Microeconomic Theory [4 ed.] 0256016372, 9780256016376

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Microeconomic theory C. E.

FERGUSON

Late Professor, Texas

J.

A&M P.

University

GOULD

Professor, University of Chicago

Fourth Edition

RICHARD

1975

D. IRWIN, INC.

Homewood,

Illinois

IrvWn-Dorsey Limited, Georgetown, Ontario

60430

L7G 4B3

Ail ngf-ti

mttted No pan

of thu publication

may be

reproduced. j’.orcJ in a triittval system, or transmitted,

any form or by any mean*, electronic, mechanical, photocopying, recording, or other* lie, without the prior in

written pcttniMion of the publisher

Fourth Edition

II

12 I) 14 15 IA 17 18

h 54

3

2

t

09

Preface

This fourth edition of Microeconomic Theory like the three earlier ,

editions, is a textbook

on

neoclassical price theory intended primarily

for undergraduate students.

The

ultimate test of a textbook

is

provided

by the market and the earlier editions did gratifyingly well by this criterion. In view of that success there has been a careful effort to retain much of the content and substance of the earlier editions in this book. There are, however, numerous changes in the fourth edition. As a general characterization, this edition places greater emphasis on the analytical aspects of economics while retaining the coverage of the

theory found in earlier editions. Specific cises.

'

changes include an expanded number of problems and exer-

Additional problems keyed to this text are in a

has been developed by Marcia Stigum. is

a

M 7 33

new

Workbook

A major addition in this

that

edition

chapter (Chapter 10) on the analytical uses of models of

competition and monopoly, which replaces the chapter on Linear Pro-

gramming. This new chapter retical tools of

is

intended to illustrate

economics can be used to analyze the

how

the theo-

effects of

such

things as taxes, subsidies, and price controls on firm and industry price

and output. Students have found this material useful in broadening their comprehension of the fundamental theoretical principles of firm and industry equilibrium. vii

vH

Preface

In Chapter 3 the thcor) of cisions involving nsl

— an

consumer behavior

is

extended to

do

area of theoretical economics tbit has re

ccivcd increasing attention jn recent )cars Tliere is also new material on consumption choices over time, showing how savings and inter

temporal consumption behavior can be analyzed using simple modifica rtons of the traditional indifference curves and budget lines The mi tenjJ on risk and consumption over tune is developed independent!) of tf e rest of the text and can lx skipped at the instructor s option Tliere arc also rather substantial revisions of the chapter

equilibrium

on general economic

showing how the basic concepts of general equilibrium

nppl) in relative!) simple economies.

Although the text is designed primaril) for undergraduates past experience shows that it has proved helpful to graduate students The book continues to contain the by now well known appendix Com prthensive Examination in Micro-Economic Thcor) for Graduate Stu dents

The

Machlup

questions

in

this

in conjunction with the

ihcor) he taught while at Johns tions are indeed

appendix

were developed b)

two semester course

Hoplms

in

Professor

Fritz

microeconomic

Machlup s ques

comprehensive (extending to topics not covered

in the

rrxr) and provide a valuable perspective of the scope of neoclassical

nue roceonomic thcor)

Man)

M *7 *3> 3>

users of earlier tditions of this book, both teachers

graduate students were kind

enough

and under

to send letters to the late Pro-

Ferguson concerning errors of substance, and obscure points These comments have been ver) helpful and I smcerel) hojie readers of fessor

the fourth edition will

now

direct their

comments

to

me on

an) issue

that arises

Acknowledgments to all of those who have contributed helpful sug gcstions arc too numerous to be listed, bur I cannot fail to mention a thoughtful review of the Third Edition b) Jerr) Green of Harvard Univemt) which provided useful guidance for much of this revision and to thank Rov Ruffin of the Umvcrsit) of Iowa /or man) valuable discussions on matters that arose during die revision JJenc Hsniott$ and her coworkers at the Umvcrsit) of Gticago provided exceptional cooperation 3 nd superb scrv

typing and preparing the manuscript While the hre Professor Ferguson did not participate directi) tn this revision

major contribution to this bool The errors that mi) remain is nonetheless mine

lus is still

rcspo^sibiiit) for

ice in

797,5

the

John p Gould

final

Contents

Introduction

Scope and methodology

of

economics

1

Scope of Economics: Economics in the Small and in the Large

and

Policy.

Methodology: Model Analysis.

An

Overview of

this

.

Norms

Book.

Advanced reading part

7

I

Theory of consumer behavior and demand

1.

Theory of

utility

Introduction:

9

and preference

The Nature of Commodities.

11 Full Knowledge.

of Consumer Preference. Utility and Preference: Indifference Curve.

Summary.

The

Utility

The Theory Surface. The

Characteristics of Indifference Curves.

Mar-

ginal Rate of Substitution. Conclusion.

2.

Theory of consumer behavior

29

Introduction: Maximization of Satisfaction. Limited

ing the Budget Line. Consumer Equilibrium:

The Relevant

modity Space. Maximizing Satisfaction Subject to IX

Money

Income. Shift-

Coma Limited Money InPart of

Contents

xi

Geometry of Average Product Curves. Geometry of Marginal Product Curves. Total Average and Marginal Products. The Three Stages of }

,

Production Linearly Homogeneous Production Functions.

6.

Production and optimal input proportions:

Two

variable inputs

Introduction: Production Table. Input Substitution

144

Production Surface:

Production Surface for Discrete Case. Production Surface for Continuous Case. Production Isoquants. Fixed-Proportions Production Functio?is. In-

put Substitution: Marginal Rate of Technical Substitution. Diminishing Marginal Rate of Technical Substitution. Economic Region of Production.

Optimal Combination of Resources: Input Prices and

Output for a Given The Expansion Path: Expenditure put

Effects.

Isocosts.

Maximizing

Minimizing Cost Subject to a Given Output. Isoclines. Changing Output and the Expansio?i Path.

Cost.

Changes in Input Price: The Substitution and Out "Inferior Factors” and the Output Effect. Analogies Between Elasticity.

Consumer and Producer Behavior. Conclusion. 7.

Theory

179

of cost

Introduction: Social Cost of Production. Private Cost of Production.

The

Role of the Entrepreneur. Short and Long Runs: Long-Run Costs and the Production Function. Short-Run Costs and the Production Function. Fixed and Variable Costs in the Short Run. Theory of Cost in the Short

Run: Total Short-Run Cost. Average and Marginal Cost. Geometry of Average and Marginal Cost Curves. Short-Run Cost Curves. Long-Run Theory of Cost: Short Run and the Long. Long-Run Average Cost Curve. Long-Run Marginal Cost. The Envelope Curve and the Expansion Path. Cost Elasticity and the Function Coefficient: The Function Coefficient.

LAC: Economies

Diseconomies of Scale. Long-Run Cost and Changes in Factor Price: Changes in Long-Run Average Cost. Changes in Long-Run Marginal Cost and Minimum AverCost Elasticity. Shape of

of Scale.

age Total Cost. Conclusion.

Advanced reading

part

,

part

216

II

III

Theory of the firm and market organization 8.

Theory

of price in perfectly competitive

markets

219

222

Demanders and Suppliers. Homogeneous Product. Free Mobility of Resources. Perfect Knowledge. Equilibrium in the Market Period: Industry Equilibrium in the Introduction. Perfect Competition:

Market Period. Price

as a R«V*

‘

Price Taking

g Device. Short-Run Equilibrium of a

Contents 12.

Theories of price

oligopoly markets

"Classical” Solutions to the

worth Case.

329

The Oligopoly Problem. Some Concepts and Assumptions

Introduction:

Some

in

xiii

Duopoly Problem: Cournot

Case. Edge-

Oligopoly Markets: Chamberlin Solution

Stability in

.

.

Sta-

Oligopoly Markets: Sweezy Solution. Theory of Games and Oligopoly Behavior. Some "Market” Solutions to the Duopoly Problem: bility in

Cartels

and

Profit Maximization. Cartels

—The Great

Turbulent Life of Cartels

and Market Sharing. Short and

Electrical Conspiracy. Price Leader-

ship in Oligopoly. Competition in Oligopoly Markets. Welfare Effects of Oligopoly.

part IV

^Jfeory 13.

363

of distribution

Marginal productivity theory of distribution competitive markets

in

perfectly

365

Demand of a Firm for Demand One Variable Productive Service. Individual Curves When Several Variable Inputs Are Used Determinants of the Demand for a Productive Service. Market Demand for a Variable Productive Service Supply Introduction.

Demand

for a Productive Service:

.

.

of a Variable Productive Service:

General Considerations. Indifference

Curve Analysis of Labor Supply. The Market Supply of Labor. Marginal Productivity Theory of Input Returns: Market Equilibrium and the Returns to Variable Productive Services. Short

Run and

Quasi Rents. Clark-

Wicksteed Product Exhaustion Theorem. Distribution and Relative Factor Shares:

Least-Cost Combinations of Inputs and Linearly

Homogeneous

Production Functions. The Elasticity of Substitution. Elasticity of Substitution

and Changes in Relative Factor

Shares. Classification of Technologi-

cal Progress. Biased Technological Progress and Relative Factor Shares

Appendix

to

Chapter 13: The Clark-Wicksteed Theorem. The Output

Elasticity of Productive Services.

14.

Theory of employment

in

imperfectly competitive markets

397

Monopoly in the Commodity Market: Marginal Revenue Product. Monopoly Demand for a Single Variable Service. Monopoly Demand for a Variable Productive Service When Several Variable Inputs Are

Introduction.

Used. Market

Demand

for a Variable Productive Service. Equilibrium

Price and Employment Monopolistic Exploitation. Monopsony: Monopoly .

Expense of Input. Price and Employment One Variable Input Is Used. Price and Employ-

in the Input Market: Marginal

under Monopsony

When

ment under Monopsony When Several Variable Inputs Are Used. Monopsonistic Exploitation. Monopsony and the Economic Effects of Labor Unions.

Advanced

reading, part IV

421

XIV

Contents

part

15

V

Theory of general equilibrium and economic welfare

423

economic equilibrium

426

Theory

of genera!

Introduction

A

Simple

Two

Person Economy

The Farmer

as Entre

Consumer Laborer General Equilibrium and Walrass Law General Equilibrium of Exchange Edgeworth Box Dia gram Equilibrium of Exchange Dertvtng the Utility Possibility Frontier General Equilibrium of Production and Exchange General Equilibrium of Production General Equilibrium of Production and Exchange Dertv

The Farmer

preneur

mg

as

the Production Possibility Frontier or Transformation Curve General

Competitive Equilibrium in a

Good Economy Equilibrium

Two Good Economy Production m a Two tn a Two Good Economy Factor Intensities

and the Relationship Between Factor Prices and Commodity Prices 16

Theory

of welfare

economics

452

Introduction Marginal Conditions for Social Welfare Welfare tion

Maxtmtza

and Perfect Competition Input Output and Distribution

General

From Production Functions to the Production Possibility Frontier Production Possibilities and the Optimum Conditions of Exchange Retracing Some Steps From the Contract Curve to the Utility Possibility Frontier From a Utility Possibility Point to the Grand Utility Possibility Frontier From the Utility Possibility Frontier Assumptions Retracing Some Steps

to the Potnt of

Constrained Bliss

Constrained Bliss and Efficiency In

and Welfare From Constrained Bliss to Prices Wages and Rent Minimum Wages and Pareto Efficiency A Dts gresuon External Economies and Welfare Economics A Final Word on Free Enterprise Social Benefits and Costs Ownership Externalities Tech puts

Outputs

Distribution

meal Externalities

Public

Good

Externalities

Externalities

and Free

Enterprise

Advanced reading part V Appendix

A comprehensive

examination theory for graduate students

479 in

microeconomic 485

Author index

52 i

Subject index

525

introduction

Scope and methodology of

economics

1.1

SCOPE OF ECONOMICS Economics

which

is

a social science that

is

concerned with the means by

dard but abstract definition often

fails

competing ends. This stanto convey just how pervasive

the scope of economics really

The

idea of allocating limited re-

scarce resources are used to satisfy

is.

enough when one contemplates a household deciding how to budget its income for purchase of clothes, housing, insurance, entertainment, transportation, and other goods and services. It is also easy to see that businesses must make allocative decisions: General Motors has to decide how to allocate its sources to satisfy competing ends

is

familiar

production resources in the production of Chevrolets, Pontiacs, and

must decide how much of tuition revenues and endowment should be spent on new buildings instead of books for the library or the hiring of additional faculty. Students have to allocate their studying time among the various courses they are taking and they also must decide how much of their time to spend in study rather than in other pursuits. Income earners must decide how much of their current earnings should be consumed now and how much should be Cadillacs. Universities

saved for future consumption.

some

On

a broader scale,

we

often think of

resources as being so abundant that they can be used to satisfy

all possible needs; air

and water are examples. But even here an 1

al-

Microeconomic theory

2

mast be made when it is recognized that certain ac pollute air and water If we drive more cars or produce more

locative dectston tivrnes

we

steel

a

1.1

and water

will have less clean air

Economics

Economics

is

in the

Small and

in

the Large

concerned both with the allocative decisions

made by

and other economic agents and with society as a whole allocates resources

individuals, households, businesses,

how

the broader question of

Economists frequently assume that consumers attempt to maximize

and businessmen or entrepreneurs attempt to maximize So defined, the goals of economic agents provide the economist

satisfaction

profit

with a frame of reference that permits systematic analysis of individual

economic behavior The behavior of one agent vis a vis another a broader view, it likely to be, in some sense, competitive But

m

is is

mutual cooperation of agents with conflicting goals that is ulti mately responsible for the production of economic goods and services

the

When

the principles of microeconomic behavior have been discov

on a macroeconomic problem that has beset economics from its inception as a science Indeed, one might say it was the attempt to resolve this problem that caused economics to become a science The problem may be stated as a question Will the independent maximizing behavior of each economic agent eventually ered our attention can be focused

result in a social organization that, in a

well being of society as a whole this

when he

5

normative sense, maximizes the

Adam

Smith suggested an answer to

presented his doctrine of the

to Smith, each individual,

hand

invisible

bent on pursuing his

own

According

best interest,

is

m

by an unseen hand, to pursue a course of action that benefits society as a whole This is a happy and optimistic doctrine It evitably led as

if

has however, been increasingly questioned as the social and industrial

mvUevs has undergone great change It all economic agents ate atomistic

m size

relative to the total

economic

Smith s invisible hand or an IBM machine will seek out an optimal organization of economic activity But, on the contrary, if all agents are not atomistic, one is

compelled to ask

if

this

optimum

large agents play an economic

game

society, either

will be reached

Or

will the very

which they achieve gains, but only at the expense of counterbalancing losses on the part of smaller units 5 The answers to these questions are not at all clear But they are very important, both from the standpoint of theory and from that of in

policy

Although the course

for

manly concerned with the

which

this text

analysis of

has been prepared

is

pn

microeconomic behavior, we must

Scope and methodology

not lose sight of the dominant quaesitum, that this end,

we

is,

of

economics

3

social welfare.

To

shall assess each facet of individual behavior in terms of

social welfare

and

finally

conclude with a chapter devoted to welfare

economics.

Norms and

I.I.b

The

Policy

discussion of goals, especially in the last paragraph above, leads

to a further discussion of welfare

norms and economic policy

( positive

economics). Economists, in their role as economists, cannot establish

normative objectives for a

society.

say that free public education

is

For example, an economist cannot

desirable or that

some minimum

level

income should be received by each family unit. Of course, as a citizen he can vote for school bond issues and for legislators who favor income redistribution; but an economist as an economist cannot determine social goals. The business of an economist is a positive, not a normative, one. That is, given a social objective, the economist can analyze the problem and suggest the most efficient means by which to attain the desired end. This book is accordingly devoted to the positive aspects of economic analysis, not to the normative decisions that a society must make. of

METHODOLOGY

1.2

A person

observing the real world of economic phenomena

fronted with a mass of data that

is,

of

human

By

it is

con-

at least superficially, meaningless.

To discover order in this morass of facts and to ingful way,

is

arrange them in a mean-

necessary to develop theories to explain various aspects

behavior, and thus to explain the otherwise meaningless data.

from the real world, it is possible to achieve a level of simplicity at which human action may be analyzed. But in the process of abstraction, the analyst must be careful to preserve the essential features of the real world problem with which he is concerned. That is to say, simplification is necessary; but at the same time a theory must capture the essence of the fundamental economic problem it is designed to abstracting

solve.

I.2.a

Model Analysis

Since this text

is

exclusively concerned with economic models and

their use in analyzing real

world economic problems,

it is

especially

important to give attention to the use of model analysis in general be-

Microeconomic theory

4

fore undertaking a stud) of specific to

do

this schematically

EXPERIMENTAL DESIGN

economic models

convenient

It is

with the aid of the follow mg diagram

EXPERIMENTAL

ATTRACTION

REAL

LOGICAL MODEL

THEORETICAL ABSTRACTION

WORLD

1

i

LOGICAL ARGUMENT

EXPERIMENTATION

1

1

UBHKVAUUrO

STATISTICAL

INTERPRETATION

The real world is usually

REAL

WORLD

THEORETICAL INTERPRETATION

CONCLUSIONS

the starting point.

A particular problem, or

merel) a desire to understand, motivates one to plicated world of reality into the

LOGICAL

CONOUSIONS

move from

domain of logical

simplicity

the

com

By means

of theoretical abstraction, one hopefully reduces the complexities of the

world to manageable proportions. The result is a logical model pre sumably suited to explain the phenomena observed By logical argu real

ment

(i.e

,

deduction) one then arrives at logical or model conclusions

However, these must be transformed, by means of tation, into conclusions

theoretical interpre-

about the real world.

Let us summarize to this point

The

economist, ha\ mg begun with

a portion of the real world, proceeds, through the use of completely theoretical first

means, to arrive at conclusions about the real world His

step entails abstraction

from the

real

world into a simplified logical

model His second step requires the use of logical argument to arrive at an abstract conclusion. His final step consists of a return to the real world by means of an interpretation that yields conclusions in terms of the concrete, sensible world of physical reality

The same

result

may presumably be

achieved by another method.

method to distinguish it from the deducttte method previously discussed Again starting from the real world, we may, by means of experimental abstraction, arrive at an experimental design That is, we may, by a process of simplification, design a statisti cal model that is useful m analyzing the real world. In this instance,

Let us call

it

the stattsttcal

however, we obtain observations of real world data rather than theorems 1

C

R

Adapted from a diagram appearing id Coombs, Howard Raiffa, and Thrall (eds ), 'Mathematical Models and Measurement Theory,” Decision Processes (New York John Wiley & Sons, Inc, 1954), p 22 R.

M

Scope and methodology

ol economics

by logical deduction. These observations, given the proper

5

statistical

interpretation, yield conclusions concerning the real world.

Although there is some disagreement over the relative merit of the two methods, the tenor of present thinking is that they are complementary. That is to say, deductive and statistical methods are mutually reinforcing rather than alternative instruments of analysis. It

however, that professional opinion on methodology

is still

is

true,

somewhat

diverse.

1.3

AN OVERVIEW OF THIS BOOK

The

authors of this book are sympathetic with the view that theory

and empirical investigation are complementary: theory provides

test-

able hypotheses about the real world, and statistical testing of these

hypotheses helps to show the direction in which the theory should be further developed and refined. In this course, however,

concerned with economic theory and economic analysis side of the

diagram in subsection

—

are only

the right-hand

Empirical testing

I.2.a.

we

is left

to the

worth noting, however, that econometricians have extensively examined, and generally validated, most of the fundamental theoretical principles presented here. specialized field called econometrics. It

To

reemphasize, this course

is

is

concerned

first

with developing well-

established microeconomic theories and second with

world problems by means of these

theories.

perhaps give some warning to the student,

To we

analyzing real

elucidate more, and

quote what Donald

one of his own books but which applies equally well to this one: "This book employs the method of austere, sustained, and I regret, largely humorless abstraction that has served economics

Dewey

said of

Given the excruciating complexity of so many of the problems I cannot see that any other method will allow us to cut through to first principles and deal with these problems acso well in the past. .

.

.

,

cording to their importance. Either

we

simplify drastically

.

resources, determine

what

is

.

is

the

same

time,

.

tasks: it

must

,

or

allocate

many

other countries,

used extensively to accomplish these tasks; and

are primarily concerned in diis course widi

At

.

to be produced, distribute die product, and

provide for growth. In the United States, as in die price system

.

2

we wander forever in the wilderness. Any society must accomplish four economic .”

we cannot

how

we

the price system works.

ignore the extent of governmental in-

Donald J. Dewey, Modern Capital Theory (New York: Columbia University Press, 1965), p. vii. *

Microeconomic theory

6

volvement sider

in the

economy and we

how governmental

will

have many occasions to con

regulations and other activities interact with

the price system

Part I of this book deals with consumer decision making and the underlying determinants of consumer demand Part II deals with the theory of

how

entrepreneurs combine resources in the production of

goods and services Part

III

examines

how

the price system works to

coordinate the decisions and behavior of consumers and entrepreneurs in the marketplace sidered

Various forms of market organization are con

m this section

Part

IV

deals with the question of

how

of productive factors such as labor and capital are determined

prices

This

problem of distribution in economic activity Part V combines these various components to see how general equi librium is achieved in the economy and then uses the results to consider how efficiently the economic system works and how well it achieves material

is

maximum

central to the

social welfare

SUGGESTED READINGS Friedman, Milton

The Methodology

Positive Economics,

of Positive Economics,

Essays tn

pp 1-43 Chicago University of Chicago

Press,

1953

Machlup, Fntz

The Problem of Verification in Economics,’ Southern Economic Journal vol 22 (1955),pp 1-21

Advanced reading Buchanan, James M. "Ceteris Paribus: Some Notes on Methodology,’’ Southern Economic Journal, vol. 24 ( 1958), pp. 259-70. Harrod, R. F. "Scope and Method of Economics,” Economic Journal, 48 (1938), pp. 383-412.

vol.

Hurwicz, Leonid. "Mathematics in Economics: Language and Instrument,” in Mathematics and the Social Sciences (ed. James C. Charlesworth ) pp. 1-11. Philadelphia: The American Academy of Political and Social Science,

1963.

Knight, Frank H. "What Is Truth in Economics?” Journal of Economy, vol. 48 ( 1940), pp. 1-32.

Political

Koopmans, T.

C. "Measurement without Theory,” Review of Economics and Statistics, vol. 29 (1947), pp. 161-72.

Krupp, Sherman Roy. "Equilibrium Theory

in

Economics and in Func-

Types of Explanation,” in Functionalism in the Social Sciences (ed. Don Martindalc), pp. 65-83. Philadelphia: The American Academy of Political and Social Science, 1965. tional Analysis as

Morgenstern, Oskar. "Limits to the Uses of Mathematics in Economics,” in Mathematics and the Social Sciences (ed. James C. Charlesworth ) pp. 12-29- Philadelphia: The American Academy of Political and Social Science, 1963.

part

I

Theory of consumer behavior and

demand

There are three sets of economic agents: consumers, entrepreneurs, and resource owners. Resource owners furnish the inputs used to produce whatever

bill

of goods

is

dictated by

market

forces. In return for

the use of their resources, the resource owners receive

This

money income,

in turn, enables

them

money income.

to function as consumers.

Entrepreneurs organize production and, ultimately, determine the supply of goods and services in free markets. Those entrepreneurs

who

organize production efficiently and are successful in anticipating con-

rewarded with money income in the form of profit. They are thereby also able to enter the market as consumers. Some people earn money income by selling resources or the use of

sumer

desires are

resources. Others earn

income by using

their special resource

preneurial skill) to organize production. All people

who

earn

(entre-

money

economic agents called consumers. There are, of course, other members of this group. Family members who are dependent upon the income earner participate in the household budget income belong to the

decisions

and

set of

are, therefore,

money income are also in the

receive

consumers. People

money by some

who

are not able to earn

type of transfer payment and

consumer category.

For our present purpose, the source of money income is not material. Only the fact that money is received by households and spent on con9

to

Microeconomic theory

Each household determines how to money income among the vast array of consumer goods

sumer goods allocate

its

is

of importance

available In other words, each household decides

upon

its

demand

for

any price may be zero for many items) The aggregate of these demand decisions con stitutes market demand, an expression of how society wants its re every item (even though the quantity demanded

at

sources allocated

The fundamental purpose of Part which market demand is formed to determinants of market demand

—

I is to

analyze the process by

find, in other

words, the basic

1

Theory

of

utility

and

preference

INTRODUCTION

1.1

tion of

what

its

Each individual or household has a fairly accurate nomoney income will be for a reasonable planning period,

the goods and services

household

is

to

spend

economic well-being.

it

its

No

wants limited

to buy.

too well defined

— of

task confronting every

money income

so as to maximize

its

individual or household, of course, actually

To some

succeeds in this task.

—perhapsThenot

some notion

say a year. It also has

extent this failure

is

attributable to the

lack of accurate information; but there are other reasons as well, such as

impulse buying. Yet in any event, the more or

maximum

less

conscious effort

from a limited money income determines individual demand for goods and services. To analyze the formation of consumer demand more accurately, we use some simplifying assumptions that do not distort the crucial aspects of economic reality. to attain

I.I.a

The Nature

The goods and

satisfaction

of

Commodities

services

called commodities. It

is

consumed by the household are genetically convenient to think of commodities as pro-

viding a flow of consumption sendees per unit of time.

The

objects of

choice are then the services provided by the commodities rather than the commodities themselves. This allows us to handle durable goods 11

Microeconomic theory

12

such as automobiles, television sets, and houses in a manner strictly analogous to nondurable goods and services such as food, haircuts, and theater tickets What at first glance might appear to be problems

from product indivisibilities are easily handled using this con vention it makes little sense to talk about an individual consuming half an automobile, but it is quite natural to think of using half (or any other fraction) of the services of an automobile per unit of time

arising

any one of a number of other strategies can be used to adjust the service flow per unit of time There is nothing in the theory that severely limits the scope of what Car pooling

we

call

rental, or

involving where to

11b

live,

work and and many other dimen

the allocation of time between

amount of income given

leisure, the

sions of

Thus, the theory allows us to analyze choices

commodities

to charity,

consumer behavior

Full

Knowledge

We assume that each consumer or family umt has complete informa tion on all matters pertaining to its consumption decisions A consumer knows the full range of goods and services available in the market, he knows precisely the technical capacity of each good or service to satisfy a want Furthermore, he knows the exact price of each good and service, and he knows these prices will not be changed by his ac ttons in the market Finally, the consumer knows precisely what his

money income

will be during the planning period

In point of fact, the assumptions introduced above are unnecessarily restrictive so far as

demand theory

demand functions and

is

concerned In order to derive

indifference curves (see below),

it is

only neces

assume that (a) the consumer is aware of the existence of some goods and services, (b) he has some reactions to them, that is, he prefers some goods to others, and (e) he has some money income so sary to

as to

make

these reacnons significant in the market Actually, the

rigid set of assumptions contained in the previous

sary only

more

paragraph are neces

when we come

to the theory of welfare economics (at the end of the book) But since an assessment of economic welfare result mg from competitive markets is the central task of microeconomic theory, the

1.1

more

restrictive

assumptions are introduced at this time

c The Theory of Consumer Preference

A

—

consuming unit

satisfaction or utility

—

an individual or a household derives from the services provided by the commodities either

1

/ Theory

of utility

and preference

13

consumed during a given time period. In the given time period, the individual or household will consume a large variety of different commodities, and as a

we

will refer to this collection of different commodities

commodity bundle. In order

—maximization money income—

to attain its objective

of satisfaction or utility for a given level of

the con-

suming unit must be able to rank different commodity bundles. That is, the consumer must be able to compare alternative commodity bundles and to determine his order of preference among them. To this end we assume that each consuming unit is able to make comparisons among alternative commodity bundles that satisfy the following conditions:

For any two commodity bundles

i.

A

and

B

the consuming unit

able to determine which provides the most satisfaction. If vides

more

satisfaction than B, then

we

say

A

is

A

it

pro-

preferred to B.

and if B provides more satisfaction than A, we say B is preferred to A. If both bundles provide the same satisfaction, we say the customer is indifferent between A and B. If A is preferred to B and B is preferred to C, then A is preferred

ii.

to C. Preference

is

a transitive relation. Similarly,

if

A

is

indifferent

and B is indifferent to C, then A is indifferent to C. If commodity bundle A is strictly larger than commodity bundle B, then A is preferred to B. One commodity bundle is said to be strictly larger than another if it contains more units of every commodity. If A contains as many units of every commodity as B and more units of at least one commodity, then A is said to be larger than B and B cannot be preferred to A (but in some in1 stances the consumer may be indifferent between them). to

Hi.

B

An

example will help to illustrate these concepts. and Y. The preferences of a Suppose there are only two goods, given consumer are shown in Table 1.1 .1 and illustrated in Figure 1.1 .1. Commodity bundle A is clearly preferred to all other bundles (by ( Hi ) since it contains more of both commodities. Bundles C and D are, byassumption, indifferent to B. The consumer is willing to take less Y if

X

1

This condition assumes that all commodities are ’goods” and that satiation never obtains no matter how much the individual consumes. Condition (Hi) is not really necessary for the theory of consumer behavior, and it is not always used. For example, wc may wish to analyze consumption choices among bundles involving a "bad” and a "good" such as pollution and automobiles (see Question 5 at end of chapter), or we may wish to assume that too much of a "good” is a “bad” (sec have listed condition (Hi) here because it Question 6 at end of chapter). holds in many situations of interest. To repeat, it is not really needed, and it in no

Wc

way

restricts

the theory.

Microeconomic theory

14

TABLE Rank Ordering Bundle

A B C

Commodity Bundle*

Amount of X

Amount of Y

Rank Order*

6

6

4

3

2

5 3 2 4 4 2

3

1

A

D

5 3

E F

1

G

H *

of

1 1.1

Mo

3 3

3

2 1 1

1

c preferred bundlet a re Jtt gtxcd a higher number

X in return

Bundle B, however, is preferred to E (the latter has less Y and the same quantity of X) Similarly, E is and the same quantity of Y ) preferred ro F (the latter has less are indifferent to F, the consumer being willing to Finally, G and substitute for Y in his consumption pattern The assumptions necessary to analyze consumer behavior can be set he gets some more

X

H

X

out in the following compact form Assumptions,

(a)

Each consumer has exact and

full

—

knowledge of

all

information relevant to his consumption decisions knowledge of the goods and services available and of their technical capacity to satisfy

market prices and of his money income is able to make comparisons of commodity bundles such that (0 for any two bundles A is preferred to B, B is pre-

wants

his

(f>)

of

Each consumer

consumer is indifferent between A and B, (it) if A is preferred (indifferent) to B and if B is preferred (indifferent) to C, then A is preferred (indifferent) to C, (ui) if bundle A is strictly larger than bundle B, then A is preferred to B ferred to A, or the

1

2

UTILITY

The

AND PREFERENCE

analysts of

consumer behavior

is

greatly facilitated

by the use

of a utility function which assigns a numerical value or utility level to

commodity bundles The reader may that the highly subjective

find

it difficult

phenomenon of consumer

to accept the idea preference,

which

obviously depends on each person’s physiological and psjchological makeup, can be so quantified. For most of our purposes, however, the particular numerical values assigned to

commodity bundles are not of

/ Theory of

1

FIGURE

tion

is

that

alternative to

it reflect

to bundle

right.

Table

In

All that

is

1.1.1

required of the utility func-

if

the consumer prefers bundle

A

than to bundle B, but the actual numerical values so

between bundle

assign the

tion.

and bundle

irrelevant.

is

commodity bundles

as the

A

same numerical value

value so assigned to

A

the utility function has to assign a larger numerical value

assigned are themselves irrelevant. Similarly, different

1

the same rankings that the consumer assigns to

commodity bundles. Thus,

B

bundle

own

and preference

1.1.1

Ordering of Bundles

significance in their

utility

A

B

if

the

the consumer utility'

is

in-

function must

to each bundle, but the particular

For example, the rank order assigned

through

H

in

Table

1.1.1.

can be thought of

numerical values assigned to these bundles by some

utility func-

Any other set of

preserved this

numbers, such as 20, 10, 10, 10, 8, 5, 5, 5, which ranking would do equally well for our purposes. A

function that assigned the values 10, 9, 8, 7, 6, 5, 4, 3 to bundles A, B, C, D, E. F, G. H, respectively, would not apply, however, utility

numbers would indicate that bundle C is whereas the consumer is in fact indifferent be-

since such an assignment of

preferred to bundle

B

tween these bundles. In

short, all

we

require of the utility function

is

Microeconomic theory

16

that

it

provide an ordinal measurement of the utility provided by com-

modity bundles, not a cardinal measurement.

The

1.2.a

Once

Utility

it is

Surface

recognized that only the ordinal properties of the utility

function are important for our purposes,

no harm

ing a specific utility function. Indeed, this

way

venient

which

we

to

is

done by considerprobably the most conis

gain an understanding of the ordinal properties in

To

with a concrete example suppose and Y that Smith obtains from consumption of goods

are interested.

illustrate

X

the utility is

2

given by the function

U = XT. In words, the utility

is

the product of the quantities of

X and Y con-

sumed by Smith Using this utility function Smith derives 100 units and 10 units of Y of utility from a bundle consisting of 10 units of 10 X 10) Smith also derives 100 units of utility from a bun( 100 and 20 units of Y or from a bundle condle consisting of 5 units of sisting of 1 unit of X and 100 units of Y Smith is thus indifferent among these bundles. Hotvever, he prefers any of these bundles to a bundle consisting of 5 units of X and 5 units of V since the latter has

X

=

X

utility

of only 25 according to the above function.

Since

we

are only concerned with the ordinal properties of the utility

function (ie., with the ranking assigned to the alternative bundles), there are

many

other utility functions that would represent Smith’s

preferences equally well For example the utility function

F = (XYy same preference ranking of the above-mentioned bundles The bundle consisting of 10 units of and 10 units of Y has utility of 10,000 with this new utility function, but so do the bundles consisting of 5 and 20 Y, and l and 100 Y, Hence both U and V tell us that Smith is indifferent among these three bundles even though the gives the

X

X

2

The

X

—

approach to utility theory atributable to Gossen (1854), and Walras (1874) treated utility as cardinally measurable The work of Pareto (1906), which had formal similarities to that of Edgeworth (1881), Antonelh (1886), and Irving Fisher (1892), among others, provided Jevons

(

original

1871

) ,

—

the foundation for the ordinal approach to utility theory

1

FIGURE Utility

cardinal value of utility depends

(10,000 compared to 100).

/ Theory of

utility

Surface

on the particular

OX!

units of

of time, utility

is

X and OY

x

The

Suppose the rate of consumption of 3

Once wc have one

we

preferences

such that /(rt )

bundle

A

f(U(A)) the

then

is

F(C)

sumer

is

OX

OXj. The curve utility

functions

same ordinal preferences. To see how, let /( z) be any function Now consider any utility function 1} > /(z0 ) whenever z > x

represents

preferred

is

and OY>> are

2

-

fixed at

is

OXZY.

function that correctly reflects the consumers ordinal

the consumer's ordinal to

bundle

> i(U(B)) = V(B)

consumer

X

QQ

is

utility surface

f

can construct an arbitrary number of alternative

that reflect the

that correctly

utility

function

consumed per period

are

Similarly, if

time, total utility

by a

utility surface is

Y

units of

PP\

the magnitude

consumed per period of

utility

3

such as the one shown in Figure 1.2.1. if

17

1.2*1

Utility functions can be represented geometrically

Thus

and preference

indifferent

y

B

so

then

V

also ranks

between bundles

= f(U(C) = f(U(D) ) )

indifferent between

C

preferences.

U(A) >

C

= F(D),

A

and so

and D. Additional

Let

F = /(£/).

If

=

11(B), but then V(A) higher than B. Similarly if then U(C) U(D) f but

=

D F

also

shows

utility functions

constructed by choosing different transformation functions like /(z).

the concan easily be

that

M/croeconom c theory

18

EPRD

sumption

is

Y

sumption of

Y

OYu

PP

con

so forth In

con

be applied to a fixed rate of for If the consumption of

X

and a variable rate is

if

total utility to the rate of

analysis can

total utility

PP',

held fixed at OX-> units per

is

FSQC relates

The same

consumption of fixed at

X

the consumption of

if

X and

units of

t

2

manner,

is

x

Y If consumption is OYu utility is OY (>OY ), utility is RR' (>PP'), and

period of time the curve

Y

OX

amounts of

variable

like

with

utility associated

then shows the total

OX

if

x

units of

SY (>PP') if the rate Thus the curve GPSA shows

X are consumed OX

per period of time,

of consumption

(>0X0,

the level of total utility

etc

associated with

OY\

units of

Y and

various rates of consumption of

HRQB shows the same thing when fixed at OY 2 units per period of time

Similarly,

of

Y

is

12b The The

is

2

X

the rate of consumption

Indifference Curve

utility surface

helps us to focus

constant utility contour or indifference

on the important concept of a curve which is the basis of the

modern (ordinal) theory of consumer behavior This concept may be explained by means of Figure 12 2 There are two goods X and Y,

OXZY

Figure

and the

total utility surface is

units of

X and OY a units of Y are consumed per

just as in

121

If

OX

x

period of time, total

—

X

consumption of is greater at the rate OX* for instance the consumption of Y remaining unchanged, the level of utility is greater But an essential feature of utility theory is that one utility is

RR'

—

If the

commodity may be substituted for another in consumption in such a way as to leave the level of total utility unchanged For example, XiX* units of X may be substituted for Y a Y units of Y without changing total utility If the rates of consumption are OX x of X and OY 3 of Y, total utility is RR' If the rates are OX* of and OY* of Y, total utility is PP' RR' Similarly, OX3 of and OY 1 of Y yield total

X

—

utility

of

SS'-PP'- RR'

In other words one level

X

RR'

may

— PP = SY

slice

or intersect the utility surface at the

and determine

all

combinations of

that will yield this constant level of utility

shown by

the dashed curve R'P'S in the

bi nation of

X and Y on

X

and

Y

These combinations are

X— Y

plane Since each

R'P'S' yields the same level of

utility,

com

a con

sumer would be indifferent to the particular combination he consumed In like manner, all combinations of and Y on the dashed curve T'Q'V' yield the same total utility (TT' QQ' VV') A consumer would thus be indifferent as to the particular combination consumed

X

—

=

1

FIGURE

/ Theory of

and preference

19

1.2.2

Surface with Constant

Utility

utility

Utility

Contours

QUANTITY OF X

But a consumer would not be indifferent between a combination of X and Y lying on R'P'S' and a combination lying on T'O'V'. Each combination on T'O'V'

is

preferred to any combination on R'P'S' be(for example,

cause the former yields a higher level of total utility

TT'>RR'). Curves such as R'P'S' and T'O'V' are called indifference curves.

—or

An indifference curve is a locus of points combination of goods each of which yields the same level or to which the consumer is indifferent. Definition:

—

A

partial set of indifference curves

such as this are called indifference 4

of

If the utility

good

I

function

consumed, X-

indifference curve

is

is

is

given by the

shown maps*

(

.

curve.

.

,

X„) where X,

amount of good 2 consumed, and so

is

Graphs

the

amount

forth, then

an

defined by the equation 17(Xi,AV--,X,)

where

.

of total utility,

in Figure 1.2.3.

is

U Xu X~,

particular

=

r

c is a constant representing the constant level of utility for that indifference

An

indifference

map

is

generated by choosing different values of

c.

Microeconomic theory

20

FIGURE 1X3 Indifference Curves

The curve

X

tions of

Similarly

and 30

labeled I in Figure

and

Y

3 might represent

combina

of utility to a certain person

utils

and IV represent

all

combinations yielding 19, 2 6, respectively The significance of the ordinal approach to

II, III,

utils

that yield 10

12

all

the recognition that the specific utility numbers attached to

utility is

—

and IV are immaterial the numbers could be 10, 19, 26, and 30, or 100, 190, 270, and 340, or any other set of numbers that in creole The salient point is that for the theory of consumer behavior,

I, II, III,

only the shape of the indifference surface

is

immaterial

The

map

matters

indifference

psychological behavioristic basis without

measurable ence are

utility

all that

The

map

—

the underlying utility

can be defined on a

making use of the concept of

and the concept of prefer bundles situated on the same in bundles lying on a higher curve

indifference curves

—

are required

all

difference curve are equivalent, all

are preferred

A consumer regards all bundles yielding the same level of as equivalent The locus of such bundles is called an indifference curve because the consumer is indifferent as to the particular bundle he consumes The higher, or further to the right, an indifference curve, the greater is the underlying level of utility (compare R'P'S' and T'QV' In Retabons •

utility

1

Figure

utility

and preference

21

Therefore, the higher the indifference curve, the more preeach bundle situated on the curve.

1.2.2).

ferred

is

1.2.C

Summary

The curve

/ Theory of

is

cardinal measure of utility associated with each indifference

immaterial.

The only requirement

is

that indifference curves

rank bundles according to preference. Thus in Figure nations on

IV

1.2.3, all

combi-

most preferred; all bundles on III are preferred to those on II and I and are less desirable than those on IV, and so on. To repeat, cardinal measurement is not required. Ordinal measurement ranking budgets first, second, third, and so ford: is sufficient. are

—

—

CHARACTERISTICS OF INDIFFERENCE CURVES

1.3

Indifference curves have certain characteristics that reflect the three

assumptions about consumer preferences discussed in subsection

For simplicity, assume that there are only

wo

goods,

X

1.1. c.

and Y. The

X—Y plane is called the commodity space. Now consider the three assumptions about

consumer preferences. The first assumption is that the consumer can compare any two bundles and decide that he prefers one or is indifferent between them. This means that there is a point on the utility surface associated with each bundle in the commodity space or that there is an indifference curve passing through each point in the commodity space." Assumption (Hi) of subsection

l.l.c, that (strictly)

larger

commodity bundles are

pre-

ferred to smaller bundles, implies that indifference curves cannot be

upward

sloping. Indifference curves are generally

some

sloping, but in

may have

cases they

drawn downward

horizontal or vertical seg-

*

ments

Third, indifference curves cannot intersect. This property in Figure 1.3.1. In this

points P, Q,

of

X 5

and

and Y)

.

R

jR

graph

I

and

is

illustrated

II are indifference curves,

and the

represent three different bundles (or combinations

must

clearly be preferred to

Q

because

it

contains

speaking, in order to assure the existence of a continuous utility function that is suggested here, an additional assumption about the continuity of consumer preferences is needed. Readers interested in the conditions needed to Strictly

establish

the existence of a continuous utility function

Debreu, The Theory of Value

consult

Gerard

Sons, Inc,

1959),

should

(New York: John Wiley &

chap. 4. r

‘

are

When

assumption (Hi) is not made we can get cases when indifference curves in whole or in part (see Questions 5 and 6 at end of chapter).

upward sloping

Microeconom c theory

22

FIGURE 1.31 Indifference Curves

Cannot Intersect

QUANTITY OF X

more of both goods

are equivalent because they are situated

In like manner,

11c,

section

indifferent to

P and Q

indifference

B

and

m subsection

(characteristic (tv)

B

is

on the same

By

are indifferent is

a

transitive

indifference curve

characteristic («), sub

relation

A

indifferent to C,

11c) R and P

—

must be

that

is,

if

A

indifferent to

is

C

R is indifferent to P and P is indifferent to Q hence R must be indifferent to Q Bur as previously shown, R is preferred to Q because it contains more of both goods Hence intersecting indiffer In our present case,

ence curves, such as those shown in Figure sible given the

A

131,

are logically impos

assumptions about consumer preferences

fourth property of indifference curves, which

is

not implied by

the assumptions about consumer preferences but

is

often used for

expository convenience, \exity

means

is

that indifference curves are

that the indifference curve lies

above

point as illustrated in panel (b), Figure

13

in panel (a) of that figure

(it is

is

not convex

2

The

its

convex Con

tangent at each

indifference curve

concave)

Properties

Indifference curves possess the following characteristics (a) indifference curves are negatively sloped (or at least not positively

an indifference curve passes through each point in com modify space (c) Indifference curves cannot intersect For expository convenience it Is often assumed that indifference curves are convex sloped)

(b)

1

FIGURE

/ Theory of utility and preference

23

1.3.2

Indifference Curves Are

Convex

MARGINAL RATE OF SUBSTITUTION

1.4

As

previously stressed, an essential feature of the subjective theory

of value

same

is

that different combinations of commodities can yield the

level of utility.' In other words, the

to the particular

consumer

is

indifferent as

combination he obtains. Therefore, as market prices

one commodity can be substituted for another in the right amount so the consumer remains just as well off as before. He will, in other words, remain on the same indifference curve. It is of considerable interest to know the rate at which a consumer is willing to substitute one commodity for another in his consumption pattern. Consider Figure 1.4.1. An indifference curve is given by the curve labeled 7. The consumer is indifferent between the bundle R, containing OXj units of and OY units of Y, and the bundle P containing OX_. and OY2 OY x units of Y. The consumer OX] units of

might

dictate,

X

X

>

is

at

willing to substitute

which he

is


0

implies

Pv

dU

0

Similarly,

the consumption of will increase utility

MUX — px MUV less than zero a decrease in Pv X (and an increase in the consumption of Y)

if

is

When

utility

maximum

at its

is

subject to the

budget constraint neither of these outcomes cun hold and that Aft/,

maximum

— — MU

V is

this

means

zero In other words, a necessary condition for

utility subject to

the budget constraint

is

that

X

and

Y

be

chosen such that

Alt;,

-

h.

MUV =

0

Pv

or

6

MU* _

ft

MUy

py

For purposes of the present argument

we

(2 2 5 )

could have equally well solved for dx

2 / Theory

We

saw

in footnote

8 of Chapter

rate of substitution of

X

for

Y

1

of

consumer behavior

MUX/MU

that

39

the marginal

V is

so (2.2.5) says the point of consumer

equilibrium requires

=

MRSX

&

•

Pv If there are several

goods the same reasoning applies to get the con-

sumer equilibrium conditions

MU

X

= MUy =

p:

CHANGES

2.3

IN

=

Mt/j ( 2 2 6) .

pt

py

.

MONEY INCOME

Changes in money income,

prices remaining constant, usually result

in corresponding changes in the quantities of commodities bought. In particular, for so-called

"normal” or "superior” goods an increase

in

money income leads to an increase in consumption and a decrease in money income to a decrease in consumption. It is of considerable interest to analyze the effects upon consumption of changes in income. To do so, we will hold nominal prices constant so as to observe the effects of income changes alone.

2.3.a

5

The Income-Consumption Curve

As explained

an increase

in subsection 2.1.C,

money income shifts movement is a parallel

in

upward and to the right, and the shift because nominal prices are assumed to be constant. In Figure 2.3.1, the price ratio is given by the slope of LM, the original budget line, and remains constant throughout. With money income represented by LM, the consumer comes to equilibrium at point P on indifference curve I, consuming 0.v, units of X. Now let money income rise to the level represented by L'M'. The consumer shifts to a new equilibrium at point Q on indifference curve II. He has clearly gained. He also gains when money income shifts to the budget line

the level corresponding to IJ'M".

The new

equilibrium

on indifference curve III. As income shifts, the point of consumer equilibrium

The

line connecting the successive equilibria

is

is

at point

R

shifts as well.

called

the income-

consumption curve. This curve shows the equilibrium combinations of c

We assume throughout the discussion

that the

good. "Inferior” goods are treated in Chapter

3.

good

is

a "normal" or "superior"

Microeconomic theory

40

FIGURE

2.3.1

The Income-Consumption Curve v

X and Y purchased at various

levels of

money income, nominal

prices

remaining constant throughout

The income-consumption curve

the locus of equilibrium budgets resulting from various levels of money income and constant money prices The income-consumption curve is positively sloped Definition:

throughout

2.3.b

its

entire

is

range when both goods are “normal” or “superior”

Engel Curves

The income-consumption curve may be used for each

to derive

Engel curves

commodity

Definition:

An Engel curve

is

a function relating the equilibrium quantity

purchased of a commodity to the level of money income The name is taken from Christian Lorenz Ernst Engel, a 19th-century German statistician

Engel curves are important for applied studies of economic welfare and for the analysis of family expenditure patterns

2 / Theory of consumer behavior

Engel curves relating the consumption of commodity

X

to

income

are constructed in Figure 2.3.2. Neither panel (a) nor panel (b) directly based

upon the

41

is

particular income-consumption curve in Figure

2.3.1; but the process of deriving

an Engel curve from an income-

consumption curve should be clear.

At is

the original equilibrium point

px * OM (or p v

P

in Figure 2.3.1,

Oh ) At the income px OM, Ox *

-

.

j

money income

units of

X are pur-

chased. This income-consumption point can be plotted

on a graph such as panel (a), Figure 2.3.2. When the budget line shifts from LM to L’M! (Figure 2.3.1), money income increases to px -OM' and consumption to Ox2 units. This income-consumption pair constitutes another point on the Engel curve graph. Repeating this process for all levels of money income generates a series of points on a graph such as panel (a) Figure 2.3*2. The Engel curve is formed by connecting these points by a line. v

FIGURE

2.3.2

Engel Curves

Two

INCOME

INCOME

(a)

(b)

basically different types of

Engel curves are shown

in panels

(a) and (b), Figure 2.3.2. In panel (a), the Engel curve slopes up-

ward rather gently, implying diat changes in money income do not have a substantial effect upon consumption. An Engel curve with tills property indicates that the good is bought when income is low, but the quantity purchased does not expand rapidly as income increases. If "food’' is treated as a single commodity, its Engel curve would look something like the curve in panel (a), even though the curve for "steak” as a separate commodity probably would not. On the other hand, steak and many other types of goods give rise to

Microeconomic theory

42

Engel curves more nearly represented by the curve in panel (b). The relatively steep upward slope indicates that the quantity bought changes

markedly with income/

Engel Curves and the Income Elasticity of

2.3.C

The income

elasticity of

demand, which

is

Demand

discussed

much more

throughly in Chapter 4, has the following

The income elasticity of demand is the proportional change in the consumption of a commodity divided by the proportional change in income Definition:

Income

elasticity

may be

related to the slope or curvature of

an Engel

curve and, in part, to the classification of commodities as superior,

normal, or inferior Consider Figure 2 3 3 Our object of

ticity

income

any point on an Engel curve. As indicated above, income elasticity ( 7} m ) is given by the formula

demand

definition

to determine the

is

at

elas-

in the

dx Af

mx

nm

Suppose a consumer of good

X

is

(2 3

'

B on

situated at point

1)

the Engel

The tangent at B is given by the straight line EF. By the definition and formula (23 1 ) income elasticity is the reciprocal of the slope

curve

,

of the tangent to the Engel curve multiplied by the reciprocal of the

The

proportion of income spent on commodity X.

curve at point

B

is

HB/EH,

so

its

reciprocal is

X bought OH and the income spent on X is

is

slope of the Engel

EH/HB. The amount HB. Thus

is

its

of

reciprocal

HB/OH. Therefore, the income elasticity at point B is Vm It

EH HB _ EH HB OH OH


is

better off in

sum and supperiod 1 when

.

(3.5.1)

,

(3.5.2)

if

3.5.

ZpV > ZfV

is

because the

shows that the period 1 bundle was not chosen period even though it could have been.

in the base

then the individual

is

better off in the base period. This

inequality

b

Index Numbers as Indicators of

Individual Welfare

Changes

pushed somewhat further by introducing three index numbers. The first of these index numbers measures the change in the consumer’s income from the base year to the given year. Since it is assumed that income equals expenditure, the incomes of the base

The

analysis can be

year and the given year are Sp°x° and the index of income change

is

respectively. Consequently,

Microeconomic theory

68

The next index number to be introduced is called the Laspeyre index. This index number measures the cost, relative to the base period, of purchasing the base-year quantities at the given-year prices. Since the cost 1

of the base-year quantities at given-year prices

index

is

Sp x,

the Laspeyre

is*

l

2p x° Zp°x° Finally, the Paasche index

(3 5 4)

*

measures the cost of purchasing the given-

year quantities at given-year prices relative to their cost at base-year prices. Since the cost

the Paasche index

of given-year quantities at base-year prices

is

2p*x\

is

II

(3 5 5)

Now

from expression (35.1), the individual is better off in period 1 if SpV Spy. Dividing both sides of this inequality by SpV, we have

>

Sp'x1

2pV >

ZpV ZaV>

’

(3 5 6)

or

E>

L

(3 5 7)

from expression (3 5.2), the individual is better off in the x° base period if 1p° )> 2pV. Dividing both sides of this inequality by Spy, we have Similarly,

Zp°x°

ZpW >

ZpV 1

Zp'x'

(3 5 8)

or

1

E

. >

1

P

’

(3 5 9)

or

E< P

(3 5 10)

From

this analysis, especially expressions (3-5-7)

and (3-5.10), four

cases are possible.

*

The

of Labor

familiar

Consumer

Statistics is

Price Index produced each month by the U.5 Bureau an index of the Laspeyre form

3 / Topics

E

1.

is

greater than either

P

or L.

By

in

consumer demand

69

expression (3.5.7), the indi-

viduals standard of living increases from period 0 to period 1. By (3.5.10) his standard of living does not fall. Hence the individual is definitely better off in period 1.

E is less than either P or L. By expression

2.

was better

By

off in the base period.

given period.

An unequivocal

(3.5.10)

,

the individual

(3.5.7) he was not better off in the

answer

is

again obtained: the individual’s

standard of living falls from period 0 to period

1.

L^> E P.ln this case neither expression (3.5.7) nor (3-5.10) is satisfied. L^> E implies that the consumer is not better off in period 1. But E^> P implies that he was not better off in period 0 either. Con3.

sequently,

P

4.

ent.

no conclusion can be drawn.

E^>

L.

This situation, though possible,

E

By expression (3.5.10), P

better off in the base period. better off in period

1.

The

But

is

totally inconsist-

was that he was

implies that the individual

E^> L implies, by

(

3.5.7

)

,

individual’s standard of living has both risen

Such a contradiction may be attributable to a change in the individual’s preference pattern. In any event, it precludes an inference concerning the change in the individual’s welfare. and

fallen!

In summary,

it is

sometimes possible to determine whether an

vidual’s standard of living has increased or decreased

number comparisons. In other

situations,

indi-

by means of index

however, the results are

in-

conclusive or contradictory. Therefore, in these cases the theory of index

numbers has nothing to contribute

to the analysis of individual welfare

changes.

APPLICATIONS OF INDIFFERENCE CURVE ANALYSIS: THE CHOICE BETWEEN LEISURE AND INCOME 3.6

theory of consumer behavior as formulated above is quite genand it leads to many interesting and important propositions con-

The eral,

cerning

demand and consumer

choice.

However,

it is

useful to simplify

the theory and to introduce leisure into the preference function. end, let us aggregate expenditures

on

all

To

that

goods and services into the

simple term income. Since by our assumptions all income is spent on goods and- services (which includes saving), this income is simply our familiar budget constraint.

At

the same time, the

amount of income

consumer deThe more one works,

received by a

pends upon the amount of time allocated to w'ork. the greater is his income. Yet the more one works, the

less is

the leisure

MIcroeconom c theory

70

time remaining to him Leisure also has utility to most people, there fundamental tradeoff between fore, each consumer is confronted with a the consumption of goods and services and the consumption of leisure The object of this section is to analyze this tradeoff in some very simple cases

3

6a The Income-Leisure Graph Consider Figure 3

61 Income

is

plotted

on the

vertical axis,

and

lei

on the horizontal axis in the rightward direction The unit of time it may be hours per day in which leisure is measured is not relevant weeks per year or any other measurement unit The essential point is that the total amount of time is fixed (say, 24 hours per day), and the sum of work time and leisure time must equal this fixed total time Thus sure

—

m

a leftward direction along the horizontal work time may be measured axis In Figure 3 61, OZ is the total time available If OC hours per day are taken as leisure, then CZ hours are spent at work Let us now' make two simplifying assumptions First the individual 4 5 may work as many hours per day as he desires Second the income per hour is the same irrespective of the number of hours worked Thus if the individual w'orks CZ hours per day and receives income of CE OG his hourly wage is CE/CZ But since CEZ and OZA are similar triangles CE/CZ OA/OZ Thus the slope of the straight

=

—

line

ZA represents the hourly w'age rate *

Exercise Suppose an individual works CZ hours per day and receives that the slope of ZB represents the hourly wage rate

income CF Show 3

6b

Equilibrium between Income and Leisure

Since income (or consumption) and leisure are competitive sources

them may be tepte 7 shown in Figure 3 6

of utility the consumer s preference pattern between

sented by an indifference 4

map

such as that

Recall that the unit of measurement of time

brevity

we speak

of hours per day

Any

For the sake of other time measurement may be sub is

s turned

*

This

6

ZA

—

irrelevant

•

not an unrealistic assumption individuals can find part time employ ment and they also can hold more than one job by moonlighting and other means In a problem at the end of the chapter we ask the reader to analyze the effect of restrictions on the number of hours that can be spent working js

is

a straight line because

we have assumed

that the hourly

wage

rate

is

constant 7

Note

that this

is

tive sources of utility

X

exactly the same as saying that goods and Y are and that there must be a tradeoff between them

alterna

3 / Topics

FIGURE

in

consumer demand

3.6.1

Income Constraint Y

INCOME

FIGURE

3.6.2

Tradeoff between Income and Leisure

LEISURE

71

Microeconomic theory

72

FIGURE

3 6 3

Consumer-Worker Equilibrium y

LEISURE

The

indifference curves

curves (see Chapter

OA

have

all

the properties of the usual indifference

13) Thus

hours of leisure and income

OC Of

come

the consumer

indifferent between

OD, and OB hours

of leisure and in

course, the higher the indifference curve, the greater

OA

Tor example, suppose that

utility

is

the consumer gains greater utility

if

is

hours of leisure are taken Then

his

income

is

OE

than

OD

if it is

61 and 3 62 together, as shown in Figure 3 6 3 In the customary manner, we may determine the point of utility maxiKwmvoa (consumer equilibrium) The maigitva.1 rate of substitu Let us

tion

Figures 3

given by the

is

The

now put

price ratio

num is

is

(

negative of the) slope of the indifference curve

given by the (negative of the) slope of ZA Equilib

attained point

E on

II,

with

CZ hours

of work and income

Indifference curve III cannot be attained at the given

wage

curve lower than II will result in less utility since there tradeoff that will

3

6c

Any

a possible

the consumer worker better off

Overtime Rates

It is

pay

make

is

rate

OB

for

now customary overtime

that union

work In the

management

contracts require extra

situation represented by Figure 3

64,

3 / Topics

"overtime”

is

any work in excess of

that the "overtime”

wage

wage. Thus the slope of of

ZFB

hours of

is

ZA

CZ

is

consumer demand

73

hours per day. Further assume

half again as great as the "straight-time”

wage and the slope and overtime wage (where CZ

represents the regular

represents the straight-time

work

in

straight time). Finally,

work overtime or not according It is clear from Figure 3.6.4

assume that the worker can

to his choice.

that the result of overtime pay for any

FIGURE

3.6.4

Overtime Rates

y

individual

is

uncertain.

A person with

an indifference

map

represented

choose to work overtime, while an individual with an 1" will never voluntarily work overindifference map represented by time. An intermediate case is illustrated by the indifference curve V.

by

I will clearly

Such an individual is indifferent between working KZ hours for KE income or working AiZ hours for A1G income. In the absence of auxiliary side agreements between union or individual worker and

overtime wages.

management,

it is

impossible to predict the effect of

Microeconomic theory

74

3.6.d

Demand

for

General Assistance Payments’

Among many of the social welfare programs that have been proposed by the federal government is one that would provide a annual income per family. This program has not yet been

for adoption

minimum

adopted, nonetheless

sequences of

we may

analyze

potential economic con-

it.

Refer to Figure 3 6

5.

Suppose the wage rate FIGURE

Demand

slope of

some

ZA.

is

represented by the

3 6.S

for General Assistance

In the absence of a guaranteed

Payments

minimum

income, an

indi-

whose indifference map is given by 1, 11 would attain equilibrium at B, working CZ hours and receiving income OYv If a minimum income of OYmla is guaranteed by the government, this individual might still work CZ hours, earn income of 0Yo , and receive supplementary payment from the government of BD Ya Fmin In this case, howvidual

=

—

.

by doing on indifference curve 11 and

ever, the individual can attain a greater level of satisfaction

no work

at all

—by moving

8

to point

E

For a much more detailed discussion, see C. T. Brehm and T. R. Saving, “The Demand for General Assistance Payments,” American Economic Review, voL 54

y-“

—

y-a = Ay~a [(x +

Ax°,

Using the binomial theorem,

we

Ax)“

—

x°]

can expand the term (x

(5.4-4)

.

+ Ax)

a

as

follows: r Qx

Now

+ Ax) a = .

1

.

X** -f-

~ A axa Ax , l

for small values of Ax,

a(a. — +— .

we may

l)xa A-}

~2 (Ax) 2 “

—— +

”•

* •

.

(5-4.5)

ignore the terms that involve 2

3

higher powers of Ax, that is, (Ax) (Ax) and so forth. Thus -1 (x Ax)“ is approximately equal to x“ The production function may be written Q~f(K, L), vQ/BL are the marginal products of capita! and labor respeemely a

/( 0 ,

cunc

and variable inputs of labor is C|Pf. At labor output is PP', and at labor input Oh, total output is PG.

input, reaches a point of Let

amount OC,. The

units of capital

The total product curve C,PP 1

in a different manner. Hold

In constructing Figure 6

0>=0

22 wc

ha\e assumed

that

'where

/(AT,

0)

$Q/dK

= f( 0, L) ~

6 / Production and optimal input proportions

149

marginal physical returns to labor for the given capital input OC,), and thereafter increases at a decreasing rate.

The same statement

applies to a typical total product curve for a

and variable capital usage. Hold the input of labor

fixed labor input

constant at OL, units.

L,PD

the curve of total output resulting from

is

variable inputs of capital. For example, used, output

is

PP';

OC units

when

when OC,

units of capital are

are employed, output

Production Isoquants

6.2.c Still

using Figure 6.2.2,

determine

let us

all the different

binations capable of producing PP' units of output.

(or "intersect”)

slice

= A A' — BB'.

PP'

the production surface

input com-

To do

OCOL

this,

at the

we

height

This slicing process generates the curve APB, a

locus of points equidistant

(A A'

— PP' = BB')

By dropping perpendiculars from each point on

C—L

DE.

is

from the C-L plane. the

APB

curve to the

plane, one obtains the input combinations associated with each

point. In other words, the curve

generating the curve A'P'B'.

APB

The

is

projected onto the

C—L

latter is a locus of points

plane,

each of

which represents a combination of inputs capable of producing the stipulated quantity of output PP' BB' RR'. For examples, AA' the following three combinations of capital and labor are points on the curve A'P'B': OC, CA'; OC u OL,; LB', OL. The curve A'P'B' is called an isoquant.

=

An isoquant

=

=

a curve in input space showing all possible combinations of inputs physically capable of producing a given level of output. The entire three-dimensional production surface can be exactly Definition:

is

depicted by a two-dimensional isoquant map.

A

portion of an isoquant map, derived from a production surface

such as

OCQL in

Figure 6.2.2,

is

shown

in Figure 6.2. 3.

3

The two

axes

measure the quantities of inputs, and the curves show the different input combinations that can be used to produce 100, 200, 300, and 400 units of output respectively. lies

the greater

Consider

is

first

As

is

obvious, die further northeast a curve

the output associated with

it.

the isoquant for 100 units of output. Each point on

curve shows a capital-labor combination that can produce 100 units of output. For example, OC, units of capital and OL, units of labor this

may be

used, or

OC3 units of capital and OL

units of labor, or

any other

input combination found by dropping perpendiculars to the axes from a point on the curve. 3

The excluded

portion of the isoquant

map

is

discussed in subsection 6.3.d.

150

I1

croeconon c tt-ecry

FIGURE 6^3 Typical Sat of Isoquants

A

ray

from the

origin, such as

capital labor input ratio ratio

OL*

or

OA'B'Cf

defines a consent

In particular, the slope of the ray

For example, at points

respectively, are

OAB

A

and B, 100 and 200

produced at the capital labor ratio

Similarly at points A',

B and ,

C', 100,

the wpi/

is

units of output,

OC\fOL

200, and 300

put respectnely, are produced at the capital labor ratio

x

= OCJ

units of ou*

OCjOL%~

ocjou ~ ocjou Along the ray OAB, v anous le\els of output are producible br the same input ratio, the magnitude of the inputs increases as one moves out along the raj but the capital labor ratio remains unchanged. This contrasts clearly with

movements along an

isoquant. In this case the

unchanged and the

capital labor ratio changes

level of output remains

continuously

These points may be summarized as follows. Relations

An

isoquant represents different input combinations

may be used

or

produce a specified level of output. For movements along an Isoquant the level of output remains constant a'-d r the input ratio changes continuously A ray from the origin d^ nes a 4 specific constant input ratio For movements along a ray, the level of oj put changes continuously and the input ratio remains cons’ant input ratios that

6.2.d

to

Fixed Proportions Production Functions

Using the isoquant device,

it is

easy to illustrate the case of fixed

proportions production functions, briefly mentioned in Chapter 5 As

6 / Production and optimal input proportions

FIGURE Isoquant

you will

recall,

Map

151

6.2.4

for Fixed-Proportions Production Funclion

production

is

subject to fixed proportions

when

one, and 1

only one, combination of inputs can produce a specified output.' For

example, consider the hypothetical production process illustrated in

Two

and labor, must be used in the fixed ratio 2:3. That is, 2 units of capital and 3 units of labor are required to produce 100 units of output. Thus 4 units of capital and 6 units of labor can produce 200 units of output; 6 units of capital and 9 units of labor can produce 300 units; and so on. Figure 6.2.4.

The

OR

inputs, capital

required capital-labor ratio

shown by the

is

slope of the ray

in Figure 6.2.4. Isoquants are constructed for 100, 200,

units of output.

shown

and 300

Rather than taking the more conventional shape

in Figure 6.2.3, the isoquants for fixed-proportions processes are

L-shaped curves. This

illustrates, for

example, that

if

3 units of labor

and 2 units of capital are employed, 100 units of output are obtainable. However, if the quantity of capital is expanded, labor input held constant,

no additional output can be obtained.

4

fixed-proportions production function, which

A

function,

may be

Similarly,

is

if

capital input

frequently called a Lcontief

represented by

.

.

0 = minimum ^

/K L\ I

—

\,

7/7 are isoquants

and

T3

are tan

and the tangents have been con structed so that they are parallel to one another That is the marginal rate of technical substitution of capital for labor is the same at points A B, and C These points have been connected by a smooth curve gents to 7

77,

and

labeled OS, which

777, respectively,

is

called

an

isocline

6 / Production and optimal input proportions

FIGURE

167

6.5.1

Isoclines

a— GENERAL PRODUCTION FUNCTION

PANEL b—LINEARLY

PANEL

Definition:

An

HOMOGENEOUS

PRODUCTION FUNCTION

isocline is a locus of points along

which the marginal

rale of technical substitution i$ constant.

may have

In general, isoclines

almost any shape.

The one

in panel

a has been constructed so as to

ramble through the isoquant map. The

special isoclines in Figure 6.3.3

have a very regular shape.

We may now

pause to point out the following Relation:

The “ridge

lines” defining the

economic region

of

produc-

inasmuch as the marginal rate of technical substitution constant along the lines. In particular (see Figure 6.3.3), OC is the isocline along which the marginal rate of technical substitution of capital for labor is infinite, OL is the isocline along which it is zero. tion are isoclines is

Now turn to panel b, Figure 6.5.1, in which the to that of

—with one important

panel a

labeling corresponds

exception: the curve

OS

has

become the ray OR. This is always true when the production function is homogeneous of degree one. In that case, all marginal products are functions of the input ratio only. Thus the marginal rate of technical substitution,

which

is

the ratio of the marginal products,

tion of the input ratio

input ratio

is

and of nothing

—

constant

else.

is itself

a func-

Therefore, whenever the

for example, 200:100, 400:200, etc.

marginal rate of technical substitution

is

—

the

constant and independent of

the absolute magnitude of the inputs. Since a ray from the origin (such as

OR

must intersect A, B. and C) where the

in panel b) defines a constant input ratio, the ray

the successive isoquants at points (such as

1 68

Mtcroeconomic theory

marginal rates of technical substitution are the same Hence we may state the following

The

isoclines associated with production functions homogeneous of degree one are straight lines Therefore since ridge lines are special isoclines the ridge lines associated with linearly homogeneous

Relations-

production functions are straight lines (providing, of course that function under consideration gives rise to an uneconomic region)

6

5b Changing Output and Turn now

the

the Expansion Path

6 5 2 Given the input prices, the output can be produced at least cost at point A,

to panel a. Figure

corresponding to isoquant I

where the isoquant

is

tangent to the isocost curve

tion of producer equilibrium

With input

KL This

is

the po$i

prices remaining constant,

suppose the entrepreneur wishes to expand output to the level corresponding to the isoquant II The new equilibrium is found by shifting the isocost curve unul

it

is

tangent to

U

Since factor prices remain

constant, the slope of the isocost curve does not change

Hence

it shifts

from KL to K'L' Similarly, if the entrepreneur wished to expand out put to the amount corresponding to the isoquant 1JJ, he would product at point C on III and K”L" Connecting all points such as A, B, and C generates the curve OL

Now

let us

assemble some facts

First, factor prices

stant Second, each equilibrium point

FIGURE

is

have remained

con-

defined by equality between

the

6.5.2

Expansion Paths

PANEL a -GENERAL PRODUCTION FUNCTION

5— LINEARLY HOMOCEN'CUS PRODUCTION FUNCTION

PANEL

6 / Production and optimal input proportions

169

marginal rate of technical substitution and the factor-price ratio. Since the latter has remained constant, so has the former. Therefore, OE is an isocline, a locus

substitution

is

cifically, it is

of points along which die marginal rate of technical

But

constant.

it is

an

isocline with a special feature. Spe-

the isocline along which output will expand

prices are constant.

We

may

when

factor

accordingly formulate this result as a

The expansion path is the particular isocline along which expand when factor prices remain constant. The expansion output will path thus shows how factor proportions change when output or expendiDefinition:

ture changes, input prices remaining constant throughout.

Turn now

to panel b. Since the isoclines of a linearly

production function are straight

lines,

homogeneous

the expansion path

is

also.

Let

us state this as the following Relation: The expansion path corresponding to a production function homogeneous of degree one is a straight line. This reflects the fact that under constant returns to scale, factor proportions depend only upon the factor-price ratio (the slope of the isocost curve);

and

in particular,

factor

proportions are independent of the level of output.

As we

shall see in

Chapter

7, the

expansion path

is

crucial in de-

termining the long-run cost of production.

6.5.c

Expenditure Elasticity 11

In Chapters 2 and 4 the income elasticity of commodity

demand was

income elasticity was related to the incomeconsumption curve; and commodities were classified as superior, normal, or inferior according as income elasticity exceeds unity, lies discussed. In particular,

in the unit interval, or

negative.

The expenditure

elasticity of a fac-

an analogous concept: its measurement is restricted the expansion path; and factors are classified as superior, normal, or

tor of

to

is

production

is

inferior according as the corresponding expenditure elasticity exceeds unity, lies in the unit interval, or

is

negative.

Let us begin with the following

Consider a well-defined factor X. The expenditure elasticity of X is the relative responsiveness of the usage of X to changes in total expenditure. In other words, the expenditure elasticity of X is the proportional change in the usage of X divided by the proportional change in Definition:

11

For a mathematical elaboration of this subsection, see C. E. Ferguson and Thomas R. Saving, "Long-Run Scale Adjustments of a Perfectly Competitive Firm and Industry," American Economic Rericw, vol. 59 (1969), pp. 774-83.

Microeconomic theory

170 total

expenditure

In

changes

this definition

total

in

movements along the expansion path

restricted to

Symbolically, the formula for the expenditure elasticity

dx x

7,1

where x

is

expenditure are

the usage of factor

X

_ dx

dc

dc

c

and

c

is

is

c

x’

total expenditure

on

factors

of production

Next tee introduce another Definition: inferior

A

be superior, exceeds unity,

factor of production Is said to

according as its expenditure elasticity is negative

normal, or lies in the

unit interval, or

This definition

is illustrated

schematically in Figure 6 5 3 Consider the

X

expansion path and concentrate on factor

Along ray

OR

both inputs

expand proportionally At points such as A the usage of factor X expands proportionally more than total expenditure along the expansion path At

all

such points the factor

is

superior

At

points such as

B

factor

usage expands proportionally less than total expenditure Expenditure elasticity lies in the unit interval,

and the factor

D the change in

usage of both inputs

ture elasticity

unity

is

Analysis

is

is

the

is

said to be normal At

proportional and the expend/

same along any ray from

the

origin

In certain

—presumably unusual— FIGURE

cases, the

6

usage of a factor may

53

Expenditure Elasticity and Factor Classification

mirof

x

6 / Production and optimal input proportions

decline

when output and

C in Figure 6.5.3

resource expenditure are increased.

the expenditure elasticity of

X

is

171

At point

instantaneously zero.

Beyond point C, the expansion path "bends back” on itself. The usage of X diminishes as expenditure is increased beyond point C. Over this range of expenditure and output, is an inferior factor. There is a further discussion of inferior factors in section 6.6, and the concept of

X

expenditure elasticity cost curves that result

6.6

CHANGES

IN

is

used in Chapter 7 to analyze the changes in

from changes

in factor price.

INPUT PRICE

you know a change in the price of a good has two theoretically discernible effects: the substitution effect and the income effect. The substitution effect is always negative; and the income effect is normally positive and reinforces it. Much the same type of effects may

From Part

I

be isolated for changes in input price. First consider

Figure 6.6.1. This graph illustrates increases in the

price of labor inputs, the price of the capital input remaining constant.

The

original factor-price ratio

is

given by the slope of the isocost curve

KLy. As this isocost curve shifts leftward to labor increases because the

purchase

same

KL2

and.

total expenditure

KLS

,

on labor

the price of will at

OL x units, then OL2 units, and finally only OL 3 units. FIGURE

6.6.1

Shifting Isocost Curves to in

Show an

the Price of Labor

Increase

first

M croeconom c theory

172

6

6a The Substitution and The

substitution

Output Effects

and output

original point of equilibrium

effects are

is

The

Q

shown

662

in Figure

level of output

is

The

indicated by

h

and the input price ratio by the slope of the isocost curve KLi and Ok x units of capital and Oh units of labor are used No* the isoquant

the price of labor increase the price of capital remaining unchanged

let

KL^

the producer maximizes the out put attainable for this given cost the equilibrium point changes from

This shifts the isocost curve to

Q

to

S

If

the lev el of output falling to that indicated by the isoquant

Ok z

In the ultimate equilibrium position

The

of labor are used

usage

total effect

therefore a decrease from

is

units of capital

/

Oh units

and

wage rate change on labor Ol3 or a reduction of hh units

of the

Oh to

of labor

The

total effect

may be decomposed

into

two components The

change in labor usage attributable exclusively to the change tive input price

is

called the substitution effect

graphically construct the fictitious isocost line structed so there

the

new

is

a

fictitious

To

in the

determine

KL

this effect

This line

equilibrium at the old output

rela

is

con

level and

input prices In other words the rise in input prices has been

compensated by an increase in expenditure level of output

A

fictitious

equilibrium

FIGURE

is

sufficient to maintain the old

reached at point

6 62

Output and Substitution Effects ol a Rise in the Price of Labor

LABOR

R

and the

6 / Production and optima / input proportions

movement from

Q

to

R represents the substitution effect,

173

the change in

input usage attributable only to the change in relative input prices, the level of output remaining constant. In input units, the substitution effect reduces

Capital

Ok 2

,

is

Ol Y

labor input from

Ol2 or by

to

,

substituted for labor, increasing capital

amount lj2 usage from Ok , to the

.

or by k x k 2 .

When

an input price increases, however, there must be a decrease in output if the level of expenditure does not increase. The output effect is

R

represented by the shift from the fictitious equilibrium point

S on

to the ultimate equilibrium point

.

The output

7X

effect leads to a

Ol3 or by the amount l2l3 Capital usage is also reduced by the output effect, from Ok 2 to Ok 3 or by k 2 k 3 The effect upon labor usage attributable to the rise in the price of reduction in labor input from

Ol2

/2

on

to

.

,

.

,

labor

is

sum

simply the

of the two effects:

=

Ills

CEffect

Summarizing, Relation:

usage of

The

to the

change

Ill'S

( Output effect)

( Substitution effect)

we have the following effect of a

this input

stitution effect

+

l ill

change

in

the price of an input upon the

two components. The subinput usage attributable exclusively

may be decomposed

shows the change in relative

in

into

input prices, output held constant. This effect

is

and a fall output effect input. The the usage of in input price to an increase, in the shows the change in input usage attributable exclusively to a change in the level of output, input prices remaining constant. It should be emphasized that these adjustments are for a fixed total expenditure. They do not allow for adjustment to a point of profit maximization. always negative

6.6.b

in

that a rise in input price leads to a reduction,

“Inferior Factors”

Just as there

may be

and the Output

inferior goods, there

production; and just as the former effect,

the latter

factor inferiority

purposes, the

The

initial

is is

same

is

12

may

be inferior factors of

associated with a negative

income

The

case of

associated with a negative output effect. illustrated in Figure 6.6.3,

which

is,

for all practical

as Figure 6.5.3.

equilibrium

is

on 7a where the slope of the isocost ratio and Olx units of labor are employed.

at

Q

KL indicates the factor-price Now let the wage rate rise so as X

point of equilibrium shifts to 12

Effect

,

to rotate the isocost curve to

S on

I2 ,

KL2 The .

and the usage of labor expands to

For a detailed treatment of factor inferiority, upon which this section is based, see C. E. Ferguson, The Neoclassical Theory of Production and Distribution (London and New York: Cambridge University Press, 1969), chap. 9-

Microeconomic theory

174

FIGURE 6

63

Optimal Input Combination to Maximize Output

OI3 To curve

see the

components of the change, construct the

K V so that f

new

reflecting the

it is

tangent to the original isoquant but has a slope

The tangency

price ratio

the combination of inputs that

were produced

R

at the

new

to

negative That

is,

inversely with

its

price for

The movement from

would be used

OU

is

in output

from the

of the factor tion

is

wage

rate

R

if

shows

the old level of output to

the substitution effect, and as

in

varies

movements along an isoquant

the fictitious equilibrium at

change In

OR

to

013

an inferior factor

An

inferior factor of

to the proper

represents the output

the reduction

an increase

this relation occurs the factor

said to be

R

this case it is negative

level to the /« level causes

Whenever

it

the quantity of an input demanded

equilibrium at S or the increase from effect of the

occurs at R, and

The movement from Q

input price ratio

OR

or the decrease from

all cases it is

fictitious isocost

in the usage

under considera

production is one that has a negative output effect or a negative expenditure elasticity 13 Definition

13

Professor Hicks calb this a

regression relation

and suggests

that an infer or

one that is particularly suited for small scale production of the product in question See John R Hicks Value and Capital 2d ed (Oxford Clarendon Press 1946) pp 93-96 esp p 96

factor

is

6 / Production and optimal input proportions

We

175

now

treading dangerously close to drawing a mistaken analogy between consumers and producers. It might be well to recount are

and cannot be drawn between the

the analogies that can

theories of

consumer and producer behavior.

ANALOGIES BETWEEN CONSUMER AND PRODUCER BEHAVIOR

6.7

We have seen that there are many analogies

between the theories of

consumer and producer behavior. Despite these technical similarities, however, there is an important difference that should not be overlooked.

The

theory of consumer behavior explains the nature of the

consumer’s equilibrium.

The

theory of producer behavior, on the other

hand, does not represent a final equilibrium. is

how

the theory

tells

us

the producer will combine inputs to produce a given output

lowest possible cost.

at the

What

It

does not explain which output the pro-

That decision depends on considerations of profit will be taken up in later chapters. For example, in

ducer will decide on.

maximization that

Figure 6.6.2 the effect of the increase in the price of labor

is

to shift

demanded of labor from l\ to ls assuming the producer spends the same amounts on inputs after the price of labor changes as he did before. In fact, as we shall see in the next two chapters, a profit maximizing entrepreneur typically will not spend the same amount after a change in factor prices. It is important to emphasize that the demand for a factor of production cannot be derived solely from a graph such as Figure 6.6.2, because more information is needed the quantity

to

determine the profit maximizing output.

6.8

CONCLUSION

Chapters 5 and 6 contain an explanation of the theory of production and of the optimal combination of inputs when input prices are constant.

We turn next to the theory of cost, which relies upon the physical

laws of production and

upon the prices an entrepreneur must pay

for his

inputs.

QUESTIONS AND EXERCISES 1.

Suppose that Transport Service must produce a certain output of cargo and passenger service per year. The Service is confronted with the- following combinations of HC100 aircraft and mechanics which can be

M croeconom c theory

176

used to yield this required output over schedule requirements

Combination

Number cf

Number of

Number

Atrcraft

Mechanics

1

60

2

61

3

62

4

63 64

3

7

If

Transport Service

many men can

it

is

Your answer

using

60

aircraft

dispense with and

acquires an additional

b

1

65 66

6

a

route pattern and meet

its

in ( 1

1

000 mechanics

maintain

still

ho*

output

its

if it

HCI00? of

called the

is

)

and

000 920 S30 800 760 730 710

in

economic theory annual cost resulting from the operation of another HC100 is $250 000 and if mechanics cost Transport Service $6000 each annually should the Service acquire a 6lst HCI00?

c

If the additional

d

Which combination

of aircraft and mechanics should Transport

system use to minimize e

/

costs?

Suppose the annual cost of an HC100 drops to $200000 and the cost of mechanics rises to $7 000 per year What combination should now be employed to minimize annual costs? Can the data presented above be used to illustrate the la* of di

mtmshing returns? 2

its

Why or why not?

Suppose that a product requires two inputs for correct to say that

if

its

production Then

is it

the prices of the inputs are equal optimal behavior

on the pan of producers

will dictate that these inputs be used

m equal

amounts? 3

The Norfolk and Western Railway

did not change from steam to

diesel

locomotives until nearly all other railroads had done so This was probably because ( a ) the wanted to conserve national oil reserves

N&W

for future generations, (b) since the railroad ran through the heart of the Appalachians coal was cheap relative to diesel fuel, (z) &

—

management with the

4

like

some economics

Iron Horse

,

(d)

all

professors

—couldnt

N

^

bear to part

of the above

A railroad would be most likely to substitute expensive signaling systems for multiple track operation

if

(a) second and third tracks

w ere heavily

taxed by the counties through which they passed, (b) signaling equip-

ment was produced by a monopolist Principles of Economics, (d)

(z)

all

none of the above

railroad officers took

6 / Production and optima I input proportions 5.

Answer

and explain your choice. Two factors of production, say A and B, have the same price. The least-cost combination of A and B for producing a given output will be at the point where the isoquant has a slope of minus 1. Assume only two factors A and B are used to produce output X.

a.

b

177

.

c.

true or false

A

decrease in the price of

If.

the marginal product of

more

leads to less of

A

more

additional cost of one of factor

A

is

5

and

its

B

being used.

price

is

$2, then the

unit of output obtained by employing

A is $2.

employment of factors A and B, the marginal product of A is 3 and the marginal product of B is 2. The price of A is $5 a unit, and the price of B is $4 a unit. Because B is

At

d.

current levels of

the less expensive factor of production, the firm can produce the

same output

employment of

increasing the 6.

marginal product of

If the

a.

lower cost by reducing the employment of

at

ginal product of

mum

Answer

c

is

L

when

is

MP L =

—

100 L

when

the price of

K

—L

and the marK, then what is the maxi-

K

is

that can be spent

$5 and the price of

$5 and the price of L P K and the price of L

is

(Advanced) When the price of K is what is the expenditure elasticity for

.

100X

amount

the total

$1,000 and the price of

part (a)

and

B.

MPK =

is

possible output

on K and L is $2? b.

K

A

K?

L

is

$5.

is

PL

,

For L? (Hint: Use the

marginal productivity equilibrium conditions to derive a relationship that expresses

MPk

and

equation

MPL

C

is

Use

in terms of

K,

PK PL and ,

the parameters of

this expression to substitute for

L

in the cost

— Pk K + P lL.)

(Advanced)

d.

.

L

If total

output

the production function

is

zero

when

K

and L are

zero,

what

F(K, L) ?

SUGGESTED READINGS 1

George H., and Mishan,

E. J. "Exploring the ’Uneconomic Region of the Production Function," Review of Economic Studies vol. 29

Borts,

(1962), pp. 300-312. Cassels,

John M. "On

the

Law

Economics pp. 223-36.

of Variable Proportions," Explorations in

New

York: McGraw-Hill Book

Co.,

Inc.,

1936.

Ferguson, C. E. The Neoclassical Theory of Production and Distribution chaps. 1-6. London and New York: Cambridge University Press, 1969. [Advanced math necessary.] ,

and Saving,

Thomas R. "Long-Run

of

*-a

Firm and Industry," American Economic Re 59 (1969), pp. 774-83. [Advanced math necessary.]

Perfectly Competitive

view, vol.

Scale Adjustments

178

Microeconomic theory

M

and Quandt, Richard E Microeconomic Theory A Mathematical Approach, 2d ed pp 58-67 New York McGrawHill Book Co Inc , 1971 [Elementary math necessary}

Henderson, James

,

,

,

Hicks, John

R

Value and Capital, pp 78—98 2d ed Oxford Oxford Uni

versity Press,

1946

Samuelson, Paul A Foundations of Economic Analysis, pp 57-76 Cam bridge, Mass Harvard University Press, 1947 [Advanced math neces sary}

7 Theory of cost

resources, jointly

7.1

INTRODUCTION

The

physical conditions of production,

and the economically

efficient

the price of

conduct of an entrepreneur

determine the cost of production of a business firm. The pro-

duction function furnishes the information necessary to trace out the isoquant map. Resource prices establish the isocost curves. Finally, efficient entrepreneurial

behavior dictates the production of any level

of output by that combination of inputs which equates the marginal rate of technical substitution

and the input-price

ratio.

of tangency therefore determines a level of output and total cost.

From

this information,

one

may

Each position its

associated

construct a table, a schedule,

or a mathematical function relating total cost to the level of output.

This

is

the cost schedule or cost function that

is

one of the subjects of

this chapter. It is

not the only subject, however, because in the short run, by

definition, all inputs are not variable.

Some

are fixed, and the entre-

preneur cannot instantaneously achieve the input combination that corresponds to economic efficiency rate of technical substitution

(i.e.,

the one that equates the marginal

with the input-price ratio)

as efficiently as possible; but in the short run, a point

path will generally not be attained.

We

long-run cost but short-run cost as well. 179

.

He will

operate

on the expansion

must thus analyze not only

Microeconomic theory

180

Before turning to the mechanics of cost analysis, however, to pause for a

somewhat broader view and

we need

to pose the question, "Just

There are two answers to this question which, under ideal circumstances, happen to become one and the same. At present we must be content with the two; but in Chapter 1 6 we set out the conditions under which the answers

what

constitutes the legitimate costs of production?”

are the same.

Social Cost of Production

7.1.a

Economists are principally interested in the social cost of production, the cost a society incurs

when

its

resources are used to produce a given

commodity. At any point in time a society possesses a pool of resources either individually or collectively owned, depending upon the political organization of the society in question object of economic activity

ing pool of resources.

is

What

to get as

From a social point of view the much as possible from this exist*

"possible,” of course, depends not only

is

and full utilization of resources but upon the specific list of commodities produced. A society could obviously have a greater output of automobiles if only small compact cars were produced. Larger, more luxurious cars require more of almost every input. But

upon the

m

efficient

their private evaluation schemes,

attach

some members of the

much greater significance to luxury cars than

to

compact cars.

Balancing the relative resource cost of a commodity with social desirability entails social cost

This broad problem

attention can

The

a knowledge of both is

may

society

its

relative

social valuations

and

deferred to Chapter 16 so that our

now be directed exclusively to social cost. bundle of resources to produce a unit of the number of units of commodity Y that must be

social cost of using a

commodity

X

is

sacrificed in the process.

Resources are used to produce both

(and all other commodities). Those resources used in cannot be used to produce Y or any other commodity. To

X

X and Y

production

illustrate

with

a simple example, think of Robinson Crusoe living alone on an island

and sustaining himself by Crusoe of an additional

and gathering coconuts. The cost to measured by the number of coconuts he

fishing

fish is

more time fishing. The concept of social cost, or as it is more frequently called, the alternative or opportunity cost of production, captures much of the essence of what economics is about. Unfortunately, this concept of cost has to forego because he spends

is

often overlooked in popular discussions of public and private policy

7 / Theory of cost

181

For example, congressional spokesmen often argue against the policy of an all volunteer armed force on the grounds that it "costs” issues.

too

much

ing

is

relative to a policy of conscription.

The

error in this reason-

government to individuals who are not the appropriate measure of the

that the cash payments by the

are drafted into military service social cost of the draft.

The

individuals drafted into military service

where they are producing goods and services like health care, houses, automobiles, and educational services. By drafting people into the armed services, society must give up some of these goods and services and this foregone production is the appropriate measure of the cost of conscription. are often taken out of civilian jobs

The alternative or opportunity cost of producing one unit commodity X is the amount of commodity Y that must be sacrificed order to use resources to produce X rather than Y. This is the social Definition:

of in

cost of producing X. 7.1. b

Private Cost of Production

There is a close relation between the opportunity cost of producing and a calculation the producer of commodity must make. The use

X

X

of resources to produce

X rather than Y entails a social cost; there

private cost as well because the entrepreneur

must pay a

is

a

price to get

the resources he uses.

Suppose he does. The entrepreneur pays a certain amount to purchase resources, uses them to produce a commodity, and sells the commodity. He can compare the receipts from sales with the cost of resources and, roughly speaking, determine whether he has

made an

accounting profit or not. But an economist would be quick to entrepreneur he should

money

make some further calculations. He commodity X.

tell

the

has invested

he had not undertaken this line of business, he could have invested his time and money elsewhere in another line of business, perhaps, or by purchasing securities with his money and using his time as an employee of another his

time and

in producing

If

—

entrepreneur.

The producer sources.

He

of

incurs

X

incurs certain explicit costs

some

implicit costs also,

and a

by purchasing full

re-

accounting of

must take these implicit costs into consideration. The pure may economic profit an entrepreneur earns by producing commodity be thought of as his accounting profit minus what could be earned in the best alternative use of his time and money. These two elements are

profit or loss

X

called the implicit cost of production.

M croeconom/c theory

182

The implicit costs incurred by an entrepreneur in producing commodity consist of the amounts he could earn in the best alternative use of his time and money He earns a pure economic profit from producing X if and only if his total receipts exceed the sum of his explicit and implicit costs Definition

a specific

Implicit costs are thus a fixed

amount

(in the short run) that

must be

added to explicit costs in a reckoning of pure economic profit.

7.1

c The Role of the Entrepreneur

The cost concepts

discussed in subsections

71a and

7

1

b

are useful

in understanding the role that the entrepreneur plays in the

economic system To take a simple example, suppose there are two towns that are geographically separated In one of these tow ns there is an abundance of apples but very

little

bread

The

reverse

is

true in the other town.

Accordingly, apples are cheap and bread expensive

and bread

is

m

town cheap and apples are expensive in the second town An

enterprising businessman

who observes

the

first

these differences stands to profit

by purchasing apples from the first town at low pnces and selling the second town. At the same time, he can pur them at high prices chase bread at low prices in the second town and sell it at high prices in the first town. The businessman will continue to engage in such trading until he drives the prices in the two towns so close together that trans-

m

portation costs, the opportunity cost of his money, plus the value of his

time are no longer covered by gains from further transactions In

this

process both the businessman and the townspeople have gamed. For

town got more bread, which they for apples which were relatively less valuable to them.

example, the people in the valued highly,

first

This simple illustration helps us see the importance of measuring costs as alternative costs as in subsection

7

1

as well as explicit costs as in subsection 7

a or measuring implicit

1b When

measured, die existence of a pure economic profit

economic

profits exist

than in

1

currently employed. Entrepreneurs efforts to profits

a signal that in the activity where

is

more highly in the activities where those

dividuals value the use of resources

costs are so

resources are

maximize pure economic

provide the mechanism by which scarce resources are directed

into activities or uses which the individuals in the society value most

highly 1

It is interesting

means that

v*

to note that the symmetry of the definition of opportunity cost

hen a pure economic profit exists in one loss in one or more other activities

pure economic

activity, there is necessarily

a

7 / Theory of cost

1 83

SHORT AND LONG RUNS

7.2

In Chapter 5 a convenient analytical fiction was introduced, namely the short run, defined as a period of time in which certain types of in-

puts cannot be increased or decreased. That

is,

in the short run there

whose usage cannot be changed regardless of the level of output. Similarly, there are other inputs, variable inputs, whose usage can be changed. In the long run, on the other hand, all inputs are are certain inputs

variable

most

—

the quantity of

efficient

inputs can be varied so as to obtain the

all

input combination.

The definition

of the long run

is

time sufficiently long, such that adjusted.

The

short run

is

reasonably clear-cut;

all factors

it is

a period of

of production can be fully

a more nebulous concept. In one nano-

second virtually nothing can be changed in the production process. In a

day

it

may be

possible to intensify the usage of certain machines; in a

ment; and in a year

may be able to rent some additional equipit may be feasible to have a new plant built. There

many

"short runs,” and the longer the time the greater

month

the entrepreneur

are obviously

the possibilities for factor substitution and adjustment. Costs of produc-

ing a given output will clearly depend on the time available to

make

adjustments in amounts used of the productive factors. Before going

and short-run costs, we provide a general overview by examining the relationship between production functions and into detail about long-

costs.

7.2.a

The

Long-Run Costs and the Production Function tools of

Chapter 6 allow us to relate costs to outputs. That

for any given output,

we can determine

the

minimum

that output can be produced given factor prices function. This

is

illustrated in

cost at

is,

which

and the production

panel (a) of Figure 7.2.1 for three

dif-

minimum total cost is determined by the isocost line Cx At output level Q 2 the minimum total cost is determined by isocost line C2 The isocost line for Q 2 is above and to the northeast of the isocost line for Q u which means, as we ferent output levels.

At output

level

Qu

.

the

,

.

expect, that costs increase with output. It is easily

seen that by repeating this procedure at all isoquants

along the expansion path E, schedule for the firm

—

'that is,

producing each output after adjusted. This

is

it is

possible to derive the long-run cost

the schedule which shows the cost of

all factors

of production have been fully

illustrated in panel (b) of Figure 7.2.1.

From panel

Microeconomic theory

184

FIGURE 721 Long Run Costs and the Production Function

TOTAL OUTPUT