Vilfredo Pareto: An Intellectual Biography Volume II: The Illusions and Disillusions of Liberty (1891–1898) [1st ed.] 978-3-030-04539-5, 978-3-030-04540-1

Table of contents :
Front Matter ....Pages i-xi
Relations between Pareto and the University of Lausanne (Fiorenzo Mornati)....Pages 1-39
Pareto as a Critical Observer of the Italian and Swiss Political Scenes (Fiorenzo Mornati)....Pages 41-92
Pure Economics (Fiorenzo Mornati)....Pages 93-128
General Economic Equilibrium (Fiorenzo Mornati)....Pages 129-140
The Economics of Welfare (Fiorenzo Mornati)....Pages 141-156
From Free-Trade Propaganda to the Theory of International Trade (Fiorenzo Mornati)....Pages 157-179
The Money (Fiorenzo Mornati)....Pages 181-200
Other Topics in Applied Economics (Fiorenzo Mornati)....Pages 201-220
The Economic Theory of Socialism (Fiorenzo Mornati)....Pages 221-235
The Law of Income Distribution and Various Statistical Complements (Fiorenzo Mornati)....Pages 237-259
Initial Development of a New Sociology (Fiorenzo Mornati)....Pages 261-271
Further General Reflections on Politics (Fiorenzo Mornati)....Pages 273-283
Early Critical Reactions to Pareto (Fiorenzo Mornati)....Pages 285-309
Back Matter ....Pages 311-319

Citation preview

VILFREDO PARETO: AN INTELLECTUAL BIOGRAPHY VOLUME II THE ILLUSIONS AND DISILLUSIONS OF LIBERTY (1891–1898) Fiorenzo Mornati

PALGRAVE STUDIES IN THE HISTORY OF ECONOMIC THOUGHT

Palgrave Studies in the History of Economic Thought

Series Editors Avi J. Cohen Department of Economics York University & University of Toronto Toronto, ON, Canada G. C. Harcourt School of Economics University of New South Wales Sydney, NSW, Australia Peter Kriesler School of Economics University of New South Wales Sydney, NSW, Australia Jan Toporowski Economics Department SOAS, University of London London, UK

Palgrave Studies in the History of Economic Thought publishes contributions by leading scholars, illuminating key events, theories and individuals that have had a lasting impact on the development of modernday economics. The topics covered include the development of economies, institutions and theories. More information about this series at http://www.palgrave.com/gp/series/14585

Fiorenzo Mornati

Vilfredo Pareto: An Intellectual Biography Volume II The Illusions and Disillusions of Liberty (1891–1898) Translated by John Paul Wilson

Fiorenzo Mornati Department of Economics and Statistics University of Turin Turin, Italy Translated by John Paul Wilson Milano, Italy

Palgrave Studies in the History of Economic Thought ISBN 978-3-030-04539-5    ISBN 978-3-030-04540-1 (eBook) https://doi.org/10.1007/978-3-030-04540-1 Library of Congress Control Number: 2018943448 © The Editor(s) (if applicable) and The Author(s) 2018 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Cover credit: INTERFOTO / Alamy Stock Photo This Palgrave Macmillan imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

In this second volume of the trilogy, we will turn our attention to the early stages of Pareto’s professional academic and, more particularly, scientific activities. The starting point will be a reconstruction of his key relations with the University of Lausanne, in as much detail and in as fully documented a manner as possible. This will be followed by an examination of the ongoing observations Pareto made regarding political events in Italy and in Switzerland between the years of 1891 and 1898. Having thus outlined the issues which stimulated and fostered Pareto’s thinking, we will trace the evolution of this latter, once again supplying detailed analysis and with the support of documentary evidence, while systematically highlighting continuities with themes appearing in the previous volume of the trilogy. We will investigate all aspects of his thinking on economics, following what appears to be the most logical sequence, passing from pure economics to the concept of general economic equilibrium, the economics of well-being, international trade and the money, the economic theory of socialism and the statistics, together with all the other topics in applied economics which occupied Pareto’s attention, such as the demographic question, the public finance, the functional distribution of wealth and the recurrence of economic crises.

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Thereafter we will identify the early elements which later would be developed, during the period covered in the next volume, into Pareto’s groundbreaking system of sociological and political ideas. We will end with an overview of immediate reactions in Italy and abroad to the publication of his first major work, the Cours d’économie politique (Course in political economy), and to his first original theory, the law of income distribution. Our treatment of these various themes will progressively reveal our interpretation of Pareto’s intellectual biography over this period, where the heights of his enthusiasm for liberal and free-trade ideas appear to give way to a rapid disillusion which led him to pursue his intellectual work for the love of science alone. We have made very selective use of sources in the field of Pareto studies, simply in order to clarify certain aspects of his life and thought. This is due mainly to the enormous dimensions these materials have attained in recent years, together with the fact that Pareto’s name appears increasingly to perform simply a tutelary function, while the person and his authentic ideas become more and more obscure. We have likewise sought to provide formal demonstrations which, while as complete as possible, are also adapted to a very broad readership. Turin, Italy

Fiorenzo Mornati

Acknowledgements

I would like to thank Roberto Marchionatti for the long discussions on the various aspects of Pareto’s thinking covered in this book, as well as (in alphabetical order) the Archives Cantonales Vaudoises (Vaud Cantonal Archives) in Lausanne, the Archives de la Commune de Lausanne (Lausanne Municipal Archives), the Banca Popolare di Sondrio (Popular Bank of Sondrio), custodian of the Vilfredo Pareto archive held at the Luigi Credaro library in Sondrio, together with Piercarlo Della Ferrera, the chief archivist, for their patient support. Lastly, I must also express my gratitude to Luisa Giacoma, lecturer at the University of Turin, for her very helpful translations of German-language texts.

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Contents

1 Relations between Pareto and the University of Lausanne  1 2 Pareto as a Critical Observer of the Italian and Swiss Political Scenes 41 3 Pure Economics 93 4 General Economic Equilibrium129 5 The Economics of Welfare141 6 From Free-Trade Propaganda to the Theory of International Trade157 7 The Money181 8 Other Topics in Applied Economics201 9 The Economic Theory of Socialism221

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10 The Law of Income Distribution and Various Statistical Complements237 11 Initial Development of a New Sociology261 12 Further General Reflections on Politics273 13 Early Critical Reactions to Pareto285 Epilogue311 Index315

List of Tables

Table 1.1 Pareto’s fiscal situation Table 10.1 Earnings in Saxony for 1890 Table 10.2 Effective income earners and theoretical income earners in Saxony for 1890 Table 10.3 First table of incomes distribution rearranged by Pareto Table 10.4 First table to calculate the α coefficient Table 10.5 Second table to calculate the α coefficient Table 10.6 Comparison between original and calculated data Table 10.7 A series of α coefficient Table 10.8 First table for estimating the Chebyshev formula

7 241 243 244 245 246 247 247 253

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1 Relations between Pareto and the University of Lausanne

Pareto began his career as a university professor in Lausanne exactly three years after his unfortunate enforced departure from the management of the ironworks. This swift transformation was largely down to chance but was also due to Pareto’s determination to seize any welcome opportunity for work, as well as to the new intellectual skills he had acquired in the meantime. Following his resignation, pending new opportunities in management which appear not to have materialised, Pareto pursued his work in amateur journalism, maintaining his former spirit of minority liberal activism, as we will see in some detail in Chap. 2. Pareto’s interest for pure economics seems to have been sparked by his fortuitous contacts with Pantaleoni together with their shared passion for radical liberalism, both political and economic. Through Pantaleoni, Pareto duly made contact with Walras and thereafter decided to devote himself systematically to mathematical economics, which initially had represented for him simply an original method of consolidating free-trade theories. His early publications in this field drew the attention of Walras, who had decided to retire from teaching but had been unable, despite all his efforts, to find a worthy successor, and who therefore resolved, urged by Pantaleoni, to support Pareto’s candidacy. © The Author(s) 2018 F. Mornati, Vilfredo Pareto: An Intellectual Biography Volume II, Palgrave Studies in the History of Economic Thought, https://doi.org/10.1007/978-3-030-04540-1_1

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We are able to reconstruct many of the phases of the complex official relations between Pareto and the University of Lausanne,1 corresponding to the periods of his first contacts (Sect. 1.1), of his appointment (Sect. 1.2), of his succession (Sect. 1.3), of his role in the foundation of the École des Sciences Sociales (School of Social Sciences) (Sect. 1.4), of his teaching activities in political economy (Sect. 1.5) and of the history of the institution itself in that period (Sect. 1.6).

1.1 First Contacts In reply to a letter of homage written by Pareto, on the 15th of October 1892, Walras, who recognised his own limitations in regard to “formal analysis”, expressed his hope that Pareto himself might be able to re-­ establish his own economic theories on a more advanced mathematical basis, referring to recent articles by Pareto2 representing what Walras considered to be “the most serious and the most gifted work on questions relating to mathematical political economy”. On the same occasion Walras informed Pareto of his decision to stop teaching and to request early retirement on grounds of ill-health.3 On the 23rd of October, Pareto thanked Pantaleoni, to whom he had sent Walras’ letter,4 for having contemplated him as successor, adding, however, that he considered himself to be “too little known to be chosen”.5 In any case, on the following 3rd of November, Pantaleoni informed Walras of his intention to insist with Pareto, whom he considered “the person best-equipped to be able continue the tradition” which Walras had initiated,6 that he should put himself forward as candidate. Walras replied immediately that he too had Pareto in mind7 and that he intended to ask the government of the canton to appoint an extraordinary professor for two courses (in pure and applied economics) to be taught directly in the current academic year, in the hope that thereafter he could be offered a chair definitively, stating that he would support “Mr. Pareto in every way within [his] power to conclude these arrangements”.8 On the 7th of November9 Pareto confided to Pantaleoni that “if the thing could be achieved, it would be a great honour” for him. However, he needed to “find a way…. to accept this much-desired post” while

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avoiding “grave consequences” in Italy.10 Thus, he answered Walras that it would be “a very great honour” for him to be called to give courses in Lausanne but that he could not come immediately, partly due to existing commitments11 and partly because, were the trial period in Lausanne not to lead to a definitive appointment, he would have to “organise things in such a way as not to entirely forsake [his] activities [in Italy], so as to be in a position to take them up again on [his] return”.12 In any case, on the 14th of November, Pareto assured Walras that, if he were to be appointed in Lausanne, he would settle there “for good”, because he was now convinced that the battle for free trade was lost in Italy and consequently it would be preferable for him to dedicate himself to the study of science. Lastly, he was confident that “[his] teaching would meet with success” because “all the people who had heard [him] speaking in public in French had told [him] that [his] diction was clear and easy to follow”.13 Pareto added that he was interested in the opportunity in Lausanne because the Italian government had prohibited him from giving courses in public, so this would allow him to “expound [his] ideas … to a fresh audience each year”, especially given that he could not afford “the luxury of publishing scientific work at [his] own expense”.14 On the 20th of January 1893, Walras informed Pareto that his chances of success appeared good, assuring him that it was characteristic of the minister responsible, Eugène Ruffy (1854–1919)15 to put off making decisions for as long as possible.16 For his part Ruffy, on the basis of Walras’ letter in which he recommended Pareto as his successor (designating him “one of [his] most brilliant disciples [and] the best-equipped to continue” his teaching in pure political economy)17 together with the letter of application sent to him by Pareto himself,18 had duly contacted the Swiss Ambassador in Paris (Charles Lardy) to check the references communicated to him by Walras19 (particularly in regard to the publishers of the “Journal des Economistes” and of the “Revue des Deux Mondes”). In the early Spring, having given up the prospect of the move to Lausanne as lost in bureaucratic delays, Pareto commented that he would “have been very happy if it had been possible”.20 Thus, it was with evident enthusiasm that, instead, he was able to announce to Pantaleoni that on the 19th of April, following an interview21 which had taken place at his house in Fiesole with Ruffy and the Dean of the law faculty,22 Louis

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Grenier (1846–1919), “everything [had] been settled”23 and that, in response to the wishes of his interlocutors, he would travel to Lausanne at the beginning of May in order to “start teaching” straightaway.24 To be precise, Pareto’s appointment was as “extraordinary Professor” for a period of a year, with a promise from Ruffy that “if the results of [his] courses [were] satisfactory”, he would be offered a chair25 at Easter 1894. On the 24th of April 1893,  the professors Grenier, Jacques Berney (1863–1898), Heinrich Ermann (1857–1940) and Ernest Roguin (1851–1939)26 were present at the meeting of the Law Faculty board, which unanimously approved Pareto’s appointment as extraordinary professor of political economy, expressing “the desire that, if possible, the teaching of pure political economy should begin this summer”.27 On the 25th of April, the government of the canton duly appointed Pareto as “extraordinary professor of political economy” for the two following semesters at an annual salary of 4000 francs.28 A few days later, Pareto wrote to a friend in Geneva, the Italianist Philippe Monnier (1864–1911), saying that he was very happy, both to have been designated successor to Walras, which “far exceeded what [he] could have expected”, and because he hoped to “find among the honest and hard-working folk of Switzerland the tranquillity required for [his] scientific studies”.29 On the 9th of May, the “Gazette de Lausanne” (the city’s most important daily and the unofficial organ of its Liberal Party)30 informed its readers that Pareto had arrived in Lausanne31 on the morning of the 8th of May (a Monday) and that he would begin “his courses shortly”.32 This same daily had previously informed readers that Ruffy and Grenier had travelled to Florence “to seek a professor of political economy to replace Mr. Walras, who is resigning”,33 adding that the professor whom the University wished to appoint was “the Marquis Wilfredo Pareto of Florence, who already has a reputation as a journalist”.34 The Lausanne newspaper commented that “it would be a brilliant acquisition for Lausanne. It is important that the chair hitherto occupied by the doyen of a school, Mr. Walras, not be left in the hands of a mediocrity. Mr. Pareto is a disciple of the master, whose health has obliged him to abandon teaching. He is a supporter of free trade, which is very rare ­nowadays. We express our most sincere hopes that the negotiations which have begun

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with him will be successful”. On the 25th of April, the “Gazette” could finally report that the canton government had appointed “Mr. Vilfredo Pareto, engineer” as professor of political economy35 in place of Walras, who had been granted his pension. On the same day, the “Revue” (the official organ of Lausanne’s Radical Party) reported that, following the resignation of Walras, “the State Council had called the professor Mr. Vilfredo Pareto to occupy the vacant chair. Although young, Mr. Pareto is already very well-known and is appreciated not only among economists, but also by all those who are interested in the absorbing issues of financial and commercial policy”.36

1.2 The Confirmation The lesser-known story of Pareto’s confirmation at the University of Lausanne is also interesting from a biographical point of view, because it demonstrates his ease in dealing with the authorities in a foreign country. Felix Roux (1855–1940), the director of the École industrielle cantonale (the state school for commercial studies) informed the government that it was no longer possible to delay the solution to the problem of finding a successor to Walras at the school. Further, referring to the fact that Walras’ tasks included teaching activities  at this school too, Roux said that, even if this requirement had not been formally demanded of Pareto, “nevertheless it would be of great interest for our school if the Department could persuade him to take over the course, even if it involves making some concessions”.37 The new  minister of the public education, the radical Marc-Emile Ruchet (1853–1912) considered Roux’s request reasonable, informing him on the 2nd of April that he would “take the necessary steps with Mr. Vilfredo Pareto to procure his valuable support in the teaching of political economy at the École du Commerce and inform you concerning the outcome of our endeavours”.38 On the same day, Ruchet duly put out feelers regarding Pareto’s39 intentions, the latter replying to the minister on the 4th of April,40 making his availability conditional on an additional remuneration in recognition of the work he would be obliged to forfeit, since the lessons requested of him, although elementary, would nevertheless require adequate preparation. Ruchet seemed

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disposed to grant all Pareto’s41 requests in full but, in the following days, Pareto appeared to change his mind completely, demanding promotion to full professor42 in return for simply performing the university teaching, and on the 13th of April the government granted this request.43 As early as the 14th of April, Pareto was once again forcing the issue, thanking Ruchet for the promotion but also reminding him that it had been agreed with Ruffy that this promotion would offer the same remuneration as that of the other full professors, and hence Pareto was able to accept the existing extraordinary Professor’s salary of 4000 francs only on a provisional basis.44 On the same day Pareto asked to be received by Ruchet45 and this request was granted directly for the following 17th of April.46 Only indirect evidence is available concerning the discussions at this meeting. The administration had prepared a note indicating that, in contrast with Pareto’s claim of receiving discriminatory treatment by comparison with the other full professors, twelve of these (out of twenty-­ seven) received 4000 francs, three 4500, four 7500, one 5000, one 5500, two 6000 and the other four less than 3000 francs.47 At this meeting, it is very likely that Pareto’s views were sought in the matter of covering the position at the École de Commerce, as on the 19th of April he wrote to Ruchet48 to inform him that his post-graduate ­student (in letters) Léon Winiarski (1865–1915)49 would be very happy to take on the task and that he, Pareto, would contribute by passing on “all the information he needs in order to … prepare his course properly”. However, on the 23rd of April, Ruchet told Roux plainly that “we regret to inform you that our approaches to Mr. Pareto have not borne fruit”, while assuring him that the search for Walras’ replacement would go on.50 At the faculty board of the 25th of June 1896, with Berney, Georges Favey (1847–1919), Erman, Roguin and Pareto present, the outgoing Dean Berney proposed that, as was customary, the position should pass to Pareto, as being the most recently appointed full professor. Pareto himself “remarked that he feared he did not possess the necessary experience to perform this task. He will accept only if the vice-Dean has the kindness to assist him in the performance of the duties involved”.51 In the end, Roguin’s willingness to offer his help induced Pareto to accept the mandate, in the course of which he presided over the Faculty board meetings of the 6th of November and 1st of December 1896, those of the 16th and 23rd of

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June,52 15th of November and 6th and 17th of December 1897, and those of the 12th and 31st of January, the 8th53 and 21st of February, the 4th of March, 26th of April, 2nd of June, 12th of July and 30th of September 1898 before giving way to Favey as his successor in leading the faculty.

1.3 The Succession In the spring of 1898, having just received his inheritance from his uncle Domenico (who had died in Genoa on the 10th of March),54 Pareto expressed his desire to stop teaching, initially as early as the 31st of December 1898. His hope was to find another liberal to replace him, but this appeared unlikely because it seemed that “nowadays everyone is a socialist”.55 The decision to put an end to teaching, made possible by the fact that he no longer needed to earn his living by working, was officially motivated by his desire to put together the ideas needed to write the treatise on sociology which he mentioned for the first time in this period.56 In truth, there were also important tax-related motives. In fact, Pareto’s additional plan was to leave his position as professor while remaining in the Vaud canton and living off his private income, in order to qualify under the fiscal provision relating to “foreigners not practising any profession within the canton who by law are exempt from tax for ten years”. He would be happy, if permitted under the terms of the regulation, to give an hour of lessons per week free of charge, failing which he would stop “teaching altogether” (Table 1.1).57 Table 1.1  Pareto’s fiscal situation Year

Assets

Professional earnings

Tax payable

1894 1895 1896 1897 1898 1899 1900

35,500 35,100 33,800 31,100 31,800 297,900 11,800

3800 4430 5050 5700 5150 5090

105.76 114.81 122.20 160.56 148.16 943.58 18.88

Source: Income tax rolls, registers for 1893–1901, Archives of the Financial Directorate, City of Lausanne, figures in Swiss francs

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Thus began a long stand-off between Pareto, on the one hand, and the University and the Department of Public Education, on the other. The first person Pareto thought of to be his replacement was his ex-­ student Nicolas Herzen (1873–1929), who in 1896 had gained his doctorate in law, but whose predilection for roman law,58 which Pareto was already aware of, soon revealed itself as irreversible. Thus, after briefly fearing that his chair might go to the French literary economist Charles Gide (1847–1932),59 who a few months earlier had given a series of lectures in Lausanne, of which Pareto had been highly critical,60 on the cooperative economy, Pareto started to think, initially with considerable scepticism, about the possibility of simply requesting an assistant.61 For this position he thought of Vittorio Racca (1876–1957), a young law graduate from the University of Parma who at the time was of socialist political leanings and who from the Autumn of 1898 would be in Lausanne to assist Pareto with his preliminary documentary research for the treatise on sociology.62 Next, possibly in an attempt to force the hands of the authorities, Pareto wrote to Ruchet on the 27th of June asking him to accept his resignation as of the following 31st of December, explaining this by reference to “the scientific research for the treatise on sociology” which he was preparing.63 On the 16th of August, Pareto and the Dean of faculty Favey were received by Ruchet, who proposed the solution of Pareto being allowed to avail himself of a substitute.64 Thus, that same day, the faculty board suggested to the Department that Pareto should be permitted to entrust to a person of his own choosing the teaching of those parts of the course he thought best for the length of time he desired. Racca was suggested for this position on the basis of his familiarity with Pareto’s teaching and his shared conception of political economy.65 On the 14th of October, just before the start of the 1899–1900 academic year, the canton government accepted this proposal.66 Racca started his brief academic career in Lausanne on the 8th of January 1900, speaking during the course on applied political economy on the theme of non-personal assets, accompanied by Pareto’s hope that, as of the following year, he would be able to substitute him “completely”.67 In any case, as early as the 11th of December 1899, Pareto had informed Ruchet that he would forgo any remuneration on the part of the university,68 with the explicit aim of “thus entering into the category

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of foreign residents who, being neither born in the canton nor practising any trade or profession, are not liable to taxes on personal assets”. Having noted Pareto’s decision and after requesting the Lausanne municipal tax authorities to “monitor and review Mr. Pareto’s position”,69 the canton government decided, on the 20th of February 1900, to have Racca, who had previously been paid by Pareto, paid an amount of 200 francs per month of teaching70 directly by the university. The new head of Department, the radical Camille Decoppet (1862–1924) tried unsuccessfully to reverse this decision, proposing that Pareto should go back to paying Racca.71 However, on the 23rd of March, following Pareto’s protests, the government decided to establish even more favourable terms of remuneration for Racca, amounting to 2400 francs per year plus 50% of the enrolment fees for his part of the course.72 In the summer of 1900, Pareto declared himself willing to decide, together with Decoppet, “something definitive, with regard to” his academic position,73 specifying that he wished only for “a modest salary” for his work, simply because “life is too expensive in Lausanne” for him to “live there without earning”. Before the change in his personal circumstances, he had received 6000 francs in all from the university (5000 francs in salary and 1000 francs from course enrolment fees) and this corresponded to the total figure he would now be required to pay in municipal and cantonal taxes if he were to remain in Lausanne. Racca having taken over half of his hours of teaching, “it is thus only right” for Pareto’s remuneration to be halved, but for this to be possible, in practice it would be necessary for his salary to be increased to 9000 francs.74 If the government should decide not to grant this request, Pareto, in spite of “the links of affection and of gratitude” that tied him to the university and to the Vaud canton, would be obliged to resign.75 Faced with Decoppet’s offer of 8000 francs (the maximum salary payable at the university of Lausanne) for a full course (i.e. without the assistance of Racca),76 Pareto answered that for the corresponding net salary of 2000 francs he could offer at the most half a course. He therefore asked Coppet “to accept definitively” his resignation, effective from whichever moment the minister chose.77 Decoppet, notwithstanding, submitted Pareto’s request for a salary of 9000 francs plus the assistance of Racca to the government, at the same time expressing his objections, both on the grounds that this would create

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“a precedent which would not fail to be invoked by numerous of Mr. Pareto’s colleagues” and because “the law does not permit us to go up to the figure in question”.78 However, the faculty board, faced with the prospect of losing Pareto, voted at the meeting of the 2nd of November 1900 for the government to accept his final demands, that is, just one hour per week of teaching, while supervising Racca’s teaching79 and retaining sole responsibility for the examinations, in exchange for an annual gross salary of 3000 francs plus 50% of the enrolment fees for his course.80 The government accepted this, maintaining for Racca the same terms as he had enjoyed since the March before, but with the proviso that the appointment could be revoked by either party at three months’ notice after the end of the academic year, which was prompted by the faculty’s reluctance to allow the fact of deputising for Pareto to confer on Racca any rights of succeeding him in his position, since the position should “remain the preserve of an economist who had proved his mettle and who had a scientific reputation comparable to that of Mr. Walras and Mr. Pareto”. From the winter semester of 1899–1900 to the summer semester of 1903, the teaching work was divided between Pareto and Racca as follows81: Pareto taught applied political economy for three hours per week in the winter semester of 1899–1900, in the summer semester of 1900 (real estate, production and commerce), in the winter semester of 1900–1901 and for one hour per week in the summer semester of 1901, the winter semester of 1901–1902 (personal assets and theory of interest), the summer semester of 1902 (production and economic crises), the winter semester of 1902–1903 (division of wealth and modern socialist systems) and the summer semester of 1903. As for Racca,82 he taught one hour per week of applied political economy (socialist systems and taxation) in the winter semester of 1900–1901, one hour per week of applied economics and two hours of the history of economic theories (general theories of political economy and their history) in the summer semester of 1901, three hours of applied political economy (of which two hours dedicated to real estate and equity assets) and two hours of social legislation83 in the winter semester of 1901–1902, three hours per week of applied political economy (of which two hours dedicated to commerce and consumption) and two hours of social legislation in the summer semester of 1902, three hours of applied political

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economy (of which two dedicated to taxation and to socialist systems up to the end of the eighteenth century) and two hours of social legislation in the winter semester of 1902–1903, an hour per week of pure political economy and two hours of history of economic theories in the summer semester of 1903. After a while, however, this arrangement ceased to satisfy for Pareto due to the (for him) fundamental question of logistics, as it necessitated a weekly return journey from Céligny to Lausanne, a journey lasting an hour each way, which he deemed “a major sacrifice”, provoking an outburst of “if only that Racca could hurry up and become famous so that I could retire definitively”.84 Thus, in the early summer of 1901, Pareto advised Racca against participating in the selection procedure for a university in Italy because very probably he would not be allowed to emerge victorious, partly due to the scheming of other candidates and partly because the fact of “having been in Lausanne” with him would constitute a penalising factor, while any setback in Italy would penalise him in Lausanne, where “with a little patience, he could end up as professor of Political Economy … in two or three years’ time”.85 This arrangement which had been so painstakingly set up came to nothing when, in October 1903, Racca suddenly failed to appear for the beginning of the new academic year. Pareto’s reaction was to request the dismissal of his assistant, declaring his willingness to begin the course himself but asking, in view of his “scientific activities” and his “health issues”,86 to be replaced as soon as possible, “at least temporarily”, but “on the same conditions” as Racca, by Boninsegni, who “knows the subject in depth”.87 Finally, on the 29th of October, Racca got in touch, with a letter from Athens addressed to the Dean, Roguin, in which he sought to justify his non-arrival as being due to a shipwreck (disastrous for his health) and promising on his return to Lausanne to make good the missed lessons.88 However, Pareto reiterated his request for a new assistant who would devote himself “wholeheartedly and punctiliously to the teaching of political economy and who would have a perfect understanding with the titular professor”, going on to say that “the collaboration with Mr. Racca deviated gradually from what it had been at the start” so that to resume it would cause “serious problems for the teaching of political economy”.89

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On the 20th of November, the government accepted Pareto’s proposal to authorise Boninsegni for teaching one hour per week under the supervision of Pareto, who would be paid the salary formerly paid to Racca and who would be responsible for paying Boninsegni, while a decision regarding the latter’s suitability to continue in the role would be taken in due course.90 No details are extant regarding Boninsegni’s early teaching experiences in Lausanne, which in any case met with Pareto’s approval and, towards the end of the academic year,91 he proposed to the rector Grenier that the new arrangement for the courses be confirmed for a period of two years, renewable.92 On the 12th of July, the government authorised Pareto to be partially substituted for a period of two years by Boninsegni, on whom they conferred the title of professor responsible for courses (professeur chargé de cours) and whose remuneration was to be paid directly by Pareto.93 For this two-year period, the organisation of the teaching was as follows: Boninsegni in the winter semester of 1904–1905 taught one hour of applied political economy (socialist systems), in the summer semester of 1905, two hours of the history of economic doctrines (history of political economy), an hour of the science of finance (the state balance sheet) and two hours of statistics; in the winter semester of 1905–1906 he taught two hours of applied political economy (equity assets and real estate), an hour of the science of finance (public debt and the general theory of financial transactions) and two hours of statistics (the graphic method and its applications) while in the summer semester of 1906 he taught three hours of applied political economy (commerce), an hour of the science of finance and two hours of statistics. Pareto, in the winter semester of 1904–1905, taught two hours of applied political economy (socialist systems) and, in the summer semester of 1905, an hour of principles of sociology and an hour of pure political economy; in the winter semester of 1905–1906, he taught two hours per week of applied political economy (population, the rate of interest) and in the summer semester of 1906, an hour of principles of sociology and an hour of applied political economy (production, consumption). However, January 1905 found Pareto once again contemplating retirement.94 He was confident that Boninsegni was able to replace him at last, since he taught “a substantial part already”. However, he noted that, on

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the one hand, “this would depend on the authorities” and, on the other, “he is competent but he doesn’t speak French very well, which is very important here”.95 The question was taken up again in the summer of 1906 when the tax commission for the  district of Lausanne assessed Pareto’s earnings at 6800 francs, which he contested vigorously, as the university paid him only 5400 francs, from which should be deducted the 2400 francs he passed to Boninsegni and to which should be added a “contribution from students” much lower than the 3800 francs required to arrive at the “fantastical” sum calculated by the commission. This decision thus constituted “the straw that broke the camel’s back” which ­persuaded him to retire “irrevocably”. He begged the minister Decoppet to accept his resignation as of the 1st of October 1906.96 However, once his anger had passed, Pareto declared himself still willing to continue teaching for the winter semester of 1906–1907 so as “to give time to find a successor”.97 The Dean, Simon de Félice (1867–1935), sought to profit from Pareto’s apparent hesitation by pointing out to Decoppet that it might be possible to persuade him to withdraw his resignation, if he were permitted to teach only in the winter semester, which was less deleterious for his health.98 At the beginning of the new academic year Boninsegni also declared his candidacy for Pareto’s position, on the basis of the continuing announcements of his resignation as well as of the three years of substitution he had just completed.99 As for Pareto, he informed the new Dean André Mercier (1874–1947)100 that he would be prepared to teach pure economics and sociology, under whatever title the authorities “saw fit” to assign him, residing continuously in Lausanne in winter for the 89 days allowed to him by law “without being subject to the progressive tax on personal assets”. As regards the “teaching of political economy with a mathematical and scientific foundation”, he proposed Boninsegni, adding that he should also be confirmed for the courses in statistics and the science of finance, while possibly being relieved of the teaching of social legislation. At the department’s request, on the 14th of December 1906 the faculty expressed its approval for Pareto’s appointment to the chair in political and social sciences (including pure economics and sociology), as well as for Boninsegni’s taking the role of extraordinary Professor in political economy.101 On the 8th of January the government nominated Boninsegni extraordinary Professor of applied political economy, social

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legislation, science of finance and statistics102 and Pareto to the chair in social and political science, with the obligation of teaching a single course in the winter semester. His remuneration was to be 1000 francs plus 50% of the enrolment fees.103 However, Pareto pointed out that the four hours per week of lessons for half a semester (which would be his new teaching commitment) were equivalent to two hours per week for a whole semester, that is, half of his existing teaching requirement, while the new salary level proposed was only a third of that previously in force. Hence, for 1000 francs he could offer only two hours of lessons per week for three months. If this was not acceptable, he would resign as of the 1st of April 1907.104 The Department accepted Pareto’s reduced availability in return for 1000 francs.105 Thus, at least in theory, Pareto’s final teaching commitments were as follows: an hour per week of sociology in the winter semester of 1906–1907 together with an hour of sociology and an hour of pure economics in the winter semester of 1907–1908.106 On the 18th of September 1908, Pareto informed Decoppet of his resignation, this time truly irrevocably, being motivated by a deterioration in his health.107 The Department requested Roguin, who was Dean once more, to investigate the justification for this latest resignation, but Roguin was obliged to report that Pareto was indeed lost to teaching, proposing, however, to retain him among the teaching staff for the sake of the prestige of the institution.108 The Department, having invited the faculty board to make proposals for Pareto’s permanent replacement, decided to advise the government to accept Pareto’s resignation for the end of the current 1908–1909 academic year and to appoint him honorary professor. However, due to the availability of Maurice Millioud (1865–1925)109 to take over the course in sociology under Pareto’s supervision, and of Pareto’s willingness in turn to convert his resignation into a request for a year’s sabbatical, on the 27th of October the government granted Pareto the period of sabbatical requested, replacing him for the coming winter semester with Millioud for sociology and with Boninsegni for pure economics, for which each of them was to receive 500 francs.110 Pareto made only two further fleeting returns to teaching, first in May 1909, when he taught the last official sociology course (consisting of only eight lessons ending on the 4th of June111) and then in May 1916, when he taught another course in sociology but with no final exams.112

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1.4 T  he Founding of the School of Social Sciences (École des Sciences Sociales) in Lausanne In the context of Pareto’s official relations with the University of Lausanne, pride of place must go to his role in the foundation of the École des Sciences Sociales. Alongside the normal teaching of political economy, from the summer semester of 1891 to the summer semester of 1896 the University of Lausanne also offered teaching in the history of civilisation and of economic doctrines, social economics, philosophy of history and elements of sociology (relating in particular to demography, social legislation, labour history and social systems) for students of law and of letters. The ­“authorised professor” teaching these courses113 was Louis Jaquemot,114 who had held the chair in political economy at Geneva since 1885 (he was Pantaleoni’s predecessor115) and who is now completely forgotten (obscure personal issues with criminal ramifications brought his university career to an end between 1896 and 1897), but who had been one of the leading lights of political and cultural life in Geneva in the 1880s and early 1890s. It was against this backdrop that the repeated attempts to introduce a regular degree course in social sciences were made, culminating in success only in 1902. At its meeting of the 5th of March 1895, following the death of the philosopher Charles Secrétan (1815–1895), the board of the faculty of letters proposed to the Commission Universitaire (the University Commission responsible for academic matters, composed of the Rector and the Deans of Faculty, henceforth referred to as the Commission) that his teaching should be divided into two areas, one covering historical and metaphysical subjects (to be taught by the above-mentioned Millioud) and the other scientific and juridical subjects, for which a teacher needed to be found.116 However, at the same meeting, a proposal was also made to create a degree course in social sciences. On the following 30th of May the boards of the faculties of law and of letters, sitting together for the occasion, agreed to the choice of Millioud for the teaching of the philosophy of history but did not agree regarding the other putative new course. The

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Commission proposed a course in physiological psychology to be taught by Alexander Herzen, the faculty of letters wished to find someone able to teach “scientific and juridical philosophy” while the faculty of law would be happy with a chair in philosophy of law, to be entrusted to a jurist. Professor Georges Renard (1847–1930), historian of French literature, excomunard, socialist and friend of Pareto, then convinced the two faculties to ask the  government to establish a degree course and a doctoral programme in political science, which they did but without success.117 The decisive attempt began at the law Faculty board meeting of the 2nd of December 1901, during which the suggestion of the lawyer Tvakhterew from Odessa to create “special doctorates” was discussed. Pareto then made his voice heard, saying that this suggestion was worthy of consideration, expressing his views that it would be “expedient” for the university to award qualifications in social sciences, particularly that of criminal anthropology. The faculty approved and set up a commission of investigation composed of the Dean, Erman, Roguin (who had supported Pareto’s position) and Pareto himself, which Millioud would be invited to join in his capacity as Dean of the faculty of letters.118 The commission, basing itself on a proposal made by Pareto (which has not been traced), formulated a project119 which, drawing on resources which were already available in the two faculties, could be immediately implemented with a view to responding forthwith “to the needs and the wishes expressed by a notable part of the student body”, as well as liberating the university from “a marked sense of inferiority with regard to other institutions of higher education in our country and abroad”.120 More specifically, the commission proposed a new general degree course awarding both degrees and doctorates, to cover, as obligatory subjects, general philosophy, sociology, political economy (including demography and history of economic doctrines), basic notions both of public and private law and political history. Optional subjects were to include a foreign language (and its related literature), anthropology as referred to social sciences, history of religions, statistics, social legislation, geography as referred to social sciences, the science of finance and international law. The parliament of the canton, prompted by the government, accepted the ­proposal, to be introduced as a modification to the law relating to the university, on the 17th of May 1902.121

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Pareto played what was certainly a more important role in the first reform of social studies at the university. During the preliminary work on a new law for university, on the 15th of July 1910 the commission administrating the École des Sciences Sociales (which included Boninsegni, Millioud, Roguin and the literary man Paul Sirven) proposed that the school should become an École des Sciences Sociales et Politiques (School of Social and Political Sciences) offering various degree courses, including a theoretical/general course, an insurance course, a preparatory course for consular and diplomatic careers and a preparatory course for journalism.122 Asked his opinion by the Dean of the faculty of law Paul Rambert (1866–1932), Pareto123 said that if the proposed practical degree courses were to be introduced as an alternative to the theoretical one, the latter would disappear, as being considered perfectly useless by the students. If, on the other hand, it was thought that “the scientific study of social sciences” could be cultivated at the university of Lausanne in order to fill a gap across Europe for “this type of teaching”, then it was necessary to make this possible by confirming the only theoretical degree course and by placing the practical courses in the École des hautes études commerciales (School for higher commercial studies) which was then in the process of being set up (and which was inaugurated on the 15th of May 1911), with which they shared “a common aim and methodology”. Pareto added that the future of the study of social sciences at Lausanne seemed promising, both because the courses at the École des sciences sociales were “very well-­ attended” and because Millioud seemed to him capable of “dispensing a truly scientific teaching of sociology”. The school’s commission was in agreement with Pareto’s view and on the 5th of May 1912 the government created an École des Sciences Sociales et Politiques (School of Social and Political Sciences), still under the aegis of the faculty of law but finally independent, offering a single, theoretical degree course.

1.5 The Teaching of Political Economy Pareto began his teaching program at Lausanne with a long experience of public speaking behind him but never having actually taught before.

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Nonetheless, he had already given thought to the contents of the teaching of political economy,124 writing to Walras that scientific demonstrations were necessary only for the élite. Instead, in order to get the truth “into heads which are sometimes extremely obtuse ….you have to repeat things which are of an outrageous simplicity a hundred times”, as he sought to do in the summer of 1891, with his anti-protectionist publications whose “value in scientific terms is nil”.125 Furthermore, having understood immediately that his readers in political economy were not familiar with mathematical analysis, Pareto, in the summer of 1892, wrote articles for the “Monde économique” with the aim of “explaining mathematical political economy to those who do not know mathematics”, which cost him “great effort because [he] wished to be understood by all”.126 In the same period, he wished to prove to an early critic, the Franco-German economist Maurice Block, that he did not “need mathematics to make [him]self understood”.127 In any case Pareto, at the time of his being called to Lausanne, hastened to inform his friend Moneta, with evident enthusiasm, that he was going to Lausanne to teach “economic liberty”.128 The “Gazette de Lausanne”129 and the “Revue”130 informed their readers that Pareto was due to give his first lesson on the 12th of May at 3 pm in lecture theatre 2 of the Old Academy  (Vieille Académie),131 on the theme “the definition of pure political economy and its method of study”. To the present day the only information we have on Pareto’s academic debut is owed to the “Revue”,132 which reported that Pareto gave his lesson in front of a crowded audience after having been introduced by the Dean, Grenier. Pareto spoke of the application of mathematics to economics, as had been so ably conceived and put into practice by his predecessor Walras. The radical party daily, describing the excellent impression made by the first lesson (lasting around 40 minutes, and “spoken rather than read”, as recommended by Walras133), saw the new professor as “still a young man, with a Mediterranean look, a pale complexion, black beard and flowing and pleasant diction”, noting that he expressed himself “perfectly correctly”, finding “the mot juste without hesitation”.134 Pareto, who planned to “dictate as much as possible of [his] lessons, as it seems to [him] that this could facilitate the task of the students and it is not for [him] a real difficulty”,135 decided once again to follow Walras’ advice by including “as little mathematics as possible in the course”.136 In fact, as

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soon as he was appointed, he had asked Walras’ advice on the preparation of the course,137 expressing his “extreme gratitude” towards his predecessor for having already prepared “the course to be taught, divided into lessons”, but leaving him “with complete freedom to do things differently, and better”.138 On learning, however, that Walras’ recommendations had done him a disservice precisely because it was feared that, like him, he would give “lessons which were comprehensible only to the few” which consequently were ill-attended, Pareto, while continuing to sing the praises of Walras, decided he would “explain things in such a way as to be understood by all”. In this way he soon gathered 22 students (increasing by the end of the course to 29, as against the 6 who had attended his predecessor’s last course139), who to him “appeared to acquire a taste for what [he was] teaching them”140 even if “when they see an equation, they get scared”.141 To help the students in their studies, Pareto also introduced the innovation of periodically distributing lithographed summaries of the lessons142 and, on a weekly basis, getting them to give “lectures in which they explain[ed] economic theories” while Pareto offered “any clarification they desir[ed]”.143 Walras immediately and courteously noted that Pareto’s course on pure economics had been “very brilliant and very popular”.144 When, at the faculty board of 29th March 1895, Erman wondered whether it might not be a good idea to introduce measures obliging students who had to sit exams to attend the relevant courses, Roguin, with Pareto’s explicit support, adopted a stance in favour of “complete liberty in this regard”.145 In November 1893 Pareto, beginning to take stock of this new experience, expressed his satisfaction that the authorities were “happy” with him, where in Italy he would have been dismissed. If among his fifty-six students “there were at least 10 or so who absorbed free-trade ideas, after a few years [he] would have contributed something to the spreading of the [free-trade] doctrine”.146 Similarly, in May 1894 he described the four semesters of the course as an explanation of the “scientific principles of free-trade”, imparted also in the hope that among the students “some may in turn go on to teach these to others”.147 However, in the spring of 1896, Pareto was forced to acknowledge that his students “know nothing of mathematics and are not curious about political economy: they wish to know just enough for the exam and no

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more!”. Realising that “the producer must deliver what the consumers want”, he thus prepared “a very elementary syllabus”,148 while “the true science of economics could be taught [only] in an institute of higher education for social sciences”.149 In November of the same year, Pareto repeated that for his course in political economy he now avoided “completely any mention of mathematics”, and spoke in terms of “the drawing of analogies between mechanical and economic phenomena” and the “calculation of probabilities applied to social and economic science” only in a pioneering parallel advanced course which was interrupted immediately for lack of students.150 A decade later, towards the end of his teaching experience, Pareto pointed out that the teaching of political economy in Lausanne “is not mathematical in any way, but it expresses in simple language the results which emerge from the use of mathematics”, so that “the students do not need to know mathematics, while the teacher must have quite an extensive command”.151

1.6 T  he Institutional Context of Pareto’s Academic Experience in Lausanne Finally, it is of interest to note the institutional framework behind Pareto’s teaching experiences in Lausanne.152 The institution which hosted Pareto was created under a law of the 10th of May 1890 (implemented through the general guidelines of the 19th of September 1890), whereby the University of Lausanne was born out of the pre-existing Academia Lausanensis, which had been founded in 1537 by the protestant canton of Bern when, having occupied the canton of Vaud a year earlier, they wished to make use of the new institution to provide protestant training for the local clergy. This reform of 1890 was undertaken by the canton both in fulfilment of a commitment it had made with the municipality of Lausanne, and also with a view to conferring on Lausanne the advantage of being among the first to join in the consensus in favour of the creation of institutions of higher education which was gathering force in Switzerland.153 The minister sponsoring it, the same Ruffy mentioned above,154 stated that the principal novelty of the reform consisted in the

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creation of the faculty of medicine, indispensable for a complete university, together with the total liberty of choice of studies for the students and of didactic approach for the teaching staff.155 This law, and specifically (as will be seen below) the arrangements concerning the faculty of law, emerged from the government bill as amended in line with the proposals of the parliamentary commission led by the radical Ernest De Collogny. The first article of the law assigned to the university the goals of preparing students for careers requiring higher education, of promulgating scientific and literary culture and of contributing to scientific ­development within the canton, while under the terms of article 2 it was placed under the responsibility of the canton. Article 3 provided for its separation into five faculties, which were protestant theology, law, letters, science and medicine, and the total number of chairs was set, in accordance with the provisions of article 10, at 36. According to article 19, the full professors were normally designated and called to the chair by the government (on the basis of a favourable prior opinion from the university), and were chosen from among academics “widely known from their published works or from public lectures on the topic to be taught”. Only in exceptional cases were open competitive examinations organised. The occupants of the chairs, as specified in articles 16 and 17, could be required to teach for a maximum of 15  hours per week, not only in the university but also in the canton’s public secondary schools. In accordance with article 14, the full teaching staff also included extraordinary professors (appointed, in accordance with article 24, by the administration) and external (“free”) professors. Article 47 stipulated that every faculty should have a board, or a council, made up of full and extraordinary professors, and that the board should appoint the Dean, in accordance with article 48. Article 9 specified that the teaching should be divided into theoretical and practical courses, lectures and student exercises. Article 11 provided that the content of lessons taught by full professors should be regulated in accordance with faculty guidelines, while extraordinary professors were free to include topics not specified in the guidelines. Article 7 of the regulations attributed to professors of all categories “freedom of teaching”.

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Article 40 provided for the university’s being able to award degrees and doctorates to students who had followed syllabuses of study approved by the Department on the basis of the recommendations of the university senate and had passed the examinations stipulated by the regulations of each faculty, in accordance with the provisions of article 42. Last of all, it is of interest to note that even from the times of the Academy the Department had always adopted a favourable attitude156 towards foreign teachers. This was evidenced by the fact that in the Academy’s last semester the foreign teachers, of whom there were only three, received, as compared to the average salary of 3600 francs for the teaching staff as a whole, a salary higher than the 4000 francs which was the maximum fixed by the law of the time (and which could be increased only in special cases). These three were Erman and Walras in the faculty of law with 5000 francs and Renard in the faculty of letters, who was the highest paid, with 6000 francs salary plus three-fourth of the enrolment fees.157 Ruffy, who was a graduate of the faculty of law, stressed the importance of the expansion of this latter, partly because Lausanne was the judicial capital of the country, having become the headquarters of the Federal Court in 1886, but more importantly because the city wished to be a candidate to host the Federal Law School which was much-mooted at the time, although it never came to fruition.158 Thus, after confirming the normal teaching syllabus for the faculty of law, including political economy, the  government planned to create a new chair in Swiss civil law (which was to include the teaching of commercial law159) and to add teaching in industrial law (where new specific legislation was being promulgated in Switzerland, an example of which was the 1877 law on factories) and in administrative law, deemed necessary for the training of jurists and of young students wishing to pursue a career in the higher administrative positions.160 The parliamentary commission, while agreeing with the government’s objectives, deemed the proposed reforms to be insufficient, considering that the law faculty in Lausanne should build on traditional studies in law to develop programmes in political and social sciences which by this time were acquiring increasing importance, especially as some universities in Switzerland were already in a position to offer complete courses of study in these disciplines, similar to that available at the École Libre des Sciences

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Politiques in Paris, which had been founded in 1871. Hence, through the appropriate reform of the curriculum at the law faculty in Lausanne, it might be possible “to attract numbers of people from other parts of Switzerland, not to mention foreigners from all over the world”.161 At the time, social and political sciences were represented in Lausanne only by their principal discipline, that is, political economy. The idea was for the gradual introduction of others which were in the process of being developed, ranging from statistics to the science of finance, political history, the history of civilisation, diplomatic history, consular legislation (which had just been introduced by the university of Bern), political geography and ethnography. To this end the Grand Council (the single-­ chamber parliament of the canton) approved the replacement of the teaching of political economy and social sciences (as proposed by the government bill) with that of social and political sciences.162 Hence, the final version of the law regarding universities in article 10 assigned seven chairs to the faculty of law (as against the single additional chair over and above the five existing ones provided for in the government bill) together with the following list of subjects to be taught, as per article 5: encyclopaedia of law163; philosophy of law164; history of law; Roman law; civil law; civil procedure; commercial law; industrial law; criminal procedure; international law; comparative law; social and political sciences (which also figured among the principal subjects taught in the faculty of letters under the title of political economy, as stated above, together with the ancillary courses taught by Jacquemot); forensic science. The legally imposed teaching requirements for the faculty of law, during the period lasting from the summer semester of 1893 to the summer semester of 1898 when Pareto was fully engaged there, were entrusted to the following members of staff: Charles Secrétan (Chair): natural law (the philosophy of law not having yet been introduced in the period in question); Louis Grenier (extraordinary): criminal law, criminal procedure and diplomatic law; Heinrich Erman (Chair): Roman law; Ernest Roguin (Chair): encyclopaedia of law, international private law and comparative legislation;

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Jacques Berney (extraordinary): public law, commercial law, French administrative law and French commercial law; Henri Brocher de la Fléchère (a Frenchman with Chair in Geneva but in Lausanne an external specialist, 1835–1907): history of law; Jean-Jacques Larguier des Bancels (extraordinary, 1844–1904): forensic science; Charles Soldan (federal judge, 1855–1900): industrial law. An interesting final consideration is that the lightest teaching loads were assigned to Larguier (teaching 1 hour per week for only 1 semester per year), and to Pareto, Brocher de la Fléchère and Secrétan with 4 hours per week, while the heaviest loads were borne by Erman (14 hours per week), by Roguin (up to 11 hours) and by Berney (up to 12 hours per week).165

Notes 1. For the seminal studies on this question see Busino (1963a) and Biaudet (1975). 2. This refers to the series of articles Considerations on the Fundamental Principles of Pure Political Economy which will receive further attention in the third chapter. 3. Léon Walras to Pareto, 18th October 1892, see Walras (1965, p. 510). 4. Pareto to Maffeo Pantaleoni, 21st October 1892, see Pareto (1984a, p. 301). 5. Pareto to Pantaleoni, 21st October 1892, ibid., pp. 304–305. 6. Pantaleoni to Walras, 3rd November 1892, see Walras (1965, p. 511). 7. As the then young Polish statistician and mathematical economist Ladislaus von Bortkiewicz had refused the position as successor to Walras, being more attracted by a possible chair at the University of Strasbourg, Walras to Charles Gide, 20th December 1892, see Walras (1965, p. 512). 8. Walras to Pantaleoni, 4th November, 1892, ibid., p. 532. 9. Pareto to Pantaleoni, 7th November 1892, see Pareto (1984a, pp. 312–313). 10. See below, n. 12. 11. In particular, the possibility, which came to nothing, of being called as a member of the Italian delegation to the forthcoming international monetary conference in Brussels.

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12. Pareto to Walras, 7th November 1892, see Pareto (1975, pp. 185–192). Pareto was alluding to his fear that a move to Lausanne might prompt his rich and now elderly uncle Domenico, whom he was due to visit in Genoa on the 16th of November (Pareto to Pantaleoni, 15th November 1892, see Pareto (1984a, p. 317), to disinherit him. But the encounter in Genoa dispelled his fears, thus allowing Pareto to inform Walras in good time that he had “been able to arrange [his] affairs here so as to be free to come to Lausanne even right away”, Pareto to Walras, 16th November 1892, see Pareto (1975, p. 198). 13. Pareto to Walras, 14th November 1892, ibid., p. 197. 14. Pareto to Walras, 13th March 1893, ibid., pp. 213–214. 15. Ruffy, who was head of the Department of Public Education and Religion (henceforth the Department) in the administration of Vaud, was at that time a leading member of the Radical Democratic Party which after 1848 had directed political affairs in the Canton of Vaud and which only in 1892 had come to an agreement with its traditional liberal opponents, “surrendering” one of the seven seats in the government, which was to be directly elected by universal male suffrage. 16. Pareto to Walras, 22nd January 1893, ibid., p. 198. 17. Walras to Ruffy, 8th December 1892, see Walras (1965, p. 529). 18. Pareto to Ruffy, 22nd December 1892, see Pareto (1975, p. 206). 19. Pareto to Walras, 22nd January 1893, ibid., p. 208. 20. Pareto to Pantaleoni, 24th March 1893, see Pareto (1984a, p. 359). 21. Which Walras had alerted him to in a letter dated 15th April 1893, see Walras (1965, p. 552). 22. Where the chair in political economy was based. 23. Pareto commented that the support of his “friends in Paris” (seemingly referring to the économistes) and “above all” the article on the political situation in Italy he had published in the “Revue des Deux Mondes” had worked in his favour, Pareto to Pantaleoni, 22nd May 1893, see Pareto (1984a, p. 372). 24. Pareto to Pantaleoni, 21st April 1893, ibid., p.  367. Pareto thanked Pantaleoni, in a letter of 23rd April 1893, ibid., p. 368, saying that this result was “largely the work” of his friend, to whom he was therefore “extremely grateful”. He was positive that, given his abysmal relations with those in power in Italy, he had “nothing to hope for” there, ibid., p. 369. Writing contentiously to his friend Emilia Peruzzi, Pareto to Emilia Peruzzi, 3rd May 1893, see Pareto (1989, p. 188), he claimed to be leaving “the mother country because there [he] could not find what

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elsewhere [he] was implored to accept”. He added the further sarcastic observation that in Italy he would never have passed the admission exam for university teaching because it was certainly administered by the politicians, his loathing for whom was fully reciprocated, Pareto to Emilia Peruzzi, 30th April 1893, see Pareto (1984d, pp. 545–549). 25. Pareto to Walras, 19th April 1893, see Pareto (1975, p. 218). 26. On the jurist and sociologist Ernest Roguin, who had a very fluctuating relationship with Pareto, see Tappy (2010). 27. Minutes of the meetings of the Law Faculty board, dossier n. 2 from 25th November 1875 to 25th January 1902 (henceforth M-LF). 28. Archives of the Canton of Vaud (henceforth ACV), KIII 252 1893. 29. Pareto to Philippe Monnier, 3rd May 1893, see Pareto (1975, p. 220). 30. On the history of the Lausanne daily during Pareto’s time in the city, see Clavien (1997). On Pareto’s intensive collaboration with the “Gazette”, see Mornati (2010). 31. On Lausanne’s political and intellectual circles of the time: see Arlettaz (1980), Meuwly and Voutat (2003, passim), Meuwly (2006, passim), (2010), and Sardet (2010). 32. University (Université), “Gazette de Lausanne”, 9th May 1893, p.  2. After having lived in via dei Bardi in the Oltrarno district of Florence between 1888 and 1891 and at Villa Rosa in Fiesole from the autumn of 1891, Pareto to Emilia Peruzzi, 19th October 1891 see Pareto (1984d, p. 487), in Lausanne Pareto resided between 1893 and 1898 in the elegant lakeside area of Ouchy, precisely in the Chalet Souvenir which was graciously described by Dina Bakounine, see Pareto (2001, pp. 60–61, note 1). From 1898 to 1900 he lived in the Reseda villa, in Lausanne’s central station area. After coming into his inheritance, Pareto decided to become a property owner, acquiring, at the end of 1900, Villa Angora in Céligny, a lakeside enclave of the Geneva canton within Vaud, where he lived until his death. Villa Angora was brilliantly and affectionately described by Manon Michels, see Michels (1935). The author, one of sociologist Roberto Michels’ daughters, had been a frequent guest at the villa as a child. 33. University (Université), “Gazette de Lausanne”, 19th April 1893, p. 2. 34. Ibid., 21st April 1893, p. 3. 35. Ibid., 25th April 1893, p. 3. The Lausanne daily added that “Mr. Vilfredo Pareto is one of the leading lights among those young economists who, following the example of Mr. Walras, are seeking to establish political economy as a pure science and even as an exact science. He is an excellent

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mathematician ….and has given a mathematical exposition of some of the essential points of the new science in a series of articles … Nevertheless, while dedicating himself to investigating the principles, Mr. Pareto is far from neglecting their practical or applied aspects …. Mr. Vilfredo Pareto is evidently a French economist as well as an Italian one; he unites a scientist’s enthusiasm for investigation with a professor’s talent for divulgation. We can only congratulate the government for having chosen such a well-qualified candidate”. 36. University (Université), “La Revue”, 25th April 1893, p. 2. 37. ACV KXIII 252 G1 1894. 38. ACV, KXIII 314/17. 39. Writing to him as follows: “Lausanne, 2nd April 1894. Professor, the retirement of Professor Walras, your predecessor in the chair of political economy at the University of Lausanne, has left the teaching of this subject uncovered at the canton’s École de commerce. We therefore need to find a solution in time for the beginning of the new 1894/1895 school year starting in September. We would be delighted if you could provide your valuable assistance, and hence we take the liberty of asking you if you would be prepared to take over this teaching assignment. The course would involve two hours per week and is of great interest and importance for the École de commerce. We look forward to receiving your response on this matter. Please accept, Professor, our highest regards”, ACV, KXIII 314/17. 40. Pareto to Ruchet, 4th April 1894, see Pareto (1975, p. 243). 41. As emerges clearly from the following note dated 5th April 1894: “Thank him for his kind acceptance. Say that his salary will be increased from 4000 francs to 5000 francs. His request will be dealt with at the time of organising the course timetable for the next academic year, and the Department will make sure this is done”, ACV, KXIII 314/17. 42. As appears from the following note emanating from the departmental administration and dated 11th April 1894: “Mr. V. Pareto, the professor of political economy, came to the office. He announced that he was unwilling to start his course again before being appointed full professor, considering himself no longer in service since his appointment as extraordinary professor came to an end at the end of the winter semester. He prefers to continue as full professor for another year on the salary of 4000 francs rather than committing himself to taking the course in political economy with a salary of 5000 francs, as he does not wish to tie himself to the École de Commerce as Mr. Walras did. In any case he will

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inform us in a fortnight or so whether he will accept the teaching role at the École de Commerce for a trial period of a year. The request for his appointment as full professor will therefore have to be presented before the government (Conseil d’État) on Wednesday in order not to delay the moment of Mr. Pareto’s resuming his teaching at the University. It would be desirable to finalise the appointment on Wednesday”, ACV, KIII 252 C, 1894/32. 43. Pareto was informed of the appointment with the following letter: “Lausanne, 14th April 1894. Dear Sir, we have the honour of informing you that at the meeting of the 13th inst., the government appointed you to the chair in political economy at the University of Lausanne, on the same terms and conditions as hitherto. We will send your nomination card by separate delivery. We are pleased to be able to establish closer ties between yourself and our educational establishment and we present our expressions of the highest esteem”, ACV, KXIII 314/17. The news was made public in a brief announcement in the university section of the “Gazette de Lausanne”, 16th April 1894, p. 3. 44. Pareto to Ruchet, 14th April 1894, see Pareto (1975, p. 245). 45. Pareto to Paul Gaillaud, 14th April 1894, ibid., pp. 244–245. 46. ACV, KXIII 252 C, 1894/32. 47. Pareto’s request was partially granted at the end of January 1895, when the government increased his annual salary from 4000 to 4500 francs, Pareto to Ruchet, 27th January 1895, see Pareto (1975, p. 263). 48. Pareto to Ruchet, 19th April 1894, see Pareto (2001, p. 78). 49. On the intellectual biography of Winiarski, the Polish sociologist, economist and friend of Walras, a fundamental source remains the issue 14 (published in 1967) of the review “Cahiers Vilfredo Pareto” which was entirely dedicated to him. Winiarski was the first of the very few students whose doctoral thesis was supervised by Pareto, obtaining his doctorate on the 4th of July 1894 with a thesis entitled Russian finances (1867–1894) with an introduction regarding taxes and public credit (Les finances russes, 1867–1894, avec une introduction sur l’impôt et le crédit public) Geneva, Studer, 1894. During the discussion of the thesis, Pareto was critical of the weakness of the part devoted to economic theory, University (Université), “Gazette de Lausanne”, 5th July 1894, p. 2. 50. ACV KXIII 314/17. On the 25th of April, Roux replied expressing his regret at what he termed Pareto’s refusal to dedicate to the École and the Gymnase “the little time we are asking of him” and his hope that the reasons given were “truly serious”, ACV KIII 252 G1, 1894/26. The matter

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was concluded on the 31st of May when Ruchet, ignoring Pareto’s proposed candidate, nominated the law graduate Sidney Schopfer, an activist with the powerful Helvetia student association which was in the orbit of the Radical Party, ACV KXIII 314/18. 51. M-LF. 52. At this meeting major changes to the faculty regulations were approved, two of which are particularly relevant: firstly, by request, candidates were authorised to present their dissertation in languages other than French (article 14, sub-clause 2); secondly, optional new courses in sociology, the science of finance, the evolution of the organisation and of judicial procedures, and forensic science were introduced (article 40). 53. At this meeting Pareto and Favey gave an account of their discussions with the Department concerning the successor to the recently deceased Berney. 54. This inheritance amounted to 266,100 Swiss francs, as shown in Table 1.1. 55. Pareto to Pantaleoni, 10th April 1898, see Pareto (1894b, p. 188). In order to facilitate the search for a liberal replacement, Pareto delayed his resignation, but only until the end of 1899 at the latest, Pareto to Pantaleoni, 25th May 1898, ibid., p. 198. 56. Pareto to Pantaleoni, 10th and 12th April 1898, ibid., pp. 188–189, 191. Pareto’s teaching schedule had until then been as follows: pure political economy for three hours per week (plus an hour of seminar) in the summer semester of 1893; applied political economy for three hours per week (plus an hour of seminar) in the winter semester of 1893–1894, in the summer semester of 1894 and in the winter semester of 1894–1895; pure political economy for three hours per week (plus an hour of seminar) in the summer semester of 1895; applied political economy for three hours per week (plus an hour of seminar) in the winter semester of 1895–1896, in the summer semester of 1896 (production and commerce), and in the winter semester of 1896–1897 (distribution, socialist systems, taxation); in the summer semester of 1897, pure political economy for three hours per week (plus an hour of seminar), as well as an hour per week of principles of sociology; in the winter semester of 1897–1898 applied political economy for three hours per week (plus an hour of seminar), as well as an hour per week of principles of sociology; in the summer semester of 1898, applied political economy for three hours per week (production and commerce) as well as an hour per week of principles of sociology; applied political

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economy for three hours per week (socialist systems, taxation) in the winter semester of 1898–1899; in the summer semester of 1899, pure political economy for three hours per week, University of Lausanne, Course program (Programme des cours), various years. 57. Pareto to Pantaleoni, 12th April 1898, see Pareto (1984b, p.  190). Pareto extended his availability for teaching free of charge to two hours per week, Pareto to Pantaleoni, 13th April 1898, ibid., p. 192. Neither did he exclude the possibility, if advantageous from a tax point of view, of moving his residence to another Swiss canton or to the island of Jersey, Pareto to Pantaleoni, 12th April 1898, ibid., p. 190. The content of a doctoral thesis (in law) entitled Taxes in Switzerland. The basis for assessment and rates (Les impôts en Suisse. Leur assiette et leur quotité), Lausanne, Corbaz, 1898, which Pareto was supervising during that period and for which the author, Max de Cerenville (1875–1948) was awarded his doctorate on the 3rd of July 1898, may have had a bearing on this project. At this time, Pareto’s fiscal situation evolved as indicated in Table 1.1, according to the tax returns of the municipality of Lausanne. It is of interest to recall that in the summer of 1891, taking the opportunity offered by a long holiday in Switzerland, Pareto had ventured to Lausanne and Geneva not only to meet Walras but also, and more importantly, to “study the Swiss tax system” in order to make an estimate of the overall tax burden for a representative family of that nation, similar to the study he had made in the summer of 1890 for a typical Florentine family, Pareto to Pantaleoni, 18th August 1891, see Pareto (1984a, p. 57), Pareto to Léon Walras, 18th August 1891, see Pareto (1975, p. 161) and Mornati (2018, pp. 199–201). This research idea was not followed up, despite some suggestions given to Pareto by Walras, 21st August and 8th September 1891, see Walras (1965, pp. 458–459, 461), Pareto to Walras, 6th and 21st September 1891, see Pareto (1975, pp.  162–163, 166). Nevertheless, Pareto observed that, in Lausanne, no indirect taxes were imposed and that the principal item of expenditure was for public education, Pareto to Moneta, 18th September 1891, see Pareto (2001, p. 27). Pareto also intended to take the opportunity to study the innovative progressive income tax introduced in the Vaud canton in 1886, Pareto to Walras, 6th September 1891, see Pareto (1975, p. 162). On the progressive tax in Vaud, see Lasserre (1981) and Sardet (2003). Lastly, it is of interest to add that shortly before the beginning of his tax dispute with the authorities in

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Vaud, Pareto had accepted a commission from the mayor of Lausanne to make an estimate of “the likely future performance” of the hydroelectric generation plants with a view to their being transferred as a monopoly to a private operator, Pareto to Samuel Cuenod, 30th December 1896, see Pareto (1989, p. 303). It has not been possible to determine Pareto’s contribution to these investigations, which in any case culminated in the city council’s decision to allocate the service to the municipality. Regarding the whole question, see Dirlewanger (1998, pp. 53–92). 58. Pareto to Pantaleoni, 31st May and 25th June 1898, see Pareto (1984b, pp. 203, 213). Grandson of the revolutionary Alexander and son of the doctor Alexander (professor of physiology in the faculty of medicine at the University of Lausanne but an acquaintance of Pareto since the 1870s when both were living in Florence), Nicolas Herzen was indeed to succeed to the chair in Roman Law at the Lausanne faculty of law from 1900 to 1923. On his biography, see Erman (1967). 59. Pareto to Pantaleoni, 23rd, 25th, 27th, 30th June and 4th July 1898, see Pareto (1984b, pp. 212–214, 216, 218). 60. Pareto to Pantaleoni, 21st and 25th January, 4th, 5th, 8th, 9th, 14th, 17th, 24th, 26th February, 8th, 18th March 1898, ibid., pp. 152–153, 156, 162–163, 165, 169, 173–174, 177–178, 180, 182, 186. 61. Pareto to Pantaleoni, 27th June 1898, ibid., p. 213. 62. Pareto to Pantaleoni, 14th and 17th January, 10th April, 1st and 14th October 1898, 18th and 29th April, 4th December 1899, ibid., pp.  147–148, 188, 236, 253, 266, 268, 283. On the biography of Racca, see Busino (1987, pp. 97–114). On the beginning of the relationship between Pareto and Racca, which was soon to become irremediably soured, as we will see below, see Racca (1935). 63. Pareto to Ruchet, 7th June, 3rd August 1899, see Pareto (1975, pp. 387, 392). 64. ACV KIII 252 1899 C 92. 65. Ibid. 66. ACV K XIII 314/28. 67. Pareto to Pantaleoni, 21st December 1899, see Pareto (1984b, p. 286). 68. Pareto to Ruchet, 11th December 1899, see Pareto (1975, p.  395). Pareto’s decision was probably also motivated by the recent decisions of the Lausanne municipal council and the Grand Council (parliament) of Vaud to resolve their growing budget deficits not through reductions of expenditure but by increasing taxes, Municipal council (Conseil

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municipal), “Gazette de Lausanne”, 26th July 1899, p. 3 and supplement pp. 1–4; Grand Council (Grand Conseil), ibid., 28th November 1899, p. 4; 29th November, pp. 2–3; 30th November, pp. 2–3. 69. ACV KX A 259 1900/1. 70. ACV KIII 252 1900 C1 20. 71. Pareto to Pantaleoni, 20th March 1900, see Pareto (1984b, pp. 306–307). 72. ACV KXIII 314/28. 73. Pareto to Decoppet, 11th and 16th July, 16th August 1900, see Pareto (1975, pp. 403–404, 406). 74. Which after tax would indeed have corresponded to 3000 francs. 75. Pareto to Decoppet, 29th August, 14th September 1900, ibid., pp. 407–408. 76. Decoppet to Pareto, 14th September 1890, ACV KXIII-314-29-1381. 77. Pareto to Decoppet, 20th September 1900, see Pareto (1975, pp. 409– 410). Pareto to Pantaleoni, 24th September 1900, see Pareto (1984b, pp. 340–341) termed the 2000 francs net as a “derisory sum”. 78. See Busino (1963a, p. 285). 79. Pareto once again expressed himself in favour of this, Pareto to Pantaleoni, 30th October 1900, see Pareto (1984b), p.  342. At the beginning of 1901, Racca (Pareto to Pantaleoni, 6th January 1901, ibid., p.  353) was also following one-to-one lessons in mathematics taught by Pasquale Boninsegni (1869–1939, on whose intellectual biography see Mornati (1999)), who was to be the new assistant, as well as successor to Pareto. 80. M-LF. Pareto accepted the new salary, although it was only one-third of what he requested, because he was in the process of moving to Céligny in the canton of Geneva, where the progressive tax on personal assets was lighter than in the Vaud canton, see de Cerenville (1898, appendix tables 9 and 23). 81. University of Lausanne, Course program (Programme des cours), various years. 82. Whose name appeared in the official schedule only as of the winter semester of 1900–1901. 83. This was a new course which Pareto had advised Racca to teach in order to attempt “to create an independent chair for himself ” alongside that in political economy, Pareto to Pantaleoni, 9th July 1901, see Pareto (1984b, p. 368). 84. Pareto to Pantaleoni, 1st November 1900, ibid., p. 344. 85. Pareto to Pantaleoni, 16th June and 9th July 1901, ibid., pp. 364, 368.

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86. The early symptoms of the heart disease that was to accompany him for the rest of his life date from this period, Pareto to Pantaleoni, 23rd April 1907, see Pareto (1984c, p. 12). 87. Pareto to Louis Grenier, 2nd November 1903, see Pareto (1975, pp. 500–501). 88. ACV KIII 252 C1 1903, dossier 90. 89. Pareto to Ernest Roguin, 8th November 1903, in Pareto, Correspondence, 1890–1923, tome XIX-­I, pp. 500–502. 90. ACV, KXIII, 314/35. Racca returned to Lausanne on the 11th of December 1903, announcing to the faculty his availability to resume his position immediately and asking to be able to stay on as a substitute until the end of the academic year (when he promised to resign), since his agreement with the university had not been formalised within the required time, ibid. On the 14th of December he wrote to Decoppet threatening legal action but, in the face of the unresponsiveness of the various authorities, on the 21st of December he began to capitulate, handing in his notice for the end of the academic year but asking to be paid for the months of November and December, ACV, KIII, 252, C1, 1903, dossier 90. The denouement of Racca’s time in Lausanne came with a letter dated 19th January 1904 in which he gave his resignation for the 31st of March 1904, ACV, KXIII, 314/35. 91. In that year the teaching timetable was projected to be as follows, University of Lausanne, Course program (Programme des cours): in the winter semester Pareto was scheduled to teach one hour of applied political economy (population, money) and in the summer semester one hour of principles of sociology and three hours of applied political economy (production, commerce, distribution, consumption); the stand-in teacher was scheduled to teach two hours of applied political economy in the winter semester (savings, banks, real estate). 92. Pareto to Louis Grenier, 1st May 1904, see Pareto (1975, p. 522). 93. ACV, KXIII, 1904, dossier 61. 94. Pareto to Guido Sensini, 18th January, 9th April 1905, see Pareto (1975, pp. 533, 543). 95. Pareto to Sensini, 9th April and 1st July 1905, ibid., pp. 544, 552. 96. Pareto to Decoppet, 11th July 1906, ibid., pp. 566–567. 97. Pareto to Arturo Linaker, 27th July 1906, ibid., p. 568. 98. ACV, KXIII, 252 C1, 1907, dossier 16. 99. Ibid. 100. Pareto to André Mercier, 24th November 1906, see Pareto (1975, pp. 576–578).

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101. ACV, KXIII, 252 C1, 1907, dossier 16. 102. On Boninsegni’s long later career at the university of Lausanne, see (Mornati, 1999, pp. 35–48, 102–134). 103. ACV, KXIII 314/41. 104. Pareto to Decoppet, 13th January 1907, see Pareto (1975, pp. 576–586). 105. ACV, KXIII 314/41. 106. University of Lausanne, Course program (Programme des cours), various years. 107. ACV, KXIII, 252 C1, 1908, 101. 108. Ibid. 109. A protestant theologian from Lausanne who from 1895 held a chair in philosophy at the university. After beginning his replacement teaching in sociology, his personal relationship with Pareto deteriorated rapidly and irreversibly. 110. ACV, KXIII, 314/45. 111. At the university (A l’université), “Gazette de Lausanne”, 7th June 1909, p. 3. 112. ACV, KXIII, 252 C, 1916. This provisional organisation for the teaching of pure economics and sociology lasted until 1926 when, with the death of Millioud (on the 8th of January 1925), Boninsegni was appointed on the 7th of September 1926 to the chair in political economy, sociology, statistics, the science of finance and social legislation. 113. See Sect. 1.6. 114. See further Mornati (2003). 115. On Pantaleoni’s experience as a professor in Geneva, lasting from 1897 to 1900, see Busino (1963b). 116. Minutes of the meetings of the board of the Faculty of Letters (henceforth M-FL). 117. Ibid. 118. Ibid. 119. ACV, Report of the investigating commission for the degree and doctorate in social sciences project, drawn up by Millioud, ACV, KXIII, 252, 1902, C1, 27. 120. Ibid. 121. ACV, KXIII, C, 1902, 56. 122. ACV, KIII, 252, C1, 1911, 87. 123. Pareto to Rambert. 21th September 1910, see Pareto (1975, pp. 708–709). 124. On Pareto’s first experiences in teaching sociology, see below, Chap. 11.

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125. Pareto to Walras, 12th September 1891, see Pareto (1975, p.  164). Walras replied offering Pareto his assistance for the “simple empirical demonstrations” which the latter had said he wished to develop, Walras to Pareto, 14th September 1891, see Walras (1965, p. 164). 126. Pareto to Papafava, 14th August 1892, see Pareto (1989, p. 167). 127. Pareto to Pantaleoni, 16th July 1892, see Pareto (1984a, p. 247). 128. Pareto to Moneta, 2nd May 1893, see Pareto (2001 p. 57). 129. University (Université), “Gazette de Lausanne”, 10th May 1893, p. 2. 130. University (Université), “La Revue”, 10th May 1893, p. 2. 131. A large building, now hosting the Canton’s High School, located in the city centre behind the Palais de Rumine, which, from the early twentieth century until the 1970s was to be the main headquarters of the university. 132. University (Université), “La Revue”, 13th May 1893, p. 2. The first official lesson of his tenure as extraordinary professor was held on an unknown date during the winter semester from the 16th of October 1893 to the 25th of March 1894, see Pareto (1892). His first lesson as a full professor was given on the 23rd of October 1894, see Pareto (1894). 133. Walras a Pareto, 22nd April 1893, see Walras (1965, p. 556). 134. From the outset Pareto had decided, by making “some kind little gestures”, to attempt to win “the goodwill of the public”, so that “the first impression [he gave] in Lausanne [would] be as modest and unpretentious as possible”, Pareto to Pantaleoni, 23rd April 1893, see Pareto (1984a, p. 368). 135. Pareto to Walras, 26th April 1893, see Pareto (1975, p. 219). 136. Pareto to Pantaleoni, 11th May 1893, see Pareto (1894a, p. 370). 137. Pareto to Walras, 19th April 1893, see Pareto (1975, p. 218). 138. Walras a Pareto, 3rd May 1893, see Walras (1965, p. 558). 139. Pareto to Pantaleoni, 29th May 1893, see Pareto (1984a, p. 381). 140. Pareto to Pantaleoni, 22nd May 1893, ibid., pp. 372–373. 141. Pareto to Pantaleoni, 26th May 1893, ibid., p. 378, Pareto to Emilia Peruzzi, 16th May and 4th November 1893, see Pareto (1984d, pp. 549, 552). There is also other indirect testimony regarding the immediate mutual liking which arose between the Italian professor who spoke perfect French and his students in Lausanne. On the 20th of May 1893, on the first anniversary of the foundation of the Lausanne branch of Lemania (a Catholic-oriented student association), the newly arrived Pareto was numbered among the speakers giving a  “much-applauded speech”, “Gazette de Lausanne”, Students (Étudiants), 24th May 1893,

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p. 3. In the same way, William Jaffé, see Walras (1965, p. 560), reported that in the early 1950s, he encountered two ex-students of Walras and of Pareto who told him of their “great relief ” at the transition from Walras, “who drily read his lectures from notes” to Pareto, who “delivered his lectures without notes and with animation”. 142. Pareto to Pantaleoni, 26th May and 18th June 1893, see Pareto (1984a, pp. 374, 384). 143. Pareto to Pantaleoni, 31st May 1893, ibid., p. 382. Pareto soon realised that “the need to explain clearly” to others involved learning “many things that [he] thought he knew but which in fact [he] didn’t”, Pareto to Pantaleoni, 26th May 1893, ibid., p. 381. 144. Walras to Gide, 1st July 1893, see Walras (1965, p. 564). 145. M-LF. 146. Pareto to Pantaleoni, 25th November and 14th December 1893, see (Pareto 1984a, pp. 404, 411). 147. Pareto to Carlo Placci, 28th May 1894, see Pareto (1975, p. 246). 148. Pareto to Pantaleoni, 22nd April and 3rd June 1896, see Pareto (1984a, pp. 440, 451). 149. Pareto to Pantaleoni, 9th June 1896, ibid., p. 457. 150. Pareto to Giovanni Vailati, 2nd November 1896, see Pareto (1975, pp. 304–305). 151. Pareto to Mercier, 24th November 1906, ibid., p. 577. 152. On this subject in general, see Tissot (1996), Zeller and Liard (2005). 153. Administrative Report of the State Council of the Vaud Canton (Rapport de Gestion du Conseil d’État du Canton Vaud), 1890, p. 3. 154. See Zeller and Liard (2005, p. 14). 155. Administrative Report of the State Council of the Vaud Canton (Rapport de Gestion du Conseil d’État du Canton Vaud), 1890, p. 6. 156. See Zeller and Liard (2005, p. 20). 157. Ibid., p. 20, note 34. 158. Administrative Report of the State Council of the Vaud Canton (Rapport de Gestion du Conseil d’État du Canton Vaud), 1890, p. 13. 159. Ibid., pp. 13–14. 160. Records of the sittings of the Great Council of Vaud Canton (Bulletin des séances du Grand Conseil du Canton Vaud), 1890, p. 34. 161. Ibid., 1890, pp. 129–130. 162. Ibid., 1890, p. 37. 163. This subject consisted in an introduction to legal studies and was introduced on the recommendation of the Commission in order to assist students in the orientation of their studies, ibid., p. 36.

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164. This subject was introduced, again following the Commission’s recommendations, in place of natural law as specified in the original government bill, on the basis that natural law is simply a variety of philosophy of history whose adherents derive all law from a number of absolute principles. The alternative German school of history, authoritatively represented in Lausanne by Erman, affords greater weight in the development of juridical institutions to external circumstances, Records of the sittings of the Great Council of Vaud Canton (Bulletin des séances du Grand Conseil du Canton Vaud), 1890, pp. 36–37. 165. University of Lausanne, Course program (Programme des cours) from the winter semester of 1892–1893 to the summer semester of 1900.

Bibliography Arlettaz, Gérard. 1980. Liberalism and society in the Vaud Canton 1815–1845 (Liberalisme et Société dans le Canton Vaud 1815–1845). Lausanne: Bibliothèque historique vaudoise. Biaudet, Jean Charles. 1975. Vilfredo Pareto and Lausanne (Vilfredo Pareto et Lausanne). In International congress on Vilfredo Pareto (25–27.10.1973) (Convegno internazionale Vilfredo Pareto, 25–27.10.1973), 75–108. Rome: Accademia Nazionale dei Lincei. Busino, Giovanni. 1963a. Pareto and the authorities in Lausanne (Pareto e le autorità di Losanna). Giornale degli Economisti ed Annali di Economia XXII: 260–303. ———. 1963b. Maffeo Pantaleoni and the teaching of political economy in Geneva (Maffeo Pantaleoni e l’insegnamento dell’economia politica a Ginevra). Cahiers Vilfredo Pareto I (1): 49–60. ———. 1987. Vittorio Racca (1876–1957). In The school of Lausanne from Léon Walras to Pasquale Boninsegni (L’École de Lausanne de Léon Walras à Pasquale Boninsegni), eds. Pascal Bridel and Giovanni Busino. Lausanne: Université de Lausanne. Clavien, Adrien. 1997. History of the Lausanne Gazette. The times of the colonel 1874–1917 (L’Histoire de la Gazette de Lausanne. Les temps du colonel 1874–1917). Vevey: Editions de l’Aire. de Cerenville, Max. 1898. Taxes in Switzerland. The basis for assessment and rates (Les impôts en Suisse. Leur assiette et leur quotité). Lausanne: Corbaz. Dirlewanger, Dominique. 1998. The industrial services of Lausanne (Les services industriels de Lausanne). Lausanne: Editions Antipodes.

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Erman, Heinrich. 1967. Nicolas Herzen (1873–1929). Cahiers Vilfredo Pareto V (11): 73–86. Lasserre, André. 1981. Public finance and development. The Vaud Canton 1831–1913 (Finances publiques et développement. Le Canton Vaud 1831–1913). Lausanne: Bibliothèque Historique Vaudoise. Meuwly, Olivier. 2006. Louis Ruchonnet 1834–1893, activities and ideals of a statesman (Louis Ruchonnet 1834–1893. Un homme d’État entre action et idéal). Lausanne: Bibliothèque historique vaudoise. ———. 2010. The political world of Vaud during Pareto’s time in Lausanne (Le monde politique vaudois au temps de Pareto à Lausanne). Revue européenne des sciences sociales XLVIII (146): 19–31. Meuwly, Olivier, and Bernard Voutat, eds. 2003. The Vaud constitutions 1803–2003, Mirrors of political ideas (Les constitutions vaudoises 1803–2003. Miroirs des idées politiques). Lausanne: Bibliothèque historique vaudoise. Michels, Manon. 1935. Pareto as I knew him. The Atlantic Monthly CLVI (3): 336–346. Mornati, Fiorenzo. 1999. Pasquale Boninsegni and the Lausanne School (Pasquale Boninsegni e la Scuola di Losanna). Torino: Utet Libreria. ———. 2003. The creation of the School of Social Sciences in Lausanne: Vilfredo Pareto’s role (La création de l’École des sciences sociales à Lausanne: le rôle de Vilfredo Pareto). In The Vaud constitutions 1803–2003, Mirrors of political ideas (Les constitutions vaudoises 1803–2003. Miroirs des idées politiques), ed. Olivier Meuwly and Bernard Voutat, 354–375. Lausanne: Bibliothèque historique vaudoise. ———. 2010. Pareto’s collaboration with the Lausanne Gazette (La collaboration de Pareto avec la Gazette de Lausanne). Revue européenne des sciences sociales XLVIII (146): 71–88. ———. 2018. Vilfredo Pareto: An intellectual biography. Volume I. From science to liberty (1848–1891). Basingstoke: Palgrave Macmillan. Pareto, Vilfredo. 1892. Inaugural lesson on political economy by Mr. Vilfredo Pareto, Associate Professor (Leçons d’ouverture d’économie politique de Monsieur Vilfredo Pareto, Professeur Extraordinaire). In Université de Lausanne, Presentation speeches and inaugural lessons (Discours d’installation et leçons d’ouverture), October 1892, Lausanne: Editions de l’Université, Lausanne, 215–229. Reprinted in Pareto (1987, 79–86). ———. 1894. Speech by Mr. Vilfredo Pareto (Discours de M.Vilfredo Pareto). Gazette de Lausanne, October 23: 6. Reprinted in Pareto (1987, pp. 115–119). ———. 1975. Correspondence, 1890–1923 (Epistolario 1890–1923), Complete works, tome XIX-1, ed. Giovanni Busino. Geneva: Droz.

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———. 1984a. Letters to Maffeo Pantaleoni 1890–1896 (Lettere a Maffeo Pantaleoni 1890–1896), Complete works, tome XXVIII.I, ed. Gabriele De Rosa. Geneva: Droz. ———. 1984b. Letters to Maffeo Pantaleoni 1897–1906 (Lettere a Maffeo Pantaleoni 1897–1906), Complete works, tome XXVIII.II, ed. Gabriele De Rosa. Geneva: Droz. ———. 1984c. Letters to Maffeo Pantaleoni 1907–1923 (Lettere a Maffeo Pantaleoni 1907–1923), Complete works, tome XXVIII.III, ed. Gabriele De Rosa. Geneva: Droz. ———. 1984d. Letters to Emilia Peruzzi 1878–1900 (Lettere ad Emilia Peruzzi 1878–1900), Complete works, tome XXVII.II, ed. Tommaso Giacalone-­ Monaco. Geneva: Droz. ———. 1987. Marxisme and pure economics (Marxisme et économie pure), Complete works, tome IX, ed. Giovanni Busino. Geneva: Droz. ———. 1989. Letters and correspondence (Lettres et Correspondances), Complete works, tome XXX, ed. Giovanni Busino. Geneva: Droz. ———. 2001. New letters 1870–1923 (Nouvelles lettres 1870–1923), Complete works, tome XXXI, ed. Fiorenzo Mornati. Geneva: Droz. Racca, Vittorio. 1935. Working with Pareto. The Virginia Quarterly Review XI (3): 375–382. Sardet, Frédéric. 2003. Tax affairs and constitutions in Vaud 1885–1913 (Fiscalité et constitutions vaudoises, 1803–2003). In The Vaud constitutions 1803–2003, Mirrors of political ideas (Les constitutions vaudoises 1803–2003. Miroirs des idées politiques), ed Olivier Meuwly and Bernard Voutat, 215–246. Lausanne: Bibliothèque historique vaudoise. ———. 2010. Pareto, Lausanne and the Canton of Vaud (Pareto, Lausanne et le Canton de Vaud). Revue européenne des sciences sociales XLVIII (146): 11–17. Tappy, Denis. 2010. Pareto and Ernest Roguin (Pareto et Ernest Roguin). Revue européenne des sciences sociales XLVIII (146): 33–44. Tissot, Laurent. 1996. Politics, society and higher education in the canton of Vaud. The University of Lausanne 1890–1916 (Politique, société et enseignement supérieur dans le Canton de Vaud. L’Université de Lausanne 1890–1916). Lausanne: Editions Payot. Walras, Léon. 1965. Correspondence of Léon Walras and related papers, 1884–1897, ed. William Jaffé. Amsterdam: North-Holland Publishing Company. Zeller, Marie-France- Liard Pierre-Alain. 2005. The professors of the University of Lausanne, 1890–1939 (Les professeurs de l’Université de Lausanne). Lausanne: Archives de l’Université de Lausanne.

2 Pareto as a Critical Observer of the Italian and Swiss Political Scenes

Pareto, from the time of his resignation from the Società Italiana delle Ferriere to the time he came into his considerable inheritance, continued his systematic critical observation of Italian politics, to which, after his move to Switzerland, he added a similar attention to Swiss politics, particularly in regard to the Canton Vaud and the city of Lausanne. This systematic and critical assessment of Italian politics throughout most of the 1890s1 (see Sects. 2.1, 2.2, 2.3, 2.4, and 2.5) was performed by Pareto in the pages of the reviews “Journal des Economistes”, “Monde économique” and “Giornale degli Economisti” (all of which were of a free-trade stamp, even if of somewhat varying gradations) from the end of May 1890 on (thus corresponding to the period in which his departure from the company had left him with ample free time). His commentaries related to the economic and financial measures introduced by the various Italian governments, which alternated in power in the course of this period, including Francesco Crispi’s second government (9th March 1889–6th February 1891), the first government of Antonio di Rudini (6th February 1891–15th May 1892), the first of Giovanni Giolitti (15th May 1892–15th December 1893), the third and the fourth (and last) of Francesco Crispi (15th December 1893–14th June 1895, 14th June © The Author(s) 2018 F. Mornati, Vilfredo Pareto: An Intellectual Biography Volume II, Palgrave Studies in the History of Economic Thought, https://doi.org/10.1007/978-3-030-04540-1_2

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1895–10th March 1896) and di Rudini’s second (10th March 1896–11th July 1896). In the summer of 1897, following the departure of Pantaleoni from the editorship of the “Giornale degli Economisti” and the ensuing friction which developed between Pareto and the new Editor Antonio De Viti De Marco due to the excessively anti-establishment tone which in the latter’s view characterised Pareto’s contributions,2 Pareto ceased to collaborate so regularly with this review and also, generally, his close monitoring of Italian political events (see Sects. 2.6, 2.7, 2.8, and 2.9) as, moving to Switzerland, he followed with growing concern the decline of the free-trade cause in Switzerland and particularly in Lausanne (Sect. 2.10). The ‘self-help’ movement was the only political movement (in a very broad sense) which did not betray Pareto’s hopes, and which he followed with an uncharacteristic benevolence, sometimes actively, on both sides of the Alps (Sect. 2.11). From these sweeping observations Pareto drew material for his many journalistic writings, and this, together with his activities at the University of Lausanne, formed the personal and intellectual context which nourished and interrelated with his scientific investigations, to be described more fully in the following chapters.

2.1 The Extended Economic Crisis While all the governments listed above were of varying political persuasions, they all appeared to Pareto to have in common the habit, with regard to political economy, of denying the existence of economic laws, in the belief that they could and should “rule economic phenomena at their pleasure” because otherwise “the people, unhappily left to their own devices, would be confronted with certain ruin”.3 In general, Pareto continued to reiterate4 that the economic crisis affecting the country throughout the period in question was the consequence of the adoption of the new protectionist customs tariff which, contrary to the convictions of the protectionists, had exacerbated the trade deficit, increasing the value of imports and decreasing that of exports because, as only “the rare few” had anticipated, the higher tariffs had increased production costs.5 Among the various manifestations of

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the crisis which Pareto cited were: the surplus of bank withdrawals relative to deposits which began to make itself felt in Campania, Sicily, Apulia and Calabria after 1888, demonstrating the ruinous effects which the change in the customs regime had had on those regions in terms of reduced exports of the local agricultural products6; the rise in average annual emigration from 137,000 to 245,000  in the three-year period 1887–1888  in comparison to the decade 1877–18867 and the fall in bank deposits, calculated by Pareto himself for the period from 31st December 1888 to 30th June 1890.8 Not until the beginning of 1893 was Pareto able to record an apparent abatement of the crisis, this however being due exclusively to an external factor, namely the break in commercial relations between France and Switzerland, which led to an increase in Italian-Swiss trade.9 At the beginning of 1894, Pareto identified a connection between the economic crisis and the contemporary revolts in Sicily and in the Tuscany’s Lunigiana region10 and, in the following month of September, proposed, as an alternative to the partisan reform of land holdings in Sicily which was championed by Crispi, “the suppression, rather than encouragement, of the abuses and misappropriations of the local petty tyrants” together with the introduction of a free customs regime, in the certainty that if Sicily had a free-trade government like Malta, it would prosper in the same manner.11

2.2 Public Finance In Pareto’s view, the victory of Francesco Crispi in the November 1890 elections in no way resolved the country’s dire financial straits, since the Sicilian politician had promised to increase military expenditure while not increasing taxes, “two things which are completely unreconcilable” given the unacceptability of the increase in public debt which would inevitably ensue.12 A few months later, with the advent of the first di Rudini government, Pareto stated that a change in the economic outlook was possible, on condition that the new government kept “its promises on the economy”.13 Furthermore, to “eliminate the main causes of the country’s tribulations”,

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the new government should have the courage to take “a firm grip on those untouchable institutions which are the ministry of war and the admiralty”.14 At the same time Pareto also noted that, at least in Italy, the stock market listing for Italian public debt was rising, partly due to the definitive fall of the Crispi government and partly to renewed faith in the “resumption of commercial and financial relations with France which [was] one of the principal planks in the program” of the new government.15 However, Pareto did not think that the quotation could rise any further, because “you have to make allowance for the new bond issues which are inevitable” (recent statements by the new minister of finance Luigi Luzzatti on the need to “be sparing with calls for capital” notwithstanding), due to the high levels of military expenditure which membership of the Triple Alliance continued to impose on Italy despite the change of government,16 especially after di Rudini’s renewal of the Alliance on the 6th of May 1892.17 However, in the spring of the same year, Luzzatti’s financial acumen was insufficient to forestall the crisis in di Rudini’s first government, which was specifically due, according to Pareto, to the Prime Minister’s reluctance to choose between the minister of war, Luigi Pelloux, who demanded a sharp increase in military expenditure, and the minister of finance, Giuseppe Colombo, who considered that tax receipts could not be further boosted.18 Pareto’s final judgement on di Rudini’s first government was that it had continued the policies of the previous Crispi government “with a bit more small-minded stinginess and a bit less idealism” and had not kept its crucial promise not to increase the tax burden.19 Nevertheless, Pareto acknowledged that Luzzatti had done “everything humanly achievable without touching the budgets of the military and of the navy”.20 Again in the spring of 1892, Pareto anticipated that the first government led by Giovanni Giolitti21 would differ from the preceding one only in a propensity to incur more debts, since military expenditure (which amounted to a quarter of overall expenditure) would not be reduced (given the confirmation of Pelloux as minister of war and the return of Benedetto Brin at the admiralty) while revenues would not increase (because of the country’s state of tax exhaustion).22 Already by the month of May, Pareto was saying that the Giolitti government “is worse than di Rudini’s; it will keep on spending blithely and will incur more debts”.23 In August, commenting on rumours concerning the possible sale of the

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railways,24 Pareto considered the sale price of 600–700 million lire to be “ridiculously low”, in the light of the 60 million lire the state was receiving per year from the sector (corresponding, at the 5% rate of interest then obtaining, to a capital value of 1200 million lire).25 In the month of October, Pareto pointed out that the Giolitti government had already begun to resort to debt, albeit “indirectly”, achieving this specifically by means of a transaction involving the state employees’ pension funds which, he said, “are verily the last resource” for an Italian government looking to balance its books.26 To be more exact, the government was currently spending 72 million lire annually for the pensions of its retired employees, which was projected to reach zero after 58 years with the progressive deaths of the beneficiaries. This shrinking annual expense was to be met, according to the government’s plans, by allocating a fixed annual sum of 36 million lire for a period of 30 years, while the difference compared to the original total would still have to be financed by the Cassa Depositi e Prestiti (‘Loans and Savings Bank’) through proceeds from the sale of government bonds already in its possession.27 At the end of 1892 Pareto duly remarked that the first Giolitti government had indeed turned the deficit of 45 million lire forecast by the previous government into a surplus of 29  million, but only by shifting expenditure onto the part of the balance sheet reserved for extraordinary items, where it would be financed, more or less openly, by new loans.28 In December 1893, Pareto noted the increase in the stock market listing for Italian public debt which had accompanied the return of Crispi to government,29 but wondered “what this rise must have cost … the Treasury in association with certain banks”.30 Pareto blamed Crispi for proposing to reduce the state deficit by an increase in taxation which, even if it were approved by parliament, would be unlikely to yield an increase in tax receipts (but might rather cause “a reduction in revenues in real terms”) because of the country’s perennial state of tax exhaustion.31 The only possible solution continued to be a reduction in public expenditure, starting from military expenditure.32 For this reason, Pareto wondered what the country had “gained” from the replacement of Giolitti with Crispi33 and, more generally, noted that “at the end of the day the gains from the new kingdom of Italy have all been for the bourgeoisie”.34

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In March 1894, Pareto, in the absence of reductions in military expenditure, began to consider as inevitable the measure which had been proposed by the minister of finance (and a former friend from his youth in Tuscany) Sidney Sonnino (1847–1922) to reduce the interest payable on state bonds.35 Noting that Sonnino was proposing to achieve a balanced budget through a reduction of 27 million lire in expenditure, an increase of 52 million lire in taxation and a reduction in the interest payable on state bonds from 4.34% to 4% which was supposed to bring 43 million lire, Pareto claimed that “all that is phoney”, adding that “it is very difficult to get a clear picture of the situation because the government is careful to hide the commitments it makes” so “the balanced budget cannot be real” until such time as military expenditure had been reduced “quite considerably”.36 And on the eve of the early elections of 26th May to 2nd June 1895, the result of which “will depend mainly on the amount of money the government is able to spend”,37 Pareto observed that in any case Crispi and Sonnino had not succeeded in eliminating the budget deficit, in spite of reductions (subsequently revealing themselves to be illusory) restricted to non-military expenditure and despite increases in the tax rates which, as Pareto had anticipated, actually resulted in a reduction of revenues.38 Pareto later observed that the first two financial years for which Sonnino had been responsible, that is, 1893–1894 and 1894–1895, produced deficits of 13 million lire and 94 million lire respectively, contrary to expectations, so that public debt, “all the more or less ingenious sophistry” aside, increased by 244 million lire from 12,389 billion lire to 12,633 billion39 lire between the end of 1893 and the end of 1894. Lastly, comparing Luzzatti’s ministerial performance with that of Sonnino, Pareto observed that while the former “often went wrong through weakness and through lack of the energy required to stand up to the powerful, he always had the good of the country at heart, so that the damage he did was not intentional”, while the latter, instead, “acted in full knowledge of the damage he was doing”, and all this for the general political interests of the government he was part of.40 In the summer of 1896, noting the increases in duties on cereals, in military expenditure and in bonuses for private shipping companies decided by the new di Rudini41 government, Pareto wondered once again whether Italy had “benefitted economically from the fall of Crispi”.42

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2.3 Customs Policy In February 1892 Pareto resumed his analysis of the consequences of the protectionist customs regime introduced in 1887.43 With regard to iron he noted that customs revenues had in fact shrunk and had been almost completely absorbed by the increased costs borne by the state for its purchases of iron, while the iron and steel industry had hardly prospered, as shown by the severe difficulties at Terni and the bankruptcy of Tardy, Pareto’s ex-ally and competitor from Savona.44 At the same time Pareto joined Pantaleoni45 and the southern winegrowers in claiming that the commercial treaty with Germany of 6th December 1891 was of little benefit to Italy, permitting as it did only a tenth of Apulian production to be exported, as the rest did not comply with certain new commodity regulations.46,47 In the same period, Pareto commented approvingly on an attempt by the socialist deputy Gregorio Agnini to abolish the duty on grain, attributing the failure of the move to the acquiescence of the Italian population towards customs protectionism.48

2.4 Monetary Policy In the summer of 1891, Pareto, in reference to the deferment of the issue of notes sponsored by Luzzatti and approved by parliament, was forced to comment that Luzzatti, “instead of preparing us for the convertibility of banknotes into coinage, is taking us towards fiat money”.49 At the same time, Pareto observed that the reduction in the base rate, which had been deliberated simultaneously with the deferment, could equally and more effectively have been achieved by increasing the country’s stock of capital through a reduction in the public deficit by means of a cutback in military expenditure.50 More generally, the authorisation given to the issuing banks to keep the notes issued extra legem in 1889  in circulation, together with the reduction from a third to a quarter of the proportion of paper money in circulation requiring to be backed in coinage, confirmed the existence of a de facto fiat money regime in Italy, which was in any case inevitable in

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the light of state of the Italian economy at the time.51 In the following month of September, Pareto remarked that, of the 644 million lire raised at the beginning of the 1880s for the purpose of abolishing the fiat money, only 200 were left in the banks’ reserves and 8 in the Treasury. He explained the outflow of the rest by the need to pay the interest on Italian public debt held abroad, which amounted to 2.6 billion lire in France, 290 million in England and 430 million in Germany.52 In the same way, the increase of currency in circulation which had been decided two years later by Crispi53 appeared to Pareto as “a to all intents and purposes a tax” because, by increasing “the spread vis-à-vis gold”, it decreased the value of the lira, thus reducing the purchasing power of those receiving “fixed salaries”, in particular the working population.54 In order to improve the country’s economic situation, it would be better to reduce the issuing of notes so as to eliminate the premium on gold, and for this “it would be necessary for the politicians to stop drawing on the deposits of the issuing banks for their own requirements”.55 In November 1891, Pareto warned that Italy’s financial situation would deteriorate further, and very drastically, were France to repudiate the Latin Monetary Union, thereby obliging Italy to withdraw its 1803 million silver ecus circulating in France (due to, again in line with Gresham’s law, the Italian fiat money56), paying them by French ecus or with gold, which would have to be procured from outside Italy.57 Pareto pointed out that France’s renunciation of this repayment amounted to a free loan which, for reasons which were unclear, was being extended to Italy.58

2.5 The Issuing Banks The most known among Italy’s economic problems of that time, and the one to which Pareto, prompted partly by his prevailing political inclinations, devoted the most attention, was the difficulties of the issuing banks, which led to the failure of the Banca Romana and which gave rise to the ensuing reorganisation of the sector through the creation of the Banca d’Italia. In regard to the organisation of the issuing banks, Pareto’s view was that “the important thing is that notes should be convertible into coinage, the rest is not so urgent”.59 While he admitted that “the free-traders hope to see freedom of issuance”, he nevertheless considered that the non-obligation to

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accept banknotes was also compatible with a regime characterised by a monopoly of issuance.60 The école métallique system, with its fixed ratio of metal reserves to total currency in circulation, was, among the various regulatory systems, “probably the most effective in guaranteeing the exchange of notes for gold… [even if ] it is certainly not the most economical in terms of coinage”.61 Rather, in his view, an issuing bank’s metallic reserves “should fluctuate in accordance with changing market conditions, in such a way as to ensure the prompt and straightforward exchange of notes at all times”.62 Pareto acknowledged that only in England, and only since 1823, had banknotes been “genuinely exchangeable for gold on request, with no complications or loopholes”.63 Lastly, regarding this topic, Pareto was an advocate of the theory that government interference in the issue of coinage was invariably insidious,64 contrasting the prosperity of Scottish issuing banks, which were free of government meddling, with the terrible crisis afflicting the Italian issuing banks whose “surveillance on the part of the state is performed so (mal)adroitly”.65 In this context, Pareto’s systematic monitoring of the question of the issuing banks commenced in the spring of 1891 with his comments on the government’s recent creation of the Istituto di Credito Fondiario (‘Real Estate Credit Institute’), at the prompting of the Banca Nazionale, which had a number of problematic real estate loans on its balance sheet. According to Pareto, this episode clearly demonstrated that even the Rudini-Luzzatti combination, although nurturing “vague intentions of honesty and integrity … will submit to any type of coordinated pressure”.66 In any case, any possible (but improbable) success met with by the new institution would not achieve anything concrete in the interests of the nation, since the whole aim of the venture was none other than “to come to the aid of compromised building companies and to clear the portfolios of the banks which had propped them up thus far”.67 Pareto was of the opinion that all Italy’s banks were dependent, directly or indirectly (i.e. through rediscount of the bills of exchange) on the Banca Nazionale, which he considered “our best credit institution and still the healthiest, despite some mistakes”, while the latter in turn sought, by indulging the government’s “every whim”, to garner the support of this latter to become the sole national bank of issue.68

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In the spring of 1892, Pareto had lamented the fact that Rudini’s government, rather than allowing the national bank and the bank of Naples to send the Banca Tiberina into bankruptcy, and thus seek to recover at least a part of the sums owing to them through the sale of its real estate assets, had, for purposes of gaining a consensus in parliament, persuaded them to take equity in the bank pending a rise in the value of the properties. Pareto’s comment was then “the goal of issuing banks should be something other than to immobilise their capital in speculative ventures of this kind”.69 In the following summer, Pareto criticised as arbitrary another attempt to support the Tiberina bank by postponing payment of its debts to the issuing banks until 1897 and, more critically, by limiting the interest payable on these to 4%, with this being further conditional on the unlikely eventuality of the Tiberina making profits.70 At the end of 1892 Pareto made haste to inform his French readers that the parliamentarians Napoleone Colajanni and Lodovico Gavazzi had just read before the Chamber the report prepared in 1889 by Senator Giuseppe Alvisi but subsequently concealed by the second Crispi government, in which were described serious administrative breaches at the Banca Romana, particularly in relation to the existence of a quantity of notes in circulation 25 million lire higher than the figure shown in the balance sheet. Pareto was pleased to note that, pending the results of a new enquiry into the issuing banks, the Giolitti government had been obliged, against its will, to reduce its proposed extension of the legal validity of banknotes from six years to three months.71 A few days later, commenting further on the now public scandal of the Banca Romana, Pareto claimed to believe that Italy was “governed by thieves, by crooks and their confederates”.72 Thus, basically, in Pareto’s view, “the politicians have found a thousand ways to put pressure on the banks, and have extracted as much money from them as they could”.73 In February 1893, reiterating that the Italian currency’s return to health depended on the independence of the issuing banks from the government and the effective implementation of the requirement on them to exchange “their banknotes on request”,74 Pareto lamented the fact that the Crispi government, with Giolitti as Minister of Finance, had failed in 1889 to arrange for the delivery of the Alvisi report75 to the magistrates, instead promoting the

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continuation of the Banca Romana’s extra-legal release of currency into circulation through its abolition of the “riscontrata”, that is, the requirement on banks for the redemption in metal reserves of their own banknotes deposited with other issuing banks. Pareto thought it “prudent” to avoid any mention of the consolidation, already contemplated since as early as 1893, of the six issuing banks into just two groupings (one resulting from the merger of the Bank of Naples with the Bank of Sicily and the other from that of the National Bank, the Banca Toscana and the Tuscan Credit Bank together with the receiver responsible for the winding-up of the Banca Romana), until such time as more information was forthcoming on “precisely what will become of the political portfolio”, referring to the bills of exchange which had been accepted solely due to political pressure and which were now lying unredeemed with the banks. The most important consortium attempting to save the Banca Romana, that is, the one led by the National Bank, would be prudent and would be acting “in the interests of the nation” only if it “categorically” refused to take on this portfolio or any further issue of credit demanded by the government for electoral purposes, limiting itself to saving what could be saved.76 Basing himself on the results of the new parliamentary enquiry into the issuing banks, which had been published on the 20th of March 1893, Pareto stated that generally in these banks, the extent of ­maladministration was proportional to the extent of “state interference”.77 Thus, the only one which was well managed was the Banca Toscana di Credito, which, thanks to “its relative unimportance, had escaped the attentions of the politicians”. Four-fifths of this bank’s assets consisted of bills of exchange discounted on bankers, as should be the case for all issuing banks.78 Similar considerations also applied to the Banca Nazionale Toscana. In the case of the other four issuing banks, especially the Banca Romana,79 what was evident instead was that their level of capital was by now less than that of their immobilised and their impaired assets, so that none of them were any longer in a position to redeem their banknotes on sight,80 having by this time become “simple agencies for the printing of paper money to keep the government and its friends happy”.81 This situation had arisen because the banks, thanks to the legal tender regime (which in practice was synonymous with fiat money), had been relieved

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of the obligation to redeem their banknotes with sound money, together with the fact that the controls provided for in the legislation82 were ineffective, demonstrating once again that while natural laws operate automatically, artificial systems require executors who, being humans, have their own “weaknesses and failings”.83 In Pareto’s view, nothing would change even with the introduction of the banking reform to implement the definitive merger between the two Tuscan banks and the National Bank to form a new Bank of Italy, the preservation of the two southern banks and the liquidation of the Banca Romana on the part of the Bank of Italy.84 The forecast overall value of immobilised and impaired assets and losses resulting from the liquidation of the Banca Romana due to be transferred to the Banca d’Italia would amount to 255 million lire, leading Pareto to express his view that the latter would not be safe even if it obtained the monopoly of issuance, together with the possible absorption of the two southern banks85 and, in an address given in Milan on the 10th of April 1893 Pareto, added that the solution involving the Banca d’Italia would bring about the failure of the issuing banks not able to exchange their banknotes for metal coinage.86 Hence, Pareto thought that the new Banca d’Italia (created on the 10th of August 1893) would experience the same difficulties as the Banca Nazionale, so that “sooner or later the state will have to intervene, if we want to avoid a repetition of the adventures of the Banca Romana”.87 Consequently, regretting the proposal to apply the legal tender regime, which had essentially brought about the failure of Banca Romana,88 to the Bank of Italy, Pareto approved the proposal made by the chambers of commerce that the new issuing bank should be subjected to the requirement to exchange their banknotes for coinage,89 but without any loopholes, such as the option, in cases where this exchange had not been performed, to reduce the right to new issues of banknotes by an amount four times greater than the amount not exchanged. Essentially, Pareto’s view was that the only way to make sure the banks exchanged their banknotes was to give citizens the right to “take legal action against them, exactly as for a trader or a banker who does not redeem a bill of exchange at the due date”.90 Thus, more in general, the supervision of the new issuing bank should be entrusted to the public and not to the government.91 Still in 1897, Pareto noted that the crisis of the issuing banks in Italy was by no means at an end and that the only

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possible solution was “to completely write off all the irregular operations which had been performed to date” and to reconstitute these banks on the model of institutions independent of politics such as the Bank of England or the Bank of France,92 which had yielded “positive results”. Pareto’s examination of the issue concludes with some interesting general reflections. First of all, by immobilising their capital and deposits in unprofitable transactions designed solely to please the government, the Italian issuing banks had, in Pareto’s view, brought about a reduction in the national wealth because they had allocated the savings entrusted to them “among various entrepreneurs … [not] according to [their] productivity in a fair manner … [but] according to the kickbacks the entrepreneurs were able or prepared to pay the politicians, which is not at all the same thing”.93 In the second place, Pareto thought the simultaneous occurrence of the Banca Romana scandal in Italy and the Panama canal scandal in France94 “not a mere chance”, as “in both countries we have similar effects due to similar causes”: in particular, the use of public resources for private ends, which characterised French opportunisme and Italian trasformismo, “must lead to scandals”.95 Furthermore, in both countries even the honest politicians had preferred to defend party interests and the prevailing form of government rather than “prevent the commission of crimes”, even though such prevention “is the first and foremost reason for which a government exists”.96 On the other hand, France, unlike Italy, had showed “a great energy of reaction”.97

2.6 Pacifist and Anti-colonialist Activism In the period under examination, Pareto continued the journalistic writings on various political movements which he had begun on earlier, now sometimes going into greater depth. Speaking of pacifism and anti-­ colonialism98 in the context of current international politics, Pareto’s ideas concerning levels of military expenditure and the effectiveness of pacifist lobbying grew out of his conviction that war is “the consequence of the rivalry between political classes, who wish to increase the number of their subjects, and, more particularly, of their taxpayers”.99

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Italy’s participation in the Triple Alliance was the consequence, firstly, of anti-Republican (and hence anti-French) feelings at the Court, and, secondly, of the protectionist instincts of the bourgeoisie which could be satisfied only with the breaking of commercial relations with France. Thirdly, fears of armed conflict with France played into the hands of military and naval suppliers who wished to justify an increase in military expenditure, while the megalomania of those who had enriched themselves in the course of the country’s unification required revenge to be exacted for the offence of the French conquest of Tunis.100 Pareto’s position, in the summer of 1892, was that the Triple Alliance, against which France and Russia were preparing a political and military alliance101 which could lead to “a catastrophe worse than any in historic memory”,102 was already capable of “obliging Italy to take part in a war which is none of its business and which could cost much more than just vast sums of money, because [if ] we win we will gain but little reward, while [if ] defeated we will be destroyed”.103 Pareto thus wondered “what benefit can come for the Italian people from the government’s support for Germany in regard to the possession of Alsace-Lorraine”.104 As regards the Italian colonial policy, Pareto, after claiming in April 1893 that “the millions that are wasted fruitlessly in Africa would be ­better spent in Sardinia, in the Roman countryside, where there are lands to be reclaimed and roads to be built everywhere”.105 At the end of 1895, speaking of the Italiana defeat at Amba Alagi, he remarked that “the Abyssinians are defending their land and their liberty”, adding that “instead of going to fight the Africans, if they had any sense, the Italians should fight their internal enemies”, that is, the politicians.106 Then, in June 1897, Pareto observed that, following the disaster at Adua, there were two opposing factions in parliament, one in favour both of military and colonial expenditure and the other contrary to both, while a small minority was in favour of reducing colonial expenditure in order to increase the military budget.107 In the spring of 1892, after noting that Italian military spending had doubled since the mid-1870s and, since the national income had not increased likewise, had become relatively much more onerous, he added that, not being necessary for maintaining the country’s independence (which had previously been achieved with a much lower

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level of expenditure) but being required solely in order to meet the demands of the imprudent membership of the Triple Alliance, it was inefficient, since keeping a similar number of soldiers cost Italy much more than it cost Austria.108 In the following summer, Pareto expressed his view that the government granted customs tariffs to the “ruling classes” in order to gain, in return, parliamentary approval for its desired military expenditure.109 Thus, an “infallible way” to render Italy “more pacifist than Switzerland” would be to finance military expenditure “through additional taxes on landholdings”.110 Hence, in September 1892, Pareto declared his “full” agreement with the ideas of an Army officer, the Captain Tito Molinari (alias Tiberio Squilletta), on the reform of the army.111 At the beginning of 1893, Pareto sought to disseminate the idea that the eight-hour working day could be achieved only by reducing military expenditure112 which in any case had been justified by misleading the population both with regard to its supposed indispensability for the country’s defence and also to the manner of its collection, through a system of taxation skewed towards indirect taxes which were difficult to detect and which weighed upon the popular classes although they gained no benefit whatever from it.113 In relation to pacifist activism, Pareto’s view was that it would be best to “establish the objective we are aiming at and then accept any help in bringing it about” and to “join together with all those who could contribute to the undermining of militarism, without worrying about their motives”.114 Thus, despite his continuing belief in Spencer’s idea whereby “commercial and military protection are one and the same”, Pareto saw no contradiction in belonging both to an anti-militaristic association which concerned itself little with free trade (like Teodoro Moneta’s Peace Society) and to a free-trade association which did not concern itself with anti-militarism (as formerly in the case of the Italian Free-Trade Association in Rome).115 On the contrary, he thought it vain to believe that militarism and free trade could be combined as the latter had sought to do in the summer of 1892.116 Thus, having taken stock of the uncertain nature of current Italian free trade’s pacifist credentials, and after stating in the autumn of 1891 that only the people could be relied upon in pursuing peace because only they were able to understand that “destroying the whole of Europe so that

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Germany can keep control of Alsace-­Lorraine against the wishes of its inhabitants is plain stupidity”,117 on the 15th of April 1893, speaking on the theme Democracy and war at a Milanese meeting of Moneta’s society, Pareto began by claiming that only democratic regimes could forestall the threat of war.118 Again, in March 1897, Pareto acknowledged that in Italy, in Germany and in France, only the socialists had “sincerely” opposed the war, by voting against military expenditure in parliament.119

2.7 R  elations with the Italian Radical and Republican Parties In December 1891 Pareto declared himself “a true democrat”, meaning by this that he considered that the “aim of life” was to “procure the greatest good of the greatest number”. However, even though he also thought that the democratic system still needed to be perfected, he considered that its failings could be corrected by reference to the principle of liberty, while aristocratic forms of government had always shown “execrable” results.120 Moreover, a few weeks earlier, on the occasion of his first visit to Lausanne, he had noticed that there “everyone [was] very courteous, but especially those in government, who treat you very well”, concluding that “it is a pleasure to breathe this air of democracy”.121 At the beginning of 1892, Pareto in any case stated that his “radical passion122 [was] nothing but an expedient” as he had the impression that “the radicals [were] not a whit more liberal than the others”, so that “when they gain[ed] power, it [was] likely” that he would be in the opposition. However, having said that, he recognised that “they are the only ones with the courage to assert certain truths which others conceal”.123 In general, Pareto considered that, in order to “achieve something useful”, it would be necessary to stop asking “people for a perfect communion of ideas which is not attainable”, instead accepting “anything that can benefit our cause” which was “to escape the clutches of those who are bleeding the country”.124 Thus, again in the summer of 1892 Pareto offered his assistance in collecting economic data for Cavallotti’s speeches, not only out of personal friendship but also because “other than [him I] see no hope” for Italy.125 Then, in October 1892, just before the early general election of the 6th and the 13th of November, Pareto declared his

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new liberal convictions, with the proviso that his “radicalism consists only in this, that when something appears to me as good and right, I can’t help advocating it”, just because it might offend some dignitary or some institution.126 He also reiterated that “those who love liberty, of whichever party, should work to limit the interference of the state and to increase the number …. of people able to achieve things without causing too much damage while observing the dictates of their conscience”.127 On the other hand, with regard to the intransigent republicans (i.e. those who refuse to take part in elections out of abhorrence of the monarchy), in Pareto’s view they “are not altogether wrong” when they say that “it’s not a question of personalities but of systems”,128 but they “are wrong then to shut themselves inside their formulas like the Catholics with their catechism”.129 In 1893, Pareto claimed that the Republican Party “is not large, but it consists almost exclusively of men whose honesty and straightforwardness are above suspicion”. However, they took part in municipal elections, if any, so that the party’s influence “in Italian political life [is] utterly null”.130 However, with the beginning of 1894, and the ferocious repression of the Sicilian “fasci”, Pareto claimed to become “more Republican with every passing day” and that he had started “to believe that the economists who say that the form of government is irrelevant are wrong”.131 He therefore regretted the separation of the socialists from the republicans, at the prompting of the former, when the two parties should join together “to attempt to remove the fetters that confine the people’s liberty”.132 In the summer of 1896, he said that if all the followers of Mazzini “had remained intransigent since 1860, by now they would have won a complete victory for sure”. Indeed, with the disasters in Africa which followed the banking scandals and the country’s enduring economic crisis, “the governing class retained power only because no opponents were manly enough to challenge them for it”.133 For this reason, he declared his preference for a republic, although “it would be only marginally better” than monarchy, partly because “if the head of state could be changed, one might hope to see an intelligent man in power who would not ruin the nation just to please the German ally”, and partly because “true monarchy saps ethical awareness”.134 However, in July 1897, Pareto commented that a republic “will never amount to anything very worthwhile” and that Italian republicans had “made an

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idol out of a name”.135 Hence, at the beginning of 1898, after claiming that “a republic, if it is not federal, will not be able to achieve anything much”, he was starting to prefer a monarchy to a republic led by someone like Crispi and to hope that the Republican Party would aim first and foremost to take control of the municipalities, “not only as a good means of taking power nationally” but also to develop “able administrators”.136

2.8 Relations with the Italian Socialist Party In this period, Pareto was further exploring his ideas concerning the Italian Socialist Party and was establishing a number of contacts in those circles.137 In particular, after describing the organisation of the socialists in Italy, he mused on possible relations between socialists and liberals and on the socialists’ prospects of coming to power. Pareto informed his American readers of the existence of two different currents in Italian socialism, one characterised by an agriculturalist cum nationalist outlook and the other following an industrialist and Marxist orientation. The latter had its base in Milan, “which is industrially the most important city in Italy”, and was led by the lawyer Filippo Turati (1857–1932), “a man of much talent”, in Pareto’s view.138 The other grouping had its origins in the region of Romagna and was spreading rapidly in the countryside from Mantua to Parma as well as in certain areas of the south, where in reality it represented “a simple desire for the partition of the land”.139 In Italy, as in France, socialism was disastrous from the point of view of economic theory (due to the foreseeably catastrophic consequences which would attend its reorganisation of the economy along collectivist lines140), but positive in the light of political theory (which sets the government the sole aim of pursuing the good of the majority) and as regards integrity. On the contrary, the sole positive aspect of the bourgeois party was its antipathy for socialist economic theory, which, however, might not be sufficient to outweigh its bad habit of allying itself with “the worst kind of evil-doer”.141 Between these two parties the winner would be the one which was able to correct its own failings and reinforce its virtues “in good time”. In the spring of 1896, Pareto predicted the victory of the socialists, firstly because “they have the merit of taking to heart what others only pay lip-service to”,142 and secondly because the bourgeois

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party made mistaken political choices such as favouring the monarchy, the army and religion143 out of moral and intellectual weakness. Moreover, as early as November 1893 Pareto had pointed out to Turati that socialism had “a very grave danger to skirt in its rise to power, i.e. the reaction that could ensue following either a premature move or as a result of an insufficient level of awareness on the part of the population”.144 In October 1898, Pareto interpreted the Socialist Party’s rising popularity as resulting from a number of causes, including government persecution (which contradicted the idea of limiting the repression of opponents “to a level acceptable to and demanded by public opinion” as suggested by “the art of government”) so that the victimisation of the socialists led them to acquire added public sympathy and internal cohesion and to be credited with “espousing excellent measures” whose ­implementation was hindered only by the “private interests of the ruling class”,145 together with the fact that “the liberals, by abandoning their banner [as champions] of honesty in politics, of public order and of legality, have yielded it to the socialists”.146 In the winter of 1891, Pareto invited Italian socialists to join with the free-traders in the struggle against abuses against property, including the duty on grain (which was also opposed by German and French socialists), while stopping short of urging them to abandon the fight for the outright abolition of property itself.147 In fact, Pareto considered, in the light of the “laws of history”, that it is precisely “those in the most wretched condition … who are likely to tolerate oppression”,148 thus challenging the socialist notion that “when things reach an extreme of misery, the people will be more likely to react” through revolution. In March 1893, the young socialist student Francesco Coletti149 responded directly to Pareto’s oft-repeated mantra that “economic liberty alone can heal the wounds which afflict society”,150 thus leading to Pareto’s first public contact with Turati’s socialist circles. According to Coletti, protectionism and state control are consequences of “capitalist ownership of property” rather than deriving from the generalised unawareness of the misconduct of politicians which existed only in Pareto’s imagination.151 Pareto replied by claiming that free-traders and socialists agreed that the “end to be pursued” should be the hedonic maximum, that is, “the greatest quantity of good for the greatest number of people”, but that they disagreed regarding the means of achieving this because the latter were convinced that it was sufficient to

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bring about the abolition of “the capitalist system of property”, while the former worried about possible “greater evils” attendant on alternative systems of government. In any case, “a large proportion of social ills” are caused simply by the “depredations committed by certain people to the detriment of the majority, with the assistance of the public authorities”.152 With his hopes rapidly evaporating of cooperation, even if it were only momentary, between free-traders and socialists, Pareto, who “while an opponent of the socialists, respect[ed] and honour[ed] them for the noble and elevated ideals which they pursue”,153 thought that “propaganda, and possibly the experiment of popular socialism, would be preferable to being further and further confined within state socialism”.154 Agreeing with de Molinari’s prediction that “our society will pass through a socialist phase”,155 he added that it was foreseeable, “with all the required accuracy”, that this socialist episode would entail “a massive destruction of wealth, bringing, as an inevitable consequence, misery and death for many”, as this was the certain result of “all systems which … go counter to the only circumstances [which can] bring about the maximum of well-­ being”.156 Pareto also wondered in particular, in regard to such a future socialist phase, why the socialists “who suffer most from government bullying, retain such unlimited faith in the beneficial effects of state actions”157 and appear to believe that “the people to whom they wish to confer the task of regulating production [are] above any error, sin or fault”.158 Then, in the summer of 1895, Pareto asserted that the “only way” which would be effective in circumventing the prospect of socialism would be to “introduce into social affairs that element of justice which currently is often lacking”.159

2.9 The Decline of Italian Liberalism Despite the increasing attention he paid to the parties of the extreme left, seeking to promote the emergence of liberal traits in them, Pareto remained attached to his liberal (in particular free-trade) positions, albeit with growing scepticism. His thoughts in this regard at the time concerned the organisation of the liberal doctrine and the prospects for liberal political action, which seemed to him increasingly remote.160

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In general, the liberals, not being able to restrict liberty to their friends alone, “have no incentive to offer [and so] cannot attract followers”. This observation allowed him to fathom “how come Italy has had authoritative men to defend the liberal doctrine without deriving any practical benefit”.161 Moreover, Pareto pointed out that when non-liberals “demand liberty, they demand it for themselves but wish to deny it to others”, while the liberals “demand it because they consider it intrinsically a good thing and thus do not worry about whether their adversaries would also enjoy its benefits”.162 Always bearing this in mind, Pareto stated in 1892 that he still approved of “the liberal political programme” expounded in 1889 by the economist Arturo de Johannis163 (at the time director of the Florentine weekly “L’Economista”), but specified that the économistes, contrary to the desire for the destruction of the state of which they are accused, want it “strong and powerful, to safeguard the lives and the property of its citizens both internally and abroad”, and that it was in order to allow it to perform these tasks to the best of its ability that they did not wish it to take on others.164 At the beginning of 1898, Pareto rejected Benedetto Croce’s characterisation of him as an idealist,165 disputing the latter’s belief that he considered something to be achievable simply because he considered it “good”.166 For example, a person who thought they could achieve the abolition of the duty on grain simply because it corresponded to the notions of “truth and justice” would be an idealist. To achieve economic liberty in Italy, however, “much more radical changes” would be needed. It was precisely because the Italian liberals “hesitated when faced with the need to make such changes that all their work was in vain, while [he] diverg[ed] from them completely because, on the basis of the premises, [he did] not fear the consequences”.167

2.10 The Decline of Swiss Liberalism In Lausanne, during the second half of the 1890s, Pareto observed with distress what he saw as the beginning of a rapid decline of the Swiss form of liberalism whose incarnation he had encountered in Vaud and had so much admired, with a democratic government made up of honest citizens and dedicated to the well-being of all the citizens and not only of the privileged few, as in Italy.168

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This decline followed a long drawn out defence of liberal institutions, in a series of referenda, against attacks originating from the state socialism. The first round monitored by Pareto was that of the 4th of March and the 3rd of June 1894, when proposals for state regulation of trades and for the right to a minimum wage were rejected by the people and by the cantons. Pareto, who had been indirectly involved in the second of these,169 acclaimed these results because the Swiss population had spoken directly, without turning to the type of reactionary government which the Italian bourgeoisie blindly relied on, incapable of understanding that it was precisely this type of government which was mainly responsible for the growing success of popular socialism.170 Pareto claimed, in particular, that it was the direct political involvement of the Swiss bourgeoisie, setting an example to their counterparts in Italy, which had made it possible to reject a proposal to increase the remuneration of diplomatic staff, which, had it been passed, as the Swiss bourgeoisie well knew, would have led to an increase in taxes and set the country on the road to the excessive tax burden which was already seen in Italy.171 In the face of this series of defeats, the supporters of the state socialism in Switzerland then tried to adopt a cleverer strategy, proposing a federal monopoly on matches only after having obtained the support of the powerful canton of Bern (where a number of private match producers hoped to transfer their unprofitable factories to the confederation) and of the humanitarian element in Swiss public opinion (in whose view the nationalisation of match factories would lead to an improvement in working conditions for the workforce). This complex manoeuvre was nevertheless rejected by majorities both of the population and of the cantons in the referendum of the 29th of September 1895.172 From these results in favour of liberalism Pareto drew the conclusion that the movement for popular socialism grew stronger in accordance with the errors committed by bourgeois governments, which in turn grew more numerous in accordance with the increased influence of state socialism. Hence, where fewer such government errors had been committed (mainly because the liberals had defended their principles in a credible manner), popular socialism also had met with less success.173 At the same time a movement of the dimensions which state socialism had now attained should not be underestimated. Hence Pareto’s concern

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that the approval, in the referendum of the 4th of October 1896, of the law for the standardisation of accounting procedures in the various private railway companies constituted an alarm bell.174 In the case of Switzerland, state socialism also sought to impose itself by suffocating the sentiments of liberty and of local autonomy to which the country owed “a prosperity which could scarcely be equalled on the European continent”, in favour of a central authority aiming to transform the cantons into innocuous jurisdictions while monopolising the railways, the issuing of currency, social insurance and commercial, civil and penal legislation.175 To Pareto, the destiny of Swiss economic liberty appeared to depend on the questions of the currency and of the railways. He thus decided to participate personally in the referendum campaign against the 18th June 1896 law, which had granted the confederation the monopoly in the issuing of currency through a bank which would be at least three-fifths controlled by the confederation itself. Pareto made speeches (in the Vaud canton at Aigle) on the 9th of January 1897 under the auspices of the Société d’utilité publique, at Lausanne on the 15th and the 22nd of January under the auspices of the Société industrielle et commerciale and at Morges on the 12th of February on the invitation of some distinguished local liberal personalities. At these meetings he intended to look only to facts in search of the best solution to the question posed in the referendum.176 In Pareto’s view it should first of all be remembered that more advanced countries tended to entrust the issuing of currency to a joint stock bank with mixed public and private capital and control. This was based on the reasoning that such a sensitive mechanism should be placed in expert hands, which, however, could certainly not be only those of the state, which were “always clumsy”.177 Having said that, the monetary situation in Switzerland,178 which Pareto saw as showing more and more high base rates with excessive fluctuations and constant devaluation of the Swiss franc, seemed to indicate the start of an economic crisis which no issuing bank would be able to forestall, although it might be possible to alleviate it if the bank, in keeping with “sound economic principles”, were able to increase the base rate and make capital available to financially healthy businesses. Instead, a state-controlled issuing bank, controlled by politicians, would, when faced by an economic crisis, tend to print more money, leading, as always,

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to inflation which would principally affect those on fixed incomes (i.e. factory workers and agricultural workers) which would in turn prompt serious rioting, as in the recent case in Sicily. In Switzerland, a “sound” monetary policy might be conducted by the single issuing bank proposed by the Union Suisse du Commerce et de l’Industrie,179 that is, an institution whose capital was made available by the existing cantonal issuing banks and which was managed by them, with the additional support of the confederation to represent the broader interests in play and of bodies representing private enterprise.180 Pareto welcomed the success obtained by opponents of a state bank in the referendum of the 28th of February 1897,181 noting also that in Vaud, with the 40,504 ‘no’ votes as against 4462 for ‘yes’, the people had shown themselves to be more devoted to economic liberty even than the English, with this pattern being generally repeated in the agricultural and/or French-speaking cantons while state socialism appeared to gather its support from the industrial and/or German-speaking cantons.182 However, the deeply rooted human illusion that “perfect happiness” is achievable in this world continued to feed dissatisfaction with the fruits of economic liberty as well as the belief that the primary source of national prosperity was the state.183 It was in this climate of ever-increasing threats to economic liberty in Switzerland that the decisive moment arrived for the referendum on the momentous law of the 15th of October 1897 on the confederation’s nationalisation of the railways. Pareto showed his understanding for the serious concerns existing in Lausanne’s liberal circles regarding this new state socialist project,184 which would lead to an enormous waste of resources. Despite this, Pareto did not participate in the referendum campaign on this occasion, claiming that he did not have the time needed to write the article on the railways which the liberal “Bibliothèque universelle et revue suisse”185 was demanding so insistently. In this article he would have defended the principle of free competition in the running of the railway system and pointed out the damage, particularly the corruption, engendered in Italy by this type of management.186 The defeat of the anti-nationalisation faction in the referendum of the 20th of February 1898 was observed by Pareto with resignation as a sign

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that in Switzerland too the battle for economic liberty was to end in disaster. The forces of state socialism and popular socialism would ruin the country as the conservatives had ruined Italy, thus demonstrating the common vices and ignorance that characterised two apparently very different parties.187 It was in Lausanne itself that Pareto witnessed the harbingers of the victory of popular socialism in Switzerland. On the occasion of the municipal elections of the 28th of November and the 2nd of December 1897, the Workers’ Party (called popular socialist in Pareto’s terminology) won a relative majority188 and, although they had not obtained the post of mayor and consequently had refused, in retaliation, to form part of the municipal governing junta together with the radicals,189 they immediately started to make use of their increased power. Thus, on the 11th of January 1898, at one of the first meetings of the new municipal council, Oscar Rapin, the ex-student of Pareto mentioned above, proposed, in the name of the Workers’ Party, to pass a motion calling for a minimum daily salary of 5 francs for the municipal workers and staff, on the basis that “any job should allow the worker to live decently, without getting into debt”, and claiming that the amount proposed corresponded to the bare minimum and that the municipality had every reason to set a good example by paying its employees an adequate salary.190 The lawyer Charles Boiceau (1841–1907), the liberal leader in Lausanne at the time, then asked Pareto’s view: this latter answered191 that the socialist proposal implied an increase in taxes and hence (as always) a questionable redistribution of income from taxpayers to workers. He added that, in order to achieve a balanced municipal budget without excessive tax increases, the number of municipal employees to whom the increase would apply should be fixed. Boiceau, in a speech made on the following 8th of February, advanced these two arguments, adding that local entrepreneurs, obliged by the competition from the municipality to increase salaries, would end up losing competitiveness.192 Nevertheless, the measure was finally approved by the municipal council and implemented by the junta, providing for a minimum daily salary of 5 francs for heads of households, 4.5 francs for married but childless employees and 4 francs for unmarried employees.193

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2.11 Self-Help The only political grouping, if it can be called such, towards which Pareto displayed unconditional sympathy, both during the later Florentine period and in Lausanne, was the self-help movement, particularly in regard to questions of cooperation and mutual aid.194 On the 12th of February 1891, Pareto195 gave a speech to the members of the Florence Association of Civil Employees (Associazione degli impiegati civili di Firenze)196 on the theme of the history of the cooperative societies, notably underlining the great progress that had been made since the advent of the two principal groups in Milan and in Rome, which were made up of civilians and military personnel, respectively.197 Pareto198 was in favour of admitting women as fully fledged members of the Association’s consumer cooperatives. The prejudice that existed against them not only belonged to a bygone age but, more importantly, was particularly damaging because women played an extremely important role in the cooperative enterprises, as was shown by the case of the Milan cooperative. Lastly, with regard to the coming reform of the statutes of the Florence consumer cooperative, Pareto suggested that professional people should also be admitted, with the vital aim of expanding membership. Thereafter, Pareto also devoted some interesting theoretical considerations to the theme of cooperation. In the summer of 1892, he pointed out that those who had predicted that the cooperatives would turn out to be “a practical form of socialism which would revolutionise society” had been completely wrong, as had those who had predicted their abject failure.199 More specifically, certain economists, basing themselves on the false assumption that “the mechanism of free competition” was universally “perfect”, had claimed that the margins of small traders were already reduced to a minimum and therefore, since the prices of products could not be further reduced, had anticipated that the consumer cooperatives would not be successful. Instead, he said, the imperfect operation of the competitive mechanism in the retail sector left ample space for “considerable improvements” to be exploited by larger stores or by consumer cooperatives.200 The competitive advantage of these derived from the large volumes of their sales, which led to a relative reduction in fixed costs,201 as well as from their honesty, which contrasted with the practices of small

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traders, whose “sole aim is to trick the customer in regard to both the price and the quality of the merchandise”. This honesty that characterised the cooperatives meant that customers did not need to waste time weighing up alternative suppliers.202 To this Pareto added that if costs, particularly fixed unit costs, could be reduced in the retail sector, “a general increase in well-being” could be achieved which would be comparable only to that resulting “from the invention of the railways”.203 Thus, contradicting Pantaleoni’s interpretation whereby there existed an intrinsic contrast between free competition and cooperation, Pareto claimed that the “cooperatives complement free competition, resulting in systems which confer a maximum of utility”.204 In contrast, producers’ cooperatives, with the exception of building cooperatives or those involved in public work tenders, were less successful, because in the world of large-scale industry the laws of free competition operated without encumbrance, so that production costs were already effectively minimised.205 Pareto’s debut in the world of self-help occurred on the 2nd of February 1894 when he gave an address in Lausanne on the theme “Charity and political economy”, at a meeting held under the auspices of the Société académique vaudoise (‘Vaud academic society’).206 Before a numerous audience of people with a philanthropic bent, probably attracted by his fame as a brilliant expounder of original ideas deriving from his teaching activities, Pareto asserted that public charity is invariably a failure and that private charity risked the same fate if not conducted in a very farsighted manner. Certainly, the experiences with private charity in Paris and with a law in Germany for compulsory insurance against accidents and illness had provided evidence not only of unacceptable abuses but also of how these had stripped the recipients of their primary duties of personal responsibility and prudence.207 In 1895, the managing committee of the Lausanne mutual aid society La Fraternité vaudoise commissioned Pareto to perform an audit on the association’s financial solidity. On the 18th of November 1895 Pareto delivered his report,208 in which he began by pointing out that the Fraternité pursued its aim of making one-off payments of 1000 francs to the families of deceased members using the funds available from the contributions of surviving members, on the basis of a model which was the

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opposite of that used by insurance companies. Where these based themselves on the principle of the self-sufficiency for each succeeding generation, the Lausanne society was organised on the basis of mutual support across generations. This system, again in contrast to the method used by insurance companies, was exposed to risks, in that it necessarily depended on the unpredictable factor of the continued arrival of new members to replace the deceased ones. The question thus arose of what was the model of financing which would minimise the risk that the association would be unable to perform its task through insufficiency of funds. The current financial model was based on contributions which remained constant with advancing age. According to Pareto, this amount was not only less than the sum then needed to finance the expected level of payments but was also too high for those under 45 years of age and too low for those older, giving rise to a dangerous disincentive for the potential new younger members who were of such vital importance to the society. Accordingly, Pareto drew the attention of the Fraternité to the need to eliminate this discrepancy, while at the same time pointing out that any recourse to very high membership fees would defeat the object of the society’s philanthropic aims. The managing committee accepted Pareto’s arguments and proposed a new model of annual contributions increasing with increases in age, which was approved by the members’ assembly of the 29th of November 1896.209 The case of the Fraternité together with Pareto’s audit were discussed on the occasion of the Lausanne convention of the Swiss statistical society (Société Suisse de statistique) on the 8th of November 1898. The mathematician Robert Leubin from Bern criticised Pareto for having given precedence to an admirable philanthropic aim and to personal initiative over concerns regarding financial solidity which should be paramount even in entities like the one in question. Pareto’s spirited response was that no one should be prevented from accepting a lower level of protection in exchange for other benefits, that not even the insurance companies were able to offer an unachievable absolute degree of security and that supervision of the insurance market by the state boded ill when it imposed the requirement to invest reserves in government bonds with their uncertain yields. Lastly, in an age when people expected the state to provide everything, praise was due to “the Fraternité for relying on its

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own efforts” and for showing “the courage and the initiative which are the prosperity and the glory of nations”.210 Still in Lausanne, on the 10th of November 1896, the cantonal parliament heard the report from the commission charged with assessing the request from the Vaud pedagogical society (Société pédagogique vaudoise) to increase the pensions of the canton’s primary school teachers, which had remained fixed, in accordance with an 1871 law at 500 francs (for schoolmasters) and 400 francs (for schoolmistresses), respectively, although the cost of living had risen considerably in the meantime. The society’s request was that these sums should be increased to 840 and 540 francs per year, with a corresponding increase for teachers’ annual contributions to the cantonal pension fund from 20 francs to 50 and from 10 francs to 20, respectively.211 In response to the society’s request, Pareto estimated that in order to maintain the equilibrium of the pension fund in the hypothesis whereby everyone completing 31 years of service could claim a pension, the acceptance of the society’s request would require further contributions from the state of 215 francs (for schoolmasters) and 109 francs (for schoolmistresses), which would amount globally to annual totals of 107,500 and 54,500 francs.212 The government’s bill confirming these arrangements was approved in parliament on the 17th of February 1897. Pareto’s reputation as an anti-state actuarial consultant continued to grow, extending to the federal level. On the 20th of June 1895 he was nominated by the parties involved as representative of the employees of the Jura-Simplon railway in the commission of experts charged with determining whether the new statute of their company pension fund was compliant with the federal law governing “mutual aid funds”.213 Pareto, having pointed out the limited scope of the mandate received from the Swiss government, requested the right to express a minority opinion, at the same time asking to be replaced if this was refused, and explaining that “technical questions cannot be resolved by majority vote”.214 In 1905 the federal railways pension and mutual aid fund215 was in difficulty. The employees of the federal railways therefore turned to Pareto for an actuarial assessment, a task which he accepted, having been promised the assistance of the university of Bern mathematician Johann Heinrich Graf.216 Pareto was critical of the manager of the fund, the same Leubin mentioned above, for his policy of investing in government bonds rather

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than in the more remunerative stocks which other funds had preferred, resulting in a shortfall of 131,080 francs in revenues, and also for having approved an excessive number of invalidity claims. He thus proposed the drafting of new statutes, the management of the fund in a manner more similar to private enterprise and the drawing up of balance sheets at five-­ yearly intervals rather than annually.217

Notes 1. On this subject, see Marongiu (1996, passim) and Fratianni and Spinelli (2001, passim). 2. Pareto to Maffeo Pantaleoni, 14th June and 1st August 1897, see Pareto (1984a, pp. 83, 94). 3. See Pareto (1891a, p. 390). 4. On Pareto’s interpretation of the crisis of the preceding years, see Mornati (2018, pp. 202–208). 5. See Pareto (1891a, pp. 388–389) and Pareto to Felice Cavallotti, 28th October 1890, see Pareto (1989a, p. 93). 6. Ibid., p. 95. 7. Pareto to Cavallotti, 7th November 1890, ibid., p.  103. Permanent emigration in 1890, which was estimated at around 123,000 people, meant a loss for Italy of around 370 million francs (calculating the value of a single emigrant at 3000 francs), see Pareto (1891b, p. 42). 8. See Pareto (1890a). 9. See Pareto (1893a, p.  95). On the break in commercial relations between France and Switzerland, which involved the reciprocal application, respectively, of the maximum tariffs on the part of France and of differential rights by the Swiss, in the wake of Switzerland’s decision not to bend to the recent recrudescence of French customs protectionism, see Humair (2004, pp. 595–616). The break, which brought an end to the 70 years of essentially free-trade Swiss customs policies, was resolved with the signing of an agreement in mid-1895, ibid., pp. 613–614. 10. See Pareto (1893b, p. 47). 11. See Pareto (1894a, p. 303). 12. See Pareto (1890a, p. 421). 13. Pareto to Pantaleoni, 17th February 1891, see Pareto (1984a, p. 18).

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14. See Pareto (1891c, d, p. 414). 15. See Pareto (1891e, p. 27). 16. Ibid. 17. See Pareto (1891f ). 18. See Pareto (1892a). But soon afterwards, see Pareto (1892b, p.  53), Pareto stated, instead, that di Rudini fell because he opposed any increase in military expenditure, albeit (in his view) “too moderately”. 19. See Pareto (1892c). 20. See Pareto (1892d, p. 82). 21. Vittorio Ellena, Bernardino Grimaldi and Lazzaro Gagliardo alternated at the head of the Treasury, while the Ministry of Finance continued to be headed by Bernardino Grimaldi. 22. ibid. 23. Pareto to Teodoro Moneta, 15th May 1892, see Pareto (2001, p. 42). 24. At that time, the state owned all the railway lines except for the Società Italiana delle Strade Ferrate Meridionali (‘Italian Company for the Southern Railways’) extending along the Adriatic line and in the southern mainland (i.e. not the islands). 25. See Pareto (1892e). 26. See Pareto (1892f ). 27. See Pareto (1892g, p. 113). 28. See Pareto (1892h, p. 90). 29. Pareto’s former friend Sidney Sonnino alternated at the head of the Ministry of Finance with Paolo Boselli (1838–1932), while the Treasury was always headed by Sonnino. 30. See Pareto (1893c, p. 111). 31. Ibid. 32. See Pareto (1894b). 33. Pareto to Napoleone Colajanni, 24th December 1892, see Pareto (1975a, p. 237). 34. See Pareto (1894c, p. 707). 35. See Pareto (1894d). 36. See Pareto (1894e, p. 21–22). 37. See Pareto (1895a, p. 88). 38. Ibid., pp. 77–78. 39. See Pareto (1895b, p. 101). 40. See Pareto (1897a, pp. 249–250). 41. With Ascanio Branca (1840–1903) at the Ministry of Finance and Giuseppe Colombo at the Treasury.

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42. See Pareto (1896a, pp. 202–203). 43. On Pareto’s attitude towards the protectionist regime, see Mornati (2018, pp. 131–135). 44. See Pareto (1892i, pp.  490–491). On relations between Pareto and Tardy, see Mornati (2018, ad nomen). 45. Specifically see Pantaleoni (1891). 46. See Pareto (1892j, pp. 65–66). 47. See Pareto (1892i, p. 494). In the spring of 1892, Pareto, see Pareto (1892k, pp.  406–407), pointed out that the Italo-Swiss commercial treaty was not renewed due to the reluctance of Italian cotton industry owners to accept a reduction in duties on imports of cotton products from Switzerland. 48. See Pareto (1892l). Besides this, Pareto, see Pareto (1892k, pp. 403– 404), noted the appearance of a laissez-faire backlash led in Milan by the Association for the defence of commercial freedom (‘Associazione per la difesa della libertà commerciale’) chaired by the silk tycoon Ludovico Gavazzi and in Naples by the Association of landowners (‘Associazione dei proprietari terrieri’) chaired by Count Girolamo Giusso. But soon afterwards, Pareto, see Pareto (1892a, pp. 79–81) and Pareto, (1892c, p. 523), was obliged to record the retribution suffered by Pantaleoni for his criticism of state intervention in foreign trade, prompting his resignation as Director of the Commercial High School in Bari. Pareto ascribed this episode to the unfounded intolerance shown by the political world towards the free-traders. 49. Pareto to Pantaleoni, 28th June 1891, see Pareto (1984a, p. 39). On Pareto’s criticisms of the measures introduced by Magliani to exit the fiat money regime, see Mornati (2018, pp. 160–163). 50. See Pareto (1891g, p. 426). More specifically, Pareto, see Pareto (1891a, p.  394), expressed the view that the interest rate, rather than being lowered to 4.5%, should, in view of the limited supply of capital relative to demand, be raised to 10% in order to stimulate the influx of new capital as well as the recovery of capital invested in failing companies. The increase in operational capital thus procured would permit a longterm reduction in the base rate, on condition that the government in turn ceased its continual destruction of capital to finance its largely unproductive expenditure. 51. See Pareto (1891f, p. 89). 52. See Pareto (1891h, p. 261).

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53. Through the decree of 23rd January 1894 authorising the three issuing banks to temporarily release 125 million lire in banknotes over and above the ceiling stipulated in law no 449 of 10th August 1893, with only a third backed by metal coinage and on the basis of favourable fiscal conditions. This measure was designed to allow a number of savings banks to counteract a run which the government considered as unjustified. 54. See Pareto (1894f, p. 714). 55. See Pareto (1894g, p. 24). 56. See Pareto (1891a, p. 395). 57. See Pareto (1891i, p. 54). 58. See Pareto (1891a, p. 396). 59. Pareto to Pantaleoni, 17th February 1892, see Pareto (1984a, p. 184) and Pareto (1896–1897, §514). 60. Pareto to Pantaleoni, 20th December 1892, see Pareto (1984a, p. 329). The point was reiterated in an address given by Pareto in Milan on the 16th of December 1892, Corriere della Sera, 18th–19th December 1892 and in Pareto (1896–1897, §510). 61. Ibid., §510. 62. Ibid., §499. 63. Ibid., §510. 64. Address given by Pareto in Milan on the 10th of April 1893, Il Secolo, 11th–12th April 1893. 65. See Pareto (1893d, p. 3). 66. See Pareto (1891j, pp. 32–33). 67. See Pareto (1891k) and Pareto (1891j). The Land Credit Union was quickly rescued by Bank of Italy. 68. See Pareto (1891l, p. 23). 69. See Pareto (1892m, p. 109). In the same period Pareto, see Pareto (1892d, p. 82), recalled with concern that it had been Giolitti (at that time in the process of forming a new government) who, as Minister of Finance in the second Crispi government, had authorised the Banca Nazionale to extend a subsidy of 50 million lire, issued extra legem, to the Banca Tiberina, soon to be caught up in the Roman building scandal. 70. See Pareto (1892n, p.  537). On this affair involving the bank, see Palermo (2006). 71. See Pareto (1892h, p. 92). On this affair, see Vitale (1972, passim). 72. Pareto to Emilia Peruzzi, 20th January 1893, see Pareto (1984d, p. 538).

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73. See Pareto (1893a, p. 94). 74. See Pareto (1893e, p. 576). 75. Ibid., p. 575. 76. See Pareto (1893a, pp. 94–95). 77. See Pareto (1893f, p. 99). 78. See Pareto (1893d, p. 11). 79. Further to this, in the summer of 1894 Pareto stated his view that from the outset of the trial of Bernardo Tanlongo (General Manager of the Banca Romana), there had been no doubt about his acquittal because juries, as human beings, “cannot bring themselves to convict a few accomplices when the main culprits go scot-free”, see Pareto (1894h, p. 130). 80. See Pareto (1893f, p. 101). 81. See Pareto (1893d, p. 11). 82. The system of control provided for a requirement imposed on the banks to publish monthly accounts, under the administrative supervision of a government commissioner, together with periodic inspections, Pareto, ibid., p. 4. 83. Ibid. 84. Pareto, see Pareto (1893g, p. 404), lamented the fact that the government wished to pay 450 lire per share to shareholders of the nowdefunct Banca Romana, even though they had failed to supervise the work of the institute’s auditors. 85. See Pareto (1893f, p. 102). 86. Address given by Pareto in Milan on the 10th of April 1893, Il Secolo, 11th–12th April 1893. In the summer of 1893, Pareto reacted negatively to the passing of the law creating the Banca d’Italia, Pareto to Pantaleoni, 11th July 1893, see Pareto (1984a, p. 385), pointing out that the increased devaluation of the lira and the fall in value of Italian bond issues following the law setting up the Banca d’Italia were a confirmation of his pessimism, see Pareto (1893h, p. 412). 87. See Pareto (1895a, p. 80). 88. See Pareto (1893i, p. 318). 89. See Pareto (1893g, p. 400). 90. Ibid., p. 401. 91. Ibid., p. 402. 92. See Pareto (1897b, p. 63). 93. See Pareto (1896–1897, §482, note 1).

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94. In 1889 the Compagnie universelle du canale interocéanique (‘Universal interoceanic canal company’), headed by Ferdinand de Lesseps, the same engineer who had successfully overseen the digging of the Suez canal, was declared bankrupt. During the 1880s, it had begun the excavations for the Panama canal, which from 1914 was to connect the Atlantic ocean to the Pacific. The scandal emerged, at the same time as that of the Banca Romana, when episodes came to light of the bribery of politicians on the part of the company in order to permit it to benefit from further bond issues. At the trial the politicians were cleared of responsibility while the administrators of the company, including Ferdinand de Lesseps, were sentenced to terms of imprisonment which, in any case, they were able to circumvent. A substantial body of literature exists on the topic: for a recent contribution see Degos and Prat (2008). 95. See Pareto (1893j, p. 718). 96. Ibid., p. 719. 97. Ibid., p. 721. 98. For Pareto’s earlier thoughts on the subject, see Mornati (2018, pp. 127–131). Pareto’s appointment was immediately welcomed by the International Arbitration and Peace Association in its publication “The Concord: Journal of the International Arbitration and Peace Association”, July 1893, pp. 138–139, naming him “an eminent advocate of the principle of friendship and international cooperation”, to which Pareto rejoined assuring “the colleagues and friends of the Society for Peace” that he would seek to “redouble his efforts to serve the common cause”, Pareto to Élie Ducommun, 14th July 1893, see Pareto (1893a, p. 194). 99. See Pareto (1896–1897, §242). 100. See Pareto (1893j, pp. 711–712). 101. Ratified in the treaty of 18th August 1892. 102. Pareto to Moneta, 11th July 1891, see Pareto (2001, p. 26). 103. See Pareto (1892o, p. 543). 104. Pareto to Pantaleoni, 29th July 1893, see Pareto (1984a, p.  388). Elsewhere Pareto expressed his lack of faith in irredentism, Pareto to Pantaleoni, 20th July 1892, ibid., p. 250. 105. See Pareto (1893k, p. 610). 106. Pareto to Emilia Peruzzi, 18th December 1895, see Pareto (1984d, pp. 580–581).

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107. See Anonymous [in reality Pareto] (1897c, p. 518). 108. See Pareto (1892p, pp. 563–564). 109. Pareto to Cavallotti, 14th August 1892, see Pareto (1989a, p. 165). 110. Pareto to Papafava, 14th August 1892, ibid., p. 165, Pareto to Cavalotti, 14th August 1892, ibid., p. 166. 111. See Squilletta (1892). The author began by remarking that it was a general feeling of scepticism regarding the durability of peace, notwithstanding the widespread pacifist sentiments, which led countries to concentrate their efforts in preparation for conflicts whose aim at this point was nothing less than the utter annihilation of the enemy. From this he inferred that whatever type of military reform was proposed, it should fulfil the requirement of “not weakening the defensive strength of the nation” (ibid., p. 184). Molinari then argued for a reform of the army along the lines of a militia, which, he argued, would meet that requirement while allowing military budgets and spending to be brought into alignment with “the nation’s economic resources and [with] today’s level of civilisation” (ibid., p. 187). Instead, the standing army consumed a considerable proportion of the country’s annual economic growth, a large sum which, instead of being spent on arms (hence “unproductively”, ibid., p. 194), could be devoted to increasing the nation’s material well-being, once it was left in the hands of the taxpayers following a corresponding reduction in taxes. The standing army also entailed a considerable opportunity cost arising from the lost production which the citizens called up for military service, who were generally young and thus at the height of their productivity, were forced to sacrifice. Having sketched out his own encompassing draft legislation for the creation of a militia (which was achievable, in his view, in five years, ibid., p. 350), Molinari, in an extensive commentary, emphasised (ibid., p.  347) that, alongside territorial recruitment (ibid., p. 440), “the foundation of the militia is conscription of one year” (at the time conscription was for thirty months) as this would permit a “uniform and generalised military training” and, in case of war, the “deployment of the youngest, most valiant and best-trained men”. This reform, in Molinari’s view, would lead to a saving of 55 million lire (ibid., p. 470) out of the 313 million lire (ibid., p. 215) spent on the army in the 1889–1890 fiscal year. 112. The macroeconomic rationale behind Pareto (1892p) was as follows: let Yd be equal to Y-ME where Yd represents the available national income, Y the total national income (calculated as an increasing function of work)

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and ME military expenditure. A reduction in military expenditure would leave an increased national income available for consumption, or alternatively the same available national income could be achieved with less work, or a combination of increased national income available and less work would also be possible. 113. Pareto’s address (Conferenza Pareto). Il Secolo, 16th–17th April 1893. 114. Pareto to Pantaleoni, 27th July 1892, see Pareto (1984a, pp. 254–255). 115. Pareto to Pantaleoni, 19th May 1892, ibid., p. 218. 116. Pareto to Pantaleoni, 12th August 1892, ibid., p. 268. 117. Pareto to Moneta, 18th October 1891, see Pareto (2001, p. 27). At this time, Pareto took part in the third International Peace Convention held in Rome from the 11th to the 16th of November, as a representative of the Florence Committee for Peace, whose non-existence for all intents and purposes he realised in the autumn of 1892 (Pareto to Moneta, 27th October 1892, ibid., pp. 45–46). To formulate the Convention’s resolutions on the topic “Peace and disarmament considered in relation to economic and social issues”, a commission was named consisting of Pareto, Captain Francesco Siccardi, the French delegates Émile Arnaud and François Bernardot and the above-mentioned Swiss journalist and 1902 Nobel Peace Prize winner Élie Ducommun. The commission proposed the following text: “The Congress has decided to urge all Societies for Peace, Workers’ Societies and friends of peace to everywhere to simultaneously encourage popular agitation in favour of replacing standing armies with militias, stipulating permanent arbitration treaties between peoples reciprocally guaranteeing the independence of the contracting parties, or alternatively the setting up of an international arbitration tribunal, and to work towards a more equitable distribution of the fruits of labour and the consequent free exchange of goods between nations, the use of arbitration to resolve conflicts between workers of different nations or between workers and bosses, and the election of representatives supporting these reforms approved by the Congress”, paper held in the Archives of the International Bureau for Peace in the United Nations library, Geneva. 118. Pareto’s address (Conferenza Pareto). Il Secolo, 16th–17th April 1893. 119. Pareto to Pantaleoni, 23rd March 1897, see Pareto (1984b, p. 57). In this regard, Pareto contested the pacifism of the new Czar Nicholas II saying that “peace should be the means to accomplish the good of our kind, rather than an end to be pursued independently of the condition

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of the people”, Pareto to Moneta, 14th November 1894, see Pareto (2001, p. 86). 120. Pareto to Pantaleoni, 22nd December 1891, see Pareto (1984b, p. 122). 121. Pareto to Teodoro Moneta, 18th September 1891, see Pareto (2001, p. 27). 122. On the first contacts between Pareto and the Italian Radical Party, see Mornati (2018, pp. 131–133). 123. Pareto informed Pantaleoni, 17th February 1892, see Pareto (1984a, p. 185), that he would “more willingly” side with the “neo-Catholics” like Stefano Jacini, were it not for the fact that “their deeds do not match their words”. 124. Pareto to Pantaleoni, 23rd February 1892, see Pareto (1984a, p. 189). 125. Pareto to Cavallotti, 30th June 1892, see Pareto (1975a, pp. 188–189), Pareto to Cavallotti, 3rd July 1892, see Pareto (1989a, p. 157). 126. See Pareto (1892q, p. 554). 127. Ibid., pp. 556–557. 128. On the history of the Republican Party at the time, see Di Porto (1963). 129. Pareto to Moneta, 14th March 1892, see Pareto (2001, pp. 37–38). 130. See Pareto (1893j, p. 682). 131. Pareto to Papafava, 9th January 1894, see Pareto (1989a, p. 214). 132. Pareto to Luigi Minuti, 24th January 1894, ibid., p. 222. 133. See Pareto (1896b, p. 397). 134. Pareto to Papafava, 14th February 1894, see Pareto (1989a, pp. 231, 233). 135. Pareto to Filippo Turati, 28th July 1891, see Pareto (1975a, p. 351). 136. See Pareto (1898a, p. 247). 137. On Pareto’s first thoughts about the socialist phenomenon, see Mornati (2018, pp. 163–166). There is a very copious literature on the origins of the Italian Socialist Party, but Arfé (1977), continues to be a useful source. 138. See Pareto (1893j, p. 678) 139. Ibid., p. 679. 140. On Pareto’s conception of socialist economic theory, see Chap. 7. 141. See Pareto (1896c, p. 523). 142. See Pareto (1896d, p. 203). 143. See Pareto (1896c, p. 525). 144. Pareto to Turati, 11th November 1893, see Pareto (1975a, p.  235). However, a few years later, referring to the street clashes which took place in Geneva in 1898, Pareto pointed out that while the bourgeois did not hesitate to “blame the troublemakers of their class … a socialist

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will never blame the troublemakers of his class”, Pareto to Pantaleoni, 22nd July 1898, see Pareto (1984b, p. 228). 145. See Pareto (1898b, p. 285). 146. Ibid., pp. 286–287. 147. Pareto to Napoleone Colajanni, 31st December 1891, see Pareto (1975a, pp. 175–176) and Pareto (1892r). 148. Pareto to Colajanni, 31st December 1891, see Pareto (1975a, p. 176). 149. Pareto (1893l, p. 172). 150. At that time completing his studies at the University of Pavia, where later for many decades he was Professor of Statistics. 151. Coletti (1893). 152. Pareto (1893m, p. 104). 153. Ibid., p. 105. Pareto wrote to Colajanni that “the main reason” why he was not a socialist was that he could not see “a way to increase state control without increasing the damage produced by politicians”,147 Pareto to Colajanni, 27th April 1892, see Pareto (1975a, pp. 185–186). 154. Consisting in the fact of ceding “state assets to each industrialist according to his needs” which is “precisely the formula of one of the socialist schools”. Pareto underlined that the only difference between state socialism and popular socialism consists “in establishing who should enjoy the favours of the state”, see Pareto (1892s, pp. 183–184). 155. Pareto (1893n, p. 94). 156. Pareto (1893o, pp. 97–98). 157. Pareto (1893p, p. 507). 158. Pareto (1896–1897, §345). 159. Pareto (1895c, p. 861). 160. On Pareto’s much more extensive, albeit fragmentary, youthful liberal ideas, see Mornati (2018, pp. 89–105). 161. Pareto (1892t, pp. 546–547). 162. Pareto to Guido Martinelli, 7th November 1894, see Pareto (1989a, p. 263). 163. Pareto to Pantaleoni, 23rd February 1892, see Pareto (1984a, p. 189). De Johannis, see De Johannis (1889), expressed the hope that this party might prompt the state not to pass a new law each day but to abolish one, in the conviction that the state’s competence needed to shrink with a country’s degree of civilisation, ibid., pp. 5–6. More particularly, he hoped for speedy justice, ibid., pp. 12–14, a reduction in state bureaucracy, ibid., p. 19, the abolition of customs duties, ibid.,

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p. 26, and “direct participation of the working classes in government [as being] the only manner to resolve the social issue”, ibid., p. 31. 164. Pareto (1893h). 165. Croce, see Croce (1898) considered the liberals to be idealists because they could not count on the social classes concerned for the achievement of their ideals, ibid., p. 237. In the same place, Croce interpreted the liberalism of the time as being based on the proposition that only through complete economic liberty can the economic hedonic optimum be achieved, which liberalism itself considered to be “identical with the maximum desirable for society”, ibid., p. 234. This thesis was of a practical nature, that is, ideological / empirical, and hence not scientific (i.e. not showing an indisputable logical connection between “premises and conclusions”), ibid., pp. 239–240. Croce credits Pareto, whom he describes as “one of the most intelligent, steadfast and sincere among today’s followers of liberalism”, with having acknowledged “the limited and approximative nature of the conclusions of liberalism”, precisely because in his Course he expressed them in mathematical terms, ibid., p. 235. 166. Pareto (1898c, p. 50). 167. Ibid. 168. Pareto (1896–1897, §256). 169. On the 13th of March 1894, Pareto had discussed the doctoral thesis in law, Rapin (1894), of the future Vaud socialist leader Oscar Rapin, see Jeanneret (2010). Notably Pareto, see University, Gazette de Lausanne, 14th March 1894, p. 3, had challenged Rapin’s proposal to introduce public works schemes in order to give work to the unemployed. Later, Pareto, see (Pareto 1896–1897, §839), presented a theoretical critique based on two arguments, the first being the fact that public works schemes modify the production coefficients of perfect competition, thus reducing social well-being, and moreover, since they are financed by increases in taxation, they also determine a disproportionate reduction not only in consumption but also in savings, and therefore, due to the latter, private investment is reduced, giving rise to a reduction in demand for labour and hence an increase in unemployment. 170. Pareto to Martinelli, 11th June 1894, see Pareto (1989a, p. 248); Pareto (1894i, p. 190). 171. Pareto to Martinelli, 4th February 1895, see Pareto (1989a, p. 267); Pareto (1895d, p. 132). 172. Pareto (1895e); Pareto (1897d, pp. 44–45).

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173. Pareto (1896e, p. 86). 174. Pareto to Papafava, 1st October 1896, see Pareto (1989a, pp.  295– 296); Pareto (1897e, pp. 449–450). 175. Pareto (1897e, p. 451). 176. Le Messager des Alpes, 6th and 13th January 1897. 177. Issuing banks and state banks (Banques d’émission et Banques d’Etat), Gazette de Lausanne, 16th January 1897, p. 3. 178. Issuing banks and state banks (Banques d’émission et Banques d’Etat), Gazette de Lausanne, 23rd January 1897, pp. 2–3. 179. The main Swiss employers’ association, founded in 1870. 180. Journal de Morges, 17th February 1897. 181. Pareto to Pantaleoni, letter of 3rd March 1897, see Pareto (1984b, pp. 46–47). 182. Pareto (1897d, pp. 47, 49). 183. Pareto (1897f, p. 424). 184. Pareto to Pantaleoni, letters of 22nd April and 17th May 1897, see Pareto (1984b, pp. 64–74); Pareto (1897f, pp. 423–424). 185. Pareto to Pantaleoni, letters of 31st March 1896, see Pareto (1984a, pp. 428–429), and of 28th May 1897, see Pareto (1984b, p. 76); Pareto to Colajanni, letter of 6th April 1897, see Pareto (1989a, pp. 314–315). 186. Pareto to Papafava, letter of 25th November 1896, see Pareto (1989a, pp. 299–300); Pareto to Pantaleoni, letter of 13th May 1897, see Pareto (1984b, p. 67). 187. Pareto to Pantaleoni, letter of 22nd February 1898, see Pareto (1984b, pp. 176–177); Pareto to Colajanni, letter of 21st June 1898, see Pareto (1975a, p. 364). 188. With 39 of 100 seats, while the radicals obtained 31, the liberals 24 and the Progress Party 6, see Office d’études socio-économique et statistiques de la Ville de Lausanne (1984, p. 64). 189. Municipal elections (Elections communales), Gazette de Lausanne, 1st December 1897, p. 2; Municipal council (Conseil communal), ibid., 15th December 1897, p. 3. 190. Municipal council (Conseil communal), ibid., 12th January 1898, p. 3. 191. Pareto to Pantaleoni, letters of 17th and 19th January 1898, see Pareto (1984b, pp. 148–149). 192. At the Lausanne municipal council on the 8th of February (Au Conseil communal de Lausanne, le 8 février), Grutli, 25th February 1898, p. 2; The municipal council (Conseil communal), La Revue, 9th February 1898, p. 2.

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193. Minutes of the municipal council meetings, RB 14/76, p.  184, Lausanne City Archives. 194. Also in relation to the rural savings banks “there is nothing but good to be said”, see Pareto (1892u, p. 428). On the founder of these in Italy, the philanthropist, academic and politician from Padua Leone Wollemborg, see Marconato (1984). 195. Pareto’s first contact with cooperative circles was on the 10th of April 1890, when he gave an address at the Fratellanza Artigiana di Firenze (the ‘Florence Crafts Guild’, the city’s most important Mazzini-inspired institution), on the topic “International employment legislation and the Berlin conference”, Il Fieramosca, 19th–20th April, 29th June 1890. Similarly, on 29th of June 1890, at Incisa Valdarno (between Florence and San Giovanni Valdarno) Pareto gave an address on economic and social questions at the ceremony of inauguration of housing built for working people by the local workmen’s society, Corriere italiano, 3rd July 1890, p. 1. Again, on the 21st of October 1892, Pareto addressed a conference organised to promote the creation of a Trade Union centre at Florence, with the aim of furthering workers’ “interests” and helping to rescue “the people from the state of inertia to which they are reduced”, aims which Pareto considered to be compatible with the principles of political economy, Pareto to Pantaleoni, 21st and 23rd October 1892, see Pareto (1984a, pp. 302–303). The Florentine weekly L’Economista good-humouredly reproached Pareto, its ex-contributor, for being a fantasist because labourers were more inclined towards protectionism than free trade, see The Trades Union centres (Le Camere del lavoro), L’Economista, 23rd October 1892, p. 684. 196. This association had been founded in 1888 with the aim of bringing together employees of the city’s public administration. Pareto became a member on the 14th of December 1890, sitting on the board of administration as well as on the commissions dealing with the members’ pension fund and with the finances of the association, Risparmio e Previdenza, February 1891, pp. 6–7. Pareto had been the first editor of this latter periodical, the official organ of the association, but had been replaced for reasons of “incompatibility” as early as the second issue, ibid., March–April–May–June 1891, p.  1. On the 15th of March, Pareto was confirmed as a member of the board of administration, ibid., November 1891, p. 78. At the assembly of the 30th of November 1891, approval was given for a project, originating from the commission of which Pareto was a member, to create an independent fund,

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based on members’ contributions, which would pay an allowance in cases of sickness as well as an indemnity to the families of deceased members, ibid., January 1892, p. 2. This was the final stage of Pareto’s brief but intense participation in the association, to which he alluded in passing when writing to his friend Arturo Linaker (1856–1932), the new president, saying that “it was a rather complicated outfit”, Pareto to Linaker, 29th April 1896, see Pareto (1975a, p. 295). 197. Corriere italiano, 14th February 1891, p. 2. 198. Pareto (1891m). 199. Pareto (1892u, p. 419). 200. Ibid., pp. 419–421. 201. In this manner the consumer cooperatives matched prices with production costs, hence minimising the latter, see Pareto (1896–1897, §923). In practice, most of them sold at prices slightly below those of the independent traders, distributing any resulting profits among their members only at the end of the year, that is, when the profits had been “certified”, ibid., §924. 202. Pareto (1892u, p. 421). 203. Pareto (1896–1897, §923). For example, in Italy a cooperative bakery was able to sell its bread at 31 cents a kilo, as against an average price nationwide of 36 cents. Since the annual consumption of bread in Italy was 40 million hundredweight, extending the cooperative approach across the whole nation would save 200 million lire, ibid. 204. Pareto to Pantaleoni, 16th December 1897, see Pareto (1984b, p. 132). In that period Pantaleoni was finalising his well-known article Pantaleoni (1898). 205. Pareto (1892u, p. 424). 206. Gazette de Lausanne, 5th February 1894, p. 1. 207. Dina Bakounine, who was present at the address, sent a summary to Emilia Peruzzi, adding that Pareto had also expressed the view that the most effective form of philanthropy for women was to save as much as possible of the family income in order to accumulate the capital needed to ensure work and a comfortable standard of living for all working families, Correspondence of Emilia Peruzzi held at Florence National Central Library, letter from Dina Bakounine of 12th–16th March 1894. 208. Pareto (1899). 209. Journal de statistique suisse, 1899, p. 46. 210. Ibid., p. 58.

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211. The Vaud canton (Canton Vaud), Gazette de Lausanne, 11th November 1896. 212. Pareto (1896f, 1897g, p. 399). 213. Pareto (1895f ). 214. Ibid. No further documentation on this topic has so far become available. 215. Which had resumed control of the pension funds of the railway companies existing prior to their merger into the federal railways which was completed by the confederation in 1902. 216. Their report was Graf and Pareto (1905). Further to this study see Busino (1975b, pp. 1176–1177). 217. Ibid., pp. 1177–1178.

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Graf, Johann Heinrich, and Pareto, Vilfredo. 1905. The Swiss Federal Railways, assessment and report on the future pension and mutual aid fund prepared by the appointed experts Prof Dr. J.H. Graf in Bern and Prof. Dr. Vilfredo Pareto, engineer, in Lausanne. End of August (Schweizerische Bundesbahnen, Gutachten und Bericht uber die zukunftige Pensions-und Hilfkasse erstattet im Auftrage des Personals von den bezeichneten Experten Prof. Dr. J.H. Graf in Bern und Pro/ Dr. Vilfredo Pareto, lngenieur in lausanne. Ende August 1905). Bern: Stämpfli. Reprinted in Pareto (1989d, pp. 89–90). Humair, Cédric. 2004. Economie development and the central state (1815–1914). A centwy of Swiss customs policies at the service of the elites (Développement économique et État central (1815–1914). Un siècle de politique douanière suisse au service des élites). Bern: Lang. Reprinted in Pareto (2005, pp. 153–318). Jeanneret, Pierre. 2010. Oscar Rapin, one of the founding fathers of socialism in Vaud and pupil of Pareto? (Oscar Rapin, l’un des pères du socialisme vaudois et élève de Pareto?). Revue européenne des sciences sociales XLVIII, 146: 61–70. Marconato, Ruggero. 1984. The person and the works of Leone Wollemborg. The founder of the rural savings banks in the 19th and 20 th centuries (La figura e l’opera di Leone Wollemborg. Il fondatore delle casse rurali nella realtà dell’Ottocento e del Novecento). Roma: E.C.R.A. Marongiu, Gianni. 1996. Fiscal history of the historic left,1876–1896 (La politica fiscale della sinistra storica 1876–1896). Turin: Einaudi. Mornati, Fiorenzo. 2018. Vilfredo Pareto: An intellectual biography. Volume I, From science to liberty (1848–1891). Basingstoke: Palgrave Macmillan. Office d’études socio-économique et statistiques de la Ville de Lausanne. 1984. Aspects of political life in Lausanne, elections 1882–1982 (Aspects de la vie politique à Lausanne, élections 1882–1892). Lausanne: Ville de Lausanne. Palermo, Stefano. 2006. The Tiberina Bank: Construction and finance in Rome, Naples and Turin (La Banca Tiberina: finanza ed edilizia tra Roma, Napoli, Torino). Napoli: Editoriale Scientifica Italiana. Pantaleoni, Maffeo. 1891. A colossal error in the Italian-German treaty (Un colossale errore nel trattato italo-tedesco). L’economista, December 20, pp. 803–804. ———. 1898. Critique of the theoretical principles of cooperation (Esame critico dei principi teorici della cooperazione). Giornale degli Economisti IX, XVI-3: 202–220; IX, XVI-4:308–323; IX, XVI-5:404–421. Pareto, Vilfredo. 1890a. Transactions on current accounts at popular savings banks and other credit institutes (Il movimento dei conti correnti presso le banche popolari ed. altri istituti di credito). L’Economista, November 16, pp. 726–727.

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———. 1890b. Letter from Italy, The elections from a political point of view (Les élections au point de vue politique). Journal des Économistes IL, IV-3: 413–422. ———. 1891a. Letter from Italy (Lettre d’Italie). Journal des Economistes L, VIII-3: 390–402. ———. 1891b. Italian statistics (Statistique italienne). Le Monde économique, July l8, pp. 62–63. Reprinted in Pareto (1967, pp. 41–45). ———. 1891c. Unemployed labourers (Operai disoccupati). Il Secolo, April 6–7. Reprinted in Pareto (1989b, pp. 416–417). ———. 1891d. Letter from Italy (Lettre d’Italie). Journal des Economistes L, VII-3: 409–418. ———. 1891e. Letter from Italy. The rent. The new Anglo-Italian bank in Rome (Lettre d’Italie. La rente. La nouvelle banque anglo-italienne à Rome). Le Monde économique, April 18, p.  381. Reprinted in Pareto (1967, pp. 27–29). ———. 1891f. Letter from Italy (Lettre d’ltalie). Le Monde économique, July 4, p. 27. Reprinted in Pareto (2005, pp. 89–90). ———. 1891g. The fiat money regime (Corso forzoso). Il Secolo, July 4–5. Reprinted in Pareto (1989b, pp. 426–427). ———. 1891h. Report (Cronaca). Giornale degli Economisti III-3: 259–264. ———. 1891i. Mr. de Rudini’s speech (Le discours de M.de Rudini). Le Monde économique, November 28, pp.  528–529. Reprinted in Pareto (1967, pp. 52–55). ———. 1891j. Land Credit Union (Le Crédit foncier). Le Monde économique, May 2, p. 430. Reprinted in Pareto (1967, pp. 31–33). ———. 1891k. Letter from Italy (Lettre d’Italie). Le Monde économique, April, 25, p. 406. Reprinted in Pareto (1967, p. 30). ———. 1891l. Letter from Italy. General market conditions and the National Bank. The Livorno debacle (Lettre d’Italie. Les conditions générales du marché et la Banque Nationale. Le krach de Livoume). Le Monde économique, April 4, pp. 330–331. Reprinted in Pareto (1967, pp. 23–25). ———. 1891m. Reforms to the statute (Riforme allo Statuto). Risparmio e previdenza, March–April–May–June, p. 12. ———. 1892a. The ministerial crisis. Persecution of free-traders (La crise ministérielle. Persécution contre les économistes libéraux). Le Monde économique, April 23, pp. 453–454. Reprinted in Pareto (1967, pp. 79–81). ———. 1892b. The new Italian Ministry. Pall Mall Gazette, May 26. Reprinted in Pareto (1984c, pp. 53–54).

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———. 1892c. Freedom of opinion (Libertà di pensiero). L’Isola, May 5–6. Reprinted in Pareto (1989b, pp. 522–524). ———. 1892d. The new ministry (Le nouveau ministère). Le Monde économique, May 21, pp. 565. Reprinted in Pareto (1967, pp. 82–83). ———. 1892e. Letter from Italy. (Lettre d’ltalie). Le Monde économique, August 6, p. 146. Reprinted in Pareto (1967, p. 86). ———. 1892f. The programme of the Giolitti Ministry. The Speaker, October 22. Reprinted in Pareto (1974, p. 59). ———. 1892g. Letter from Italy (Lettre d’Italie). Le Monde économique, October 22. Reprinted in Pareto (1967, pp. 113–116). ———. 1892h. The budget balance. The issuing banks (L’équilibre du budget. Les banques d’émission). Le Monde économique, December 31, pp. 734–735. Reprinted in Pareto (1967, pp. 90–93). ———. 1892i. Further damage from protectionism in Italy (Ancora dei danni della protezione in Italia). Rassegna di scienze sociali e politiche, February 15, pp. 709–713. Reprinted in Pareto (1989b, pp. 490–494). ———. 1892j. Letter from Italy. Italian wine and the commercial treaty with Germany (Lettre d’Italie. Les vins italiens et le traité de commerce avec l’ Allemagne). Le Monde économique, January 9th, pp.  37–38. Reprinted in Pareto (1967, pp. 65–67). ———. 1892k. Letter from Italy (Lettre d’ltalie). Journal des Economistes LI, IX-3: 400–409. ———. 1892l. Just protection from hunger (L’equa protezione della fame), Il Secolo, February 2–3. Reprinted in Pareto (1989b, pp. 485–486). ———. 1892m. Letter from Italy. Mr. Luzzatti’s concerns. The exchange rate for gold. The Tiberina bank (Lettre d’Italie. Les préoccupations de M. Luzzatti. Le change de l’or, La Banque Tiberina). Le Monde économique, April 9, pp. 415–416. Reprinted in Pareto (2005, pp. 105–110). ———. 1892n. Different yardsticks (Due pesi e due misure). L’Isola, August 2l–22. Reprinted in Pareto (1989b, pp. 537–539). ———. 1892o. Cards on the table (Carte in tavola). L’Isola, August 28–29. Reprinted in Pareto (1989b, pp. 540–543). ———. 1892p. Military expenditure and the ills of Italy (Le spese militari e i mali del!’Italia). Milano: Gattinoni. Reprinted in Pareto (1989b, pp. 562–567). ———. 1892q. Government and citizens (Governo e cittadini). L’Idea liberale, October 23. Reprinted in Pareto (1989b, pp. 554–557). ———. 1892r. The Honourable De Amicis’ speech and political economy (La conferenza dell’onorevole De Amicis e l’economia politica). L’Isola, February 17–18. Reprinted in Pareto (1989b, pp. 495–497).

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———. 1892s. The Honourable De Amicis’ speech and political economy again (Ancora sulla conferenza dell’onorevole De Amicis e l’economia politica). L’Economista, March 20, 183–185. ———. 1892t. The future destiny of the liberals.I (Le sorti future della parte liberale.I). L’Idea liberale, August 28. Reprinted in Pareto (1989b, pp. 544–547). ———. 1892u. The cooperative societies (Les sociétés cooperatives). Journal des Economistes LI, XI-1: 419–429. ———. 1893a. Financial scandals. The commercial movement. Socialist laws (Les scandales financiers. Le mouvement commerciales. Les lois socialistes). Le Monde économique, February 4, pp. 118–119. Reprinted in Pareto (1967, pp. 94–95). ———. 1893b. The Italian market (1893) (Le marché italien (1893)). In The financial market in 1893–1894 (Le marché financier en 1893–1894), ed. Arthur Raffalovich. Paris: Guillaumin. Reprinted in Pareto (1970, pp. 47–56). ———. 1893c. Italy’s economie crisis (La crise économique en Italie). Le Monde économique, December 30, p. 751. Reprinted in Pareto (1967, pp. 110–112). ———. 1893d. State intervention in Italy’s issuing banks (L’intervention de l’Etat dans les banques d’émission en Italie). Journal des Economistes LII, XV-I: 3–28. ———. 1893e. Measures adopted for the issuing banks (Provvedimenti per le banche di emissione). Il Secolo, February 8–9. Reprinted in Pareto (1989b, pp. 573–576). ———. 1893f. Enquiry into the banks. The new issuing bank (L’enquête sur les banques. La nouvelle banque d’émission). Le Monde économique, April 1, pp. 342–343. Reprinted in Pareto (1967, pp. 99–102). ———. 1893g. Report (Cronaca). Giornale degli Economisti IV, VI-5: 398–404. ———. 1893h. Letter from Italy (Lettre d’ltalie). Journal des Economistes LII, XV-3: 408–413. ———. 1893i. Report (Cronaca). Giornale degli Economisti, IV, VI-4: 313–320. ———. 1893j. The Parliamentary Régime in Italy. Political Science Quarterly, VIII, VIII-4: 677–721. ———. 1893k. President Cleveland’s speech (Il discorso del presidente Cleveland). Il Secolo, April 8–9. Reprinted in Pareto (1989b, pp. 607–610). ———. 1893l. Dialogue of the dead (Dialogo dei morti). Giornale degli Economisti, IV, VI-3: 165–172. ———. 1893m. Diogenes’ answer regarding the causes and remedies of modern-­day scandals (La risposta di Diogene sulle cause e sui rimedi degli scandali odierni). La Critica sociale, April 1, 104–105.

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———. 1893n. This damn laissez-faire, II (Ce maudit laissez-faire, II). Le Monde économique, September 30. Reprinted in Pareto (1984c, pp. 91–94). ———. 1893o. This damn laissez-faire, III (Ce maudit laissez-faire, III). Le Monde économique, October 7. Reprinted in Pareto (1984c, pp. 95–98). ———. 1893p. Report (Cronaca). Giornale degli Economisti, IV, VI-6: 504–508. ———. 1894a. Report (Cronaca). Giornale degli Economisti IX-3: 301–306. ———. 1894b. A time for sacrifices (L’ora dei sacrifizi è suonata). Il Secolo, January 11. Reprinted in Pareto (1989b, pp. 705–706). ———. 1894c. No tax increases (Nessun aumento di imposte). L’idea liberale, January 14. Reprinted in Pareto (1989b, pp. 707–710). ———. 1894d. The reduction in Italy’s public bonds yield (La réduction de la rente italienne). Le Monde économique, March 10: 751. Reprinted in Pareto (1967, pp. 113–114). ———. 1894e. The Italian finances (Les finances italiennes). Journal des Economistes, LIII, XVIII-I: 3–25. ———. 1894f. The increase of currency put into circulation by the issuing banks (L’aumento della circolazione delle banche di emissione). Il Secolo, January 2. Reprinted in Pareto (1989b, pp. 714–716). ———. 1894g. Italy’s finances (Les finances italiennes). Journal des Economistes, LIII, XVIII-I: 3–25. ———. 1894h. The Tanlongo verdict (Le verdict Tanlongo). Gazette de Lausanne, August 2. Reprinted in Pareto (2005, pp. 130–132). ———. 1894i. Report (Cronaca). Giornale degli Economisti, V, IX-2: 186–190. ———. 1895a. The dictatorship in Italy (La dictature en Italie). Bibliothèque Universelle et Revue Suisse, C, LXVI-196: 76–92. ———. 1895b. The financial market in 1895 (Le marché financier en 1895). In The financial market in 1894–1895 (Le marché financier en 1894–1895), ed. Arthur Raffalovich. Paris: Guillaumin. Reprinted in Pareto (1970, pp. 76–103). ———. 1895c. Two tracts for the voters (Due scritti per gli elettori). L’Idea liberale, May 12. Reprinted in Pareto (1989b, pp. 857–861). ———. 1895d. Report (Cronaca). Giornale degli Economisti, VI, XI-2: 126–132. ———. 1895e. The plebiscite on the match monopoly in Switzerland (Il plebiscito sul monopolio dei fiammiferi in Svizzera). L’Idea liberale, October 6. Reprinted in Pareto (2005, pp. 184–186). ———. 1895f. Further to the mutual aid and pension fund of the Jura-Simplon railway company: letter to the Federal Council (Encore à propos de la Caisse de secours et des pensions de la Compagnie des chemins de fer Jura-Simplon: lettre au Conseil Féderal). Letter of 9th December. Reprinted in Pareto (2005, pp. 189–192).

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———. 1896–1897. Course in political economy (Cours d’économie politique). Lausanne: Rouge. ———. 1896a. Report (Cronaca). Giornale degli Economisti, XIII-2: 202–207. ———. 1896b. Report (Cronaca). Giornale degli Economisti, VII, XIII-4: 394–399. ———. 1896c. Report (Cronaca). Giornale degli Economisti, VII, XII-5: 523–526. ———. 1896d. Report (Cronaca). Giornale degli Economisti, VII, XIII-2: 202–207. ———. 1896e. Against and for socialism (Pro e contro il socialismo). Il Secolo, June 21–22. Reprinted in Pareto (1989c, pp. 84–86). ———. 1896f. Report on the schoolmasters’ retirement pensions (Rapport sur /es pensions de retraite des régents). Lausanne: Self-Publication. 10th August. Reprinted in Pareto (1989d, pp. 378–395). ———. 1897a. Report (Cronaca). Giornale degli Economisti, VIII, XIV-3: 249–254. ———. 1897b. Statism in Italy, II (L’étatisme en Italie, Il). Bibliothéque universelle et revue suisse, CII, VI-I: 53–66. ———. 1897c. Report (Cronaca). Giornale degli Economisti, VIII, XIV-6: 516–519. ———. 1897d. The referendum from an economic point of view (Le référendum au point de vue économique). Journal des Economistes, LVI, XXX-1: 41–51. ———. 1897e. Statism in Italy, I (L’étatisme en ltalie, I). Bibliothéque universelle et revue suisse, CII, V-15: 449–463. ———. 1897f. Report (Cronaca). Giornale degli Economisti, VIII, XIV-5: 423–426. ———. 1897g. Supplementary report on the retirement pensions of the schoolmasters and schoolmistresses (Rapport supplémentaire sur! es pensions de retraite des régents et des régentes). Lausanne: Self-Publication. 17th January. Reprinted in Pareto (1989d, pp. 396–400). ———. 1898a. Letter to the editor (Lettera al direttore). L’Idea, January 26. Reprinted in Pareto (1989c, pp. 247–248). ———. 1898b. The dangers of reaction (I pericoli della reazione). Il Secolo, October 1–2. Reprinted in Pareto (1989c, pp. 285–289). ———. 1898c. Italian protectionism (Protezionismo italiano). Critica sociale, February 16, pp. 49–50. ———. 1899. Report on the “Fraternité” insurance scheme (Rapport sur les bases de l’assurance de la “Fraternité”). Journal de statistique suisse: 104–110. Reprinted in Pareto (1989d, pp. 119–125).

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———. 1967. Letters from Italy (Lettres d’Italie), Complete works, tome X, ed. Giovanni Busino. Geneva: Droz. ———. 1970. The Italian financial market (1891–1899) (Le marché financier italien (1891–1899)), Complete works, tome II, ed. Giovanni Busino. Geneva: Droz. ———. 1974. Various writings (Écrits èpars). Complete works, tome XVI, ed. Giovanni Busino. Geneva: Droz. ———. 1975a. Correspondence, 1890–1923 (Epistolario 1890–1923), Complete works, tome XIX-1, ed. Giovanni Busino. Geneva: Droz. ———. 1975b. Correspondence, 1890–1923 (Epistolario 1890–1923), Complete works, tome XIX-2, ed. Giovanni Busino. Geneva: Droz. ———. 1984a. Letters to Maffeo Pantaleoni 1890–1896 (Lettere a Maffeo Pantaleoni 1890–1896), Complete works, tome XXVIII.I, ed. Gabriele De Rosa. Geneva: Droz. ———. 1984b. Letters to Maffeo Pantaleoni 1897–1906 (Lettere a Maffeo Panta/ eoni 1890–1896), Complete works, tome XXVIII.Il, ed. Gabriele De Rosa. Geneva: Droz. ———. 1984c. Myths and ideologies (Mythes et idéologies). Complete works, tome VI, ed. Giovanni Busino. Geneva: Droz. ———. 1984d. Letters to Emilia Peruzzi 1878–1900 (Lettere ad Emilia Peruzzi 1878–1900), Complete works, tome XXVII.II, ed. Tommaso Giacalone-­ Monaco. Geneva: Droz. ———. 1989a. Letters and Correspondence (Lettres et Correspondances), Complete works, tome XXX, ed. Giovanni Busino. Geneva: Droz. ———. 1989b. Political writings. The development of capitalism (Scritti politici. Lo sviluppo del capitalismo). Complete works, tome XVII, ed. Giovanni Busino. Geneva: Droz. ———. 1989c. Political writings. Reaction, liberty, fascism (Scritti politici. Reazione, libertà, fascismo). Complete works, tome XVIII, ed. Giovanni Busino. Geneva: Droz. ———. 1989d. Statistics and mathematical economics (Statistique et économie mathématique). Complete works, tome VIII, ed. Giovanni Busino. Geneva: Droz. ———. 2001. New letters 1870–1923 (Nouvelles lettres 1870–1923), Complete works, tome XXXI, ed. Fiorenzo Mornati. Geneva: Droz. ———. 2005. Unpublished works and Addenda (Inédits et Addenda). Complete works, tome XXXII, ed. Fiorenzo Mornati. Geneva: Droz. Rapin, Oscar. 1894. The right to work: Its history, foundations and implementation (Le droit au travail: son histoire, ses fondements, sa réalisation). V. Fatio printers. Lausanne: Fatio.

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Squilletta, Tiberio. 1892. The armed nation. A study of the new organisation of the army (La Nazione armata. Studio di un nuovo ordinamento dell’esercito). Giornale degli Economisti, III, V-3, 183–221: III, V-4: 344–375; III, V-5: 428–478. Vitale, Eligio. 1972. The reform of the issuing banks and the Italian “banking scandals” of 1892–1896 (La riforma degli istituti di emissione e gli “scandali bancari” in Italia, 1892–1896). Roma: Camera dei Deputati, Segretariato Generale, Archivio Storico.

3 Pure Economics

As we have seen in our retracing of his intellectual activities in the course of the previous two chapters, it was against the background, and with the stimulus, of his relations with the University of Lausanne and of his ongoing passion for the political arena, that Pareto finally and definitively turned his full attention to his scientific work. His attention was concentrated principally on the subject of political economy, mainly as a result of his didactic commitments. In this and the following five chapters, we will examine Pareto’s interpretation of the discipline, looking in logical sequence at each of the areas which appear to be the most important, that is, pure economics (in the sense of the foundations of economic theory), general economic equilibrium, the economics of well-being, the theory of international trade, the economics of socialism, the currency and other topics of applied economics. In this chapter we summarise Pareto’s ideas about the scope of economics (Sect. 3.1), the methodology of economics (Sect. 3.2), the statistical computation of the final degree of utility (Sect. 3.3, the most important theoretical issue according to Pareto), the formal derivation of the law of demand (Sect. 3.4) and of the law of supply (Sect. 3.5).

© The Author(s) 2018 F. Mornati, Vilfredo Pareto: An Intellectual Biography Volume II, Palgrave Studies in the History of Economic Thought, https://doi.org/10.1007/978-3-030-04540-1_3

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3.1 E  arly Reflections on the Nature and Limits of Pure Economics While it is impossible to disagree with the theory, expressed at the time by the chair socialists, concerning the “relativity of economic laws as a general principle”, nevertheless Pareto did not agree with their claim that no “general economic laws” exist, as it is evident that “all men, with their many shared anatomical, biological and psychological characteristics, would display points of similarity also in their economic behaviour”.1 In the early stages of his academic research into economic theory, Pareto concluded that pure economics facilitated the study of precisely these general laws2 because “it helps to raise us above the level of our unruly passions” and to “save us from the consequences of one of the most frequent causes of errors in the science of economics”.3 While Pareto considered, on the one hand, that the pure4 and the empirical branches of political economy5 “far from being in conflict, can be usefully employed in harness”,6 on the other hand, he saw that pure economics “often strays into metaphysics”.7 Pareto in his early critique of the principal writings of Edgeworth, Jevons and Walras,8, explained his desire to help avoid the danger of pure economics following “the tendency to subordinate experience to theories”9 by examining “very closely what are the postulates, both explicit and implicit, of [the] reasoning in order to determine when, and to what extent, these laws could be applied in the real world”.10 Pure economics should, in Pareto’s view, consider its axioms as simple hypotheses, to be drawn from experience, as befits an experimental science,11 “deducing how economic phenomena would unfold if those hypotheses were true and comparing these deductions with experience”, considering each hypothesis “to be true in accordance with the number of its verifications”.12 Hence, as early as February 1894, “the sticking point” between Pareto and Walras was the fact that the latter “already anticipates a time when reliable information becomes available, so that economic phenomena can be predicted accurately, and already speaks of how we could then proceed”, while Pareto considered “that time to be … so remote” that it was

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not even worth discussing it.13 In any case, Pareto remained “completely against” the tendency of the new school of economics to “show how economic phenomena would unfold”14 starting from “principles … which are claimed to be evident”.15 His view was that pure economics “is not above any other natural science, but neither is it below”, and, as such, “it is neither optimistic nor pessimistic”.16 In the same period, Pareto claimed that “it should be recognised” explicitly that “theories of pure economics cannot take into account all the circumstances surrounding natural phenomena, so that they constitute only a partial study of the phenomena, as opposed to a full and complete description”.17 Thus, he recognised that while Walras’ general equilibrium represented “a first, and currently unique, mathematically-­ based approximation of economic phenomena”, it only clarified “certain aspects of real-world phenomena, while neglecting others”, and that this was in any case inevitable.18 Nevertheless Pareto, since “all human sciences” are approximate, did not propose to abandon a science such as pure economics, suggesting rather that one should “proceed very cautiously and with constant reference to experience”.19 Thus, Walras’ theory of general equilibrium should be embraced because, despite its limitations, “it genuinely examines the key element of phenomena” in that it accepts that economic phenomena “are dominated by consumption”.20 Lastly, Pareto added that the “hedonistic theories [which characterise pure economics] … can be valid only when referred to actions which are repeated extremely frequently and which are such that their consequences are easily understood by the categories of people that perform them”.21 A treatise on political economy should therefore cover three different areas, in Pareto’s view, “which it is time we separated completely”.22 The first of these was pure economics, defined by him as the science of “ophemility”, that is, a relationship “of mutual advantage between an entity and a person”.23 Pure economics, “given any type of society”, seeks to “determine which economic transactions will take place in it”.24 Pareto emphasised that a science of this type, limiting itself to showing people “the necessary consequences of certain actions … can be equally valuable for free-traders and for socialists, or any other sect”.25

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3.2 Methodology in the Study of Economics Bearing in mind these initial considerations, themselves showing a certain scepticism in regard to the heuristic potential of pure economics, as well as a certain indifference (if not intolerance) on the part of Pareto towards abstract methodological debate,26 it is nevertheless of interest to seek to assemble, and to place in logical and chronological order, some of his widely scattered methodological speculations.27 The starting point for scientific enquiry, according to Pareto, was that “the time for ontology is over”, so that each science “studies the physical properties of entities without worrying about exploring their essence”,28 with the sole purpose of “connecting a large number of facts by means of the smallest possible number of principles”.29 However, although he considered that “the human mind proceeds from the known to the unknown”, with the specific consequence that “when we possess extensive information about the equilibrium of a physical system, this equilibrium can provide a template for our conception of equilibrium in economics”,30 Pareto admonished strongly that “the use [of ] this type of reasoning by analogy is legitimate, and can be highly useful, in elucidating the sense of a proposition”, but would lead us to “fall into grave errors, were we to attempt to employ it to demonstrate the proposition itself, or even to form a presumption of its validity”.31 In the context of this preconceived anti-metaphysical orientation, Pareto described as “excellent” the Preliminary Discourse on the Study of Natural Philosophy by the astronomer John Herschel, known to have provided part of the inspiration behind Mill’s Logic.32 Specifically, according to Herschel, experience constituted the only source of human knowledge regarding nature, and this could be acquired through observation and/or experimentation.33 It is through the observation of events unfolding in a non-random fashion that we are able to infer the notions of cause and effect and hence that of natural laws. The properties of a causal relationship include those where the effect is always subsequent, proportional and an increasing and reversible function, in relation to the cause.34 The laws of nature are always permanent, consistent and understandable, allowing us, firstly, to explain all the individual phenomena to which they refer, and, secondly, to formulate increasingly general laws, which, however, will

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always remain imperfect and require verification through the comparison of their implications with the individual phenomena themselves.35 In the same fashion, in December 1891, Pareto reiterated that, as far as logic was concerned, he agreed “almost entirely with Mill36 and with [Alexander] Bain”, particularly with the view that experience is the only source of human knowledge and the only truth criterion, implying that “whatever leads to conclusions that match experience is true, and whatever leads to the opposite is false, while whatever cannot be proved experimentally remains doubtful”.37 Thus, for example, in the question of international trade, he preferred Walras’ theory to that of Auspitz and Lieben simply because “it corresponds to the facts, while the other does not”.38 As regards the question of scientific research, Pareto, again agreeing with Mill’s formulation that “the syllogism does no more than render the premises, under another guise, in the conclusion”,39 stated that the first precaution consisted in the need to perform “a very minute examination of the premises”, precisely because the rest of the syllogism was “a more or less mechanical procedure”.40 In fact, according to Pareto (and in confirmation of a conviction which was already apparent in his university thesis),41 “the true enemy of science is reasoning which takes on the semblance of rigour and which takes its departure from false premises or, worse still, ones which each person can interpret as they wish”.42 Thus, “the hypotheses [i.e. the premises] must be accepted or rejected on the basis of their intrinsic value and not of the extent to which they fit with our calculations”,43 particularly bearing in mind the fact that “if the premises are false or incomplete, the result will be similarly false or incomplete”.44 So, in relation to pure economics, Pareto considered that if we posit that people are “perfect hedonists, we will be very near the truth”, unlike “if we assume them to be wholly sensible and rational”,45 or if we suppose that they act “always intentionally”, which he thought was “the most unlikely scenario … [as] people are guided more by habit than by reason”.46 Pareto also admitted that in political economy, “as in every other science”, it was essential to attempt “to identify the most general and rational causes”, while underlining that this should be done “while departing as briefly as possible from the solid terrain of observation”.47 Pareto’s second admonition was that economic phenomena should be viewed as “movements of mutually-attracting ­bodies”,48

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recognising that it was characteristic of those who had not studied natural sciences49 to experience difficulties “in conceiving of relations between phenomena other than that of cause and effect”.50 As a third caveat, Pareto stated that “the human mind has enormous difficulty comprehending a large number of phenomena at the same time”, so … that “it must pass from the simple to the complex”,51 making use in practice of the method of “successive approximations”, which consists in proceeding as follows: “isolate the principal component of the phenomenon … examine the most important perturbations followed by the less important ones … group together the various notional phenomena being considered in order to form a complex whole, which will correspond much more closely to the reality”.52 Finally, in his early assessments of the results of scientific approaches to economics, Pareto, claiming that, in general, scientific progress consisted in “presenting ideas of uniformity” and “replacing differences considered to be qualitative with quantitative ones”,53 concluded that the history of economic theory records the gradual separation of the theory from art and the formulation of ever more concise formal representations of economic phenomena.54 This constitutes the background against which Pareto’s critical reflections on the application of mathematics to political economy should be viewed. From the outset of his short-lived, tumultuous and sterile direct intellectual contacts with Walras,55 Pareto reiterated that “mathematics alone is not much use in teaching people how to reason correctly”.56 In particular, Pareto did not accept, as Walras appears to have done, that “the use of mathematics excludes the empirical method in political economy”. If this was the choice, Pareto would do without mathematics, “since in all physical sciences the empirical method reigns supreme”, and from it we learn also that “the truths in which we are most confident are really no more than extremely probable”, implying that we should always be ready “to replace them with others, should these correspond more closely with the facts”.57 Hence, it was only by remembering the “general tendency of all the natural sciences [to] progress towards ever-greater perfection” by applying the quantitative method to “the bulk” of their operations, rather than the traditional qualitative method,58 that Pareto was able to c­ onclude

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that political economy would likewise derive “no less benefit”59 from the use of the quantitative method. In confirmation of another position which had already been apparent in his degree thesis,60 Pareto nevertheless warned that “the mistake which must be avoided is to believe that an argument based on dubious premises could acquire greater rigour simply because it makes use of algebraic symbols”.61 He then made a distinction between calculus and the geometric method (based on the logical sequence of definitions, as used, e.g. in the New Theory of the Rotation of Bodies (Nouvelle théorie de la rotation des corps) by the French mathematician and physicist Louis Poinsot), pointing out that the former should be used “only when every other solution would be ineffective”, since it “has the defect of disguising the intimate connection between the various propositions”.62 In general, the mathematical method, whether in the analytical or the geometric version, should thus be adopted with “great caution”, firstly because “the longer the chain of deductions … the greater the chances of errors deriving from the uncertainty of the premises”, and secondly because by doing so it is impossible to properly cross-check every intermediate proposition in the sequence “against the notions that [are] held to be true”,63 as when reasoning “in the normal way”. Pareto last of all stressed that that “mathematics should only be used when it allows the formulation of certain relationships between facts which could not be expressed so easily, or even at all, in ordinary language”.64 It was exactly, but only, “in order to gain an precise and really complete understanding of the relations established between phenomena through economic equilibrium” that “the assistance of mathematics is indispensable”.65 This consideration led him to claim that in pure economics “the use of mathematics is [hence] entirely secondary”, thus dissociating himself from Walras’ view.66 Going on from this, Pareto pointed out that political economy “can only be a science of averages, nor can it ever aim to foresee or explain the actions of single individuals”67 and, that it is exclusively by virtue of being a science of averages that calculus can be applied to it: actually it is only an army’s demand for horses that can pass from 100,000 to 100,001 units, “that is to say, [changing] by almost imperceptible degrees”,68 as is necessary to justify the use of calculus. He also noted that in the absence “of general equations resembling those of dynamics for the science of e­ conomics”,69 any dynamic

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phenomena had necessarily to be studied “as a sequence of consecutive states of equilibrium which are progressively disturbed”, thus leaving “acceleration” out of account, referring to the significant phenomenon whereby “in passing from one state of equilibrium to another there is usually an overcompensation”.70 Furthermore, in mechanics and in chemistry, likewise, “the study of dynamic properties follows on from that of static properties”.71

3.3 T  he Final Degree of Utility: Theoretical Concept and Statistical Computation In Pareto’s opinion, the work which illustrated the hypotheses of pure economics “most comprehensively” was Edgeworth’s Mathematical Psychics, which views “man as a pleasure machine” and in which the study of pleasure is conceived as consisting in the study “of the equilibrium … of forces tending to procure the maximum good for each individual” together with the study “of the equilibrium [of the forces] tending to procure the maximum utility for all”.72 Pareto considered that in pure economics the term utility was employed in a sense “not corresponding to the common usage” in that it indicated “simply the property possessed by certain things of satisfying people’s needs”.73 For this reason, it was better to replace it with the more precise neologism of ophemility.74 Since “ophelimity refers to a relationship between an individual and an item75 … if the individual remains unchanged while the item changes, comparison between ophelimities will cause no problems”.76 If, on the other hand, the individual changes and the item does not, any change in ophelimity will be due to the change in the individual; lastly, if both the item and the individual change, it will be impossible to distinguish, within the variation in ophelimity, “the components caused by changes to the item or to the individual”.77 Since “the new political economy” was based entirely on the concept of the final degree of ophelimity (in the sense of the increase in ophelimity resulting from a small increase in the quantity of an item consumed), in Pareto’s view “the need to obtain as much information as possible in regard to the item is evident”, just as Jevons had expressly wished.78

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In relation to the important question of the measurability of ophelimity, “one must distinguish between the existence of this notional measurement and the means of physically performing it”,79 recalling that even “in the natural sciences, many quantities exist which can only be measured indirectly”.80 Having established this, Pareto stated that “it has to be admitted” that the final degree of utility “depends on the preceding quantities consumed”,81 whereas he considered it “hard to conceive that the consumption of an economic good could be performed in the same way as a continuing sensation”.82 Nevertheless, as happens “in the majority of natural sciences”,83 since “discontinuous functions are much more difficult to process”, it was acceptable to consider the consumption as continuous, as long as “the error arising from this is negligible”.84 Moreover, even if it were accepted that, in general, the final degree of utility is represented by decreasing curves,85 it would be better to interpret this decrease simply “as an empirical phenomenon”, having “numerous exceptions”, as Edgeworth had “correctly noted”,86 the most important of these being savings, whose final degree of utility, according to Pareto, is generally constant.87 Lastly, in order to arrive at a “practical” solution, an “absolute scale of the substantiality of needs”88 must be identified, that is, a scale on which the needs are arranged in a decreasing order of urgency and which is valid for any individual and for any moment in time.89 According to Pantaleoni, this scale “exists, even if very little is known about its characteristics”. In the light of the above, Pareto remarked that, if an individual exchanges a quantity of A with a quantity of B, “being free to perform this exchange or otherwise”, it is because the possession of B yields him “greater pleasure” than the possession of A.90 The hedonistic principle interprets this exchange (also referred to as the economic transformation of goods) as continuing until “maximum total ophelimity” is reached, or until “a positive infinitesimal final degree of [ophelimity] is gained”.91 If these differing manners of performing the exchange correspond in analytical terms, they differ from the “practical” point of view, since the former implies that the individual in question is “aware of the overall [ophelimity] of an economic good”, a circumstance which Pareto considered to be “very rare”,92 while Edgeworth considered that global ophelimity is always extant.93 Pareto’s view, however, was that “our mind grasps

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only the notion of the final degree of utility” and therefore, in keeping with his aforementioned methodological outlook, that the second of the two analytical methods was preferable.94 Lastly, having noted that an individual taking part in an exchange does not in any case compare “the final degrees of utility of the items exchanged” but limits himself to “expenditure which by experience he deems necessary”,95 Pareto pointed out that the exchange of goods can also be performed “on the basis of variations in prices”96 or of the “impression made on our mind by the idea of a future need”.97 Generalising and formalising the theorem regarding exchanges, Pareto imagined that each of the goods exchanged had a price expressed in quantities of another, which thus acted as a currency whose price was in turn expressed in units.98 If P represents the function of global ophelimity which, following Edgeworth,99 depends on the quantity r of all consumer goods possessed, the exchange of A and B will continue until it no longer yields any further incremental increase in ophelimity,100 that is, when101

( ∂P / ∂ra ) dra + ( ∂P / ∂rb ) drb = 0



or

∂P / ∂ra = ( −drb / dra ) ∂P / ∂rb



or

∂P / ∂ra = (1 / pb ) ∂P / ∂rb







Thus, in general

∂P / ∂ra = (1 / pb ) ∂P / ∂rb = (1 / pc ) ∂P / ∂rc = ….



which, if we assume, following Walras and Jevons, that the final degree of utility φ of an item depends exclusively on that item itself,102 we get103

ϕa ( ra ) = (1 / pb )ϕb ( rb ) = (1 / pc )ϕc ( rc ) = ….



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At this point, Pareto added that the non-comparability of the final degrees of utility for various individuals “so cherished” by Pantaleoni did not seem so important because, if we assume that demand for an item “depends on the varying desires” of individuals to consume it, and is a known quantity, “it is clear that some average level of desire which would produce that level of demand can also be calculated”. Moreover, the possibility of being able to determine that average level “is a matter of life and death for the new theories” because, as stated above, “the science of economics is a science of averages”.104 Pareto then showed105 that, if an item’s final degree of utility for each individual depends only on that item, then the average final degree of utility also depends on the item in question, providing that savings,106 in Walras’ sense of “a simple reserve of consumption from the past serving to provide for future needs of consumption”107 enter the equation. More precisely, in the case of two items, collective savings can be represented as the variable balance figure for s in the budget equation, which thus becomes ra + pb rb = s





so allowing the values of r to retain their independence. The laws of supply and demand ∂pb/∂ra, ∂pb/∂rb108 can then be derived by observation. By partial differentiation of

ϕa ( ra ) = (1 / pb )ϕb ( rb )





in relation to ra and rb, the following two equations are obtained



ϕa′ ( ra ) =  −ϕb ( rb ) ( ∂pb / ∂ra ) / pb2 ; 0 = pbϕb′ ( rb ) − ( ∂pb / ∂rb )ϕb ( rb )  / pb2

{

}



from which, by substituting the laws of supply and demand, φa(ra) e φb(rb)109 can be determined by integration.

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Having thus shown how final degrees of utility can theoretically be ascertained, Pareto proposed to “pause for a moment to see how [they] could be calculated in practice”.110 At the outset, Pareto did not accept Daniel Bernoulli’s principle whereby the utility of a lira for an individual is equal to the relation between this lira and the number of lire already in the same person’s possession. Pareto thought it “impossible to demonstrate” that, if one represents the utility of a lira for a person who possesses 100 lire, this utility will become half (rather than a third or a quarter) if the individual possesses 200 lire.111 Instead, the methodology that should be adopted was as follows: first, classify the items, establishing a unit of measurement for each category; then, determine the law of demand for each, on the basis of observation of consumption and prices; finally, infer the average final degree of utility of each type from its law of demand.112 The law of demand is determined by interpolation. Since statistical data on prices and on consumption “will unfortunately not be precise enough to permit the use of the quadratic method for a long time … it will suffice to make abundant use of Cauchy’s [interpolation] method”.113 For items A and B (where the price of B is the dependent variable), this will allow us to find the interpolating polynomial

log pb = M 0 + M1ra + N1rb + M 2 ra2 + P2 ra rb + N 2 rb2 + … The two further interpolating polynomials



log ϕ a ( ra ) = A0 + A1ra + A2 ra2 + …; log ϕb ( rb ) = B0 + B1rb + B2rb2 + …

can also be posited. If we take the logarithms of

ϕa ( ra ) = (1 / pb )ϕb ( rb )







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we obtain log pb = log ϕb ( rb ) − log ϕa ( ra )





and also

M 0 = B0 − A0 ; − M1 = A1 ; N1 = B1 ; − M 2 = A2 ; N 2 = B2 ;..



thus allowing us to derive the coefficients of the laws of φa and φb from the coefficients of the law of the price of B, with the exception of B0 and A0 whose only the difference is known.114 Pareto expressed the view that alcoholic beverages would be among the first goods for which it would be possible to establish the average final degree of utility, thanks to the availability of reliable statistics.115 Pareto also specified that, where a law of supply and of demand is known, the average final degrees of utility can be calculated only along the points where the corresponding price line (starting from the point representing the quantity of the assets initially possessed) is tangential to the curve of indifference. Thus, in order to ascertain the entire law of the final degrees of utility, all the laws of supply and demand must be known, which is achievable by varying the initial quantities of the assets possessed.116 Further, if two items are interchangeable, then once the constant or variable proportion in which they can be exchanged has been determined, the quantities jointly consumed can be added together, yielding the “quantity of an imaginary item whose final degree of utility can substitute those of the original two”.117

3.4 The Law of Demand Supposing,118 on the other hand, that prices are expressed not in terms of an item but of a virtual currency whose price therefore corresponds to the unit and whose final degree of utility is m, then, apart from the n equations,119

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m = (1 / pa )ϕ a ( ra ) = (1 / pb )ϕb ( rb ) = (1 / pc )ϕc ( rc ) = ….,



consider also the budget constraint120

pa ra + pb rb + pc rc + … = 0



If the n equations shown above are differentiated partially in relation to pa, the following equations are obtained



2 ∂m / ∂pa = (1 / pa ) ( ∂ra / ∂pa )ϕ a′ − 1 / ( pa )  ϕa ;   ∂m / ∂pa = (1 / pb ) ( ∂rb / ∂pa )ϕb′ ; ∂m / ∂pa = (1 / pc ) ( ∂rc / ∂pa )ϕc′ ; …

which can be transformed, by means of simple algebraic processes, into the following



∂ra / ∂pa = pa ( ∂m / ∂pa ) (1 / ϕ a′ ) + (1 / pa ) (ϕa / ϕ a′ ) ; ∂rb / ∂pa = pb ( ∂m / ∂pa ) (1 / ϕb′ ) ; ∂rc / ∂pa = pc ( ∂m / ∂pa ) (1 / ϕc′ ) ; …

By multiplying the first of these equations by pa, the second by pb, the third by pc … and adding them together, we obtain, for the left-hand sides

pa ( ∂ra / ∂pa ) + pb ( ∂rb / ∂pa ) + pc ( ∂rc / ∂pa ) + … = Sa ;



for the right-hand sides121



pa2 ( ∂m / ∂pa ) (1 / ϕ a′ ) + ϕ a / ϕ a′ + pb2 ( ∂m / ∂pa ) (1 / ϕb′ ) + pc2 ( ∂m / ∂pa ) (1 / ϕc′ ) +… = ( ∂m / ∂pa ) T + (ϕ a / ϕ a′ )



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and hence Sa = ( ∂m / ∂pa ) T + (ϕ a / ϕa′ ) .





By differentiating the budget constraint partially relative to pa

ra + pa ( ∂ra / ∂pa ) + pb ( ∂rb / ∂pa ) + pc ( ∂rc / ∂pa ) + … = 0



is obtained, or

ra + Sa = 0



or

ra + ( ∂m / ∂pa ) T + (ϕ a / ϕ a′ ) = 0



or

∂m / ∂pa = − ra + (ϕ a / ϕa′ )  / T

where the sign of the left-hand side remains equal to the sign of the quantity

ra + (ϕ a / ϕa′ )



By substituting ∂m/∂pa in ∂ra/∂pa; ∂rb/∂pa; ∂rc/∂pa; …. the laws of supply and demand for items A, B, C … can be obtained (the supply corresponding to negative demand). If A is an item in demand, ra is positive and hence the sign of ra+(φa/φ′a) is ambiguous, which means the sign of ∂m/∂pa is likewise ambiguous, implying that the sign of the quantity ∂rb/∂pa, ∂rc/∂pa,… is also ambiguous. On the other hand, by substituting ∂m/∂pa in ∂ra/∂pa and developing and simplifying it,

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{

}

2 2 ∂ra / ∂pa = − pa ra + (ϕ a / pa ) ( pb ) / ϕb′ + ( pc ) / ϕc′ + … / (T ϕa′ )  

is obtained, where the right-hand side is a negative quantity, thus implying that demand for an item will fall with increases in its price, if the prices of other items remain unchanged. Supposing122 furthermore that all the prices vary, the following total differentials will emerge dra = ( ∂ra / ∂pa ) dpa + ( ∂ra / ∂pb ) dpb + …; drb = ( ∂rb / ∂pa ) dpa + ( ∂rb / ∂pb ) dpb + …; … dm = ( ∂m / ∂pa ) dpa + ( ∂m / ∂pb ) dpb + …





By substituting in the last equation above123 ∂m / ∂pa = − ra + (ϕ a / ϕa′ )  / T ; ∂m / ∂pb = − rb + (ϕb / ϕb′ )  / T ; …



we obtain

{

}

{

}

dm = − ( ra + (ϕ a / ϕa′ )  / T dpa + − rb + (ϕb / ϕa′ )  / T dpb + …



= − ( ra dpa ) / T − ( rb dpb ) / T −…− (ϕa / ϕa′ ) / T  dpa − (ϕb / ϕb′ ) / T  dpb …

or124

dm = − ( dσ + dτ ) / T





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By substituting in dra125



∂ra / ∂pa = pa ( ∂m / ∂pa ) (1 / ϕ a′ ) + (1 / pa ) s (ϕ a / ϕ a′ ) ; ∂ra / ∂pb = pa ( ∂m / ∂pb ) (1 / ϕ a′ ) ;



we obtain dra =  pa ( ∂m / ∂pa ) (1 / ϕ a′ ) + (1 / pa ) (ϕa / ϕ a′ )  dpa + pa ( ∂m / ∂pb ) (1 / ϕ a′ ) dpb … = ( pa / ϕ a′ )



( ∂m / ∂pa ) dpa + ( ∂m / ∂pb ) dpb … + (1 / pa ) (ϕa / ϕa′ ) dpa = ( pa / ϕa′ ) dm + (1 / pa ) (ϕa / ϕa′ ) dpa



and, by symmetry

drb = ( pb / ϕa′ ) dm + (1 / pb ) (ϕb / ϕa′ ) dpb ; …



The values for dra, drb, … are obtained by substituting the final value of dm, as defined above, in the respective equations. Although Pareto claimed that his analysis of demand was “more exhaustive than usual”, he recognised that “it is still incomplete”, as the variation in the price of an item can cause both the quantity and the numbers of the consumed items to vary, although this can still be taken into account by varying the number of addends in the named Sa and T quantities and by substituting the partial differentials in the equations with finite-difference ratios, as the variation in the number of items consumed “would be unlikely to correspond to infinitesimal variations” in the price.126 So far, we have dealt with consumption in relation to independent items. If, however, items A and B are substitutes, and hence interdependent in terms of consumption,127 then

ra + brb = a



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(where a and b are constants). As the same need is satisfied, to differing degrees, by items A and B, their respective contributions to overall ophelimity can be represented as128 x = ra / rb





implying that the consumer will maximise his ophelimity when

ϕ x dx + ϕc drc = 0; ϕ x dx + ϕd drd = 0; …



However129

{

}

2 dx = a / b ( rb )  dra  



implying



{

}

2 ϕ x a / b ( rb )  dra + ϕc drc = 0;   

or, the consumer maximises his ophelimity when



{

}

2 ϕ x a / b ( rb )  = ϕc / pc = ϕd / pd …  

which implies that, in the case of items with substitutes, the negative relation between price and demand is no longer valid, since the following condition of maximisation of ophelimity for independent items no longer applies

ϕa / pa = ϕb / pb = ϕc / pc ….



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111

So the case130 of items where demand goes up with the increase in price could occur, at least initially.131 Referring explicitly to Edgeworth’s approach to the study of demand, Pareto also took into consideration132 an individual possessing a positive and finite quantity of two items A and B, which could therefore be represented as a point on the quarter of the Cartesian plane where both axes are positive. The value for overall utility to the individual should then correspond to this point. Among the infinite number of curves crossing the point, Pareto recalled Edgeworth’s distinction between the curve of indifference, “distinguished by the non-variation of utility on it”, and the curve of preference, defined as “that according to which the individual prefers to act”.133 Pareto in an original way observed that these curves exist even where there is no overall utility.134 If an infinitesimal line dt is traced beginning from the same point, then

dt 2 = d ρ a 2 + d ρb 2



is obtained (where the values ρs represent quantities possessed at the conclusion of the exchanges), with a resulting variation of overall utility135

dU = ϕ a d ρ a + ϕb d ρ b



If the line dt were traced along a curve of indifference, then the equation for the latter would be136

0 = ϕ a d ρ a + ϕb d ρ b



Conversely, the equation for the curve of preference can be obtained137 by substituting the first-order condition for the maximisation of dt2, that is,

0 = 2 d ρ a δ d ρ a + 2 d ρ bδ d ρ b



in the first-order condition of the maximisation of dU, which is

0 = ϕ aδ d ρ a + ϕbδ dϕb



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F. Mornati

leading to138

d ρ a / ϕ a = d ρ b / ϕb



If total utility exists, it is represented by a surface, with the result that the curves of indifference “are the projections of the contour lines139 of this surface onto the plane ρa ρb”, while the curves of preference “are the projections of the [curves] of maximum slope onto the same plane”.140 Thus, in transforming the quantities of A and of B in his possession, an individual will seek to travel up the surface of utility “following a curve of maximum slope”.141 More specifically,142 the individual will travel up the curve of maximum slope

pb = − ( d ρ a / d ρb )



until “a very short stretch of it is superimposed” on a “curve of indifference”. As a matter of fact, in that very short stretch “continuing onward, going back or halting will make no difference for that individual”. If, following this very short stretch, the surface descends (i.e. total utility declines), “the individual will come to a definitive halt” and “a stable equilibrium will be reached”. If the surface ascends, “the individual may still come to a halt, but it will be an unstable equilibrium and he may easily continue and start to climb again”. Generalising for more than two items and assuming once again the existence of a total utility U, the following equations will be obtained143:

∂U / ∂ρ a = ϕ a ; ∂U / ∂ρb = ϕb ; U / ∂ρc = ϕc …;



together with the prices (variable or constant), expressed in terms of quantities of item A,

pb = −∂qa / ∂qb ; pc = −∂qa / ∂qc …



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113

(where q represents the quantities possessed during the exchanges); the point of indifference 0 = ϕ a d ρ a + ϕb d ρ b + ϕc d ρ c + …





which, if integrable, yields the utility function U = μ (where μ is a positive constant); the point of preference d ρ a / ϕ a = d ρb / ϕb = d ρc / ϕc = …;





where prices are known, the following relation (representing a budget constraint where the quantities of items other than A are independent) dqa = ( ∂qa / ∂qb ) dqb + ( ∂qa / ∂qc ) dqc + …





which can be transformed into dqa + pb dqb + pc dqc + … = 0





The transformations of the quantities will continue until a locus of indifference is reached. Here, since the quantities are equal to each corresponding ρ, matching the point of preference and the budget constraint we derive

− (ϕb / ϕa ) d ρb − (ϕc / ϕa ) d ρc −… = d ρ a = − pb dqb − pc dqc + … = 0

and hence

(ϕb − pbϕa ) d ρb + (ϕc − pcϕa ) d ρc + … = 0

from which, since the dρ values are independent, the equations

ϕb − pbϕa = 0; ϕc − pcϕa = 0;…





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or the known equations

ϕa = ϕb / pb = ϕc / pc …



These final equations represent “the point where the transformations of economic assets cease, in a stable or unstable equilibrium”.144

3.5 The Law of Supply If, on the contrary, A refers to a commodity being offered, ra will be negative, so that in

∂m / ∂pa = − ra + (ϕ a / ϕa′ )  / T

the sign of ra+(φa/φ′a) will likewise be negative and hence also the sign of ∂m/∂pa, implying that the quantities ∂rb/∂pa, ∂rc/∂pa, … are positive. Thus, with the increase in the price of a commodity on offer, the demand for other commodities increases whilst quantities offered diminish. As for the sign of ∂ra/∂pa I, it is ambiguous, since the quantity is determined by the sum of addends with opposing signs.145 Having established this, Pareto considered it was “almost certain” that φ of A depended on the quantities possessed of all commodities, as otherwise “our various satisfactions [would be] independent of each other”, when at least “to some extent, it is certain that this is not the case”.146 Hence, in this case, the quantities of the commodities available at the conclusion of the exchanges are, for each commodity, a function of the final degree of utility of all the commodities



ra = ψ a (ϕ a ,ϕb ,ϕc ,…) ; rb = ψ b (ϕa ,ϕb ,ϕc ,…) ; rc = ψ c (ϕa ,ϕb ,ϕc ,…) ; …

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115

which can be converted into ra = ψ a (ϕ a , pbϕ a , pcϕ a ,…) ; rb = ψ b (ϕa , pbϕ a , pcϕa ,…) ; rc = ψ c (ϕa , pbϕa , pcϕ a ,…) ; …



which is equivalent to ra = ψ a (ϕ a , pb , pc ,…) ; rb = ψ b (ϕ a , pb , pc ,…) ; rc = ψ c (ϕ a , ( pb ) , pc ,…) ; …



If prices remain constant, the budget constraint reappears

ra + pb rb + pc rc + … = 0



which, assuming

X = ra + pc rc + … = ψ a + pcψ c + …



becomes

X + pb rb = 0



an equation which, taken together with

pbϕ a = ϕb ( rb ,ψ c ,…)



leads, if the other variables are taken as given, to a relationship between pb e rb which constitutes the law of supply and demand for commodity B.147

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F. Mornati

Further, from

X + pb rb = 0



can be derived

rb = − ( X / pb ) = − X / (ϕb / ϕa ) .



If we exclude the possibility of φa and φb are cancelled simultaneously, then rb is nullified by the value of φa, which cancels out X, as well as by the null value of φa. Given that “between the two roots of an algebraic equation, its derivative will have at least one root corresponding either to a maximum or a minimum value”,148 Pareto declared that in this manner he had “corroborated” Walras’ hypothesis stating that “in general, supply, after having risen in line with the price, must then diminish and probably end up being asymptotic to the price axis”.149 The cost of production for a commodity which can be produced in unlimited quantities corresponds to the degree of utility which the last infinitesimal quantity produced represents for its producer, which in turn is determined by that of the consumer of the commodity.150 In the end, from the production point of view, commodities, according to Pareto, can be divided into three categories on the basis of whether “the sum of sacrifices required to produce a single unit” (i.e. the cost of production) increases, remains the same or diminishes with increases in the quantity produced. In all three cases production will continue until the quantity is reached where the sacrifice is equal to the commodity’s final degree of utility.151 In the first case this correspondence is attained through the accompanying increase in the sacrifice and decrease in the final degree of utility,152 in the second case through the decrease in the final degree of  utility153 and in the third case on the supposition that the final degree of utility decreases more rapidly than the sacrifice.154

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Notes 1. Pareto (1893a, 96). In general, Pareto thought it absurd to expect “the absolute” from science, which is only “a series of explorations in an unknown territory”, Pareto to Giovanni Vailati, 10th February 1897, see Pareto (1975, p. 333). 2. More precisely, the aim of pure economics (being a theory of value) is to “demonstrate” the trading of goods at certain prices (“real phenomena” which can be “observed”) as the “consequence of one or very few principles”, see Pareto (1892a, pp. 405–406). Pareto conceives his first thoughts on mathematical economics, presented in the series of articles entitled Considerations on the Fundamental Principles of Pure Political Economy, as his response to the stimulus derived from reading Pantaleoni (1889), which he judged to be “clear and accurate”, Pareto to Pantaleoni, 6th July 1891 see Pareto (1984b, pp. 42, 47), together with Edgeworth (1881), Pareto to Maffeo Pantaleoni, 31st January 1892 see Pareto (1984b, p. 173). 3. Pareto (1892b, p.  27). From a personal point of view, Pareto in the summer of 1891 had already stated that the fact of not having “the slightest chance of ever becoming anything in Italy” allowed him to “hope in nothing but also fear nothing”, which left him in a position where he was able to “always look at things from an objective angle and never from a subjective one”, Pareto to Pantaleoni, 18th August 1891, see Pareto (1984b, pp. 36–37). Moreover, Pareto had no doubt that the truth “must be studied for its own sake”, see Pareto (1892c, p. 19), and initially conceived “the criterion for the validity of a theory” as consisting in its ability to “explain phenomena taking place in the past” and to “foresee those in the future”, see Pareto (1893a, p. 97). Later he came to understand the truth as the relation between mental phenomena (i.e. within the observer) and real-world phenomena (i.e. outside the observer), Pareto to Adrien Naville, 16th February 1897, see Pareto (1975, p. 327) and to Benedetto Croce, 27th May 1897, ibid., p. 342. 4. Corresponding to theoretical mechanics, see Pareto (1891, p.  219), since both disciplines study the properties of notional entities, see Pareto (1892d, p. 17). 5. Corresponding to applied mechanics, see Pareto (1891, p. 219). 6. Pareto (1892e, p. 1). Thus, Pareto to Pantaleoni, 2nd May 1891, see Pareto (1984b, p.  33), Pareto lauded Pantaleoni’s article, Pantaleoni

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(1891), because “it is precisely by continuing along this path that ­progress can be made in political economy”. Here Pantaleoni established the weighted average prices of the 12 principal categories of exports and 19 of imports, for each year, deriving the weighting from the relative proportion of the overall value of exports and imports constituted by each of these categories. Assigning the value of 100 to the year 1878, the indices fall more or less continually, reaching a value of 72 for the prices of imports and 75 for exports in the year 1889. 7. Pareto to Pantaleoni, 2nd May 1891, see Pareto (1984b, p. 33). 8. Pareto (1892a, p. 406). 9. Ibid. 10. Ibid., p. 409. 11. Pareto (1896, §629, note 1). 12. Pareto to Pantaleoni, 9th December 1891, see Pareto (1984b, pp. 107–108). 13. Pareto (1894a, p.  162). Similarly, Pareto, see Pareto (1892d, p.  18), underlined that “the thing one must never forget …. is that the results of theories cannot be applied en bloc and uncritically in practice”. He also added that his “one and only criterion, in practice, for favouring or not favouring a given step” was whether or not it would “increase the (material, moral, aesthetic, etc.) happiness of the greatest number”, Pareto to Walras, 28th April 1896, see Pareto (1975, pp. 292–293). 14. Pareto (1891, p. 218). In the same way, according to Pareto, the criticisms of the chair socialists regarding the “excessively absolutist character of political economy” were “absolutely justified” when made in relation to “desired practical applications [of the propositions] with no allowance made for the distinctions which had been discounted precisely in order to establish the general theory”, Pareto (1896, §557). 15. Pareto (1892f, p.  497). However, Pareto also acknowledged that “no science’s principles are true in absolute terms”, Pareto (1892a, p. 405). 16. Pareto (1893b, pp. 681–682). 17. Pareto (1892g, p. 239). 18. Pareto (1894a, p. 142). 19. Pareto to Pantaleoni, 6th July 1891, see Pareto (1984b, p. 48). 20. Pareto (1894b, p. 80). Pareto had stated that “the ultimate limit to which all phenomena tend is always a human need”, see Pareto (1892d, p. 17). 21. Pareto (1892a, p. 420). 22. Pareto (1894c, p. 71).

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23. The second area corresponded to the “science which examines the history of economic development”, and it would be “pointless to debate whether [it] is more, or less important” than the science of ophemility, Pareto (1894d, p. 73). The third was “the popularisation of science”, Pareto (1894e, p. 75). 24. Ibid. 25. Pareto (1894c, p. 71). 26. Thus, after immediately stating that any method, whether quantitative or qualitative (such as history) is acceptable, provided that it serves to “increase the quantity or the quality of human knowledge”, Pareto (1892a, p. 390), and after emphasising that “there is no scientifically infallible method, only more or less valid ones”, Pareto (1894d, p. 4), Pareto had brusquely stated that “all this debate on methodology is a waste of time, we should concentrate on results” and that “a valid method …. can be judged by its results”, Pareto (1896, p. III). 27. On Pareto’s methodology, see Tarascio (1968), Marchionatti and Gambino (1997), Bruni (2006). 28. Pareto (1892a, p. 397). Thus, Pareto to Adrien Naville, 11th January 1897, see Pareto (1975, p. 324), repeated that if pure economics wished to imitate the fruitful example of the natural sciences, which had started to make progress only when they had “based themselves on secondary principles, instead of obstinately attempting to discover the essence of things”, it should seek as far as possible to avoid trespassing on the field of psychology. 29. Pareto (1894a, p. 71). 30. Pareto (1896, §589). 31. Ibid., §§590, 592 note 1. 32. On the debate regarding the epistemological interpretation (inductivist or deductivist) of the Herschel (1830), see recently Cobb (2012). 33. Herschel (1830, §67). 34. Ibid, §§26, 145. 35. Ibid, §§33, 124. 36. On Pareto’s youthful reflections in favour of Mill’s Logic, see Mornati (2018, pp. 105–108). 37. Pareto to Pantaleoni, 9th December 1891, see Pareto (1984b, pp. 106–107). 38. Pareto to Walras, 15th March 1892, see Pareto (1975, p. 183). 39. Mill understood a syllogism to represent “reasoning from generals to particulars”, more precisely the operation of “inferring a proposition

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from propositions equally or more general”, see Mill (1843, p.  162). Remembering that a syllogism is divided into a major premise (consisting of a universal proposition asserting that entities possessing one attribute possess, or do not possess, another attribute, e.g. “all men are mortal”) and a minor premise (consisting of the identification of a subject possessing the primary attribute featuring in the major premise: “Socrates is a man”). The combination of the two propositions prove the conclusion (the subject of the minor premise possesses the second attribute of the major premise, or otherwise: “therefore Socrates is mortal”), ibid., p. 177. Mill underlined that “if the premises are true, the conclusion must inevitably be so”, ibid., p. 166. Mill also added that “a syllogism can prove no more than is involved in the premises”, ibid., p. 83. 40. Pareto to Pantaleoni, 3rd October 1891, see Pareto (1984b, p. 70). These considerations on syllogisms were also valid for mathematics, which is “a syllogism machine” (Pareto to Pantaleoni, 9th December 1891, ibid., p. 107) and also for experimental sciences, in the sense that their “axioms are no more than the sum of an inconceivably large number of experiences” (Pareto to Pantaleoni, 9th December 1891, ibid., p. 107). 41. Mornati (2018, p. 20). 42. Pareto to Pantaleoni, 9th December 1891, see Pareto (1984b, p. 118). 43. Pareto (1892g, p. 206). 44. Pareto (1896, §426). 45. Pareto (1892a, p. 418). 46. Pareto to Pantaleoni, 9th December 1891, see Pareto (1894b, p. 48). 47. Pareto (1892a, p. 396). 48. Pareto (1896, §225). 49. Pareto observed that the scarcity of readers of works on “social sciences adopting a scientific approach” was responsible for the lack of specialists in those sciences with a “scientific mindset”; hence those working in the areas of political economy and social sciences “are engaged in literature, or in art, but never in science”, Pareto to Vailati, 12th September and 6th October 1896, see Pareto (1975, pp. 301, 303). 50. Pareto (1896, §225, §559 note 1). 51. Ibid., §557 note 2. 52. Pareto (1895, p. 66) and (1892d, p. 18). 53. Pareto (1893–1894, p. 13). 54. Pareto to Pantaleoni, 19th February 1897, see Pareto (1894c, p. 37). 55. On the theoretical disagreements between Pareto and Walras, see Tarascio (1999) and Legris-Ragni (1999).

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56. Pareto to Pantaleoni, 31st May 1893, see Pareto (1984b, p. 382), Pareto to Walras, 21st September 1891, see Pareto (1975, p. 166), Pareto to Pantaleoni, 17th September and 3rd October 1891, see Pareto (1984b, pp. 58, 65). 57. Pareto to Walras, 2nd August 1893, see Pareto (1975, pp. 226–227). 58. Pareto (1892a, p. 389). 59. Ibid. 60. Mornati (2018, p. 20). 61. Pareto (1892h, p. 12). 62. Ibid. 63. Pareto (1892a, p. 399). 64. Pareto (1896, §559 note 4). 65. Ibid., §584. 66. Pareto to Pantaleoni, 19th February 1897, see Pareto (1984c, pp. 55–56). 67. Pareto (1892i, p. 145). 68. Pareto (1892j, p. 22). 69. Pareto (1895, p. 67). 70. Pareto (1894a, p. 164). 71. Pareto (1895, p. 67). 72. Pareto (1892a, pp. 409–410), Edgeworth (1881, pp. 15–16). 73. Pareto (1893c, p. 22 note 1). 74. Pareto (1892k, p. 8, n. 5). On the other hand, by utility, which is in any case a vague term, Pareto (1896, §§5, 11) means “the property possessed by an item of being favourable to the development and the prosperity of an individual…”. Hence an item may be simultaneously useful but not ophelimic, or ophelimic but not useful, as well as both ophelimic and useful. Pareto, ibid., §628 specifies that, for any individual, utility and ophelimity differ through “lack of information” (a lack which prevents the individual from foreseeing all the consequences of his or her actions), and also through “lack of intensity of certain sensations” (preventing an individual from accurately anticipating future harm). 75. Pareto also underlines that since ophelimity constitutes “an advantageous relationship between an item and an individual, and since both these latter are essential, nothing can be useful in absolute terms”, Pareto (1892k, p. 8). 76. Pareto (1896, §643). 77. Ibid., §644.

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78. Pareto (1892i, pp.  136–137). Recent studies on Considerations are Weber (2001, pp. 546–551) and Pareto (2007, pp. xi–xxix). 79. Pareto (1892k, p. 8). 80. Pareto (1892c, p. 21). 81. Pareto (1892l, p. 10). 82. Pareto (1893c, p. 1.) 83. Pareto (1892l, p. 12). 84. Pareto (1892f, p. 504). 85. Pareto to Pantaleoni, 3rd October and 9th December 1891, see Pareto (1984b, pp. 65, 115). 86. Edgeworth (1881, p. 34). 87. Pareto (1893c, p. 2). There is no lack of intuitive descriptions of the curves of final degrees of utility. Given that a basic necessity has the dual properties of causing “terrible suffering” when not available and of “a small quantity” being enough to satisfy the corresponding need, the curve of its final degree of utility is such that its lowest point is “not too far from its origin, very near the x-axis and such that on the left the curve rises rapidly while on the right it rapidly overlaps the x-axis”, Pareto, ibid., p. 14. Instead, for those items which are generally consumed “for pleasure”, the curve of the final degrees of utility is “more inclined” towards the x-axis, i.e. approaches it when large quantities of the asset are involved, ibid., pp. 14–15. 88. Pareto to Pantaleoni, 6th July 1891, see Pareto (1984b, p. 46). 89. Pantaleoni (1889, pp. 62, 64). 90. Pareto (1892k, p. 7). 91. Pareto (1892a, p. 414). 92. Pareto also recalled that as people are not able to “determine for themselves” the maximum of pleasure, it is probable that they “proceed somewhat by chance”, modifying “their conduct” if they see that they have failed to reach this maximum, so that “the exchanges would oscillate around the point of maximum satisfaction”, Pareto to Pantaleoni, 20th September 1891, see Pareto (1984b, p. 63). 93. Pareto (1893d, 281) and Edgeworth (1881, p. 20). 94. Pareto (1892a, pp. 414–415). 95. Pareto to Pantaleoni, 6th July 1891, see Pareto (1984b, p. 49). 96. This consideration means that, for example, when prices fall buyers withdraw from the market (in expectation of further lucrative falls) only to return when prices rise again (fearing having to pay excessive prices later).

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97. Pareto (1892a, pp. 416–417). 98. Pareto (1892f, pp. 485–486). 99. Edgeworth (1881, p. 20). 100. Pareto (1892m, p. 14). 101. Since ra and rb are indeed of oppositing signs (in the exchange), the exchange of A for B will always imply dra+pbdrb = 0 or pb = −(dra/drb) or −(drb/dra) =1/pb. 102. Thus supposing that ∂P/∂ra = φa… 103. Pareto (1892f, pp. 486–487). 104. Pareto to Pantaleoni, 14th August 1892, see Pareto (1984b, p. 275). 105. Pareto (1892i, pp. 145–147). 106. Ibid., pp. 145–147. 107. Ibid., p. 130. 108. Concerning which see below Sects. 3.4 and 3.5. 109. Pareto (1892i, p. 132). Pareto, ibid., pp. 126–129 showed that, in the absence of savings, knowledge of the laws of supply and demand is not sufficient to determine the final degrees of utility. 110. Ibid., p. 131. 111. Pareto (1893c, p. 7). 112. Pareto (1892i, p. 134). 113. Ibid. A numerical instance of the method is given below, §10.3.1. 114. Ibid., p. 135. 115. Ibid., p. 150. 116. Pareto (1893d, pp. 293–296). 117. Pareto (1892i, p. 139). 118. Ibid., pp. 121–124. 119. On this topic see the classic works Slutsky (1915), Hicks and Allen (1934), Chipman (1976, pp. 67–75). 120. Where, if the item A is the means of payment, ra is negative, while all other values of r are positive. 121. Since T = [(pa)2/φ′a+(pb)2/φ′b+(pc)2/φ′c+…], is a negative quantity because φ′a, φ′b, φ′c… are, by hypothesis, negative quantities. 122. Pareto (1892i, pp. 125–126). 123. Obtained by symmetry in relation to ∂m/∂pa = −[ra+(φa /φ′a)]/T. 124. Where dσ = (radpa)+(rbdpb)+… and dτ=(φa/φ′a) dpa+(φb /φ′b) dpb+…. 125. Obtained by symmetry in relation to ∂rb/∂pa = pb(∂m/∂pa)(1/φ′b). 126. Ibid., pp. 124–125. 127. Pareto (1896, §974, note 1).

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128. Supposing, for example, that item A is qualitatively superior to B, substituting B with A (or A with B) increases (or decreases) the satisfaction of the need. 129. dx = (rbdra−radrb)/(rb)2 = dra[rb−ra(drb/dra)]/(rb)2. Since d(ra+brb=a) implies dra+bdrb = 0 or –(1/b) = drb/dra), by substituting dx = dra[rb−ra(drb/dra)]/ (rb)2 we arrive at the formula shown in the text. 130. Now referred to as Giffen goods. 131. Pareto (1896, §977). 132. Pareto (1893d, p. 281). 133. Ibid.; Edgeworth (1881, pp. 21–22). 134. Pareto (1893d, p. 281). 135. Ibid., p. 282. 136. Ibid. 137. δ is the sign of the differential when the variable to be differentiated is the differential d. 138. Ibid. 139. Or the locus of the points on the surface which are equidistant from the horizontal plane below. 140. Ibid., p. 283. 141. Ibid., p. 284. 142. Ibid., pp. 284–285. 143. Ibid., pp. 285–286. 144. Ibid., p. 287. 145. Pareto (1892i, pp. 123–124). 146. Pareto (1893d, p. 299). 147. Ibid., pp. 307–308. 148. Ibid., p. 311. 149. Ibid., p. 308. 150. Pareto (1892b, p. 25). 151. Ibid. 152. Ibid. 153. Ibid. p. 26. 154. Ibid.

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Bibliography Bruni, Luigino. 2006. Pareto’s methodological project. International Review of Economics LIII-4: 423–450. Chipman, John S. 1976. The Paretian heritage. Revue européenne des sciences sociales XIV-37: 65–173. Cobb, Aaron D. 2012. Is John F. W. Herschel an inductivist about hypothetical inquiry? Perspectives on Science XX-4: 409–439. Edgeworth, Francis Ysidro. 1881. Mathematical psychics. An essay on the application of mathematics to the moral sciences. London: Kegan Paul. Herschel, John Frederick William. 1830. Preliminary discourse on the study of natural philosophy. London: Longman, Rees, Orme, Brown, Green and John Taylor. Hicks, John R., and Roy G.D. Allen. 1934. A reconsideration of the theory of value. Economica XIV, I-1: 52–76. Legris, André-Ragni Ludovic. 1999. Coverage of the field of economics in the works of Vilfredo Pareto: A perspective on the dispute with Léon Walras. Revue européenne des sciences sociales XXXVII-116: 325–346. Marchionatti, Roberto, and Enrico Gambino. 1997. Pareto and political economy as a science: Methodological revolution and analytical advances in the economic theory in the 1890’s. Journal of Political Economy CV-6: 1322–1348. Mill, John Stuart. 1843. A system of logic ratiocinative and inductive, being a connected view of the principles of evidence and the methods of scientific investigation. London: John W. Parker. Reprinted in Mill (1974). ———. 1974. The collected works, ed. John M.  Robson, vol. VIII.  Toronto: University of Toronto Press; London: Routledge and Kegan Paul. Mornati, Fiorenzo. 2018. Vilfredo Pareto: An intellectual biography. Volume I. From science to liberty (1848–1891). Basingstoke: Palgrave Macmillan. Pantaleoni, Maffeo. 1889. Principles of pure economics (Principi di economia pura). Firenze: Barbera. ———. 1891. Indices of variations in import and export prices in Italy from 1878 to 1889 (Indici della variazione dei prezzi di importazione e di esportazione in Italia dal 1878 al 1889). Giornale degli Economisti II, II-5: 497–509. Pareto, Vilfredo. 1891. Let do, let pass (Lasciate fare, lasciate passare). Giornale degli Economisti II (1891), III-3: 218–234. ———. 1892a. Considerations on the fundamental principles of pure political economy. I (Considerazioni sui principi fondamentali dell’economia politica pura.I). Giornale degli Economisti III, IV-5: 389–420.

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———. 1892b. The new economic theories. Letters to the editor of the “Monde économique”. IX (Les nouvelles théories économiques. Lettres au directeur du “Monde économique”. IX). Le Monde économique, September 24. Reprinted in Pareto (1987, pp. 25–27). ———. 1892c. The new economic theories. Letters to the editor of the “Monde économique”. VII (Les nouvelles théories économiques. Lettres au directeur du “Monde économique”. VII). Le Monde économique, September 3. Reprinted in Pareto (1987, pp. 18–21). ———. 1892d. The new economic theories. Letters to the editor of the “Monde économique”. VI (Les nouvelles théories économiques. Lettres au directeur du “Monde économique”. VI). Le Monde économique, August 27. Reprinted in Pareto (1987, pp. 15–18). ———. 1892e. The new economic theories. Letters to the editor of the “Monde économique”. I (Les nouvelles théories économiques. Lettres au directeur du “Monde économique”. I). Le Monde économique, July 23. Reprinted in Pareto (1987, pp. 1–2). ———. 1892f. Considerations on the fundamental principles of pure political economy. II (Considerazioni sui principi fondamentali dell’economia politica pura.II). Giornale degli Economisti III, IV-6: 485–512. ———. 1892g. Messrs. Auspitz and Lieben’s theory of prices and professor Walras’ observations (La teoria dei prezzi dei signori Auspitz e Lieben e le osservazioni del professor Walras). Giornale degli Economisti III, IV-3: 201–239. ———. 1892h. On an error by Cournot in applying mathematics to political economy (Di un errore del Cournot nel trattare l’economia politica colla matematica). Giornale degli Economisti III, IV-1: 1–14. ———. 1892i. Considerations on the fundamental principles of pure political economy. III (Considerazioni sui principi fondamentali dell’economia politica pura.III). Giornale degli Economisti III, V-2: 119–157. ———. 1892j. The new economic theories. Letters to the editor of the “Monde économique”. VIII (Les nouvelles théories économiques. Lettres au directeur du “Monde économique”. VIII). Le Monde économique, September 10. Reprinted in Pareto (1987, pp. 22–24). ———. 1892k. The new economic theories. Letters to the editor of the “Monde économique”. III (Les nouvelles théories économiques. Lettres au directeur du “Monde économique”. III). Le Monde économique, August 6. Reprinted in Pareto (1987, pp. 7–9). ———. 1892l. The new economic theories. Letters to the editor of the “Monde économique”. IV (Les nouvelles théories économiques. Lettres au directeur

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du “Monde économique”. IV). Le Monde économique, August 13. Reprinted in Pareto (1987, pp. 9–11). ———. 1892m. The new economic theories. Letters to the editor of the “Monde économique”. V (Les nouvelles théories économiques. Lettres au directeur du “Monde économique”. V). Le Monde économique, August 20. Reprinted in Pareto (1987, pp. 12–14). ———. 1893–1894. First course in applied political economy, academic year 1893–1894 (Premier cours d’économie appliquée, année académique 1893–1894). Lausanne: Self-Publication. Reprinted in Pareto (1982). ———. 1893a. This damn laissez-faire. III (Ce maudit laissez-faire. III). Le Monde économique, October 7. Reprinted in Pareto (1984a, pp. 95–98). ———. 1893b. Hedonic maxima (I massimi edonistici). L’idea liberale, November 12. Reprinted in Pareto (1989a, pp. 679–684). ———. 1893c. Considerations on the fundamental principles of pure political economy. IV (Considerazioni sui principi fondamentali dell’economia politica pura.IV). Giornale degli Economisti IV, VI-1: 1–37. ———. 1893d. Considerations on the fundamental principles of pure political economy. V (Considerazioni sui principi fondamentali dell’economia politica pura. V). Giornale degli Economisti IV, VII-4: 279–321. ———. 1894a. Mathematical theory of foreign exchange (Teoria matematica dei cambi forestieri). Giornale degli Economisti V, VIII-2: 142–173. ———. 1894b. Opening lecture on political economy by Mr. Vilfredo Pareto, Extraordinary Professor (Leçons d’ouverture d’économie politique de M.  Vilfredo Pareto, professeur extraordinaire). In Discours d’installation et leçons inaugurales, ed. Université de Lausanne, 215–229. Lausanne: Editions de l’Université Reprinted in Pareto (1987, pp. 79–86). ———. 1894c. Economic theories. I (Les théories économiques. I). Le monde économique, June 30. Reprinted in Pareto (1987, pp. 71–73). ———. 1894d. Economic theories. II (Les théories économiques. II). Le monde économique, August 11. Reprinted in Pareto (1987, pp. 73–75). ———. 1894e. Economic theories. III (Les théories économiques. III). Le monde économique, August 25. Reprinted in Pareto (1987, pp. 75–78). ———. 1895. Mathematical theory of foreign exchange (Théorie mathématique des changes étrangers). In Congrès de Caen (Caen Congress), ed. Association Française pour l’Avancement des sciences (French Association for the Advancement of Science). Paris: Au Secrétariat of the Association. Reprinted in Pareto (1989b, pp. 65–75). ———. 1896. Course in political economy (Cours d’économie politique). Lausanne: Rouge.

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———. 1975. Correspondence, 1890–1923 (Epistolario 1890–1923), Complete works, tome XIX-1, ed. Giovanni Busino. Geneva: Droz. ———. 1982. First course in applied political economy, academic year 1893–1894 (Premier cours d’économie appliquée, année académique 1893–1894). Geneva: Droz. ———. 1984a. Myths and ideologies (Mythes et idéologies). Complete works, tome VI, ed. Giovanni Busino. Geneva: Droz. ———. 1984b. Letters to Maffeo Pantaleoni 1890–1896 (Lettere a Maffeo Pantaleoni 1890–1896), Complete works, tome XXVIII.I, ed. Gabriele De Rosa. Geneva: Droz. ———. 1984c. Letters to Maffeo Pantaleoni 1897–1906 (Lettere a Maffeo Pantaleoni 18970–1906), Complete works, tome XXVIII.II, ed. Gabriele De Rosa. Geneva: Droz. ———. 1987. Marxisme and pure economics (Marxisme et économie pure), Complete works, tome IX, ed. Giovanni Busino. Geneva: Droz. ———. 1989a. Political writings. The development of capitalism (Scritti politici. Lo sviluppo del capitalismo). Complete works, tome XVII. ed. Giovanni Busino. Geneva: Droz. ———. 1989b. Statistics and mathematical economics (Statistique et économie mathématique). Complete works, tome VIII. ed. Giovanni Busino, Geneva: Droz. ———. 2007. In Considerations on the fundamental principles of pure political economy, ed. Roberto Marchionatti and Fiorenzo Mornati. London: Routledge. Slutsky, Eugen. 1915. On the theory of the budget of the consumer (Sulla teoria del bilancio del consumatore). Giornale degli Economisti e Rivista di Statistica XXXVI, LI-1: 1–25. Tarascio, Vincent. 1968. Pareto’s methodological approach to economics. A study on the history of some scientific aspects of economic though. Chapel Hill: The University of North Carolina Press. ———. 1999. The problem of scope: Walras and Pareto. Revue européenne des sciences sociales XXXVII-116: 315–324. Weber, Christian E. 2001. Pareto and 53 percent ordinal theory of utility. History of Political Economy XXXIII-3: 541–576.

4 General Economic Equilibrium

In Pareto’s view, studies on demand and supply were simply a preliminary to the study of general equilibrium which, insofar as it constituted a representation (even if only a first approximation) of economic phenomena, he considered to be the principal issue in economic theory. He thus contrasted Alfred Marshall, who “has not yet understood what general equilibrium is and, more specifically, does not grasp the mutual interdependence among economic phenomena”,1 with Walras, whose equations represented a development of Ce qu’on voit et ce qu’on ne voit pas (What is seen and what is not seen) by Frédéric Bastiat2 and more specifically “they interpret the whole range of economic phenomena and … lend themselves to any amplification necessary in order to take every detail into account”.3 In this regard, the major points will be briefly outlined below, from Pareto’s first characterisation of general equilibrium, displaying a certain number of additions in relation to Walras’ original (Sect. 4.1), to Pareto’s exposition of Walras’ version (Sects. 4.2 and 4.3) and to some of his comments relating to the consequences of the introduction of monopolies into the general equilibrium of free competition (Sect. 4.4).

© The Author(s) 2018 F. Mornati, Vilfredo Pareto: An Intellectual Biography Volume II, Palgrave Studies in the History of Economic Thought, https://doi.org/10.1007/978-3-030-04540-1_4

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4.1 T  he General Equilibrium of International Trade The first occasion when Pareto made use of the model of general equilibrium dates to March 1892 and was given by the need to show that the model “is able to take account, at least in part” of the indirect effects of duties.4 Pareto imagines two countries, I and II (where I produces only item A, with a production level of qIa, demand levels of dIa, dIIa, and price levels of pIa, pIIa, while II produces only item B with a production level of qIIb, demand levels of dIb, dIIb, and price levels of pIb, pIIb), and then formulates the following hypotheses: assume a single production factor T, available in quantities oIt, oIIt, demand of dIt, dIIt and prices of pIt, pIIt; assume also an identical numeraire N 5 for I and II, with quantities available of qIn, qIin; initially international trade only concerns the commodities and not the numeraire; in relation to the concept of production coefficient, defined as the quantity of the factor of production required to produce a unit of each product, these quantities are a for A and b for B; the final degrees of utility of the production factor, of the products and of the numeraire (φIt, φIa, φIb, φIn e φIIt, φIIa, φIIb, φIIn)6 are given for average citizens of I and II. Pareto then formulates the following equations7,8,9,10,11,12,13:



aqIa = oIt ; bqIIb = oIIt pIa = apIt ; pIIb = bpIIt oIt pIt = qIa pIa ; oIIt pIIt = qIIb pIIa ϕIt = pItϕIn ; ϕIa = pIaϕIn ; ϕIb = pIbϕIn ; ϕIIt = pIItϕIIn ; ϕIIa = pIIaϕIIn ; ϕIIb = pIIbϕIIn qIa = dIa + uIa ; qIIb = dIIb + uIb dIIa pIIa = uIIb pIb ; dIb pIb = uIa pIa



Pointing out that the last four equations are original, even if they are “a legitimate consequence” of those of Walras, Pareto observed that a system of 14 independent equations accompanying the same number of variables (oIt, pIt, qIa, pIa, dIa, dIb, pIb, oIIt, pIIt, qIIa, pIIa, dIIa, dIIb, pIIb)14 had been established, which Pareto consequently considered to be resolved.15

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Therefore, in a system of this type, “a variation in any given element … can cause variations in the values of all the variables”.16 For example, if h represents the costs of transportation of B from II to I, then the equation pIb = pIIb + h will obtain, and if in I a duty is applied to the import of B, this duty can be represented by substituting h′ for h, where h′>h and h′−h corresponds to the amount of the duty.17 The substitution of h′ for h will thereby cause a variation in the values of all the variables.18

4.2 W  alras’ General Equilibrium of Trade and Production In February 1894, in a first commentary on Walras’ general equilibrium of free competition19 in trade and production,20 Pareto observed that it comprised “three categories of equations”,21 of which the first “expresses the commercial equilibrium of the market”:



ϕ1a ( r1a ) = ϕ1b ( r1b ) / pb = ϕ1c ( r1c ) / pc = …; ϕ2 a ( r2 a ) = ϕ2 b ( r2 b ) / pb = ϕ2 c ( r2 c ) / pc = …; … r1a + pb r1b + pc r1c + … = 0; r2 a + pb r2 b + pc r2 c + … = 0; …

with A, B, C … T, S, … representing the m commodities and the capitals (or productive services)22; r representing the quantities of all these items exchanged by the single θ individuals 1, 2, ….; 1 (=pa), pb, pc,… representing the prices, expressed in terms of commodity A; and φ… corresponding to the final degrees of utility for the individual commodities and for the single individuals (amongst which are included the final degrees of utility of savings and of productive services, which ­encompasses money23). The equations in question are therefore (m+n−1)θ+θ=(m+n)θ. Pareto then underlines that the condition of maximum well-being (where the final degrees of utility in relation to prices are equal for each

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individual) does not entail that “the appropriation of economic items produces a maximum of well-being”, precisely because of the initial hypothesis “that the economic items were appropriated”.24 This ophelimic maximum further constitutes an “limit” around which in practice the economy oscillates, “sacrificing a greater or smaller number of individuals”. Pareto considered it in any case evident that this sacrifice would be even greater if the oscillations took place around a point other than the maximum.25 The second category of equations “simply express the fact … that, under free conditions”,26 “capital will flow towards industries offering excellent returns, and withdraw from those bringing losses, until such time as the selling price corresponds to the cost price”.27 These are thus the m−1 equations28:



pb = bt pt + bs ps + …; pc = ct pt + cs ps + …; …

where the productive services are T, S, … while the constant or variable quantities of the productive services necessary to produce a unit of b, c, … are bt, bs,…; ct, cs,…;… and the prices of the productive services are pt, ps… The third category of equations demonstrates that the quantity of productive services demanded by the market corresponds to the quantity needed to obtain the quantity of commodities produced.29 These are the n equations:



Rs = as Ra + bs Rb + …; Rt = at Ra + bt Rb + …; …

This system of equations for the general equilibrium of trade and production is “completely predetermined” since, corresponding to the equations (m+n)θ+m−1+n which are independent of each other, there is an equal number of variables, that is, the (m+n)θ quantities of commodities and productive services which are individually demanded or supplied, together with the prices m−1+n.30

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4.3 W  alras’ General Equilibrium of Capitalisation Walras’ general equilibrium of capitalisation is based on the hypothesis that savings are accumulated (by foregoing the consumption of commodities) and that these savings are borrowed and transformed into capital (this transformation being considered by Pareto to be “a form of production of economic items like any other”31), which in turn is used for the production of economic items.32 If the return of the savings borrowed is certain, then the gross rent will be equal to the net rent, whereas if it is not certain, the saver can protect himself by paying an insurance premium, so that, in that case, the net rent is less than the gross rent.33 Similarly, there is a gross rent of capital from which the net rent is arrived at by deducting the amount corresponding to depreciation.34 In conditions of free competition, the net rent of capital will in the end correspond to the net rent of borrowings (respectively representing the return and the cost of the operation of transforming the savings into capital).35 In formal terms: ps, pt, … represent the net return on a unit of capital S, T, …; i the net return on a unit of savings ε; ∏s, ∏t, … represent the units of savings required to produce a unit of S, T, … Under free competition the following conditions will therefore obtain36



ps = i ∏ S ; pt = i ∏ t ; … from which can be derived the conditions



i = ps / ∏ S = pt / ∏ tT ;…



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Pareto demonstrates37 that this condition for the allocation of savings corresponds to the optimum in terms of maximising the ophelimity of the exchangers, while remaining always “a central point around which the reality oscillates”.38 If the quantity δRs of the capital S is increased, then the capital T will diminish by the same amount, so that the following correspondence obtains: ∏ S δ Rs = ∏ t δ Rt





δRs e δRt modify the quantities of capital and commodities produced and the prices so that the following formulae obtain as dRa + bs dRb + … = dRs + δ Rs ; at dRa + bt dRb + … = dRt − δ Rt ; …



which, multiplied by ps, pt,… and added together, yield

( ps as + pt at + …) dRa + ( ps bs + pt bt + …) dRb + …

= ps dRs + psδ Rs + pt dRt − pt dRt + …



or alternatively

pa dRa + pb dRb +…− ps dRs − pt dRt −… = psδ Rs – pt dRt



or again, remembering the condition for maximum ophelimity of a society,39

0 = psδ Rs − pt dRt



or lastly, dividing the elements one at a time by ∏s δRs = ∏t δRt,

pS / ∏ S = pT / ∏T is arrived at.



This shows that the system of general equilibrium for trade and production can be extended to capitalisation, with the following provisos.

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Since savings are now being taken into consideration, for the θ individuals the equations are modified from (m+n)θ to θ(m+n+1), with n now referring to pre-existing capitals in the quantities originally available, which consequently continue to have the value of the n preceding equilibrium equations through which the quantity of services demanded in the market and the quantity required to obtain the quantities of merchandise produced are made to correspond. For entrepreneurs who produce m commodities the preceding m equilibrium equations will continue to apply. However, for entrepreneurs who convert savings into ν′ new quantities of pre-existing capital (S, T, V, …) or into ν new capital (H, K, …) the following will now apply: –– the budget equation

Rε = ∏ S RS′ + ∏T RT′ + ∏V RV′ + …∏ H RH + ∏ K RK +…



–– the ν′+ν−1 equilibrium equation for capitalisation (the allocation of savings between the various types of productive capital)

pS / ∏ S = pT / ∏T = pV / ∏V … pH / ∏ H = pK / ∏ K …



–– ν′+ν the equilibrium equations for production (i.e. the correspondence between the selling price, considered to be ∏, and the cost of production of a unit of capital, with yS… representing the rates of depreciation)



∏ S = sS ( pS + yS ∏ S ) + sT ( pT + yT ∏T ) + …; ∏ H = h S ( p S + y S ∏ S ) + hT ( pT + yT ∏T ) + …; …

Thus the (m+n)(θ+1)+2(ν′+ν)+θ equations are arrived at, of which however only (m+n)(θ+1)+2(ν′+ν)+θ−1 are independent of each other.40 The independent equations for the general equilibrium of trade, ­production and capitalisation thus allow the determination of an equivalent number of variables, that is, the m+n−1 prices of commodities and of pre-existing capital, the (m+n+1)θ quantities of commodities, capitals

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and savings exchanged, the ν′+ν quantities of pre-existing and new capital produced, the ν′ prices of new quantities produced of pre-existing capital and the ν prices of new capital. Pareto concludes by summing up the general equilibrium of free competition as referring to a situation in which, for any given price level: individuals acquire commodities in quantities corresponding to the respective weighted elementary ophelimities, making use of revenues drawn from their own capital or from their own savings; the entrepreneurs transform capital productive services at their disposal into commodities, in such a manner that the price and the production cost will correspond for each type; the entrepreneurs transform too savings into new capital until the point where net rent and the yield on savings correspond.41

4.4 General Equilibrium with Monopolists As far as monopolists are concerned, in Pareto’s view these are not concerned with the incremental ophelimity of the merchandise which is monopolised but, modifying the price by varying the quantities sold, they aim to maximise returns yielded by the sale.42 Thus, if B is a commodity monopolised, the monopolist will seek to maximise pbrb, with the first-order condition for this maximisation being

∂ ( pb rb ) / ∂rb ) = 0



More generally, if individual 1 has a monopoly of commodity B, individual 2 of commodity C and the other θ−2 individuals do not hold monopolies, for the purposes of the general equilibrium of exchange the result will be: –– the θ budget equations of the relevant consumers



r1a + pb r1b + pc r1c + … = 0 r2 a + pb r2 b + pv r2 c + … = 0 …

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–– the m−1 equilibrium equations of the exchange43 r1b + r2 b + r3c + … = 0 r1c + r2 c + r3c + … = 0 …



–– the (m−1)θ equations of maximisation of ophelimity of the individual consumers



∂ ( p0 r1b ) / ∂r1b ) = 0,ϕ1a ( r1 A ) = ϕc ( r1c ) / pc ) = ϕd ( r1d ) / pd …; ∂ ( pc r2 c ) / ∂r2 c ) = 0,ϕ2 a ( r2 a ) = ϕb ( r2 b ) / pb ) = ϕd ( r2 d ) / pc …; ϕ3 a ( r3 a ) = ϕ3b ( r3b ) / pb = ϕ3c ( r3c ) / pc ….; …

Therefore, the equations for the exchange which are independent of each other are θm+m−1, and the solution of these determines the quantities of commodities exchanged θm and the corresponding prices m−1. Since the prices are higher in a monopoly and the quantities exchanged are lower in comparison to the situation under free competition, the ophelimity of non-monopolist traders will be reduced. The maximum ophelimity obtained in this type of economic system is thus “lower than the maximum obtained under free competition, which is the absolute maximum”.44 Lastly, if there is a monopoly producer of commodity B, the equilibrium condition

pb = bs ps + bt pt + … = π b



is replaced by45

d ( pb − π b ) Rb  / dRb = 0.



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Notes 1. Hence Marshall, adding “nothing of note to our stock of knowledge”, makes excessive use of mathematics, Pareto to Pantaleoni, 17th June 1895, see Pareto (1984, pp. 417–418). 2. Pareto to Pantaleoni, 9th July 1895, ibid., pp. 423–424. Here Pareto is alluding to Bastiat (1850). 3. Pareto to Pantaleoni, 9th July 1895, in Pareto, Letters to Pantaleoni, 1890–1896, p. 425. 4. Pareto (1892, p. 213). 5. This constitutes an “exceptional” numeraire which does not represent a product, unlike those envisaged by Walras, ibid., p.214. 6. Ibid., pp. 214–215. 7. Ibid., pp. 216–217. 8. The equations are independent from each other and establish the correspondence between “the quantity of the production factor used [and] the quantity being offered”. 9. The equations are independent from each other and establish the correspondence between “the sale price and the cost of production”. 10. The equations, which are not independent of each other because they can be obtained from the two preceding pairs of equations, establish the correspondence between “the cost of production and the price of the product”. 11. The equations are independent from each other and establish the conditions of “maximum satisfaction”. For their derivations see Sect. 4.3. 12. The equations are independent from each other and establish the “conditions of exchange between the two markets”. 13. The equations are independent from each other and represent the balance of trade for II and for I. 14. Ibid., pp. 215–217. 15. This model was later profoundly contested in the 1930s by the mathematicians Abraham Waldand John von Neumann because it does not ensure that the solutions are economically significant, that is, not negative. The two academics thus gave birth to a new, completely mathematically based line of research regarding general economic equilibrium which was completed in the 1950s by Ken Arrow, Gerard Debreu, Lionel McKenzie and Weintraub (1983). Anyway, it should also always be borne in mind that the traditional Walras-Pareto model was further developed between the late 1930s and the late 1940s by John Hicks and Paul Samuelson, Marchionatti and Mornati (2016).

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16. Pareto (1892, p. 223). 17. Ibid. 18. Ibid., p. 224. 19. Represented by the situation where traders do not seek to modify market prices, Pareto (1896–1897, §46). 20. On Walras’ and Pareto’s differing conceptions of general equilibrium, Donzelli (2006), Bridel and Mornati (2009). 21. Pareto (1894, p.  143). Pareto (1896–1897, §286) specified that the equations for general equilibrium relate “always … to units of time”. 22. Pareto (1894, pp. 145, 149). 23. If the total quantity of a product is offered “at whatever price”, its final degree of utility is annulled and it disappears from the equations, ibid., p. 149. 24. Pareto (1896–1897, §§64–65). 25. Ibid., Sect. 67. 26. Pareto (1894, p.146). 27. Pareto (1895, p.67). 28. Item A is not included because, as indicated in the text, it is considered as a numeraraire and hence with fixed price of 1. 29. Ibid., p. 148. 30. Ibid., p. 149. 31. Pareto (1896–1897, §123). 32. Ibid., §105. 33. Ibid., §115. 34. Ibid., §§125–126. 35. Ibid., §132. 36. Ibid., §133, note 1. 37. Ibid., §724, note 1. For the sake of formal simplicity, depreciation is ignored initially. 38. Ibid., §134, note 1. 39. For the derivation of this formula, see Sect. 5.2. 40. Ibid., §135, note 1. 41. Ibid., §135. 42. Ibid., §144, note 4. 43. The equation r1A+r2A+r3A+… = 0 is obtained by adding together the first series of equations while taking account of the second series. 44. Ibid., §141, note 4 45. Ibid., §147. Mutatis mutandis, the same considerations apply if the producer holds a monopoly in the production of a capital, ibid., §148.

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Bibliography Bastiat, Frédéric. 1850. Ce qu’on voit et ce qu’on ne voit pas. Reprinted in Bastiat (1854, pp. 336–392). ———. 1854. Economic sophistry, Short pamphlets. II (Sophismes économiques, Petits pamphlets II), Complete Works, tome V. Paris: Guillaumin. Bridel, Pascal, and Fiorenzo Mornati. 2009. On general equilibrium as a “branch of metaphysics” (De l’équilibre général comme « branche de la métaphysique »). Revue économique LX-4: 869–890. Donzelli, Franco. 2006. Walras and Pareto on the meaning of the solution concept in general equilibrium theory. International Review of Economics LIII-4: 491–530. Marchionatti, Roberto-Mornati, Fiorenzo. (2016). Economic theories in competition. A new interpretation of the debate on the general economic equilibrium theory in the 1930s. Panoeconomicus, LXIII-5: 503–523. Pareto, Vilfredo. 1892. Messrs. Auspitz and Lieben’s theory of prices and professor Walras’ observations (La teoria dei prezzi dei signori Auspitz e Lieben e le osservazioni del professor Walras). Giornale degli Economisti III, IV-3: 201–239. ———. 1894. Mathematical theory of foreign exchange (Teoria matematica dei cambi forestieri). Giornale degli Economisti V, VIII-2: 142–173. ———.1895. Mathematical theory of foreign exchange (Théorie mathématique des changes étrangers) in Association Française pour l’Avancement des sciences (French Association for the Advancement of Science), Congrès de Caen (Caen Congress), Paris, Au Secrétariat of the Association. Reprinted in Pareto (1989, pp. 65–75). ———. 1896–1897. Course in political economy (Cours d’économie politique). Lausanne: Rouge. ———. 1984. Letters to Maffeo Pantaleoni 1890–1896 (Lettere a Maffeo Pantaleoni 1890–1896), Complete works, tome XXVIII.I, ed. Gabriele De Rosa. Geneva: Droz. ———.1989. Statistics and mathematical economics (Statistique et économie mathématique). Complete works, tome VIII. ed. Giovanni Busino, Geneva: Droz. Weintraub, Eliot R. 1983. On the existence of a competitive equilibrium: 1930–1954. Journal of Economic Literature XXI-1: 1–39.

5 The Economics of Welfare

For Pareto, now an academic, the economics of welfare represents the logical link between general equilibrium on the one hand and the ­ critique of economic policy on the other. In this chapter, the various phases of the most original element of Pareto’s economic thinking, tracing its origins quite evidently to his liberal activism, will be reconstructed.1 Thus, having alluded to some of his early reflections on the economics of welfare (Sect. 5.1), as well as to an interesting but isolated empirical exercise on this topic (Sect. 5.2), his first attempts at formalisation of the theme will be described (Sect. 5.3), followed by the first delineation of the notion that was later to become known as the Paretian optimum (Sect. 5.4). We will conclude with the early implications that Pareto identified deriving from his demonstration of the optimality of free competition (Sect. 5.5).

© The Author(s) 2018 F. Mornati, Vilfredo Pareto: An Intellectual Biography Volume II, Palgrave Studies in the History of Economic Thought, https://doi.org/10.1007/978-3-030-04540-1_5

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5.1 E  arly Thoughts on the Economics of Welfare One of Pareto’s earliest reflections on welfare dates to March 1891 when he interpreted the production of commodities on the part of a given population during a given period as being the integral, for all the ­generations then living, of the number of citizens of every generation multiplied by the average production of each age group. Using this definition of social production, it is possible, at least theoretically, to extrapolate the variations in parameters (particularly that of “sanitary conditions”) which determine the numbers of citizens of all age groups.2 A few months later, Pareto received from Pantaleoni the drafts of an original attempt to provide a theoretical foundation for liberalism which had been developed by Pantaleoni himself together with his pupil Angelo Bertolini.3 In his comments, Pareto argued that laissez-faire is simply the least harmful among economic systems “for civilised peoples such as the Europeans”, and stated that free competition, even if it really gives rise to a collective hedonistic maximum “corresponding to the specific interests of the ruling class” would not necessarily be adopted. In reality, those in power often take decisions based principally on their indirect effects (as in the case of Italian protectionism which, despite being damaging to the interests of the Italian ruling class, was nevertheless adopted in order to bolster Italy’s participation in the Triple Alliance, which was considered essential to its interests).4 In the same period, Pareto nevertheless affirmed that “the maximum quantity of good in human society is attainable by maintaining the most scrupulous respect for the fruits of the work of each individual”.5 Thus, Pareto stated that “government intervention arbitrarily favouring one group at the expense of another will always lead to an absolute loss for the nation”.6 For example, Pareto pointed out that the increase in the duty on wool introduced in 1887 yielded 1 million lire in additional revenues for the state and increased revenues for protected industrialists by 9 million lire, which anyway “brought them little benefit” since “the industry is far from being in a flourishing state”. It would therefore “have been better for all concerned” if the country had paid the producers an indemnity to quit the business, as long as it amounted to a sum less than 9 million lire, in order for the nation to be free to procure cheaper foreign wool products.7

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At the beginning of 1893, Pareto, after stating his belief, in common with the majority of free-traders, that utility derives from a “combination” of capital and labour, reiterated that the maximum of utility is attained when there is “free competition” between capital and labour. He infers from this that the maximum of utility is massively reduced if labour is not able to compete freely with capital (as, e.g. in the case of slavery), or, similarly, when capital is not able to compete freely with labour (as in the case of socialism).8

5.2 An Interesting Empirical Exercise This first phase of Pareto’s analytical attention to welfare also extended to an interesting analytical experiment. An investigation by Luigi Bodio had shown that in Italy, for the financial year 1889–1890, against a total figure for state expenditure on the railway system of 210 million lire and revenues from the state’s share in the earnings of the railway companies of 80 million, the state also derived other benefits from the railways (such reductions in tariffs amounting to 40 million lire and tax revenues from the operators of 53 million), further reducing the deficit to be financed from tax receipts to a figure of 37 million lire. However, Bodio also estimates a further “benefit that the nation derives from the railways”, which he valued at 146 million lire, corresponding to the savings accruing from the use of railways rather than roads for transportation, so that all in all the benefits of the railways more than outweighed their net costs to the state.9 At this point, Pareto has recourse to the analytical reasoning which Bodio had adapted from the German mathematician Wilhelm Launhardt (1832–1918) in formulating his estimates, and which involved envisaging: –– a circle whose centre represented the point of production and whose radius r represented the limit of distance (decreasing in accordance with increases in transport tariffs) at which the transportation of the product was worthwhile; –– the total quantity of the item transported being proportional to the area of the circle, that is, to the quantity r 2π;

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–– the average distance travelled by a unit in question being equal to (2/3)r, with the consequence that kilometre-tonnes transported were proportional to (2/3)r3π. Pareto has doubts with regard to whether this reasoning is “true” in the case of Italy, where the hypothesis of the circle could be valid only for the Po plain, while “traffic is not equally intense in all directions, but varie[s] with these”.10 Nevertheless, Pareto demonstrates that Bodio’s conclusions could still be considered “as true, especially since the calculation is largely approximative”, even if, in a formulation more nearly resembling the Italian situation, a volume of traffic varying with the different directions is imagined and an ellipse in place of a circle.11 On the basis of these new suppositions, Pareto arrived at the following conclusions: –– the total profits of the railways were

U = ( 3m − 2 ) / 2  α T

where α = the railway tariff, m = the reciprocal of the portion of r in which transport took place, T = total kilometre-tonnes travelled on the railways; –– the total profits of the ordinary roads were

U1 = ( 3m − 2 ) / 2  α1T1

where α1 = the road tariff, T1 = total kilometre-tonnes travelled on the roads. The advantage of the railways over the roads was thus12 equal to U−U1=[(3m−2)/2]αT(1−α2/α12) and hence was positive insofar as α was lower than α1.

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5.3 Towards the Paretian Optimum In June 1882, as he was beginning his exploration of the analytical aspect of welfare, Pareto claimed that a society may be represented with the function φ(r,u,v), with r constituting the index variable representing the varying quantities of an commodity available, u the index variable r­ epresenting the varying types of commodity available and v the index variable ­representing the final degrees of utility of currency for various individuals. By means of this function it is thus possible to “imagine ideal societies and draw conclusions which can be compared with the real-world context in order to learn how closely our hypotheses resemble reality, and from there take appropriate steps to incorporate any necessary modifications”.13 Pareto further affirmed that the maximum utility of a society is achieved when the following function is maximum14: t1

∫ {U + λ (r

a



t0

+ pb rb + …) dt}

where the value appearing after the Lagrange multiplier λ represents savings. If we suppose that ra represents the unknown and that the other r values are determined by the conditions of maximisation of individual utility

ϕa ( ra ) = (1 / pb )ϕb ( rb ) = (1 / pc )ϕc ( rc ) = …,



the first-order condition for the maximisation of the integral is

∂U / ∂ra + ∂U / ∂rb drb / dra + …λ (1 + pb ∂rb / ∂ra + …) = 0.



This condition, being

∂U / ∂ra = ϕ a ( ra ) ; ∂U / ∂rb = ϕb ( rb )…ϕ a′ = (1 / pb )ϕb′ ( drb / dra )…



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can be reformulated as

ϕa ( ra ) + ϕb ( rb ) pb (ϕa′ / ϕb′ )…+ λ (1 + p2 bϕ a′ / ϕb′ + …) = 0



or15 as

ϕa ( ra ) + λ + p2 b (ϕa′ / ϕb′ ) ϕa ( ra ) + λ  + … = 0



or as

ϕ a ( ra ) + λ ] [1 + p2 b (ϕa′ / ϕb′ ) + … = 0

which, since the second factor is positive, can be solved by the solution to

ϕa ( ra ) + λ = 0



that is, by

ϕa ( ra ) = −λ



Hence, social utility is maximised if the final degree of utility of commodity A, the currency, is constant. Pareto underlines that φa(ra) must be constant not in relation to variations in the quantity of A but “in all the various exchanges under consideration”.16

5.4 The First Version of the Paretian Optimum The enquiries which led Pareto to the first analytical version of what was to become the Paretian optimum started from the affirmation that in real life we observe people “looking after their own affairs, either spontaneously or because obliged by others”.17 It is only through experience, and hence not a priori, that we know that “in economic matters it is better to rely on one’s own efforts than those of others”. To this inductive proposition, making use of the principle (which was also empirical, in Pareto’s

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view) that “in economic activities mankind seeks to obtain the maximum benefit with the least sacrifice”, Walras made the deductive addition that “free competition produces the maximum welfare”.18 In July of 1894, Pareto noted that Walras19 had shown that ­competition maximises the utility of society in conditions of stable prices and production coefficients, price variability not being “a question … of great moment in practical terms”, whilst variability in the production coefficients is important in permitting the comparison of the coefficients which minimise the cost of production (constituting a property of free competition) with those “yielding maximum utility for society”.20 The cost prices are



π a = at pt + as ps + av pv + …; π b = bt pt + bs ps + bv pv + …; π c = ct pt + cs ps + cv pv + …; …

where A (the numeraire), B, C … are the m commodities; T, S … are the productive factors and p represents their prices (in theory constant, since conditions of free competition are being examined); a represents the production coefficients of A, b those of B and c those of C ; … The production coefficients of each of the m commodities are “connected” by an equivalent number of implicit functions

Fa ( at , as …) ; Fb ( bt , bs …) ; Fc ( ct , cs …) ;…



from which it can be inferred that at depends on the other n−1 a, bt on the other n−1 b and ct depends on the other n−1 c, and so on. Hence, the n−1 first-order conditions for the minimisation of πa are



∂π a / ∂as = ( ∂at / ∂as ) pt + ps = 0; ∂π a / ∂av = ( ∂at / ∂av ) pt + pv = 0; …

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and so the complete group of first-order conditions for the minimisation of the values of π is represented by (n−1)m equations which, added to the m equations defining all the π, yield the mn independent equations which will permit the determination of the equivalent number of production coefficients minimising the values of π.21 The procedure for comparison with the coefficients maximising social utility begins from the transformation, in the manner of Walras (i.e. making use of relative prices), of all the commodities consumed by an individual into the utility of one single commodity.22 For example, if an individual consumes 1 kilo of meat and 1 kilo of wheat per day and the relative price is 2 kilos of wheat per 1 kilo of meat, it can be said that the individual “enjoys the utility of 3 kilos of wheat … of which 1 kilo directly and the other two kilos after having transformed them into meat”. Applying this method to all individuals and to all the commodities consumed by each individual, “the total volume of wheat representing the sum total of all the utility shared between those individuals” can be obtained.23 The second step consists in converting into wheat the value of the utility sacrificed by the same individuals in providing the productive services necessary for the production of commodities for consumption. Once established the personal methods of division of the two quantities of utility, the utility enjoyed per head will grow with increases in overall utility enjoyed while the utility sacrificed per head will diminish with decreases in overall utility sacrificed.24 The third step consists in realising that “the hedonistic maximum” is obtained when “with the lowest overall quantity of sacrifices the maximum total quantity of utility to be enjoyed is obtained”: this implies that, if we want to change the personal division of enjoyment and sacrifices, it would be better to leave the social hedonistic maximum unaltered and to proceed “by depriving certain individuals in order to give to others”.25 The fourth step consists in determining which production coefficients lead to the hedonistic maximum. If as increases by das, the increase in utility enjoyed by an individual, measured in terms of item A, is equal to

∂ra / ∂as + ( ∂rb / ∂as ) pb + ( ∂rc / ∂as ) pc + … das

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and the corresponding increase of utility for all of society is equal to

∂Ra / ∂as + ( ∂Rb / ∂as ) pb + ( ∂Rc / ∂as ) pc + … das

whilst the corresponding increase of utility sacrificed by the society is equal to

( ∂Rt / ∂as ) pt + ( ∂Rs / ∂as ) pc + … das Thus, the hedonistic maximum is obtained when



∂Ra / ∂as + ( ∂Rb / ∂as ) pb + ( ∂Rc / ∂as ) pc + … − ( ∂Rt / ∂as ) pt − ( ∂Rs / ∂as ) pc − … = 0



The m(n−1) equations thus determined and the equations connecting the production coefficients m together determine the production coefficients maximising net social utility.26 The fifth and final step begins by differentiating the n equalising equations in relation to as, for each productive service T, S, …, as well as the quantities required and the quantity needed to produce the quantity of commodities to be consumed.27 This yields

∂Rt / ∂as = (∂at / ∂as ) Ra + (∂Ra / ∂as )at + (∂Rb / ∂as )bt + (∂Rc / ∂as )ct +… ∂Rs / ∂as = Ra + (∂Ra / ∂as )as + (∂Rb / ∂as )bs + (∂Rc / ∂as )cs +…

…



from which, by multiplying the first element by pt, the second by ps, and so on and adding them, the equation pt ( ∂Rt / ∂as ) + ps ∂Rs / ∂as + … = pt ( ∂at / ∂as ) Ra + ( ∂Ra / ∂as ) ( pt at + ps as + …) + ( ∂Rb / ∂as ) ( bt pt + ps bs + …)

+ ( ∂Rc / ∂as ) ( pt ct + ps cs + …) + … ps Ra + …



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can be arrived at, which in turn becomes28



− Ra  pt ( ∂at / ∂as ) + ps  = ( ∂Ra / ∂as ) pa + ( ∂Rb / ∂as ) pb + ( ∂Rc / ∂as ) pc + … − pt ( ∂Rt / ∂as ) − ps ∂Rs / ∂as −…



and, under free competition,29 it becomes identical to that for the hedonistic maximum30 0 = ( ∂Ra / ∂as ) pa + ( ∂Rb / ∂as ) pb + ( ∂Rc / ∂as ) pc + …− pt ( ∂Rt / ∂as ) − ps ∂Rs / ∂as −…





Pareto hastens to underline that, as “this proposition relates to the production and not to the distribution of economic items, it should be therefore equally acceptable to free-traders or socialists”.31 For this reason, “if one wishes to achieve the maximum of ophelimity, the only alternatives for regulating production are either absolute free competition or total organisation, as proposed by the socialists… The second system appears to present insurmountable practical difficulties”.32 On the contrary, “intermediate systems can never yield, even theoretically, the maximum of ophelimity”, as they involve, not only a transfer of wealth, but also a destruction, which is “often very substantial”.33 Pareto also proposed a second demonstration of the optimality of free competition which was formally virtually definitive, and which took as its starting point the consideration34 that variations in the production coefficient will cause the utility of individual 1 to vary, as follows

ϕ1a ( r1a ) ( ∂r1a / ∂as ) + ϕ1b ( r1b ) ( ∂r1b / ∂as ) + … das

or alternatively as follows35

{∂r

1a

/ ∂as + ( ∂r1b / ∂as ) pb + …}ϕ1a ( r1a ) das = λ1ϕ1a ( r1a ) .



Similarly, following das, the variations in the utility of the other θ-1 individuals will be λ2φ2a(r2a)…

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If all the λ = {∂ra/∂as+(∂rb/∂as)pb+…}das are all positive (or all negative), each individual will, following da s, see his personal utility increase (or  diminish), so that it can be stated that das causes social utility to increase (or diminish). If, on the other hand, das causes some values of λ to increase and others to diminish, it will cause the utility of some individuals to increase while diminishing that of others, with no possibility of “establishing a compensating mechanism between the various individual utilities, because they are measured in different units”.36 Nevertheless, the values of λ, representing “quantities” of the same item A,37 can be added together, indicating the total of positive values of λ with ς and that of the negative values of λ with σ. If

ζ − σ is positive ( negative )



then it is possible (or not possible) to completely compensate those having negative values of λ leaving a residue (or shortfall). Therefore, it is (or is not) expedient to continue to allow the value of as to vary, in the same direction followed thus far. Hence the value of as corresponding to the maximum social utility is that for which38

ζ − σ is null

5.5 Implications of the Optimality of Free Competition Pareto identified a variety of important and explicit conclusions deriving from the demonstration that free competition maximises social utility (in regard to which he does not express any preference39). For example, given free rein, people “naturally pursue the maximum welfare, unless they are blinded by ignorance”,40 with the divergence between “the dimensions of the observed phenomenon and the dimensions of the phenomenon which yields the maximum utility”41 being diminished by the struggle for survival and correspondingly increased by whatever attenuates that struggle (in particular the various forms of protectionism).42 Pareto also repeated

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that with the demonstration of the optimality of free c­ ompetition, he had not intended “either to pardon, or even excuse the abuses which exist in our societies” (which in fact he attributed to “state intervention”).43 Neither had he wished to imply the exclusion “a priori [of ] any set of rules governing property”, but simply to show the value of “all [those rules] which are able to withstand the test of competition” and which might “very well co-exist”.44

Notes 1. On the formal aspects of the Paretian optimum, Montesano (1991, 1997), Scapparone (1997); on the most important theoretical development, Allais (1989); on its role in the history of economic analysis, Berthonnet (2016); on its heuristic significance, Hennipman (1992). 2. Pareto to Pantaleoni, 26th March 1891, see Pareto (1984, pp. 29–30). 3. Bertolini and Pantaleoni (1892). The two authors affirm that by means of optimum individual or collective action (i.e. action performed in accordance with the hedonistic principle) both individual and collective hedonistic maxima can be achieved, ibid., pp. 293–294, note 1. By individual hedonistic maximum they mean “a state of welfare more complete than any other”, while by collective hedonistic maximum they refer to the equal distribution of items only in the case where all the individuals have an equal aptitude “for happiness”. Where this is not the case, they intend the term to refer to an unequal distribution of items whereby a greater quantity of items is received by those having a higher degree of this aptitude, ibid., pp.  301, 303. Lastly, of the four possible combinations between types of action (individual or collective) and types of maximum result (individual or collective), Pantaleoni and Bertolini give particular emphasis to free competition, seen as “a pronounced form of individual action” which permits the attainment of both the individual hedonistic maximum and the collective hedonistic maximum, ibid., pp. 297–298. 4. Pareto to Pantaleoni, 6th December, see Pareto (1984, pp. 98, 100–101). 5. Pareto (1891, p. 692). 6. Pareto (1892a, p. 110). 7. Pareto (1892b, p. 228). See below §6.3 in more detail. 8. Pareto to Luigi Bodio, 4th January 1893, see Pareto (2001, p. 49). 9. Bodio (1891, pp. 71–72d, 147–149). 10. Pareto (1892c, 156–157).

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11. Ibid. 12. In the hypothesis that this corresponds to T1/T=α3/α13, ibid., note to pp. 160–162. 13. Pareto (1892d, p. 508). 14. Pareto (1892e, pp. 153–155). 15. Since φb(rb)=φa(ra)pb. 16. Pareto (1892d, p. 508). 17. Pareto (1892f, p. 756). 18. Ibid. 19. Walras (1889, pp. 228–252). 20. Pareto (1894a, pp. 48–49). 21. Ibid., pp. 49–50. 22. Ibid., pp. 50–51. 23. Shortly after this, Pareto (1896–1897, §§645–648), while recognising that “between two persons, no comparison in ophelimity is strictly possible” added that “one compares the sensations of people from the same society on a daily basis, and sometimes also those from different societies”, which seemed admissible to him as long as they did not depart “too much from a certain average type”, in other words as long as there are “certain underlying features in common between those compared”. 24. Pareto (1894a, p. 51). 25. Ibid. So, if the maximum total social utility is equal to 100, of which 10 is given to a person A and the remaining 90 to the rest of society, then if, with the production coefficients remaining unaltered and accordingly the maximum total utility, it was decided to increase the part going to A to 20, then the additional 10 would be deducted from the rest of society, which consequently would retain 80. If, however, the production coefficients were modified, the maximum utility available would, by definition, decline to 80 which would imply that in order to give 20 to A, the part remaining for the rest of society would decrease to 60. Pareto (1894b, p.  139) highlighted the fact that, when modifications are made to the production coefficients, “the loss to society is generally much greater than the advantage accruing to some of its members through [the said change]”, which implies “if it is desired to protect an industry, it would be better, from a strictly economic point of view, to grant a direct subsidy than protectionist safeguards” since the latter would cause a modification in the production coefficients of free competition, ibid., p. 140. 26. Pareto (1894a, pp. 53–54). 27. Ibid., pp. 55–56.

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28. Since under free competition pa  =  at  pt+as  ps+av  pv+…; pb  =  bt pt+bs ps+bv pv+…; … obtains. 29. Because (∂at/∂as)pt + ps = 0 as seen above. 30. Walras to Pareto, 9th July 1894, see Walras (1965, p. 605), complimenting him on the ingeniousness of this first demonstration and bestowing on him the title of “master of mathematical economics”. 31. Pareto (1894a, p. 61). 32. Pareto (1896–1897, §906). 33. Ibid. 34. Pareto (1894a, pp. 58–59). 35. Since [φ1b(r1b)/φ1a(r1a)] = pb 36. Ibid., p. 60. 37. With the prices expressed in terms of quantities of commodity A, Pareto (1894a, p. 60). 38. Ibid., pp.  64–65. Walras to Pareto, 19th July 1894 see Walras (1965, p. 607), was less enthusiastic with regard to the second demonstration as he was exclusively concerned with free competition. Pareto to Léon Walras, 20th July 1894 see Pareto (1975 p. 250), pointed out that “it is not at all evident” that it is specifically the coefficients of free competition which yield the maximum welfare, since “the socialists … themselves” insisted that welfare could be increased by modifying these coefficients. Walras to Pareto, 22nd July 1894 see Walras (1965, p. 610), agreed that the variability of the production coefficients “in principle encapsulate the whole issue of free trade” and Pareto to Léon Walras, 23rd July 1894 see Pareto (1975, p. 251), expressed his hope that “by following this path it will be possible to establish the theory of free trade on a rational basis”. Finally, Walras to Pareto, 25th July 1894 see Walras (1965, p.  611), expressed his belief that the summation of the values of λ represents “an achievement of pure political economy” which would permit Pareto to “establish the whole discipline of applied political economy … because it provides a solution not only to the question of free trade but also to those relating to extensive or intensive cultivation, machinery, etc.”. 39. Pareto (1894c, p. 73). 40. Pareto (1893a, p. 578). 41. Pareto (1896–1897, §630). 42. Ibid., §§635, 640. 43. Pareto (1893a, p. 66). 44. Pareto (1894d).

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Bibliography Allais, Maurice. 1989. The general theory of surplus (La théorie génerale des surplus). Grenoble: Presses Universitaires de Grenoble. Berthonnet, Irène. 2016. Pareto-efficiency from Pareto to contemporary economics. History of Economic Ideas XXIV (3): 165–186. Bertolini, Angelo, and Maffeo Pantaleoni. 1892. Notes on the concept of individual and collective hedonistic maxima (Cenni sul concetto di massimi edonistici individuali e collettivi). Giornale degli Economisti III, IV (4): 285–323. Bodio, Luigi. 1891. On certain indices for measurement of economic flows in Italy (Di alcuni indici misuratori del movimento economico in Italia). Rome: Reale Accademia dei Lincei. Busino, Giovanni, ed. 1991. Pareto today (Pareto oggi). Bologna: Il Mulino. Hennipman, Piet. 1992. The reasoning of a great methodologist: Mark Blaug on the nature of Paretian welfare economics. De Economist 140 (4): 413–445. Montesano, Aldo. 1991. The ophelimic maximum for the collectivity: Definitions, analyses, interpretations (Il massimo di ofelimità per la collettività: definizioni, analisi, interpretazioni). In Busino, Giovanni, ed. (1991, pp. 115–138). ———. 1997. Pareto’s analysis of efficiency and its interpretation. History of Economic Ideas V-3: 7–18. Pareto, Vilfredo. 1891. Indiscreet curiosity. Letter to the editor (Curiosità indiscreta. Lettera al direttore). L’Economista, November 1, pp. 690–692. ———. 1892a. Letter from Italy. The concerns of Mr. Luzzatti, the gold exchange, the Tiberina Bank (Lettre d’Italie. Les préoccupations de M. Luzzatti, Le change de l’or, La Banque Tiberina). Le monde économique, April 9, pp.  415–416. In Pareto, Inédits et Addenda (Unpublished writings and addenda), p. 110. Reprinted in Pareto (2005, 107–111). ———. 1892b. Messrs. Auspitz and Lieben’s theory of prices and professor Walras’ observations (La teoria dei prezzi dei signori Auspitz e Lieben e le osservazioni del professor Walras). Giornale degli Economisti III, IV (3): 201–239. ———. 1892c. On the benefits of the railways for the nation (Dell’utile che procurano al paese le ferrovie). Giornale degli Economisti III, IV (2): 154–162. ———. 1892d. Considerations on the fundamental principles of pure political economy. II (Considerazioni sui principi fondamentali dell’economia politica pura. II). Giornale degli Economisti III, IV (6): 485–512. ———. 1892e. Considerations on the fundamental principles of pure political economy. III (Considerazioni sui principi fondamentali dell’economia politica pura. III). Giornale degli Economisti III, V (2): 119–157.

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———. 1892f. An ethical State (Stato etico). L’Idea liberale, April 29. Reprinted in Pareto (1989, pp. 755–760). ———. 1893a. Report (Cronaca). Giornale degli Economisti IV, VII (6): 572–578. ———. 1893b. Introduction à Karl Marx, Le Capital, extraits faits par M. Paul Lafargue. Paris: Guillaumin: III-LXXX. Reprinted in Pareto (1987, pp. 33–70). ———. 1894a. The maximum utility produced under free competition (Il massimo di utilità dato dalla libera concorrenza). Giornale degli Economisti V, IX (1): 48–66. ———. 1894b. Course in applied political economy (Cours d'économie politique appliquée). Lausanne: Self-Publication. Reprinted in Pareto (2005, pp. 133–183). ———. 1894c. Economic theories. I (Les théories économiques. I). Le monde économique, June 30. Reprinted in Pareto (1987, pp. 71–73). ———. 1894d. Collective ownership (Proprietà collettiva). L’idea liberale, March 11. Reprinted in Pareto (1989, pp. 737–738). ———. 1896–1897. Course in political economy (Cours d’économie politique). Lausanne: Rouge. ———. 1975. Correspondence, 1890–1923 (Epistolario 1890–1923), Complete works, tome XIX-1, ed. Giovanni Busino. Geneva: Droz. ———. 1984. Letters to Maffeo Pantaleoni 1890–1896 (Lettere a Maffeo Pantaleoni 1890–1896), Complete works, tome XXVIII.I, ed. Gabriele De Rosa. Geneva: Droz. ———. 1987. Marxisme and pure economics (Marxisme et économie pure), Complete Works, tome IX, ed. Giovanni Busino. Geneva: Droz. ———. 1989. Political writings. The development of capitalism (Scritti politici. Lo sviluppo del capitalismo). Complete Works, tome XVII. ed. Giovanni Busino. Geneva: Droz. ———. 2001. New letters 1870–1923 (Nouvelles lettres 1870–1923), Complete Works, tome XXXI, ed. Fiorenzo Mornati. Geneva: Droz. ———. 2005. Unpublished works and addenda (Inédits et Addenda). Completre Works, tome XXXII, ed. Fiorenzo Mornati. Geneva: Droz. Scapparone, Paolo. 1997. The maximum of collective ophelimity in the Cours d’économie politique. History of Economic Ideas V (3): 35–48. Walras, Léon. 1889. Elements of pure political economy (Éléments d’économie politique pure). Lausanne: Rouge. ———. 1965. In Correspondence of Léon Walras and related papers, 1884–1897, ed. William Jaffé. Amsterdam: North-Holland Publishing Company.

6 From Free-Trade Propaganda to the Theory of International Trade

In the period under examination, Pareto returned to the themes relating to international trade,1 which he had earlier broached during his period of amateur journalism, in order to develop their theoretical aspects, and specifically to consolidate them within the framework of general economic equilibrium and the economics of well-being.2 Thus, after describing the free-trade principles to which Pareto had subscribed over the preceding 20 years (Sect. 6.1), we will delineate the arguments, made from a free-trade perspective yet analytical in character, which he advanced against the protectionist-oriented reasoning of Cournot and of Auspitz and Lieben (Sect. 6.2), before characterising in more detail Pareto’s first extended contribution to the theory of international trade (Sects. 6.3 and 6.4). Lastly, we will re-examine a number of other instances of the empirical analysis he applied concerning the consequences of customs protection (Sect. 6.5).

© The Author(s) 2018 F. Mornati, Vilfredo Pareto: An Intellectual Biography Volume II, Palgrave Studies in the History of Economic Thought, https://doi.org/10.1007/978-3-030-04540-1_6

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6.1 Pareto’s Original Ideological Position It is worth reviewing Pareto’s free-trade convictions prior to his theoretical investigations on international trade. He clearly viewed the consequences of customs protection as being the despoliation of “part of the national wealth” and “robbing Peter to pay Paul”.3 If the first of these consequences alone had obtained, “protectionism would long have disappeared, because sooner or later all nations would have recognised … that it did nothing but harm to their interests”.4 However, in point of fact, protectionism was imposed on nations by those who stood to gain from the second phenomenon to a degree which would more than compensate their share of the loss deriving from the first.5 They were assisted in this by the fact that “a large number of people share in the negative consequences of protectionism” so that “the ill-effects suffered by each individual are slight” and “they let it pass”, whereas “the number of people deriving a benefit is small” so that “for each of these the benefit is substantial” and “they make every effort to bring it about”.6 Thus, in September 1894, Pareto observed that the Italian government’s tenacity in maintaining customs protection, despite the clear evidence of its catastrophic consequences, showed that the adoption of the policy was no error made in good faith, but was a decision made with “vested interests” in mind.7 On a more theoretically subtle level, Pareto observed that the propositions “equal protection for all yields the same results as free trade” and “a global increase in all values is impossible” are alike.8 It is true that any exchange can be presented as a relation in which the value of the numerator shows the quantity of a commodity being exchanged for a quantity of another commodity, which is represented by the denominator. Thus, if all the numerators and all the denominators vary by the same proportion (as in the case of equal protection for all), all the relationships remain unaltered. If the protection is only for some, then only some of the relationships will be modified. Pareto then makes the observation that equal protection for all, were it achievable in practice, would give “the same … result … as free trade, leaving aside the complication and the expense involved” in implementing the protection.9 But it is precisely these ­factors, in reality, that render equal protection for all a worse solution, from the point of view of the country as a whole, than free trade.10

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However, the free-traders were defending “the interests of people who, either out of ignorance or for other reasons, do not show the least gratitude” while they were undermining the interests of “people who will not forgive us for it”. For this reason, they would need to be content with the approval of their “conscience” and of a small number of “friends”.11 Furthermore, Pareto considered that the fact that the reduction in Italian imports that followed the move to protectionism of 1887 led to an (even greater) reduction in exports constituted a demonstration “of the law that products must be exchanged with other products”.12 He had no doubt that the price of a protected commodity was higher than the price of the same commodity unprotected, as the protectionists themselves acknowledged. There again, “if the duty did not cause the price to rise then why would the owners desire it?”13 Lastly, with regard to commercial treaties, he observed that, from the free-trade point of view, these have the dual advantage of leading on to free trade and of lending stability to international trade, causing it to grow in comparison to a protectionist state of affairs.14 On the other hand, from the protectionist point of view,15 commercial treaties, if national tariffs are not set at too prohibitive a level, are “the most important factor for a country’s economic future”, and for this reason they should be designed unscrupulously with the objective of selling as much as possible to the other party while buying as little as possible.16

6.2 P  areto’s Criticisms of the Contributions to the Theory of International Trade Made by Cournot and by Auspitz and Lieben Pareto’s critiques of the attempts made by Cournot and by Auspitz and Lieben to “demonstrate the value of protection”17 marked the beginning of his more theoretical reflections on international trade,18 and were in keeping with his preceding position during his activist period. In particular, Cournot: understood national income to refer to the sum of private incomes; used: A to refer to the export market; B to refer to the import market; M to refer to the item exported from A to B; pa e Da

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to refer to the autarchy price and demand for M in B; p′a, D′a, Δ, E to refer to the price, the domestic production, the domestic demand and the quantity of M produced by A and exported to B (with the consequence that D′a = Δ+E); p′b and D′b to refer to the price and the production of M in conditions of free exchange in B.19 From Cournot’s point of view the transition from autarchy to free trade is accompanied by the following consequences. In A: the producers of M obtain a variation in income amounting to p′aD′a − paDa which, assuming p′a > pa and D′a>Da, implies p′a D′a > pa Da20; consumers of M, if they desire to continue consuming, must procure the sum of (p′a−pa)Δ, which must be subtracted from their consumption of other items. Thus, for these consumers, the result is as if they had seen their income reduced by (p′a−pa)Δ.21 This leads to the following variation in the national income of A



pa′ Da′ − pa Da − ( pa′ − pa ) ∆ = pa′ ( Da′ − ∆ ) − pa ( Da − ∆ ) = pa′ E − pa ( Da − ∆ ) .



This must be a positive quantity, because p′a > pa and E > (Da−Δ) and represents “the calculation of the real value of resulting growth in the revenue of the exporting nation”.22 In B, on the other hand: the producers of M, assuming pb  >  p′b and Db > D′b, suffer a loss of income amounting to pbDb−p′bD′b23; those who consumed M prior to the reduction in its price will be able to devote the amount saved (pb−p′b)Db to the consumption of other items. For these consumers it is thus as if they had seen their income increase by (pb−p′b)Db.24 Cournot concluded that in B there will be a variation in national income of

pb Db − pb′ Db′ − ( pb − pb′ ) Db = pb′ ( Db − Db′ ) .



This is a positive value which represents “the real reduction in the national income of B as a result of the imports”.25 Cournot also pointed out that no allowance was made, because it “is not measurable”, for the fact that those in B who acquire greater quantities of M as a result of the reduction in price “will be able to seek a more gratifying use for a portion of their revenues”.26

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Having described this, Pareto claimed that “Cournot’s use of these variations in national income to undermine Smith’s theory on the benefits of free trade does not correspond to good logic”, since Cournot did not follow the demonstration of the claimed reduction in national income with the further demonstration “that a real reduction in national income is an ill”. In reality, with the capital and the labour saved as a result of the reduction in national income it was possible to “procure other material goods, thus leading to a growth in incomes”.27 A comment from Edgeworth28 regarding what he called the “beautiful and original reasoning” with which the Austrian mathematicians Rudolf Auspitz and Richard Lieben believed they had demonstrated29 “what conditions of supply and demand are favourable to the endeavour of one nation to gain by taxing the imports from (or exports to) another” which caused Pareto to deliver his outburst “protectionism is a folly and a fraud and no amount of mathematics can prove otherwise!”30 and to which he later gave a more formal development.31 From the starting point of the reasoning used by the two Austrians, Pareto took into consideration first, the curve of the utility which a nation derives from the importation of a given type of commodity, and then the curve of the utility which the same nation must sacrifice in order to accomplish the importation (corresponding to the utility which the exporting country will gain from the transaction), as well as the two curves of utility derived from these. If there are no duties, the quantity imported will correspond to the point of intersection of the two derived utility curves. Corresponding to the quantity imported thus defined will be a global utility of the two nations concerned which will be equal to the difference between the ordinate of the utility curve of the importing nation and the ordinate of the utility curve of the exporting nation (the former curve being superimposed on the latter). The degree of utility enjoyed by the importing country will be equal to the (positive) difference between the ordinate of the curve of utility and the ordinate of the derived curve of utility.32 If a duty is imposed, the consequences will be that the quantity exchanged will be reduced to that where the difference between the ordinates of the derived curves of utility is equal to the duty. The global utility of international trade is reduced, since the utility of each participating

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country is reduced, even if “the amount of the duty goes to the benefit of the country imposing it, so that it is possible that this country will have a greater revenue than it would under conditions of free trade”.33 Since “it could very well be that the ill-effects suffered as a consequence of the increase in production costs for all other commodities [following the introduction of the duty]” are greater than the advantage supposedly obtained by the protectionist country,34 Pareto concluded that “as regards the theory of international trade, to consider a single category of merchandise separately from the others can only lead to false conclusions”.35

6.3 Pareto’s Theory of International Trade Pareto’s positive and analytical approach to international trade commenced from a definition of the advantage which a country derives from it. He imagined the case of two countries, I and II, each of them independently producing and consuming both item a and item b, but where with the commencement of international trade, I starts to produce exclusively a and II b.36 In this latter situation, Pareto gives the following definitions37: qIa+(qIbpIb)/pIa = the quantity produced of a, of which qIa is the quantity formerly produced in autarchy (which continues to be consumed domestically), while (qIbpIb)/pIa is the quantity of a produced making use of resources that were previously consumed for the production of b; (qIbpIIb)/pIa is the quantity of a which must be transferred to II to obtain the quantity of b which I formerly produced in autarchy; h represents the unit cost of transport from I to II; (qIbpIIb)/pIa+(qIbh)/pIa) = qIb[(pIIb+h)/pIa] is the total quantity of a which I must consequently produce and transfer to II in order to obtain b. This means that, of (qIbpIb)/pIa, only the quantity

( qIb pIb ) / pIa − qIb ( pIIb + h ) / pIa  = qIb ( pIb − pIIb − h )]) / pIa

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remains available for domestic consumption. In the case where this is positive (i.e. where (pIb−pIIb−h)>0), this represents the “profit”, which I derives from the international trade “according to the theory of international trade”. This profit thus corresponds to the additional quantity of a in comparison to the preceding situation of autarchy and is available for consumption by I. The remainder is transferred to II to obtain the quantity of b which I previously produced in autarchy. Having established the above, we now imagine two countries X and Y which exchange σ items, among which currency.38 We will adopt the following indices of the variables: with regard to prices, the first index refers to the country where the commodity is produced, the second to the country where it is sold, while the third relates to the commodity in question. For example, pxyb describes the price of commodity b produced in X and sold in Y; quantities consumed are referred to with R followed by two indices. For example, Rxa = refers to the quantity of a consumed in X; quantities produced are shown by Q with two indices, for example, Qxa = the quantity of a produced in X; quantities exchanged are shown by R with a single index, the quantity of a exchanged between X and Y being referred to by Ra; transport costs are represented by Z with a single index, so that Zc = the cost of transportation of commodity c; thus, pxyc = pxxc+Zc, that is, the price, expressed in the numeraire of X, of the commodity c produced in X and sold in Y is equal to the price of commodity c produced and sold in X plus the cost of transport of commodity c from X to Y; the prices and the transport costs shown without an accent are expressed in the numeraire of X while those with accent are expressed in the numeraire of Y, with the numeraire commodity being commodity a produced and consumed in X (so that pxxa = 1, p′xxa = the price of the numeraire of X expressed in the numeraire of Y and hence, for example, p′xxc = p′xxa pxxc = the price, expressed in the numeraire of Y, of commodity a produced and consumed in X). If all the commodities are produced in both countries, it will be possible to establish, for each of these latter, the system of equations for general equilibrium which will determine equilibrium prices and quantities for

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the commodities produced there. Moreover, the new variables will have to be determined, specifically p′xxa together with the quantities of the commodities traded internationally. If b is one of the commodities that X imports from Y, this process will continue until

pxxb > pyxb



pxxb = pyxb



and will cease when

obtains, in the wake of a reduction in production of b in X which decreases pxxb and of an increase in production of b in Y which increases pyxb. In similar circumstances exchanges between X and Y of the other σ-1 commodities will also cease. If X exports a, c, … and imports b …, its balance of trade will be in equilibrium if

Ra pxxa − Rb pxxb + Rc pxxc …+ Ra Z a … = 0



an equation which, with the signs inverted, is also valid for Y. Hence there are σ+1 new equations which permit the determination of the all new variables mentioned above. Going into greater depth, Pareto noted that, if the prices of commodities X and Y are not expressed through the same numeraire, then the proposition is no longer valid whereby a commodity is exported until the point where its price in the exporting country is lower than that in the importing country, but will cease when the price of the commodity is the same in the two countries. The relation between prices expressed with the same numeraire will need to be replaced by the relation between the ratio of the prices of the two commodities in X (both prices are expressed in the numeraire of X) and the ratio of the prices of the same two commodities in Y (both prices are expressed in the numeraire of Y).39 Actually,40 since X imports commodity b from Y if the following relation obtains

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pxxb > pyxb or (1 / pyxb ) > (1 / pxxb )



165



likewise Y imports commodity c from X if the following relation obtains pyyc > pxyc .





Hence, multiplying the two inequalities element by element we obtain

(p

yyc

/ pyxb ) > ( pxyc / pxxb ) or ( pyyc p′xxa ) / ( pyxb p′xxa ) > ( pxyc / pxxb ) or alternatively ( p′yyc / p′yxb ) > ( pxyc / pxxb ) .



In other words, when the numeraires for X and Y are different, export of commodity c from X to Y will occur together with export of commodity b from Y to X if the ratio between the prices of the two commodities in X (expressed in the numeraire of X and inclusive of transport costs) is less than the ratio between the prices of the two commodities in Y (expressed in the numeraire of Y and inclusive of transport costs). The exchanges will cease when the following condition obtains

p′yyc / p′yxb = pxyc / pxxb



and this will be arrived at, starting from the inequality examined above, through a reduction in the first element (due to the fact that in Y the increase in imports of commodity c causes a reduction in production and consequently in the cost and therefore in the price of that commodity, while the increase in exports of commodity b causes an increase in production and consequently in the cost and hence in the price of that commodity), together with an increase in the second element (due to the fact that in X the increase in exports of commodity c causes an increase in production and consequently in the cost and therefore in the price of that commodity, while the increase in imports of commodity b causes a reduction in production consequently in the cost and hence in the price of that commodity).

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At this point Pareto arrived at the most important issue, pointing out that country X, exporting c to Y and importing b, can gain advantages or sustain losses deriving from the exchange and/or the production and/or the possible impact of customs duties.41 If xc represents the export duty and xb the import duty, both expressed in shares of the value of the respective exchanged quantities, country X will receive the following amount in customs duties42

Θ = pc xc Rc + pb xb Rb



If at the same time xb is reduced very slightly and dΛ = padRa + pbdRb + …−psdRs−ptdRt−…43 represents the consequent variation, expressed in the numeraire of X, in all the quantities that the individuals belonging to X consume of commodities a, b, … and sacrifice of commodities s, t,…, the maximum ophelimity for X is given by

dΘ + d Λ = 0

also if, in the continuation of the argument, Pareto, implicitly, considers dΘ negligible compared to dΛ. If, on the other hand, we assume that the quantities consumed are unchanged, we obtain

d Λ = − ps dRs − pt dRt −…



Having established this, Pareto described the following logical consequences of the effects of the very slight reduction in xb. We define Rs = R′s + Rs, Rt = R′t + Rt …where Rs represents the quantity of services s which is fully employed, R′s represents the quantity of services s employed for the production of all the commodities and Rs the quantity of services s employed in export operations of goods from X….44 If X exports only c to Y (in the quantity Rc) and imports only b: the transport cost for Rc is

Z c Rc = ps Rs + pt Rt + …;



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the quantity of b produced in X will be

Rb′ = Rb − Rb



(where R′b = the quantity of b produced, Rb= the quantity of b consumed and Rb =  the quantity of b imported); the quantity of c produced in X will be

Rc′ = Rc + Rc



(where R′c= the quantity of c produced, Rc = the quantity of c consumed and Rc= the quantity of c exported); the total quantities of s, t,… employed will be



Rs = as Ra + bs Rb′ + cs Rc′ …+ Rs Rt = at Ra + bt Rb′ + ct Rc′ …+ Rt ; ….;

the balance of trade for X will be

pxyc Rc − pyxb Rb = 0.



By fully differentiating all the equations of the quantities employed for s, t,… and by multiplying by ps, pt,… we arrive at



ps dRs = ps das Ra + ps dbs Rb′ + ps dcs Rc′ … + ps dRs + ps as dRa + ps bs dRb′ + ps cs dRc′ + … pt dRt = pt dat Ra + pt dbt Rb′ + pt dct Rc′ … + pt dRt + pt at dRa + pt bt dRb′ + pt ct dRc′ + … ….

Then, by adding up the differential equations thus determined, since the hypothesis that dRa, dRb, dRc,… are null45 continues to obtain (and hence also dR′b = −dRb as well as dR′c = dRc), and assuming that Rs, Rt,… remain unchanged, we arrive at

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ps dRs + pt dRt +… = ( ps das + pt dat + …) Ra + ( ps dbs + pt dbt + …) Rb′ + ( ps dcs + pt dct + …) Rc′ + … − ( ps bs + pt bt + …) dRb + ( ps cs + pt ct + …) dRc + …



which, if the signs are inverted, by substitution46 and bearing in mind that the coefficients for commodities other than b and c remain unchanged, leads to



d Λ = − ( ps dbs + pt dbt + …) Rb′ − ( ps dcs + pt dct + …) Rc′ + pyxb dRb − pxyc dRc



which, in view of the fact that47

dpxxb = ps dbs + pt dbt + …





dpxxc = ps dcs + pt dct + …



finally leads to d Λ = ( − Rb′ dpxxb − Rc′ dpxxc ) + ( pyxb dRb − pxyc dRc ) = − ps dRs − pt dRt −…





Since “protectionist measures have the aim of increasing the quantity of services consumed”, they have the effect of reducing dΛ, that is, they cause “a destruction of wealth”. On the other hand, dΛ increases with increases in

(p

yxb

dRb − pxyc dRc )



that is, if the difference between the variation in the value of imports and the variation in the value of exports increases48; and/or, just as it is obtained automatically whether customs tariffs are lowered, if both of the following expressions are reduced (or at least one, with the other remaining unchanged)49

dpxxb and dpxxc.



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Pareto presented this argument in a different and less complicated manner. Assuming still the context of a change in the exploited quantities of services t, s,… with the consumed quantities of commodities a, b, … remaining unaltered50, individual 1’s utility will vary by the quantity

dV1 = −ϕ1s dr1s − ϕ1t dr1t −…



that is,51 by the quantity

dV1 = ( − ps dr1s − pt dr1t −…)(ϕ1a / pa ) = d λ1 (ϕ1a / pa )



which in turn entails a variation in social utility corresponding to

d Λ = d λ1 + d λ2 + … = − ps dRs − pt dRt −…



Assuming also52 that: ρab is the quantity of a exchanged with b; ρba is the quantity of b exchanged with a; pa, pb refer to the prices of a and b expressed through a common numeraire; the quantities produced of the other commodities are unchanged, together with their production coefficients. So if both ρab and ρba and the production coefficients of a and of b vary, then



dRs = as d ρ ab − bs d ρba + Ra das + Rb dbs dRt = at d ρ ab − bt d ρ ba + Ra dat + Rb dbt …

By changing all the signs and multiplying the first equation by ps, the second by pt, … and adding up, we arrive at



d Λ = − pa d ρ ab + pb d ρba − Ra ( ps das + pt dat + …) − Rb ( ps dbs + pt dbt + …)



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which is to say d Λ = − pa d ρ ab + pb d ρba − Ra dpa − Rb dpb = d Λ1 + d Λ 2





where d Λ1 = − pa d ρ ab + pb d ρba





represents the variation in utility due to the exchange while d Λ 2 = − Ra dpa − Rb dpb





describes the variation in utility owing to production. The sign of dΛ253 is: null when the price of the commodities does not vary with variations in the quantities produced; positive (or negative) when the domestic price of the imported commodity (i.e. b) decreases (or increases) with decreases (or increases) in the quantity produced (an important example of this is when quantities of wheat imported increase (or decrease)) and the domestic price of the exported commodity (i.e. a) decreases (or increases) with decreases (or increases) in quantity produced, as in the equally important case of increases (or decreases) in the quantity of industrial products produced (and then exported). Further, from the equation for the balance of trade54

pa ρ ab − pb ρba = 0



pa / pb = ρba / ρ ab



we get

or (through differentiation)

pa d ρ ab − pb d ρba + ρ ab dpa − ρ ba dpb = 0



or alternatively (inverting the signs)

− pa d ρ ab + pb d ρba − ρ ab dpa + ρ ba dpb = 0



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or

d Λ1 = ρ ab dpa − ρba dpb



where ρab (ρba) can be redefined as the quantity exported (or imported) of a (or b). Given that



ρ ab dpa − ρba dpb = ρ ab  dpa − ( ρba / ρ ab ) dpb  = ρ ab  dpa − ( pa / pb ) dpb  = ρ ab pb ( pb dpa − pa dpb ) / pb 2  = ρ ab pb d ( pa / pb ) = ρ ab pb d ( ρ ba / ρ ab )



dΛ1 will thus always increase with increases in the ratio between quantities imported (ρba) and quantities exported (ρab). Lastly, when dΛ1 and dΛ2 are of opposing signs, in order to determine the variations in social well-being, we need to make a direct use of

d Λ = − ps dRs − pt dRt −…



which allows Pareto to reiterate that protection, pursued with the aim of “increasing the quantity of capital services used in production”, invariably leads “to a destruction of wealth”.55 Hence Pareto reiterated that “from a strictly economic standpoint” it was better to award the industry to be protected “a direct subsidy” in place of the more damaging protective duty56. He also added that agricultural protection was less deleterious than industrial protection because if nothing else it conferred lasting returns on the landowners, representing “so much wealth saved from destruction” while the returns it bestowed on industrialists were transitory in that they were cancelled out by competition which restored parity to prices and production costs.57

6.4 A Reformulation of Ricardo’s Theorem In the context of his survey of the theory of international trade, Pareto also proposed a generalisation of Ricardo’s theorem.58

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A country exports the quantities ρa, ρc,.. of commodities a, c,…, with production costs pa, pc,.. and transport costs σa, σc,... If, in the rest of the world, a, c,… have prices p"a, p"c,.., expressed in the currency of the exporting country, then in the exporting country the prices will be

pa′ = pa′′ − σ a ; pc′ = pc′′ − σ c ;…



In the same way, if the country imports quantities ρb, ρd, of commodities b, d,…, whose production costs are pb, pd,.. and whose transport costs from the rest of the world are σb, σd,.., then, if in the country b, d,… have prices p′b, p′d,.., their prices in the rest of the world will be

pb′′ = pb′ − σ b ; pd′′ = pd′ − σ d ;…



Pareto then pointed out that, under conditions of free competition, the following obtains for all the commodities exchanged pa = pa′ ; pb = pb′ ;…





from which, by division, we obtain pa / pb = pa′ / pb′ ;…





We suppose, also, that

pa′′′ = pa′ / pm ; pb′′′ = pb′ / pm ;…



represents the prices of the commodities in the country expressed in the currency of the rest of the world (where pm is the price of this latter expressed in the currency of the country). This signifies that

( pa′′ / pm ) = p IV a = ( pa′ + σ a ) / pm ; ( pb′′ / pm ) = p IV b = ( pb′ − σ b ) / pm ;…

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or, alternatively,

p IV a = pa′′′ + (σ a / pm ) ; p IV b = pb′′′ − (σ b / pm ) ;…



will represent the prices of the commodities in the rest of the world expressed in the currency of the rest of the world. From the above we can obtain



pa / pb = pa′ / pb′ = ( pa′ / pm ) / ( pb′ / pm ) = pa′′′ / pb′′′ =  p IV a − (σ a / pm ) ]/[ p IV b + (σ b / pm )  ;…



After expressing his view that “the usual form” of Ricardo’s theorem is

pa / pb = p IV a / p IV b ;…,



Pareto pointed out that this thus represents simply the specific case where transport costs are “negligible, or proportional” to production costs.

6.5 N  ew Empirical Analyses of the Effects of Customs Protection In this period Pareto also produced numerous new assessments of the effects of the protectionist policies. In 1894, he observed that one of the consequences of the 1887 protectionist customs policy was the decline in the price of olive oil from 160 francs in 1885 to 151 francs in 1889, while the price of a hundredweight of iron bars rose from 17 francs in 1885 to 18.4 francs in 1889. This implied that “the same quantities of capital services and of manpower, converted first into olive oil and then exchanged for iron” would have yielded 9.4 hundredweight of iron59 in 1885 but only 8.2 hundredweight60 in 1889. In other words, to obtain the same quantity of iron in 1889 as in 1885 it was necessary to use 14.6%61 more productive services, thus modifying the production coefficients, with the automatic consequence of reducing the wealth of the country.62

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In the summer of 1897, Pareto points out that the duty on cereals caused an increase in the price of bread, both directly, by increasing the price of grain and thus of flour (in the week of 12th–18th July 1897 the price of the same measure of grain was 16.5 francs in free-trade Belgium but 25.5 francs in protectionist Italy) and indirectly, by encouraging milling monopolies, since the duty created a disincentive for consumers wishing to purchase flour abroad directly.63 At the beginning of February 1898, at the time of the parliamentary debate on the government bill number 11 of the 21st January 1898 provisionally reducing the duty on cereals from 75 to 50 lire a tonne until the following 30th of April, which was ratified by parliament with an extension to the 31st of May, Pareto reiterated that significant benefit “to the national economy could accrue only from a complete and permanent removal of the duty on cereals”, with the farming community compensated by a reduction in the land tax, which in turn could be financed through a reduction in military expenditure.64 Without doubt, a reduction in military expenditure from its then level of 340 million lire to the average of 20 years earlier would have brought a saving of 103 million lire with which the government would have been able to finance both the shortfall of 46 million lire in revenues received annually from the customs duty on cereals and also a halving of the land tax.65

Notes 1. In this regard, see Mornati (2018, pp. 153–160). 2. For an earlier study of this issue, Maneschi (1993). 3. Pareto to Felice Cavallotti, 14th August 1892, see Pareto (1989a, p. 165). 4. Pareto to Emilia Peruzzi, 22nd February 1894, see Pareto (1984a, p. 565). 5. Ibid., pp. 565–566. 6. Ibid., p. 566. 7. Pareto (1894a, p. 303). 8. Pareto to Maffeo Pantaleoni, 20th March 1891, see Pareto (1984b, p. 21). 9. Ibid., pp. 22–23. 10. Pareto to Pantaleoni, 26th March 1891, ibid., p. 27. In confirmation of the fundamental importance assumed by the battle for free trade for

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Pareto at this time, it is interesting to recall that in the first letter to Walras, Pareto asked him particularly, in anticipation of the forthcoming referendum on the Swiss customs tariff, whether there was a Swiss freetrade association he could contact, Pareto to Léon Walras, 23rd July 1891, see Pareto (1975, p. 160). On the 18th of October 1891 the Swiss people gave their verdict, in the referendum on the new customs tariffs, more protectionist than the existing ones, proposed by the government on the 2nd of May 1890, under pressure from majorities in the industrial and agricultural sectors, and which had been approved in parliament on the 10th of April 1891. The free-trade position, from which the demand for a referendum originated, was championed by the League against the increases in the cost of living (Ligue contre le renchérissement de la vie), which had in fact been mentioned by Walras, albeit without enthusiasm, in his reply to Pareto, 28th July 1891, see Walras (1965, p. 457). This latter lobby was made up of representatives from the export industry, a section of the working people’s trade union movement and by the nascent cooperative movement. It was led by the Neuchâtel federal councillor Numa Droz (a right-wing radical, at the time Foreign Minister). The new tariffs were approved by 212,000 votes to 147,000 as well as by the majority of the cantons, Humair (2004, pp. 545–580). A few weeks later, Pareto to Pantaleoni, 25th December 1891, see Pareto (1984b p. 131), had no hesitation in stating that Walras, “from his chair in Lausanne”, “would have performed a more useful service” by participating in the protectionist campaign rather than “giving a more or less rigorous demonstration that market equilibrium is reached by increasing the price through increased demand”. 11. Pareto to Pantaleoni, 18th August 1891, see Pareto (1984b, p. 56). 12. Pareto (1891a, p. 415). 13. Pareto to Emilia Peruzzi, 22nd February 1894, see Pareto (1984a, p. 566). 14. Pareto, Traités de commerce, in Nouveau dictionnaire d'économie politique, publiés sous la direction de L. Say et de J. Chailley. Avec supplément. Paris, Guillaumin, 1892, vol.  II, pp.  1046–1050, see Pareto (1984c, pp. 75–76). 15. Pareto, ibid., p. 77, also claimed that the protectionists “have never been capable of formulating their ideas clearly”. 16. Ibid. 17. Pareto to Pantaleoni, 6th and 8th July 1891, see Pareto (1984b, pp. 42, 45).

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18. Furthermore, Pareto to Pantaleoni, undated (but in late July or early August 1892), see Pareto (1984b, p. 259) expressed his continuing belief that “neither mathematics nor political economy alone will ever be enough to provide the solution to the problems of interventionism and of protectionism: sociology, history, physiology are needed”. 19. Cournot (1838, pp. 173–174). 20. Ibid., p. 175. 21. Ibid., p. 176. 22. Ibid., pp. 176–177. 23. Ibid., p. 178. 24. Ibid., pp. 178–180. 25. Ibid., p. 180. 26. Ibid. 27. Pareto (1892b, pp. 5, 8). 28. Edgeworth (1889, pp. 540, 559–560). 29. Auspitz and Lieben (1889, §§80–82). 30. Pareto to Pantaleoni, 1st January 1892, see Pareto (1984b, p. 147). 31. Pareto (1892c). 32. Ibid., p. 207. 33. Ibid., p. 208. 34. Also, according to Pareto, ibid., p. 211, it is impossible “in any way to consider … the entire sum which the government derives from the duties as profit for the country” since “in the case of modern governments …. the more money they have, the more they spend”. 35. Ibid., p. 209. 36. Pareto (1892d, note to pp. 159–160). 37. These, obviously, are valid also for II. 38. Pareto (1896–1897, § 294, note 1). 39. Ibid., §855. 40. Ibid., §856, note 1. 41. Ibid., §862. 42. Ibid., §863, note 1. 43. Ibid., §721, note 2. 44. Ibid., §863, note 2. 45. Ibid., §863. 46. Specifically, dΛ=−psdRs−ptdRt−…; in equilibrium psbs+ptbt+…= pxxb= pyxb; pscs + ptct +…=pxxc = pxyc 47. On the basis that the prices of t, s, … do not change, ibid., §864. 48. Ibid., §867.

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49. Ibid., §§868–870. 50. Pareto (1895, p. 488). 51. Since ps(φ1a/pa)=φ1s… 52. Ibid., pp. 492–494. 53. Ibid., p. 495. 54. Ibid., pp. 492, 496–497. 55. Ibid., pp. 495–496. 56. Pareto (1896–1897, §882). The same reasoning had been already advanced by Pareto (1891b, p. 493) when he observed that, in the Italian steel industry, since customs revenue per worker were greater than the average salary, “it would be quicker just to allow Italians to purchase their requirements abroad and to pay the salary of the workers without making them work [or by assigning them] various other useful jobs of private or public utility”. Pareto (1891c, pp. 400–402) on the same topic pointed out that in 1889 the duty on iron and steel cost the country around 30 million francs, of which only 8 million (corresponding to the volume of imports multiplied by the duty) accrued to the state. This sum, divided between the 14,500 iron- and steelworkers, corresponded to 2100 francs per head, which amounted to twice the average value of their real earnings. 57. Pareto (1896–1897, §889). 58. Pareto (1895, pp. 482–484). 59. That is, 160/17. 60. That is, 151/18.4. 61. That is, 9.4/8.2. 62. Pareto (1894b, p. 143). 63. Pareto (1897, pp. 219–220). 64. Pareto (1898, p. 250). 65. Ibid., p. 251.

Bibliography Auspitz, Rudolf-Lieben, Richard. 1889. Enquiry into the theory of prices (Untersuchungen über die Theorie des Preises). Leipzig: Duncker und Humblot. Cournot, Augustin. 1838. Research on the mathematical principles of the theory of wealth (Recherches sur les principes mathématiques de la théorie des richesses). Paris: Hachette.

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Edgeworth, Francis Ysidro. 1889. On the application of mathematics to political economy. Journal of the Royal Statistical Society LII-4: 538–576. Humair, Cédric. 2004. Economic development and the central state (1815–1914). A century of Swiss customs policy at the service of the élites (Développement économique et État central (1815–1914). Un siècle de politique douanière suisse au services des élites). Bern: Lang. Maneschi, Andrea. 1993. Pareto on international trade theory and policy. Journal of the History of Economic Thought XV-2: 210–228. Mornati, Fiorenzo. 2018. Vilfredo Pareto: An intellectual biography. Volume I. From science to liberty (1848–1891). Basingstoke: Palgrave Macmillan. Pareto, Vilfredo. 1891a. (Letter from Italy) Lettre d’Italie. Journal des Economistes L, VIII-3: 409–418. ———. 1891b. Nando, known as Marzocco. Letter from a wine producer (Nando, detto Marzocco. Lettera d’un vignaiuolo). Giornale degli Economisti II, II-5: 492–496. ———. 1891c. (Letter from Italy) Lettre d’Italie. Journal des Economistes LVI, VIII-6: 390–402. ———. 1892a. Trade agreements (Traités de commerce) in Say-Chailley (1892): 1046–1050. Reprinted in Pareto (1984c, pp. 73–81). ———. 1892b. On an error committed by Cournot in dealing with political economy through the use of mathematics. (Di un errore del Cournot nel trattare l'economia politica colla matematica). Giornale degli Economisti III, IV-1: 1–14. ———. 1892c. Messrs. Auspitz and Lieben’s theory of prices and professor Walras’ observations (La teoria dei prezzi dei signori Auspitz e Lieben e le osservazioni del professor Walras). Giornale degli Economisti III, IV-3: 201–239. ———. 1892d. On the benefits of the railways for the nation (Dell’utile che procurano al paese le ferrovie). Giornale degli Economisti III, IV-2: 154–162. ———. 1894a. Report (Cronaca). Giornale degli Economisti IX: 301–306. ———. 1894b. [Course in applied political economy] ([Cours d'économie politique appliquée]). Lausanne: Self-Publication. Reprinted in Pareto (2005, pp. 133–183). ———. 1895. Mathematical theory of international trade (Teoria matematica del commercio internazionale). Giornale degli Economisti VI, X-4: 476–498. ———.1896–1897. Course in political economy (Cours d’économie politique). Lausanne: Rouge. ———. 1897. Protection and hunger (Protezione e fame). Il Secolo, August 11–12. Reprinted in Pareto (1989b, pp. 219–221).

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———. 1898. The duty on grain (Il dazio sul grano). Il Secolo, January 31– February 1. Reprinted in Pareto (1989b, pp. 249–252). ———. 1975. Correspondence, 1890–1923 (Epistolario 1890–1923), Complete Works, tome XIX-1, ed. Giovanni Busino. Geneva: Droz. ———. 1984a. Letters to Emilia Peruzzi 1878–1900 (Lettere ad Emilia Peruzzi 1878–1900), Complete Works, tome XXVII.II, ed. Tommaso Giacalone-­ Monaco. Geneva: Droz. ———. 1984b. Letters to Maffeo Pantaleoni 1890–1896 (Lettere a Maffeo Pantaleoni 1890–1896), Complete Works, tome XXVIII.I, ed. Gabriele De Rosa. Geneva: Droz. ———. 1984c. Myths and ideologies (Mythes et idéologies), Complete Works, tome VI, ed. Giovanni Busino. Geneva: Droz. ———. 1989a. Letters and Correspondence (Lettres et Correspondances), Complete Works, tome XXX, ed. Giovanni Busino. Geneva: Droz. ———. 1989b. Political writings. Reaction, liberty, fascism (Scritti politici. Reazione, libertà, fascismo), Complete Works, tome XVIII, ed. Giovanni Busino. Geneva: Droz. ———. 2005. Unpublished works and Addenda (Inédits et Addenda), Complete Works, tome XXXII, ed. Fiorenzo Mornati. Geneva: Droz. Say, Léon-Chailley Joseph, ed. 1892. (New dictionary of political economy) Nouveau dictionnaire d’économie politique. Vol. II. Paris: Guillaumin. Walras, Léon. 1965. In Correspondence of Léon Walras and related papers, 1884–1897, ed. William Jaffé. Amsterdam: North-Holland Publishing Company.

7 The Money

Unlike Walras, who considered the money to fall within the scope of pure economics,1 Pareto placed it squarely in the field of applied economics, while devoting some interesting theoretical speculations to themes such as its final degree of utility (Sect. 7.1), its circulation (Sect. 7.2), the problems of the Latin Monetary Union (Sect. 7.3) and the international currency system in the context of general equilibrium (Sect. 7.4).

7.1 The Final Degree of Utility for Money As early as March of 1892, after again stating his opinion that “Walras is right that in theory, all commodities need to be taken into consideration”, drew the “important conclusion … that the final degree of utility of currency cannot be considered as a constant”, a theorem for which he thought he “could provide a rigorous demonstration”, since he was equally aware that it “departs significantly from what has been believed hitherto”.2 In terms of formal analysis, let us suppose that an increase of dλ in the quantity of gold at an individual’s disposal would allow him to increase consumption of commodities A,B,… by dra, drb… and to reduce by drs, © The Author(s) 2018 F. Mornati, Vilfredo Pareto: An Intellectual Biography Volume II, Palgrave Studies in the History of Economic Thought, https://doi.org/10.1007/978-3-030-04540-1_7

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drt… his utilisation of assets S,T… (i.e. the sacrifice, or opportunity cost), then the variation in utility for him will be represented by

dU = ϕ a dra + ϕb drb + …− ϕ s drs − ϕt drt −…



or alternatively3

dU = ( pa dra + pb drb + …− ps drs − pt drt −…)ϕ a / pa



or again, supposing that padra + pbdrb + …− psdrs − ptdrt − …= dλ e φa / pa=μ,

dU = µ d λ ovvero µ = dU / d λ

from which he inferred that μ, the final degree of utility of gold, was the result of the “ophelimity gained by the individual [divided] by the small quantity of gold which procured it for him”.4 In the same way, if we suppose,5 in the manner of Walras, that the given quantity qa of capital asset A is devoted entirely to the purchase of a quantity r of other assets, at given prices defined in terms of A, we arrive at the budget equation

qa = pb rb + pc rc + …



where, if φa(qa) is constant (remaining, e.g. equal to quantity m), the n-1 equations

m = (1 / pb )ϕb ( rb ) = (1 / pc )ϕc ( rc ) = ….



will allow the determination of the n-1 variables r as a function of m and of the prices. These values of r could take the form

rb = ψ b ( mpb ) ; rc = ψ c ( mpc ) ;…



which would lend the following form to the budget equation

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qa = pbψ b ( mpb ) + pcψ c ( mpc ) + …

183



and this in turn would imply (if we assume qa as constant) that the addends must be constant, that is, that the corresponding quantities

pb rb = Ab ; pc rc = Ac ;…



must be so. In the light of these latter values,

m = (1 / pb )ϕb ( rb ) = (1 / pc )ϕc ( rc ) = ….



become

ϕb ( rb ) = ( mAb ) / rb ; ϕc ( rc ) = ( mAb ) / rc ;….



Pareto then repeated that the final degree of utility of the capital asset A is not constant because, were that the case, the consumer goods should: have the degrees of utility of the “highly particular” form shown above; possess a constant elasticity of demand; and be unchanging in number, given that the budget equation had taken the form

qa = Ab + Ac + …



Pareto in any case acknowledged that, in actual fact, there are many cases where the variation in the final degree of utility of currency is so slight that it can be ignored.6 In particular, since in the international market the prices of the goods are more or less fixed, then in regard to these it can be said that a low degree of final utility for gold for a given population suggests low degrees of utility for all the goods, which means that “this population is more or less glutted with every type of economic item”.7 However, since the prices of goods traded within small markets vary, then in relation to these goods a low final degree of utility for gold can be due not only to a low degree of utility of the goods traded but also to a high price level of these.8

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Moreover, and more generally, if and only if m is constant, the price curve for a good (e.g. such as b)

pb = (1 / m )ϕb ( rb )



will coincide with the curve of the final degree of utility for the good in question.9 Pareto followed these theoretical analyses with the statement that while he considered Walras’10 original theory of money “worthy of great admiration”, he did not agree neither with its aim, which was to limit variations in “social affluence as measured in money”11 as much as possible, or to make sure that “a certain average price value for social affluence does not vary”,12 nor with its proposed mechanism, which was “state intervention”.13 Actually, “the only thing that counts for the individuals making up a society is obtaining the highest possible level of overall ophelimity, and this does not depend on whether a certain price remains constant or not”.14 Noting lastly that, for Walras, the level of social affluence to be maintained constant was expressed by the equation

pb rb + pc rc + …



implying that the consumers would have increased (or diminished) the consumption of products whose price had diminished (or increased) and that the producers of the items whose price had diminished would incur losses exactly equal to the gains enjoyed by producers whose goods had increased in price, while Pareto expressed his fear that “these are precisely the fluctuations which are damaging, especially as they offer the politicians new opportunities to rob their own citizens”.15

7.2 Thoughts on the Circulation of Money In Pareto’s view, “money is a commodity like any other”, from which he concluded that “anyone who is in possession of it has the right to dispose of it as he wishes” and that any attempt to prevent the exercise of this

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right would be destined to fail, while still succeeding in “profoundly disturbing the entire economic life of the nation”.16 Pareto thus considered that “in order to ensure sound money,17 the government should have as little involvement as possible”.18 In particular, in regard to the minting of money, Pareto wanted the government to limit itself to controlling the weight and the denomination of coins, without attempting to determine the entity either of their value or of their quantity, both of which tasks should be left to the market,19 if the objective was to maximise social well-being, that is, a situation where the ratio between the final degree of utility and the price of money is the same as the equivalent ratio for all other commodities.20 Pareto then specified that the money serves as a unit of measurement of wealth (or numeraire), as a means of domestic and international payments (i.e. money in the original sense),21 as a store of value (or “fiduciary money … a commodity … where it is not the present utility which is considered but the future utility”).22 Pareto also noted the existence of “artificial money”, consisting of money issued illegally by private individuals but also by governments, particularly in the form of paper money23 and of fiat money, which private individuals are compelled to accept by government obligation and which banks in turn are obliged to exchange upon request for gold.24 Pareto noted that depending on whether the money is genuine (or artificial), the difference between the selling price and the marginal cost of production is zero (or is positive).25 Having established this, Pareto declared that in practice “the circulation of sound money should be made up of genuine and legitimate coins together with fiduciary fragments of little or no value”.26 Generally speaking, in Pareto’s view, “to honour one’s commitments and not to issue artificial money is not only the honest thing to do, but also represents the best investment a country can make”, bringing with it the benefit of very low interest rates as these are not compounded by indemnities against devaluation.27 If prices are expressed “in sound money”, the general equilibrium “is entirely predetermined”, while if they are expressed “in artificial money”, there is an additional variable, corresponding to the price of sound money in artificial money. At this point the determination of general equilibrium will require the reduction of the number of variables by establishing “the quantity of artificial money in circulation”, while the quantity of

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sound money will be determined by reference to all the other variables. From this Pareto concluded also that, while sound money can be issued freely, “the issue of artificial money must be regulated”.28 In reality, general equilibrium can equally well be established on the basis of artificial money as of sound money. However, prices will increase proportionally with the quantity of money only in the former case,29 while in the latter case prices will increase less than proportionally because the consequent reduction in its level of ophelimity will cause a reduction in the use of surrogates, thus limiting price increases.30 Moreover, according to Pareto, only a part of the money in circulation “is influenced by and follows market fluctuations”, with the remainder continuing to circulate. The non-fluctuating part of the money in circulation could therefore be replaced with paper money “with no repercussions for the economy”, on condition that the paper money were always convertible into gold “on sight and at par value”.31 Pareto further specified that, in a context of artificial money within a closed economy,32 an increase (or decrease) in the supply of money would give rise to a proportional increase (or reduction) in prices only if the two states of general equilibrium under consideration were independent, which, however, would not be the case due to the existence of contractually fixed prices. Moreover, since, in that case, prices of the majority of goods would in any case increase (or fall), holders of the contracts in question could meet their obligations through the use of a lower (or higher) quantity of goods than that specified in the contract, so that creditors (or debtors) “are despoiled”, in contrast with the neutral outcome in terms of distribution specified by the quantitative theory. Pareto also added that increases in the quantity of artificial money “cause increases in production and in exchanges, often leading to economic crises which can destroy a greater or smaller quantity of wealth”.33

7.3 The Problems of the Latin Monetary Union Pareto was convinced that gold and silver had become “the sole monetary metals through natural selection”.34 They possess, as money and as commodities, two differing final degrees of utility which are equalised, under

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conditions of free coinage, by means of transformations from money to commodities and vice versa, performed naturally by the public.35 Monetary history36 also illustrates the empirical law whereby “bad money drives out good” (Gresham’s law),37 which entails the conclusion that bimetallism is possible only in “exceptional cases where the values of silver and of gold naturally maintain, over a certain number of years, the same ratio to each other as would have been legally imposed”.38 It would be possible to maintain bimetallism on a stable basis only if it were universal, but pure economics cannot teach us whether it “would be of real benefit to humanity”.39 On the other hand, as “no-one would pay in gold, if money of lower value could be used”, artificial money and sound money can coexist only if the quantity of artificial money is lower than the quantity of sound money.40 In this context, in August 1892 Pareto stated that his “position on the monetary issue corresponds to the orthodox view in political economy, i.e. monometallism based on gold” and that he did not thus accept “any type of subterfuge for supporters of fiat money” and concurred with the Latin Monetary Union41 only “because in practice it amounts to monometallism based on gold with the auxiliary of silver”.42 More particularly Pareto observed that “monometallism based on gold is the monetary system of all the major civilised peoples. The trend appears evident and the general introduction of a monetary system with gold as numeraire seems assured”.43 In line with this position, in the spring of 1891 Pareto had commented disapprovingly that the owners of the silver mines in the United States (one of the biggest producers of the metal), had succeeded, through a group of congressmen whose election they had engineered, in gaining approval for the law of the 14th of July 1890 (the so-called Sherman Silver Purchase Act) obliging the government to “engage in major purchases of silver ingots”, thereby increasing the price of silver, and now were also pushing for the freedom to mint silver, which would further increase the price.44 Once again in keeping with his philosophy of monometallism based on gold, Pareto in April 1893 praised the new president, the democrat Stephen Grover Cleveland, for his plan to increase the purchasing power of the national currency45 through a ban on state purchases of silver.46

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In October 1892 Pareto disputed Italian criticisms of the Latin Monetary Union on the basis that it was rather “France and Switzerland who might complain about Italy having obtained a forced loan by exporting its silver coins to them”.47 Pareto continued by praising Switzerland for having issued relatively few silver coins and forecast that the Confederation, on the basis of its geographical position, its neutrality and “the predisposition of its inhabitants for banking and commerce”, if it could also gain “full confidence in its money, might achieve a position of pre-eminence as a banking centre”, just as England, which, through its “sound money” had become “the clearing house for the international markets”.48 In Pareto’s view, Switzerland was actually the country which had derived the least benefit from the Union. There were in fact 59 million francs’ worth of foreign silver coins, mostly Italian, circulating in the Confederation which could have been bought, on the free market, for 32 million francs (a silver coin being worth just 2.75 francs), which suggested a free loan made by Switzerland to the other member states amounting to 27 million francs.49 After Switzerland, France was the country which had derived the least benefit from the Union, despite bearing “all the burden … to satisfy the utopias of the bimetallists”.50 France continued to hold large quantities of silver which it could not sell for fear of provoking a collapse in the price, but between 1865 and 1885 the price nevertheless fell by one-fifth. Moreover, the country had allowed itself to be flooded with foreign coins worth 500 million francs, without taking precautions regarding the procedure for redemption of these on the part of the issuing countries, and these had a value on the open market of only 300 million francs, thus generating a free loan of 200 million.51 On the other hand, the countries which appeared to have derived the most benefits from the Union were Belgium and Italy. The number of Belgian silver coins circulating abroad was in the region of 500 million but, in Pareto’s view, since Belgium was “a prosperous country”, it would honour its obligations.52 As regards Italy, between 400 and 500 million worth of its silver coins were in circulation outside the country, representing a free loan which had encouraged “the abuse of credit”, which had been one of the causes of the prolonged economic crisis in Italy in the early1890s.53

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Nevertheless, Pareto did not consider the dissolution of the Union desirable because “anything which tends to unite different peoples will have a beneficial influence on the progress of civilisation”. More specifically, since “there would be great benefits if everywhere the same weights, the same measures and the same currency were used … and we should seek to extend [the Union] to other countries” but, to attain this end, the process would need “to be implemented in good faith and to be based on truth”.54 A step in the right direction was represented by the Italian government’s recent proposal, backed by Switzerland but refused (incomprehensibly, in Pareto’s view) by France, to exclude small denomination coins from the Union and also, Pareto hoped, silver coins. In this manner, each nation would have to retain these coins, or if they wished to allow them to circulate abroad, should undertake to redeem them, not at the dissolution of the Union, “but as and when they were presented to the banks”.55

7.4 T  he International Monetary System in the Light of General Equilibrium The term exchange rate refers to the price, in the currency of nation X, of a unit of money of nation Y. If the two nations use the same currency (e.g. gold), the exchange rate cannot vary beyond the gold points, ­representing the material cost of transporting gold from X to Y or vice versa,56 as otherwise payments would be made by the direct transfer of gold instead of by other more costly means such as fiduciary paper money, top bills of exchange, and so on. If the balance of trade of both the countries with the same currency is in equilibrium, the exchange will take place on equal terms, while it will be unfavourable (or favourable) to the nation whose balance of trade is negative (or positive).57 With this in mind, the theory of the international monetary system (referred to by Pareto as “theory of foreign exchange”, aiming to “explain how, when the monetary equilibrium is disturbed, it automatically re-­ establishes itself ”58), was presented by Pareto with reference to a hypothetical country Y and the rest of the world X, allowing him to focus on the consequences that the export and import of the numeraire commodity

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(which could indeed be gold, but “without in any way prejudicing the issue of the choice of monetary standard”59) would have in Y.60 The quantity of gold required by Y is represented by the following61:

Rm = am Ra + bm Rb + …



where the coefficients am, bm,… could also be variable. On this basis, in the quantitative theory of money, if Y exported (or imported) gold (which hypothetically was not produced there62), the reduction (or increase) in the quantity existing in the nation would cause its final degree of utility to increase (or fall) so that63 it would cause the prices of all other goods produced in Y to fall (or increase). This in turn would, given constant prices for goods produced in X, constitute an incentive (or disincentive) for exports from Y and a disincentive (or incentive) for its imports, leading automatically to a positive (or negative) balance of trade such that the nation in question would recover (or be deprived of ) the quantity of gold exported (or imported),64 and “this in itself corresponds roughly to the facts”, indicating that the general equilibrium obtaining prior to the variations in the quantity of gold was stable, “suggesting that, if perturbed, it generates forces tending to re-establish it”.65 In an interesting development of general equilibrium,66 Pareto found that if the prices of goods exported by Y are reduced to the quantity67

δ pb = (1 − x ) pb , δ pc = (1 − x ) pc , …



then exports of these goods will increase by

gbδ pb , gcδ pc , …,



which will require an increase in the production of B,C,…., leading to an increase of

∆Rt , ∆Rs …



in demand for the productive services S, T …This, in turn, will give rise to an increase in the prices of these latter corresponding to

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  The Money 



lt ∆Rt , ls ∆Rs ,…



and this, again, will lead to the following increases in the prices of B,C,….

∆pb , ∆pc , …



which will, variously, reduce the quantities of B,C,… consumed in Y by the following amounts

kb ∆pb , kc ∆pc , …



and will diminish the reduction in the prices of goods exported by Y to the following values

(δ pb − ∆pb ) , (δ pc − ∆pc )…

implying that exports of B,C,… will increase only by the following amounts

gb (δ pb − ∆pb ) , gc (δ pc − ∆pc )…



Moreover, if the following equations obtain in Y:

Rt = bt Rb + ct Rc + …; Rs = bs Rb + cs Rc + …;…



then the following equations will be produced

∆Rt = bt ∆Rb + ct ∆Rc + …; ∆Rs = bs ∆Rb + cs ∆Rc + …;… If the following equations also obtain:



pb = bt pt + bs ps + …; pc = ct pt + cs ps + …;…

then the following equations will be produced





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∆pb = bt ∆pt + bs ∆ps + …; ∆pc = ct ∆pt + cs ∆ps + …;…



whence, by substituting the values Δpt, Δps,… we arrive at the equations

∆pb = bt lt ∆Rt + bs ls ∆Rs + …; ∆pc = ct lt ∆Rt + cs ls ∆Rs + …;…



from which, by substituting the values for ΔRt,… we arrive at the equations68

∆pb = Bb ∆Rb + Bc ∆Rc + …; ∆pc = Cb ∆Rb + Cc ∆Rc + …;…



From the values69

Ra = Ra + ρ a ; Rb = Rb + ρb ; …



the following equations are produced by differentiation

∆Rb = ∆Rb + ∆ρb ; ∆Rc = ∆Rc + ∆ρ c ; …



whence, by substituting the values for ΔR and the Δρ, the following equations are obtained



∆Rb = −kb ∆pb + gb (δ pb − ∆pb ) = gbδ pb − ( kb + gb ) ∆pb = gbδ pb − kb′ ∆pb ;





∆Rc = −kc ∆pc + gc (δ pc − ∆pc ) = gcδ pc − ( kc + gc ) ∆pc = gcδ pc − kc′ ∆pc .



From these, assuming that the values for Δp are lower than the corresponding values for δp, we obtain the equations

∆Rb = gbδ pb ; ∆Rc = gcδ pc ; …



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which, substituted in the Δpb, Δpc,…, lead us to the equations

∆pb = Bb gbδ pb + Bc gcδ pc + …; ∆pc = Cb gbδ pb + Cc gcδ pc + …;…



which can be reformulated as



∆pb = Bb gb (1 − x ) pb + Bc gc (1 − x ) pc + … = (1 − x ) ( Bb gb pb + Bc gc pc +…) = (1 − x ) π b ; ∆pc = (1 − x ) π c ; …

Hence, the definitive values for the reduction in prices of exported goods will be the following

δ pb − ∆pb = (1 − x ) ( pb − π b ) ; δ pc − ∆pc = (1 − x ) ( pc − π c ) ; …



In general, the export of gold and the ensuing repercussions on the general equilibrium will also entail the following price reductions with regard to productive services

(δ pt − ∆pt ); (δ ps − ∆ps )…

The only exception to this is gold, the export of which will, in Pareto’s view, bring about not only the above-mentioned increase in final degree of utility but also an increase in price which will be counteracted by the resulting incentive for the import of gold, all of which will culminate in70

δ pm = 0



whence it is possible to infer that the positive quantity ∆pm = lm ∆Rm = lm ( bm ∆Rb + cm ∆Rc + …) = lm ( bm gbδ pb + cm gcδ pc + …)

= (1 − x ) lm ( bm gb pb + cm gc pc + …)



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F. Mornati

represents the variation (in which neither the sign nor the value are, consequently, arbitrary) in the discount rate (corresponding to the price for the use of the money) determined by the export of gold. If, on the other hand, the export of gold is offset through the issue of paper money,71 the prices will not be reduced and so, in order to finance the remaining deficit in the balance of payments, the export of gold will continue until the country’s currency in circulation is wholly in the form of paper money. At this point, export prices will be reduced not formally but practically, through the devaluation of the country’s paper money in relation to gold (the so-called agio of gold).72 More in detail,73 if the export of gold were offset by the issue of paper currency, then in order to revert to metal currency it would be necessary to restore the lowest prices required by the equilibrium of the balance of payments and this would be achieved by raising the value of the national currency, which could be effected through a reduction in the global quantity of coinage and/or boosting demand by “growth of trade and industry”. From this, Pareto concluded, further confirming a position he had first developed in a non-formal manner as early as 1880,74 that the use of “a foreign loan of gold to escape from fiat money would be a vain and dangerous procedure”. Another issue regarding the international monetary system which was tackled by Pareto was the “allocation of sound money on open markets”.75 If general equilibrium were established separately in each of two markets X and Y and these later began trading, not all the goods produced should be traded (because this would lead to the re-establishment of general equilibrium applying to the two markets together) but only σ of these, gold included. Hence there are σ+1 new variables: the quantities exchanged of the σ commodities and the price, expressed in the numeraire of X, of the numeraire of Y. These variables will be determined by reference to the following equations, also new: the correspondence of the selling price in X and in Y for each of the σ commodities; the correspondence of sums received and paid by each of the countries (the resulting equilibrium of the balance of payments is, by definition, the same for both countries). The subsequent subdivision of the gold between the countries “as determined by free competition” will “lead to the maximum ophelimity” for both.76

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Notes 1. On Walras’ theory of money, Baranzini (2005). On the Lausanne school’s theory of money, P. Bridel, Money and General Equilibrium Theory: from Walras to Pareto (1870–1923), Cheltenham, 1997. 2. Pareto to Maffeo Pantaleoni, 19th March 1892, see Pareto (1984, p. 197). 3. Since in equilibrium we have φa/pa = φb/pb; …φa/pa=φs/ps; φa/pa=φt/pt; … 4. Pareto (1896–1897, §385, note 2). 5. Pareto (1892a, pp. 493–494). 6. Ibid., p. 496. 7. Ibid., p. 498. 8. Ibid., pp. 498–499. 9. Pareto to Pantaleoni, 26th May 1893, see Pareto (1984, p. 375). 10. Pareto (1893a, p. 23). On the other hand, Pareto to Maffeo Pantaleoni, 17th October and 13th November 1892 see (Pareto, pp.  301, 316), stated that in his view the book on money by the Bologna free-trader economist Tullio Martello was “more imposing … than anything else he [Pareto] had read on [the] subject”. In publishing Martello (1883), Martello’s aim had been “to place natural economic law beyond the whims of government criticism and judgement” by setting “freedom and integrity in transactions” against the various monetary systems imposed by law, including monometallism (p. II). Actually, the truth is that it is only the physical and chemical properties of gold and silver which make them suited to monetary (or industrial) uses (pp. 55, 75). On this basis Martello, turning his attention to bimetallism, pointed out that under conditions of free exchange, gold and silver could circulate simultaneously as money only if the ratio between their nominal values were exactly the same as that for their commercial values, which could arise only by chance (pp. 185–186). Hence, the simultaneous circulation of the two metals as money would be possible only in the absence of free trade, implying that the state possessed a monopoly of both, which would reduce the circulation of metals to the equivalent of fiat money, but would be much simpler to manage (pp. 193–196). Thus, true bimetallism would correspond to the situation where both metals alternate in circulation, with only the momentarily less costly of the two circulating at any given time (pp. 134–135). The nominal ratio itself is an absurdity, because it seeks in vain to violate the law of value which states that an

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F. Mornati

exchange will be concluded if the parties concerned hope thereby to gain a positive net utility. Given that judgements concerning utility are subjective and hence extremely variable, this will give rise to similarly variable rates of exchange (p. 199). For this reason, Martello comes out in favour, not of monometallism, which “reduces and weakens the mechanism of exchange, …slowing down and delaying the circulation of wealth in the economy” (p. 293), but of “allowing the people to select as a medium of exchange that commodity with they deem best suited to the purpose”. Thus, the optimal monetary system in Martello’s view is polimetallism, which would involve the free circulation of any metals which the participants spontaneously adopted as a currency, without government interference either in the choice of metals or in the fixing of their exchange rates (p. 283–284). 11. Because “nobody has bothered to demonstrate that the small benefit that might be gained by artificially controlling the non-periodic variations in social affluence might not be accompanied by greater ills triggered by such interference with natural laws”, Pareto (1893a, p. 24, note 1). 12. Pareto (1896–1897, §390). 13. Because “history shows that when governments interfere with the coinage it is generally for the purpose of debasing it”, whereas “it would appear beneficial for the good of society” to avoid “adjustments to the money”, Pareto (1893a, p. 24, note 3). Similarly, Pareto to Léon Walras, 2nd August 1893, see Pareto (1975, p. 226). 14. Pareto (1896–1897, §390). 15. Pareto (1893a, p. 33, note 1). 16. Pareto (1893b, p. 631). 17. That is, a money whose content of precious metal is equal to that specified by law. 18. Pareto (1893–1894, p. 96). 19. Ibid., p. 118. 20. Ibid., pp. 147–148. 21. Ibid., p. 91. Pareto noted that historically, “the numeraire become[s] the money”. 22. Ibid., p. 89. 23. Ibid., p. 96. The beneficiaries of the issue of paper currency are generally debtors, including the government (which pays less interest on public debt) and entrepreneurs (who pay lower salaries until such time as wages move into line with the new, higher, prices, Pareto (1896–1897, §327).

  The Money 

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The victims, that is, the creditors, seek to safeguard their own interests. If they are moneylenders, they will insist on “a substantial insurance indemnity” which will obviously cause the interest rate to rise, Pareto (1896–1897, §330). According to Pareto (1896–1897, §344), countries will abstain from issuing artificial currency only if they see an advantage in maintaining sound money, as in the case of England at that time. 24. Pareto (1896–1897, §274). 25. Ibid., §297, note 1. 26. Pareto (1893c, 505). 27. Pareto (1896–1897, §464). 28. Ibid., §§287–288. 29. Ibid., §290. In addition, the quantitative theory of money “is severely perturbed” in the sense that variations in price are not perfectly proportional to those in the quantity of money, Pareto, ibid., §299. The theory is more accurate when the variations in the supply of money are more significant, Pareto, ibid., §300. 30. Ibid., §292. 31. Ibid., §§303–305. 32. Ibid., §308. Countries making use of artificial money cannot exchange it abroad due to the fact that the extreme variability of rates renders it unacceptable, ibid., §312. 33. Ibid., §308. 34. Pareto (1893–1894, p. 90). 35. Pareto (1892b, p. 28). 36. Investigated minutely in Pareto (1893–1894, pp. 89–115) and in Pareto (1896–1897, §§333–371). 37. Pareto (1896–1897, p.  116). Gresham’s law was viewed by Pareto (1896–1897, §370) as a corollary of the theorem of general equilibrium stability. Certainly, if the latter is based on a given quantity of money, any increase in this quantity will have to leak from the economy either by exportation or by demonetisation “and it is evident that it will be the sound money, having a higher value, that will go out of circulation”. 38. Pareto (1893–1894, p. 116). 39. Ibid. 40. Pareto (1896–1897, §§320–321). 41. The Union was formed in 1865 by France, Belgium, Italy and Switzerland, with Greece joining two years later. 42. Pareto a Pantaleoni, 9th August 1892, see Pareto (1984, pp. 264–265).

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43. Pareto (1896–1897, §372). 44. Pareto to Francesco Papafava, 25th April 1891, see Pareto (1989b, p. 129). 45. Pareto (1893d, 608). 46. Pareto (1893e, p. 313). 47. Pareto a Pantaleoni, 2nd October 1892, see Pareto (1984, pp. 264–265). Pareto was alluding to the fact that the fiat money regime obtaining in Italy had de facto pushed Italian silver coins, which were seldom used in payments due to their high value in comparison to bank notes, into France and Switzerland, from whence they would need to be redeemed by Italy only at the moment of dissolution of the monetary union. 48. Pareto (1893–1894, p. 108). 49. Pareto (1893f, pp. 15–16). 50. Ibid., p. 20. 51. Ibid., pp. 20–23. 52. Ibid., p. 24. 53. Ibid., pp. 24–25. 54. Ibid., p. 31. 55. Ibid., p. 32. 56. Pareto (1896–1897, §§284, 293). 57. Pareto (1893–1894, p. 141). 58. Pareto (1895a, p. 481). 59. Pareto (1895b, p. 65). 60. Pareto (1984, pp. 154–155). Pareto to Pantaleoni, 13th January 1894, see Pareto (1984, p. 412) described this idea as “an example of the new laws discovered by the new theories”. 61. Pareto (1894, p. 155) 62. Ibid., p. 159. 63. Once again following from φm(rm) = (1/pb)φb(rb) = (1/pc)φc(rc) = …. 64. Pareto (1894, pp. 155–156); Pareto (1895b, p. 69). 65. Ibid., p. 69; Pareto (1894–1894, p. 143); Pareto (1896–1897, §313). 66. Pareto (1894, pp. 158–161). 67. Where x represents the ratio between the quantity of coins remaining in Y following the export of gold and the quantity of coins existing before the export of gold, ibid., p. 158. 68. Because Δpb = btltΔRt+bslsΔRs+… = btlt(btΔRb+ctΔRc+…)+bsls(bsΔRb+csΔ Rc+…)… = b2tltΔRb+btltctΔRc+…+b2slsΔRb+bslscsΔRc+… = (b2tlt+b2sls+…) ΔRb+(btltct+bslscs+…) ΔRc+… = BbΔRb+BcΔRc+…

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69. Where the values for Ra, Rb,… represent the quantities produced in Y and the values for Ra, Rb,…represent the quantities consumed there, while the values for ρa, ρb, ρc,…, if positive (or negative), represent the quantities exported (or imported). 70. Ibid., pp. 156, 162. 71. That is, to assist the country’s manufacturers who have been damaged by the reduction in the prices of their products, Pareto (1895b, p. 70). 72. Pareto (1894, p. 157). 73. Ibid., pp. 168–169; Pareto (1896–1897, §325). 74. Mornati (2018, pp. 160–163). 75. Pareto (1896–1897, §295, note 1). This topic had already been covered, less succinctly, in Pareto (1894). 76. Pareto (1896–1897, §295).

Bibliography Baranzini, Roberto. 2005. Léon Walras and the money without veil (1860–1886) (Léon Walras e la moneta senza velo (1860–1886)). Turin: Utet Libreria. Bridel, Pascal. 1997. Money and general equilibrium theory: From Walras to Pareto (1870–1923). Cheltenham: Elgar. Martello, Tullio. 1883. The money and the errors which surround it (La Moneta e gli errori che corrono intorno ad essa). Florence: Le Monnier. Mornati, Fiorenzo. 2018. Vilfredo Pareto: An intellectual biography. Volume I. From science to liberty, 1848–1891. Basingstoke: Palgrave Macmillan. Pareto, Vilfredo. 1892a. Considerations on the fundamental principles of pure political economy.II (Considerazioni sui principi fondamentali dell’economia politica pura.II). Giornale degli Economisti III, IV-6: 485–512. ———. 1892b. The new economic theories, Letters to the editor of the “Monde économique”.X (Les nouvelles théories économiques. Lettres au directeur du “Monde économique”.X). Monde économique, October 8, pp  397–398. Reprinted in Pareto (1987, pp. 27–29). ———. 1893a. Considerations on the fundamental principles of pure political economy.IV (Considerazioni sui principi fondamentali dell’economia politica pura.IV). Giornale degli Economisti IV, VI-1: 1–37. ———. 1893b. Silver’s coins (Gli spezzati d’argento). Il Secolo, July 6th–7th. Reprinted in Pareto (1989a, pp. 630–632). ———. 1893c. Report (Cronaca). Giornale degli Economisti IV, VI-6: 504–508.

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———. 1893d. President Cleveland’s speech (Il discorso del presidente Cleveland). Il Secolo, April 7th–8th. Reprinted in Pareto (1989a, pp. 607–610). ———. 1893e. Report (Cronaca). Giornale degli Economisti IV, VI-4: 313–320. ———. 1893f. The future of Latin monetary union (L’avenir de l’Union monétaire latine). Bibliothéque universelle et Revue suisse October: 5–34. ———. 1893–1894. (First course in applied political economy, academic year 1893–1894) (Premier cours d’économie appliquée, année académique 1893–1894). Lausanne: self-publication. Reprinted in Pareto (1982). ———. 1894. Mathematical theory of foreign exchange (Teoria matematica dei cambi forestieri). Giornale degli Economisti V, VIII-2: 142–173. ———. 1895a. Mathematical theory of international trade (Teoria matematica del commercio internazionale). Giornale degli Economisti VI, X-4: 476–498. ———. 1895b. Mathematical theory of foreign exchange (Théorie mathématique des changes étrangers) in Association Française pour l’Avancement des sciences (French Association for the Advancement of Science), Congrès de Caen (Caen Congress). Paris: Au Secrétariat of the Association. Reprinted in Pareto (1989, pp. 65–75). ———. 1896–1897. Course in political economy (Cours d’économie politique). Lausanne: Rouge. ———. 1975. Correspondence, 1890–1923 (Epistolario 1890–1923), Complete Works, tome XIX-1, ed. Giovanni Busino. Geneva: Droz. ———. 1984. Letters to Maffeo Pantaleoni 1890–1896 (Lettere a Maffeo Pantaleoni 1890–1896), Complete Works, tome XXVIII.I, ed. Gabriele De Rosa. Geneva: Droz. ———. 1982. [First course in applied political economy, academic year 1893–1894] [Premier cours d’économie appliquée, année académique 1893–1894]. Geneva: Droz. ———. 1987. Marxisme and pure economics (Marxisme et économie pure), Complete Works, tome IX, ed. Giovanni Busino. Geneva: Droz. ———. 1989a. Political writings. The development of capitalism (Scritti politici. Lo sviluppo del capitalismo), Complete Works, tome XVII. ed. Giovanni Busino. Geneva: Droz. ———. 1989b. Letters and Correspondence (Lettres et Correspondances), Complete Works, tome XXX, ed. Giovanni Busino. Geneva: Droz. ———. 1989c. Statistics and mathematical economics (Statistique et économie mathématique), Complete Works, tome VIII. ed. Giovanni Busino. Geneva: Droz.

8 Other Topics in Applied Economics

In the Course in Political Economy and in the writings immediately preceding it, Pareto focused his attention, albeit less extensively, on other topics in applied economics such as the demographic question (Sect. 8.1), questions relating to the science of finance (Sect. 8.2), the functional distribution of national income (Sect. 8.3) and economic crises (Sect. 8.4).

8.1 The Demographic Question1 Prompted by his teaching duties, Pareto decided to return to the demographic issue2 and to develop it more exhaustively. His starting point was a graphical representation of the Italian population involving a system of three axes, which he adapted from the Italian statistician Luigi Perozzo.3 The population was then represented by the three-dimensional space obtained by tracing from each point on the curve indicating births (which showed the number of births for each year) the corresponding life expectancy curves (showing the numbers surviving among those born each year).4 Pareto demonstrated that the population between the ages of 20 and 50 © The Author(s) 2018 F. Mornati, Vilfredo Pareto: An Intellectual Biography Volume II, Palgrave Studies in the History of Economic Thought, https://doi.org/10.1007/978-3-030-04540-1_8

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(i.e. the working population who maintained the rest of the population) was equal to just over 40% of the total if the number of births remained constant, declining to 40% if the number of births grew in line with the geometric progression 1.01.5 Basing himself on various empirical studies, Pareto concluded that demographic variations were determined at least in part by economic variations,6 from which he inferred that the production of human capital, that is, people, is influenced by the law which states that “savings are directed towards the production of those types of capital most important in bringing about the highest possible degree of ophelimity”.7 From the economic point of view, “the maximum benefit for a population” is achieved by the minimisation of infant mortality united with “a high level of mortality” when people begin to consume more than they produce.8 However, Pareto immediately specified that support for the elderly constituted “one of mankind’s first moral responsibilities” in its emergence from a state of barbarism and he consequently lauded the contemporary “movement for the establishment of pension funds”, with the proviso that, since these represented “an extravagance for society”, the movement could achieve its aims only by increasing the productivity of labour and/or by reducing the dissipation of the fruits of this labour (e.g. in military expenditure).9 Theoretical studies regarding the production of human capital took as their starting point the idea that this type of production is not motivated by the possible profits that can be derived from it. Such studies should therefore be conducted by reference to the theories of Malthus, that is, the idea that every living species has “a reproductive potential higher than is reflected in observed patterns of growth”, implying that the living population at any given moment is the result of two forces. The first of these, the generating force, is the one which drives growth, while the other, opposed to it, limits this growth in accordance with the constraints of available subsistence,10 bearing in mind also that “real rates of reproduction [cannot] equal the maximum rate which the species is capable of ”, as this would be incompatible with the limited space available on earth.11 The opposing force12 in turn consists of a combination of preventive checks (i.e. those limiting the birth rate)13 and repressive checks (i.e. those increasing the death rate).14 It was the complementary nature of these two checks, of which the first appears to have greater influence than

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the second in advanced countries,15 which led to Malthus’ well-known admonition “not to bring too many children into the world, if you do not wish to see them decimated by death”.16 Pareto pointed out however that Malthus was wrong in claiming that social welfare depended only on limiting increases in population, since it also depended on political economy in a broad sense, as this determined the quantity of subsistence available.17 Pareto thus insisted, in agreement with Tullio Martello, that an excess of population could also be interpreted as the effect of a scarcity of subsistence caused by misconceived economic policies.18 Generally speaking, “the birth rate, the death rate and economic circumstances are interconnected by … extremely complex laws and it is impossible to say which of these is the cause of the others”. Hence, “in conditions of equilibrium, if economic circumstances remain constant, any growth in the birth rate will cause the death rate to grow too, and, in truth, both these phenomena interact with the economic context”.19 The conclusion is that “the maximum level of ophelimity can be obtained only when the supply of human beings is proportional to the demand for human capital”, implying that “the egotism of parents, bringing more children into the world than they are realistically able to support, is the cause of the majority of human ills”.20 In the spring of 1896, Pareto stated that “the followers of Malthus must also accept the methods without which Malthusianism is an empty term”21 and, a few months later, he repeated that he did not wish “to have children, because he [didn’t want] the responsibility of bringing another human being into this evil world”.22 In the same way, Pareto subjected to critical examination the untested notion that a country with low infant mortality (e.g. Switzerland) had an “appreciable economic advantage” compared to a country with higher infant mortality (such as Bavaria), because, in order to produce the same number of adults, it would have to generate and raise a smaller number of chidren.23 Pareto, on the basis that a person, after the 20th year of life, should produce at least as much as he or she consumed, made reference to the well-known German statistician Ernst Engel’s estimate of the costs of raising a new-born child, according to which pregnancy cost 100 marks and the expense thereafter increased by 10 marks for each succeeding year, as well as to the mortality tables which had been published by

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Luigi Bodio.24 Thus, for 100,000 births the cost would be 10 million marks and for the 81,532 children still alive in Switzerland after the first year of life the cost would be 8,968,520 marks, and so on. Adding up all the expenses of raising children to the age of 20 and dividing by the number of surviving children at that age, the average cost which emerges is 4429 marks in Switzerland and 4458 in Bavaria.25 As there were 68,899 20 year olds in Switzerland as against 57,190 in Bavaria, Pareto observed that Switzerland, with a 20% greater number of 20  year olds, had an expenditure which was only 1% lower per head, which was explained both by reference to the idea that “countries with low rates of infant mortality retain many children in the early years who die before becoming adults” and to the fact that expenditure on children who die at a very early age is obviously less than expenditure on those who die at a later age.26 The near equivalence observed in the cost of raising children to the age of 20  in a number of countries might be interpreted as “a fairly momentous natural law”.27 Similar considerations apply also to estimates of the capital a country loses on account of emigration. The wave of emigration from Germany during the 1880s was thus calculated to have cost the country 4.4 billion francs, with Italian emigration in the period 1887–1893 calculated to have cost Italy 3.3 billion francs.28

8.2 On the Science of Finance29 According to Pareto, “trying to find a just tax … is an almost impossible task”, since “only considerations of utility and of opportunity” apply.30 In fact, Pareto was convinced that the government sought to “grab as much as it can from taxes …. to pay off its pals and to grease the palms of politicians”, with no “other limit than the resistance of taxpayers”. So, seeing as “the bulk of the proceeds is wasted, lost, destroyed”, he reiterated that “the best system of taxation is simply that of reducing it”,31 especially as, in direct contradiction of Walras, he was of the view that “in many countries the state, by imposing higher and higher taxes, hinders any ­improvement in the people’s conditions”.32 Lastly, Pareto confirmed his belief that “nothing could be more false than the idea that taxation is

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proportional to necessary expenditure. On the contrary, it is expenditure itself which is proportional to the tax proceeds made possible by the patience of taxpayers”.33 Nevertheless, while retaining his anti-taxation stance, Pareto, in contrast to his friend Martello, whose volume Progressive Taxation in Theory and in Practice (L’imposta progressiva in teoria ed in pratica) had appeared at that time, thought that the progressive tax, in regard to the merits of which he remained undecided “for now” (in 1895), “is neither absurd in theory nor impossible in practice”.34 In particular, he considered a progressive tax, whereby the tax rate increased in a continuous manner without taking away the whole of a person’s income, to be feasible.35 More generally, Pareto in any case thought that in order to procure the highest possible proceeds from taxation, the best approach was fiscal moderation, avoiding placing taxpayers in the dilemma of “not telling the truth or being ruined”.36 In relation to the case of Italy, Pareto pointed out that “taxes have three failings: they are too high in absolute terms, they hinder the creation of wealth, instead of targeting it after it has been created and, lastly, they are paid only in part to the state, with the rest going to private individuals”. This latter was a reference to customs protection, suggesting that the state should collect the profits enjoyed by protected producers (8 million lire per annum for refiners of sugar alone), and, better still, abolish customs duties, thus relieving taxpayers of 200 million lire of expenses, half of which it could claim in taxes and use to bolster public finances.37 From a historical viewpoint, Pareto thought, once again in regard to Italy, that the increase in proceeds from sales taxes from 437 million lire in 1871 to 806 million lire in 1889 suggested that these “have furnished the point of least resistance in augmenting the revenues”, especially as this was accompanied by a worsening economic situation for the population.38 Pareto also noted that during the 1880s the landowners had been “powerful enough” to secure a reduction in land taxes,39 while house owners had accepted a small increase in tax on their properties only because they were able to pass this on to their tenants, while declaring, with the connivance of the state, much lower sums in rent than they had actually received.40

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Tolerance was also shown to evasion of income tax (i.e. the tax on income) on the part of those close to the politicians, so that this tax “falls back upon the plain people and on those who enjoy no power and no patronage”.41 Pareto also observed, “maybe it was a coincidence, but the fact is that the extension of the franchise has brought an increase in the impositions of the state”, alluding to the fact that the introduction of the 1882 law extending the vote by 600,000 to 2 million people in 1882 and to almost 3 million in 1892 had been accompanied by an increase in takings from indirect taxes from 443 million lire in 1880 to 561 million in 1886 and to 628 million in 1890.42 At the beginning of 1898, Pareto made a comparative statistical summary of Italian and Swiss public finances, concluding that “in Italy they seek to meet excessive expenditure by encumbering the population with income taxes” while “in Switzerland necessary expenditure is covered by taxes on income”.43

8.3 N  ew Considerations on Functional Distribution: Rent, Wages and Rates of Interest Here too Pareto, returning once again to some of the scattered thoughts initiated some years earlier,44 illustrated the results of further investigations into functional distribution which were more exhaustive than previously. In general, Pareto considered it “a very common error to believe that in a negotiation one party can only gain if the other loses”, while in reality “the greater the quantities of utility produced the more they will benefit both parties”, concluding that “the biggest problem in political economy is to identify what circumstances would lead to the acquisition of the greatest possible quantity of utility with the least effort”.45 He also noted that the functional distribution of income “cannot be determined independently of all the other variables in the economic panorama”.46 In Pareto’s view, if competition is “unconfined” and the mobility of capital is “absolute”, the production of utility generates a rent exactly equal to “the current return on capital”, that is, a null yield. This means

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that the rent is not null (it can be negative as well as positive, although negative rents are “much less common and relatively unimportant” compared to positive rents47) in circumstances where competition is limited and/or where the mobility of capital is impeded.48 Moreover, “often”, those investigating the question of rent have “some ulterior motive” (e.g. to “justify the system of land ownership” through a dismissal of the existence of the corresponding rent), adding a “particular difficulty” to studies in this field.49 However, according to Pareto, if it were possible to show that a positive rent had been “expropriated to the community” or that it “was produced by societal investment” or again that “it tends to grow continuously without any effort on the part of the owner”, then this would prove that “the right thing to do” would be to seek a way to return this rent to the community, which in turn would be advisable only if it could be established that this would not lead to more critical indirect consequences than the recovery of the rent for the general public.50 In particular, according to Pareto, “since land is private ownership, a rent is paid for its use which is determined by the general equations for production and can be higher or lower than the interest on the capital expended on it”.51 More generally, Pareto52 observed that if savings are transformed into capital T,V,…, the following balancing equation53 i = pT / ∏T = pV / ∏V =;…





will be transformed, with the passage from one point of economic equilibrium to the other i′ = pT′ / ∏′T = pV′ / ∏′V ;…





We have too:

h = ( ∏′T + ∏′V +…) / ( ∏T + ∏V +…)



Pareto defined the following quantities τ as the rents for the capitals T,V, …,

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τ T = pT′ − ∏T hi′,τ V = pV′ − ∏V hi′,…



which can be reformulated as

τ T = pT′ 1 − ( ∏T / ∏′T ) h  , τ V = pV′ 1 − ( ∏V / ∏′V ) h  …

If the transformation of savings into the capitals T,V,… is performed “as easily” as formerly, then the following obtains54

( ∏′T / ∏T ) = ( ∏′V / ∏V ) = … = h

and hence the rents are null whilst, in general, they are not equal to zero. From a practical standpoint, Pareto concluded that: in passing from one state of general equilibrium to another, for many land assets a positive rent is obtained which is quite different from incorporated “interest on capital”55; the rent does not apply to land assets alone, even if the rent from land holdings is the most important type in markets which are closed to commercial relations abroad56; the existence of the rent “certainly reduces the level of ophelimity enjoyed by society” because it hampers the process of equalising of net interest rates, so that this rent can be seen as “a tax paid by the rest of society to owners of real estate”, even if the population might derive some political advantage “from the existence of a powerful body of property holders”.57

As regards wages, at the end of 1892, in reviewing the recent volume (“which every economist should read”) The Economy of High Wages, an Inquiry into the Causes of High Wages and the Effects on Methods and Cost of Production, by Jacob Schoenhof, Pareto claimed that political economy had shown long before that high wages could be reconciled with low production costs through higher productivity.58 For example, in the United States wages are much higher than in Europe because American workers “produce more” than European ones, partly thanks to “more powerful and efficient machinery” but also because they are better housed and fed and worked “shorter hours”.59

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Finally, Pareto began his analysis of interest rates by remarking that it was necessary to distinguish “very clearly” between savings and capital (and hence also their respective returns) because the former “represents the raw material for” the latter. The transformation can be performed by specialised “entrepreneurs” who acquire “the use of the savings” and transform them, together with other capital, into “new capital”, the exploitation of which they then sell on.60 The term savings, on the other hand, refers to “economic items which individuals have refrained from consuming … with a view to [their] future consumption or rental”.61 Since mankind “can but compare sensations of the moment …. people compare the suffering they feel from their current abstinence in regard to these economic items … with the pleasure they feel at the same moment in contemplating the future benefits they hope to derive from the savings … the act of saving thus [becoming] partly, or even completely, instinctive, [since people only concern themselves] with this immediate pleasure”.62 In the case of savings accumulated for the purpose of rental, this serves “to transform future assets into present assets” and this transformation consists precisely in the production of capital or the financing of production in general.63 Thus, the lender of savings “is a person who prefers future assets to present assets”. On occasion “this preference can be so marked that the lender may be resigned to receiving nothing”, but more frequently “the preference depends largely, or even exclusively, on the return which the lender receives”.64 The borrower of savings, by contrast, needs the money in order to bring forward a consumption or in the hope of making a profit by putting the savings to use in production.65 The net remuneration of capital, that is, the rate of interest, is calculated by deducting “expenditure necessary for maintaining the capital in good order and preventing any dissipation” from the gross return. Where there is competition between producers of capital, the various net returns will be equalised at the single remuneration of the savings.66 More particularly, “the interest on capital is linked by certain equations to all the other variables involved. It would be very difficult to determine it separately”.67 If one wished in any case to seek a single rationale for interest, it should be identified “in the appropriation of economic assets. It is certain that if these assets were not appropriated, there would be no

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price for their loan”.68 Pareto then added that collectivisation would nullify the rent but not the interest, “at least as regards new capital”, since its production would require the socialist state to make use of monies which, under conditions of free competition, would be termed interest for the use of the capital sum.69 In the light of all the above, Pareto contended that it would be a preconception to consider “low interest rates as a sign of a country’s prosperity”. In reality, there would be no way of knowing if the low rates were the result of an abundance of capital or of a lack of demand for it.70

8.4 Economic Crises71 Pareto not only thought it was impossible to prevent economic crises because it occurred “periodically” although not “at regular intervals”72 but also doubted whether it would be beneficial to do so since it was possible that “this … was one of the conditions for economic progress” constituting “a manifestation of the vitality of the economic system”.73 Nevertheless, “measures designed to attenuate the intensity of the crises could be very valuable”.74 In Pareto’s view “a crisis arises” when industrialists and merchants “making use of credit from the banks … extend themselves well beyond their means”.75 More generally, “crises appear to originate in the psychological phenomenon whereby people constantly alternate between an excess of confidence and an excess of apprehension”.76 Moreover, since the final degrees of utility of consumer goods are always positive,77 in Pareto’s view, economic crises always affect only a limited number of sectors where entrepreneurs have overestimated the final degree of utility of their product, leading to an excess of production, given that a generalised excess of production is impossible. Crises can be divided into two categories, those caused by external factors (changes in the production coefficients or in consumer tastes)78 and those caused by subjective factors (“the capacity of the majority of people belonging to a society to experience, at any given moment, sentiments which lead them to act in a similar manner”).79

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The arrival of the crisis is characterised by the increases in consumption and in production, the latter thanks to large investments of capital derived from increased recourse to savings and credit on the part of entrepreneurs. These phenomena are related because “very often” the increase in consumption is caused by increased wages paid by entrepreneurs who have increased production following the said increase in consumption, with a knock-on effect on other businesses, which in turn are stimulated to increase production, stimulating further consumption, and so on.80 However, since it is not possible to continue indefinitely consuming more than is produced, as happens in this initial period, with the difference financed by credit, the initial boom period is inevitably followed by a slump,81 the consequences of which are felt (in terms of reduced prices for the assets in their possession) by “those speculators engaged in playing games of chance, who do not merit our pity, being pests whose disappearance can only be beneficial to society”, by the owners of mobile capital assets, “on occasion” by the owners of real estate assets, and lastly by the workers themselves.82 In this phase consumption declines, savings are renewed and gradually the “ills of the crisis” are forgotten, so that a new cycle can begin.83 Pareto described an economic crisis as a trend involving oscillations in prices, in bank reserves and in lending. The crisis is characterised by the maximum levels of prices and credit together with the minimum levels of reserves.84 The resolution of the crisis is then accompanied by reductions in prices and in loans and by increases in bank reserves and in interest rates. In this phase the issuing of paper money can be of help, providing it is for “a very short time” and not in quantities that would impede the necessary (particularly reduction in prices.85 Pareto then observed that debtors ­ “imprudent speculators”) who would be ruined by the fall in prices accompanying the slump phase of the crisis, seek to limit the damage by pressing the government to print paper money, with the specific aim of putting a brake on the decreases. However, in doing this, although they may safeguard their own personal interests, they also “prevent the crisis from reaching its conclusion, prolonging it and in the end making it more intense”.86 Pareto performed an analysis of the Italian economic crisis of that time by reference to this model. In 1887, the high levels of the loan portfolios appearing on the banks’ balance sheets87 revealed the onset of the crisis,

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whose phase of liquidation began in 1888, continuing in a normal manner until mid-1889, when cash reserves once again returned to a value exceeding that of the portfolio.88 At that point, had it not been for government interference, the crisis would have been “probably over”89 by the spring of 1890. Instead, the government, against the advice of the renowned Genoese economist Gerolamo Boccardo, which was to allow interest rates to rise in view of the excessive demand for credit, prompted the National Bank to extend loans “to failing businesses”,90 thus prolonging and aggravating the crisis.91 All this was done in order to avoid revealing to the country, through a hike in interest rates, the squandering of capital due to the government’s own “adventurous” foreign policy.92 In April 1891, Pareto reiterated that “it is precisely in the commitment of excessive sums in unproductive ventures and for armaments that the current crisis was born. Now what is required is the allocation of the country’s remaining capital to productive uses”.93 Pareto was well aware that economic crises were not “a static phenomenon” but were “dynamic”, in the sense that “real prices oscillate perpetually around certain average prices which in turn are not constant, but vary over time”.94 Dynamic phenomena themselves are the result of oscillatory cycles and if these tend in the same direction and relate to “an economic subsystem” then they will duly lead to a crisis.95 Pareto pointed out that oscillations in the economic phenomenon are normal, since this latter is a “living entity”, and therefore it is “completely arbitrary” to specify the amplitude of oscillations which is required before a crisis can be declared.96

Notes 1. On this question, see the classic Spengler (1944) and the more recent addition Boianovsky (2001). 2. On Pareto’s earliest reflections concerning the demographic question, see Mornati (2018, pp. 152–153). 3. Pareto (1893–1894, pp. 35–36), Pareto (1896–1897, §156). 4. Pareto (1893–1894, p. 39), Pareto (1896–1897, §156). 5. Ibid., §§159–162. 6. Ibid., §179.

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7. Ibid., §171. On the other hand, Pareto pointed out that it is particularly in the case of human reproduction that “the hedonistic maximum of the individual [can be in contrast] with that of the country or of the species”, §173. 8. Pareto (1893–1894, p. 37). 9. Ibid., p. 37. 10. Ibid., p.  40. Pareto (1896–1897, §217). Pareto considered Malthus’ claim that effective population growth followed an arithmetical progression to be false, and “unsubstantiated” his claim that virtual growth, that is, growth determined by the generating force alone, followed a geometric progression, ibid., §§200, 212. 11. Pareto (1893–1894, pp.  41–42), Pareto (1896–1897, §196). Pareto (1893–1894, p.  47) concluded from this that socialist promises that “with better social organisation mankind could indulge its procreative instincts uninhibitedly” were not credible. 12. Ibid., pp. 64, 66. Pareto, ibid., pp. 80–81 emphasised the futility of government measures to incentivise or to disincentivise births. 13. That is, checks to procreation caused by obstacles or delays to marriage and, after marriage, bans or limits on child-bearing. The former category, unlike the latter, is in any case influenced by variations in economic circumstances, ibid., p. 70, Pareto (1896–1897, §226). 14. Anything provoking premature death in children, in particular infectious diseases (which can often be the result of poverty), Pareto (1893– 1894, pp. 76, 79–80). 15. Pareto (1896–1897, §230). 16. Pareto (1893–1894, p. 51). Pareto (1893a, p. 7) having then reiterated that Malthus “was right” in affirming that “the human race, like any other animal species, possesses a natural tendency to breed beyond the limit of subsistence”, denounced Malthus’ opponents for “the injustice … of expecting to measure this phenomenon precisely by reference to the two progressions which have been the subject of so much foolish debate”. 17. Pareto (1896–1897, §222). 18. Ibid., §223. 19. Ibid., §225. 20. Ibid., §268. 21. Pareto to Pantaleoni, 20th May 1896, see Pareto (1984a, p. 449). 22. Pareto to Pantaleoni, 28th October 1896, ibid., p. 478. 23. Pareto (1893b, p. 451).

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24. Ibid. 25. Ibid., pp. 451–452. 26. Ibid., pp. 452, 454–455. Pareto pointed out that, out of 100.000 born, 37,806 (25,281) children in Bavaria (Switzerland) die in the first five years of life, while 2382 (3197) die between the ages of 15 and 20, ibid., p. 455 and Pareto (1893–1894, p. 83). 27. Pareto (1893b, p. 456). 28. Pareto (1896–1897, §254). 29. On this topic see the  classic Fasiani (1949) and  the  recent McLure (2007) and Fossati (2011). On Pareto’s thought with regard to the science of  finance in  his pre-academic period, Mornati (2018, pp. 146–151). 30. Pareto to Pantaleoni, 21st December 1897, see Pareto (1984b, p. 134). 31. Pareto to Edwin Seligman, 5th January and 1st March 1896, see Pareto (1975, pp. 282, 284). The view had already been expressed in this period in Pareto to Maffeo Pantaleoni, 12th and 14th August 1892, see Pareto (1984a, pp. 266, 268, 272). 32. Pareto to Leon Walras, 28th April 1896, see Pareto (1975, p. 290). 33. Pareto to Edwin Seligman, 1st March 1896, ibid., p. 284. 34. Pareto to Tullio Martello, 15th December 1895, ibid., p. 274. 35. If the rate for progressive taxation were p+[(b(x−x0))/x], where x represents overall income, x0 the minimum income, p the rate applying to the minimum income and b the rate applying to the ratio between the difference between overall income and the minimum income in relation to overall income, it follows that the maximum rate (corresponding to x0 = 0) is p+b, implying that, if p+b 1 (as in the case in question), so that the second addend tends towards zero,

α R =  A ( a + hα )  / (α − 1) ( a + h )   

or

R =  N h ( a + hα )  / (α − 1)



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or again, since Nh = P = the overall population

R / P = ( a + α h ) / (α − 1) = z



where z represents income per head. By differentiating z in relation to h, a and α,



2 dz = α / (α − 1)  dh + 1 / (α − 1)  da − ( h + a ) / (α − 1)  dα  

is obtained, which in turn suggests that, firstly, if inequality among incomes remains unchanged (i.e. if da  =  dα  =  0), then an increase in income per head will lead to an increase in minimum income and vice versa. Secondly, a reduction in income inequality (i.e. a reduction in the value of α and an increase in that of a) will entail an increase in income per head, with the minimum income remaining unchanged. Thirdly, an increase in income per head is also compatible with an increase in inequality of income distribution (i.e. an increase both in a and in α), if the increase in a is very substantial. Pareto reiterated this conclusion, underlining that the increase in minimum income and/or the reduction in income inequality demand that “total incomes grow more quickly than the population”, thus encapsulating his own long-standing Malthusian cum free-trade positions.64 Hence, improvement in the well-being of the poorer classes is a problem not of income redistribution but one of productivity and of demographic responsibility.65 At that time a reduction in α accompanied by an increase in h was in fact ongoing, thus contradicting the socialist thesis regarding growth in inequality of income.66 Nevertheless, Pareto hastened to add, in contrast with the optimism of Ammon and, more particularly, of Leroy-Beaulieu and the économistes optimistes, that there were no guarantees of this situation continuing because the increases in levels of production brought by technological advances could be more than outweighed by the continuing destruction of wealth at the hands of “state socialism”.67 In general, Pareto considered that the income curve emerged from the equilibrium between “human qualities and shortcomings … and the

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surrounding context”.68 Thus, the socialists were right in proposing direct intervention on “the forces acting on society” as a means of modifying the income curve, but were deluded in believing that to achieve this it was sufficient to collectivise the ownership of capital, as “the forces acting for the differentiation of society would continue to act”69 and so if ownership of only real estate and movable assets were collectivised, the income curve for the resulting society “would resemble what we see now, at least in part”.70

10.4 Thoughts on Interpolation The development of the law of income distribution prompted Pareto to further reflection on the statistical methods used. The function of interpolation is to replace the “exceedingly complicated” curve representing any given phenomenon with a “simpler” curve which would permit the discernment of the “general laws” attendant on that phenomenon. This substitution can be performed in “an infinite number of ways, depending on the aim intended”.71 Pareto pointed out that any curve y  =  f (x) (where y represents the observed value and x the time when it is observed) can be exactly ­reproduced by means of a Chebyshev formula possessing the required number of terms, such as y = B0 + B1Ψ′1 + B2Ψ′2 + B3Ψ′3 (with y representing the estimated values, B the constants, Ψ functions of x, that is, the variable of the time of observation, which is assumed to increase arithmetically). However, this perfect reproduction does not tell us anything new about the phenomenon being investigated, whereas if the number of terms is less than in the perfect reproduction illustrated, the original curve is replaced with a simpler one where the rate of approach to the original curve is not uniform.72 Pareto specified that interpolation techniques permit not only the representation of a phenomenon but also the “identification of the relations between phenomena”, where the theory will suggest the possible existence or not of a relationship between two phenomena and with statistics revealing only whether the relation in question exists in reality or not.73

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Table 10.8  First table for estimating the Chebyshev formula Year

x

y

1846 1847 1848 1849 1850

1 2 3 4 5

145,664 135,845 138,230 141,883 152,744

Source: Pareto (1899, p. 116)

Pareto acknowledged that in practice the determination of the interpolating curve is “a tough problem which can be resolved only by someone highly proficient in mathematics”. This was why Pareto had “developed numeric mirrors” with the aim of assisting non-mathematicians in estimating the Chebyshev formula.74 Pareto provided an interesting example of these applied to the interpolation of wedding-events (represented by the y variable) in England and Wales (Table 10.8). The first approximation75 is given by B0 = (∑ y)/n, whereby the yearly arithmetical average number of weddings is equal to 142,873.2. The second approximation76 is given by B1 = (∑ yΨ1)/(∑ (Ψ1)2, where Ψ1 = z = x − (n + 1)/2 is equal to 2019.8. The third approximation77 is given by B2  =  (∑ yΨ2)/(∑ (Ψ2)2, where Ψ2 = [z2 − (n2 – 1)/12]3 is equal to 1014.952. The first development, y = 142.873,2 + 2.019,8Ψ1 + 1.014,952Ψ2, is then obtained, and this can be further expanded.

Notes 1. Pareto to Pantaleoni, 22nd July 1893, see Pareto (1984, p. 387). 2. Pareto (1893–1894, p. 27). 3. Ibid., p. 29. Pareto to Pantaleoni, 3rd October 1891, see Pareto (1984, p. 70), claimed that the Bertrand (1889) “is not a good book” due to its erroneous premises and that his author is “a good mathematician but a very bad philosopher”. Among various other alternative works on the computation of probability Pareto described as “excellent”, ibid., Liagre (1879). His author, the Belgian general and mathematician Joseph Liagre, sets out to study, for didactic purposes, a priori probabilities (where causes

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which are treated as known are combined in order to reconstruct consequences) and a posteriori probabilities (where consequences which are treated as known are used to reconstruct causes) and enlarges on their applications, particularly in the field of geodesics, pp. 17, 19. Furthermore, Pareto (1892, p. 393) did not feel able to “accept Mill’s statements on the use of computations of probability”, possible alluding to the objectivist claim that “before applying the doctrine of chances to any scientific purpose, the foundation must be laid for an evaluation of the chances, by possessing ourselves of the utmost attainable amount of positive knowledge. The knowledge required is that of the comparative frequency with which the different events in fact occur”, Mill (1974, p. 539). 4. Pareto (1893, p. 25). 5. By cause, Pareto, ibid., p.  26, note 1, meant “simply a conjuncture which, when it occurs, generates a certain probability of a consequent conjuncture”. 6. Ibid. 7. Pareto (1893–1894, p. 28). 8. Ibid. 9. Ibid., pp. 29–32. 10. Ibid., p. 33. 11. Pareto (1893, pp. 7–8). 12. Ammon (1900). 13. See above, §3.3. 14. Pareto (1895a). 15. Ibid., p. 60. 16. Ibid., p. 67. 17. Pareto (1902–1903, p. 9, note 1). 18. Pareto (1896–1897, §961, note 4). 19. Pareto also informed Ammon of his income law in a letter dated 30th November 1900, Banca Popolare di Sondrio Vilfredo Pareto letter archive, saying that it showed that “the distribution of income did not depend only on chance, but implied a certain law of heterogeneity among individuals”. 20. Ammon (1900, p. 180). 21. Ibid., p. 178. 22. Ibid. No account is taken of the final range, from 9600 marks up, because the normalised percentage value would be even smaller than for the two preceding ones, which in turn “are not representable in graphic form due to their minute dimensions”.

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23. Ibid., p. 179. 24. Ibid., pp.  178, 330. Ibid., Ammon underlined that for an in-depth investigation of income distribution “one must … be capable of grasping the variations of a mathematical function resulting from the variations of specific scale dimensions”. 25. Ibid., pp. 179–180. 26. Ibid., pp. 180–181. 27. Ibid., pp. 183. 28. Ibid. 29. Ibid., p. 184. 30. Ibid., p. 330. 31. Ibid., p. 332. 32. Ibid. 33. Pareto (1895a, p. 60). 34. Ibid. 35. Pareto (1896a). 36. Benini (1894) presented the table shown in the first two columns of Table 10.3, ibid. p. 866: Pareto (1896a, p. 4), reformulated Benini’s table with the addition of the third and fourth columns, without specifying that the reformulation was his work and ignoring small incomes, because “they are easy to disguise”, Pareto (1896–1897, §959). 37. Pareto (1896a, p. 2). 38. Ibid and Pareto (1896–1897, §958, note 1). 39. Pareto (1896b, p. 83). 40. Pareto (1895a, p. 60). 41. Pareto (1896a, p. 5). 42. Pareto (1896b, pp. 84–87). 43. Pareto (1896–1897, §§958–959). 44. Pareto (1896b, p. 83). 45. See, for example, Benini (1906, pp.  185–186) and Niceforo (1935, pp. 475–478). 46. Pareto (1896–1897, §959). 47. Pareto (1895a, pp.  61–62), Pareto (1896–1897, §§959–960). Pareto (1895a, p. 64) admitted in passing that α (in his essay substituted with h) “depends on all the quantities characterising the economic context” and that only as a first approximation could it be considered as a constant,

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although he notoriously neglected this caveat. This constitutes a quite interesting example of a conflict between the General Equilibrium framework and the search for constants in Pareto’s work during this period. 48. Pareto (1986–1897, §957). Pareto to Gustave de Molinari, 18th November 1896, see Pareto (1975, p. 307) justified the debate over the “chance” hypothesis by reference to the need to present a complete coverage of the topic for didactic purposes. 49. Pareto (1896–1897, §962, note 1). 50. Ibid. §962. 51. Ibid. §1026. By “prime subjects” Pareto was referring to “individuals capable of more intense vital activity”, ibid., §1030. Pareto, ibid., tome 2, pp. 416–419 showed, through a complicated exercise in the calculation of probability, that the law of income distribution could be conceived as a consequence of the hypothesis postulating the varying capabilities of differing social categories to generate income. 52. Pareto to Tullio Martello, 15th December 1895, see Pareto (1975, p. 275). 53. Pareto (1895a, p. 64). Pareto (1896a, pp. 8–15) determines the proportional rate of taxation which would yield the same revenues as any given progressive tax. 54. Leroy-Beaulieu (1881), whose importance appears essentially to be more as a target for attack than as a source of inspiration for Pareto’s law of income distribution. 55. Ibid., p. 515. 56. Pareto (1895b, p. 33). 57. Pareto (1896–1897, §965, note 1). 58. Pareto, ibid., §964 was able to establish the unambiguous nature only of the concept of income equality, as well as the fact that it was attainable in two different ways, that is, the impoverishment of the rich or the betterment of the poor. It was Leroy-Beaulieu’s proposition that the incomes of the poor increased more rapidly than those of the rich which prompted Pareto to adopt the second definition. 59. Where a represents a constant which is very small for total income, is positive for capital and negative for wages, ibid., §959, note 3. 60. Since the logarithms of ux = (h + a/x + a)α, will yield logux = αlog(h + a)  − αlog(x+a), an expression whose differentiation relative to a and to α lead to the formula appearing in the text. 61. Since h