors change, they are not counted in calculating marginal costs, as conventionally defined. In the short term, when capital is fixed for a given time, the fixed costs are a fixed amount that has to be paid regardless of the level of output, and therefore do not enter into conventionally defined marginal costs as opposed to average costs. This conventional economics view of marginal cost is elaborated in, for example, Richard Kahn’s The Economics of the Short Period (1989). In the short term – defined as a production period in which capital equipment remains unchanged – the marginal cost of production is equal to marginal prime cost, where prime cost consists of labour, raw materials and interest on working capital. Fixed costs are defined as the portion of total cost which does not vary with output in the short term, and include management or organisation, rent, upkeep, rates and interest charges additional to the interest on working capital. Overhead costs are defined as fixed costs plus normal profits, interest on fixed capital and depreciation of fixed capital. Profitmaximising equilibrium is said to occur where marginal cost equals marginal revenue, but in the short term marginal cost includes neither overhead cost nor fixed cost.

In Chapter 11, entitled ‘The Business Man is Not a True Economic Man’, Kahn argued that when ordinary businessmen declare that they do not accept the marginalist theory of pricing and profit maximisation, they are guilty of ‘failure to comprehend the marginal principle’; he declared that their ideas ‘must be regarded as distinctly erroneous’.12 He based his argument on ‘the supremacy of prime cost and the comparative irrelevance of fixed cost, and still more of overhead cost’ (Kahn 1989, 159). But this distinction between fixed costs and marginal costs is questionable when applied to the MPTD. The physical quantity of capital equipment may be fixed for a given period of time, but this does not mean that its cost ceases to be accountable. Its cost will still be relevant to current production costs through either ongoing interest charges on borrowed fixed capital, or ongoing provision for dividends on equity fixed capital, or rents on leased property and equipment. Any prudent businessperson will wish to incorporate an appropriate allowance for these ongoing fixed capital costs in calculating the marginal cost of employing extra units of the variable factors. Factors may be fixed (or held constant) in a physical sense at a given time, but the costs of fixed factors occur and recur at each successive instant – per minute, per month or per year. This wider connotation of marginal cost may be described as the ‘true marginal cost’, and the pro-MPTD and anti-MPTD debate could be seen as analogous to the debate between the marginalist theory of pricing and the full-cost theory of pricing (see Lee (1984a) and the extensive literature cited there). However, the marginalist theory of the price of a factor of production involves an additional problem and complication by comparison with the marginalist theory of the price of a product, namely the problem of disentangling the contributions and costs of the variable and fixed factors. The notion of ‘true marginal cost’ is discussed in Wiles (1961), where it is argued that marginal cost is commonly but mistakenly identified by economists with variable costs, as opposed to fixed costs, and fixed costs are defined as ‘those which within some arbitrary period of time can remain constant while output varies’ (Wiles 1961, 8; emphasis in original). Marginal cost, in Wiles’ view, should include wear and tear on machinery due to use, and should also include interest – for example, interest on an overdraft to finance more work in progress. These two costs are commonly neglected in considering marginal cost. Normal profit can also form part of marginal cost – ‘for instance if a partnership or small business raises more proprietors’ capital or simply ploughs back profit to finance more work in progress’. Since such expansion must be financed, it follows that marginal cost ‘always includes an element of either interest or normal profit’ and that marginal cost ‘is much higher than is commonly thought’.13

From an accountant’s point of view, the distinction between direct and overhead costs is described as ‘a mere accounting convenience’ and the process of allocating overhead costs to different factors or different processes or different products is described as ‘the accountant’s arbitrary practices’. Costs are called direct if the accountants succeed in dividing them into different proportions. Any remaining costs are lumped together as overheads, and spread by ‘some rule of thumb’ (Wiles 1961, 11). The acknowledged arbitrariness of the accountant’s practice in the disentanglement and allocation of overhead costs points to the essential theoretical indeterminacy of the MPTD. A contrary view is that there is no need for capital to have a share of the marginal product that follows the employment of a marginal unit of labour, and no need for a portion of the cost of the fixed capital to be included in the true marginal cost, because the existing fixed capital is already catered for; if it was not receiving its due reward it would not exist; it would go elsewhere. A similar argument was used by Marshall in an early note on the distinction between fixed and circulating capital: ‘the produce of any manufacture must replace the circulating capital consumed in making it, but not that of the fixed capital used’ (cited in Whitaker 1975, I, 221). This contrary view does not take into consideration the fact that although the quantity of the existing capital may be fixed at the time when the marginal unit of labour is employed, the cost of that capital is an ongoing cost in the form of interest, rent, sinking funds or dividends. It also leaves unanswered the question of the source of the funds used to cater for the existing fixed capital. Is the fixed capital being serviced out of the marginal products that have occurred after the application of previous marginal units of labour? If so, the marginal products of the previous units of labour could not have gone in full to the marginal units of labour. Some of the marginal products of labour would have had to be reserved for payments to fixed capital. Labour would be crosssubsidising capital, contravening the principle of the MPTD. If fixed capital has been supported out of the products of previous marginal units of labour, does the same thing occur for current marginal units of labour? If that is not true of the current marginal unit of labour, there is no reason for it to be true for the previous marginal unit, or for the one before that and so on; or for any marginal unit of labour. The contrary view which says that capital is already catered for merely pushes the problem back in time, into an infinite regress. It would thus not be appropriate for a profit-maximising firm to estimate the size of its marginal cost simply by the cost of the marginal unit of the variable factor. A simplistic application of the MC = MR rule that considers the cost of only the variable factor would fail to recognise the contribution made by the other factors, even if constant in quantity, to the creation of the marginal product. To equate the marginal cost of the marginal product of

labour with the wage cost of the marginal unit of labour would be to underestimate marginal cost; just as, to equate the specific marginal product of labour (SMPL) with the marginal product after labour (MPAL) would be to overestimate the specific marginal product of labour.14 If marginal cost, in this ‘true’ or wider sense, is defined as the change in total cost associated with the employment of the marginal unit of a factor, not just as the cost of that marginal unit, the concept of marginal cost would be symmetrical with that of marginal revenue defined as the change in total revenue associated with the employment of the marginal unit of a factor.

8 The normative language of the nonnormative MPTD Stigler (1941, 297) criticised J.B. Clark’s ethical system, not only because of its ‘dubious merits’, but also because it regrettably suggested that neoclassical economics is ideologically biased towards the existing economic order. Clark performed one function for which economics has less cause for gratitude. In all of his major works, although perhaps to a decreasing extent through time, he introduced what has been called a ‘naïve productivity ethics’ – his marginal productivity theory contained a prescription as well as an analysis.1 The dubious merits of this ethical system need not concern us, but it is a cause for regret that Clark’s exposition, more than that of any other eminent contemporary economist, afforded some grounds for the popular and superficial allegation that neo-classical economics was essentially an apologetic for the existing economic order. Clark was a made-to-order foil for the diatribes of a Veblen. Groenewegen (1990, 34) has said that ‘Clarkian parables and the productivity ethics based on them must now be relegated to errors from the past’. But a survey of modern literature on the MPTD suggests that this relegation has been only partially successful.2 In many modern works the language used in defining the MPTD frequently employs expressions that implicitly or explicitly assert monocausality, and that therefore lend themselves to normative conclusions, even if that was not the intention of the authors. In references to the marginal product of a factor, it is common to find possessive pronouns, such as ‘its’, ‘his’, and ‘their’; or phrases involving the use of the possessive case, such as ‘each factor’s’; or causative expressions such as ‘added by’, ‘results from’ and ‘contributed by’ – all of which suggest monocausality and proprietorial rights. The following examples taken at random are an indication of the prevalence of these linguistic usages (in each case, the relevant words have been italicised): • ‘The value of each factor in production is determined by its marginal contribution to total output’ (Ekelund and Hebert 1975, 384). • A firm will hire factors ‘up to the point where each factor’s marginal product is just equal to its income payment’ (Ekelund and Hebert 1975, 384).

• ‘The marginal-product of a productive factor is the extra product or output added by one extra unit of that factor, while other factors are being held constant’ (Samuelson 1958, 504). • ‘Each of the three factors will be paid its marginal product’ (Samuelson 1958, 589). • ‘It seems reasonable that what workers receive is related to what they produce.’3 • ‘A factor of production receives as much income as corresponds to its contribution to production’ (Pen 1971, 76). • The marginal product of labour is ‘the additional amount of product ̉∂Q which results from one additional unit of labour ∂L’ (Pen 1971, 431). • The ‘marginal revenue product’ of a factor is ‘the addition to revenue resulting from the sale of the product contributed by an additional unit of the variable factor’ (Lipsey 1975, 347). • The marginal product of labour is the ‘additional output attributable to the hiring of one more worker’ or the ‘contribution that a worker makes to the revenue’ (Dernburgh and McDougall 1976, 189). • The marginal productivity theory ‘holds that the payment for any factor of production tends to be about equal to the value of its marginal product’, and that ‘if the wage of any factor is less than the value of the output that an additional unit could produce, successive units of that factor will be employed until the inequality vanishes’ (Dorfman 1987, III, 323). • The marginal productivity theory enables us to determine ‘the productive factor’s specific contribution to the making of the final product’ (Waud 1986, 679–80). • The ‘marginal product of labour’ is ‘the increase in total product that results from a one-unit increase in the quantity of labour employed’ (McTaggart et al. 1999, 10.5). Such expressions could be interpreted to mean that there is a monocausal link between the change in the total product and the application of an additional unit of the variable factor, i.e. that the additional unit is the sole cause of the change in the total product. An explicit or instinctive application of a Lockean concept of property rights gives a distinctly normative tone to such expressions.

The last two of the above quotations (from Waud, and McTaggart et al.) are particularly relevant as examples of explicit or implicit assertions of monocausality, with consequent normative overtones. In describing the variable factor as ‘the productive factor’, Waud appears to deny any productive input from the fixed factors, and in employing the term ‘specific contribution’ revives J.B. Clark’s (1899) use of ‘specific’. This suggests that, at least in the minds of some modern exponents, the MPTD is capable of disentangling the specific products of the variable factors ( i.e. that the Clarkian version of the MPTD has survived), and that it survives among ‘qualified economists’ today despite Bronfenbrenner’s statement4 to the contrary. Bronfenbrenner accused MPTD critics of identifying specific productivity and marginal productivity. Waud (1986) is evidence that this identification is not confined to critics. In McTaggart et al. the implication of monocausality is reinforced by taking as an example the production of hamburgers in which a ‘oneunit increase in labour input from two to three workers, increases output from 60 to 80 hamburgers’ (10.6). If taken literally, this is a miraculous instance of Godlike, ex nihilo creativity. The one extra unit of labour creates 20 hamburgers without using any extra meat, tomato or lettuce; without the use of any knife, spatula, or grill; and without a building to work in or a site to put it on. The modern orthodox view is that the J.B. Clark normative version of the MPTD is untenable and should be replaced by the positive, non-normative version.5 However, the above selection of orthodox versions indicates that vestiges of the Clarkian version appear to have survived – if not in the intentions of the authors, at least in their choice of language. A reader could understandably come to think that the authors are suggesting the existence of a monocausal, proprietorial relationship between the marginal unit of the variable factor and the marginal product, especially as these expositions of the MPTD are not usually accompanied by any statement to the contrary.6 Readers who are not privy to the intentions of MPTD expositors could be forgiven for thinking that ‘of’ in the phrase ‘marginal product of labour’ has its familiar, everyday, common-sense, proprietorial meaning, i.e. that the ‘marginal product of labour’ means the ‘marginal product specifically created by labour’. They would not be acting illogically or unreasonably if they concluded, using an acquired or instinctive Lockean view of property rights, that the MPTD carries legitimate normative implications, i.e. that the marginal product of labour ought to belong entirely to the marginal unit of labour. And they would have to be forgiven for thinking that the MPTD is being presented, not only as a principle of economics, but as a principle of social justice.

Some modern versions of the MPTD contain an explicit denial that the MPTD seeks to identify specific marginal products (i.e. a denial that the MPTD attempts to unscramble eggs), and some explicitly deny J.B. Clark’s claim that the MPTD bears normative implications. But the denials are more often than not betrayed by language that is highly suggestive – even if not intentionally so – of monocausality and disentanglement, with proprietorial and normative implications. Some of the authors profess to discard the search for causal connections, but continue to make use of the language of causation. The temptation to relapse into the language of monocausality and sole proprietorship seems difficult to resist, and consequently modern expressions of the MPTD never fully escape from issuing (at least implicitly) Clark-type moral judgements. In some cases readers are given the clear (though possibly mistaken) impression that the presenters of the MPTD are deliberately seeking to impart a normative message. Their monocausal and quasi-normative language gives to the equality of marginal product and factor reward a halo of moral righteousness, and suggests that at least some of the authors harbour a lingering belief that specific marginal products can be disentangled. Whatever their intentions, their words convey the impression, when they speak of the marginal product of labour, or when they calculate the first partial derivative of output with respect to labour, that they believe they are extracting from the joint product the amount of product that is specifically produced by the marginal unit of labour, and that therefore the MPTD establishes a moral justification for the distribution of factor rewards. Furthermore, even if expositions of the MPTD were accompanied by an explicit warning that the connection between the marginal unit of labour and the MPAL is neither monocausal nor proprietorial, thus removing any Lockean normative implications, they would still be liable to understandable misinterpretations insofar as they do not state explicitly that the marginal product in question is the net marginal product, and insofar as they do not advert to the fact that in practice the calculation of the fully net marginal product of a factor is indeterminate, rendering the MPTD redundant as a theory of income distribution. It would seem therefore that vestigial remnants of the Clarkian, normative MPTD survive, even if unintended or denied, in the language of the many past and present versions of the MPTD that abound with implicit expressions of specific causality and proprietorial relationship. This suggests that, for many expositors, the positive MPTD is imbued with an unspoken ethical principle, and remains in effect an ethical theory of distribution, while masquerading as a positive theory and vigorously denying that it is an ethical theory.7

Vivian Walsh (1989, 885) has argued that, although the American opponents in the capital controversy conceded victory to Joan Robinson and Sraffa, ‘the same old theory’ continues to be presented ‘as if the whole controversy had never taken place’, with the textbooks ‘happily conducting business as usual, selling the illegitimately drawn ideological conclusions of the marginal productivity ‘theory’ of distribution for the edification of the young and the ignorant’. It is paradoxical that the following words of Wicksteed, written with reference to the use of the term ‘utility’ at a time when he had not yet published his version of the MPTD, now seem to express very neatly the way in which normative elements retain a lingering presence within a theory that pretends to be non-normative: It is an old trick of the Economists to take a word which has an ethical meaning, to empty it of all moral signification by express definition, and then consciously or unconsciously suffer it to carry its moral sanctions and associations with it into all kinds of unmoral or immoral applications. (Wicksteed 1888, 14; cited in Steedman 1994, 86).

9 General conclusion: neither normative nor positive The multicausal nature of the MPAL and the impossibility of causal disentanglement effectively eliminate any normative implications from the MPTD. In the context of a Lockean theory of property rights, the MPTD carries normative implications for factor rewards only if the marginal product of a factor is monocausal – which is never the case – or only if the specific marginal products of the various factors can be disentangled – which is impossible. Without disentanglement, no moral judgements concerning the distribution of rewards among the factors can be logically deduced from a Lockean theory of property rights. There are no logical grounds (based on that theory) for concluding that the marginal unit of labour has a moral right to the ownership of the marginal product that occurs after the employment of that unit (i.e. the MPAL).1 Some defenders of the MPTD argue that it is a positive law of distribution, not a normative law, and that because it is not concerned to identify specific marginal products and to establish rights of ownership, its validity as a positive law is in no way affected by the impossibility of disentangling the specific products. They argue that normative judgements of the J.B. Clark variety can be either ignored or rejected; and that the MPTD can be substantiated as a purely positive law, as a valid criterion for profit maximisation and equilibrium, and as a theoretical and practical principle of income distribution. They deny its moral imperative, but assert its commercial imperative. They reject it as a rule of ethics, but retain it as a rule of efficiency.2 But if the foregoing critique is valid, the claim of the MPTD to be a positive law can no more be substantiated than its claim to be a normative law. In order for the equation ‘Wage = MPAL’ to be a theoretically complete and practically useful principle of distribution, ‘MPAL’ would have to be interpreted as ‘net MPAL’ (and as fully net, not just partially net). But calculation of the fully net MPAL involves a number of serious difficulties: 1 Circular and simultaneous causation. It requires simultaneous determination of the rates of return on all the factors, given that all the factors and their rates of return are interdependent. As Wieser recognised, the tasks of assembling a comprehensive system of simultaneous equations would be extremely onerous.

2 Equilibrium condition. Even if a satisfactory system of simultaneous equations could be established, they would be of no practical use unless realworld quantities could be given to the coefficients of the variables. But the only realworld quantities available are those found in the marketplace where they are the outcome of the bargaining between buyers and sellers. The resulting solution of the equations would therefore merely tell us what happens to be the current situation. As Wicksell argued, it would not indicate whether or not the existing situation is an optimum, profit-maximising or equilibrium situation. A simultaneously determined solution is consistent with a situation of ongoing disequilibrium. 3 The appropriate portion of the fixed costs. The argument advanced above is that, in the case of labour, for example, the profit-maximising equilibrium condition should be ‘fully net MPAL = wages’, but the calculation of the fully net MPAL requires some rule or criterion for determining the appropriate portion of the ongoing costs of the fixed capital that should be deducted from the gross MPAL. The MPTD does not appear to have provided such a rule or criterion. There would seem therefore to be no justification for the claim that the MPTD can provide a practical solution to the problem of distribution, or a solution that is independent of, and an alternative to, the bargaining power theory of distribution. Some economists, past and present, have sought to establish the credentials of the subject as a hard science, and have seen in the MPTD a scientific and clear-cut solution to the problem of distribution. They appear to cling to the MPTD either because no better theory has been advanced, or for fear of the vacuum that might remain if it were abandoned – a vacuum that might be filled by class struggle or by the arbitrary intervention by government in the redistribution of income.3 They have felt that, without the MPTD, economics would be forced to admit that the distribution of income cannot be explained by a scientific formula (such as MPL = wage) – an admission which would seriously weaken the claim of economics to be a hard science – but that distribution is the result of the complex and unpredictable interaction of the bargaining powers of the factor owners. The marginalist approach in general, and the MPTD in particular, are often presented and eulogised as a unified, general and scientific theory that explains the prices of all products and all productive services, with the demand-and-supply theory being explicitly or implicitly disparaged as inferior or unscientific or lacking in analytical content. Ricardo summed up this disparaging attitude when he wrote to Malthus on 9 October 1820: ‘You say demand and supply regulates value – this, I think, is saying nothing’

(Ricardo 1951–73, VII, 279; cited in Kurz 1999, 149). Ricardo searched in vain for the ‘natural value’ that underlies the values set by the market forces of demand and supply. The MPTD involves a similar vain search. It seeks to discover a law of distribution that in some mysterious and deep way goes beyond and below the distribution that is determined by the bargaining between suppliers and demanders. It refuses to acknowledge that a bargaining power theory is a unified, general and scientific theory of distribution. The scientific aspirations of the MPTD have been abetted by the denial of normative pretensions – a denial that leads supporters to claim for the MPTD the status of a law of a positive, non-normative science. However, as is argued above, this denial is often accompanied by the retention of causative and quasi-normative language, so that, on the one hand, the MPTD claims to be positivist and scientific but, on the other hand, expresses that claim in language that hints of moral rectitude. This combination of purported scientific certitude and an implicit ethical imperative has served to rationalise and justify the MPTD, and has probably made a significant contribution to its popularity and longevity.4 The history of the MPTD may be interpreted as an unsuccessful endeavour to find a substitute for a crude bargaining power or higgling explanation of distribution; as an unwillingness to admit indeterminacy; and as an attempt to introduce scientific certainty and determinacy into an area of human affairs that does not admit of certainty and determinacy. It may also be seen as a fruitless search for a theoretical alternative to the harsh reality of the marketplace, where outcomes are affected by a contest of economic strength; and as an abortive attempt to escape from an uncertain and unpredictable world of interpersonal conflict and class struggle into one that is safe and harmonious, where the distribution of income is ordained by the higher authority of a mechanistic natural law. The inability of the MPTD, or of any other theory of distribution so far, to attain these goals raises the possibility that there may, in fact, be no alternative to a bargaining power explanation of distribution, and that the only realistic and defensible theory of income distribution is the one that the MPTD tries to supplant – namely the theory that labour gets what capital does not, or vice versa – which is hardly worthy of being dignified by the pretentious title of ‘theory’ or ‘law’. Supporters of the MPTD perceive it to be scientific, probably because it involves some mathematics; and they perceive a bargaining power theory of distribution to be unscientific or prescientific. But if ‘science’ is defined in the broad sense of a ‘particular branch of knowledge or study’ (Oxford English Dictionary), and if it is conceded that a theory can be scientific even if it is not mathematical, then a bargaining power theory of distribution can legitimately claim to be ‘scientific’. Despite the many attempts over the years

to validate the MPTD, economics would appear to be no further advanced along the road to finding a theory of distribution that is ‘scientific’ in the narrow, mathematical sense.

Appendix A W.S. Jevons (1835–1882) and the MPTD Some writers have attributed a marginal productivity theory of distribution to William Stanley Jevons. B.H. Higgins, for example, held that ‘His isolated statements on the subject show that Jevons considered wages to be equal to the marginal productivity of labour in competitive equilibrium’. According to Higgins, Jevons’ clearest formulation of the MPTD was probably: ‘the wages of a working man are ultimately coincident with what he produces, after the deduction of rent, taxes and the interest of capital’ (Jevons [1871] 1970, 256). Higgins also believed that Jevons had shown that ‘the rate of interest is equal to the marginal productivity of lengthening the period of production’ (Higgins 1935, 107). However, Stigler criticised Higgins1 for ‘too freely’ attributing a marginal productivity theory of wages to Jevons. Stigler argued that when Jevons discussed the effect of additional units of labour on a given quantity of land, his analysis resembled ‘only in superficial form … a true marginal productivity theory of wages’. He added that, in The State in Relation to Labour (1882, 99ff.), one of Jevons’ last works, Jevons ‘seems to deny the possibility of isolating the product of labor from that of other productive resources combined with it’,2 but added that Jevons’ argument was ‘very confused’ (Stigler 1941, 21). Stigler did not give a precise reference for this interpretation. He was perhaps referring to a passage where Jevons asked whether a workman ‘can claim any right of property in his skill’, adding that: ‘It may be at least plausibly said that in his education and training a skilled operative expends no small amount of capital, which remains invested in him’ (Jevons 1882, 98–9). This could possibly be taken to imply that the product of labour is not the product of labour alone, but is due to the capital invested in him as well as to his labour – thus giving rise to the disentanglement objection raised later by critics of the MPTD. Schumpeter (1954, 940) disagreed with Stigler on this point, and argued that there is in Jevons a marginal productivity theory of wages. Dobb also disagreed with Stigler, arguing that Jevons made use of marginal productivity theory in explaining the rate of return on capital. Dobb concluded that Jevons ‘certainly does introduce what is essentially the notion of marginal productivity’, but recognised that Jevons ‘failed to develop explicitly a general theory of distribution’.3 However, a strong indication that Jevons’ theory of distribution, as presented in the first edition (1871) of The Theory of Political Economy, was not a

marginal productivity theory, may be seen in his emphasis on supply and demand as determinants of distribution. For example, he stated: ‘The common law is that demand and supply of labour and capital determine the division between wages and profits’ (cited in Steedman 1972, 48) and, as Steedman argued, Jevons never abandoned that position. But his theory of distribution did not proceed beyond an enunciation of the general principle of demand and supply, and remained indeterminate.4 It relied upon his harmonistic view of society, and on his belief that ‘the supposed conflict of labour with capital is a delusion’.5 It relied on the vague aspirational and ethical hopes that labour and capital would receive their ‘legitimate share’, their ‘due value’ and a ‘proper fraction’ of the produce,6 and, as Steedman has noted, it is, to that extent, an ethical theory of distribution. A marginal productivity theory is not of course inconsistent with a supplyanddemand theory. Marginal productivity is one of the elements that govern demand. But the fact that Jevons chose to highlight the role of supply and demand without referring to marginal productivity suggests that the latter did not play a prominent role in his theory of distribution in the first edition of The Theory of Political Economy. However, recent studies have suggested that an MPTD may be found, at least implicitly if not explicitly, in the Preface to the second edition (1879) of The Theory of Political Economy. For example, Steedman (1997, 61, 62) argues that, in the 1879 Preface, ‘Jevons did in effect proclaim a ramified marginal productivity theory of rents, wages, quasi-rents and the rate of interest’ (61). [Jevons] was in effect outlining a comprehensive marginal productivity theory of all the forms of income from production, in which the traditional theory of rent was to be extended to cover also wages and interest – which is not, of course, to say that Jevons could even have filled in that outline in a logically watertight manner’ (62). Steedman concludes (1997, 64) that ‘Jevons certainly attempted to sketch a complete marginal productivity theory of distribution, even if he was far from successful in providing one’. Other researchers, such as Flatau (2004) and White (forthcoming), have also noted that in the 1879 Preface there may be found strong evidence of a movement by Jevons towards a marginal productivity theory of distribution, but acknowledge that he did not fully develop it as a universal law. Intimations of an MPTD are evident in Jevons’ statement that ‘the productiveness of labour’ is represented by dx/dl, and by his reference to a person being ‘recompensed by the last increment of labour which he applies to land by the rate of production dx/dl’ (Jevons 1970, 220, 222). But the 1879

Preface contains the following piece of contrary evidence: ‘we must regard labour, land, knowledge and capital as conjoint conditions of the whole produce, not as causes each of a certain portion of the produce’ (Jevons 1970, 68). This could be interpreted as another admission of the disentanglement objection which, as noted above, appeared also in The State in Relation to Labour (1882) and which, if correct, renders any causally based MPTD ineffectual. The 1879 Preface also stated: ‘Each labourer must be regarded, like each landowner and each capitalist, as bringing into the common stock one part of the component elements, bargaining for the best share of the produce which the conditions of the market allow him to claim successfully’, and ‘Every one gets the most which he can for his exertions’ (Jevons 1970, 68–9, 71). This emphasis on bargaining appears to negate any adherence to the MPTD. For those who regard the MPTD as a major theoretical achievement, Jevons would merit considerable honour if it could be shown that he had contributed to its development. But those who regard the MPTD as a regrettable episode in the history of economics would say that his contribution to the MPTD had merely assisted in shunting the car of economic science on to yet another wrong line. Whether or not the MPTD can be attributed to Jevons, there can be no doubt that Jevons, along with Walras and Menger, developed the language and concept of marginalism, and accustomed economists to think in marginal terms, thus preparing the ground for a ready acceptance of the MPTD.

Appendix B Marshall’s concept of net marginal product: fully net or partially net? It was stated above that Marshall’s concept of net marginal product could be interpreted in two ways: (1) fully net or (2) partially net. In Appendix B, the textual evidence for the two possible interpretations is reviewed. Evidence for interpretation (1) – i.e. that ‘net product’ is net of an appropriate portion of the cost of the fixed capital, as well as net of extra variable costs – may be found in Marshall’s statement: The doctrine that the earnings of a worker tend to be equal to the net product of his work, has by itself no real meaning; since in order to estimate net product we have to take for granted all the expenses of production of the commodity on which he works, other than his own wages.1 In addition, in Economics of Industry the labourer’s ‘net return’ was defined as the ‘value of the produce he takes part in producing after deducting all other expenses of producing it’ (Marshall and Marshall 1879, 133; emphasis added). The expressions ‘all the expenses’ and ‘all other expenses’, if taken literally, would include an appropriate portion of the fixed costs; but, on the other hand, the fact that the Marshalls did not explicitly mention in this context a deduction for the contribution of the fixed capital casts some doubt on this interpretation. Even stronger evidence for interpretation (1) occurs in the statement: The net product to which the normal wages of any group of workers approximate, must be estimated on the assumption that production has been pushed to that limit at which the output can be just marketed with normal profits, but not more. (Marshall 1949, 554; 1961, I, 667) This seems to imply that, in calculating the net product of labour, deductions should be made not only for other variable costs, such as materials and power, and not only for interest on borrowed funds, but also for normal profits.2 In another context, namely in defining the term ‘National Dividend’ as the ‘net annual revenue of the country’, Marshall referred briefly to the meaning

of ‘net’. He stated that in estimating the aggregate of commodities produced during a year, allowance had to be made ‘for the replacement of raw material consumed during the year and for the wear and tear of machinery’.3 He stated: ‘The word net has of course no fixed meaning: it merely indicates that certain deductions, specified in the context, have to be made’, and he added that ‘no corresponding reduction is made for the wear and tear of human agents of production … for the ageing and exhaustion of the workers’ (Marshall 1961, II, 589–90). The deduction for wear and tear of machinery suggests a movement towards what has been described above as the concept of a fully net marginal product, but, since it does not include a deduction for either interest on borrowed capital or profits and dividends on equity capital, it is not in fact fully net. Although Marshall’s text leaves open the possibility of different interpretations, Joan Robinson believed that his concept of net marginal product included a deduction for profit on equity capital, as well as deductions for extra items of variable capital, i.e. it was a fully net MPAL, rather than merely partially net: The wage is equivalent to what Marshall called the marginal net product of labour – that is the value of average output per head minus a gross profit sufficient to pay for replacement and net profit at the going rate on the value of the capital per man employed. (Robinson 1970, 310) The same opinion is expressed in a slightly different form in other places: The marginal product of an additional man employed provides the wage per man-year and the profit on the capital required to employ him. It is far from being the case that each ‘factor’ separately receives its marginal product. Manplus-capital earns the marginal product. (Robinson 1971, 57) The marginal product of labour is equal to the wage only when the rate of profit is zero. (Robinson 1973a, 137) The marginal net product of labour (after allowing for raw materials, power and maintenance of plant) is equal to the wage plus profit. (Robinson 1973a, 132)4

However, the definition of marginal net product of labour given in Robinson and Eatwell (1973) – ‘Net product is the value of the increment of product expected from employing a man minus the additional expenses that would be involved in employing him’ (41) – does not explicitly include profit as one of the deductions. Textual evidence to support interpretation (2) – that Marshall’s ‘net product’ was intended to be only partially net, i.e. net only of any extra variable costs that need to be employed along with the marginal unit of labour – may be found in several places. In an example where extra value is given to ale by the use of additional hops, he said that the net product of the extra hops is the extra value of the ale, assuming that ‘no further trouble or expense of any kind is involved by this additional use of hops’. The word ‘further’ suggests that he was referring, not to the fixed costs, but only to further variable costs. A second example used by Marshall reinforces this interpretation. Referring to the optimum number of shepherds to be employed by a farmer, he supposed that an extra shepherd would enable a farmer to increase his annual output by 20 sheep without ‘any further expenditure on plant or stock’. The ‘net product’ of an additional shepherd was thus said to be 20 sheep; and Marshall restated the principle that the employment of each agent is adjusted so that ‘in its marginal application, its cost is proportionate to the additional net product resulting from its use’ (Marshall 1949, 427; emphasis added). Here again, the use of the expression ‘any further expenditure on plant or stock’ and the monocausality implied by the phrase ‘resulting from its use’ add weight to the view that Marshall’s ‘net marginal product’ was intended to be net of variable costs only,5 and that he believed that, when the extra variable costs are deducted, the resulting net product is the result of the extra shepherd, thus ignoring the causative role of the fixed capital. A third item of evidence supporting the view that when Marshall spoke of ‘net product’ he did not mean ‘net of the costs of fixed capital’ is that he explicitly identified the ‘net product’ as the partial derivative of the production function (Marshall 1961, II, 567; cited in Whitaker 1988, 129). The partial derivative of the production function with respect to labour measures the change in output that follows a change in the use of labour, but does not measure what portion of that change in output is caused by the nonlabour factors that are held constant. If the partial derivative of labour with respect to labour is identified with the ‘net product’ of labour, then the ‘net product’ is not net of (a proportionate part) of the cost of the fixed factors. Further evidence that Marshall meant partially net rather than fully net when speaking of net marginal product may be seen in the relatively limited

amount of attention he gave to the problem of the depreciation of capital equipment. As noted by Hicks: It is indeed quite remarkable how little there is in Marshall’s book about depreciation. There is a footnote in which he recognizes that it is a problem, but the footnote just ends with a reference to an accounting textbook. He has evidently decided that for his purposes, the accountant’s solution will do. Gross can in that way be reduced to net, and it is net returns that are equalized by competition in the long period. (Hicks 1974, 313; Hicks referred to the footnote on pp. 354–5 of Marshall (1961, I). The accounting textbook was ‘Matheson’s Depreciation of Factories and Their Valuation’) If Marshall did not recognise that fixed capital contributed to the marginal product of labour (MPAL), he would have had no need to show how an appropriate portion of the cost of the fixed capital should be deducted from the gross MPAL in order to calculate the fully net MPAL. This interpretation supports the view that Marshall’s concept of net marginal product of labour involves a deduction for the cost of additional units of variable factors that need to be employed along with the marginal unit of labour (i.e. ‘auxiliary on-costs’), but does not involve a deduction for the cost of the factors that are not varied, even though those non-varied factors continue to make a causal contribution to the marginal product. When Marshall used ‘net’ in this context he clearly meant partially net, not fully net.

Appendix C Wicksteed’s recantation Wicksteed later appears to have either retracted or modified his proof of the adding-up theorem. The retraction or modification may have been influenced by criticisms from Pareto and Edgeworth. In reviewing Pareto’s Manual of Political Economy (1906) in the Economic Journal of 1906, Wicksteed praised Pareto for stressing the interdependence of phenomena: Pareto, more, I suppose, than any other economist, has taught us to realise and keep in view the fact that the marginal significance of any object of desire is, as a general rule, a function not only of the quantity we possess of that object itself, but also of the quantity we possess of many, perhaps of all, other objects of desire.1 He also praised Pareto for his insistence on ‘synthesis’ as well as ‘analysis’: [I]f we separate out any phenomenon A for examination, and pursue our speculations to a point at all remote from any given concrete position, we must at once check our results by examining the corresponding changes in B, C, D, &c., which will probably accompany it; or, in his own terminology, we must never carry our analysis far without checking it by synthesis. (Wicksteed 1906, 554) But in a footnote to the latter statement, Wicksteed acknowledged and accepted criticisms that Pareto (and Edgeworth) had previously made of his Co-ordination: By the direct application of this principle Prof. Pareto exposed (in his Cours and in his Anwendungen der Mathematik auf Nationalökonomie) the fallaciousness of some of the reasoning in my own ‘Co-ordination of the Laws of Distribution.’ And it was by an implicit application of the same principle that Prof. Edgeworth performed the same task elsewhere. I should like to take this opportunity of acknowledging the justice of both their criticisms. (Wicksteed 1906, 554n.) This footnote acknowledgement by Wicksteed of Pareto’s criticism does not refer explicitly to Wicksteed’s proof of the adding-up theorem. The context of the footnote suggests that Wicksteed was here referring to Pareto’s concept

of synthesis – which is a more general criticism, not related specifically to the adding-up theorem. It seems likely that, if Wicksteed’s recantation or modification of his addingup proof was influenced by Pareto, it was influenced by Pareto’s argument,2 in the Manual (1906), that Euler’s theorem could not be used to prove the adding-up theorem because it involved the calculation of partial differentials; but partial differentials cannot be calculated if – as is the case with the MPTD – the variables are not independent. A further acknowledgement and acceptance by Wicksteed of criticisms from Pareto and Edgeworth occurred in a footnote in his Common Sense of Political Economy (1910). Wicksteed referred to paragraph 6 of his Coordination as ‘a premature attempt to solve the general problem of distribution’, adding that ‘Professors Edgeworth and Pareto subsequently shewed [sic] that the solution itself was erroneous’ and that paragraph 6 ‘must be regarded as formally withdrawn’ (Wicksteed [1910] 1933, I, 373n.).3 However, this acknowledgement and withdrawal by Wicksteed does not appear to have been a result of Pareto’s interdependence criticism. As Steedman has pointed out: It must be noted clearly, first that Wicksteed did not withdraw the work as a whole, but only its paragraph 6, and secondly that Wicksteed’s proof of the adding-up theorem under linear homogeneity and perfect competition is contained in paragraph 5. Paragraph 6, which he did declare to be withdrawn, concerns the extension of the result of paragraph 5 to the cases of imperfect product markets and of more than two inputs.4 Steedman adds (1987b, 917): ‘Wicksteed appeared to withdraw the sixth section’, but ‘there has been considerable discussion of just how that apparent withdrawal ought to be interpreted’. According to Steedman (1987a, 22), the view that Wicksteed’s recantation of the MPTD was merely verbal, and not a rejection of the substance of his earlier argument, is supported by the fact that Wicksteed continued to use marginal productivity theory in his Common Sense.5 Wicksteed argued in the Common Sense that when we have found the effect of ‘the withdrawal of a defined small amount of one factor, at the margin’, we have determined the ‘relative marginal efficiency of a unit’ of each factor, and we have ‘arrived at the principle on which they must share in the proceeds’ (Wicksteed [1910] 1933, 369). More formally he stated that ‘the proportions in which the various factors that combine in any one group are to share in the product is determined by their relative significance at the margins in increasing or

diminishing it’, and he concluded: ‘This gives us a complete theoretical solution of the problem of distribution.’ However, this conclusion falls a long way short of a clearly articulated marginal productivity theory of distribution. The Common Sense does not contain a formal proof of the adding-up theorem, and does not answer the objections of Pareto and Edgeworth. Robbins was of the view that Wicksteed had become dissatisfied with his proof of the adding-up theorem, and had in fact withdrawn it (Robbins 1930, 248; 1933, xi). However, Robbins believed that the grounds for Wicksteed’s dissatisfaction were ‘technical and mathematical’, and that ‘the criticisms which have been made by Pareto and others relate to the nature of the assumptions made rather than to the internal logic of the argument’ (Robbins 1930, 249). In Robbins’ view, Wicksteed did not renounce ‘the productivity analysis in general’; and the version presented in the Common Sense ‘does not differ so noticeably from that of the Essay as to suggest that the earlier version was to be regarded as wholly misleading’ (Robbins 1930, 249). According to Robbins, ‘Wicksteed’s proposition was not untrue; the only criticism to which it is exposed is that its demonstration was incomplete’.6 Robbins also noted that Wicksteed was still using the marginal productivity mathematics in his classes in 1905 – i.e. after the criticisms of Pareto and Edgeworth. He saw this as ‘strong presumptive evidence that Wicksteed did not regard these criticisms as invalidating the general marginal productivity theory and that his acknowledgement that the solution was ‘erroneous’ merely referred to the form in which the mathematical argument had been developed’.7 Stigler discounted this particular argument by Robbins by pointing out that Wicksteed’s first public retraction of the adding-up theorem did not occur until 1906. Stigler argued therefore that the fact that Wicksteed was teaching it in classes in 1905 is not relevant; and that it is conceivable that Wicksteed continued to present the mathematical arguments in classes in 1905, even though he had retracted them – following the example of J.S. Mill in not withdrawing the Wages Fund Theory from his Principles of Political Economy even after he appeared to have retracted it. Stigler nevertheless supported Robbins’ general view on Wicksteed’s recantation, arguing that the retraction was ‘merely verbal’. He based this interpretation on the view that Wicksteed ‘continued to retain the fundamental assumption, that the production function is homogeneous and linear’ (Stigler 1941, 332–3). Stigler believed he had found several items of textual evidence proving that Wicksteed retained the assumption, and that the strongest proof is to be found in the following statement in the chapter on

rent in the Common Sense: ‘The scale of 1260 quarts per 80 land-units under 60 hours’ cultivation is the scale of 630 quarts per 40 land-units under 30 hours’ cultivation,’ (Wicksteed 1910, II, 555). According to Stigler, ‘This is as explicit a statement that the production function is linear and homogeneous as could well be demanded’; and from this Stigler concluded: ‘there seems to be [no] doubt that Wicksteed retained his original theory.’8 However, Stigler’s interpretation of Wicksteed’s statement ‘The scale of 1260 quarts …’ could be questioned. Was it intended by Wicksteed as an assumption concerning the nature of the production function, or was it simply a statement of arithmetical proportionality? It is significant that the statement occurred in Wicksteed’s chapter on rent in the Common Sense and not in his chapter on distribution, and that he did not relate the statement to his chapter on the addingup theorem in his Co-ordination. However, even if the textual evidence supports the view that Wicksteed retained the notion that the production function is homogeneous and linear, was Stigler correct in concluding that Wicksteed’s recantation was ‘merely verbal’? As noted above, Edgeworth mocked the assumption that a homogeneous and linear production function is a characteristic of the real world, but Pareto’s objection was more fundamental. It questioned the integrity of the mathematical processes involved in the proof of the adding-up theorem, not merely the extent of its applicability to the real world. The retention or nonretention of a homogeneous and linear production function would not remove Pareto’s objection. The fact that Wicksteed acknowledged and did not rebut the criticisms of Edgeworth and Pareto suggests that his retraction of the MPTD was more than verbal.9 Having being persuaded that Wicksteed had not abandoned ‘the general marginal productivity theory’, Stigler was then faced with the task of explaining why Wicksteed ‘ever made a verbal abandonment of the thesis of the Co-ordination’. He was convinced that Wicksteed’s verbal abandonment was not due to ‘the cogency of his critics’ view’. It may have been due in a ‘small part’ to the ‘sheer weight of the prestige of Edgeworth and Pareto’, but the real reason, according to Stigler, was ‘the widespread confusion in Wickstseed’s theory of the laws of return’, and in particular Wicksteed’s ‘failure ever to subject the firm to analysis’ and hence his inability ‘to develop fully the implicit assumptions on which his argument rests’ (Stigler 1941, 334–5; emphasis in original). An alternative interpretation of Wicksteed’s alleged recantation has been given by Hutchison (1953). Whereas Robbins and Stigler believed either that Wicksteed did not recant or that his recantation was more verbal than real, it is Hutchison’s view that Wicksteed did in fact recant but did so

unnecessarily: ‘[Wicksteed] in the face of the not-very-well-conceived criticism of Edgeworth and Pareto, quite unnecessarily withdrew the central proposition of his [Co-ordination]’ (Hutchison 1953, 106). In a paper presented as the Presidential Address to Section F of the British Association in 1913,10 Wicksteed appears to have reaffirmed his belief in the MPTD – which he called the ‘differential’ theory of distribution – without referring to the adding-up theorem. If in 1913 he had in fact recanted his belief in the validity of the adding-up theorem, and if his recantation had not been merely verbal, then the Presidential Address would surely have been an appropriate occasion to announce the recantation. There is no such announcement, and the Address reaffirms the principle that factor rewards are proportionate to factor inputs. For example, he stated: ‘None of these heterogeneous factors [of production] can be dispensed with, and therefore the product in its totality is dependent upon the co-operation of each one severally’; and ‘their distributive share of the product depends … on the differential amount of their effect’ (Wicksteed 1914, 7, 17; emphasis in original). It seems therefore that in 1913 Wicksteed maintained his attachment to the MPTD and to the adding-up theorem. Also, in 1913, in a review of S.J. Chapman, Political Economy, Wicksteed did not criticise Chapman’s exposition of the MPTD, despite criticising other aspects of Chapman’s book. He quoted, without disapproval, Chapman’s statement: ‘the value of every other agent in production is the transmitted value of what it adds to production at the margin’, and in his own words stated that ‘all values of factors of production are derived from the value of their products’ (Wicksteed 1913, 73, 74), thus appearing to endorse the MPTD. However, evidence that by 1916 Wicksteed had withdrawn his proof of the adding-up theorem was published in 1964 in an article entitled ‘Wicksteed’s Recantation of the Marginal Productivity Theory’ by Joseph Dorfman. The article contains a letter written in 1916 by Wicksteed to J.M. Clark. In 1915 Clark had told Wicksteed that he (Clark) had worked out a geometric proof of the adding-up theorem (i.e. that the sum of the marginal products equals the total product) to which Wicksteed in 1916 replied: ‘I was and am extremely interested in your independent arrival at my old conclusion; and it would be interesting indeed if you were to rehabilitate it after I had abandoned it. But I fear it cannot be done’ (Dorfman 1964, 294–5). In this letter Wicksteed undermined the mathematical credibility of the MPTD. He did not merely say that he was unable to provide a mathematical solution to the adding-up problem; rather, he said ‘it cannot be done’. It would be interesting to know whether Stigler ever responded to Wicksteed’s 1916 letter published in Dorfman (1964).11

Despite Wicksteed’s assertion to the contrary, J.M. Clark apparently remained convinced that the adding-up problem could be proved, and that Wicksteed (and Flux) had proved it: [J.B. Clark] was correct in concluding that, under static conditions, the sum of the marginally-imputed shares would absorb the whole product; but it was left for other economists – Wicksteed and Flux – to produce a mathematically-satisfying demonstration and definition of the key condition necessary to this result. (J.M. Clark 1952, 611; quoted in Dorfman 1964, 294–5) Wicksteed would obviously have been aware of the attempted solution offered by Flux in 1894 (see below). Wicksteed’s blunt 1916 statement that ‘it cannot be done’ must therefore have referred to Flux’s solution as well as to his own, and to what is sometimes called the Wicksteed-Flux solution. But although Wicksteed’s recantation of the mathematical proof of the adding-up problem should logically have led him to a recantation of the MPTD itself, there is no explicit textual evidence that Wicksteed took that logical step.

Notes Introduction 1 An anonymous reader has noted that a more comprehensive study of the history of the MPTD could include other contributors, such as Jean-Baptiste Say, George Poulett Scrope and Thorstein Veblen. Say and Scrope did not have an MPTD as such, but they attempted, each in his own way, to present a theory of distribution that would counter the exploitative and redistributive implications of the labour theory of value; and Veblen, as mentioned below, was a critic of J.B. Clark. 1 Basic concepts 1 The term ‘factor’ (from the Latin ‘facere’, to make or do) implies a causal influence. If the ceteris paribus assumption is interpreted as removing the ongoing causal influence of the factor that is held constant, then, linguistically speaking, it is not logically legitimate to say that a factor is being held constant. If it is not exerting a causal influence, then it is not a factor. 2 It is argued below that, although the concept of the fully net MPAL can be clearly and unambiguously defined, the unambiguous measurement of the fully net MPAL is impossible and unknowable. In practice it can be measured only by applying arbitrary rules for the allocation of overheads. 2 Forerunners and founders 1 Black (1971, 14–15). Longfield ‘formulated a theory of profits as determined by the marginal productivity of physical capital and a theory of wages as determined by the specific productivity of the labourer’ (Black 1987, 237). 2 Black (1971, 15). More or less explicit statements of a productivity theory of distribution have also been attributed (Henry 1995, 47–51) to JeanBaptiste Say (1803), Samuel Bailey (1825), Samuel Read (1824) and Nassau William Senior (1836). 3 Although Butt may be eligible for entry into the neoclassical pantheon owing to his intimations of the MPTD, his strong advocacy of protectionism

for Ireland might make him unwelcome among proper neoclassicals (see Butt 1846). 4 Knight, for example, stated: ‘We find in Menger barely the germ of a theory of production, or of distribution’ (Knight 1950, 23). 5 Stigler added that Menger appears not to have known of Thünen’s work. 6 Stigler (1941, 153). One is tempted to ask how many inadequacies can a theory have, and how serious can the inadequacies be, before the theory ceases to be ‘essentially correct’. 7 Wieser ([1888] 1956, 74; emphasis in original). As examples of joint products Wieser referred to the stone-cutter who hews the block and the sculptor who chisels it; the rifle and the cartridge; and the artist and his materials (Wieser 1956, 72, 86). 8 However, Uhr (1960, 63) argued that Wieser’s definition of the productive contributions of the various factors referred to ‘not their marginal, but their total, productive contribution’. 9 1956, 89–90n. On this and other limitations to Wieser’s solutions, see Dobb (1973, 195–98). 10 i.e. as explained below under Marshall, the problem of distinguishing the gross marginal product and the net marginal product. 11 As argued above, ceteris paribus does not mean ceteris inefficacibus. 12 Uhr (1960, 64n), referring to a 1900 article (in Swedish) by Wicksell. 13 Letter to J.B. Clark, July 1900, cited in Whitaker (1975, I, 39). As Groenewegen (1995, 151, 180) has noted, Marshall in the first edition of his Principles said: ‘The term ‘marginal’ increment I borrowed from von Thünen’, but in the second and later editions this was altered to: ‘The term ‘marginal’ increment is in harmony with von Thünen’s methods of thought and was suggested to me by him, though he does not actually use it’ (Marshall 1961, 37). Groenewegen (1995, 151) argues that Marshall’s acknowledgements of his indebtedness to Thünen were ‘extravagant’. 14 Stigler (1941, 344). Groenewegen (1995, 186) argues that this statement by Stigler ‘is quite generous to the Marshalls and ignores Jevons’s contributions to the subject in Theory of Political Economy’. 15 Marshall (1961, II, 583). For variations on these statements in other editions of the Principles, see Marshall (1961, II, 583–8). The phrase ‘due to’

implies a monocausal and proprietorial relationship between the marginal product and the marginal labourer, and implicitly rejects any causal influence of the non-variable factors, even if that was not the intention. 16 Stigler (1941, 356). As noted below, in a 1916 letter to J.M. Clark, published in 1964, Wicksteed appears to recant the adding-up theorem, saying ‘it cannot be done’. 17 The term used by Marshall was ‘marginal net product’, but to facilitate discussion of the distinction between fully net and partially net (see below), it has been more convenient to alter this to ‘net marginal product’. Whitaker (1988, 129) notes that Marshall sometimes used ‘marginal efficiency’ or ‘marginal net efficiency’ instead of ‘net product’. 18 Marshall (1949, 337; 1961, I, 406; emphasis in original). See also Marshall (1961, II, 582): The net product of a machine is the value of the work that it does, after deductions have been made for expenses of working it, among which are included the earnings of management. And, in like manner, the net product of a man’s labour is the value of the produce which he takes part in producing after deducting all the other expenses of producing it. This passage occurred in the first edition of the Principles. In the second edition, Marshall referred to the ‘(gross) earnings of management’. 19 In a ‘Mathematical Appendix’ Marshall noted a further difficulty in interpreting the phrase ‘net product’ of an agent of production. If a producer (in Marshall’s example, a builder of villas) increases the supply of the product, the price of the product might fall, to an extent that depends on the elasticity of demand. To calculate the ‘net product’, it is not sufficient therefore to consider only the revenue from the sale of the extra produce; it is also necessary to allow for the reduced revenue from the sale of the previous units of production, owing to the reduced price per unit. It is possible for total receipts to diminish. However, he argued that this complication could be ignored when ‘studying the action of an individual undertaken with a view of illustrating the normal action of the causes which govern the general demand for the several agents of production’; and that for the purpose of ‘illustrating a part of the general action of the law of distribution we are justified in speaking of the value of the net product of the marginal work of any agent of production as the amount of that net product taken at the normal selling price of the product’ (Marshall 1961, I, 849–50). 20 The textual evidence is reviewed in Appendix B.

21 This argument is applicable to the short term when factors such as capital equipment are assumed to be fixed, as well as to the long term when capital equipment is variable. In discussing the marginal product and marginal cost of labour, Marshall appears not to have taken account of the cost of capital equipment in the short term. The argument would also be applicable whether an investment decision or a production decision is being considered. 22 Whitaker (1974, 6) provides an alternative view of Marshall’s reluctance: ‘The reluctance to be more explicit about marginal productivity might have resulted from Marshall’s desire for simple exposition, or his mistrust of pushing the logic too far.’ But Whitaker adds: ‘By the later-1880s Marshall was certainly equating factor prices to the partial derivatives of production functions … so that his full development of the demand side of his distribution theory can probably be dated at the mid-1880s.’ 23 Supply-side considerations would include not only the quantity and quality of potential employees but also any factors that affect their eagerness to work, their bargaining power and their current economic status, which will in turn be affected by historical, social and institutional factors such as inheritance, educational opportunities, property rights in land and other natural resources, power structures, bargaining strengths, and the laws relating to the activities of trade unions. 24 This would appear to be an implicit recognition of the ‘false separatism’ objection later raised by Hobson. If the individual’s net product cannot be separated mechanically, how can its value be separated? In a footnote on p. 447 Marshall noted that in the official Census of Production the net product of a factory is taken as ‘the excess of the gross value of its output over the value of the materials used by it’, but he did not explicitly relate this to the definition of the net product of an individual labourer. 25 On the other hand, it may be argued that a bargaining power solution is in fact a determinate solution to the problem of distribution, in the sense that distribution is determined not according to a theory or law, but as an outcome of the interplay of market forces. This circularity argument is discussed in more detail below, when the views of Joan Robinson and some of her critics are considered. 26 In quoting this, Steedman (1992, 17–18) notes that ‘Wicksteed goes out of his way, in fact, to urge the banal obviousness of the claims that a firm will pay each factor no more than its marginal (value) product and that no factor need accept less’. 27 Wicksteed ([1894] 1932, 46). As Steedman (1987a, 22) has stated, if the reward of entrepreneurship is regarded as a residual profit, there is no adding-

up problem; the problem arises ‘only when every form of income is related to the marginal product of some input’ (emphasis in original). 28 Stigler (1941, 320–4). Steedman (1987a, 21) also recognises that it was Wicksteed in Co-ordination who ‘first clearly stated, and attempted to resolve’ the adding-up problem. Although Stigler lavishly praised Wicksteed’s Co-ordination as ‘magnificent’, he was apparently not so impressed with the quality of Wicksteed’s actual proof, describing it as ‘a very complex set of symbols and six pages of clumsy and involved mathematics’ (Stigler 1941, 328). In his vindication of the adding-up theorem, Stigler preferred to use the proof (employing Euler’s theorem) provided by A.W. Flux in his review (1894a) of Wicksteed’s Co-ordination (see below, under Flux). Stigler said (1941, 326n) that Wicksteed did not refer to Euler, and that Flux was the first to associate the adding-up theorem with Euler. 29 Letter to Flux, 2 July 1894; cited in Steedman (1992, 13). As Steedman notes, Wicksteed had received lessons in differential calculus from Mr John Bridge, a mathematics tutor at University College, London, but it seems that Bridge had not instructed Wicksteed on homogeneous functions and Euler’s theorem, and that Wicksteed had never heard of Euler’s theorem before reading Flux’s review. As noted above, Wicksteed may have retracted his proof of the adding-up theorem. See below, Appendix C. 30 A group consisting of Shaw, Wicksteed, Foxwell, Edgeworth and others had met fortnightly since 1885 at the home of Henry R. Beeton, a stockbroker, to discuss economic questions. The Economic Club developed out of this group (note by Dan H. Laurence in Shaw 1965, I, 235). The group later developed into the British Economic Association and then into the Royal Economic Society (Steedman 1987, 916). 31 Shaw (1996, 58–9). At first, Shaw appears to have been favourably disposed towards Wicksteed and the MPTD, but in a letter of 21 January 1890 to Graham Wallas, Shaw made a flippant and disparaging comment on Wicksteed’s marginal productivity theory. Referring to a recent meeting at the home of Henry Beeton, Shaw wrote: At Beeton’s Wicksteed turned up. He had been working out the fact that if a man undertakes productive operations which require a great many tools, they will not be productive at all if he has not tools enough. With a few simple curves he managed to extract from this position a degree of mental confusion that bids fair to last us the whole season. Despite these uncomplimentary words, Shaw appears to have retained his high regard for Wicksteed. Brian Tyson notes that in 1904 Shaw called

Wicksteed ‘my master in economics’ (Shaw 1996, 63). But in 1928, in raising the disentanglement objection, Shaw appears to have distanced himself from Wicksteed and the MPTD. He argued that to reward each factor according to what ‘she’ produces (Shaw was writing for intelligent women) would be a desirable goal, but that it is impossible to identify the specific contributions of the factors: ‘When a farmer and his laborers sow and reap a field of wheat nobody on earth can say how much of the wheat each of them has grown’ (Shaw [1928] 1929, 21). 32 Steedman (1992, 42). Groenewegen (1990, 30) supports Steedman’s view, and refers to the ‘scientific probity’ that characterised Wicksteed’s critique of Marx. 33 For example, G.L.S. Shackle, while fully agreeing that it is profitable to employ labour up to the point where wages and the value of the marginal product of labour are equal, nevertheless admitted that the adding-up problem is ‘still lacking a tidy and complete solution after nearly seventy years’ (1959, 115). 34 Steedman (1992, 30) describes it as a ‘memorable, if unfair, quip’. 35 Further objections to the use of Euler’s theorem in the attempted proof of the addingup theorem are presented below – notably, Pareto’s interdependence argument. 36 Stigler (1941, 331) stated that ‘Euler’s theorem holds rigorously only if the price of the commodity remains constant’. It should also be said that the theorem is applicable to the MPTD only if the output remains constant. 37 Schultz (1932, 292) argued, in defending Pareto against Hicks, that ‘Statics should not be confused with dynamics. The marginal productivity theory is part of a statical theory of equilibrium.’ The proposition being advanced in this study is that the MPTD is essentially a dynamic theory, not a static theory, because changes to the variable factors do not occur simultaneously. If they occurred simultaneously, there could be no ceteris paribus assumption. 38 The use of Euler’s theorem to solve the adding-up problem in the MPTD would thus appear to be an instance of what Joan Robinson described as ‘the neglect of historic time in the static equilibrium theory of the neoclassics’ (Robinson 1973b, xii). 39 The ceteris paribus assumption thus plays a contradictory role in attempts to provide a mathematical proof of the MPTD by the use of partial differentiation. It enables partial differentiation of the production function –

because it removes, by assumption, Pareto’s interdependence objection that would render partial differentiation illegitimate. But it also means that the changes in the variables occur sequentially, not simultaneously – as one factor changes, the others are assumed to remain constant – which means that the total product (P) does not remain constant (as required in the WicksteedFlux solution) as the variations occur. The ceteris paribus assumption therefore nullifies the Euler theorem solution of the adding-up theorem, because Euler’s theorem applies to a situation where changes to the variables occur simultaneously. As already noted, if the adding-up theorem cannot be proved, the MPTD must be false. 40 Tarascio (1973, 401) has noted that Walras recognised Pareto as a discoverer of the MPTD, even though Walras ‘was not on particularly friendly terms with Pareto’. Walras regarded Barone as another co-discoverer (Tarascio 1967, 140). On Barone and Montemartini, and their relationship with Pareto, see Stigler (1941, 356–64). 41 ‘Pareto’s role in the development of the marginal productivity theory has been obscured by those who focused attention on his later critique of the theory’ (Tarascio 1973, 401). 42 Unless this condition prevails, it is mathematically impossible to calculate partial differentials – because calculation of partial differentials requires that one factor changes while the others remain constant. If the factors are necessarily combined in fixed proportions, this ceteris paribus assumption cannot be made; when one factor changes, the other factor or factors must change also. If the variability of factor proportions is not commonly possible in the real world, then the situations in which the MPTD is capable of practical application are limited. If two factors A and B must be combined in fixed proportions, then, in calculating marginal cost, A and B must be considered as a combined dose of a single factor, (A + B). The problem then is to disentangle the specific productive contributions of A and B, and to determine an appropriate level of reward for each. 43 It has been argued that Stigler’s objection to fixed factor proportions and fixed coefficient production functions was induced by his ‘enthusiasm for neoclassical distribution theory’ and a desire ‘to discredit the view that industrial prices were set by adding standard markups to prime costs’ (Yordon 1992, 465). I am grateful to Fred Lee for drawing my attention to this article. 44 If factor proportions cannot be varied, partial differentials cannot be calculated, and therefore Euler’s theorem cannot be used to solve the addingup problem.

45 The assumption of constant returns to scale (i.e. the assumption that the production function is linear and homogeneous) is essential if Euler’s theorem is to be used to solve the adding-up theorem. 46 This interdependence argument is broader, and more serious, than the fixed factor proportions argument. Demands for the different factors of production can be interdependent, even though the proportions in which the factors are used are not strictly fixed by technical considerations. 47 Pareto (1902, 91–2): ‘We believe that he goes too far here and that this simplification distances us too far from reality.’ 48 Pareto (1902, 90, 92): ‘If we thus signal some small faults of the work [by Aupetit], it is precisely because we do not find any great ones.’ 49 Schultz (1932, 294). Schultz was disturbed not only by the content of Hicks’ criticisms of Pareto but also by the personal tone of those criticisms. According to Hicks, Pareto claimed that ‘he had found in his equations the one perfect method of economic analysis, besides whose results all the doctrines of ‘literary economists’ were mere fragments of knowledge’. Hicks described this as ‘a great claim’ and said: ‘to hope that from any single line of approach, all the facets of economic life would be equally illumined, was probably to indulge in a vain illusion.’ With a touch of sharp irony, he added that Pareto’s ‘arrogance’ was ‘one of his more pleasing characteristics’ (Hicks 1932b, 84; quoted in Schultz 1932, 295). 50 Pareto (1971, 444, 466; emphasis in original). Pareto did not explicitly present this argument in the context of his criticisms of the MPTD, but it has an obvious application to the MPTD. Stigler, in his comments on Pareto and the MPTD, did not address this criticism. Oskar Lange noted the problem of ‘proper aggregation’ in his example of the difficulty of measuring in practice the price of rye in Poland in 1959. The price will vary in different parts of the country and at different times of the year and for different kinds of rye. A single aggregate for the price of rye in Poland in 1959 requires the practical identification and combination of these differences. As Lange noted, ‘Reality is much richer than the economic category ‘the price of rye’’ (Lange 1963, 122–3). However, in general, the literature seems to have been more concerned with treating the MPTD as a theorem of pure mathematics than with calculating real-world numbers for the coefficients. (I am grateful to an anonymous reader for this reference to Lange.) 51 Stigler (1941, 369–70). Cf. Tarascio (1967, 141): ‘Walras’ refusal to recognize Wicksteed’s role [in developing the MPTD] was perhaps unwarranted.’

52 Barone’s proof appeared in the Giornale degli Economisti (1896). It had not been published when Walras wrote this 1895 postscript to his ‘Note’. Walras claimed that Barone’s proof had been deduced from his (Walras’) theory. 53 Schultz (1929, 508 n.516) argued that although several other economists – American, English and Italian – broached the theory of marginal productivity at the same time as Walras, ‘only Barone and Walras and (especially) Pareto succeeded in developing a rational, mathematical theory and in relating it to the general pricing process’. See under ‘Pareto’ below for Pareto’s criticisms of Walras’ marginal productivity theory, and for Walras’ response to Pareto’s criticism. 54 On Walras’ reason for the omission, see his letter to Wicksell, in Gårdlund (1958, 338–9), cited below under ‘Wicksell’. 55 Jaffé, in Walras (1954a, 9). For further details on Walras’ note on Wicksteed, see Walras 1954a, 386, 604–6, 610. 56 Pareto (1901; quoted by Schultz 1929, 547–8). Translated in Stigler (1941, 365–6) as: ‘In these theories quantities are treated as independent variables, which are not independent, and the equations which are written in order to determine the minimum costs are not admissible.’ 57 Letter published in Schultz (1929, 547–9), by courtesy of Professor Etienne Antonelli. 58 Schumpeter described Walras’ use of a system of equations for defining equilibrium as ‘the Magna Carta of economic theory’ (1954, 242). 59 Carl Uhr, in his Economic Doctrines of Knut Wicksell (1960), noted that Stigler had developed in an explicit way some aspects that Wicksell had left implicit, and described Stigler’s developments as ‘elegant’ (Uhr 1960, 70). See Uhr (1960, 62–76, 147–157) for a detailed account of Wicksell’s mathematics. 60 On several occasions Stigler claimed to have found support for the MPTD in writers who were unaware of it, or who were reluctant to admit it, or who had rejected it. As well as claiming that Wicksell had developed the MPTD in Value, Capital and Rent in 1893, even though Wicksell himself was unaware of it, Stigler, as we have seen, claimed that Marshall gave outright acceptance of the MPTD, even though Marshall never admitted it; and also claimed that Wicksteed retained his proof of the adding-up theorem, even though in 1916 Wicksteed said ‘it cannot be done’.

61 [1893] 1970, 25. Although Wicksell did not say so explicitly, the use of the verb ‘belongs’ implies a proprietorial and monocausal relationship between wages and the MPAL. 62 Wicksell ([1893] 1970, 141–2). The MPTD was treated in Value, Capital and Rent in the context of Böhm-Bawerk’s views on the relation between a lengthening of the period of production and the return on capital. Wicksell derived formulas to show what production period will maximise wages if the rate of interest is given; and to show what production period will maximize the rate of interest if the level of wages is given. 63 Wicksell attributed the law to Malthus and Thünen but, as noted above, it is doubtful whether Malthus had conceived of a marginal productivity theory. 64 In this article in 1900 Wicksell applied the MPTD only to labour, excluding the ‘landowner-employer’, but, as noted below, in his Lectures on Political Economy in 1901, he excluded only capital. 65 In his article in 1900 he defined ‘capital’ – presumably referring to aggregate capital – as ‘a single coherent mass of stored-up labour and storedup land, accumulated over the years ([1900] 1958a, 108). The inclusion of ‘stored-up labour’ and ‘stored-up land’ in the definition of capital is somewhat unusual. 66 This problem of the measurement of capital (and hence, the applicability of the MPTD to capital) became a prominent feature of debates on the MPTD. See, for example, Sraffa, Kaldor and Joan Robinson below. 67 Cited in Harcourt (1972, 16; King 2002, 80; emphasis in original). 68 He noted that some investments – for example, houses, roads, and certain soil improvements – can continue to contribute their productive power for centuries (1958a, 117). 69 G.L.S. Shackle (1970, 6), for example, said that a proof of the adding-up theorem is ‘at least implicit’ in Value, Capital and Rent. 70 The scale of production would be ‘immaterial’ in the sense that it would not affect the rate of return; but it would not be immaterial to the amount of the return. The same rate of return applied to a larger scale of production would result in a larger amount of return. 71 In Gårdlund (1958, 335). A free translation would be: I am pleased to see that you have suppressed the note concerning Wicksteed. In effect Barone’s criticisms that you presented in the note did not appear to me to be quite fair.

The restriction of the marginal productivity theorem to cases where total production is a linear homogeneous function of the factors of production (land, labour) which Wicksteed introduced and which appeared to Barone to be so superfluous, is in reality nothing more than your own assumption of free competition between entrepreneurs, because obviously that competition can occur only on condition that small-scale production is proportionally as lucrative as large-scale, which is precisely the meaning of Wicksteed’s restriction. 72 In Gårdlund (1958, 338–9). The date given in Gårdlund for Walras’ letter is ‘29bre 1900’, which would seem to be iorrect, as Wicksell’s letter, to which Walras was obviously replying, is given a date of ‘28.X.00’. A free translation would be: Your observation on marginal productivities merits serious examination. I am not getting involved in this controversy, for the same reason that I withdrew the note on Wicksteed: Having not made an indepth study of the question, I prefer to limit myself to referring to it, as it is outside my theory. 73 See above under ‘Flux’ for the role played by the assumption of constant returns in the Wicksteed-Flux solution. 74 The assumption that average costs are constant is less restrictive and more general than the assumption that the production function is linear and homogeneous, i.e. the assumption of constant returns to scale. A firm that has constant returns to scale will have constant average costs, but a firm can have constant average costs without having constant returns to scale. The distinction between ‘constant returns to scale’ and ‘constant (average) costs’ is not always made clear in the literature. 75 The firm ‘at this maximum … may therefore be regarded momentarily as being subject to constant returns’ (Wicksell 1958b, 123; emphasis in original). The expression ‘constant returns’ would here appear to mean constant average costs, rather than constant returns to scale, under which a given percentage increase in all the factors leads to the same percentage increase in the product. 76 In saying that wage costs increase from aw to (a+1)w when the number of workers increases by one man, Wicksell was in effect saying that the firm is operating in a position of constant average costs. An increase in wage costs from aw to (a+1)w means that the extra worker is receiving the average wage (w) (i.e. that the marginal wage equals the average wage), which of course means that the average wage is constant. 77 The steps in his algebraic proof were presumably the following. If k′ is the average cost after the employment of the extra unit of labour, then

k′ = [(a+1)w + br] / (Q + qa) and the firm will be operating at constant costs when k′ = k; i.e. when [(a+1)w + br] / (Q + qa) = (aw + br) / Q from which it follows that w/qa = (aw + br)/Q = k. Thus, when k is constant, i.e. when k′ = k, w/qa = k. when k is increasing, i.e. when k′ > k, w/qa > k when k is decreasing, i.e. when k′ < k, w/qa < k 78 If they occurred simultaneously, one could not be held constant while the other changed. There could be no ceteris paribus assumption. 79 This and the next quotation from Webb (1888) are reprinted in Webb and Webb ([1898] [1902] 1972). 80 The introduction (by T. Wilson) to the 1964 collection of papers read to Section F of the British Association for the Advancement of Science referred to the ‘analytical difficulties’ evident in Webb’s paper (Smyth 1964, 11). Webb’s paper was presented at the meeting of the British Association at Newcastle in 1889. Smyth (1964, 65) stated that the paper was previously unpublished and that it has been reproduced from notes in the British Library of Political and Economic Science. 81 Webb (1887–8, 190), citing Sidgwick, Principles of Political Economy, Book ii, ch. vi. 82 As Henry (1994, 73) notes, J.B. Clark’s Distribution of Wealth ‘leaves little doubt that the new theory is politically significant’. 83 J.B. Clark has been described as the ‘marginalist Locke’ (Ellerman 1992, 257). There are of course other theories of property rights – such as Karl Marx’s ‘from each according to his ability, to each according to his needs’; or

Henry George’s ‘equal rights to natural resources’; or J-J. Rousseau’s social contract theory. This paper is restricted to a discussion of the Lockean or contributor theory, as that is the theory that underlies the arguments of J.B. Clark and pervades most subsequent discussions of the MPTD. 84 J.B. Clark (1892–3, 263). He described this extra labour as ‘virtually unaided labor’, an expression that seems to contradict the statement earlier on the same page: ‘None of our material comforts are brought into existence by the unaided efforts of laborers’ (1892–3, 263). 85 In fact, a refutation of J.B. Clark’s belief in disentanglement had been implicitly provided by J.S. Mill: When two conditions are equally necessary for producing the effect at all, it is unmeaning to say that so much of it is produced by one and so much by the other; it is like attempting to decide which half of a pair of scissors has most to do in the act of cutting; or which of the factors, five and six, contributes most to the production of thirty. (Mill [1848] 1909, 26) 86 The inclusion in economic models of the equilibrium condition ‘wage = MPAL’, where the right-hand magnitude is defined as the increase in total product that occurs when the marginal unit of labour is employed, or as the first partial derivative of the total product with respect to labour, is therefore logically indefensible and must undermine the credibility of all such models. 87 Henry (1995, 87) argues that a further limiting feature of J.B. Clark’s version of the MPTD is that he ‘supplied no proof of the necessary ‘product exhaustion’ theorem, nor specified that linear homogeneous production functions were necessary for his argument to hold’. 88 At the same meeting of the American Economic Association a paper entitled ‘The theory of wages’ was presented by Stuart Wood, and was published in the same issue of the Publications (Vol. 4, 1889, 5–35). Stigler (1947) claimed that Wood was ‘one of the independent discoverers of the marginal productivity theory’, and described this claim as ‘substantial’ (1947, 640). The claim has subsequently been repeated in some histories of economic thought. For example, Schumpeter (1954, 941) stated that the ‘marginal productivity theory, in a very advanced version … sprang readymade from the brain of Stuart Wood’, and acknowledged that Stigler had done justice, ‘but not more than justice’, to Stuart Wood’s performance. Gordon (1973, 32) also praised Wood’s contribution, stating that Wood ‘worked out the essentials of the marginal productivity theory as a unified theory of distribution’, and adding that ‘little attention was paid to him by

established economists – Marshall made only one inconsequential reference to him in his Principles and J.B. Clark did not notice him at all in his Distribution of Wealth’. However, the claim that Stuart Wood was a discoverer of the MPTD is questionable. The only statement made by Wood in ‘The theory of wages’ (or in other publications – see Wood 1888–9, 1891) that could be related to the MPTD is the following: ‘the relative final utilities of labor and of capital fix their relative prices’ (Wood 1889, 14: cited in Stigler 1947, 644). In citing this passage, Stigler interpolated in square brackets after ‘relative final utilities’ the expression ‘[marginal productivities]’. But his justification for suggesting that when Wood said ‘final utilities’ he meant ‘marginal productivities’ is, to say the least, rather tenuous. Wood did not use the expression ‘marginal productivity’ and gave no indication that he conceived of ‘final utility’ as the change in total output which follows the application of an additional unit of a variable factor. It would seem that Wood was merely applying the marginal utility analysis of Jevons, rather than the marginal productivity analysis of Thünen, Wieser, Wicksteed and J.B Clark. If Wood had discovered the MPTD in 1888, or even been aware of it, why did he not mention it in ‘A critique of wages theories’ (1891)? That article, not mentioned by Stigler, traced the history of the theory of wages from Ricardo to Thornton, and dealt with the development and downfall of the wages fund theory. Wood concluded that ‘No new doctrine has replaced the abandoned theory, or obtained the same general assent of scholars or of laymen’ (Wood 1891, 461). This suggests that in 1891 Wood was neither a discoverer nor a proponent of the MPTD. Furthermore, the following statement in another publication by Wood – a statement not cited in Stigler (1947) – could be interpreted as supporting the interdependence objection raised by Pareto, Hobson, Davenport, Adriance, and so on: ‘rates of interest and of wages are mutually dependent, and neither can be definitely ascertained without at the same time ascertaining the other’ (Wood 1888–9, 74). On the basis of this statement, it could be claimed that Wood was a precursor of the circularity objection raised by Joan Robinson and other critics of the MPTD in the Cambridge capital theory controversy rather than an independent discoverer of the MPTD. 89 In a ‘Supplementary Note’ to the 1889 paper, J.B. Clark referred to ‘nolabor capital’ (67) or ‘unaided capital’ (68), i.e. capital that ‘is obliged to create its product virtually without aid from the human part of the working organism’ (67). He also argued that the reasoning used to prove that rent does not enter into the price of commodities may also be used to prove that wages are not an element of price (64–7). If land is used up to the point where the marginal land does not earn a rent, then for the same reason labour would be used up to the point where the marginal unit of labour does not earn a wage. He applied the same logic to interest: ‘If rent is not a price making element then interest is not so’ (1889, 65).

90 J.B. Clark (1890–1, 308). He added: ‘There is no particular man who is the last to arrive in point of time, but any one may become the final man by giving up his work for a few days and then applying for it again.’ 91 J.B. Clark (1890–1, 313); quoted by Bhaduri and Robinson (1980, 105), who were of the opinion that Clark ‘vulgarised’ Marshall’s theory of distribution. 92 J.B. Clark (1892–3, 263). He described this extra labour as ‘virtually unaided labor’, an expression that seems to contradict the statement earlier on the same page: ‘None of our material comforts are brought into existence by the unaided efforts of laborers.’ 3 Followers and critics, 1900 to 1920: from Hobson to Adriance 1 Hobson’s use of ‘attend’, rather than ‘caused by’ or ‘owing to’ is a significant linguistic recognition of the multicausality of the marginal product. It divorces causality from correlation. 2 Hobson (1972, 147). In a review of this work, J. Laurence Laughlin said, ‘There is no doubt about this general truth’ (1903–4: 318). 3 Edgeworth (1904, 167n). In the September 1904 issue of the Journal of Political Economy, Hobson replied: ‘Professor Edgeworth, in the Quarterly Journal of Economics (January 1904) appears to think the differential calculus will assist him to find the productivity of the marginal shepherd by starting from the productivity of an infinitesimal margin of him.’ 4 Hobson here is assuming that, when the nine shepherds are employed, the land and capital are fully employed; that there is no surplus carrying capacity; and that the addition of the extra tenth shepherd and his sheep will result in proportionately less nutriment for the sheep of the previous nine shepherds. Such circumstances would appear to preclude the possibility of any ‘addition in the productivity of the business’. 5 The confusion generated by this 1903–4 article was not attenuated by Carver’s reply (1904–5) – see below under ‘Carver’ – or Hobson’s rejoinder (1904–5), and did little to advance the persuasiveness of Hobson’s critique of the MPTD. 6 As the following statement by C.J. Bliss suggests, the use of differential calculus is merely ‘the hat on the head’ of the MPTD. With reference to

situations where calculus cannot be used because production functions are not differentiable, Bliss remarked: Anyone who believes that our ‘theory of income distribution’ in equilibrium, such as it is, is destroyed when marginal concepts are taken from it is in the same confused state as a man who would be who bemoaned the beheading of a friend who had done no more than remove his hat. (Bliss 1975, 99–100) Calculus is of course essential in the attempt to prove the validity of the adding-up theorem by the use of Euler’s theorem. 7 See, for example, the definition of the MPTD in Blaug (1968, 432) cited below. 8 Tendentious, but not obviously incorrect. Hobson could have expressed himself more clearly. 9 Hobson (1969, 115). Hobson’s use of an arithmetical example (1969, 110) to support his criticism of the MPTD was criticised by Marshall because the numbers chosen by Hobson were inappropriate. However, as Schneider (1996, 53–6) has shown, an appropriate set of numbers can be devised. For a detailed analysis of Hobson’s criticism of the MPTD, see Schneider (1996, Ch. 3, ‘Income distribution and price’, 38–57). 10 I am grateful to Greg Smith for drawing my attention to this chapter. 11 Hobson (1910, 304). Hobson’s position on disentanglement appears to have been later given some recognition from Schumpeter when he described the problem of isolating the contribution of each factor to the final product as ‘a real and non-trivial difficulty’ (Schumpeter 1954, 914). 12 Hobson (1969, 136). On the legitimacy of the current distribution of property rights in productive resources, see also Chapter 9 (this volume). 13 Hobson (1968, 174–5). Hobson’s criticism of the ‘false separatism’ of the MPTD was taken up by a number of contemporaries. Frank Albert Fetter, for example, in his Principles of Economics (1904), rejected the idea that particular portions of the product could be imputed to particular agents: ‘There is no such thing as a separate determinable physical productivity that is due to labour’ (I, 210). He concluded that the absence of a causal nexus between the marginal product and the marginal unit of the variable factor means that, on a Lockean or contributor theory of property rights as used by

J.B. Clark, the MPTD ceases to provide a moral justification for the existing pattern of distribution. 14 He later cited Veblen’s definition of a ‘vested interest’ as ‘the legitimate right to get something for nothing’ (Hobson 1926, 146). 15 Carver (1901, 581). It is interesting to note that, for Carver, the MPTD was a theorem that is concerned with causes, and that it succeeded, by the ‘method of difference’, in establishing causal connections. Later supporters of the MPTD, equally enthusiastic in their support, and using the same method, denied the causative nature of the MPTD. 16 Carver (1901, 581). Critics of the MPTD would no doubt have welcomed the millstones metaphor as support for their anti-disentanglement position. 17 Carver (1904, 164–5). No consideration is given here to the difficulty of distinguishing ‘the amount which it can add’ from the amount causally attributable to the fixed factors. 18 Carver (1904, 263). Edgeworth appears to have had some reservations about the applicability of the MPTD to the remuneration of managers. Referring to the above quotation from Carver (1904), Edgeworth said: ‘we could have wished that the author had been more explicit; but we do not feel disposed to be so ourselves at present’ (Edgeworth [1904] 1970, 145). 19 Edgeworth (1904, 167). The phrase ‘produced by the last increment of a factor’ suggests a monocausal relationship between the marginal unit of a factor and the marginal product. 20 See Edgeworth (1904, 182), cited above, where he said, referring to the WicksteedFlux attempt to prove the adding-up theorem by making use of the assumption of a homogeneous function: ‘There is a magnificence in this generalisation which recalls the youth of philosophy.’ 21 Edgeworth (1925, 249). Earlier, Edgeworth had said ([1925] 1970, 75–6): ‘I do not hold with the writers who attach a mighty importance to the question whether, if all the factors are increased in a certain proportion, say α:1 (where α is greater than 1), the product is or is not increased in that proportion’. The passage in which this statement occurred was described by Stigler (1941, 343) as ‘most ambiguous’. In my opinion, however, Edgeworth’s statement is not at all ambiguous. It clearly reiterates Edgeworth’s view that the assumption of a homogeneous production function is quite unrealistic. This unambiguous view is unacceptable to those who base the proof of the adding-up theorem on the homogeneity assumption.

22 The MPTD is also inconsistent with J.M. Clark’s observation that under adverse circumstances a firm will pay its labour less than its immediate marginal product, because it needs to pay the interest on its bonds ‘out of the marginal products of its variable factor of production’ and thus ‘protect its overhead’ (J.M. Clark 1923, 469). 23 Edgeworth (1925, 251). Stigler noted (1941, 342, n.3) another statement by Edgeworth which, although in this case admittedly ambiguous, seems to deny that the sum of the marginal products times the factors will exhaust the total product. 24 As noted above, Edgeworth expressed similar reservations on this point in his review of T.N. Carver, The Distribution of Wealth (1904). 25 Stigler (1941, 344). However, Stigler had to admit that Edgeworth’s marginal productivity theory was ‘not amplified’ (1941, 131–3). 26 Chapman (1904–14, II, 14). A slightly different definition was given in Chapman (1904–14, III, 8): ‘Distribution should be proportional to the contribution which each person makes to the value of the product.’ 27 Chapman (1904–14, II, 20). If capital receives some portion of the product created by labour, then the internal consistency of the MPTD is thrown into question, because it would no longer be true that wages would be equal to the product of the marginal labourer. 28 He applied this idea to land also: ‘labor is the essential agent in production, and neither land nor capital produces anything’, but he added: ‘The doctrine that labor is the one essential agent in production is, of course, very different from the doctrine that labor is entitled to the whole product’ (Taussig 1910, 143, 144). 29 Taussig (1910, 138). As noted below, this circularity objection was later discussed in detail by Joan Robinson and others. 30 Despite his significant contribution to the history of the MPTD, Adriance does not appear in standard histories of economics. The following information, kindly supplied by Rosalba D. Varallo, Special Collections Assistant, Seeley G. Mudd Manuscript Library, Princeton University, may therefore be of interest. Adriance graduated (A.B. 1900, A.M. 1903) from Yale University, and taught finance and economics at Princeton University from 1907, as preceptor, lecturer and assistant professor. During World War I, on leave from the University, he served as Director of the Bureau of Research of the War Trade Board and was commissioned as a Major in the Statistics Division of the Army General Staff. After the war, he worked for the

Guaranty Trust Company of New York as head of the investment training programme – there is a photograph in The Guaranty News (Vol. VIII, No. 7, 1919) – and later for an investment counsel firm. I am also grateful to Rosalba Varallo for biographical information on Richard A. Lester (see below), Professor of Economics at Princeton University and later Dean of the Faculty in the Graduate Program at the Woodrow Wilson School of Public and International Affairs. 31 Although (as noted above) Adriance in principle supported Hobson on disentanglement, he criticised Hobson for saying that when the employment of an extra fisherman yields an extra catch, the extra catch is attributable to the fisherman. According to Adriance, Hobson in this example ignored the productive role of the equipment. In the terminology adopted in this study, the criticism would be that in this example Hobson ignored the causative role of the fixed factors, and assumed that ceteris paribus meant ceteris inefficacibus. 4 Followers and critics, 1920 to 1940: from Cassel to Fraser 1 Cassel did not refer in this context to the concept of marginal net product, used by Marshall to express the same qualification. 2 The use of ‘due to’ suggests that Cassel believed that, when the other factors are constant, there is a monocausal connection between the marginal unit of the variable factor and the marginal product. 3 Cassel (1932, 181). In reviewing The Theory of Social Economy, Edgeworth commented on the role accorded by Cassel to demand and supply: ‘The writer appears to think that price determined by the play of demand and supply affords the only satisfactory principle for the distribution of capital and labour’ (Edgeworth 1920, 534, citing Cassel 1932, 61, 109, 185). 4 Cassel (1935, 122). His comments on the uncritical acceptance of the MPTD are probably just as relevant now as they were in his time. 5 Cassel (1935, 126). See Gustafsson (1987, 376): ‘Following Marshall, Cassel explained prices by reference to supply and demand, and following Walras, he devised a general equilibrium model for market prices in the form of a system of simultaneous equations.’ 6 The similarity of these ideas with those of Wieser and Marshall was not acknowledged by Cassel in this context.

7 In 1926 Valk had received an Honorable Mention in a competition for the best original treatise on the theory of wages. The adjudication committee included Laurence Laughlin, John Bates Clark and Wesley C. Mitchell. 8 Knight (1921, 103). In saying that argument about the validity of the MPTD is ‘inappropriate for economists’, did Knight fear that social ‘chaos’ would occur, not only if the MPTD is rejected, but even if it is discussed? 9 However, Knight seemed to think that a partial differential expresses a causal relationship: ‘The marginal utility and marginal productivity theories are considered verbal approximations of the partial differential equation, which is the general form of a causal law’ ([1928] 1956, 94). 10 Edgeworth’s critical review of J.M. Clark (1923) has been noted above, under ‘Edgeworth’. He argued that this adding-up proposition would be true only if entrepreneurship is regarded as one of the variable factors (Edgeworth 1925, 248). 11 The ‘costs we can trace are only a part of the costs of the business as a whole, which it must somehow manage to cover’ (J.M. Clark 1923, 18; cited in Shute 1997, 44). 12 Letter from Sraffa to John Eatwell (20 September 1974), quoted in an editorial comment by Luigi Pasinetti, in Pasinetti 1998, 322. 13 Blaug (1975, 27, 32). Blaug criticises Sraffa because ‘Like the other Cambridge critics, he chooses to ignore the general equilibrium version of ‘marginal productivity theory’’ (Blaug 1975, 23). As noted below, Blaug appears to base his support for the MPTD (at a micro level) on a belief in the powers of simultaneous equations to produce a general equilibrium solution. 14 Sraffa (1960, 63). Sraffa noted that, in their respective theories of value, Torrens, Ricardo, Malthus and Marx incorporated the notion of the residue of the fixed capital employed in the production process, but that ‘afterwards it seems to have fallen into oblivion’ (Sraffa 1960, 94–5). 15 A similar view was put by Hahn (1972, 8): the neoclassical theory of distribution ‘has no causal significance’. 16 Whatever the reason for the altered view, the significance of the alteration was clear. Within a Lockean principle of property rights, a non-causal MPTD becomes devoid of proprietorial and normative consequences. 17 Dobb ([1970] 1988, 117). According to Dobb (1973, 248), the previously unknown concept of the reswitching of techniques, with its implications for

the concept of a continuously differentiable production function and hence for the integrity of the MPTD, was launched by Piero Sraffa’s Production of Commodities by Means of Commodities (1960); the reswitching of techniques ‘represented, perhaps, its most important single contribution to ‘a Critique of Economic Theory’, and occasioned a debate that will one day, no doubt, become celebrated’ (Dobb 1973, 252). 18 ‘A long road has to be travelled before this abstract proposition can be used in the explanation of real events’; ‘we cannot go on from this to conclude that this equality of wages and marginal products will actually be found in practice; for the real labour market is scarcely ever in equilibrium in the sense considered here’ (Hicks 1932a, 10, 18; cited in Rothschild 1994, 65). 19 See, Chapter 7 (this volume), for Hicks’ views on the allocation of overheads. 20 Hicks claimed to have invented the expression ‘constant returns to scale’ to refer to a production function that is homogeneous of the first degree: It may be that I was myself responsible for naming it … I am sure that when I first used it I was conscious that I was inventing it … in a paper entitled ‘Distribution and Economic Progress: a revised version’ which appeared in the Review of Economic Studies in 1936 … but the name is rather obvious, and there may well be others who have claims. However that may be, the name caught on. Though earlier economists did not have the name, we can see, looking back, that the concept is implied in many of the things they said. He also noted that, although Kaldor had wanted to dispense with constant returns to scale, he himself, while sympathising with Kaldor’s desire to dispense with it, had not found it easy to do so, and thought that experience had shown how hard it was to dispense with it (Hicks 1989, 9–10). 21 See Flatau (2002) for an assessment of the significance of Hicks’ The Theory of Wages (1932a) in the history of neoclassical distribution theory. 22 Edgeworth: ‘There is a magnificence in this generalisation which recalls the youth of philosophy’ (as quoted above). 23 Hicks had earlier said that, in his discussion of the adding-up theorem, he was concerned ‘solely with the internal coherence of the conditions of economic equilibrium’, and that the discussion should not be complicated ‘with the consideration of phenomena which only arise in the real world because the economic system is not in equilibrium’ (1932a, 234). In

discussing increasing returns, he seems however to have introduced a disequilibrating real-world phenomenon. 24 Walras expressed himself in so crabbed and obscure a manner that it is doubtful if he conveyed his point to anyone who did not possess some further assistance. Anyone who knows the answer can see that Walras has got it; but anyone who does not must find it almost impossible to get it from Walras. (Hicks 1932a, 234) 25 The symbols and equations are reproduced here as in Hicks (1932a, 237– 8), except that, in order to facilitate discussion, his equations are numbered in a different way, and some comments in square brackets have been inserted. 26 See also, below, the views of Wicksell and Kaldor on the assumption of constant returns to scale. 27 Stigler argued that the minimum cost condition is somewhat unrealistic – because it implies that there is no tendency to diminishing returns, and that increasing returns can go on indefinitely. If that happens, equilibrium will be impossible (1941, 233–9). 28 As Makowski and Ostroy (1992, 373–4) expressed it, a restrictive assumption was replaced by a weaker one: ‘The critics pointed out that the requirement of constant returns to scale in the production functions of individual firms was an unnecessarily restrictive assumption for the validity of marginal productivity theory; i.e., adding up could be obtained under much weaker conditions.’ The argument being presented here is that Hicks replaced the condition of constant returns to scale by the weaker condition of minimum points, but it could have been replaced by the even weaker condition of constant costs. 29 As commented above, Hicks’ mathematics requires only the condition of constant costs, not minimum costs. 30 The mathematical simplicity of this argument deprives the adding-up theorem of the ‘scientific’ image sometimes attributed to it. 31 The equality of marginal costs and average costs requires only the assumption of constant costs; it does not of course require the assumption of constant returns to scale. However, if we accept the fact that the MPTD is concerned with a situation where changes in the factors occur consecutively rather than simultaneously, then the debate about the role of constant returns

to scale in the MPTD becomes redundant. The phenomenon of constant returns to scale is one in which the changes in the factors occur simultaneously, not consecutively. Against those who would argue that the assumption of constant returns to scale is unrealistic, because it rarely occurs in the real world, it could be argued on the contrary that it is a necessary feature of the real world, not just of a world of perfect competition, because of the uniformity of nature. If a set of factors produces a certain output in one instance, then there is no reason why the same set of factors, or a multiple of all of them, could not produce the same output, or an equal multiple of the output, in another instance. 32 ‘Soon after its birth, the Theory of Wages began to look like the last gasp of an ancien régime’ (Hicks 1963, 305; Hamouda 1993, 16). 33 This is not quite consistent with what Hicks had said in his 1932 article in Economica (1932b), which showed that adding-up also occurs when costs are constant. Costs can be constant even if they are not at a minimum, and without constant returns to scale. As argued above, the mathematical argument in the Theory of Wages (1932a) showed that adding-up occurs when costs are constant. The argument did not require that costs should be at a minimum. 34 Hobson (1972, 147); quoted (with the omission of ‘separate’) in Douglas (1957, 65). Hobson continued, answering his question: ‘Obviously not, for if the dose of capital had been withdrawn instead, or the dose of land, the same effect would have ensued’ (Hobson 1972, 147). 35 Keynes’ user cost may be seen as a development of Marshall’s net marginal product, although a precise comparison is difficult because, as argued above, the textual evidence does not clearly indicate whether Marshall intended a fully net marginal product or a partially net marginal product. 36 Keynes (1936, 73). Keynes’ case for the inclusion of disinvestment as part of marginal cost may also be compared with Sraffa’s case for incorporating into the calculation of values the cost of the durable instruments of production, along with the means of production that are entirely used up in the process. See above under ‘Sraffa’. 37 It is not clear from Keynes’ text whether he intended that interest on loan capital should be included in user cost as part of what the entrepreneur ‘pays out to other entrepreneurs for what he has to purchase from them’. 38 For a succinct summary of the Lester–Machlup debate, see Lee (1984a, 1984b); McNulty (1980, 185–6); Kaufman (1988, 174–9). For a recent and

detailed account of the debate, with particular reference to minimum wage regulation, see Prasch (forthcoming) which includes details of Machlup’s rejoinder (Machlup 1947) to Lester’s reply (Lester 1947). 39 Eiteman (1945, 284) had argued that attempts to apply marginal analysis in a multiprocess industry lead to ‘hopeless complexity’, and are absurd: Under the circumstances it is absurd to claim that entrepreneurs strive, consciously or unconsciously, to expand their scale of operations until marginal costs equal marginal returns. As a matter of fact, the concept of marginal output is foreign to the thinking of the average plant manager, possibly because the simplest practical application of marginal-analysis to multi-process industry is too complex to constitute a working guide in practice. 40 Machlup (1946, 544). Nevertheless, Machlup insisted that he wished to encourage, not disparage, empirical research. 41 Machlup had made an earlier contribution to the MPTD debate through a detailed analysis of some of its leading terms. He defined the marginal productivity of a factor of production as ‘the schedule of the increments in total ‘product’ obtainable through application of additional units of the ‘factor’’, and as ‘the schedule of increments in product due to additional units of the factor used with a given (unchanged) amount of other factors’ (Machlup [1936] 1950, 158, 171–2; emphasis in original). But his analysis did not extend to the nature of the causative connection between the marginal unit of a factor and the marginal product. The nature of the causality implicit in the phrases ‘obtainable through’ and ‘due to’ was not explained. If monocausality was intended, Lockean-based normative conclusions could be logically drawn. Multicausality would require a solution to the disentanglement problem (to find the SMPL or the fully net MPAL). 42 Chamberlin (1967, 242; emphasis in original). The statement that constant returns to scale will occur only under pure competition could be questioned. There seems to be no inherent reason why a monopoly could not be operating under conditions of constant returns to scale. 43 It is clear that Chamberlin attached great importance to his distinction between ‘value of the marginal product’ and ‘marginal revenue product’. He also noted that the term ‘marginal revenue’ had been ‘exploited so ingeniously elsewhere’ by ‘Mrs. Robinson’ (Chamberlin 1967, 248). 5 Followers and critics after 1940: from Kaldor to Blaug

1 In a later publication, Kaldor stated that the ‘basic difficulty with the whole approach [i.e. the MPTD] does not lie … in this so-called ‘adding-up problem’’ (Kaldor 1960, 220). 2 See also Kaldor (1960, 220): The basic difficulty with the MPTD lies ‘in the very meaning of ‘capital’ as a factor of production … For a general equilibrium system, capital goods cannot be regarded as factors of production per se (in the manner suggested by Wicksteed), otherwise the same things are simultaneously treated as the parameters and the unknowns of the system.’ This is another aspect of, or a further development of, the interdependence problem raised by Pareto. 3 See above for Pareto’s views on fixed factor proportions, and Stigler’s criticisms. 4 Bronfenbrenner (1971, 183). If that statement by Bronfenbrenner (‘no qualified economist …’) is correct, then J.B. Clark, the American founder of the MPTD, must be classified as an unqualified economist. When Clark spoke of the equality of wages and the marginal product of labour, he was clearly referring to the product specifically caused by labour. By contrast, Rima (1991, 277) described J.B. Clark as ‘the first major American economist’. 5 Robinson (1973b, x). Harcourt suggests that there is some doubt about the accuracy of her retrospective claims. He has noted that in her early publications up until the mid1930s, although she had enthusiastically adopted the revolutionary Keynesian theory of output and employment as a whole, ‘she was still prepared to use a neoclassical theory of distribution, marginal products and all that’ (Harcourt 1996, 321). 6 Robinson (1970, 310; emphasis in original). The definition of marginal net product in this quotation leaves some points unclear, but approximates to the concept of fully net marginal product of labour, discussed above. However, in some other statements by Robinson there is some uncertainty about whether fully net or partially net is meant. Robinson (1973a, 132) states: ‘The marginal net product of labour (after allowing for raw materials, power and maintenance of plant) is equal to the wage plus profit.’ However, it is not clear whether ‘profit’ in this statement refers only to the profit on the variable capital – such as raw materials, power and maintenance – in which case the net product is partially net; or whether ‘profit’ includes also the profit in the fixed capital, in which case the net product would be fully net. In Robinson and Eatwell (1973, 41) ‘net product’ is defined as ‘the value of the increment of product expected from employing a man minus the additional expenses that would be involved in employing him’. The expression ‘additional expenses’ was probably intended to refer to the expenses of employing

additional materials, power, supervision and so on to accompany the additional unit of labour, and may also have been intended to include the interest on the working capital required to employ the extra man, but what is not clear or certain is whether it was also intended to include a proportionate share of the expenses associated with the fixed capital. 7 Trevor Swan, for example, interpreted Robinson as saying: ‘the social Capital, considered as a factor of production accumulated by saving, cannot be given any operative meaning – not even in the abstract conditions of a stationary state’ (Swan 1956, 344: emphasis in original), and added: ‘Joan Robinson is correct in so far as she is complaining that the neo-classical tradition contains no indication of how a ‘technical unit’ for capital may be derived’ (Swan 1956, 348). 8 Although Robinson had serious reservations about the measurement of capital, she also said that the measurement of capital is a secondary question, and that the real difficulty lies in comparing imagined equilibrium positions with real historical processes that take place over time (Robinson 1974, 57– 8). She was also critical of attempts made during the Cambridge capital theory controversy to overcome the capital measurement problem by the use of the concept of ‘plastic capital’ or ‘putty’ (Robinson [1974] 1979, V, 56: ‘putty is a parable, not to be taken literally’). The disentanglement problem – one of the main criticisms of the MPTD – is not resolved by talking about ‘plastic capital’ and ‘putty’, instead of picks and shovels. The concept of ‘plastic capital’ may be seen to have been foreshadowed in J.B. Clark’s distinction between ‘capital’ and ‘capital goods’ – the former being a fund of productive goods and an abiding entity; the latter being a succession of productive goods. Clark’s distinction was discussed by Veblen (1907–8, 162) who preferred the terms ‘financial capital’ and ‘industrial capital’, and who noted Fisher’s similar distinction between ‘capital value’ and ‘capital’. (I am grateful to an anonymous reader for bringing Veblen’s article to my attention.) 9 The Robinson circularity argument attacks the MPTD considered as a positive, nonnormative theorem, but if its validity as a positive theorem is rejected, then so too must its validity as a normative theorem. It is perhaps worth noting, however, that it is not necessary to invoke Robinson’s circularity argument in order to refute the normative claims of the MPTD. It is sufficient to recognise that normative claims require (on a Lockean principle of property rights) identification of causal contributions, and that the causal contributions of the various factors to a multicausal product are incapable of disentanglement.

10 The circularity objection may also be expressed by reference to discounted values. According to the MPTD, the rate of interest, being the return on capital, depends on the marginal productivity of capital, which depends on the discounted values of the expected future returns from the capital; but discounting requires knowledge of the rate of interest. 11 ‘The basic reason’ for the unmeasurability of capital ‘is that capital cannot be both an exogenous (determining) variable and an endogenous (determined) variable at one and the same time’ (Harcourt 2001, 191; emphasis in original). 12 Although this fundamental challenge to the practical usefulness of the MPTD is well known, it is rarely mentioned in modern textbook accounts of the MPTD. 13 For example, if a tax is levied on the value of land, the value of the land will affect the amount of tax paid, but the amount of tax paid will in turn tend to affect the value of the land. 14 Weizsäcker (1971, 97–8); quoted in Harcourt (1976, 36–7), who continues with a rebuttal of the claim that Joan Robinson did not understand the nature of the solutions to sets of simultaneous equations. 15 Advocates of Wieser’s solution by means of simultaneous equations say, or imply, that it is a ‘determinate’ solution, by which they seem to mean algebraically determinate. The problem is to show that it is also quantitatively determinate. In the literature on the subject, ‘determinate’ seems to be interpreted as merely ‘algebraically determinate’. 16 The ‘unchanged factors’ would include the existing human capital as well as the existing physical capital (including land). 17 ‘Reswitching (or double-switching) is the possibility that the same technique may be the most profitable of all possible techniques at two or more separated values of the rate of profits even though other techniques are the most profitable ones at rates of profits in between. Capital-reversing is the possibility of a positive relationship between the value of ‘capital’ and the rate of profits when the switch from one technique to another is considered. (Harcourt 1976, 29; emphasis in original) It is not the purpose of this study of the history of the MPTD to reassess the extensive literature of the reswitching and capital reversing debate. The

debate is briefly referred to here merely in order to note comments that have been made on its relevance to the validity of the MPTD. 18 See also Robinson (1975). 19 Reswitching ‘violates the uniqueness of the relation between capital intensity and the rate of interest’. Capital reversing, by creating ‘a positive relation between capital intensity and the interest rate’, violates ‘the inverse nature of that relation’ (Cohen 1989, 234). 20 The existence of reswitching has also been denied. For example, Hicks argued that substitutions of techniques, or at least the most important substitutions, are irreversible; something is learned by the substitution, ‘so that if input-prices reverted to their old ratios, it is not the old technique which would be reintroduced, but something new. Once that is granted … there can, by definition, be no re-switching’ (Hicks 1975, 367; emphasis in original). 21 Note also the comment by Joan Robinson: ‘Neoclassical theory is no better off even when there is no reswitching’ (Robinson 1974, 348n; quoted in Harcourt 1976, 51). 22 Ng also stated: ‘No circular reasoning is involved if we bring back the general equilibrium framework’ (Ng 1974b, 128). However, it may be more correct to say that in a general equilibrium framework, where all the variables are endogenous, circularity is ubiquitous. 23 Ng (1974b, 127). Ng also argues that the partial derivative used by the neo-MarxistKeynesians differs from that used by the neoclassicals. The former includes an inventory revaluation; the latter excludes it (Ng 1974b, 126). 24 ‘the distribution of income is perfectly determinate on marginal productivity principles within a general equilibrium model incorporating demand factors. The assertion that the contrary is true is this generation’s Cambridge (England) myth’ (Johnson 1974, 22). 25 Johnson (1973, 37, 117); quoted in Harcourt (1976, 28). The phrase ‘their contributions’ could be interpreted in a way that has implications for the ethical entitlements to ownership, and for the status of the MPTD as a purely ‘positive theory’. 26 Johnson (1973, 20) wrote the second term on the left side of the equation as:

̉ 27 The attempt to use Euler’s theorem to prove the adding-up theorem thus seems not to have given adequate consideration to the time factor, and reinforces the idea stressed by Marshall, and more recently by Joan Robinson and others during the Cambridge capital theory controversy, that economic theories will often be deficient if they do not incorporate an element of historic time. 28 Johnson (1973, 21). Johnson, following Knight and Stigler, argued that perfect competition necessarily implies constant returns to scale, because ‘if there are increasing returns to scale for the firm one firm will become a monopoly and the conditions of competition will cease to apply, whereas if there are decreasing returns to scale firms will become infinitesimally small, a condition inconsistent with the facts of empirical observation’ (Johnson 1973, 21). However, the view that increasing returns to scale will lead to monopoly is debatable. That would be true if one firm enjoyed increasing returns while other firms did not; or if one firm constantly enjoyed increasing returns to scale to a greater degree than other firms; but it would not be true if increasing returns to scale were enjoyed to an equal degree by many firms. ‘Increasing returns to scale’ means that when a firm’s inputs all increase by (say) 10 per cent, its output will increase by more than 10 per cent. There is no necessary reason why this situation should not be enjoyed by many firms acting in competition. In addition, the argument that firms will become ‘infinitesimally small’ if they have decreasing returns to scale is unconvincing. ‘Decreasing returns to scale’ will mean that output increases by a smaller proportion than the increase in inputs (i.e. that costs per unit of output rise), but it does not necessarily mean that a firm is decreasing in size. 29 Blaug (1962, 404), with minor changes in later editions. As frequently noted above, the word ‘its’ presents a possible ambiguity. 30 An exception might be Gustav Cassel (see above). 31 The applicability of the MPTD at the macro or aggregate level has also been rejected by Del Punta (1971), who reproaches modern champions of the marginal productivity theory for attempting to defend it in the context of macro models, when in fact it is a microeconomic principle: ‘what is true, on the logical plane at least, in micro-economics may not be true at all in macroeconomics. But if it were, it would first have to be proved so. And so far no such proof has ever been supplied’ (Del Punta 1971, 216). He argues that modern neoclassical defenders of the MPTD who apply it in aggregate growth models ‘should have quite simply and honestly admitted’ that they do

so because ‘they do not know of any other ‘law’ of distribution that is more convincing’. They should also ‘make it quite clear that no proof has ever been provided of the validity of this theory in a macro-economic and dynamic context’ (Del Punta 1971, 217). 32 In this context, Blaug suggests that ‘it would be a great advantage if the phrase ‘marginal productivity theory of distribution’ were banished from the literature’; and ‘it would have been better if no one had ever used the phrase ‘the marginal productivity theory of distribution’. I have tried to avoid it altogether, since it just creates misunderstanding and makes us think about the one-sector model’ (in Caravale 1983, 196, 123; see also Blaug 1975, 7). 33 In the second and later editions, ‘the new theory of distribution’ is altered to ‘the new marginal-productivity theory of distribution’. In the third and later editions, the first sentence continues ‘than those posed by Smith, Ricardo and Mill’. 34 ‘In the neoclassical tradition, the theory of income distribution is a theory of factor pricing’ (Blaug 1978, 511). 35 This similarity between the two concepts appears to be implicitly acknowledged by Blaug in the expression ‘Variations in factor prices, and hence in relative shares’ (Blaug 1962, 416; emphasis added). 36 In his extensive mathematical treatment of the MPTD in Economic Theory in Retrospect, Blaug does not refer to Pareto’s interdependence objection. 37 Blaug (1978, 511); the word ‘share’ is italicised in the fourth and fifth editions. 7 Miscellaneous considerations 1 The distinctions between these two meanings of MPL, between the proprietorial ‘of’ and the non-proprietorial ‘of’, and between ‘of’ and ‘after’, do not appear to have received the attention they deserve in the literature. It may be objected that there is one situation in which the monocausal SMPL and the multicausal MPAL are the same. That would be the situation where there is only one factor of production – for example, where labour alone is used to provide a service, without any contribution from capital and land. But, of course, if there is only one factor of production, there is no distribution problem; and, more fundamentally, is it physically possible for any commodity to be produced or any service to be supplied with only one factor of production? Labour requires, at the very least, food, water and air.

2 In other words, the disentanglement problem resurfaced in another form. For J.B. Clark, the problem was to disentangle the SMPL from the MPAL. For Marshall and the modern version of the MPTD, the problem is to disentangle the net MPAL from the gross MPAL. 3 Here ‘should’ is being used in a purely commercial or book-keeping sense, as distinct from a Clarkian, normative sense. 4 If the ‘short period’ is defined as a period in which the cost of capital does not need to be considered by the firm when setting the prices of its products and the returns to other factors, and the ‘long period’ is defined as a period in which the cost of capital does need to be considered for those purposes, then the argument being advanced in this study is that there is no such thing as a short period. 5 ‘Neither has the accountant found a solution – only a name and a set of (essentially arbitrary) rules’ (Hicks 1974, 312). 6 At a particular time and place it may be desirable for wages to be greater than the SMPL, either for economic reasons such as to stimulate consumer demand, or to use high wages as an encouragement for greater labour productivity, or for extra-economic reasons, such as to improve the health, education and living standards of low-paid workers. See Ng (1974b). 7 Similarly, if capital receives as profits the full value of the gross MPAK, then capital is exploiting labour, because the gross MPAK exceeds the SMPK. The gross MPAK is not produced by capital alone. 8 See also Taylor (1960, 367): ‘the ‘marginal-productivity’ analysis involved a wider generalization of, from, or beyond the Ricardian-classical ‘law of diminishing returns’.’ 9 Its claim to be a demand-side theory of wages might also be challenged on the grounds that marginal productivity does not determine wages, but, rather, wages determine marginal productivity. As noted above, the latter position would be a wage theory of marginal productivity, not a marginal productivity theory of wages. It would be more correct to say that, like the two blades of a pair of scissors, wages and marginal productivity are mutual demand-side determinants. 10 See R. Dorfman (1987, 324). 11 See Lee and Keen (2004).

12 This perception of the competence of businessmen in these matters is similar to that of Machlup in his debate with Lester in 1946 as outlined above. 13 Wiles (1961, 8–13; emphasis in original). Wiles refers in this context to a situation he describes as one of ‘partial adaptation’, i.e. a short-term situation in which the fixed factors remain constant – as opposed to ‘total adaptation’. He also notes that wear and tear can be negligible and can be neglected in a situation where ‘obsolescence will be more rapid than the shortest possible life of the plant’. 14 This argument, if valid, has implications for econometric modelling. It follows, for example, that ‘wage = marginal product of labour’ is not an equilibrium situation, and that a model using this equation as an equilibrium condition would be misspecified. 8 The normative language of the non-normative MPTD 1 Cf. The Philosophy of Wealth (Boston, 1885), esp. pp. 135, 169; The Distribution of Wealth, Preface; also pp. 3, 4, 6, 7, 9, 49 n., 323–24 n. ff. [Stigler’s footnote]. 2 Commenting on the distribution theory of Clarence Ayres, Walker (1980, 661) noted: It is true that the intrusion of normative attitudes into the description and interpretation of economic phenomena is all too frequent, and this is especially prevalent in connection with the distribution of income [where] normative elements are grafted onto an ethically neutral analytical framework … In itself, marginal productivity analysis is neutral … It does not deal with the ethical justifiability of the functional distribution of income. A contrary view, stressing the non-neutrality of marginalism (and hence, by implication, of the MPTD) was expressed by Blum (1947, 651–2): marginalism is not simply used as a tool to analyze the theoretical aspect of the wage-employment problem. It is also used as a tool to analyze economic policy problems. If used for this purpose, marginalism implies value judgments which are hidden behind the formality of the approach. It is no coincidence that marginalism is and has always been an instrument for combating such measures of social reform as the minimum wage legislation … the marginal significance of marginalism in a dynamic situation approaches zero. 3 Reynolds (1963, 160). Is ‘reasonable’ the word that pure economics can use when it really wants to say ‘ethical’ or ‘just’?

4 Bronfenbrenner: ‘no qualified economist has maintained a specificproductivity theory’ (1971, 183; as cited above). 5 The following comment by Robert Solow sums up the modern orthodox view: ‘J.B. Clark may have thought that the marginal product of anything was its ‘just reward’. But no participant in this debate, on either side, would take that notion seriously’ (Solow 1975, 51). 6 In this regard, it is interesting to note the definition of marginal product of labour given in Robinson and Eatwell (1973). Whereas the definitions of MPL found in most textbooks make use of words carrying monocausal and sole proprietor significance – words such as ‘created by’, ‘results from’, ‘his’, ‘their’ – Robinson and Eatwell define MPL as ‘the amount of output that would be lost if a unit of labour were withdrawn’ (1973, 40), a definition which does not imply that the marginal output is caused by the marginal unit of labour, or that the marginal unit of labour has some exclusive proprietorial and moral right to the marginal product. 7 In this respect, the history of the MPTD supports the view that ‘Over the 20th century, repeated efforts have been made to expunge values and norms from neoclassical economies. But American neoclassical economics has never really capitulated’ (Persky 2000, 107). 9 General conclusion: neither normative nor positive 1 Although the MPTD itself cannot legitimately claim to carry normative implications for the distribution of income and wealth, there are of course other considerations that might give rise to legitimate normative judgements about distribution. If, for example, the existing ownership of natural resources, capital and educational advantages have been achieved by methods deemed to be not in accord with standards of distributive justice, or if commercial operations of buying and selling have not conformed to standards of commutative justice, then it is unlikely that a just distribution will occur as the consequence of the interaction of the bargaining powers of the factors of production. 2 It could perhaps be argued that, even if the normative status of the MPTD is denied, it retains a quasi-normative status as a positive law; because, if it is a valid positive law, like the laws of the ‘hard’ sciences, it is part of the natural order or the Divine plan. It could also be noted that the separation of the positive MPTD from the normative MPTD gives rise to an interesting philosophical dilemma. The

positive MPTD claims that profit-maximising equilibrium occurs where factor returns equal the non-specific marginal products of the factors, but it denies that any moral judgments can be legitimately deduced concerning the justice or injustice of the resulting distribution. The normative MPTD, as developed by J.B. Clark, claims that distributive justice will occur only if factor returns equal the specific marginal products of the factors. Therefore, a situation of profit-maximising equilibrium (as defined by the positive MPTD) will not necessarily be a situation of distributive justice (as defined by the normative MPTD) – which raises the possibility of a Mandevillian conflict between ethics and economics, or between what is economically desirable and what is considered, on a Lockean principle of property rights, to be ethically desirable. 3 As noted above, it is clear that at least some of the support for the MPTD is based on psychological and ideological considerations, involving either antiopen-market paranoia, or anti-government paranoia, or both. 4 It has been suggested that the success of the MPTD may be attributed to the power of political conservatism, i.e. that the MPTD has been adopted and promoted by those who wish to justify and eulogise a laissez-faire distribution of income, and to distract attention from radical, alternative explanations of distribution. While this may be a correct account of the motivation of some advocates of the MPTD, it should also be recognised that the MPTD has fervent advocates among interventionist and socialist economists. Appendix A: W.S. Jevons (1835–1882) and the MPTD 1 Stigler also made the same criticism of Amoroso (1925–6, 98–9) and Walras (1926, 375). 2 As noted above, this disentanglement problem became one of the main arguments of critics of the MPTD, such as Hobson, Davenport and Adriance. 3 Dobb (1973, 186, 188). Dobb also criticised Stigler’s view that Jevons’ concept of capital and of the rate of return did not depart far from classical theory (1973, 188). 4 ‘Jevons’s theory [of distribution] determined nothing; the interest rate, the wage rate, all prices and all quantities are left undetermined’ (Steedman 1972, 51). 5 Jevons (1882, 98); cited in Steedman (1972, 49).

6 The competition to obtain proper workmen will strongly tend to secure to the latter all their legitimate share in the ultimate produce … Every labourer ultimately receives the due value of his produce after paying a proper fraction to the capitalist for the remuneration of abstinence and risk. (Jevons 1879, 272, 273; cited in Steedman 1972, 49) Appendix B: Marshall’s concept of net marginal product: fully net or partially net? 1 Marshall (1949, 430; 1961, 518; emphasis added). See also Marshall (1961, II, 584) for earlier versions. Blaug argues (1985, 415) that this statement ‘is open to various interpretations but it seems to deny the mutual and simultaneous determination of factor prices’, but Whitaker (1988) argues that this statement ‘seems more radical when taken out of context than it does in context, when it appears as little more than an awkward way of stressing mutual interdependence’ (131). According to Whitaker (1988), Marshall was ‘essentially a marginal-productivity theorist’ (165) and ‘not a precursor of modern criticisms of marginal-productivity theory’ (127). 2 In the same context, Marshall argued that ‘the environment (or Conjuncture) plays a part at least coordinate with a man’s energy and ability in governing that net product to which his wages ever approximate under the influence of competition’ (Marshall 1949, 554; 1961, I, 667), but he did not argue that, in calculating the net product of labour, a deduction should be made for the productive input of the environment or Conjuncture. 3 The term ‘net’ was being used by Marshall in the above quotations in the context of the National Dividend. It does not necessarily follow that, when discussing the concept of net marginal product in relation to the MPTD, he intended that ‘net’ should be interpreted in the same way. 4 Later in the same work Robinson referred to ‘interest on working capital’ (133) as a deduction. 5 See also Marshall (1949, 432) where he defined the net product of employers as ‘the net increase of the money value of their total output after allowing for incidental expenses’. Appendix C: dWickstead’s recantation

1 Wicksteed (1906, 553–4). Wicksteed’s praise for Pareto on this point, and for the ‘dignity and calmness’ with which the ‘purely abstract portions’ of the Manual were written, did not prevent him from reacting strongly to other portions. For example, he was not impressed by Pareto’s remark: ‘When [in England] elections are coming on, the candidates do not blush to send their wives and daughters to beg for votes, and to offer their hands and lips to a gross and unwashed populace’ (Wicksteed 1906, 556; citing Pareto’s Manual, 140). He disapproved of Pareto’s ‘free use of sarcastic and pejorative epithets’ (Wicksteed 1906, 556). 2 See above, under ‘Pareto’, for further details and discussion of this argument by Pareto. 3 The footnote on page 373 of the Common Sense, after formally withdrawing paragraph 6 of the Co-ordination, concluded with the statement: ‘and the solution now offered in the text must take its place’ (Wicksteed [1910] 1933, I, 373n). 4 Steedman (1987a, 22, emphasis in original). Steedman also noted that Wicksell (1934, 101) was under the impression that Wicksteed had withdrawn the whole of the Coordination, for reasons that Wicksell found ‘difficult to understand’. 5 Steedman also notes (1994, 92) that a lecture delivered by Wicksteed in 1913 on ‘The distinction between earnings and income, and between a minimum wages and a decent maintenance: a challenge’ contained an exposition of the marginal productivity theory. 6 Robbins (1933, xi). A slightly different comment was made in Robbins (1930, 249): ‘Wicksteed’s proposition is not untrue; the only criticism to which it is exposed is that, in certain circumstances, its assumptions render it inapplicable. It is not so exhaustive as its author at first supposed. This is not a grave defect in a new theory.’ To say that a proposition is ‘not untrue’ but that its demonstration is ‘incomplete’ raises some interesting linguistic questions. What is the difference between ‘true’ and ‘incomplete’? How can a proposition be known to be true if the proof of it is incomplete? What degree of incompleteness is required before a true proposition has to be reclassified as untrue? This statement by Robbins on Wicksteed’s adding-up proof can be compared with the statement (quoted above) by Stigler (1941, 153) that Menger’s theory of distribution is ‘essentially correct’ despite ‘its inadequacy’. 7 Robbins (1933, xi). A 1934 review by Hicks of the 1933 reprint of Wicksteed’s Common Sense did not refer to this question of Wicksteed’s alleged recantation. Hicks described the Common Sense as ‘not merely a

good textbook, but an economic classic’. He commended Wicksteed for his ‘original contributions to the pure theory of value’ and compared him to Galileo: ‘Wicksteed stands to Pareto in the same sort of relation as Bruno or Galileo to Copernicus. What in Pareto is essentially a mathematical dodge to overcome a logical and mathematical difficulty, becomes in Wicksteed a philosophical revolution’ (Hicks 1934, 351). 8 Stigler (1941, 334). Stigler wrote: ‘There seems to be doubt …’, presumably a proofreading error. 9 As noted above, some later writers have maintained that the validity of the adding-up theorem does not depend on an assumption of a linear homogeneous production function. If that is correct, then although the debate about whether Wicksteed did or did not retain that assumption is interesting in the context of Wicksteed’s intellectual biography, it is of no relevance to the wider question of the validity of the adding-up problem. 10 The address was published in the Economic Journal in 1914, but the version published in a 1962 selection of papers read to the British Association in 1913 shows that it had been shortened and expurgated in 1914. The full version contains some memorable passages. For example, it said that the labour-cost theory of value has been ‘discredited and hardly dares to announce itself openly’ and described its passing as the ‘cleansing of economic doctrine from the baneful sequelia of this disease of its youth’ (Smyth 1962, 250). Both versions (1914 and 1962) concluded with the hope that the methods of economic exposition would be revised by ‘convinced apostles of the differential economics’ and that political economy would no longer be a ‘mere armoury of consecrated paradoxes’: For myself I cannot but believe that if this were accomplished, all serious opposition to the doctrine would cease, that there would once again be a body of accepted economic doctrine, and that Jevons’s dream would be accomplished and economic science re-established ‘on a sensible basis’… and the roughly understood dicta bandied about in the name of Political Economy would at any rate stand in some relation to truth and to experience, instead of being, as they too often are at present, a mere armoury of consecrated paradoxes that cannot be understood because they are not true, that everyone uses as weapons while no one grasps them as principles. (Wicksteed 1914, 22–3) 11 Those who believe that the adding-up theorem can be proved, and has been proved, may want to argue that Wicksteed’s reason for saying ‘it cannot be done’ was that he did not have sufficient mathematical ability to understand the proofs. As Stigler noted, Wicksteed admitted that his

‘knowledge of mathematics is so limited’ and apologised for his ‘want of systematic mathematical training’ (cited in Stigler 1941, 326). See also the comments by Steedman, quoted above, on Wicksteed’s mathematical limitations.

References Adriance, W.M. 1914–15. “Specific productivity”, Quarterly Journal of Economics, 29: 149–76. Alchian, A.A. and Allen, W.R. 1968. University Economics, 2nd edn, Belmont (California): Wadsworth. Amoroso, L. 1925–26. “W.S. Jevons e la economia pura”, Annali di Economia, II: 83–106. Asimakopulos, A. ed. 1988. Theories of Income Distribution, Amsterdam: Kluwer. Aupetit, A. 1901. Essai sur la théorie générale de la monnaie, Paris: Guillaumin. Barone, E. 1896. “Studi sulla distribuzione”, Giornale degli Economisti, 12: 107–55, 235–52. Bhaduri, A. and Robinson, J. 1980. “Accumulation and exploitation: an analysis in the tradition of Marx, Sraffa and Kalecki”, Cambridge Journal of Economics, 4: 103–15. Black, R.D.C. 1971. Introduction, pp. 5–29, The Economic Writings of Mountifort Longfield, New York: Augustus M. Kelley. ——1987. “Longfield, Mountifort”, in Eatwell et al., III, 237. Blaug, M. 1962. Economic Theory in Retrospect, London: Heinemann. ——1968. Economic Theory in Retrospect, 2nd edn, London: Heinemann. ——1972. An Introduction to the Economics of Education, Harmondsworth: Penguin. ——[1974] 1975. The Cambridge Revolution: Success or Failure? A Critical Analysis of Cambridge Theories of Value and Distribution, revised edn, London: Institute of Economic Affairs. ——1978. Economic Theory in Retrospect, 3rd edn, Cambridge: Cambridge University Press. ——1980. The Methodology of Economics: or How Economists Explain, ch. 9 “Marginal productivity theory”, Cambridge: Cambridge University Press.

——1985. Economic Theory in Retrospect, 4th edn, Cambridge: Cambridge University Press. ——1996. Economic Theory in Retrospect, 5th edn, Cambridge: Cambridge University Press. Bliss, C.J. 1975. Capital Theory and the Distribution of Income, Amsterdam: North Holland. Blum, F.H. 1947. “Marginalism and economic policy: a comment”, American Economic Review, 37: 645–52. Böhm-Bawerk, E. 1906–7a. “Capital and interest once more: I. Capital vs capital goods”, Quarterly Journal of Economics, 21: 1–21. ——1906–7b. “Capital and interest once more: II. A relapse to the productivity theory”, Quarterly Journal of Economics, 21: 247–82. Bowley, M. 1937. Nassau Senior and Classical Economics, London: George Allen & Unwin. Bradford, W. and Harcourt, G.C. 1997. “Units and definitions” in Harcourt and Riach, 107–31. Brennan, H.G. and Waterman, A.M.C. 1994. Economics and Religion: Are They Distinct?, Boston, MA: Kluwer. Bronfenbrenner, M. 1971. Income Distribution Theory, Chicago, IL: AldineAtherton. ——1985. “Marginal productivity, a rehabilitation”, in Feiwel 1989. Butt, I. 1838. Rent, Profits, and Labour. A Lecture Delivered Before the University of Dublin in Michaelmas Term, 1837, Dublin: William Curry. ——1846. Protection to Home Industry: Some Cases of Its Advantages Considered. The Substance of Two Lectures Delivered Before the University of Dublin, in Michaelmas Term, 1840, Dublin: Hodges and Smith. Cannan, E. 1905. “The division of income”, Quarterly Journal of Economics, 19 (May): 341–69. ——1917. A History of Theories of Production and Distribution in English Political Economy from 1776 to 1848, London: P.S. King. ——[1925–6] 1963. “Distribution”, in Palgrave 1963, Vol. I, 595–6.

Caravale, G. ed. 1983. The Crisis in Economic Theories, Milan: Franco Angeli Editore. Carver, T.N. 1901. “Clark’s Distribution of Wealth”, Quarterly Journal of Economics, 15 (August): 578–602. ——1904. The Distribution of Wealth, New York: Macmillan. ——1904–5. “The marginal theory of distribution”, Journal of Political Economy, 13 (March): 257–66. Cassel, G. [1925] 1929. Fundamental Thoughts in Economics. First published in English in 1925. Reprinted 1929, London: Ernest Benn. ——[1918] 1932. The Theory of Social Economy, first German edn, 1918, first English edn, 1923, revised English edn, 1932, London: E. Benn. ——1935. On Quantitative Thinking in Economics, Oxford: Clarendon Press. Chamberlin, E.H. 1934. American Economic Review, 24, Supplement. Symposium on Imperfect Competition, 23–7. ——1937. “Monopolistic or imperfect competition”, Quarterly Journal of Economics, 51: 557–80 ——1942. The Theory of Monopolistic Competition. A Re-orientation of the Theory of Value, 4th edn, Cambridge, MA: Harvard University Press. First edn, 1933. ——[1936] 1967. “Monopolistic competition and the productivity theory of distribution”, in Viner. Paper read at a meeting of the American Economic Association in 1933; summarised in part in American Economic Review, 1934, 24 (sup.), 23; reprinted, except for the first two paragraphs, in Chamberlin, Theory of Monopolistic Competition, 3rd edn 1938, 4th edn 1942, ch. 8, 177–90. Chapman, S.J. 1904–14. Work and Wages, 3 vols; Vol. I, Foreign Competition, 1904; Vol. II, Wages and Employment, 1908; Vol. III, Social Betterment, 1914, London: Longmans, Green & Co. ——1906. “The remuneration of employers”, Economic Journal, 16: 523–8. ——1912. Political Economy, London: Thornton Butterworth. Clark, J.B. 1889. “The possibility of a scientific law of wages”, Publications of the American Economic Association, 4(1): 39–69.

——1890–1. “Distribution as determined by a law of rent”, Quarterly Journal of Economics, 5: 289–318. ——1892–3. “The ultimate standard of value”, Yale Review, I, 258–74. ——1902. “Is authoritative arbitration inevitable”, Political Science Quarterly, 17(4): 553–67. ——1904. The Problem of Monopoly, New York: Columbia University Press. ——1906–7. “Concerning the nature of capital: a reply”, Quarterly Journal of Economics, 21: 351–70. ——[1899] 1956. The Distribution of Wealth. A Theory of Wages, Interest and Profits, New York: Kelley & Millman. ——[1907] 1968. Essentials of Economic Theory, New York: Augustus M. Kelley. ——[1925–26] 1963a. “Distribution, Ethics of”, in Palgrave 1963, I, 596–9. —— [1925–26] 1963b. “Distribution, Law of”, in Palgrave 1963, I, 599–602. Clark, J.M. 1923. Studies in the Economics of Overhead Costs, Chicago, IL: University of Chicago Press. ——[1931] 1950. “Distribution”, Encyclopaedia of the Social Sciences, V, 167–73; reprinted in Fellner and Haley, 58–71. ——1952. “J.M. Clark on J.B. Clark”, in Spiegel 1952. ——1968. “John Bates Clark”, International Encyclopedia of the Social Sciences, ed. D.L. Sills, Vol. 2, 504–8. Cohen, A. 1989. “Prices, capital and the one-commodity model in neoclassical and classical theories”, History of Political Economy, 21(2): 231–51. Cohen, A.J. and Harcourt, G.C. 2003. “Whatever happened to the Cambridge capital theory controversies?”, Journal of Economic Perspectives, 17(1): 199–214. Creedy, J. 1986. Edgeworth and the Development of Neoclassical Economics, Oxford: Blackwell.

Dasgupta, P., Gale, D., Hart, D. and Maskin, E. 1992. Economic Analysis of Markets and Games: Essays in Honor of Frank Hahn, Cambridge, MA: MIT Press. Davenport, H.J. [1913] 1929. The Economics of Enterprise, New York: Macmillan. ——[1908] 1964. Value and Distribution. A Critical and Constructive Study, New York: Augustus M. Kelley. Del Punta, V. 1971. “Sterility of ‘Cambridge School’ criticism of the Marginal Productivity Theory”, Rivista di Politica Economica, Selected Papers, No. 5, 191–230. Dernburg, T.F. and McDougall, D.M. 1976. Macroeconomics, 5th edn, New York: McGrawHill. Dobb, M.H. 1928. Wages, London: Nisbet. ——1959. Wages, Welwyn, Herts: James Nisbet. Revised version. ——1973. Theories of Value and Distribution Since Adam Smith: Ideology and Economic Theory, Cambridge: Cambridge University Press. ——[1970] 1988. “The Sraffa system and critique of the neo-classical theory of distribution”, De Economist, 118, NR. 4; reprinted in Sraffian Economics, Vol. I, 114–29. Dorfman, J. 1964. “Wicksteed’s recantation of the marginal productivity theory”, Economica, 31: 294–5. Dorfman, R. 1987. “Marginal productivity theory”, in Eatwell et al., III, 322– 5. Douglas, P.H. [1934] 1957. The Theory of Wages, New York: Kelley & Millman. Eatwell, J. 1987. “Returns to scale”, in Eatwell et al., IV, 165–6. Eatwell, J., Milgate, M. and Newman, P. eds. 1987. The New Palgrave: A Dictionary of Economics, London: Macmillan. Edgeworth, F.Y. 1904. “The theory of distribution”, Quarterly Journal of Economics, 18: 159–219. Reprinted Edgeworth 1970, 13–60.

——1907. “Appreciation of mathematical theories. – II”, Economic Journal, 17: 524–31. ——1920. “Professor Cassel’s treatise”, Economic Journal, 30: 530–6. ——1925. ‘Review of J.M. Clark, Studies in the Economics of Overhead Costs’, Economic Journal, 35: 245–51. ——[1904] 1970. ‘Review of T.N. Carver, The Theory of Distribution, Economic Journal’, 1904. Reprinted Edgeworth 1970, 144–5. ——[1925] 1970. Collected Papers Relating to Political Economy, 3 vols. Reprinted as Papers Relating to Political Economy, 1970, 3 vols in one, New York: Burt Franklin. Eiteman, W.J. 1945. “The equilibrium of the firm in multi-process industries”, Quarterly Journal of Economics, 59: 280–6. Ekelund, R.B. Jr. and Hebert, R.F. 1975. A History of Economic Theory and Method, New York: McGraw Hill. Ellerman, D.P. 1992. Property and Contract in Economics: The Case for Economic Democracy, Oxford: Blackwell. Feiwel, G.R. ed. 1989. Joan Robinson and Modern Economic Theory, Basingstoke: Macmillan. Fellner, W. and Haley, B.F. eds. 1950. Readings in the Theory of Income Distribution, London: George Allen & Unwin. Ferguson, C.E. 1969. The Neoclassical Theory of Production and Distribution, Cambridge: Cambridge University Press. Fetter, F.A. 1904. The Principles of Economics, New York: Century. Flatau, P. 1997. “Fair wages and just outcomes. Marshall and Pigou on the labour market and redistribution”, History of Economics Review, 26: 109–24. ——2001. “The methodology of early neoclassical distribution theory: universalism, the deductive method and ethics”, History of Economics Review, 34: 33–55. ——2002. “Hicks’s The Theory of Wages: its place in the history of neoclassical distribution theory”, History of Economics Review, 36: 44–65.

——2004a. “Jevons and the theory of wages”, Paper presented at the Conference of the History of Economic Thought Society of Australia, University of Western Australia, 7–9 July. ——2004b. “Jevons’s one great disciple: Wicksteed and the Jevonian revolution in the Second Generation”, History of Economics Review, 40: 69– 107. Flux, A.W. 1894a. ‘A Review of P.H. Wicksteed, Essay on the Co-ordination of the Laws of Distribution’, Economic Journal, 4: 308–13. ——1894b. “Extract from lecture introductory to session of evening classes for 1893–4 at Owens College, Manchester, on ‘Jevons and his work’, by A.W. Flux, Cobden Lecturer in Political Economy”, Economic Journal, 4: 339–42. ——1904. Economic Principles. An Introductory Study, London: Methuen. Fraser, L.M. 1947. Economic Thought and Language. A Critique of Some Fundamental Economic Concepts, London: Adam and Charles Black. Gårdlund, T. 1958. The Life of Knut Wicksell, trans. Nancy Adler, Stockholm: Almqvist & Wiksell. Gordon, S. 1973. “The wage–fund controversy: the second round”, History of Political Economy, 5: 14–35. Groenewegen, P.D. 1990. “Neoclassical value and distribution theory”: the English-speaking pioneers”, in Hennings and Samuels, 13–51, with commentary by John Creedy, 52–8. ——1995. A Soaring Eagle: Alfred Marshall 1842–1924, Cheltenham: Edward Elgar. Gustafsson, B. 1987. “Cassel, Gustav”, in Eatwell et al., I, 375–6. Hagemann, H. and Hamouda, O.F. 1994. The Legacy of Hicks: His Contributions to Economic Analysis, London and New York: Routledge. Hahn, F.H. 1972. The Share of Wages in the National Income. An Enquiry into the Theory of Distribution, London: Weidenfeld & Nicolson. Hamouda, O.F. 1993. John R. Hicks: The Economist’s Economist, Oxford, UK, and Cambridge, USA: Blackwell.

Hansson, B.A. 1990. “The Swedish tradition: Wicksell and Cassel”, in Hennings and Samuels, 251–79. Harcourt, G.C. 1969. “Some Cambridge controversies in the theory of capital”, Journal of Economic Literature, 7(2): 369–405. ——1972. Some Cambridge Controversies in the Theory of Capital, Cambridge: Cambridge University Press. ——1975. “Decline and rise: the revival of (classical) political economy”, Economic Record, 51: 339–56. ——1976. “The Cambridge controversies: old ways and new horizons – or dead end?” Oxford Economic Papers, 28: 25–65. ——1977. “The theoretical and social significance of the Cambridge controversies in the theory of capital: an evaluation”, Revue d’Economie Politique, 87(2): 351–75. ——1979. “Non-neoclassical capital theory”, World Development, 7: 923– 32. ——1996. “Some reflections on Joan Robinson’s changes of mind and their relationship to Post-Keynesianism and the economics profession”, in Marcuzzo et al. ——2001. 50 Years a Keynesian and Other Essays, Basingstoke: Palgrave. ——2002. ‘Review of Mandler 1999’, Economic Journal, 112: F379–F381. Harcourt, G.C. and Massaro, V.G. 1964. “Mr. Sraffa’s Production of Commodities”, Economic Record, 40: 442–54. Harcourt, G.C. and Riach, P.A. eds. 1997. A “Second Edition” of the General Theory, 2 vols, London: Routledge. Hatta, T. 1987. “Capital perversity”, in Eatwell et al., I, 354–6. Hayek, F.A. von, 1934. “Carl Menger”, Economica, New Series, 1: 393–420. Hennings, K. and Samuels, W. eds 1990. Neoclassical Economic Theory, 1870 to 1930, Amsterdam: Kluwer. Henry, J.F. 1983. “John Bates Clark and the marginal product: an historical inquiry into the origins of value-free economic theory”, History of Political Economy, 15: 375–89.

——1994. “John Bates Clark: the religious imperative”, in Brennan and Waterman, 61–76. ——1995. John Bates Clark. The Making of a Neoclassical Economist, London: Macmillan. Herford, C.H. 1931. Philip Henry Wicksteed: His Life and Work, London: Dent. Hicks, J.R. 1932a. The Theory of Wages, London: Macmillan. ——1932b. “Marginal productivity and the principle of variation”, Economica, 12: 79–88. ——1932c. ‘Reply to Schultz (1932)’, Economica, 12: 297–300. ——1934. ‘Review of P.H. Wicksteed, The Common Sense of Political Economy, 1933’, Economica, New Series, 1: 351–4. ——1936–7. “Distribution and economic progress”, Review of Economic Studies, 4: 1–12. ——1963. The Theory of Wages, 2nd edn, London: Macmillan. ——1974. “Capital controversies: ancient and modern”, American Economic Review, 64(2): 307–16. ——1975. “Revival of political economy: the old and the new”, Economic Record, 51: 365–7. ——1989. “The assumption of constant returns to scale”, Cambridge Journal of Economics, 13: 9–17. Higgins, B.H. 1935. “W.S. Jevons – a centenary estimate”, The Manchester School, 6(2): 103–11. Hobson, J.A. 1903–4. “Marginal units in the theory of distribution”, Journal of Political Economy, 12: 449–72. ——1904–5. “The marginal theory of distribution: a reply to Professor Carver”, Journal of Political Economy, 13: 587–90. ——1910. “The marginal productivity theory. A reply to criticism”, Economic Review, 20: 301–10.

——1926. Free-thought in the Social Sciences, London: George Allen & Unwin. ——[1914] 1968. Work and Wealth. A Human Valuation, New York: Augustus M. Kelley. ——[1910] 1969. The Industrial System. An Inquiry into Earned and Unearned Income, New York: Augustus M. Kelley. ——[1900] 1972. The Economics of Distribution, Clifton, NJ: Augustus M. Kelley. Homan, P.T. [1928] 1968. Contemporary Economic Thought, Freeport, NY: Books for Libraries Press. Hutchison, T.W. 1953. A Review of Economic Doctrines 1870–1929, Oxford: Clarendon Press. Jevons, W.S. 1871. The Theory of Political Economy, London: Macmillan. ——1879. The Theory of Political Economy, 2nd edn, London: Macmillan. ——1882. The State in Relation to Labour, London: Macmillan. ——1931. The Theory of Political Economy, 4th edn, reprinted London: Macmillan. ——[1871] 1970. The Theory of Political Economy, edited with introduction by R.D. Collison Black, Harmondsworth: Pelican Books. Johnson, H. 1973. The Theory of Income Distribution, London: Gray-Mills. ——1974. “The current and prospective state of economics”, Australian Economic Papers, 13: 1–27. Joye, M.P. and Blayney, P.J. 1990. Cost and Management Accounting Practice in Australian Manufacturing Companies: Survey Results, Monograph No. 7, University of Sydney: Accounting and Finance Foundation. Kahn, R. 1989. The Economics of the Short Period, London: Macmillan. Kaldor, N. 1950. “Distribution, theory of”, Chambers Encyclopedia, Vol. 4, 553–6.

——1956. “Alternative theories of distribution”, Review of Economic Studies, 23(2): 83–100. Reprinted in Kaldor 1960, 209–36. ——1960. Essays in Value and Distribution, London: Gerald Duckworth. Kaufman, B.E. 1988. “The postwar view of labor markets and wage determination”, in Kaufman, ed. How Labor Markets Work, Lexington, MA: D.C. Heath, 174–9. Keynes, J.M. 1936. The General Theory of Employment Interest and Money, London: Macmillan. King, J.E. 1995. Post Keynesian Economics: An Annotated Bibliography, Aldershot: Edward Elgar. ——2002. A History of Post Keynesian Economics Since 1936, Cheltenham: Edward Elgar. Knight, F.H. 1928. “Historical and theoretical issues in the problem of modern capitalism”, Journal of Economics and Business History, 1(1) November. Reprinted in Knight 1956, 89–103. ——[1930] 1935. “Statics and dynamics. Some queries regarding the mechanical analogy in economics”. Translated from the original German. Reprinted in The Ethics of Competition and Other Essays, London: George Allen & Unwin, 161–85. ——1950. Introduction, in Menger [1871] 1950. ——1956. On the History and Method of Economics. Selected Essays, Chicago, IL: University of Chicago Press. ——[1921] 1965. Risk, Uncertainty and Profit, Hart, Schaffner & Marx. Reprinted New York: Harper & Row. Kregel, J. [1973] 1975. The Reconstruction of Political Economy. An Introduction to PostKeynesian Economics, London: Macmillan, 1st edn, 1973; 2nd edn, 1975. Kurz, H.D. 1999. “From classical rent theory to marginal productivity theory: the works of F.B.W. Hermann and J.H. von Thünen”, in Mongiovi and Petri, 145–64. Lancaster, K. 1969. Introduction to Modern Microeconomics, Chicago, IL: Rand McNally.

Lange, O. 1963. Political Economy, Vol. I, General Problems, trans. A.H. Walker, Oxford: Pergamon Press; first Polish edn, 1959. Langfield-Smith, K., Thorne, H. and Hilton, R.W. 1998. Management Accounting. An Australian Perspective, 2nd edn, Sydney: McGraw-Hill. Laughlin, J.L. 1903–4. “Hobson’s theory of distribution”, Journal of Political Economy, 12: 305–26. Lee, F.S. 1984a. “The marginalist controversy and the demise of full cost pricing”, Journal of Economic Issues, 18(4): 1107–32. ——1984b. “Whatever happened to the full-cost principle (USA)?”, in Wiles and Routh, 233–9. Lee, F.S. and Keen, S. 2004. “The incoherent emperor: a heterodox critique of neoclassical microeconomic theory”, Review of Social Economy, 62(2), 169–200. Lester, R.A. 1946. “Shortcomings of marginal analysis for wage-employment problems”, American Economic Review, 36: 63–82. ——1947. “Marginalism, minimum wages, and labor markets”, American Economic Review, 37: 135–48. Lindahl, E. ed. 1958. Knut Wicksell. Selected Papers on Economic Theory, London: George Allen & Unwin. Lipsey, R.G. 1975. An Introduction to Positive Economics, 4th edn, London: Weidenfeld & Nicolson. Machlup, F. 1946. “Marginal analysis and empirical research”, American Economic Review, 36: 519–54. ——1947. “Rejoinder to an antimarginalist”, American Economic Review, 37:148–54. ——[1936] 1950. “On the meaning of the marginal product”, Explorations in Economics, New York: McGraw-Hill, 250–63. Reprinted in Fellner and Haley, 1950. ——1967. “Theories of the firm: marginalist, behavioral, and managerial”, American Economic Review, 57(1): 1–33. McNulty, P.J. 1980. The Origins and Development of Labor Economics, Cambridge, MA: MIT Press.

McTaggart, D., Findlay, C. and Parkin, M. 1999. Microeconomics, 3rd edn, South Melbourne: Addison Wesley Longman Australia. Makowski, L. and Ostroy, J.M. 1992. “The existence of perfectly competitive equilibrium à la Wicksteed”, in Dasgupta et al., 370–403. Malthus, T.R. [1820] 1989. Principles of Political Economy, Variorum edn, 2 vols, ed. J. Pullen, Cambridge: Cambridge University Press for the Royal Economic Society. Mandler, M. 1999. Dilemmas in Economic Theory. Persisting Foundational Problems of Microeconomics, Oxford: Oxford University Press. Marcuzzo, M.C., Pasinetti, L.L. and Roncaglia, A. 1996. The Economics of Joan Robinson, London: Routledge. Marshall, A. 1925. Memorials of Alfred Marshall, ed. A.C. Pigou. ——1949. Principles of Economics. An Introductory Volume, 8th edn, London: Macmillan, 1st edn, 1920. ——1961. Principles of Economics, ed. C.W. Guillebaud, 2 vols, 9th (variorum) edn, London: Macmillan for the Royal Economic Society. Marshall, A. and Marshall, M.P. 1879. Economics of Industry, London: Macmillan. Menger, C. [1871] 1950. Principles of Economics, trans. J. Dingwall and B.F. Hoselitz, Introduction by F.H. Knight, Glencoe, IL: The Free Press. Mill, J.S. [1848] 1909. Principles of Political Economy, ed. W.J. Ashley, London: Longmans, Green & Co. Mongiovi, G. and Petri, F. eds. 1999. Value, Distribution and Capital. Essays in Honour of Pierangelo Garegnani, London and New York: Routledge. Moss, L.S. 1973. “Isaac Butt and the early development of the marginal utility theory of imputation”, History of Political Economy, 5(2): 317–38. Nell, E.J. 1973. “The fall of the House of Efficiency”, Annals of the American Academy of Political and Social Science, 409: 102–11. Newman, P. 1987. “Euler’s theorem”, in Eatwell et al., II, 196. Ng, Y-K. 1974a. “Harcourt’s survey of capital theory”, Economic Record, 50: 119–29.

——1974b. “The neoclassical and the neo-Marxist-Keynesian theories of income distribution: a non-Cambridge contribution to the Cambridge controversy in capital theory”, Australian Economic Papers, 13: 124–32. Paish, F.W. 1964. Benham’s Economics. A General Introduction, 7th edn, London: Sir Isaac Pitman & Sons. Palgrave, R.H.I. [1925–6] 1963. Palgrave’s Dictionary of Political Economy, ed. H. Higgs, 2nd edn, 3 vols, reprinted 1963, New York: Augustus M. Kelley. Pareto, V. 1901. L’économie pure. Résumé du cours professé à l’Ecole des Hautes Etudes Sociales à Paris, 1901–2. ——1902. ‘Review of A. Aupetit 1901’, Revue d’économie politique, 16: 90–3. ——[1906] 1971. Manual of Political Economy, trans. from the French edn of 1927 by Ann S. Schwier, London: Macmillan. Pasinetti, L. ed. 1998. Italian Economic Papers, Vol. III, Il Mulino: Oxford University Press. Pen, J. 1971. Income Distribution, Harmondsworth: Penguin Books. Persky, J. 2000. “The neoclassical advent: American economics at the dawn of the 20th century”, Journal of Economic Perspectives, 14(1): 95–108. Pigou, A.C. [1933] 1968. The Theory of Unemployment, New York: Augustus M. Kelley. Prasch, R.E. (forthcoming). “Professor Lester and the neoclassicals: the ‘marginalist controversy’ and the postwar academic debate over minimum wage legislation: 1945–1950”, Journal of Economic Issues. Reynolds, L.G. 1963. Economics, Homewood, IL: Richard D. Irwin. Ricardo, D. 1951–73. The Works and Correspondence of David Ricardo, ed. Piero Sraffa with the collaboration of M.H. Dobb, Cambridge: Cambridge University Press for the Royal Economic Society. Rima, I.H. 1991. Development of Economic Analysis, 5th edn, Homewood, IL: Irwin. Robbins, L. 1930. ‘The economic works of Phillip Wicksteed”, Economica, 10: 245–58.

——1933. Introduction, in Wicksteed [1910] 1933, vii–xxiii. ——1934. Introduction, in Wicksell 1934. Robertson, D.H. [1931] 1950. “Wage grumbles”, in Economic Fragments, London: P.S. King & Son, 42–57, reprinted in Fellner and Haley, 221–36. Robinson, J. 1933a. The Economics of Imperfect Competition, London: Macmillan. ——1933b. ‘Review of P.H. Wicksteed, The Co-ordination of the Laws of Distribution’, Economic Journal, 43: 301–4. ——1934. “Euler’s theorem and the problem of distribution”, Economic Journal, 44: 398–414. ——1953–54. “The production function and the theory of capital”, Review of Economic Studies, 21: 81–106. ——1970. “Capital theory up to date”, Canadian Journal of Economics, 3(2): 309–17. ——1971. Economic Heresies, New York: Basic Books. ——1973a. “Marginal productivity”, in Collected Economic Papers, Vol. 4, Oxford: Blackwell, 129–38. First published in Indian Economic Review, April 1967. ——1973b. Foreword, in Kregel [1973] 1975, ix–xiii. ——1974. History versus Equilibrium, London: Thames Polytechnic. ——1975. “The unimportance of reswitching”, Quarterly Journal of Economics, 89:1, 32–9, with replies by P. Samuelson, R. Solow and J. Robinson, 40–55. ——[1974] 1979. “History versus equilibrium”, Collected Economic Papers, Oxford: Blackwell, Vol. 5, 57. ——1979. Aspects of Development and Underdevelopment, Cambridge: Cambridge University Press. ——and Eatwell, J.L. 1973. An Introduction to Modern Economics, London: McGrawHill.

Rothschild, K.W. 1994. “The theory of wages revisited”, in Hagemann and Hamouda, 60–74. Routh, G. 1975. The Origin of Economic Ideas, London: Macmillan. Samuelson, P.A. 1958. Economics. An Introductory Analysis, 4th edn, New York: McGrawHill. Scazzieri, R. 1987. “Reswitching of technique”, in Eatwell et al., IV, 162–4. Schneider, M. 1996. J. A. Hobson, Basingstoke: Macmillan. Schultz, H. 1929. “Marginal productivity and the general pricing process”, Journal of Political Economy, 37(5): 505–51. ——1932. “Marginal productivity and the Lausanne School”, Economica, 12: 285–96, with a reply by J.R. Hicks, 297–300. Schumpeter, J.A. 1954. A History of Economic Analysis, Homewood, IL: Irwin. Shackle, G.L.S. 1959. Economics for Pleasure, Cambridge: Cambridge University Press. ——[1954] 1970. Foreword, in Wicksell, 1970, 6–13. Shaw, Bernard [1928] 1929. The Intelligent Woman’s Guide to Socialism and Capitalism, London: Constable. ——1965. Collected Letters, 1874–1897, ed. Dan H. Laurence, London: Max Reinhart. ——1991. Bernard Shaw’s Book Reviews: Originally Published in the Pall Mall Gazette from 1885 to 1888, ed. Brian Tyson, University Park, PA: Pennsylvania State University Press. ——1996. Bernard Shaw’s Book Reviews: 1884–1950, ed. Brian Tyson, University Park, PA: Pennsylvania State University Press. Shove, G. 1933. ‘Review of J.R. Hicks, The Theory of Wages, 1932’, Economic Journal, 43: 460–73. Smyth, R.L. ed. 1962. Essays in Economic Method: Selected Papers Read to Section F of the British Association for the Advancement of Science, 1860– 1913, London: Duckworth.

Smyth, R.L. ed. 1964. Essays on the Economics of Socialism and Capitalism: Selected Papers Read to Section F of the British Association for the Advancement of Science, 1886–1932, London: Duckworth. Solow, R.M. 1975. ‘Comment’ (48–52) on Robinson 1975. Spiegel, H.W. ed. 1952. The Development of Economic Thought. Great Economists in Perspective, New York: John Wiley & Sons. ——1991. The Growth of Economic Thought, 3rd edn, Durham, NC: Duke University Press. Sraffa, P. 1926. “The laws of returns under competitive conditions”, Economic Journal, 36: 535–50. ——1960. Production of Commodities by Means of Commodities. Prelude to a Critique of Economic Theory, Cambridge: Cambridge University Press. ——[1925] 1998. Sulle relazioni fra costo e quantità prodotta, Annali di Economia, 2(1): 227–328. Translated as “On the relations between cost and quantity produced”, by John Eatwell and Allesandro Roncaglia, and published in Pasinetti, 323–63. Steedman, I. 1972. “Jevons’s theory of capital and interest”, Manchester School, 40(1): 31–52. ——1987a. “Adding-up problem”, in Eatwell et al., I, 21–2. ——1987b. “Wicksteed, Philip Henry”, in Eatwell et al., IV: 915–19. ——1989. “P.H. Wicksteed’s Jevonian critique of Marx”, in From Exploitation to Altruism, Cambridge: Polity Press. ——1992. Introduction, in Wicksteed, 3–45. ——1994. “Wicksteed: economist and prophet”, in Brennan and Waterman, 77–101. ——1997. “Jevons’s Theory of Political Economy and the ‘marginalist revolution’”, European Journal of the History of Economic Thought, 4(1): 43–64. Stigler, G.J. 1941. Production and Distribution Theories: The Formative Period, New York: Macmillan.

——1947. “Stuart Wood and the marginal productivity theory”, Quarterly Journal of Economics, 61: 640–9. Stiglitz, J.E. 1974. “The Cambridge–Cambridge controversy in the theory of capital: a view from New Haven: a review article”, Journal of Political Economy, 82: 893–903. Streissler, E. 1987. “Wieser, Friedrich, Freiherr von”, in Eatwell et al., IV, 921–2. ——1990. “Menger, Böhm-Bawerk, and Wieser: the origins of the Austrian School”, in Hennings and Samuels, 151–89. Swan, T. 1956. “Economic growth and capital accumulation’, Economic Record, 32: 334–61. Tarascio, V.J. 1967. “Léon Walras: on the occasion of the publication of his correspondence and related papers”, Southern Economics Journal, 34: 133– 45. ——1973. “Vilfredo Pareto: on the occasion of the translation of his Manuel”, Canadian Journal of Economics, 6: 394–408. Taussig, F.W. 1910. “Outlines of a theory of wages”, Publications of the American Economic Association, 3rd series, Vol. 11: 136–56. ——1911. Principles of Economics, 2 vols, New York: Macmillan. Taylor, F.M. [1921] 1925. Principles of Economics, New York: The Ronald Press Company. Taylor, O.H. 1960. A History of Economic Thought, New York: McGrawHill. Thünen, J.H. von 1966. Von Thünen’s Isolated State, trans. C.M. Wartenberg, Oxford: Pergamon. Thurow, L. [1975] 1976. “A do-it-yourself guide to marginal productivity”, Appendix A, 211–30, in Generating Inequality, London: Macmillan. Uhr, C.G. 1960. Economic Doctrines of Knut Wicksell, Berkeley and Los Angeles: University of California Press. Valk, W.L. 1928. The Principles of Wages, London: P.S. King.

Veblen, T. 1907–8. “Professor Clark’s economics”, Quarterly Journal of Economics, 22: 147–95. Viner, J. ed. [1936] 1967. Explanations in Economics. Notes and Essays Contributed in Honor of F.W. Taussig, reprinted New York: Augustus M. Kelley. Walker, D. 1980. “Clarence Ayres’s critique of orthodox economic theory”, Journal of Economic Issues, 14: 649–80. Walras, L. [1926] 1954a. Elements of Pure Economics or the Theory of Social Wealth, translation by William Jaffé of the Edition Définitive (1926), Homewood, IL: Richard D. Irwin for the American Economic Association and the Royal Economic Society. ——[1896] 1954b. “Note on Mr. Wicksteed’s refutation of the English theory of rent”, Recueil publié par la Faculté de Droit de l’Université de Lausanne, reprinted as an Appendix to the 3rd edn of the Eléments 1896. Reprinted Walras 1954a, Appendix III, 489–95. Walsh, V. 1989. “A view of Joan Robinson’s last decade”, in Feiwel, 881–91. Waud, R.N. 1986. Economics, 3rd edn, New York: Harper & Row. Webb, S. 1887–8. “The rate of interest and the laws of distribution”, Quarterly Journal of Economics, 2: 188–208. Webb, S. [1889] 1964. “On the relation between wages and the remainder of the economic product”, in Smyth, 65–73. Webb, S. and Webb, B. [1898] [1902] 1972. Problems of Modern Industry by Sidney & Beatrice Webb, Freeport, NY: Books for Libraries Press. Weintraub, S. 1972. “Marginal productivity and macrodistribution theory”, Western Economic Journal, 10: 45–56. Weizsäcker, C.C. von 1971. “Ende einer Wachstumstheorie?”, Kyklos, 24: 97–101. Whitaker, J.K. 1974. “The Marshallian system in 1881: distribution and growth”, Economic Journal, 84: 1–17. ——ed. 1975. The Early Economic Writings of Alfred Marshall, 1867–1890, 2 vols, London: Macmillan for the Royal Economic Society.

——1988. “The distribution theory of Marshall’s Principles”, in Asimakopulos, 105–32. White, M.V. (forthcoming). “Strange brew: the antinomies of distribution in W.S. Jevons’ Theory of Political Economy”. Wicksell, K. [1901, 1906] 1934, 1935. Lectures on Political Economy, 3rd Swedish edn, trans. E. Classen, edited with an Introduction by Lionel Robbins, 2 vols, London: Routledge. ——[1900] 1958a. “Marginal productivity as the basis of distribution in economics”, Ekonomisk Tidskift, 305–37, reprinted in Lindahl, 93–120. ——[1902] 1958b. “On the problem of distribution”, Ekonomisk Tidskrift, 424–33, reprinted in Lindahl, 121–30. ——[1893] 1970. Value, Capital and Rent. English translation by S.H. Frowein, Foreword by G.L.S. Shackle, 1954, London: George Allen & Unwin; reprinted 1970, New York: Augustus M. Kelley, 1st edn, Über Wert, Kapital und Rente, 1893. Wicksteed, P.H. 1888. Getting and Spending. Papers on the Meaning and Uses of Money, London (Twelve articles originally published in The Inquirer). ——1906. “Review of Pareto’s Manuale di Economia Politica”, Economic Journal, 16: 553–7. ——1913. “Review of S.J. Chapman, Political Economy (1912)”, Economic Journal, 23: 72–5. ——1914. “The scope and method of political economy in the light of the ‘marginal’ theory of value and distribution”, Economic Journal, 21: 1–23. A fuller version of this paper appears in Smyth (1962). ——[1894] 1932. An Essay on the Co-ordination of the Laws of Distribution, London: London School of Economics and Political Science. ——[1910] 1933. The Common Sense of Political Economy, 2 vols, ed. Lionel Robbins, London: Routledge & Kegan Paul. ——[1894] 1992. The Co-ordination of the Laws of Distribution, revised edn, ed. with Introduction by I. Steedman, Aldershot: Edward Elgar. Wieser, F. [1888] 1956. Natural Value, ed. W. Smart, trans. C.A. Malloch, 1893; reprinted Kelley & Millman, New York, first German edn, 1888.

Wiles, P.J.D. 1961. Price, Cost and Output, Oxford: Blackwell. Wiles, P. and Routh, G. eds. 1984. Economics in Disarray, Oxford: Blackwell. Wood, S. 1888–9. “A new view of the theory of wages”, Quarterly Journal of Economics, 3: 60–86, 462–80. ——1889. “The Theory of Wages”, Publications of the American Economic Association, 4: 5–35. ——1891. “A critique of wages theories”, Annals of the American Academy of Political and Social Science, 1: 426–61. Yordon, W.J. 1992. “Stigler’s adaptable and indivisible plant and the micro/macro schism”, History of Political Economy, 24(2): 455–70.

Index adding-up (or, exhaustion-of-product) problem or theorem, 4, 5, 7, 17, 20, 24, 27, 28, 29, 30, 31, 33, 35, 36, 37, 38, 46, 47, 48, 49, 72, 88, 91, 94, 103, 105, 106, 112, 116, 126, 127, 135, 136, 162, 163, 164, 165, 166, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 184, 189 Adriance, W.M., 3, 81–2, 97, 134, 135, 137, 175, 178, 187 Amoroso, L., 187 Antonelli, E., 172 Aupetit, A., 37 Ayres, C., 186

Bailey, S., 167 bargaining power theory of distribution, 6, 26, 66, 88, 91, 94, 98, 101, 115, 119, 120, 122, 124, 129, 132, 133, 140, 153, 154, 157, 169, 187 Barone, E., 40, 41, 46, 136, 171, 172, 173 Beeton, H.R., 170 Bhaduri, A., 175 Black, R.D.C., 12, 167 Blaug, M., 63, 98, 128–33, 136, 176, 179, 184, 185, 188 Bliss, C.J., 23, 24, 27, 176 Blum, F.H., 186 Böhm-Bawerk, E., 130, 172 Bowley, M., 12 Bradford, W., 98

Bridge, J., 169 British Economic Association, 170 Bronfenbrenner, M., 117–18, 135, 149, 182, 186 Bruno, 189 Butt, I., 11, 13, 20, 167

Cambridge capital theory controversy, 1, 64, 79, 96, 117, 118, 121, 122, 175, 182, 184 Cannan, E., 73 capital, measurement and aggregation of, 5, 51, 98, 101, 116, 117, 119, 120, 122, 131, 132, 136, 171, 173, 182, 183 capital reversing, 122, 124, 183 Caravale, G., 185 Carver, T.N., 68–71, 92, 107, 176, 177 Cassel, G., 3, 83–8, 134, 135, 178, 184 causation, 92–4 causation, circular, 26, 120, 121, 136 causation, reciprocal, 120 ceteris paribus and ceteris inefficacibus, 3, 7, 9, 33, 34, 73, 126, 132, 138, 167, 168, 170, 174, 178 Chamberlin, E.H., 112–13, 181 Chapman, S.J., 66, 73, 74–6, 165, 177 circular reasoning, 5, 33, 51, 64, 79, 101, 116, 117, 118, 119, 120, 121, 122, 123, 136, 169, 175, 177, 183, 184 Clark, J.B., 1, 2, 19, 25, 33, 35, 43, 49, 51–60, 65, 68, 69, 72, 73, 74, 77, 78, 79, 81, 82, 88, 89, 92, 93, 94, 95, 99, 100, 107, 108, 113, 114, 121, 130, 137,

138, 142, 148, 149, 150, 152, 167, 168, 174, 175, 176, 178, 182, 185, 186, 187 Clark, J.M., 52, 53, 54, 56, 57, 72, 92, 94–6, 166, 168, 177, 178, 179 class conflict, class struggle, class war, class structure, 2, 51, 98, 119, 120, 131, 153, 154 Cohen, A., 183 commutative justice, 187 composite dose criticism, 63 constant costs, 47, 105, 106, 173, 180 constant returns to scale, or homogeneous function of the first degree, 29, 30, 36, 37, 40, 46, 47, 48, 72, 103, 105, 106, 112, 116, 117, 125, 126, 127, 136, 163, 164, 165, 169, 171, 173, 174, 177, 179, 180, 181, 184, 189 Copernicus, 189 correlation, distinguished from causation, 9, 69, 93, 176 Creedy, J., 31

Davenport, H.J., 3, 71, 76–8, 97, 134, 175, 187 Del Punta, V., 119, 184, 185 Dernburgh, T.F., 149 diminishing returns, 12, 143, 186 discounted marginal product, 79, 80, 135 disentanglement, or separability, or separate productivity, 1, 4, 6, 17, 18, 19, 32, 38, 44, 51, 54, 55, 57, 59, 65, 66, 71, 74, 75, 76, 77, 78, 81, 89, 90, 92, 94, 100, 101, 102, 107, 108, 113, 118, 121, 122, 123, 124, 132, 134, 135, 141, 143, 146, 149, 150, 152, 155, 156, 170, 171, 174, 176, 177, 178, 181, 182, 183, 185, 187 dislocation argument, 62, 92

distribution and redistribution, of income and wealth, 2, 5, 51, 52, 53 distributive justice, 6, 53, 55, 73, 83, 97, 187 Dobb, M.H., 99–101, 136, 156, 168, 179, 188 Dorfman, J., 166 Dorfman, R., 122, 149, 186 Douglas, Major, 2 Douglas, P.H., 107–8, 135, 180

Eatwell, J., 159, 179, 182, 186, 187 Economic Club, 170 Edgeworth, F.Y., 3, 31, 32, 46, 62, 71–4, 103, 108, 134, 135, 136, 162, 163, 165, 170, 176, 177, 178, 179 Eiteman, W.J., 110, 181 Ekelund, R.B., 148 Ellerman, D.P., 174 equilibrium position or condition, 19, 21, 22, 97, 104, 105, 108, 109, 118, 121, 132, 136, 138, 139, 152, 153, 179, 180, 186, 187 ethical implications see normative implications Euler’s theorem, 4, 6, 7, 20, 24, 29, 30, 31, 34, 35, 36, 37, 41, 85, 103, 106, 118, 125, 126, 127, 130, 135, 136, 163, 169, 170, 171, 176, 184 exploitation, 2, 52, 56, 76, 142

false separatism, 1, 12, 61, 65, 67, 100, 114, 134, 169, 176 Fetter, F.A., 176

Fisher, I., 183 fixed or overhead or indirect costs, allocation of, 7, 23, 95, 101, 115, 132, 140, 141, 146, 153, 167, 182 Flatau, P., 156, 179 Flux, A.W., 20, 29, 30–5, 48, 95, 103, 134, 135, 166, 169, 173, 177 Foxwell, H., 170 Fraser, L.M., 113–15, 135 full cost, or average cost, theory, 109, 111, 146

Galileo, 189 Gärdlund, T., 172, 173 George, Henry, 2, 52, 137, 174 Gordon, S., 175 government intervention, 2, 153 Groenewegen, P.D., 148, 168, 170 Gustafsson, B., 178

Hahn, F.H., 179 Hamouda, O.F., 106, 107, 180 Harcourt, G.C., 23, 52, 98, 119, 122, 173, 182, 183, 184 Hatta, T., 122 Hayek, F.A. von, 15 Hebert, R.F., 148 Hegelian darkness, 50, 137

Henry, J.F., 57, 167, 174 Herford, C.H., 29 Hicks, J.R., 36, 102–7, 130, 136, 160, 170, 171, 179, 180, 183, 184, 185, 189 Higgins, B.H., 155 Hobson, J.A., 1, 3, 12, 38, 51, 61–8, 71, 75, 76, 78, 81, 92, 97, 100, 102, 107, 108, 114, 121, 125, 143, 169, 175, 176, 177, 178, 180, 187 homogeneous function of the first degree see constant returns to scale Hutchison, T.W., 15, 56, 135, 165

ideological aspects, 2, 5, 7, 19, 50, 52, 67, 68, 82, 148, 186, 187 imputation theory, 4, 15, 17, 18, 19, 20, 107, 108 indivisibility of inputs, 143 interdependence factors or variables, 37, 46, 127, 130, 135, 163, 170, 171, 175, 182, 185

Jaffé, W., 41, 172 Jevons, W.S., 29, 99, 155–7, 168, 175, 188, 189 Johnson, H.G., 125–8, 136, 184

Kahn, R., 145 Kaldor, N., 116–17, 136, 173, 179, 180, 181 Kaufman, B.E., 181 Keen, S., 186 Keynes, J.M., 108–9, 123, 181, 184 King, J., 98, 173

Knight, F., 90–4, 137, 167, 178, 184 Kurz, H., 11, 153

laissez-faire, 2, 187 Lange, O., 171, 172 Laughlin, J.L., 176, 178 Laurence, D.H., 170 Lee, F.S., 171, 181, 186 Lester, R.A., 109–12, 178, 181, 186 Lipsey, R.G., 149 Locke, John, or Lockean theory of property, 5, 25, 54, 55, 57, 77, 114, 139, 141, 142, 149, 150, 151, 152, 176, 179, 181, 183, 187 Longfield, M., 11, 12, 13, 20, 167 Loria, A., 97

McDougall, D.M., 149 McNulty, P.J., 181 McTaggart, D., 149 Machlup, F., 9, 109–12, 181, 186 Makowski, L., 180 Malthus, T.R., 11, 153, 172, 179 Mandeville, B., 187 Mandler, M., 1 marginal cost, true, 144–7

marginal product, fully net and partially net, 3, 21, 22, 23, 24, 25, 26, 99, 100, 102, 109, 115, 121, 132, 139, 141, 151, 152, 158–61, 167, 181, 182 marginal product, gross and net, 10, 20, 21, 26, 64, 100, 107, 138, 168, 178, 181, 185 Marshall, A., 3, 9, 10, 19–27, 45, 62, 63, 64, 87, 100, 107, 118, 130, 134, 138, 144, 147, 158–61, 168, 169, 172, 175, 176, 178, 181, 184, 185, 188 Marshall, M.P., 158 Marx, Karl, 2, 29, 50, 52, 120, 123, 137, 170, 174, 184 Menger, C., 15, 16, 134, 157, 167, 189 method of difference, 69, 177 Mill, J.S., 73, 164, 174, 185 minimum cost condition, 105, 106, 136, 180 Mitchell, W.C., 178 monocausality and multicausality, 3, 4, 5, 6, 9, 10, 14, 25, 32, 33, 53, 54, 55, 57, 75, 82, 94, 95, 97, 100, 115, 123, 124, 134, 135, 140, 142, 143, 145, 148, 150, 151, 152, 177, 178, 181, 185, 186 moral implications see normative implications Moss, L.S., 12, 13 MPAL (marginal product after labour), 3, 8, 9, 14, 25, 26, 33, 54, 55, 61, 69, 70, 95, 96, 101, 102, 113, 133, 138, 140, 141, 142, 147, 152, 181, 185

natural justice, 2 natural law, 5, 52, 53, 54, 58, 60, 99 Nell, E.J., 124–5, 137 Ng, Y.-K., 119, 121, 123–4, 136, 184, 185 Nicholson, J.S., 32 no-rent instruments, 57, 58

normative implications, 1, 2, 5, 6, 7, 29, 51, 53, 54, 69, 71, 77, 82, 90, 92, 93, 94, 96, 114, 115, 121, 125, 135, 137, 138, 149, 150, 151, 156, 176, 179, 181, 186, 187

overhead costs see fixed costs

Pareto, V., 3, 35–9, 41, 46, 48, 126, 130, 135, 162, 163, 165, 170, 171, 172, 175, 182, 185, 188 Pasinetti, L., 179 Pen, J., 149 Persky, J., 187 Petty, W., 11 Pigou, A.C., 109, 117 political and social implications, 5, 19, 52, 67, 81, 90, 92, 119, 137 positive law or theorem, 1, 2, 5, 6, 7, 114, 121, 125, 135, 138, 150, 154, 183, 184, 187 post hoc ergo propter hoc, 9 principle of scarcity, 85, 86, 87, 88, 134 productivity theory of distribution, 12, 13 proprietorial ‘of’, 3, 9, 10, 14, 53, 97, 138, 143, 185 putty, or plastic capital, 182 reswitching, or double switching, 101, 119, 122, 123, 179, 183, 184

Reynolds, L.G., 186 Ricardo, D., 19, 29, 39, 117, 153, 175, 179, 185, 186 Rima, I.H., 182

Robbins, L., 27, 42, 135, 164, 165, 189 Robertson, D.H., 1, 101, 118 Robinson, Joan, 4, 27, 30, 85, 98, 105, 118–23, 124, 136, 151, 159, 169, 170, 173, 175, 177, 181, 182, 183, 184, 186, 187, 188 Rothschild, K., 102 Rousseau, J.-J., 174 Routh, G., 11, 29 Royal Economic Society, 170 Russell, B., 101, 118

Samuelson, P.A., 149 Say, J.-B., 167 Scazzieri, R., 122 Schneider, M., 176 Schultz, H., 39, 41, 170, 171, 172 Schumpeter, J.A., 11, 12, 15, 16, 24, 155, 172, 175, 176 Scrope, G.P., 167 second order of smalls argument, 63, 64 Senior, N.W., 167 separate productivity, law of see false separatism Shackle, G.L.S., 170, 173 Shaw, Bernard, 29, 101, 118, 170 Shove, G., 107 Sidgwick, H., 174

simultaneous equations, 4, 7, 17, 18, 38, 39, 87, 88, 121, 132, 134, 136, 152, 178, 179, 183 Smith, Adam, 19, 185 Smith, G., 176 SMPL (specific marginal product of labour), 3, 8, 9, 14, 25, 33, 35, 54, 55, 61, 69, 70, 95, 96, 101, 102, 113, 132, 140, 141, 142, 147, 181, 185 Smyth, R.L., 174, 189 social class implications, 67 social justice, 150 socialism, 2, 5, 52, 187 sociological aspects, 82, 131 Solow, R.M., 186 Spiegel, H.W., 56 Sraffa, P., 4, 96–9, 105, 118, 136, 151, 173, 179, 181 Steedman, I., 11, 29, 143, 151, 156, 163, 169, 170, 188, 189, 190 Stigler, G.J., 3, 15, 16, 20, 24, 25, 28, 29, 31, 32, 36, 37, 38, 39, 40, 42, 46, 62, 63, 64, 74, 76, 135, 148, 155, 164, 165, 166, 167, 168, 170, 171, 172, 174, 175, 177, 180, 182, 184, 186, 187, 188, 189, 190 Streissler, E., 17 supply-side considerations, 144 Swan, T., 182

Tarascio, V.J., 35, 36, 38, 171, 172 Taussig, F.W., 78–81, 134, 135, 137, 177 Taylor, F.M., 88–90, 134, 186 Thornton, W.T., 175

Thünen, J.H. von, 14–17, 19, 20, 21, 42, 56, 134, 167, 168, 172, 175 togetherness of the factors, 77, 78, 134 Torrens, R., 179 trade unions, 2, 60, 131, 137 Tyson, B., 170

Uhr, C., 18, 46, 168, 172 user cost, 108, 109, 181

Valk, W.L., 88, 178 Varallo, R.D., 178 variable or fixed proportions of factors, 15, 16, 36, 37, 116, 171, 182 Veblen, T., 60, 148, 167, 177, 182 Viner, J., 112

Walker, D., 186 Wallas, G., 170 Walras, L., 38, 39–42, 46, 47, 87, 103, 105, 130, 136, 157, 171, 172, 173, 178, 180, 187 Walsh, V., 151 Waud, R.N., 149 Webb, B., 174 Webb, S., 50–1, 136, 174 Weintraub, S., 124

Weizsäcker, C.C. von, 121, 136, 183 Whitaker, J.K., 19, 20, 21, 147, 168, 169, 188 Wicker, Professor, 82 Wicksell, K., 3, 4, 18, 38, 42–50, 103, 105, 108, 130, 135, 136, 137, 168, 172, 173, 180, 188 Wicksteed, P.H., 3, 20, 27–30, 31, 32, 35, 39, 40, 42, 46, 47, 48, 91, 94, 95, 103, 105, 116, 117, 130, 134, 135, 136, 143, 151, 162–6, 168, 169, 170, 172, 173, 175, 177, 182, 188, 189, 190 Wieser, F. von, 15, 17–19, 38, 87, 107, 108, 134, 135, 137, 152, 167, 168, 175, 178, 183 White, M., 156 Wiles, P.J.D., 146, 186 Wilson, T., 174 Wood, S., 174–5

Yordon, W.J., 171

zone of indifference, 107