Price Theory [1 ed.] 020230969X, 9780202309699

Citation preview

This Page Intentionally Left Blank

www.Transactionpub.com

Contents    

Contents    

Contents    

Contents    

iv

Designing Clothes

iv

Designing Clothes

Fourth printing 2008

Fourth printing 2008

New material this edition copyright © 2007 by Transaction Publishers, New Brunswick, New Jersey. Copyright © 1962, 1976 by Transaction Publishers, New Brunswick, New Jersey.

New material this edition copyright © 2007 by Transaction Publishers, New Brunswick, New Jersey. Copyright © 1962, 1976 by Transaction Publishers, New Brunswick, New Jersey.

All rights reserved under International and Pan-American Copyright Conventions. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without prior permission in writing from the publisher. All inquiries should be addressed to Transaction Publishers, Rutgers—The State University of New Jersey, 35 Berrue Circle, Piscataway, New Jersey 08854-8042. www.transactionpub.com

All rights reserved under International and Pan-American Copyright Conventions. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without prior permission in writing from the publisher. All inquiries should be addressed to Transaction Publishers, Rutgers—The State University of New Jersey, 35 Berrue Circle, Piscataway, New Jersey 08854-8042. www.transactionpub.com

This book is printed on acid-free paper that meets the American National Standard for Permanence of Paper for Printed Library Materials.

This book is printed on acid-free paper that meets the American National Standard for Permanence of Paper for Printed Library Materials.

Library of Congress Catalog Number: 2006050464 ISBN: 978-0-202-30969-9 Printed in the United States of America

Library of Congress Catalog Number: 2006050464 ISBN: 978-1-4128-0965-8 Printed in the United States of America

Library of Congress Cataloging-in-Publication Data Friedman, Milton, 1912Price theory / Milton Friedman. p. cm. Includes bibliographical references and index. ISBN-13 978-0-202-30969-9 (pbk. : alk. paper) ISBN-10 0-202-30969-X (pbk. : alk. paper) 1. Microeconomics. I. Title. HB171.5.F75 338.5'—dc22

iv

Library of Congress Cataloging-in-Publication Data Friedman, Milton, 1912Price theory / Milton Friedman. p. cm. Includes bibliographical references and index. ISBN-13 978-1-4128-0965-8 (E-Book) ISBN-10 1-4128-0965-7 1. Microeconomics. I. Title.

2007 2006050464

Designing Clothes

HB171.5.F75 338.5'—dc22

iv

2007 2006050464

Designing Clothes

Fourth printing 2008

Fourth printing 2008

New material this edition copyright © 2007 by Transaction Publishers, New Brunswick, New Jersey. Copyright © 1962, 1976 by Transaction Publishers, New Brunswick, New Jersey.

New material this edition copyright © 2007 by Transaction Publishers, New Brunswick, New Jersey. Copyright © 1962, 1976 by Transaction Publishers, New Brunswick, New Jersey.

All rights reserved under International and Pan-American Copyright Conventions. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without prior permission in writing from the publisher. All inquiries should be addressed to Transaction Publishers, Rutgers—The State University of New Jersey, 35 Berrue Circle, Piscataway, New Jersey 08854-8042. www.transactionpub.com

All rights reserved under International and Pan-American Copyright Conventions. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without prior permission in writing from the publisher. All inquiries should be addressed to Transaction Publishers, Rutgers—The State University of New Jersey, 35 Berrue Circle, Piscataway, New Jersey 08854-8042. www.transactionpub.com

This book is printed on acid-free paper that meets the American National Standard for Permanence of Paper for Printed Library Materials.

This book is printed on acid-free paper that meets the American National Standard for Permanence of Paper for Printed Library Materials.

Library of Congress Catalog Number: 2006050464 ISBN: 978-0-202-30969-9 Printed in the United States of America

Library of Congress Catalog Number: 2006050464 ISBN: 978-0-202-30969-9 Printed in the United States of America

Library of Congress Cataloging-in-Publication Data Friedman, Milton, 1912Price theory / Milton Friedman. p. cm. Includes bibliographical references and index. ISBN-13 978-0-202-30969-9 (pbk. : alk. paper) ISBN-10 0-202-30969-X (pbk. : alk. paper) 1. Microeconomics. I. Title. HB171.5.F75 338.5'—dc22

Library of Congress Cataloging-in-Publication Data Friedman, Milton, 1912Price theory / Milton Friedman. p. cm. Includes bibliographical references and index. ISBN-13 978-0-202-30969-9 (pbk. : alk. paper) ISBN-10 0-202-30969-X (pbk. : alk. paper) 1. Microeconomics. I. Title.

2007 2006050464

HB171.5.F75 338.5'—dc22

2007 2006050464

Table of Contents

XldirleTransactiorl Irltroduction Preface Preface to Price Theon: X I'rovisional Text Chapter 1. Introduction 2. Theory of Demand 3. T h e "Welfare" Effects of Taxes 4. T h e Utility Analysis of Uncertainty 5 . T h e Relatiollsllips Between Supply Curves and Cost Curves 6 . T h e Law of Variable Proportions and a Firm's Cost Curves 7. Derived Demand 8. T h e Theory of Distribution ~ v i t hFixed Proportions 9. T h e Theory of Marginal Prodl~ctivityand the Demand for Factors of Production 10. Marginal Producti~ityAnalysis: Some General Issues 11. T h e Supply of Factors of Production 12. Wage Determination and Unemployment 13. T2'ages in Different Occupations 14. Relatior1 Retween tlle Functional ant1 Personal Distribution of Income 15. T h e Size Distribution of Income 16. Profits 17. Tile Theory of Capital and the Rate of Interest Appendix

A. Reading Assignrrlents B. Problems Index

rii XY

XI-ii

This Page Intentionally Left Blank

www.Transactionpub.com

AldineTransaction Introduction

AldineTransaction Introduction

Milton Friedman had a profound effect on his students, and on graduate education in economics generally at the University of Chicago. This impact is evidenced in a variety of ways,1 one of which is via his role in the unfolding Chicago tradition in price theory—a role that includes the present volume, Price Theory, and the courses that gave rise to it. The Chicago price theory tradition began with Frank Knight and Jacob Viner in the 1920s and ’30s. Over the ensuing decades, this distinctive approach to price theory has come to span the Department of Economics, the Graduate School of Business, and the Law School at Chicago, and a legion of students and others have spread it around the globe. The tradition includes, besides Knight, Viner, and Friedman, Chicago luminaries such as Henry Simons, Aaron Director,2 George Stigler, Gary Becker, Ronald Coase, Richard Posner, Kevin Murphy, and Steve Levitt. It has recently been institutionalized in a university-wide research center, The Becker Center on Chicago Price Theory, directed by Levitt,3 whose best-selling Freakonomics (2005) is the latest piece of evidence for what this distinctive approach to price theory—here, tag-teamed with, informing, and informed by sophisticated empirical analysis—can add to the way that we think about the world. Milton Friedman was born in Brooklyn, New York, on July 31, 1912. He studied mathematics and economics at Rutgers University, receiving his B.A. in 1932. He enrolled in the graduate program in economics at the University of Chicago that same year but transferred to Columbia University in 1933. Although Friedman returned to Chicago in 1934-35, it was from Columbia that he eventually received his Ph.D., in 1946. Much of the period from 1935 to 1946 was spent outside of academia, including at the National Bureau of Economic Research and wartime service at U.S. Department of the Treasury and the Statistical Research Group,

Milton Friedman had a profound effect on his students, and on graduate education in economics generally at the University of Chicago. This impact is evidenced in a variety of ways,1 one of which is via his role in the unfolding Chicago tradition in price theory—a role that includes the present volume, Price Theory, and the courses that gave rise to it. The Chicago price theory tradition began with Frank Knight and Jacob Viner in the 1920s and ’30s. Over the ensuing decades, this distinctive approach to price theory has come to span the Department of Economics, the Graduate School of Business, and the Law School at Chicago, and a legion of students and others have spread it around the globe. The tradition includes, besides Knight, Viner, and Friedman, Chicago luminaries such as Henry Simons, Aaron Director,2 George Stigler, Gary Becker, Ronald Coase, Richard Posner, Kevin Murphy, and Steve Levitt. It has recently been institutionalized in a university-wide research center, The Becker Center on Chicago Price Theory, directed by Levitt,3 whose best-selling Freakonomics (2005) is the latest piece of evidence for what this distinctive approach to price theory—here, tag-teamed with, informing, and informed by sophisticated empirical analysis—can add to the way that we think about the world. Milton Friedman was born in Brooklyn, New York, on July 31, 1912. He studied mathematics and economics at Rutgers University, receiving his B.A. in 1932. He enrolled in the graduate program in economics at the University of Chicago that same year but transferred to Columbia University in 1933. Although Friedman returned to Chicago in 1934-35, it was from Columbia that he eventually received his Ph.D., in 1946. Much of the period from 1935 to 1946 was spent outside of academia, including at the National Bureau of Economic Research and wartime service at U.S. Department of the Treasury and the Statistical Research Group,

I would like to thank Dan Hammond and Irving Louis Horowitz for their insightful comments on an earlier draft of this introduction.

I would like to thank Dan Hammond and Irving Louis Horowitz for their insightful comments on an earlier draft of this introduction.

vii

vii

02Introduction Friedman.indd 7

8/23/2006 10:05:35 AM

02Introduction Friedman.indd 7

8/23/2006 10:05:35 AM

AldineTransaction Introduction

AldineTransaction Introduction

Milton Friedman had a profound effect on his students, and on graduate education in economics generally at the University of Chicago. This impact is evidenced in a variety of ways,1 one of which is via his role in the unfolding Chicago tradition in price theory—a role that includes the present volume, Price Theory, and the courses that gave rise to it. The Chicago price theory tradition began with Frank Knight and Jacob Viner in the 1920s and ’30s. Over the ensuing decades, this distinctive approach to price theory has come to span the Department of Economics, the Graduate School of Business, and the Law School at Chicago, and a legion of students and others have spread it around the globe. The tradition includes, besides Knight, Viner, and Friedman, Chicago luminaries such as Henry Simons, Aaron Director,2 George Stigler, Gary Becker, Ronald Coase, Richard Posner, Kevin Murphy, and Steve Levitt. It has recently been institutionalized in a university-wide research center, The Becker Center on Chicago Price Theory, directed by Levitt,3 whose best-selling Freakonomics (2005) is the latest piece of evidence for what this distinctive approach to price theory—here, tag-teamed with, informing, and informed by sophisticated empirical analysis—can add to the way that we think about the world. Milton Friedman was born in Brooklyn, New York, on July 31, 1912. He studied mathematics and economics at Rutgers University, receiving his B.A. in 1932. He enrolled in the graduate program in economics at the University of Chicago that same year but transferred to Columbia University in 1933. Although Friedman returned to Chicago in 1934-35, it was from Columbia that he eventually received his Ph.D., in 1946. Much of the period from 1935 to 1946 was spent outside of academia, including at the National Bureau of Economic Research and wartime service at U.S. Department of the Treasury and the Statistical Research Group,

Milton Friedman had a profound effect on his students, and on graduate education in economics generally at the University of Chicago. This impact is evidenced in a variety of ways,1 one of which is via his role in the unfolding Chicago tradition in price theory—a role that includes the present volume, Price Theory, and the courses that gave rise to it. The Chicago price theory tradition began with Frank Knight and Jacob Viner in the 1920s and ’30s. Over the ensuing decades, this distinctive approach to price theory has come to span the Department of Economics, the Graduate School of Business, and the Law School at Chicago, and a legion of students and others have spread it around the globe. The tradition includes, besides Knight, Viner, and Friedman, Chicago luminaries such as Henry Simons, Aaron Director,2 George Stigler, Gary Becker, Ronald Coase, Richard Posner, Kevin Murphy, and Steve Levitt. It has recently been institutionalized in a university-wide research center, The Becker Center on Chicago Price Theory, directed by Levitt,3 whose best-selling Freakonomics (2005) is the latest piece of evidence for what this distinctive approach to price theory—here, tag-teamed with, informing, and informed by sophisticated empirical analysis—can add to the way that we think about the world. Milton Friedman was born in Brooklyn, New York, on July 31, 1912. He studied mathematics and economics at Rutgers University, receiving his B.A. in 1932. He enrolled in the graduate program in economics at the University of Chicago that same year but transferred to Columbia University in 1933. Although Friedman returned to Chicago in 1934-35, it was from Columbia that he eventually received his Ph.D., in 1946. Much of the period from 1935 to 1946 was spent outside of academia, including at the National Bureau of Economic Research and wartime service at U.S. Department of the Treasury and the Statistical Research Group,

I would like to thank Dan Hammond and Irving Louis Horowitz for their insightful comments on an earlier draft of this introduction.

I would like to thank Dan Hammond and Irving Louis Horowitz for their insightful comments on an earlier draft of this introduction.

vii

vii

viii   

viii   

aldinetransaction introduction

Division of War Research. However, Friedman did not totally remove himself from academia during this time: He held appointments at Columbia, Wisconsin, and Minnesota before joining the faculty at Chicago in 1946.4 Friedman received his training in price theory from Viner in 1932, and he was appointed to the economics faculty at Chicago in 1946 to replace Viner, who had been lured away by Princeton, in the core graduate price theory classes, Economics 300a and 300b.5 This was not Friedman’s first foray into teaching price theory. The course had its roots in a graduate course on the “Structure of Neo-Classical Economics,” which he taught at the Columbia University Extension from 1938 to 1940, and many of the readings and materials that Friedman used for this course were carried over into his course at Chicago. He taught price theory from 1946 until 1964—ironically only just after the publication of the original edition of this book—and again from 1972 to 1976. It was during the former period that future Nobel laureates James Buchanan, Gary Becker, and Robert Lucas sat the course. That Friedman occupies a place at the center of the Chicago price-theoretic tradition may come as a surprise to that generation of economists who identify the name “Milton Friedman” with macroeconomics generally and monetarism in particular. Indeed, Gary Becker (1991, p. 140) has labeled Friedman “Mr. Macro” to George Stigler’s “Mr. Micro.” While most of Friedman’s scholarly work and thesis supervision during his period teaching price theory were in the area of monetary economics, he helped to solidify the Chicago tradition in price theory via his teaching. In fact, an argument can be made that price theory is the most significant aspect of Milton Friedman’s legacy as a teacher. The present volume is a revised edition of Price Theory: A Provisional Text, which was published by Aldine in 1962. The original version was based on notes from Friedman’s lectures taken by David I. Fand and Warren J. Gustus in 195152. Given the importance of the price theory course in the Chicago program and the lack of any texts that did an adequate job of covering the material upon which Friedman lectured, Fand thought it a good idea to prepare such a set of notes for his own benefit and for circulation among the graduate students. The notes proved to be very popular and circulated for a decade in mimeographed form. Finally, after repeated prompting, Friedman agreed to work them up for publication, revising, rewriting, and supplementing the Fand and Gustus material (see Fand 1999). The analysis was enlarged and extended in the revised version of the book, which Friedman prepared when he resumed teaching price theory in the early 1970s. The most distinctive aspect of Friedman’s approach may be its Marshallian emphasis, which combined solid theoretical analysis and applications to actual economic problems. Friedman’s close friend, George Stigler,6 wrote to him in 1946 hypothesizing an essential commonality between their respective approaches to economics, and the roots of this in Marshall: “I shall conjecture,” said Stigler, “that you like a firm skeleton of rigorous theory well skinned with concrete illustrations, in the manner of Marshall and Burns, all oriented in ac-

02Introduction Friedman.indd 8

viii   

8/23/2006 10:05:35 AM

aldinetransaction introduction

Division of War Research. However, Friedman did not totally remove himself from academia during this time: He held appointments at Columbia, Wisconsin, and Minnesota before joining the faculty at Chicago in 1946.4 Friedman received his training in price theory from Viner in 1932, and he was appointed to the economics faculty at Chicago in 1946 to replace Viner, who had been lured away by Princeton, in the core graduate price theory classes, Economics 300a and 300b.5 This was not Friedman’s first foray into teaching price theory. The course had its roots in a graduate course on the “Structure of Neo-Classical Economics,” which he taught at the Columbia University Extension from 1938 to 1940, and many of the readings and materials that Friedman used for this course were carried over into his course at Chicago. He taught price theory from 1946 until 1964—ironically only just after the publication of the original edition of this book—and again from 1972 to 1976. It was during the former period that future Nobel laureates James Buchanan, Gary Becker, and Robert Lucas sat the course. That Friedman occupies a place at the center of the Chicago price-theoretic tradition may come as a surprise to that generation of economists who identify the name “Milton Friedman” with macroeconomics generally and monetarism in particular. Indeed, Gary Becker (1991, p. 140) has labeled Friedman “Mr. Macro” to George Stigler’s “Mr. Micro.” While most of Friedman’s scholarly work and thesis supervision during his period teaching price theory were in the area of monetary economics, he helped to solidify the Chicago tradition in price theory via his teaching. In fact, an argument can be made that price theory is the most significant aspect of Milton Friedman’s legacy as a teacher. The present volume is a revised edition of Price Theory: A Provisional Text, which was published by Aldine in 1962. The original version was based on notes from Friedman’s lectures taken by David I. Fand and Warren J. Gustus in 195152. Given the importance of the price theory course in the Chicago program and the lack of any texts that did an adequate job of covering the material upon which Friedman lectured, Fand thought it a good idea to prepare such a set of notes for his own benefit and for circulation among the graduate students. The notes proved to be very popular and circulated for a decade in mimeographed form. Finally, after repeated prompting, Friedman agreed to work them up for publication, revising, rewriting, and supplementing the Fand and Gustus material (see Fand 1999). The analysis was enlarged and extended in the revised version of the book, which Friedman prepared when he resumed teaching price theory in the early 1970s. The most distinctive aspect of Friedman’s approach may be its Marshallian emphasis, which combined solid theoretical analysis and applications to actual economic problems. Friedman’s close friend, George Stigler,6 wrote to him in 1946 hypothesizing an essential commonality between their respective approaches to economics, and the roots of this in Marshall: “I shall conjecture,” said Stigler, “that you like a firm skeleton of rigorous theory well skinned with concrete illustrations, in the manner of Marshall and Burns, all oriented in ac-

aldinetransaction introduction

Division of War Research. However, Friedman did not totally remove himself from academia during this time: He held appointments at Columbia, Wisconsin, and Minnesota before joining the faculty at Chicago in 1946.4 Friedman received his training in price theory from Viner in 1932, and he was appointed to the economics faculty at Chicago in 1946 to replace Viner, who had been lured away by Princeton, in the core graduate price theory classes, Economics 300a and 300b.5 This was not Friedman’s first foray into teaching price theory. The course had its roots in a graduate course on the “Structure of Neo-Classical Economics,” which he taught at the Columbia University Extension from 1938 to 1940, and many of the readings and materials that Friedman used for this course were carried over into his course at Chicago. He taught price theory from 1946 until 1964—ironically only just after the publication of the original edition of this book—and again from 1972 to 1976. It was during the former period that future Nobel laureates James Buchanan, Gary Becker, and Robert Lucas sat the course. That Friedman occupies a place at the center of the Chicago price-theoretic tradition may come as a surprise to that generation of economists who identify the name “Milton Friedman” with macroeconomics generally and monetarism in particular. Indeed, Gary Becker (1991, p. 140) has labeled Friedman “Mr. Macro” to George Stigler’s “Mr. Micro.” While most of Friedman’s scholarly work and thesis supervision during his period teaching price theory were in the area of monetary economics, he helped to solidify the Chicago tradition in price theory via his teaching. In fact, an argument can be made that price theory is the most significant aspect of Milton Friedman’s legacy as a teacher. The present volume is a revised edition of Price Theory: A Provisional Text, which was published by Aldine in 1962. The original version was based on notes from Friedman’s lectures taken by David I. Fand and Warren J. Gustus in 195152. Given the importance of the price theory course in the Chicago program and the lack of any texts that did an adequate job of covering the material upon which Friedman lectured, Fand thought it a good idea to prepare such a set of notes for his own benefit and for circulation among the graduate students. The notes proved to be very popular and circulated for a decade in mimeographed form. Finally, after repeated prompting, Friedman agreed to work them up for publication, revising, rewriting, and supplementing the Fand and Gustus material (see Fand 1999). The analysis was enlarged and extended in the revised version of the book, which Friedman prepared when he resumed teaching price theory in the early 1970s. The most distinctive aspect of Friedman’s approach may be its Marshallian emphasis, which combined solid theoretical analysis and applications to actual economic problems. Friedman’s close friend, George Stigler,6 wrote to him in 1946 hypothesizing an essential commonality between their respective approaches to economics, and the roots of this in Marshall: “I shall conjecture,” said Stigler, “that you like a firm skeleton of rigorous theory well skinned with concrete illustrations, in the manner of Marshall and Burns, all oriented in ac-

02Introduction Friedman.indd 8

viii   

8/23/2006 10:05:35 AM

aldinetransaction introduction

Division of War Research. However, Friedman did not totally remove himself from academia during this time: He held appointments at Columbia, Wisconsin, and Minnesota before joining the faculty at Chicago in 1946.4 Friedman received his training in price theory from Viner in 1932, and he was appointed to the economics faculty at Chicago in 1946 to replace Viner, who had been lured away by Princeton, in the core graduate price theory classes, Economics 300a and 300b.5 This was not Friedman’s first foray into teaching price theory. The course had its roots in a graduate course on the “Structure of Neo-Classical Economics,” which he taught at the Columbia University Extension from 1938 to 1940, and many of the readings and materials that Friedman used for this course were carried over into his course at Chicago. He taught price theory from 1946 until 1964—ironically only just after the publication of the original edition of this book—and again from 1972 to 1976. It was during the former period that future Nobel laureates James Buchanan, Gary Becker, and Robert Lucas sat the course. That Friedman occupies a place at the center of the Chicago price-theoretic tradition may come as a surprise to that generation of economists who identify the name “Milton Friedman” with macroeconomics generally and monetarism in particular. Indeed, Gary Becker (1991, p. 140) has labeled Friedman “Mr. Macro” to George Stigler’s “Mr. Micro.” While most of Friedman’s scholarly work and thesis supervision during his period teaching price theory were in the area of monetary economics, he helped to solidify the Chicago tradition in price theory via his teaching. In fact, an argument can be made that price theory is the most significant aspect of Milton Friedman’s legacy as a teacher. The present volume is a revised edition of Price Theory: A Provisional Text, which was published by Aldine in 1962. The original version was based on notes from Friedman’s lectures taken by David I. Fand and Warren J. Gustus in 195152. Given the importance of the price theory course in the Chicago program and the lack of any texts that did an adequate job of covering the material upon which Friedman lectured, Fand thought it a good idea to prepare such a set of notes for his own benefit and for circulation among the graduate students. The notes proved to be very popular and circulated for a decade in mimeographed form. Finally, after repeated prompting, Friedman agreed to work them up for publication, revising, rewriting, and supplementing the Fand and Gustus material (see Fand 1999). The analysis was enlarged and extended in the revised version of the book, which Friedman prepared when he resumed teaching price theory in the early 1970s. The most distinctive aspect of Friedman’s approach may be its Marshallian emphasis, which combined solid theoretical analysis and applications to actual economic problems. Friedman’s close friend, George Stigler,6 wrote to him in 1946 hypothesizing an essential commonality between their respective approaches to economics, and the roots of this in Marshall: “I shall conjecture,” said Stigler, “that you like a firm skeleton of rigorous theory well skinned with concrete illustrations, in the manner of Marshall and Burns, all oriented in ac-

AldineTransaction Introduction    ix

AldineTransaction Introduction    ix

cordance with your general view of how economic life runs. In any case, I do.”7 Friedman himself confirmed Stigler’s assessment in his opening remarks to students in Econ. 300a:

cordance with your general view of how economic life runs. In any case, I do.”7 Friedman himself confirmed Stigler’s assessment in his opening remarks to students in Econ. 300a:

Marshall’s “Principles,” viewed contemporaneously, i.e., as if he were writing today instead of a century ago, is still the best book available in economic theory. This is indeed a sad commentary on the economics of our time. Marshall’s superiority is explained primarily by his approach to economics as contrasted with the modern approach. Marshall is interested in economics as a real problem rather than as a form of geometry. Economics was to him an engine of analysis, a tool to study the economic system as it actually works.8

Marshall’s “Principles,” viewed contemporaneously, i.e., as if he were writing today instead of a century ago, is still the best book available in economic theory. This is indeed a sad commentary on the economics of our time. Marshall’s superiority is explained primarily by his approach to economics as contrasted with the modern approach. Marshall is interested in economics as a real problem rather than as a form of geometry. Economics was to him an engine of analysis, a tool to study the economic system as it actually works.8

This Marshallian emphasis is part of the Vinerian heritage at Chicago—a heritage of which Friedman was clearly conscious.9 In an interview several decades later, Friedman, reflecting on Viner’s price theory course, remarked upon Marshall’s use of mathematics as “an engine of analysis,” and then went on to say that “there was no doubt that Viner viewed it as an engine of analysis, and no doubt when you were in his course that you came away with the feeling that economics really had something to say about real problems and real things” (Hammond 1992, pp. 104-105).10 In fact, Marshall’s Principles of Economics was the main text for Friedman’s course until its replacement by the present material. Such was the pervasiveness of the Marshallian approach in Chicago thinking that it even gave rise to a ditty:

This Marshallian emphasis is part of the Vinerian heritage at Chicago—a heritage of which Friedman was clearly conscious.9 In an interview several decades later, Friedman, reflecting on Viner’s price theory course, remarked upon Marshall’s use of mathematics as “an engine of analysis,” and then went on to say that “there was no doubt that Viner viewed it as an engine of analysis, and no doubt when you were in his course that you came away with the feeling that economics really had something to say about real problems and real things” (Hammond 1992, pp. 104-105).10 In fact, Marshall’s Principles of Economics was the main text for Friedman’s course until its replacement by the present material. Such was the pervasiveness of the Marshallian approach in Chicago thinking that it even gave rise to a ditty:

I read my Marshall completely through From beginning to end and backward too I read my Marshall so carefully That now I am professor at U of C.

I read my Marshall completely through From beginning to end and backward too I read my Marshall so carefully That now I am professor at U of C.

This continued attachment to Marshall came at a time when the profession, under the influence of scholars such as Kenneth Arrow, Gerard Debreu, and Paul Samuelson, was moving toward the use of ever more sophisticated forms of mathematical modeling.11 This only served to increase the distinctiveness of the Chicago approach over time. One artifact of Friedman’s Marshallian bent was that he paid scant attention to general equilibrium theory—something Becker (1991, p. 143) later suggested was a shortcoming of the course—at a time when the Walrasian approach was in its ascendancy. The seeming simplicity of the Marshallian approach—especially as against the mathematical pyrotechnics of Walrasian general equilibrium theory—has a tendency to mask the level of insight that it can provide. Robert Lucas has said that Friedman’s course showed “the breadth of problems that you could address with economic reasoning…the range of problems included everything. So we got the impression, and rightly so, that we were getting a powerful piece of equipment for dealing with any problem that came up in human affairs” (Snowdon and Vane, 1998, pp. 120-21). Gary Becker expresses very similar sentiments about Friedman’s approach and its impact when he says that,

02Introduction Friedman.indd 9

8/23/2006 10:05:36 AM

This continued attachment to Marshall came at a time when the profession, under the influence of scholars such as Kenneth Arrow, Gerard Debreu, and Paul Samuelson, was moving toward the use of ever more sophisticated forms of mathematical modeling.11 This only served to increase the distinctiveness of the Chicago approach over time. One artifact of Friedman’s Marshallian bent was that he paid scant attention to general equilibrium theory—something Becker (1991, p. 143) later suggested was a shortcoming of the course—at a time when the Walrasian approach was in its ascendancy. The seeming simplicity of the Marshallian approach—especially as against the mathematical pyrotechnics of Walrasian general equilibrium theory—has a tendency to mask the level of insight that it can provide. Robert Lucas has said that Friedman’s course showed “the breadth of problems that you could address with economic reasoning…the range of problems included everything. So we got the impression, and rightly so, that we were getting a powerful piece of equipment for dealing with any problem that came up in human affairs” (Snowdon and Vane, 1998, pp. 120-21). Gary Becker expresses very similar sentiments about Friedman’s approach and its impact when he says that,

02Introduction Friedman.indd 9

8/23/2006 10:05:36 AM

AldineTransaction Introduction    ix

AldineTransaction Introduction    ix

cordance with your general view of how economic life runs. In any case, I do.”7 Friedman himself confirmed Stigler’s assessment in his opening remarks to students in Econ. 300a:

cordance with your general view of how economic life runs. In any case, I do.”7 Friedman himself confirmed Stigler’s assessment in his opening remarks to students in Econ. 300a:

Marshall’s “Principles,” viewed contemporaneously, i.e., as if he were writing today instead of a century ago, is still the best book available in economic theory. This is indeed a sad commentary on the economics of our time. Marshall’s superiority is explained primarily by his approach to economics as contrasted with the modern approach. Marshall is interested in economics as a real problem rather than as a form of geometry. Economics was to him an engine of analysis, a tool to study the economic system as it actually works.8

Marshall’s “Principles,” viewed contemporaneously, i.e., as if he were writing today instead of a century ago, is still the best book available in economic theory. This is indeed a sad commentary on the economics of our time. Marshall’s superiority is explained primarily by his approach to economics as contrasted with the modern approach. Marshall is interested in economics as a real problem rather than as a form of geometry. Economics was to him an engine of analysis, a tool to study the economic system as it actually works.8

This Marshallian emphasis is part of the Vinerian heritage at Chicago—a heritage of which Friedman was clearly conscious.9 In an interview several decades later, Friedman, reflecting on Viner’s price theory course, remarked upon Marshall’s use of mathematics as “an engine of analysis,” and then went on to say that “there was no doubt that Viner viewed it as an engine of analysis, and no doubt when you were in his course that you came away with the feeling that economics really had something to say about real problems and real things” (Hammond 1992, pp. 104-105).10 In fact, Marshall’s Principles of Economics was the main text for Friedman’s course until its replacement by the present material. Such was the pervasiveness of the Marshallian approach in Chicago thinking that it even gave rise to a ditty:

This Marshallian emphasis is part of the Vinerian heritage at Chicago—a heritage of which Friedman was clearly conscious.9 In an interview several decades later, Friedman, reflecting on Viner’s price theory course, remarked upon Marshall’s use of mathematics as “an engine of analysis,” and then went on to say that “there was no doubt that Viner viewed it as an engine of analysis, and no doubt when you were in his course that you came away with the feeling that economics really had something to say about real problems and real things” (Hammond 1992, pp. 104-105).10 In fact, Marshall’s Principles of Economics was the main text for Friedman’s course until its replacement by the present material. Such was the pervasiveness of the Marshallian approach in Chicago thinking that it even gave rise to a ditty:

I read my Marshall completely through From beginning to end and backward too I read my Marshall so carefully That now I am professor at U of C.

This continued attachment to Marshall came at a time when the profession, under the influence of scholars such as Kenneth Arrow, Gerard Debreu, and Paul Samuelson, was moving toward the use of ever more sophisticated forms of mathematical modeling.11 This only served to increase the distinctiveness of the Chicago approach over time. One artifact of Friedman’s Marshallian bent was that he paid scant attention to general equilibrium theory—something Becker (1991, p. 143) later suggested was a shortcoming of the course—at a time when the Walrasian approach was in its ascendancy. The seeming simplicity of the Marshallian approach—especially as against the mathematical pyrotechnics of Walrasian general equilibrium theory—has a tendency to mask the level of insight that it can provide. Robert Lucas has said that Friedman’s course showed “the breadth of problems that you could address with economic reasoning…the range of problems included everything. So we got the impression, and rightly so, that we were getting a powerful piece of equipment for dealing with any problem that came up in human affairs” (Snowdon and Vane, 1998, pp. 120-21). Gary Becker expresses very similar sentiments about Friedman’s approach and its impact when he says that,

I read my Marshall completely through From beginning to end and backward too I read my Marshall so carefully That now I am professor at U of C.

This continued attachment to Marshall came at a time when the profession, under the influence of scholars such as Kenneth Arrow, Gerard Debreu, and Paul Samuelson, was moving toward the use of ever more sophisticated forms of mathematical modeling.11 This only served to increase the distinctiveness of the Chicago approach over time. One artifact of Friedman’s Marshallian bent was that he paid scant attention to general equilibrium theory—something Becker (1991, p. 143) later suggested was a shortcoming of the course—at a time when the Walrasian approach was in its ascendancy. The seeming simplicity of the Marshallian approach—especially as against the mathematical pyrotechnics of Walrasian general equilibrium theory—has a tendency to mask the level of insight that it can provide. Robert Lucas has said that Friedman’s course showed “the breadth of problems that you could address with economic reasoning…the range of problems included everything. So we got the impression, and rightly so, that we were getting a powerful piece of equipment for dealing with any problem that came up in human affairs” (Snowdon and Vane, 1998, pp. 120-21). Gary Becker expresses very similar sentiments about Friedman’s approach and its impact when he says that,

   

   

aldinetransaction introduction

aldinetransaction introduction

The emphasis in his course on applications of theory to the real world set the tone for the department. It was considered necessary to have a strong command of basic price theory, especially so-called partial equilibrium supply and demand analysis. Yet the theory was not an end in itself or a way to display pyrotechnics. Rather the theory became worthwhile only insofar as it helped explain different aspects of the real world (1991, p. 142).

The emphasis in his course on applications of theory to the real world set the tone for the department. It was considered necessary to have a strong command of basic price theory, especially so-called partial equilibrium supply and demand analysis. Yet the theory was not an end in itself or a way to display pyrotechnics. Rather the theory became worthwhile only insofar as it helped explain different aspects of the real world (1991, p. 142).

This view of price theory as “a tool to solve problems rather than a set of problems to be solved”12 comes through very clearly in Appendix B to this book, which contains roughly twenty pages of problems. As Friedman notes in his Preface to the 1962 edition of this work,13 many of these are the outcome of discussions with George Stigler and Aaron Director, the latter of whom taught price theory in the Law School at Chicago during the same period that Friedman was teaching it in the Economics Department.14 These problems are applications, not rehearsals of technique. They involve using economic reasoning to analyze issues related to toll roads, automobile safety regulations, royalties, taxicab licensing, monopoly pricing, and tax incidence, and many of the problems were lifted directly from the headlines of the period. The applied emphasis is reflective of the book’s presentation of price theory as an approach or way of thinking, rather than a purely technical exercise in applied mathematics, and it shows the power of some basic calculus and graphical analysis, teamed with rigorous analytical reasoning. This last aspect points to a theme that unites this book with the larger body of Friedman’s work, including his macro and monetary economics: his conviction that economics needs to be relevant, to deal with real-world problems rather than consisting in purely abstract speculation and theoretical game-playing. For Friedman, this has two implications. First, the theory must be useful, in the sense that it serves as a “language” or “filing system” that allows one to clarify one’s thoughts about the phenomena under consideration. Relevance means that theory alone is not sufficient, however; the theory must give rise to a set of propositions that are empirically testable and useful for purposes of prediction. That is, economics, according to Friedman, needs to be more than just a language; it must also be a set of substantive empirical propositions.15 As Hammond (2006) has put it, for Friedman, “empirical facts were the very point of theory.” The teaming of analytical sophistication and high-powered statistical analysis is a hallmark of Friedman’s work across the discipline. The Chicago approach has taken what most economists call microeconomics into areas hitherto unimagined. While by no means homogeneous in their perspectives on or their use of price theory, those who identify with the Chicago price-theoretic tradition focus on the central role that prices play in a variety of contexts and how the incentives provided by these prices are driving forces in determining social-economic outcomes. One sees in Friedman’s brand of price theory something a bit more restrained than the hardcore rational choice theory that Becker and others have applied across the social spectrum over the last few decades. Yet, the Economics 301 course currently taught by Gary Becker and Kevin Murphy is very obviously in the heritage of Friedman’s course, its distinc-

This view of price theory as “a tool to solve problems rather than a set of problems to be solved”12 comes through very clearly in Appendix B to this book, which contains roughly twenty pages of problems. As Friedman notes in his Preface to the 1962 edition of this work,13 many of these are the outcome of discussions with George Stigler and Aaron Director, the latter of whom taught price theory in the Law School at Chicago during the same period that Friedman was teaching it in the Economics Department.14 These problems are applications, not rehearsals of technique. They involve using economic reasoning to analyze issues related to toll roads, automobile safety regulations, royalties, taxicab licensing, monopoly pricing, and tax incidence, and many of the problems were lifted directly from the headlines of the period. The applied emphasis is reflective of the book’s presentation of price theory as an approach or way of thinking, rather than a purely technical exercise in applied mathematics, and it shows the power of some basic calculus and graphical analysis, teamed with rigorous analytical reasoning. This last aspect points to a theme that unites this book with the larger body of Friedman’s work, including his macro and monetary economics: his conviction that economics needs to be relevant, to deal with real-world problems rather than consisting in purely abstract speculation and theoretical game-playing. For Friedman, this has two implications. First, the theory must be useful, in the sense that it serves as a “language” or “filing system” that allows one to clarify one’s thoughts about the phenomena under consideration. Relevance means that theory alone is not sufficient, however; the theory must give rise to a set of propositions that are empirically testable and useful for purposes of prediction. That is, economics, according to Friedman, needs to be more than just a language; it must also be a set of substantive empirical propositions.15 As Hammond (2006) has put it, for Friedman, “empirical facts were the very point of theory.” The teaming of analytical sophistication and high-powered statistical analysis is a hallmark of Friedman’s work across the discipline. The Chicago approach has taken what most economists call microeconomics into areas hitherto unimagined. While by no means homogeneous in their perspectives on or their use of price theory, those who identify with the Chicago price-theoretic tradition focus on the central role that prices play in a variety of contexts and how the incentives provided by these prices are driving forces in determining social-economic outcomes. One sees in Friedman’s brand of price theory something a bit more restrained than the hardcore rational choice theory that Becker and others have applied across the social spectrum over the last few decades. Yet, the Economics 301 course currently taught by Gary Becker and Kevin Murphy is very obviously in the heritage of Friedman’s course, its distinc-

02Introduction Friedman.indd 10

   

8/23/2006 10:05:36 AM

aldinetransaction introduction

02Introduction Friedman.indd 10

   

8/23/2006 10:05:36 AM

aldinetransaction introduction

The emphasis in his course on applications of theory to the real world set the tone for the department. It was considered necessary to have a strong command of basic price theory, especially so-called partial equilibrium supply and demand analysis. Yet the theory was not an end in itself or a way to display pyrotechnics. Rather the theory became worthwhile only insofar as it helped explain different aspects of the real world (1991, p. 142).

The emphasis in his course on applications of theory to the real world set the tone for the department. It was considered necessary to have a strong command of basic price theory, especially so-called partial equilibrium supply and demand analysis. Yet the theory was not an end in itself or a way to display pyrotechnics. Rather the theory became worthwhile only insofar as it helped explain different aspects of the real world (1991, p. 142).

This view of price theory as “a tool to solve problems rather than a set of problems to be solved”12 comes through very clearly in Appendix B to this book, which contains roughly twenty pages of problems. As Friedman notes in his Preface to the 1962 edition of this work,13 many of these are the outcome of discussions with George Stigler and Aaron Director, the latter of whom taught price theory in the Law School at Chicago during the same period that Friedman was teaching it in the Economics Department.14 These problems are applications, not rehearsals of technique. They involve using economic reasoning to analyze issues related to toll roads, automobile safety regulations, royalties, taxicab licensing, monopoly pricing, and tax incidence, and many of the problems were lifted directly from the headlines of the period. The applied emphasis is reflective of the book’s presentation of price theory as an approach or way of thinking, rather than a purely technical exercise in applied mathematics, and it shows the power of some basic calculus and graphical analysis, teamed with rigorous analytical reasoning. This last aspect points to a theme that unites this book with the larger body of Friedman’s work, including his macro and monetary economics: his conviction that economics needs to be relevant, to deal with real-world problems rather than consisting in purely abstract speculation and theoretical game-playing. For Friedman, this has two implications. First, the theory must be useful, in the sense that it serves as a “language” or “filing system” that allows one to clarify one’s thoughts about the phenomena under consideration. Relevance means that theory alone is not sufficient, however; the theory must give rise to a set of propositions that are empirically testable and useful for purposes of prediction. That is, economics, according to Friedman, needs to be more than just a language; it must also be a set of substantive empirical propositions.15 As Hammond (2006) has put it, for Friedman, “empirical facts were the very point of theory.” The teaming of analytical sophistication and high-powered statistical analysis is a hallmark of Friedman’s work across the discipline. The Chicago approach has taken what most economists call microeconomics into areas hitherto unimagined. While by no means homogeneous in their perspectives on or their use of price theory, those who identify with the Chicago price-theoretic tradition focus on the central role that prices play in a variety of contexts and how the incentives provided by these prices are driving forces in determining social-economic outcomes. One sees in Friedman’s brand of price theory something a bit more restrained than the hardcore rational choice theory that Becker and others have applied across the social spectrum over the last few decades. Yet, the Economics 301 course currently taught by Gary Becker and Kevin Murphy is very obviously in the heritage of Friedman’s course, its distinc-

This view of price theory as “a tool to solve problems rather than a set of problems to be solved”12 comes through very clearly in Appendix B to this book, which contains roughly twenty pages of problems. As Friedman notes in his Preface to the 1962 edition of this work,13 many of these are the outcome of discussions with George Stigler and Aaron Director, the latter of whom taught price theory in the Law School at Chicago during the same period that Friedman was teaching it in the Economics Department.14 These problems are applications, not rehearsals of technique. They involve using economic reasoning to analyze issues related to toll roads, automobile safety regulations, royalties, taxicab licensing, monopoly pricing, and tax incidence, and many of the problems were lifted directly from the headlines of the period. The applied emphasis is reflective of the book’s presentation of price theory as an approach or way of thinking, rather than a purely technical exercise in applied mathematics, and it shows the power of some basic calculus and graphical analysis, teamed with rigorous analytical reasoning. This last aspect points to a theme that unites this book with the larger body of Friedman’s work, including his macro and monetary economics: his conviction that economics needs to be relevant, to deal with real-world problems rather than consisting in purely abstract speculation and theoretical game-playing. For Friedman, this has two implications. First, the theory must be useful, in the sense that it serves as a “language” or “filing system” that allows one to clarify one’s thoughts about the phenomena under consideration. Relevance means that theory alone is not sufficient, however; the theory must give rise to a set of propositions that are empirically testable and useful for purposes of prediction. That is, economics, according to Friedman, needs to be more than just a language; it must also be a set of substantive empirical propositions.15 As Hammond (2006) has put it, for Friedman, “empirical facts were the very point of theory.” The teaming of analytical sophistication and high-powered statistical analysis is a hallmark of Friedman’s work across the discipline. The Chicago approach has taken what most economists call microeconomics into areas hitherto unimagined. While by no means homogeneous in their perspectives on or their use of price theory, those who identify with the Chicago price-theoretic tradition focus on the central role that prices play in a variety of contexts and how the incentives provided by these prices are driving forces in determining social-economic outcomes. One sees in Friedman’s brand of price theory something a bit more restrained than the hardcore rational choice theory that Becker and others have applied across the social spectrum over the last few decades. Yet, the Economics 301 course currently taught by Gary Becker and Kevin Murphy is very obviously in the heritage of Friedman’s course, its distinc-

AldineTransaction Introduction    xi

AldineTransaction Introduction    xi

tive Chicago flavor being evidenced in a reading list that includes myriad works published before 1980, including Friedman’s Price Theory, Becker’s Economic Theory (1971), and Knight’s The Economic Organization (1933). Just as Friedman himself is near the headwaters of this long teaching tradition at Chicago, so too is his Price Theory part of an equally long tradition of price-theoretic texts in the Chicago mold. Knight’s The Economic Organization, Stigler’s The Theory of Competitive Price (1942, later revised multiple times as The Theory of Price), and Becker’s Economic Theory (1971) are all part of this tradition. A brief perusal of the currently popular graduate texts by Hal Varian (1992), David Kreps (1990), and Andreu Mas-Colell, Michael Whinston, and Jerry Green (1995) makes crystal clear the distinctive nature of the Chicago approach. The tradition has been carried on at the undergraduate level in David Friedman’s Price Theory: An Intermediate Text,16 Deirdre McCloskey’s The Applied Theory of Price, and Steven Landsburg’s Price Theory and Applications, which, like their graduate-level counterparts, present a very different approach to the subject than their more orthodox competitors. Whatever one’s feelings about the Chicago approach—and there is certainly a wide range of opinion here—it has had a profound influence within and beyond economics, and within and outside the academy. While the Chicago tradition in price theory remains very much alive, it is good to see, too, that the AldineTransaction publishing program will keep Milton Friedman’s Price Theory readily available to future generations of students and scholars.

tive Chicago flavor being evidenced in a reading list that includes myriad works published before 1980, including Friedman’s Price Theory, Becker’s Economic Theory (1971), and Knight’s The Economic Organization (1933). Just as Friedman himself is near the headwaters of this long teaching tradition at Chicago, so too is his Price Theory part of an equally long tradition of price-theoretic texts in the Chicago mold. Knight’s The Economic Organization, Stigler’s The Theory of Competitive Price (1942, later revised multiple times as The Theory of Price), and Becker’s Economic Theory (1971) are all part of this tradition. A brief perusal of the currently popular graduate texts by Hal Varian (1992), David Kreps (1990), and Andreu Mas-Colell, Michael Whinston, and Jerry Green (1995) makes crystal clear the distinctive nature of the Chicago approach. The tradition has been carried on at the undergraduate level in David Friedman’s Price Theory: An Intermediate Text,16 Deirdre McCloskey’s The Applied Theory of Price, and Steven Landsburg’s Price Theory and Applications, which, like their graduate-level counterparts, present a very different approach to the subject than their more orthodox competitors. Whatever one’s feelings about the Chicago approach—and there is certainly a wide range of opinion here—it has had a profound influence within and beyond economics, and within and outside the academy. While the Chicago tradition in price theory remains very much alive, it is good to see, too, that the AldineTransaction publishing program will keep Milton Friedman’s Price Theory readily available to future generations of students and scholars.

Steven G. Medema

Steven G. Medema

Notes

Notes

1. The breadth and depth of this impact is reflected in the excellent collection by J. Daniel Hammond (1999). This introduction relies heavily on Hammond’s (1999) introduction and the essay by David Fand (1999), as well as Hammond’s (2006) recent essay on the history of Chicago price theory. 2. Simons and Director established and solidified the price-theoretic tradition in the Law School at Chicago through their course, “Economic Analysis of Public Policy.” 3. The Becker Center, originally named The Chicago Initiative on Price Theory, is “aimed to sustain and strengthen a powerful methodology, which emphasizes the role of prices in the fundamental functions of an economic system and which values the development of testable hypotheses, efficient modeling, and rigorous applications” (http://pricetheory.uchicago. edu/about_center.htm). 4. For further biographical information, see Friedman and Friedman (1998). 5. The Price Theory sequence was originally numbered 300a and 300b but was renumbered 301 and 302 in 1959. See Hammond (2006). 6. Friedman and Stigler had been graduate students together at Chicago in the 1930s, had served together in the Statistical Research Group at Columbia University in the waning days of the Second World War, and spent 1945 as faculty colleagues—and office-mates—at the University of Minnesota. Both left Minnesota in 1946—Friedman for Chicago and Stigler for Brown. Stigler did not join the faculty at Chicago until 1958. Hammond and Hammond (2006) gives a very nice window into this personal and professional relationship over the period 1945-57.

1. The breadth and depth of this impact is reflected in the excellent collection by J. Daniel Hammond (1999). This introduction relies heavily on Hammond’s (1999) introduction and the essay by David Fand (1999), as well as Hammond’s (2006) recent essay on the history of Chicago price theory. 2. Simons and Director established and solidified the price-theoretic tradition in the Law School at Chicago through their course, “Economic Analysis of Public Policy.” 3. The Becker Center, originally named The Chicago Initiative on Price Theory, is “aimed to sustain and strengthen a powerful methodology, which emphasizes the role of prices in the fundamental functions of an economic system and which values the development of testable hypotheses, efficient modeling, and rigorous applications” (http://pricetheory.uchicago. edu/about_center.htm). 4. For further biographical information, see Friedman and Friedman (1998). 5. The Price Theory sequence was originally numbered 300a and 300b but was renumbered 301 and 302 in 1959. See Hammond (2006). 6. Friedman and Stigler had been graduate students together at Chicago in the 1930s, had served together in the Statistical Research Group at Columbia University in the waning days of the Second World War, and spent 1945 as faculty colleagues—and office-mates—at the University of Minnesota. Both left Minnesota in 1946—Friedman for Chicago and Stigler for Brown. Stigler did not join the faculty at Chicago until 1958. Hammond and Hammond (2006) gives a very nice window into this personal and professional relationship over the period 1945-57.

02Introduction Friedman.indd 11

8/23/2006 10:05:36 AM

02Introduction Friedman.indd 11

8/23/2006 10:05:36 AM

AldineTransaction Introduction    xi

AldineTransaction Introduction    xi

tive Chicago flavor being evidenced in a reading list that includes myriad works published before 1980, including Friedman’s Price Theory, Becker’s Economic Theory (1971), and Knight’s The Economic Organization (1933). Just as Friedman himself is near the headwaters of this long teaching tradition at Chicago, so too is his Price Theory part of an equally long tradition of price-theoretic texts in the Chicago mold. Knight’s The Economic Organization, Stigler’s The Theory of Competitive Price (1942, later revised multiple times as The Theory of Price), and Becker’s Economic Theory (1971) are all part of this tradition. A brief perusal of the currently popular graduate texts by Hal Varian (1992), David Kreps (1990), and Andreu Mas-Colell, Michael Whinston, and Jerry Green (1995) makes crystal clear the distinctive nature of the Chicago approach. The tradition has been carried on at the undergraduate level in David Friedman’s Price Theory: An Intermediate Text,16 Deirdre McCloskey’s The Applied Theory of Price, and Steven Landsburg’s Price Theory and Applications, which, like their graduate-level counterparts, present a very different approach to the subject than their more orthodox competitors. Whatever one’s feelings about the Chicago approach—and there is certainly a wide range of opinion here—it has had a profound influence within and beyond economics, and within and outside the academy. While the Chicago tradition in price theory remains very much alive, it is good to see, too, that the AldineTransaction publishing program will keep Milton Friedman’s Price Theory readily available to future generations of students and scholars.

tive Chicago flavor being evidenced in a reading list that includes myriad works published before 1980, including Friedman’s Price Theory, Becker’s Economic Theory (1971), and Knight’s The Economic Organization (1933). Just as Friedman himself is near the headwaters of this long teaching tradition at Chicago, so too is his Price Theory part of an equally long tradition of price-theoretic texts in the Chicago mold. Knight’s The Economic Organization, Stigler’s The Theory of Competitive Price (1942, later revised multiple times as The Theory of Price), and Becker’s Economic Theory (1971) are all part of this tradition. A brief perusal of the currently popular graduate texts by Hal Varian (1992), David Kreps (1990), and Andreu Mas-Colell, Michael Whinston, and Jerry Green (1995) makes crystal clear the distinctive nature of the Chicago approach. The tradition has been carried on at the undergraduate level in David Friedman’s Price Theory: An Intermediate Text,16 Deirdre McCloskey’s The Applied Theory of Price, and Steven Landsburg’s Price Theory and Applications, which, like their graduate-level counterparts, present a very different approach to the subject than their more orthodox competitors. Whatever one’s feelings about the Chicago approach—and there is certainly a wide range of opinion here—it has had a profound influence within and beyond economics, and within and outside the academy. While the Chicago tradition in price theory remains very much alive, it is good to see, too, that the AldineTransaction publishing program will keep Milton Friedman’s Price Theory readily available to future generations of students and scholars.

Steven G. Medema

Steven G. Medema

Notes

Notes

1. The breadth and depth of this impact is reflected in the excellent collection by J. Daniel Hammond (1999). This introduction relies heavily on Hammond’s (1999) introduction and the essay by David Fand (1999), as well as Hammond’s (2006) recent essay on the history of Chicago price theory. 2. Simons and Director established and solidified the price-theoretic tradition in the Law School at Chicago through their course, “Economic Analysis of Public Policy.” 3. The Becker Center, originally named The Chicago Initiative on Price Theory, is “aimed to sustain and strengthen a powerful methodology, which emphasizes the role of prices in the fundamental functions of an economic system and which values the development of testable hypotheses, efficient modeling, and rigorous applications” (http://pricetheory.uchicago. edu/about_center.htm). 4. For further biographical information, see Friedman and Friedman (1998). 5. The Price Theory sequence was originally numbered 300a and 300b but was renumbered 301 and 302 in 1959. See Hammond (2006). 6. Friedman and Stigler had been graduate students together at Chicago in the 1930s, had served together in the Statistical Research Group at Columbia University in the waning days of the Second World War, and spent 1945 as faculty colleagues—and office-mates—at the University of Minnesota. Both left Minnesota in 1946—Friedman for Chicago and Stigler for Brown. Stigler did not join the faculty at Chicago until 1958. Hammond and Hammond (2006) gives a very nice window into this personal and professional relationship over the period 1945-57.

1. The breadth and depth of this impact is reflected in the excellent collection by J. Daniel Hammond (1999). This introduction relies heavily on Hammond’s (1999) introduction and the essay by David Fand (1999), as well as Hammond’s (2006) recent essay on the history of Chicago price theory. 2. Simons and Director established and solidified the price-theoretic tradition in the Law School at Chicago through their course, “Economic Analysis of Public Policy.” 3. The Becker Center, originally named The Chicago Initiative on Price Theory, is “aimed to sustain and strengthen a powerful methodology, which emphasizes the role of prices in the fundamental functions of an economic system and which values the development of testable hypotheses, efficient modeling, and rigorous applications” (http://pricetheory.uchicago. edu/about_center.htm). 4. For further biographical information, see Friedman and Friedman (1998). 5. The Price Theory sequence was originally numbered 300a and 300b but was renumbered 301 and 302 in 1959. See Hammond (2006). 6. Friedman and Stigler had been graduate students together at Chicago in the 1930s, had served together in the Statistical Research Group at Columbia University in the waning days of the Second World War, and spent 1945 as faculty colleagues—and office-mates—at the University of Minnesota. Both left Minnesota in 1946—Friedman for Chicago and Stigler for Brown. Stigler did not join the faculty at Chicago until 1958. Hammond and Hammond (2006) gives a very nice window into this personal and professional relationship over the period 1945-57.

xii   

xii   

aldinetransaction introduction

aldinetransaction introduction

7. Letter from Stigler to Friedman, August 19, 1946, quoted in Hammond and Hammond (2006, p. 26). Friedman and Stigler actually had rather extensive debates over the proper interpretation of Marshall and the utility of his Principles for contemporary theorizing, and Friedman read both Marshall’s Principles and Stigler’s The Theory of Price (1946) in preparation for teaching his first price theory class at Chicago. See the correspondence in Hammond and Hammond (2006). The reference to “Burns” here is to Arthur Burns, who was, variously, professor of economics at Columbia University, director of the National Bureau of Economic Research, and chairman of the Council of Economic Advisors. 8. Quoted in Hammond (2006). This statement comes from Friedman’s lecture notes for Econ. 300a. 9. Knight, who taught price theory with Viner, was much more the abstract theorist. 10. The commonality between the courses taught by Viner and Friedman extends to the reading lists, which have significant overlap, most especially in their use of Marshall’s Principles, but also, for example, Henry Schultz’s “The Meaning of Statistical Demand Curves,” Viner’s “Cost Curves and Supply Curves,” John Bates Clark’s The Distribution of Wealth, John Stuart Mill’s Principles of Political Economy, and Adam Smith’s Inquiry into the Nature and Causes of the Wealth of Nations. See Hammond (2006). 11. See, for example, Arrow and Debreu (1954), Debreu (1959), and Samuelson (1947). 12. Hammond (2006). 13. See p. xviii, infra. 14. Director was also Friedman’s brother-in-law. 15. See Chapter 1, pp. 7-8, infra, as well as Friedman’s “The Methodology of Positive Economics” (1953). 16. Now out of print. The book can be found on the web at http://www.daviddfriedman. com/Academic/Price_Theory/PThy_ToC.html. David Friedman is Milton Friedman’s son.

7. Letter from Stigler to Friedman, August 19, 1946, quoted in Hammond and Hammond (2006, p. 26). Friedman and Stigler actually had rather extensive debates over the proper interpretation of Marshall and the utility of his Principles for contemporary theorizing, and Friedman read both Marshall’s Principles and Stigler’s The Theory of Price (1946) in preparation for teaching his first price theory class at Chicago. See the correspondence in Hammond and Hammond (2006). The reference to “Burns” here is to Arthur Burns, who was, variously, professor of economics at Columbia University, director of the National Bureau of Economic Research, and chairman of the Council of Economic Advisors. 8. Quoted in Hammond (2006). This statement comes from Friedman’s lecture notes for Econ. 300a. 9. Knight, who taught price theory with Viner, was much more the abstract theorist. 10. The commonality between the courses taught by Viner and Friedman extends to the reading lists, which have significant overlap, most especially in their use of Marshall’s Principles, but also, for example, Henry Schultz’s “The Meaning of Statistical Demand Curves,” Viner’s “Cost Curves and Supply Curves,” John Bates Clark’s The Distribution of Wealth, John Stuart Mill’s Principles of Political Economy, and Adam Smith’s Inquiry into the Nature and Causes of the Wealth of Nations. See Hammond (2006). 11. See, for example, Arrow and Debreu (1954), Debreu (1959), and Samuelson (1947). 12. Hammond (2006). 13. See p. xviii, infra. 14. Director was also Friedman’s brother-in-law. 15. See Chapter 1, pp. 7-8, infra, as well as Friedman’s “The Methodology of Positive Economics” (1953). 16. Now out of print. The book can be found on the web at http://www.daviddfriedman. com/Academic/Price_Theory/PThy_ToC.html. David Friedman is Milton Friedman’s son.

References

References

Arrow, Kenneth J. and Gerard Debreu (1954) “Existence of an Equilibrium for a Competitive Economy.” Econometrica 22 (July): 265-90. Becker, Gary S. (1971) Economic Theory. New York: Knopf. ______ (1991) “Milton Friedman, 1912-.” In Edward Shils, ed., Remembering the University of Chicago: Teachers, Scientists, and Scholars. Chicago: University of Chicago Press. Reprinted in Hammond (1999). Debreu, Gerard (1959) The Theory of Value. New York: J. Wiley and Sons. Fand, David I. (1999) “Friedman’s Price Theory: Economics 300 at the University of Chicago in 1947-1951.” In J. Daniel Hammond, ed., The Legacy of Milton Friedman as Teacher, volume 1. Aldershot: Edward Elgar Publishing, pp. 9-21. Friedman, David (1986) Price Theory: An Intermediate Text. Cincinnati: Southwestern. Friedman, Milton (1953) “The Methodology of Positive Economics.” In Essays in Positive Economics. Chicago: University of Chicago Press. ______ (1962) Price Theory: A Provisional Text. Chicago: Aldine. Friedman, Milton and Rose D. Friedman (1998) Two Lucky People: Memoirs. Chicago: University of Chicago Press. Hammond, J. Daniel (1992) “An Interview with Milton Friedman on Methodology.” Research in the History of Economic Thought and Methodology 10: 91-118. ______ (1999) The Legacy of Milton Friedman as Teacher, 2 vols. Aldershot: Edward Elgar Publishing. ______ (2006) “The Development of Postwar Chicago Price Theory.” In Ross Emmett, ed., The Elgar Companion to the Chicago School. Aldershot, Edward Elgar publishing, forthcoming.

Arrow, Kenneth J. and Gerard Debreu (1954) “Existence of an Equilibrium for a Competitive Economy.” Econometrica 22 (July): 265-90. Becker, Gary S. (1971) Economic Theory. New York: Knopf. ______ (1991) “Milton Friedman, 1912-.” In Edward Shils, ed., Remembering the University of Chicago: Teachers, Scientists, and Scholars. Chicago: University of Chicago Press. Reprinted in Hammond (1999). Debreu, Gerard (1959) The Theory of Value. New York: J. Wiley and Sons. Fand, David I. (1999) “Friedman’s Price Theory: Economics 300 at the University of Chicago in 1947-1951.” In J. Daniel Hammond, ed., The Legacy of Milton Friedman as Teacher, volume 1. Aldershot: Edward Elgar Publishing, pp. 9-21. Friedman, David (1986) Price Theory: An Intermediate Text. Cincinnati: Southwestern. Friedman, Milton (1953) “The Methodology of Positive Economics.” In Essays in Positive Economics. Chicago: University of Chicago Press. ______ (1962) Price Theory: A Provisional Text. Chicago: Aldine. Friedman, Milton and Rose D. Friedman (1998) Two Lucky People: Memoirs. Chicago: University of Chicago Press. Hammond, J. Daniel (1992) “An Interview with Milton Friedman on Methodology.” Research in the History of Economic Thought and Methodology 10: 91-118. ______ (1999) The Legacy of Milton Friedman as Teacher, 2 vols. Aldershot: Edward Elgar Publishing. ______ (2006) “The Development of Postwar Chicago Price Theory.” In Ross Emmett, ed., The Elgar Companion to the Chicago School. Aldershot, Edward Elgar publishing, forthcoming.

02Introduction Friedman.indd 12

xii   

8/23/2006 10:05:36 AM

aldinetransaction introduction

02Introduction Friedman.indd 12

xii   

8/23/2006 10:05:36 AM

aldinetransaction introduction

7. Letter from Stigler to Friedman, August 19, 1946, quoted in Hammond and Hammond (2006, p. 26). Friedman and Stigler actually had rather extensive debates over the proper interpretation of Marshall and the utility of his Principles for contemporary theorizing, and Friedman read both Marshall’s Principles and Stigler’s The Theory of Price (1946) in preparation for teaching his first price theory class at Chicago. See the correspondence in Hammond and Hammond (2006). The reference to “Burns” here is to Arthur Burns, who was, variously, professor of economics at Columbia University, director of the National Bureau of Economic Research, and chairman of the Council of Economic Advisors. 8. Quoted in Hammond (2006). This statement comes from Friedman’s lecture notes for Econ. 300a. 9. Knight, who taught price theory with Viner, was much more the abstract theorist. 10. The commonality between the courses taught by Viner and Friedman extends to the reading lists, which have significant overlap, most especially in their use of Marshall’s Principles, but also, for example, Henry Schultz’s “The Meaning of Statistical Demand Curves,” Viner’s “Cost Curves and Supply Curves,” John Bates Clark’s The Distribution of Wealth, John Stuart Mill’s Principles of Political Economy, and Adam Smith’s Inquiry into the Nature and Causes of the Wealth of Nations. See Hammond (2006). 11. See, for example, Arrow and Debreu (1954), Debreu (1959), and Samuelson (1947). 12. Hammond (2006). 13. See p. xviii, infra. 14. Director was also Friedman’s brother-in-law. 15. See Chapter 1, pp. 7-8, infra, as well as Friedman’s “The Methodology of Positive Economics” (1953). 16. Now out of print. The book can be found on the web at http://www.daviddfriedman. com/Academic/Price_Theory/PThy_ToC.html. David Friedman is Milton Friedman’s son.

7. Letter from Stigler to Friedman, August 19, 1946, quoted in Hammond and Hammond (2006, p. 26). Friedman and Stigler actually had rather extensive debates over the proper interpretation of Marshall and the utility of his Principles for contemporary theorizing, and Friedman read both Marshall’s Principles and Stigler’s The Theory of Price (1946) in preparation for teaching his first price theory class at Chicago. See the correspondence in Hammond and Hammond (2006). The reference to “Burns” here is to Arthur Burns, who was, variously, professor of economics at Columbia University, director of the National Bureau of Economic Research, and chairman of the Council of Economic Advisors. 8. Quoted in Hammond (2006). This statement comes from Friedman’s lecture notes for Econ. 300a. 9. Knight, who taught price theory with Viner, was much more the abstract theorist. 10. The commonality between the courses taught by Viner and Friedman extends to the reading lists, which have significant overlap, most especially in their use of Marshall’s Principles, but also, for example, Henry Schultz’s “The Meaning of Statistical Demand Curves,” Viner’s “Cost Curves and Supply Curves,” John Bates Clark’s The Distribution of Wealth, John Stuart Mill’s Principles of Political Economy, and Adam Smith’s Inquiry into the Nature and Causes of the Wealth of Nations. See Hammond (2006). 11. See, for example, Arrow and Debreu (1954), Debreu (1959), and Samuelson (1947). 12. Hammond (2006). 13. See p. xviii, infra. 14. Director was also Friedman’s brother-in-law. 15. See Chapter 1, pp. 7-8, infra, as well as Friedman’s “The Methodology of Positive Economics” (1953). 16. Now out of print. The book can be found on the web at http://www.daviddfriedman. com/Academic/Price_Theory/PThy_ToC.html. David Friedman is Milton Friedman’s son.

References

References

Arrow, Kenneth J. and Gerard Debreu (1954) “Existence of an Equilibrium for a Competitive Economy.” Econometrica 22 (July): 265-90. Becker, Gary S. (1971) Economic Theory. New York: Knopf. ______ (1991) “Milton Friedman, 1912-.” In Edward Shils, ed., Remembering the University of Chicago: Teachers, Scientists, and Scholars. Chicago: University of Chicago Press. Reprinted in Hammond (1999). Debreu, Gerard (1959) The Theory of Value. New York: J. Wiley and Sons. Fand, David I. (1999) “Friedman’s Price Theory: Economics 300 at the University of Chicago in 1947-1951.” In J. Daniel Hammond, ed., The Legacy of Milton Friedman as Teacher, volume 1. Aldershot: Edward Elgar Publishing, pp. 9-21. Friedman, David (1986) Price Theory: An Intermediate Text. Cincinnati: Southwestern. Friedman, Milton (1953) “The Methodology of Positive Economics.” In Essays in Positive Economics. Chicago: University of Chicago Press. ______ (1962) Price Theory: A Provisional Text. Chicago: Aldine. Friedman, Milton and Rose D. Friedman (1998) Two Lucky People: Memoirs. Chicago: University of Chicago Press. Hammond, J. Daniel (1992) “An Interview with Milton Friedman on Methodology.” Research in the History of Economic Thought and Methodology 10: 91-118. ______ (1999) The Legacy of Milton Friedman as Teacher, 2 vols. Aldershot: Edward Elgar Publishing. ______ (2006) “The Development of Postwar Chicago Price Theory.” In Ross Emmett, ed., The Elgar Companion to the Chicago School. Aldershot, Edward Elgar publishing, forthcoming.

Arrow, Kenneth J. and Gerard Debreu (1954) “Existence of an Equilibrium for a Competitive Economy.” Econometrica 22 (July): 265-90. Becker, Gary S. (1971) Economic Theory. New York: Knopf. ______ (1991) “Milton Friedman, 1912-.” In Edward Shils, ed., Remembering the University of Chicago: Teachers, Scientists, and Scholars. Chicago: University of Chicago Press. Reprinted in Hammond (1999). Debreu, Gerard (1959) The Theory of Value. New York: J. Wiley and Sons. Fand, David I. (1999) “Friedman’s Price Theory: Economics 300 at the University of Chicago in 1947-1951.” In J. Daniel Hammond, ed., The Legacy of Milton Friedman as Teacher, volume 1. Aldershot: Edward Elgar Publishing, pp. 9-21. Friedman, David (1986) Price Theory: An Intermediate Text. Cincinnati: Southwestern. Friedman, Milton (1953) “The Methodology of Positive Economics.” In Essays in Positive Economics. Chicago: University of Chicago Press. ______ (1962) Price Theory: A Provisional Text. Chicago: Aldine. Friedman, Milton and Rose D. Friedman (1998) Two Lucky People: Memoirs. Chicago: University of Chicago Press. Hammond, J. Daniel (1992) “An Interview with Milton Friedman on Methodology.” Research in the History of Economic Thought and Methodology 10: 91-118. ______ (1999) The Legacy of Milton Friedman as Teacher, 2 vols. Aldershot: Edward Elgar Publishing. ______ (2006) “The Development of Postwar Chicago Price Theory.” In Ross Emmett, ed., The Elgar Companion to the Chicago School. Aldershot, Edward Elgar publishing, forthcoming.

AldineTransaction Introduction    xiii

AldineTransaction Introduction    xiii

Hammond, J. Daniel and Claire H. Hammond, eds. (2006) Making Chicago Price Theory: Friedman-Stigler Correspondence, 1945-1957. London: Routledge. Knight, Frank H. (1933) The Economic Organization. Chicago: The University of Chicago. Reprinted New York: A.M. Kelley, 1951. Kreps, David (1990) A Course in Microeconomic Theory. Princeton, NJ: Princeton University Press. Landsburg, Steven (2004) Price Theory and Applications, 6th ed. Cincinnati, OH: Southwestern. Levitt, Steven D. and Stephen J. Dubner (2005) Freakonomics. New York: HarperCollins. Mas-Colell, Andreu, Michael Whinston, and Jerry Green (1995) Microeconomic Theory. Oxford: Oxford University Press. McCloskey, D. N. (1985) The Applied Theory of Price, 2nd ed. New York: Macmillan. Samuelson, Paul A. (1947) Foundations of Economic Analysis. Cambridge, MA: Harvard University Press. Snowdon, Brian and Howard R. Vane (1998) “Transforming Macroeconomics: An Interview with Robert E. Lucas Jr.” Journal of Economic Methodology 5 (June): 115-46. Stigler, George J. (1942) The Theory of Competitive Price. New York: Macmillan. ______ (1987) The Theory of Price, 4th ed. New York: Macmillan. Varian, Hal (1992) Microeconomic Theory, 3rd ed. New York: Norton.

Hammond, J. Daniel and Claire H. Hammond, eds. (2006) Making Chicago Price Theory: Friedman-Stigler Correspondence, 1945-1957. London: Routledge. Knight, Frank H. (1933) The Economic Organization. Chicago: The University of Chicago. Reprinted New York: A.M. Kelley, 1951. Kreps, David (1990) A Course in Microeconomic Theory. Princeton, NJ: Princeton University Press. Landsburg, Steven (2004) Price Theory and Applications, 6th ed. Cincinnati, OH: Southwestern. Levitt, Steven D. and Stephen J. Dubner (2005) Freakonomics. New York: HarperCollins. Mas-Colell, Andreu, Michael Whinston, and Jerry Green (1995) Microeconomic Theory. Oxford: Oxford University Press. McCloskey, D. N. (1985) The Applied Theory of Price, 2nd ed. New York: Macmillan. Samuelson, Paul A. (1947) Foundations of Economic Analysis. Cambridge, MA: Harvard University Press. Snowdon, Brian and Howard R. Vane (1998) “Transforming Macroeconomics: An Interview with Robert E. Lucas Jr.” Journal of Economic Methodology 5 (June): 115-46. Stigler, George J. (1942) The Theory of Competitive Price. New York: Macmillan. ______ (1987) The Theory of Price, 4th ed. New York: Macmillan. Varian, Hal (1992) Microeconomic Theory, 3rd ed. New York: Norton.

02Introduction Friedman.indd 13

8/23/2006 10:05:36 AM

02Introduction Friedman.indd 13

8/23/2006 10:05:36 AM

AldineTransaction Introduction    xiii

AldineTransaction Introduction    xiii

Hammond, J. Daniel and Claire H. Hammond, eds. (2006) Making Chicago Price Theory: Friedman-Stigler Correspondence, 1945-1957. London: Routledge. Knight, Frank H. (1933) The Economic Organization. Chicago: The University of Chicago. Reprinted New York: A.M. Kelley, 1951. Kreps, David (1990) A Course in Microeconomic Theory. Princeton, NJ: Princeton University Press. Landsburg, Steven (2004) Price Theory and Applications, 6th ed. Cincinnati, OH: Southwestern. Levitt, Steven D. and Stephen J. Dubner (2005) Freakonomics. New York: HarperCollins. Mas-Colell, Andreu, Michael Whinston, and Jerry Green (1995) Microeconomic Theory. Oxford: Oxford University Press. McCloskey, D. N. (1985) The Applied Theory of Price, 2nd ed. New York: Macmillan. Samuelson, Paul A. (1947) Foundations of Economic Analysis. Cambridge, MA: Harvard University Press. Snowdon, Brian and Howard R. Vane (1998) “Transforming Macroeconomics: An Interview with Robert E. Lucas Jr.” Journal of Economic Methodology 5 (June): 115-46. Stigler, George J. (1942) The Theory of Competitive Price. New York: Macmillan. ______ (1987) The Theory of Price, 4th ed. New York: Macmillan. Varian, Hal (1992) Microeconomic Theory, 3rd ed. New York: Norton.

Hammond, J. Daniel and Claire H. Hammond, eds. (2006) Making Chicago Price Theory: Friedman-Stigler Correspondence, 1945-1957. London: Routledge. Knight, Frank H. (1933) The Economic Organization. Chicago: The University of Chicago. Reprinted New York: A.M. Kelley, 1951. Kreps, David (1990) A Course in Microeconomic Theory. Princeton, NJ: Princeton University Press. Landsburg, Steven (2004) Price Theory and Applications, 6th ed. Cincinnati, OH: Southwestern. Levitt, Steven D. and Stephen J. Dubner (2005) Freakonomics. New York: HarperCollins. Mas-Colell, Andreu, Michael Whinston, and Jerry Green (1995) Microeconomic Theory. Oxford: Oxford University Press. McCloskey, D. N. (1985) The Applied Theory of Price, 2nd ed. New York: Macmillan. Samuelson, Paul A. (1947) Foundations of Economic Analysis. Cambridge, MA: Harvard University Press. Snowdon, Brian and Howard R. Vane (1998) “Transforming Macroeconomics: An Interview with Robert E. Lucas Jr.” Journal of Economic Methodology 5 (June): 115-46. Stigler, George J. (1942) The Theory of Competitive Price. New York: Macmillan. ______ (1987) The Theory of Price, 4th ed. New York: Macmillan. Varian, Hal (1992) Microeconomic Theory, 3rd ed. New York: Norton.

This Page Intentionally Left Blank

www.Transactionpub.com

Preface

Shortly after the initial edition of this book a7as published, I shifted for nearly a decade from teaching price theory to teaching monetary theory. Three years ago, I reslimed teaching price theory. Next year (the academic year 1975-76), I plan to teach i t for the last time. Hence, if I were ever to revise substantially the provisional version that was published in 1962, now seemed the time to do so. I cannot pretend that the present version is the finished treatise that I had in mind (or in youtltful dreams) in the earlier years of teaching the course. Rut it is a much expanded and, I hope, improved version. I have filled in four of the six gaps that I enumerated in the preface to the initial version. T h e two I have not filled in are industrial organization, for reasons given at the end of chapter 6 , and the theory of general equilibrium, because there al:e such good extant expositions of the clasqical T17alrasian general equilibrium apl~rozrchand I am rrot colnpetent to present a succinct yet faithful exposition of the rnore recent general equilibrium developnlents, particul;~riyin tile fielcl of gro.cvt1i models. In addition, I rather suspect that these de\-elopments are as yet in n preliminary and unsatisfactory state. I n atldition to filling in the designated gaps, I Ilzrve added a discussion of personal probability to complete the utility an;rlpsis of choices involving uncertainty and have inserted n largely expository lecture on the Phillips curw, wllicll I gave in September 1974 in London. 7'his topic may seem to belo~tgin monetary theory rather tllan in price tl~eory.However, I believe that it belongs in I ~ o t hfor , reasons that I trust (lie text inakes clear. I have included in this etlition, ;is I did in the initial version, illy (IZISS reading list and ;I tolleciion of the problems that I have assigned to the class to ~vorkon home. I llave 11cen gratified at the professional attention attracted b y the problems in the initial vel.sion. However, I have not kept so I cannot protrack of tile articles and notes that they have stin~~ilated, vide comprehensive references. I have yetairled in this etlition all tlle problems from the initial etlition and have simply added the prohlenlr that 1

1

PREFACE

have assigned since then. My heaviest debt for problems remains to Aaron Director and George J . Stigler, but I hahe continued to borrow from other colleagues as well. I n preparing this edition, I have benefited from criticisms and suggestions of a number of reade~s,including teachers who have used the book in their courses. Marshall Colberg was particularly helpful. T o him ant1 the others who sent me comments, my sincere thanks. I am deeply indebted also to my secretary, Gloria Valentine, who, in preparing the manuscript for this edition, continued her unbroken record of displaying a degree of efficiency exceeded only by her good cheer. I cannot end this preface without recording the great personal satisfnction that I have derived from teacliilig price theor\ to successive qeneldtions of able and enthusiastic graduate students. Tlie formal structure of price theory has an aesthetic qualitj that has alwajs reminded me of tlie famous last lines of Keats's "Ode on a Giecian Urn": "Beauty is truth, truth beauty,"-that is all Ye know on earth, and all ye need to know. Milton Friedman Ely, Vermont A ~ ~ g u3,s t1975

Preface to Price Theory: A Provisional Text I t is now mole than a decade since the contents of this book were first mimeog~aphedand used In classes 111 p i c e t h e o ~ jat the U n i ~ esit) i of t period, 1 haxe been extlemelj reluctant to Chicago. T h r o u g h o ~ ~that hale these notes offered fox gene1 1' 1 sale Tlle leluctance has deliled h o m my dissatisfaction nit11 their sclappj natule, flom my intention to use them as a basis for a fuller and more wtisfactolj tleatmerlt of p i c e tlleorx, and from my optimistic belief that I mould be able to turn to the preparaAs '111 empirical economist, Ilourtion of the fuller tl eatment ~nornent,~rilx. e\e1, I cannot neglect the e~itlencet11,it has c~ccumulntedin that decade Clea~ly,I must ieject the hjpotllcsi, that a fullel treatment is imminent. hforeo\el, it has not been feasible to keep the mimeoqraphetl notes £lorn getting fairlj nide circulation Hence, despite m\ continued dissatisfaction with them, it has seemetl best to make them yenerall\ a\ ailable. These notes had their oriqin in the entleprenelilsllip of Daxid I Fand .\then he was a student at the Unl\ersit\ of Clllcago He induced I V a ~ l e n J Gustus to collabolate in prep,ilinq summaries of lect~uesin a twoquarter course in p i c e t h e o ~ jtliat I ha\e gixen at the U n i ~ e r s i t jof Chicago since 1946 I went oxel the summalies, iexi5etl them in detail, \mote altelnatixe xelsions £01 some, substituted ple\iouslj v ~ i t t e nbut unpubllshed matelial for others, ant1 inselted, 1,oth then and at i n t e r ~ a l ssince, published material that seemed p'il ticulally lele\,lnt These notes ~vould out but fol Fanct'i and Gustus's wolk, and I am rlevel haxe been biouqht much indebted to them. I n the pleserlt version, the replinted nlaterial intlude5 an article on "The 'Tl'elfare' Effects of an Intome T a x and all Excise Tax," a r e ~ i s e d in tlie J o r i ~ n a lof Pollt1cal Econxersion of an article that first c~l)peci~ed o m y , reprinted here flom m) Essclps In Pocl t 1 - r ~E c o n o ~ n ~ c ns ;few pages on statistical cost curves from a comment of mine in Dltslnrss Concenl:atlon and Pllce Policy; palt of ari article of mine that appealed in David h1cCord 12'right (ed.), T h e Impact of thr b n z o n , 'rnd an article on "Choice, Chance, and the Personal Distlibution of Income," replinted

from the Joul-nu1 of Political Economy. I am indel~tedto the Iiriiversity of Chicago Press, Princeton University Press, and David LIcCortl i\'riglit for permission to reprint. I n teaching the course on price theory since these notes have been available, I have found that the chief gaps in them, which it is necessary to supplement by class presentation, are in respect to ( I ) the tlieory of the division of iriconle between cul-rent consumption arld the accumulation of wealth; (2) industrial organization, with special reference to ~)rohlemsin the economics of the individual firm; (3) fact and theory about the size distribution of income; (.4)tlle tlieory of profits; (5) capital theory-the final section of the notes on this topic have t ~ ~ r i ~ out e dto be too succinct and condensed, particularly with respect to tlle ;~ritllrneticof tlie relation between inconle streams and capital values and the stock-flow a~lalysisembedded in that section; and (6) the theory of gerleral equilibrium. I have added to this version of the notes two ;~ppel~dixes that may help to fill these gaps as xvell as supplement the notes. Aljperidix A gives the readirlg list that I have usetl in nly course. Appendix I3 gives a col1ec:tion of some of tlle problems that I have ;issigned to tile class to ~ r o r kon during our so-called reading period. Tlle problems are in two parts, those in part 1 having been assigned during the first qltartei- and tllose in part 2 (luring the second quarter. For want of any better sequence, I have listed tlleln i r l each part simply in the cllronological order in ~vhichthey were assigned. I have used tlie part 1 problerns primarily as ;I means to fill tllc gap nnmbered (2) above; hence, these deal mostly ~vitllthe interpretation of intlustrial practices. T h e answers to some of tllese problems can now 11e fo~ttltl in the literature, but 1 have made no attempt to give references. As every teacher knows, class prol~leinsand exam questions are ahnost conlmunity property. I cannot myself trace the source of most of tl;r l~rol~lerns given, except that I know my heaviest debts are to Aaron Director ant1 George 1. Stigler, from trhom I have borrowed shamelessly.

Introduction

Tliese notes deal with price theory. T h e larger part is devotetl to tlre pricing of final products;'tlie rest, to the theory of tlistril~ution.Tile reasoil for tlevotirig more attention to tlie pricing of final products is that the theory of distribution is a special case of the theory of pri~iilg,t.oiicerrled wit11 the pricing of factors of protluction. Herice, the princiljles that explairl prices ill the product mxrkets also exp1;riri prices in the factor markets. ~\le/rnlngofEro?zo~tlic\: Economic T l z ~ o ? ?

Economics i i the scicl~teof how a pn~ticttl,lisociet~s o l ~ e sits econonlic p o b l e i n ~An economic piobleix exists xtlieile~eitcnlcc nle'ln5 ale 11sed to sati5f) rtlte?nnt~veelids If tlie mean5 'lie not scalce, t l l e ~ e1s no problem ~t all; there is Niir,l~ia I1 the rne'lnr 'tie 5c'lice but there is o ~ l l y1' single end, the problem of lio~zto use tlie means is a tetllnoloqic,rl pioblenl. No ~ a l u ejuclgmerlts erltei into its solt~tion,on11 knonletlge of plqsical and technical le1,itionrliips Fol ex,rmple, suppose qi\ en amouilts of ii on, I'ihor, etc. ,tie 'tx '~ildble.~ntl'tie to he u5etl to build ,111 enqine of rnauimum t cs Liio~vletlqc 11o1,epouel. Thi, ;, .I pun cl\ tecllnical pl ciblenl t l ~ lecluii solel) of ellgilleel illg ant1 of ph\ jic'11 5t ience Alteinati~ely, let the object i ~ ebe to build the "best" engine, wlieie the colicept of "lje5t" iilrol~es t weight, s i ~ eetc. , There is no longei a single not only horsepower, I ~ u also l tecllnic,11Lnouletlgc tan Lield a end. No amount of pulel) p h ~ s i c , ~lore generally, tile demand for any protluct is always a joint dem;~ndfor the resources used to produce it. T h e demand for a commodity or service may be c l c ~ i u r dfroin the demand for some final good: e.g., the dernarld for carpenters' labor is derived from the demand for houses. Consumer demand for final protlllcts is the ultimate soilrce of the derived tlcmand for resources. For sllort periods, lio~vever,the tlemarld of ctealers can varj- independently of the demand of filial consumel-s. T h e demand of dealers, in turn, may 11e strongly influenced and affected by expectations concerning future prices, a factor that generally l~laysa m~lcll snlaller role in determining - consumer c!cm;rntl. For this reason, the usual tools of denland and supply may not be very useful in a stucly of day-today fluctuations in this t)pe of market. Of course, fol-mall) they could still tl ha\-e to 11e be usctl for this purpose, but rn;tjor attention ~ v o ~ i l then placed on changes in thern ra!her thari mo\.ements along thcln. Ailother ~vayof pllttillg this point is t!~at, summalires the limitations of the intli~iclu,rl'sie5oulces Gixen that LT(X. Y, Z, . .) is to lje subject t o tlle con\ti,\int of XP, YP, ZPL . . . = I, the m~~xirni7ecI ~ri inn! be emp1o)ed. Tlleiefore we rrletllod of the L a g l , ~ n g i ~ rrlriltiplie~ write

+

U ( X , Y , Z . . . ) + X(XP,+YP,+ZP,+

+

+

. . . - I).

Differentiating this expie5siorl nit11 respect to X, Y , Z, . . . and X we obtain

us + XP,

=0

Us + A P , = O U,+XP,=O

XP,

+ UP, + ZP, + . . .

-

I =0

u,- u . . . . = 1. T h e economic meanp, p, Pz ing of this is that marginal utility per penny's worth of commodity X must equal that of commodities Y , Z, . . . . This common marginal utility per penny is equal to A, whicll is Marshall's marginal utility of money." u, = p, T h e interpretation of this is Another way to state this result is u, p, F ~ o mthis it f o l l o ~ ~that s

u

---1= - - 2 =

u x that represents the rate at ~vhichthe individual is zuilling to substitute

u,

Y for X, while-px lepresents the rate at whicll he can s-r~bstitute Y for X on p, the market. T h e cquiliblium condition is that the rate at which the individual is willing to sui~stituteY for X be equal to tlle rate at wllicll he can substitute Y for X, since if he were willing to substitute fewer units of Y for one unit of X than he can get on the market by giving u p one unit of X, then it will pay him to do so, and conr ersely. This result can be illustrated diagrammatically, as in Figure 2.12. I n

this case, we assume that the marginal u t i l i t ~of X i, independent of the amount of Y; i e., that tlie utilitie5 of the t n o tornmotlities are intle~xnclcnt.Tlie unit on the hori/ontal axis is '1 penny's rvo~tll of X or Y. T h e '~ T h e consumel i5 in eqr~ibar equal to I ieplesents the i n t l i \ i d u , ~ l income Iiljrium \then ire has 50 ,111ocnted his intome that lie leceiles ~onsti-ate foi- ~ o u r s e i fthat the curves in Fig. 24 are fill. a sr~periorgood 1,111 l i o e for a11 inferior good, and to draw a col.rtspoiltling diapi-3111for a n inferior good. in r l ~ ecorrect ovdcr

Theory of Demand

55

sets of working conditions (nonpecuniary advantages and disadvantages), available to the individual. F i g ~ ~ 2.25 r e plots a hypothetical set of indifference curves for an individual. T h e vertical axis measures consumption, or the total value of consumer services per unit time. As noted, a maximization process is implicitly supposed to be behind each value of consumption: consumption is assumed allocated among alternative services so as to maximize utility. T h e horizontal axis measures the number of llours of work per week. There is a vertical line at 168 hours a week, because that is the maximum physically available. Tlle indifference curves are drawn as first declining then rising as the length of the work week is increased. T h e declining segment implies that some work is a "good," i.e., that the individual would be willing to sacrifice some consumption in order to he able to work, that if he hat1 an alternative source of income, he would be willing to pay in order to work. Beyond some number of hours, Ilowever, Figure 2.25 ast ~vorkis a "bad," that it involves disutility and indisumes t l ~ additional viduals will not be willing to work additional hours unless they are com-

work per week

pensated by getting additional coils~imption.T l i e indiffel-ence curves are shown as ultimately asymptotic to tlre 1111)sically maxiniuni limit of 168 liours per xveek. T l i e I~igherthe inclifference curve, tlie higher the utilityi.e., for a given amount of l a l ~ o r the , greater tlie consumption the highelthe utility. n t not exist; xvork may Ile 1-ey:rrdetl Oljviously, tlie decliilirlg ~ e g ~ n e nla) as a "i)acl" regardless of liow short tlie work week. T h e decliniilg segtnent is iiicludetl ltere to ill~tstratea gelleral point. rvliicl~is p;rrticul:rrly e ~ , i d e n t for labor services, namely, that wllether a particular service is a "gootl" o r a "bad" is not ;I tecllnical plieiioinenon dependent on its pl1ysic;il cl~aracteristics b u t a market phenornerlon de1)eiltling o n consumer prefererlces a n d on market supply a n d demand. 7'he same l~hysicalitem nlay Ile ;i "gootl" o r a "bad" depentling or1 circumstarlces. If tlie illarket price is positive, it is a good; if negative, a I);itl. T o ill115tratein a trivial w a j , tlie kind of singing that is done by a rock star is obviously a "gootl," since tlie public is ~villingto pay a lligli price to listen to it; the kirltl o l singing some of us d o is a "bad," since Ive wo11ltl have to pay people to listen to us. .As mttsical tastes cllange, xvliat lvas at one time a "good" may become a "h;rtl," ant1 coriversely. T o illl~stratein a inore flintlamental way, in nloclern advanced societies, almost the ollly Ilartl, 11;lck-breaking pli~sicallaljor that can be observetl is clone 1)y people for sport and they typically pay Tor the privilege of engaging in sucll 1al)or. T2'11at has for inillenia bee11 a conlias I,ec.olne a "good." s ~ > i c u o ~"bad" ts Tlre straight line5 0T~IT ant1 T\"lSf in Figure 2.25 are lines of a t t a i n a l ~ l e coml~inations,or IIudget lines. 'The line 011' correspontls to the case in ~vllicllthe intliviclual Iias n o s o t w e of income otlier th:ttl pa)meilt for l a l ~ o rservices, so i t starts at the origin. 'The slope of the line is tlie wage rate per h o u r (net of taxes, etc., so that it SIIOTYS the ;ullount availahle to add to consumption). T h e point of tangency gives OL as the alnortnt of labor that will enable tlie illtlividual to o l ~ t a i nthe l~igliestindiffei.enc-e curve. Note that it is tlie "higliest" a n d not tlie "lowest" int1iRerenc.e curve becatwe tile cnrves are concave upwai-tls, whiclt is tlie funtlanlet>tal justification for clra~viilgthem that ~ v a y . T l i e line T\i'T\Tf correspontls to ;I case in ~vlriclithe intlividu;~llias a 11o111al)oi- source of irlcornc of OTV. As drn~z.11,lle is tllerel,) let1 to retlllce tlie length of the ~ v o r k i n g~vcekto 01,'. Tllis result is not of course inevitaljle. I t simply reflects the particr~larset of intliffererlce cui-~es,tllougl~it tloes seen1 like the result to he ~ w p e c t e d ,nt lea\t for iiori1al)or income above some miniinurn. T h e kind of analysis used in the preceding section to clerive detn::nd curves froin consumer ilic1ifferellc.ecurves can cleady Ile used 11~1-e to tlerix-e supply curves of lal~oi-for diffeiont c o n ~ l ~ i n a t i o nofs wage r;ites and lionlabor income, arid tlre earlier an;tl>sii; of income a n d su1)stitution effects can be carried over here. J'ou will find it useful to d o so.

Theory of Demand

57

Let us turn nour to the decision a l ~ o uhow t m11c11of current receipts from tlie sale of resource services to spend on current consumption and liow much to adtl to accumulated wealth, or altei-nativel) how much to subtract from ~vealtllto adtl to current receipts for spending on current consumps will be used ancl expanded fl~rtherin some directions tion. ( T l ~ i analysis in chapter 17.) It is tempting to try to incorporate this decision into utility analysis 11y tlie same device as we have just incorpoi-ated tlie decision about how many lioui-s to work, namely, b y adding another axis to the indifference diagram on ~vhicliis measured savings, or the number of dollars per year atldecl to accumulatetl wealth. Indeed, Leon l'l'alrar succumbed to this tei~lptatiorlin the latest edition of his great book, ElCments d'dconomie politiq~iep w e , p~tblishedin English translation uncler the title, Elements of P1i1-eEconomir.~,after having resisted it in earlier e ~ l i t i o n s . ~ T h e difficulty ~vitlitliis apparently siniple extension of the utility analysis to cover saving can IIe seen by supposing it to he follolved by measuring consumption on one axis and tlie rate of saving on the otlier, both meastiretl as i111mber of tlollars per year. l2'liat is then the price ratio that is relevaiit? Clearly it is 1 : a dollar per )ear can a l w a ~ sbe added to savings 11) suljtractiiig a tlollar from consumption. I n his desire to incl~lclea suh5 t i t ~ t i o neffect, I\-alras defined the variable to be measured along the saving axis not ;is the riurnljer of dollars per year clevoted to saving but as a commodity E, equal to tlie pern1;inent income stream purcllased tvitli the ~;~viiig i.e., , the permanent income stream, r, 1-ielded by one dollar of wealth, where r is the rate of interest. T h e price of one unit of E is tlien 1 - or tlie reciprocal of the interest rate (if r = .05, it costs $20 to buy $1 a r year). However, tliis makes the two axes tioncomp;iral~le:consumption is a flow, dollars per year: E is a rate of change of a flow, a second derivative, dollars per year pet. ye;rr. TVitIl ;i properly specified utility function, the indifference curves remain the same over time regardless of which point on them is attained, so long as the basic untlerlying conditions are the same. Not so with indifference curves for consumption and the Tb'alras commodity E. .\ positive E adds to the stock of ~vealtliso as tirrie passes, the individual becomes ~ve;iltliierant1 ~vealthier.For tlie same level of consumption, tlie rate at ~vlliclitile intlil-idual will be willing to sul~stitutestill further additions to wealtll for further atlditions to consumption will decline. T h e indifference curves so defined will cllange. Tlle difficulty with the simple approach is that saving is not another commotlity like food, clothing, etc., ~vliiclloffers utility in accordance with 7. Milton Frietlman, "Leon TValras and Ilis Economic System," America?a Economic Revieru, 45 (December 1955): 900-909.

the rate of saving. Saving is a way of substituting future consumption for present consumption. For a satisfactory analysis of saving, we have to take account of its basic role, not simply add an axis to an indifference diagram. I t is essential to consider more than one time period. Accumulated wealth, unlike saving, may have certain characteristics that make it in part a good like other consumption services, insofar as it provides a reserve against emergencies. This service can be measured along an indifference curve axis, and part of income regarded as used to purchase it. T h e income used to purchase it is the difference between the (anticipated average) maximum return that can be obtained from the wealth anci the actual (anticipated average) return from holding the wealth in a form that provides greater utility as a reserve. If we neglect this role of wealth, the case that it is easiest to present on an indifference diagram'is one that Ir~:ingFisher analyzed: the hypothetical case of a finite period, most simply, a two-year period. This case is given in Figure 2.26. T h e vertical axis measures consumption in year 1, the horizontal axis, consumption in year 2. T h e diagonal line shows equal consumption in the two years. Let R, be receipts in the first year, R, receipts in the second, and r the rate of interest, and. assume that the individual to whom the figure applies can borrow or lend any sum at the interest rate r that he can repay or make available out of his receipts. T h e rnaxirnr~m amount he could then spend on consumption in year 1 if lie spent nothing in year 2 would be

R' is the mnximunr amount lie could borrow and repay wit11 because l+r his receipts in the secoi~d)ear. T I 7 is Iiis initial wenltll and defines tile intercept A on the vertical axis of the line of attainable tombinations. T h e maximum amount he could spend on consumption in \ear 2 if he \pent nothing in year 1 is

(4)

(1

+ r) IV

= R, (1

+ r) + R,.

T h e line AR thus is the line of attainable coin11in;ltions. Tlle rate of 51111stitution in the market is such that t!ie indi~'ibua1can add (1 r) dollars of consumption in year 2 for eacli clollar reduction in consumptiorl in year poi1;t P sl;o~v$a choicc in~ol.iixlghiglic-r ton1. As drawn, tlie eq~~i!ibl-ium sumption in year 2 than in year 1, but that i s o f course n 1.esu1t of the particular set of indifference curves aild tlle particula1- Interest rate. \\re can use this simple model to il1uitr;tte the concept of time preference lte consrlmp-the rate at which individuals are xvilling to s r ~ l ~ s t i t ~future tion for present consumption. T'Iie ].ate of time preference is t h ~ i sthe slope of the indifference curve and hence varies from point to point in the

+

'

Theory of Demand

59

Consumption Ye

Cl

Year 2

diagram. At a point co~lespondinpto high con~umptionin )ear 1, low consumption in year 2, the iridi\idual piefers additional future consumpt ~ o nto present consumption, i.e , he -ivoultl be willing to g i ~ ue p Inole than S1 of curient conswnption to add $ 1 to future conYumption. Con.irersely, at a point toriesponding to lligh future concilinption, low present consumption, the individual prefers ;~dditionalcuirent consumption to future consumption, i e , it mould take more than $1 of future tonsumption to coinpensate him for g i ~ i n gup $1 of current consumption. T h e late of time preference is tllelefore a variable, depending on the lexels of present and future tonsuml,tioil. 4t point P, the inte of tiine preference is equal to ndjusts his the market rate of ruhstitution (1 + r) I~ecausethe ii~tli~icliial time pattern of consumption to biirlg ,111out t l ~ equalit\. t I t is cornlnon to say that ~ndiliduals"untlcieqt~rnatethe future" or haxe a "prefe~encefor tlie piesent o\ei the future" 01 "distount the future." to i u c l ~expressions is to define them in teims One wa) to assiqn a m e , ~ n i n g of the rate of time plefeleiite on the diagon'il line in Figure 2 26 Ilong tllii line, futrile consr~nlptionis equal to plesent consumption I t seems ieason~lbleto say that an i r ~ d i \ i d ~ iis a lneutl 'rl betveer1 piesent and futuie if the slope of the indiffe~enceculres £01 points on this line is unit\, or Inole genelnlly if tlie indiffeience cui-\es nre s\llrrnetlical nlmut this line An iildiridual undeiestimates the futule i f the intlifference curies fol s poiiltr on this criiTe 'ile flatter than the - 45' lines and o ~ e ~ e s t i m a t ethe fntule if they ale steepel Mole genelall\, u e c,rn ,a\ lie untlerestimates tile f u t ~ u eif tlie indiffelence cur\es ,lie as\rnnletllc,il a l ~ o u tthe diagonal line in S I ~ L I I a w,ij t11,it a point to the left of the tliayonnl is on a lliglle~ Indifference culre than its 11111101 image to tlie i ~ g l l of t the d i a g o n ~ ~ l .

T o return to the determinants of consrtn~ptio~l antl saving, we are back in a iarnilinr situatioil. It appears that the pattern of corisulnl,tioii tleperlds on three F ariahles: R,, R,, I , yet it is t leal tiom Figure 2 26 tli,it oril) two R2 and r, namely wealth and the variables are important: W = R, 1+r' interest rate:

+

C = f(r, W). If Tve interpret R, and R1as measuied incomes in the tu70veais, consumption in each year depends not on income but on wealth (or "peimnnent iricome"). O n the other hand, if we define salings as the difieience between saxings does tlepend on income, measured income and consum~~tion, because

I n this model, there are two motives for saving: to "straighten out the income stream," that is, to make consumption steadiei- over time than receipts-this motive causes R, to enter into equation fi; and to earn a return on savings, this motive causes r to enter into equation 5. T I T in eqll;ttion 5 can be regarded as playing a dual role as a mezisure both of nvailal~leopportunities and of the consumption service of a reserve against emergencies. A special case of equation 5 arises if tile inclifference curves in Figure 2.26 are similar in the 5ense that all indifference curves have the same slope along any ray from the origin. Equation 5 then reduces to

or, to include other factors that might affect consumption not included in our simple representation:

where u stands for these other factors. I n this special case, we coultl define the consumer's numerical rate of time preference 11). the common slope along the diagonal. If he has neutral time prefel-ence in this sense, the11 for an)- positive rate of interest, future consumption will exceed present consumption. If he discounts the future, t l ~ e nfor some positive rates oft interest current coilsumption will exceed future consunlptiori. Tlle simple time period motlel can also be usetl to illustrate the effect of a difference between the rate of interest at ~ i h i c the l ~ ir~tli\itlu;tlcar1 11orrow and the rate at which he can lend. This difference may arise simply from the costs of financial interinetliatioi~between bori-elvers antl lerlders or from the difference between 1111nan ant1 nonhuman capital that nlzikes human capital generally less satisfactory as collateral for n loan. Let r,, be the rate of interest at which he call borrow and r,, at rvhicll lie can lcntl, with r, > r,. Then the budget line will have a bend as ~ I IFigure 2.27 at

T h e o r y of Demand

61

the point coirespondillg to ieceipts (R,, Itl) in the two )ears. There is then rio ~~n,iinl~iguolti measule of ~realtli,nrid the fin'll outcome ma) tleperld on the initial j~o\ition.tlepeiitling on ~tllcreit is arid tlie sll,ipe of the indifference curies.

C1 = C2

Geriernliring this analysis to an indefinite time period is easy to do formally, hart1 to do irl two-tlirnensional graplir. Tlle fori~lalgeneralization is that the ecoilorllic agent is regarded as Ila\ring a utility function that is a fuilctiorl of the ~vllolefuture pattern of consumption:

~rliereC(t) lepre5cntc tllc flov of con5ulnptiori , ~ ttirne t and t extends fro111 tlie tlille peiiotl in questlor1 to the irltlefirlite futule, saa t,, to w . He also is r egaltled a5 11'11 iiig ~n oppoi tunit) set

tll'tt stinlm,iii~estlie dltc~ri,iti\e time patteins of cons~iniptionthat are ,~\,lilnl,leto him. He is then ~ e g a ~ d easdmaxinli7irig the u t i l i t ~funttiorl in eqiiation 9 sul~jectto the oppoi tunita 5et of equation 10 This generali~ationi i pelfec t l ~genei'11 nncl peifectl\ ernpt\ T o g i r~ it content, i t i s rircess,ri\ to speci,\li/e eql1,Ltlons 0 m t l 10 For cx,imple, equation 9 can be speciali7ed b) supposing that there exists some illtein,~llate

of discount, sa) p, such that a particular form of equation 9 can be written

i n ~ z ~ h i tcase, l l of course, any moi~otoilictiansformatiori of equation 11, say will also d o providetl F' (I!) > 0. E q ~ ~ a t i o10n can be specialized by s~lpposing that there exists some market rate of irltereit 1- such that ;illy pattern of consumptiorl is available for w11icIi (13)

1r(t0)2

(L

~(t)e~"dt,

~ v h e r e12' is the similarly tliscouiltctl ~ a 1 1 l eof the intli\.itlual's anticipateti sti-e;~mof receipts in the future. T h e r e has I ~ e e nmllcll analysis, cspeci;~lly ill the literature on gl-o~vtliinotlels, usiilg sucll speci:tlizations b u t 110 such specialization as )et has reason to 1)c singled out as deserving p;~rticular confidence. O n e Tvay to present all indefinite tirne pcriotl in a t ~ ~ ~ o - t l i m e ~ l s i o r ~ : ~ l graph is to specialire the opportunit) set i n equation 10 I!, s~lpposingthat l t.rvo-clirnension:tl: a the only a1teril;ttives a~.ailaljleto tlic i n t l i v i t l ~ ~ aare rate of consumption of C, for oiic time unit, say a je;tl.; :I rate of coilrrlmption of C , Cor the intlefinite future thel.e;tfter. Foi- this to Ile ;it all reasonable, we must suppose tlie iiidividual to lrave a n illfinite life wit11 unchangt l ill fact is not. I t sinlply i5 ;i ~ v a yof ing tastes. 'This 111:1y seem : ~ l ~ s u rbut relxese~ltingthe obsen.et1 11llenorncnon that the family, not tlie intlividiiriit, ant1 that in tlecitling on currerlt conual, is the 11;i~iccorlst~nll~tion sumption versus futllre consum11tioi1, the person making tlie clccision takes into account the r~tilityt1i;it his tlescenclants ~ v i l lderive from consumption as ~ v e l l:IS hi5 own. T h e infinitely livetl a n d uncllariging indiT idual thrls represeriti the long-livetl family line. T l ~ o u g l lIligl~lyspecial, the two-dimensional re11resent:rtion brings out one importailt feature of the saving-spending 11roc.css conce;~led11) the two-period example. L e t R, he the rate of flow of receipts in the firbt year, R, the assumed steady rate of fiow inclefirlitel~thereafter, and r ail assumed coilstant rate or lend. T h e n his of interest over time at wlliclr the intlividual can l)orl-o~v initial wealth is

x\hei-e 1- elltel s illto the tlenomin,itoi of the fir~11 term rather than 1 + r as ill equation 3, betause R1 is lrcie ,r l ~ c ~ p c t n intome al sticanl rather tllail simpl) a one-period ~ c t e i p tT h i s i r ~ i t i , ~~vealtli l tlefines the point A, the oll is rnaxi~lluincorlsrui~lptionin tlie fiiit peiiod if c o n s t ~ ~ ~ l p t ithereafter 7~10T . h e m a x i m ~ ~torlsuml~tiorl m 'rfter the encl of tllc fii5t )en1 is R,, the est o n tlle filst )e,il's receipt if conp e i p e t ~ ~ ieceipt al t h e i e a t t e ~plus i n t e ~

Theory of Demand

+

63

sumption in the first year is zero, or rR,, so r W = rRl R, defines point B, and the line connecting them is the line of attainable combinations. Its 1 slope with respect to the C, axis is -, or the number of dollars of current r consumption that must be given up to add $1 per year to all future consumption; wit11 respect to the C, axis, the slope is r, or the number of dollars that can be added to future coilsumption 1,). giving u p $1 of current consumption. Figure 2.28 is drawn for an interest rate of .20 in order to make it possible to distirlguisll the different points. Pl is the equilibrium position, involving as the figure is drawn, lower consumption in the first year than indefiilitely in order to raise future consumption. Let us iiow move one year alleacl and look at the situation that the only alteriiatives are a rate of consumption again, again ass~~miiig of C, for one year ant1 of C, tllei-eaftcr (this is the r~iisatisfactoryelement of the analysis because, of course, Tve ~vouldexpect the individual at time 0 to clioose a ~ v l ~ ofuture le pattern of consumption and not proceed in this step-at-a-timefashion). Tlle indifference curves are the same, since we have tastes, but the opportunity assumed the individual to have ~~nclianging line is different l~ecausesaving in year 1 has added to his wealth. T h e new opportunit>- line (4'R') ~villgo through the point on the diagonal corresporldiilg to the al)sciss;l of PI. T h e new equilibrium is P,.

Tlle tlaslled line is the locus of sucll poirits of equililjrium i n successive the years :rntl tlefiiles the intli\.iclual's future coilsunlption patll. As (11-a~vn, tlaslied line cuts the tli;tgonal a t P::. At tllis poirtt tlle rate of time l~refcrence of the iiltlivitlual as clefincd earlier (for :t constant level of consumption) equals the rate at ~ v h i c hhe can sul~stitutecurrent for frttili-e income. T h i s is a point ~vllichif att:ii~ledT\-illbe ~ n a i n t a i n e d . sucll that P, i s the S~tpposewe had started the intlividual ~ v i t l l;I ~ve:~ltll equililjri~iin.T h e n the irttlivit1~1;tl~ \ - o ~Iiaxe ~ l d t1iss;i~edin the sense of reduciiig ~vealtllto a d d to current consumption. H e xvoulcl have follo~vetl the p a t h suggested by the zigzag line down the dashed line until agiiirl he arrix-ed a t P,. T h e ac1vant:ige of this c.onstructio11 is that it brings out tlle difference ) tllc equibetween the equilibrium stock of \ve;llth (tlesiretl \ . \ ~ a l t l iant1 librium rate of approac-11 to that stock of wealth. Tlie wcaltll corresponcling to point P:: is the eqtiilibrium stock c ~ fwealth. If tlie intli\-itlual does not have that stock of wealth, lle will move to~vartlit. T h e r e ~ v i l l11e a n e q u i l i b r i ~ i mrate at ~vhicliIle will ur;lnt to rno1.e t o ~ v a r dit that will depend 110th on 1 1 0 ~far ~ he is froin liis desired ~ v e a l t hand on \\.hat his current ~vealtllis. T h e consit1er;ttions cleterminiiig the tlesiretl stock of \ve;lltli are cliffereilt from tl-iose t l e t c ~ ~ m i n i nIio~v g fast IIC wants to move to\v;~rtl it, though this distiiictioii is Ijlui-red 117 tile t~vo-dinlensioilalrep~.escut:itionin Figure 2.28. 111 that figlti-e, in orcler for the]-e to Ije a n ecluililjriurri stock of ~vcaltli. it is ncc.ess;ir) that tlle slope of the inclifferente c ul-ves 1)ecomc flat tcr don: the diagonal line as r\.cnltli ii~c.rc;tses:tliat i,, th;it it require larger ant1 larger increments irl fnttire co~~sluniptioii to cornperts;lte for g i ~ i i l gu p S1 of current co~?suinption,or, :~lterr~;tti\ely, tliat the 111-eference for prescnt over future constlnlption inc.rcase xvitll xve;rltli. 'Tllis seeins i n t n i t i ~ e l ?perltl verse. I t seems ri1oi-e plausiljle tliat if :III)tliing tlle I-excrse ~ v u ~ ~occnr. If tlie intlifference curves xvcre similar i i ~the sense tllat tile) all l1:t~etile s:tnle slolx along any 1.2). fl.on1 the origiil. tllc c1:tslletl line ~voulcl,unlike tllc tl:lshetl line i11 Fig1u.e 2.28, ne\.el. cut the tli;tgonal. It ~voultlIje rather suc.11 a ray. I l l~elorvtlie tli;tgon;tl, it 'ivoultl i u l l ~ l )intlefini~e;iccrimtil:ttio~lo f ~vcnltll:iT a b o ~ e indefinite , tlec~unlil:~tioi~. But ill I~otllc;iscs there ~votrltl or dec~imlilation.Foi- inodei-n be a n e q u i l i l ~ r i u mrate oC ;tcc~imulatio~l prog~'es"i\e societies, t l ~ e r eis rlo irlcoilsisterlc.y between ol~jervablephe11oi11ei1;i :iiid ;I 1-epresent;ttion iriiplying iiitlefinite ;icc.uniiilation. Tllis is a vcr) incomplete treatment of a \.el.)- complex prci:jleii~ Its plii.I-'ose is to illustrate 11o.c~tlie app;tr;rtus we have tle\.eloped can illuiiiiilate such problems.

The "Welfare" Effects of Taxes

This tllaptei cliscusse~the relatixe effects on ~ ~ ~ e l tofa ian e excise tax and an income tax. I t demonstl,~test11~1t'ti1 alleged "proof" of the supeliorit) of the intome tax is no pioof at all, tl~oughi t has iepeatedly been cited as one It then outlines a "tolrect" an,il)iii of the pio1)lenl. T h e explicit content of the paper 15, ho\ve\ei, onl\ indilectl) related to sts majol ~ i n 1 u , l ~ i c l lis to sllov 1 ) ~example the tliflerence bctueen tmo x som i s this point of \ i e ~,t the pi esent appi o.~chesto economlt ~ ~ n ~ ~ l Fi 11ape1 1s an extentlet1 footnote ro .in d l ticle in the f o ~ nu1 r ~ of Polztzral Et o n o m ) , 111 TI liicll 1 torltiastetl t x o clcfiriitiolla of the demand culxethe usual one, ~vhitllsupposes nlo~le\incoille and illone\ prices of other colninodi ties the sarue ioi diffei cnt points 011 ~i single demaiitl cur\ e, and ' ~ 1 1nltel n n t ~ l e defin~tioil,n h i ~ h1 , ~ t t l i l ~ r ~to t e hlfietl d hlaisllall ,ri~cl~ ~ l ~ i c l l ~ L I P I ~ S C?Sr a l intome to be the s'line.' I ,~igueclthat the usual definition hClsdslseli out oi, ,111tlieflects, ;ln esserltiall~aiitl~inetical,irltl descriptixe n a~t i;~ e definlt~on,an analj tical d p p oac11 to ecoIloinlc r ~ ~ ~ atliel la l~t e~~ T h i \ chal~tel-is r.cpriiitetl fro111mv Ersnyc ilr l'ositiue Economict (l'nirersity of Chicago Pi-c\\, IDi;), p11. 100-1 ,?, 1;). pc?-niiwio~iof t h c pl~!~li\llcr; copyright 1953 by tlie L'ni\ersity of Cllicago. 1-he figur(.\ h a ~ e11ee1i rcnuml~erctlant1 the foot~iotesdiffcrentlv designated to conform to the re\t of rlic book. Thiu chapter is \ \ l i t t e n in the spirit of the "new" uelfare economics, I ) e c a ~ ~ stlic e technical pl-oblclli it dcals rvith has been considered primarily it1 those tcr111sand despitc srrious d o u l ~ t ss h o u t the acceptability a n d validity of this approach to not-mativc ccononiics. T h c xaluc of the general approach is a separate and I ~ r o a d e rissue, not co~lsidcredhere, except for tlie parenthetical comtiicnt in note 4. 1. Miltor1 F r i e d ~ n a n ,"'The Alarsliallian Demarlcl Curve," Jozirnal of Political Econo m y , 57 (1949): 463-95.

and problem-solving approacll; and that the usual definition is in consequence less useful for most purposes. Tlle quantitative difference between the two demand curves is small if the percentage of income spent on the comn~odityirl question is small, as it generally is in ~ictualapplications, and approaclles zero as that percentage approaclles zero. Nonetheless, the difference in concept is highly important precisely because it does reflect a fundamental differerice in approach. T h e following discussion makes n o explicit use of a deinantl curve. Yet it will be seen that the widely used analysis of the welfare effects of income and excise taxes, wllich it shows to he erroneous, is cut from the same clot11 as the usual definition of the demancl curve-hot11 reflect the arithmetical approach to economic analysis. Of course, no ;~pproacllmakes error inevitable. An analyst may xvirl tlirougll to correct results despite deficiencies in his approach and tools. Yet the fact tliat able ;lntl sophisticated analysts have bee11 ~nisletlaffords arnple e~.itlerlcethat the defect is not unimportant.

T h e A l l e g ~ d"P?oof" of the Slrpr?107 i i y of o n Inconlp T a x Figuie 3.1 surnrnari~es'111 ansiu of the same probletn hy Ilarold Hotelling i n " T h e General Welfare in Rclatiorr to Plohlems of 'Taxation and of Railrvay ant1 I'tility Rates." Econo17ietrica, 6 I jttly. 3038): 24S-69, ehp. 249-51. But this is a serious c,rror; s i ~ ~ cHotelli~lg e avoids t h e Pallac\ that ]liar.; the anal\sc\ listctl ill tile prececling paragraph. .In intercha~lgebetween IIotelling ant1 Ragtlar Fi.irch on Hotelling's article, I.:coitornetricn, 7 (April, 1939): 45-60. tleals rathcr o1)liq~relywith tile p o i t ~ t\\-it11rvlliclr the PI-eserlt note is concerned. .kt hottorn, the rnajor difference hct\\.eeil F1.isch ant1 Iiotclliug is that Frisch interprets Hotellirrg'. proof a < identical rvith that gi\cn I,\ [ouepl~,altl1ougI1, of cotu-se, Joseph's p ~ o o fis 11ot iefcrrctl to ancl had not appcarcd i r ~p1-int ~ r h c nFri\c.h \$late. Fricch fails to see the force of IIotclling's emphasis o n tile essetitial point of difference, namely, that Hotelling taker account of conditiot~sof co\t of prodtrction. T h e "11roof" is critically rxami~letlant1 cc,ii.cctlv criticized by Ea1.l R. Rolph a n d C;eol.ge F. Bleak, in " T h e TVe1far.e ,Aipects of Excise 1-axes," Jolcl-~znlof Political Ecol7. analysis har much in conltnon with that of the o~tt?,Y i il:el,ruar\, 1949): 4 ~ 5 5 'I'heir preient chapter: ther point ol.lr rsscntially the iame detects ill thc "proof" ant1 gi\e an essentially correct a ~ l a l ~ sof i e the plobletn. .I col-rcct a~lniysisof lie problem is also give;^ hy I. hf. D. Little, A C~itiqzceof It'elfa~e Ecotiorr~icr (Oxfortl, 1950), pp. 157-79. 111 art article, "Direct versus Indirect Taxes," E r o ~ ~ o r t ~l oi zc i r ~ ~ n l50 , iScpteml~er, 19.51): .,I 1-84, rvllich came to my attention only aftei the prc.;ellt chapter \\.a\ in the llail(is of the printer, Little also poitlic o u t the defects i l l tllc usltal anal!uis. 1-he chief difference betx\.een the preierlt chapter ant1 the relexallt pi11ts of the papc1.s 1))- Kolph a n d Break a n d by I.ittle i\ that Lhc prcscnt cliaptel. i c p ~ i ~ n a r iconcer~iecl l\ rrith the methotlological issue involred in the analysis; the others xvitii the subbtantive icsr~e. .#

v--

;?-

68

PRICE THEORY

Suppose, now, that instead of the excise tax, an income tax hat1 been ime t corposed to yield the same revenue ("Irlconle T a x A"). T h e l ~ l ~ t l g line responding to this income tax is parallel to AK, since prices are assumed to be unaffected. hlo~.eover,it must go tlirougii P, if the re\-enue from tlie income tax is to be equal to the revenue froin tlle excise tax: under the excise tax, tlle inclividual spends his xvllole money incoruc, ~vlliclli \ t;rken to be the same wllichever tax is imposetl, on the Ijundle of goocls irltlicatetl 11). P,; this expenditure equals the tax payment plus tlie cost of P, at pretax prices. In consequence, if he pays the same amount in taxes under an income tax, lle will be able to buy the bundle indicated 11y P, a t the pretax prices with the rest of llis income. T h e budget line under the income tax is therefore DE. But, with this budgec line, tlle inctiviclual will not in fact bu) the bundle iildicatecl 11);P,; he \itu;tl patterns of thought engentlered 1))- tlie usual approacll to demarld curl-er. Consitler, f o ~ example, . tlie butlget lines XB ant1 XC in Figure 3.1. I t is obvious tlirectly, a n d ~vitlloutthe use of i~~tliffel-e~lce curves, that the alternatives n\ailahle to tlie consumer ~vllerithe I~utlgetline i5 ;\C ;n-e clearly inferior to those available TI-lienthe I~utlgetline is .4B. T\'llerl i t is .4R, lie can, if he xvislles, 1la1.c an)- of tlie altel-natir-cs ;r~~;ril;tl)le wlieii i t is AC p1u.s all the 1111ndlesi n the tria~igle.\CB. C;enel-aliziltion of tile an:~lysisfor a n isolated intli~.itlualto tlie community ;ts a ~ v l ~ o tliel-efore le supposes tliat the mcl-e i m ~ ~ o s i t i oofn the excise tax retluces tlie r;tngc o f :~lterilativcsopen to every c.onsuinei- in a way that is c ~ ~ l c u l ; ~ 11)b l esinlplc aritllrnetic. H o ~ vcan this be? Tlle imposition of the excise tax pel- se tloes not cliange ; ~ n yof the technical 1-oduction 11ossil)ilities; i t tloes not 11y itself lesreli the pl-1ysic;rl resoul-cei ar-ailrll~leto the coillmlmity. It ma); retluce tlie quantity of i-esources ;\vailaljle to p r o t l ~ ~ cXe ant1 1' if the 111.oceetl5are usetl to p r o t l ~ ~ c c goocls ~ ~ n t l estate i - clirection ~v11ic.11formerly were not prod~lced(sxy gootls Z).Rtrt, i n that c;lse, Figure 3.1 is not at all adequ;\te, since ail additional axis ~voultlbe lieetletl to represent goods Z. N o r e i ~ n l ~ o r t a l lthe t , reduction in tlie altel-n;rtives open to tlie corisunler ~voultlthen tlepend on pllysical ;rntl teclinical po\sihilities, the kinds o f resources needed for the goods protlncetl 1)). tlic state, a n d similar factors; tlie retl~lctioncannot IIe computed 1)). simple aritlimetic. fn-om the knowletlge s u n ~ m a r i ~ eind Figure 3.1. Tlie abol-e analysis says notliing abo11t the destination of the proceeds of the excise tax: it ~voultl11ot he c!l;tngetl if the proceedi were iinpou~lcledor used to give a per-unit sul~sidyon Y 01-Lni inconle 5~111sidyto consumers. But in an)- of tliesc cases the tax ~ \ - o ~ r lnot t l Iiave I-ctluced the range of altcrn;rtives tecllnic;~lly:~v;lilal~lc. IS prices xverc tcrriporaril!; rigid, tlle supply of rlloney fixed except for the cl~angcshi-ought about 11). t l ~ etas, ancl tlie procectls of the tax impountletl, u n c m p l o ~ m e n tinight of coun-se occur in the shol-t r u n (tllougll there is tllcn consideral)le ;ulnl~iguit)-in the as,~irnptionthat X ancl Y are the only gootlr i n the world.) 7'11is ~ \ . o i ~ lnot, tl Iio~vever,I)c a stable positioil; 111-ices woulcl tend to fall i.elative to money i~lc.orne,~vllich~voclldsliift the line C \. to the right. More import;rnt, if prices tlid not fall relative to money inconie, the most significant implication oC either the excise tax 01- the i~lcoirletax ~vorlldbe tlie s;nne, namely, that either terlcletl to protluce unemployment nntl n reductio~lin the alternatives availal~leto cons~unlei-s.T h e difference het~veenP, a n d ;I point at the original prices equivalellt in utility t o P, (the point of tangency be-

tween a budget line parallel to AB and the indifference curve through P,) is small compared to the difference between either and PI; indeed, the ratio of the former difference to the latter difference approaches zero as the excise tax (or equivalent irlcome tax) approaches zero.5 I t follo~vsthat, if rigidity of prices and creation of unemployment are considered the major consequences, the conclusion would have to be that the income tax and excise tax have essentially identical effects or1 "~velfare"and that any difference between their effects is of the "second order of smalls." T h e analysis cannot be saved by this route. It is clearly irltenclecl to be a "long-run" analysis-comparative "statics," not dynamics-as is amply demonstrated by both the corlsiderations just cited antl the assumed complete shifting of the excise tax. Ll'e can therefore abstract from any shortr u n price rigidities and suppose complete adaptation to the new circumstances. But then it is clear that Figure 3.1 alone tells nothing about the final effects of either tile income tax or the excise tax. For example, suppose the excise tax is useti to gixe a per-unit subsidy on Y. T h e slope of the new budget line would tile11 be known (and might be that shown by AC if tlie excise tax and subsid)- Lvere adjusted appropriate1)-), but its position ~vouldnot be; for its position wolrld Ije tleterrilirled riot alone b y tlie tastes of consumers ant1 by arithmetic calculatiorl but ;rlso 1))' tile technical possibilities open to tlie community.

In 01tlel to bi ing tlle techriit '11 posslbili ties into the p~ctlirc,let 11s suppoje thdt TVC ale de~lli1igwit11 ,\ tommunit) of m,tilr itlelltit nl lndir idu,~ls -ide~ltical in taitei 'tnd piefelentes and ,~lsoiri kind .lntl qu,i~itit\of lesoul t es ov net1 11.1 e'lch intlir idual. 111 this t onnn11nit1, e\ el J incli~iclu'il tl the same I)tindle of gootls, so ~ \ e \\ill tr'lr e tile sanic iuconle c i ~ ~consunle car1 leplesent the positiori o f the commrulit\ br the posit~orlof ail\ oire iudi~itlual,ai in Figuic 3 2 Cr~renthe lesolu ces n\ ailable to tllc (0111munit), tllele nil1 he sonle set of tombillations of X .ind T1 tltat ~t i~ tetlln il~c~rl!)possible to ploclutc Thew can be iepicseritcd In ,I ~ ~ l o t l u t t i oilldifTeicnte clur e Sirice i l l 0x11 Ilr pothetic,rl conlrnunitr ehelr ~iltliridu'rl tz ill co~liuinean ,iliquot sll,ri e of each c o n ~ m o d i,t ntt ~ cLrndi\ ide the cooldinates ot this piocluctior~cuire I,\ tile i ~ u n ~ bofc i~n t h ~itlu,~lsand lot the ies~iltoil ~ i l i )one i ~ ~ t l i \ i d u a li~idiflelente 's ni,lp G H 011 F i q ~ u e3 2 is sutli a pi otluc tion possil~ilitj( urr e I t sllon 5 tlic 'iltct n.i ti1 e combinations 5 , Tlie tliffeience I)et\\ccrl PI and P.! col.sesponds to tlic "inco~necffert" as definetl 137; Slrrtsky: bcr.i\.ce~lP, an11 the poirlt at tllc original prices on the qame indifference cllrxc as to the "inc.ome effrct" :is definetl I,\ Hick\. .As \loink Ilas shown, tlie tlifference 1,ct\\ecn the t \ \ o incol~ieeffects nppi-oaches 7eso 1.clati~eto tile i ~ : c o t ~effect ~ e itself as the price cllange appi-oaclici zero. See Jacob .T. LIosak, "On the Tntcrprctatioi~ of the l:ui~tla~:irntalF.clnatioil of Value Tlleol)," in Oscar 1 nngc, I~sancis lfclntvre, antl ~I~lieodorr S. Yr~temaieds.), Slirriirs ill J l o l i i ~ ~ ~ i c ~It-irtor i~i lo ~ ~ iart0 i r ~ E r o ~ i o ~ ~ w l r(Chiics a g o : L ~ l i ~ c v s iof t y Cllicrtgo Piess, 191'1),p p G9-74.

The "Welfare" Effects of T a x e s

71

of X and Y that are tecllnically available to each individual, given that every intlividual ends up wit11 the same combination. I t should be empllasizetl that Figure 3.2 is for an individ11;11ant1 therefore does not involve iriterpersonal comparisons; we are interested here in an "allocative," not a "distributive," problem and can a11str;ict from the distributive problem b y dealing wit11 a society cornposed oT idelltical indil-iduals. If the society were initially at a position of full competitive e q ~ ~ i l i b r i ~ ~ i n , each individual ~vouldbe at P,. At tllis point, tlie rate of substit~ltionin cons~~inption (the slope of the consumption indifference curve) is equal to the rate of substitution in purchase 011 t l ~ ema]-ket (the price ratio sllown by the slope of the budget line), ~vliich,in turn, is equal to the rate of substitution in production (the slope of the protlut.tion indifferente curve). Technical possibilities are being fully exploited, as slio~vnb y the fact that PI is on the frontier of the alternati~estecliriic.ally capal~leof being producetl (these obi-iously include not only those on GP,H but also those I~etween the production indifference curve and tlie origin). How can xve represent a proportional income tax on this diagram? If the proceeds are impounded or retm-ned to intlividuals iri the form of a per capita subsidy, the diagram ol~viouslyremains completely ~~nchangetl. For \ I N 11 ;rn i~lcometax 2nd SU?IS~C!! do not nlter the relativr I,!-ices of X a ~ ? tU, l the consumption indifference curves, or the protluction possibilities. They are a purely nominal matter on the present level of analysis. If the proceetls of the income tax are spent 117 the state to protluce, 5;iy, Z, ~ c i t hrcsources formerly used to p1-ocluce X or Y, the 111-oduction possi1)ilities are clearly cllangetl. Tllere will n o ~ v1)e n neu7 protluctiori irltlifference curve, sho~vingthe alternative corn1)inations of X ant1 \- capable of being produced, given the production of a specified amount of Z. But the change in

the prodl~ctionindifference curve clcpentls only o n the amount of Z produced, not o n how the funcls are raised. If IVC sup~)osethis amount of Z to be given a n d fixed, tlre new production indiffercric.e curve \\.ill IIC the same wlletller a n iiicome tax o r a n excise tax is inlposetl; hence, in investigating any difference bet~veena n income tax and an exciie tax, we can, without loss of generalit). suppose GP,H to be the protluction i~rtlifference curve after tlle subtraction of resources to protluce Z. Figure 3.2 can tlierefore represent the situation I1otl1 before a n d after a proportion:~lincome tax for purposes of comparing srlcll a tax ~t-it11a n excise tax. TVliat now of a n excise tax? O n e co~lditiorlis ol)viot~s.T h e position of ecluilibrium must be on the production intlifference crn.vc GH. -Any position above the production indifference curve is tecl1nic;rlly iinpoisiblc with tlie available reso11rtes; an) position below it does riot involve full use of available resources a n d is therefore ~ m s t a b l eUeyont! . this, the essential feature of a n excise tax for o u r purposes is tliat it 1e;lds to a divergence l ~ e tween two prices-tlie price p ; ~ i dby tlie consumel- ant1 the price received b) the 1jro(lucer-and, hence, 11et~vcentwo price ratios that were formerly the same-the price ratio relevant to the consumer : ~ n dthe price ratio rele\,ant to the p r o t l ~ ~ t e iT- h. e terins on ~vl1ic.hthe consrlrller can sul)stitute one cornmotlity for tlie other i n pttrcllase o n the market, ~ v h i l ekeepi11g total expenditures the ; % m e niust , be ca1cul;ttet~ from ])i,ices inclusive of tax; the terms on ~vliiclitlic producer can s~r1)stitrrteo l ~ ecoinniodity for the other in sale on the market, .ivliile keeping total receipts the same, must I)e c.~rlculatctlI'roiii the prices exclrl,i~-eof tax. F:qirilil)~.irrmfor c.orlsunlers requires t l ~ tlre t I-ate at ~ s l i i c lcorrsr1met.s ~ c;ln s u l ~ i t i t u t eill purch:~se he c q u ; ~ lto the rate at ~ v l ~ i cthe\ li are \villiilg to strl~\titirtein c o ~ i i u l n l ~ t i o n : iildifth;lt is, that the corlsurllei. buclget line be tangeilt to ;L cons~~nlptioir fererlce curve. Equililjri~inlfor pi-otlucers reqt~ircstllat the rate at \\.l~icll producers can sulxtitute i n a l e he equal to tlie rate ;it ~vliiclithey can s u b stitute in production: that is, tllat a const;rnt-I-ecei1,ts line 1)e tailgent to the pi-oduction indifference cllr\-e. X position o l e q l ~ i l i l ~ r i satisfying ~~m these conditions is given 11). P,, in Figure 3.3. 'I'l~eline 1.1 is the I~utlgetl i ~ i e as i t apjjears to the consumel-; the lirrc K L , the const;~rlt-receiptsline as it appears to protlrlce1.5. T h e t ~ v otlivcrge becar~seof Excise T a x A on X, ~ ~ l l i cI lTi ~ ; I1)e ~ 1.egartlet1 :IS cleterrni~iir~g tlie angle l ~ e t ~ ~ the e e ntwo lines ;i11(1 ~vllichnlearls tlxtt the extra amount of X consumers c;ln purchase 11). giving u p one unit of Y is less t l l a ~ itlre extra ;rmolrnt of X pro(111cersneet! to sell to 1-ecoup the loss from sellirig one fewer uriits or \' _-It P,:, K L is tarlgellt to the ~ x o d u c t i o nindifferenc,e c~u-1-e;irld IJ to a const~nlptiorlindiffererrce curve. T h e ratio of the price of Y to the price of X xvhen the excise tax is in effect (at P,,) cannot, as is assunietl i n drawirig Figure 3.1, be c;rlculated simply from the initial price ratio ; ~ P, t a n d the rate of tlie tax. I t depends also o n production consitlel-ntions. T h e less concave the ~ ~ r o t l u c t i opossin bility curve, tile larger the fi-action of the tax that will 1,e slliftetl to t l ~ e

T h e "Welfare" E f e c t s of T a x e s

73

consumer and the smaller the iraction that will be shifted to the producer, and converselj-. Tlle ~viloleof the tax ~villhe shiftetl to the consumer, in the sense that the relative price of the two co~nmoditiesexclusive of tax will be the same at P, as at P,, only if the production possibility curve is identical ~ v i t hAB. Given the shapes of the cur\-es as i11 Figure 3.3, P, is rlecessarily inferior to PI, in the sense that the intlividual is on a 1o1,ver indifference curve. Given t h a ~the initial position is one of fttll competitive equilibrium ~ v i t h no taxes or subsidies, i.e., that i t is PI, Excise T a x iZ is inferior to Income T a x A. Suppose, Ilo~vever,that the initial position had been P, illstead of PI, not l~ecauseof go\ernrrlelital taxes or sul~sitliesljut 1)ecause of some other tlc~.iationfrom fully conlpetitive conditions, say because of monopolistic conditio~lsin the production of X wllic11 protlnce tlic same position of cqui1il)i-ium as Excise T a x L imposed l urltler fully competitive contlitions. Let an excise tax now 11e impoietl or1 conlmodity Y of the same percentage say l, 50 percent (call this Excise T a x B), arltl let us cornas Excise T a x L pare this wit11 an irlconle tax (Income T a x K) yielding the same revenue to the government. '1he analysis surnrnari~eclin the disct~ssionof the ;~lleged"proof" could Ije repented for this excise tax and income tax ant1 it ~vouldyield the same conclr~sion-that tlle income tax is preferable to the excise tax, since nothing is said in that analysis aljorlt the nature of the initial position, except possibly that it be ;I positioil in ~vliicllthere are no differential excise taxes or subsitlies.fj 6. This clualification is nccc\san if tlic two t a x ? compared are to h a ~ enot only the same dil.cct tax jieltl but also to arlrl the same amount to the total tax yield.

74

PRICE THEORY

Yet Figure 3.3 shows that this conclusion is wrong. Excise T a x B precisel) offsets the effect of the assumed monopolj in the production of X; it eliminates the di~ergencep ~ o d u c e dby that moriopoly between the price rdtio relevant to consumers (the ratio of market prices inclusive of taxes) and that ]elex ant to producers (the ratio of marginal revenues exclusi~eof taxes). T h e two ratios coincide and, in consequence, P, is the equilib~ium position with Excise T a x B imposed 011 an initial porition P, On the other hand, the imposition of Income T a x R leaves the dixerqence b e t ~ t e e nthe two ratios unchanged and l e a ~ e sP, the e q u i l i b ~ i u mposition. Hence Excise T a x R is preferable to Income T a x R, given that both are imposed when the initial position is P,.

At tl1i5point the reader ma\ ell 11e temptecl to regard the allegetl proof as rehabilitated, to say that "of course" its xali(lit~3depends on the nssump tion that the initial pos~tionis one of full cornpet~tileequililxium and tliat, while the users of the "ploof" h a ~ e11een careless in not statin? this assumption explicitl~,the\ ha\ e doubtless re( ornizetl it.; iiecessit~ A reexamination of the "ploof" \vill, hoxveler, shoa that no "asstu~l~~,)tion" about the nature of the initial position ~villrender i t a ~ a l i c lploof of tlie lelelant economic proposition T h e conclusion to wllic11 ~t is snit1 to lead may be colrect ~vheilthe iilitial position i s a position of full competiti~c equilibrium; but the 'iryument cloes not demonitrate that it iq correct 01 ~ t h vit is cort ec t T h e alleged s\lloyism, "Socl 'ites is .I man. Soc~ates is X , therefol e a11 men are X," happens to lead to a co11ect "concl~lsion"\t hen X stantls for " m o ~tal," tl~ouqhnot when X stancl to1 "C,leel, h'onetheless, the ,issumption tliat X itantls for "mol tal" w111 not lerldel ~t a lalid svllogism T h e pa~,illelis exact. thc cillcyed ploof tllat an Income tau i s superior to an excise ta\ is not a proof nt all; no c l c p in the nlleyetl p ~ o o f depends f o ~its x,ilidit\ on the charactel of the initial poi~tion;hencc. no n coilxert it into ,I T .rlid p~oof, "arsumption" 'tbout the initial ~ ~ o i i t i ocan though the final statement in tlie "p~oof"ma\ be collect for some conditions and not for 0 t h s Tlle "correct" analjsir shows tllat no reneral st'iten~entt a n 1,e matle about the ~ e l a t i l eeffects on "~ielfare"of T\ hat 12-e l ~ a \ ebeen c'tlliny "in condicome taxes" and "excise taxes " F\elrtlling depends on the init1~11 tions under xvllicll t!lr taxek 71e imposed But e ~ e ntliis \taterncnt tloc nor "

-

7. Note the difference hetw-cen this case for thc cornmunitv and the case fox. art isolated i n r l i ~ i d u a l\\hetl the initial position ;~h-eaclyillvolves a spccial excise tax. In that case, though the anal\sis ic n o tlifferent, the nicar~ingant1 interpl.ctntiotl of the conclusion is, a$ noted in prc,cec!ini: footilotcs. Rut e l e n £01 the irltli\itlual, o t l ~ e rtlcviations from competiti\e conditions a t the initial position d o not affect the ~ a l i d i t yor meaning of any step in the proof.

The Utility Analysis of Uncertainty

As long as economists took serionsly tlie irituitive notioil of dinlinisliirlg marginal utility, it was impossible for tllern to rationalize oljservetl I~ehavior wit11 respect to clioices involving uncei-t;iirity 11y a siniple extension of the theory of utility maximization. T h i s can be seen imrnecliately fro111 the following exarnple. Consitlei- a g:rnll~lethat involves a 50 percent c1laric.e of ~vinnirlga n d a 50 percent cllance of losirig S 100.00. T h e ~natllematicalexpectation of t h i ~ganll~leis 7el.o. If tile mal.gin;~l~1tilit)-of rnoney is taken as diminishing, the moral expec.tation of this gnnll)le, i.e., the expectecl change in utility as a result of accepting this gainl)le, is less tlian Lero o r negative, since the gain in utility l~.onlan e x t r ; ~S100.00 is less than the loss i n utility from the loss of $100.00. .\cccptalic.e of tile gainljle implies a loss of utility; Ilerlce, Xlarsl~allancl others cor~clutlcdtllxt g a ~ n b l i n gis "i1.1-ational." Activities sucli as ganll)liiig were supposecl not to Ije espl;rinal~le o n tlie grouncls of niaximirntion of utilit),. If, Ilo~vevel.,Tve tlrop tlic ;rsumption of diminisl~ingmarginal utility, it tnrns out tli~ttwe can use the same Iiypothesis of utilit) rnaxinlization in the aii;tlysis of choices i i l ~ ~ o l v irlg uncertainty as i n the ana1)sis of other clloicex. Once uncertainty is introduced, tlie object of choice is n o longer a !IIUIdle of goocis of k n o ~ v ncon~pofitionbut a set of exclusive nlternatixes, e;rch witll-some specified probability. T\'e can regard a sum of money-or a n income-as representing each possiljility (since the o1)timum allocation of tile income aInong different goocts has a1re;ltly been covered by the theory of choice under conditions of certaint!.). O n e ol~jectof choice wortlcl then be a probabilitj- distril>ution of incoine; for example, a probabilit),

sufficiently indicate tlie limitations on the direct applicability of the results. Llihat I, in common wit11 the other writers 011 this problem, have called an income tax has little or no kinship with the taxes actually levied under that name. Tlle latter are fundamental excise taxes more or less broad in scope. Even a straight proportior~alirlcome tax on a broadly clefined tax base does not fall equally on a11 goods ant1 services protlucetl with available resoul-ces; inevitably it leaves untouclled goods and services not produced tllrougll the market: leisure, household activities, etc. It therefore makes the rate at ~vlliclltlle consumer can substitute tlleln for marketable goods and services different from the rate at ~vllichit is technically possible to substitute them. This effect is clearly greater if the income-tax base is more rlarro~vlydefined, an exemption is allo~vctl,or the rates are progressive. Tlle most that one can infer from the ;rnalysis is perhaps a presumption that, the hroader the scope of the tax and tlic more equal its incidence, the less likclv it is to falsifv rates of substitution. But even this is at best a ~xesumptionto be testetl in each case. Lrnfortl~nately,formal analysis can seldom if ever give easy ans~versto hard pro1)lems. Its role ir quite .tlifferent: to suggest the considerations relevant to an ;\iisxver a n d to provide a useful means of orgalli~ingthe analysis. T h e "correct" analysis is clearly ;rpplicable to marly prol~lemsother than the p;irticular one to ~vllicllit is here applietl. Forces otller tlla11 taxes may proclrtce clivergences l)ct\veen tlle rates of substittttiorl wllose equalit): is rlie esse~ltialcondition of all "optimlinl" in the sense implicit in the above cliscltssion. For exaniple, ;IS :!lre;rtly notecl, monopoly protluces such ;I divergence, and it is this tlivergence th:tt constitutes the fundamental ai-gument, on strictly allocative grounds, against mollopoly. Similarly, Marshall's argument for taxes on tlecrcasirlg-return industries and subsidies to inc1.easi11g-returnindustries, to the extent that it is valid, involveq a divergence bet~veenthe production incliffel-ence curve relevant to tlle prodrtccr and the procluction intlifferer~cccurve relevant to society and hence ;I clix-el-gence1,et~reenthe rate ;I( 11.11ic.ha 111-oducerjr~dgestllat he can substitute commodities in production ant1 tlle rate at ~rllicl1pl.oducers as a whole c;ln actually (lo so. 111fact, OLII- simple Figure 3.3 contains tlle essellce of rnucll of modern welfare ecorlomics. T o return to the initial theme, tlie appl-oacl~to economics underlying the us11;11demand curve is tlle a11proac11ur~clcrl!-illgtlle superficial analysis erribotliecl in Figure 3.1; tlle apl~roachundcl.lying tile alternative demantl curve along 11-llicli "real incorne" i q !i.eld con5tant is tile nppl-onch cmboclietf in Figures 3.2 and 3.3: one 1z.110 startetl wit11 this approach ~voultl Ile heavily insulated against analyses sltcll :ts that eml~odicclin Figure 3.1. T h e great defect of tlle approach u ~ l t l e r l ~ i ithe ~ g ustlal demand curve is that it emphasizes ;~~.itllrnetic. con~irle~.ntion\: the great virtue of the 2111~xoacli~tnderlyingthe itlternative clemarld c w \ e is that it ernl,llasi~eseconomic considerations.

T h e Ctilit) Analysir of Cncertainty

77

P, of r e c e i ~ i n ga n income I,, P1 o t leceiling a n income I,, P , of iccci.i'ing ,in income I,, etc., the stml of the pl o1)aljilities being unit\. hnotlicr object of choice I\ ould I)e a diffe~ent plol) tllilit) distl il,rition IZ'e can now take as o u r problem the -onst1 ut tion of theor) to r ationali/e choice among such objects.

Maximizing Expected Ufiliiy Let B stand for a generalized object of choice of this type, i t . , for a set o r "bundle" of alternative incomes a n d associatetl pi-ol)abilities. (If we want to contrast different sets, .cvc shall use subscripts; i.e., B, will stand for one set, R, fox another, ctc.). T\'e shall assume that the iiitlividual car1 rank t.llese objects of clloice ancl that these rankings olje)- the transitivity rer~uirement,so tll;it if he ranks B, a11ol.e K, a n d R, ahove B:,, he will rank B, above B:,. Let thc function G(B) descrilje this ranking, i.e., G(R) is a function tllat attaches a 11uml)er to eacli object o r Ij~mtlle(each B), a n d these rlumbers have tlie property that tlie irldil-idual will clioose a R ~ v i t l l a Iligher number i n preference to a B wit11 a lo.c\~el.number, i.e., the n u m bers give a ranking of all buntlles iri 01-der of his preference. In line with the langui~gew e d i n the t11eo1.y of clloices under colltlitiorls of certaint), G(K) (;in be tlescribed as gi~.ingtlie "utilit)" attacllecl to v;rrio~~s prol)al~ilitytliatributiol~sof income. Vp t o tllis point, the tl1col.y tlescriljed is allnoit perfectly geriernl and, accoi-clingly, almost perfectly empty. I t simpl) GI) 5 that indivic11i;rls ritnk ;iltei-natives and clioose among those ;rv:~il;il)leto them the one they rank tl a n d transitivity of higliest. Its only content is in the s ~ ~ p p o s econ5istency clloices. T h e function C;(R) ~ v cliare irltrotiucetl is simpl) n il~ortliandexcan lje s~ipposetlto have a conpression for the st;tcelilent tllat i~ltli~.itllials sistent and transitive ~.;lnkiqgof possil~leoljjecti; of clioicc. T\'c coultl, even ill prirlciple, tleterniinc ; i i l i~ltli~itlttal's G(B) 0111) 11) ol~servinghis choice :inlong :!I1 possiljlc ol)jects; if some object R Ilad Ilevel. been offered to Iiim, Ive coultl never ca1cul:tte its place in the ~.;rnkingfi-orn other choices. A special tlieory c.onsists i n specif)i~igcoinetl~irlga l ~ o u tthe form of G(B). O n e ~jarticulai.special tl~eol.)that we shall consider is as follo~vs: Let tlie object of choice B consist of a pro1)abilit)- P, of i n c o ~ n eI,, P, of income I, . . . , P,, of irlcoine I,. T h e special tlieory tlicn is that G(B) can be rvritten as

~vlzercF(1) is s i n ~ p l ysome function of I . Stated differently, this special theory c.onsists of the liypotl~esistliitt tllel-e existi a function F(1) ~vllicllhas the property that G(B) c;tlcul;ited ;is in equation 1 yields a correct ranking of

possible objects of choice. T o illt~stratethe meaning of the concept, suppose a pal ticular B ;rnd F as in Table 4.1. Tlle mathematical expectation of this bundle is 200, gi\e11 by ZPI. T h e G of this bundle is 18 3 / 4 given b! I P F(1). I t is important to emphasize the fact that the hvpotllesis G(B) = 2 P F(1) is a Tery special one. Fol example, consider the follo~vingthree bundles: B1, B,, and B,, as in Table 4.2. I n B,, the indi\ idual has an eLen cliance of

~vinniiigor losing S50.00. In B,, the individual has ;1i1even chance of winrlirlg or losing S1OO.OO. I n B,, the individual has a 25 percent chance of ~ v i n r ~ i nS1OO.OO, g a 25 percent cllance of ~vinniizg550.00, a 25 percent cllance of losing S50.00, and a 25 percent chance of losing $100.00. Suppose we k11o.i~that the incli~idualis indifferent with respect t o accepting B, or B,; i.e., G(B,) and G(B,) are identical. Under the special theory, this irnplies that G(B,) is equal to G(Bl) and G(B,), i.e., that tlle individual is inclifferent among B,, B,, and B,,. I n discussing 0111- special theory further, we may start wit11 the extreme case of clloices alnorlg certain incomes. I n this case, ;I bundle B consists of a single income, say I, with ;I probal~ilityof ;rtt;iining it of unity, say PI = 1, and the probability of attainirlg any other irlcome equal to Lero. I n this case, G(B) = PP, F(Ij) = F(1). This is the reason wllr. F(I) i~ generally caliec! the ''uti!itf' of certain i~lcolxei.T\'c illnll lin7;i- occ,isinil 1,rier r o raise some questions about this usage, b u t fol- the lnonlcrlt xzre ma) xccept it as a conr.enient manner of speaking. So long 21s we restrict oursel1-es to such choices, the most .ive could learn about F(1) ~vould11e the sign of its tlerivative, i.e., wlietller F increased 01- dccre;rsetl with 1. I11 consequence, as we saw in our earlier discllssion of certainty, if we lxid one F(l) that rationalired such clloices, any function of F wit11 ;I positive first derivati~re

The C7tility Analysis of Uncertainty

79

would d o so as well; i.e., if F(1) works, then any function f(F[I]) will d o as well provided f'> 0. Now let us introduce ciouble valued alternatives. Consider an individual who is confronted by a set of incomes (a bundle, B) consisting of two incomes (I, and I,) with probabilities P,, P, (P, + P, = 1). T h e expected income 7 = P,I, + P,I,. T h e utility of this expected income is equal to F(1). U, the expected utility, is equal to P,F(I,) + P,F(I,). If the curve relating the utility of income to income is concave from below, then the expected utility or 0 is less than the utility of the expected income or ~ ( 7 ) . Therefore, an individual offered 1 for certain would (if any special theory is correct) prefer this to a chance of obtaining I, or I,. If the curve, howis greater than ever, is convex from below, then the expected utility or the utility of the expected income F(f). Therefore, an individual would prefer a gamble of I, or I, in preference to a certainty of 7. This is shown diagrammatically in Figure 4.1.

Utility

I

'2

FI om choices such as we lla\e just been consideling, we shall sho.iv that if we accept the special l n ~ ~ o t h e sofi sG (B) = 2 PF(I), it is possible to derile an F(I) function that i 5 a l h i t l a l ~onlv with lespect to sc'ile nnd origin. Let 11s assume that if I = 0, then F(1) = 0; and if I = 1, then F(1) = 1. \Ire now Iin\e cllrriinnted indeterminai1c.i nit11 lespect to scale dncl origin. hTowwe slixll show h o ~ vwe mny dete1m:ne F(I) for I = 2 Assume the individu,ll is ofkelcd $1 00 for eel t'tin (call this bundle B,) 01 a gamble of PI that he \rill lecei\e riothiny: and 'I chance of P, = 1 - PI illat he mill r e c e i ~ e$2.00 (call t l ~ I)undle s B2) Let us find a P, sucli that tlic :ndl\idual is indifferent betlveeri these t n o t lloiccs. Suppo5e thnt this \ alue of PI tulnecl out to be 1/4. Since the indi~idu'tlis indifferent 1)ct~veenthe5e two bundles, G (R,) = G(U,'I. Since G = CPF(I), ~t folloxrs thnt F(1) = P,F(O) + P2F(2). Since we

80

17K1CE THEORY

llave assluned that F(0) = 0 and F (1) = 1, it fo1lou.s that 1 = 0

+ P2F(2).

1

From tlris it follo\vs that F(2) = --; or sillce P, = 3l.1, F(2) = 4/3. Iri a sinliP, lar fashion, the utility of all other incomes can IIC calculatctl. We have been able to derive F(2) uniquely because we Ilave made arbitrary assumptions concerning scale and origin. hlore generally, we sllould say that if any F(1) will rationalize choices, any function aF(1) + 11 will do likewise, provided that a > 0, whicll brings out the indeterminancy wit11 respect to scale and origin. TVe have just seen that we can derive an F (I), rtnique except for origin ant1 unit of measure, from knowledge of the clioices made by an intlividual among a limited set of bundles, each coritairling at most two possible incomes (in the example just given, the bundles B, and B, of that example plus other sets of two incomes, one of 1vliic11 is zero throtlgho1it). But once we know F(I), it is clear that we know llorv the individual would rank any coilceivable bundle, if the .special il~col-yi.s -oalirI, since rve can compute a G(R) for any B. It follo~vsthat tlie special theory has very real content, i t . , is capable of being refuted. T,\-e shall now try to draw a n F(I) function tllat wot~ldappear to be capable of accounting for most of the observed plienomeria. We ol)ser\.e that people do riot go around t1li.o~vingmoney away alld infer that people clioose rnore inco~liein preference to less. This implies that F'(1) > 0. I\'e know that people buy irtsurance even tliougll it is ;~ctuariallytunfair. This implies that F"(I) < 0 for so~ncincomes. O n the otlier hantl. T\-ekrio~vthat people, including those who I)try insurance, gamble. This would be illconsistent if the ganlt~leswere itler1tic;tl rvitli the risks tlley insure against. but tlley are not. Generally, the g;lnll)les they buy ni-e like lotteries. rvhiclr offer a small chance of a large prize. T o rationalire there we may tlrarv a curve as in Figure -1.2. I n this figui-e, Region X is the region of insurance T h e indil-idual here prefers to take a certain small loss ill llis income in preference to the small cllarlce of a large loss. This i \ because the utility of the expected income is greater than the expectecl utility. T h e existerice of regiol~B explains the pllenonienon of gambling. Reca~iseof its existence, even people in region ~1may j~referthe small cllance of a large gain to the large chance of a small loss. T h e utility of the expectecl income is less tllati the expected utility. Zone C is necessary to account for tlre famous St. Petersburg paradox, ~vllicllmanifests itself nlso ill tlie structure of prizes in lotteries. If it .isere not for the fact that the utilit) ciirve again I~ecomes concave at some point, people shotzld be xvilling to pay nn infinite amount of money to play the game iiirolved in the St. Petersh~u-gparac1ox.l Like1. T h e St. Petcrs11u1-g paradox I-efers to tlie follo~t-iiigIrypothc~icalgatlic of cliance .I (fail.) coin is ro,ictl ~epe;:tctllv until a tliffel.cnt side conies u p for t h c first tirni.. T h e pla)cr ~ c c e i ~ c21:s roul)le.: xv1ie1'e R is the length of the rut1 fi.e., the. ti~unl,el.of heatls that cotuc I I befo1.e ~ the first tail, 01. the tluml~erof tails that come up before the first

T h e Utility Analysis of Uncertainty

utility

81

I

Income FIGURE 4.2

wise, we ~houlclexpect lottelies to hale one big prize instead of several if the utilit) curie did not again becorne concaTe at some point. Pel l-rnps a 01 d shol~ldbe said nlxjut the relationship of all this to the problerrl of m e a s u ~ a l ~ utilit\ le If this Ilypothe5is is colrect, then we can tonstrtict an F (I) functioll, wllicll is onlv indeteiminate with respect to r . ileetl not regarcl F(1) as a utility function. Inscale ant1 oliqin. H o ~ v e ~ ewe tleetl, n e earlier defiiletl G(B) as the titilit) function. S o w it is obvious that, even under our special t l l c o ~ r ,if one G(B) will rationalize choices, any [unction of G(K) will do so p ~ o l i d e dit does not change the order of the ~ a n l i n q ;i.e., if jou h a l e one G(R) = f P -F(1), then an) other function H[G (K)] = H[zPF(I)] will clo so, p r eliding H' > 0. Oui special t l l e o ~ \[,in he stated most generally as follows: Theie exists a \et of funttioils aF(1) + 1) n i t h (1 p o s i t i ~ enncl b arbitrar), such that the Fet of f u ~ l t t i o n sH[G(B)] = I 1 (fP[aF(I) 111) with H' > 0 yields a correct 01 tlering of the indix i d t ~ i l ' s preference fox altelnatixe p~obabilit! distribu-

+

head). 'rile cluestion i u . llo~vmuch 1\o11ltl anyone pay for the privilege of playing the game? It is easy to see that the actual-in1 value of the game is infinity, since each possibility l~a an actuarial value of I , anti r1le1.eare an infinite nlunber of possibilities.

T h e cuppoued paiaclos ic t h a ~it is imp1ausil)le that anyone would be xvilling to pay a !el., large SIIIII, Ict alone an illtlefinite sum, f o r the pr-ivilege of playing the game. Bertlot~llicoined the tel.111 tt~o,nlrxpel-tntiotl for the value that would be attached to such a. game 1'7; contrast 'ivith its n~nthrrtznlicalexpectation.

tions of income, in the sense that if he is offered the choice between any two probability distributions (say B, and B,) he will choose B, in preference to B,, be indifferent between B, and B,, or choose B, in preference to B, ac.

>
e \veuld make i i posrible to gcr as fine ;r comparison probabilit) scale for the individilal a5 desired, ;ind accortling1)-, to determine the probability he assigns to a n y hypotlletical event to an)- desired degree of accuracy. T h e combined hypothesis that each indis-idrtal acts a5 if he assigned a personal probability and a utility value to any hypothetical event and

chose among alternatives available to him in sucll a way as to maximize expected utility is now a l~ypothesisthat in principle contains 110 m o b servable elements. T h e assertion that individuals act as if they assigned persolla1 proljabilities to all possible events is an hypothesis ahout behavior, not a description l or an assertion that an individual will give a of i ~ ~ d i v i d u apsychology meanirlgful answer to a question about the probability he assigns to an event, sucll as the continuation of parliamentary democracy in Britain. If the event in question does not much affect his life or, even if it does, does not affect the part of his behavior subject to his control, there is no reason he should devote any effort to making u p liis mind about such a question, and he will tloubtless give an offhand answer. 011 the other hand, if an important part of his behavior tlepends on whetller parliamentary democracy continues in Britain (in terms of our hypotlletical experiment, if the reward or loss triggered by that outcome is sizable), it will be worth his while to fonn a definite opinion. T h e personal probability npproacll bypasses much of the dispute in the literature about "objective" and "subjective" probabilities. One way the personal probability approach can be linked with that distinction is to classify those sets of probabilities as "01)jective" for wlxich personal probabilities of the -curve in Figure 5.l(d) is not comp!etely defined; if points to the left of it are attain-

Relationships Between Supply and Cost Curves

87

able, it is a "backward-bending" supply curve; if points above it are, it is a "forward-falling" supply curve. Tllere is some uncertainty as to how best to specify "given condition of other things it is generally appropriate to hold the same. supply," i.e., However, this problem has little bearing on the issues to be discussed here, so we shall follow what seems to be current practice and include in the "other things" requiring explicit mention at least (1) technical knowledge -"the state of the arts;" (2) the prices of commodities closely related to this commodity in production (e.g., tlle price of wool for the supply curve of mutton, the price of industrial structures for the supply curve of residential housing); and (3) the supply curves of factors of production to the specific group of suppliers considered. I t should be noted that the "specific group" for which a supply curve is constructed need not include all suppliers of the "specific commodity" for which it is constructed. For example, the "specific group" could be "producers of wheat in Iowa"; the commodity could be wheat in general, ~vhetherproduced in Iowa or elsewhere. As another example, the "specific group" could be an individual firm; the commodity, a product produced by many such firms which together comprise an industry. Note that i t a n 3 holds constant tlle supply curves of the factors of production to the specific group. Accordingly, its content may change as one proceeds from, say, a firm to an industry. T o the firm, for example, the supply ciirves of some factors may be corlsiderecl horizontal, so that item 3 is equivalent to lloldiilg their prices constant. T o the industry, the supply curves of these same factor5 may not be Ilorizontal, so item 3 is equivalent to permitting their prices to vary along the supply curve. Note also that this definition of a supply curve holds for both short-run ant1 long-r:in supply curyes. T h e difference between short-run and longrun curves is in the precise content of item 3, i.e., the assumed shapes of supply crirves of factors. T h e shorter ~ l l erun, the larger the number of f;ictors .rvllose supply curves will be taken as vertical or nearly so.

T h e Folnznl R~-eclkdournof the 0 1 ~ t p lof ~ fan Ind~isllyinto flre O~rtp~rf of Indznirl~lnlF ! ? r n ~ I n Figure 3.2, the curve SS represents the s~ipplycurve of all suppliers of commotlit) X for commodit;; X. I t is an "industry" slt-pply curve, showing the nlinimurn price r r t which e a c l ~quantity ~,~:or~ltl be supplied. T!?is curve is the one that is ortlinarily of interest in the analysis of concrete problems. Further investigatioll into the supply curves or cost ciirves of individual f i r i n is undertaken to learn something about wll)- the shape of SS is what it is. rather than bccallse of any special interest in the intlividual firm as such. T h e curve SS has direct empirical meaning. For given conditions with respect to items 1, 2, and 3, there will in fact exist some minimuln price at

which a particular quantity of X will 11c slipplietl pel- unit tirne. T h e quantity O Q ~villI3e supplied at a minirirunl price QP; tlie quantity OQ', at a nlininl~tlnp i c e Q'P'; ant1 so on. Of course, tlle pl-ecise ih;~peof SS will depend on the precise content of items 1 to 3, mtl, in p:~rticular,or1 the shape of tlie supply cnrl~esof factors of PI-od~ictionto the intlustry. Tliese factor supply curves will tent1 to tlepentl on the period of time allowed for adjustment, so short-ruri and long-run suppl!. curves can Ile considered as yielded by different specifications of item 3.

Price of X

Now suppose the deniaritl curve Jvere DD. ant1 market price PQ, output OQ. Tliis outptlt would in fact 11e supplietl 11) a nunll)er of differelit firms, and one could mark off on the line EP = 0&the amount sul,plird 13)-e:ic!l firm. For example, Eq, nligllt be supplied bj- fir111 1, q,q, by firrrl 2, q,q,, 11) firm 3, etc. If the deina~ldcurve rvere D'D' instead. of DD, the price ~vould be P'Q', the output OQ', ant1 one co~tltlsimilarly mark off on E'P' the aniourlt supplied b) each fil-111-E'q: by fir111 1, q,'q: by firm 2, qaqa by firni 3, etc. Suppose this were done for each price, arid the points for each firm connected, as has been done on Figure 5.1 for firms 1, 2 , ant1 3. S,S, then

Relationshifis Between Supply and Cost C u w e s

89

shows the contribution that firm I ~voulclmake to the total output at various prices, given that tlle entire iildustry expandetl along SS. I n general, however, it will not be a "supply curve of firm 1 £01. commodity X," as that term was defined previously. One reason is that as the industry expands, the prices of factors will change as required by the given supply curves to the industry. T o the individual firm, this will typically involve a shift in the supply curves of factors to it, and hence a change in the conditions of supply. Another reason is that as the industry expands, tecllnological conditions may change for the indixlidual firm, though not for the industry, again involving a change in the conditions of supply. S,S, might perhaps be called a quasi-supply ru?-ue of film 1. Similarly, the horizontal difference between S,S, and S,S, sllows the contribution of firm 2 to the industry's output at various prices. This construction implicitly allows for cllarlges in the number of firms at different prices for the product. At a price below that at which S,S, cuts the vertical axis, no output at all is supplied by firms 1, 2, or 3; these firms cvoulcl not "enter" the industry at such prices. At a higher price, firms 2 and 3 would "enter" the industry; at a still higher price-above that at which S,S, cuts the vertical axis-firm 1 woultl enter. T h e actual expansion in supply slio~vnby SS is in general a result of both expansion in the output of each firm separately and an increase in the number of firms. At eacll point on the supply curve of the industry, say point P, there is implicit some set of quantities of factors of production used in producing t y X. For example, let the factors of producthe corresponding q ~ ~ a n t i of tion be designated by A. B, C, etc. Then output OQ, offered for sale at price QP, is produced by using some quantities of A, R, C; say quantities a, b, c, etc. Output OQ' is similarly produced by using, say, a', b', c', etc. of s Given the supply curves of the factors of production to the ~ a r i o u factors. the industry, these quantities imply certain prices of the factors of production, say pa, p,, p,, etc., for- output OQ; pi, pb, pi, etc. for output OQ'. If the supply cui-ves of all factors were horizontai, these prices would be the same for all outputs; otherwise, the prices will differ for different outputs, so to each point on SS (and hence on S,S,, S,S,, etc.) there is implicitly attached a set of prices of the factors of production. Following AIarshall (see principle.^, p. 344), we could indicate the relation between the supply price of the pl-oduct and the quantities and prices of the factors 11y su1)dividing the ordinates of SS (like PQ) just as we subi ~: l d e dthe abscirzae (EP in Figure 5.2). Figure 5.3 ill~~strates this point. T o produce an output O Q under the given conditions, the quantity OA of .4 will be used. T h e number of units 0 4 Oh of OA per unit of product will he -. T h e n - p, is the price of the 0Q Q amount of L that l is nretl per nnit of 111-ocluct;t h i ~number is represented in Figlne 5.3 b) QP,. Similarl~,if OB is tlle quantit) of B nsed to produce

.

.

OB output 0 Q and p, the price per unit of B, then P P- - - p,; and so the '-OQ total supply price PQ can be subdivided into the supply prices of the factors of production used to produce OQ of X. Note that the scales for A, B, etc. at the bottom of Figure 5.3 are linked to the scale for X, and that equal horizontal distances on these scales in general will not refer to equal quantities. For example, suppose OQ is 4 / 3 of OQ'; it does not follow that OA is 4/ 3 of OA', or O B 4/ 3 of OB', since the combination of factors used to produce O Q need not be the same as that used to produce OQ .' If the supply of A is more elastic than the supply of B, it is likely that the amount of A used will increase by more than one-third and the amount of B by less than one-third, when the output of X is increased by one-third. Similarly, P,Q and Pi Q' will in general be prices for different sized units of A-they are prices for whatever amount of A is used per unit of product (of X), and for the reasons just cited, the amount of A per unit of product may be different a t 0 Q than at OQ .'

of X time I

I

I

I

iA'

IA

I

I

O1

I

0

I

B'

I 0

Quantity of A per unit t i m e Quantity of B per unit time

As we shall see later, if we are to explain the existence of marly firms and admit the possibility of economic determinants of the s i ~ eof firms, we sllall need to assume the existence of one or more factors specific to thc individual firm and not capable of being rented or hired by other firms. T\'e shall use the term entl-eprcneurial capacity to descril~ethe complex of such factors possessed by a firm. I t is implicit in the construction of Figure 5.3 that the price of such factors is whatever is necessary to make the sum of segments like QP,, PIP,, etc. exhaust QP. T h a t is, if "total cost" is take11 to makes "total cost per include the return to such factors, our constructio~~ unit of product" always equal to price.

Relationships Between Supply and Cost Curves

91

T h e Formal R e l a t i o n between t h e S u p p l y Curue of t h e Individual Firm and its C o n t r i b u t i o n t o the Industry's O u t p u t Let us now turn our attention from the industry to the individual firm but waive, for the time being, the ploblem of defining either the zndzvzdual film or its entlep?pneulznl cnpaclty. I n Figure 5.4, curve S,S,, reproduced fiom Figure 5.2, shows the amount of X that firm 1 would provide at various prices of X, gi\en the supplj curxes of the factors of production t o t h e zndustry and given that the industry expands along its supply curte. As we have seen, at each point on S,Sl there is implicit some set of prices of the factors of production, say pa, pi,, . . at point d ; p:, pb, . . . , at point d'.

Suppose the price of X were OE', so that the individual firm is at point d' and is producing O q l of X. Under the conditions for which S,S, is drawn, we know that if the price of X were OE, the individual firm would be at d instead of d'. T h e difference between d and d' can be vie~vedas a resultant of two kincls of forces: (1) the reaction of firm 1 to n higher price of X in light of technical and factor market conditions as the firm sees them when it is at d';and (2) the reaction of firnl 1 to the change in technical and factor market conditions as the firm sees then1 brought about by the reaction of all firms to the higher price of X. T o separate these t ~ v otypes of reactions, let us shift from the kind of quasi-supply curve given by SIS, to a supply curl-e of firm I for X. T h a t is, let us now suppose the contlitions on the factor markets to firm 1 to be given and to be t l ~ esame as a t t l ' on SIS,. For simplicity let us suppose that firm 1 has no monopsonistic power over any factors whose amount it

can a'tly, so that supply cturei of suth f'lctors ale l ~ o r i ~ o r l t aatl piices of p i , p,:, . . . , the prices that implicitlt colrespontl to d' ' G ~ \ e nthese plices, thele will be some optimunl comt~inationof facto~stor protl~~clnq n n ) giaen output, and some minimuin md~ginalcost of p~otlucinqan\ gilen output. If, for ana gibe11 output, t11~ltmarginLil cost is less th'ln the price, the firm llas an i n c e n t i ~ eto expand output, ~ n c con\ l elselh 4cco1tl ingly, the marginal cost curhe £01 the yiaen prices of fnctors will be the firm's supply curae for X, giaen that tlie film staJs in business. IYe know that at tile specified p~icesfor the factols of production ant1 a price of OE' for the pioduct, the firm pioduces Oq;'. Accortfinglj, the marginal cost curve corresponding to p:, p,', . . will pass througli d', it is repiesented on Figure 5 1 as XIC'. This cunxe is draavn slopinc u p ~ z a l dbecause u e are dealing with a competiti~eindustlj. If the cmac sloped tloajn. production at a rate at which piice was equal to malqinnl cost ~ l o u l dill~ o l v elosses. Tlle film would eitlle~close down or exp,~ncIto take la antage of lower marqinal costs. Such "inteinal economies" ~ t o u l dtllus mean the absence of any limit to size. Accordingly, we assume "inteinal cliscco~iomies." These can be rationali7ecl in the long-run t,y the fixed entrepreneurial capacity of the firm and in the short-run bx this and other factors whose amount cannot be varied. DISECOVOhlIES EXTERNAL

4 F F E C T I N G MARGIN %I C 0 5 7 CUR\ FS

If the price of X weie t A e n a, OE rather t l ~ a n0 E ' solel\ to film 1. I ~ u as t OE' fol all otllel firms, curae hlC' azould tell the whole stor\ If the snppl\ culves of facto~sto the industrb wele upwnrtl-sloping, film I ~votiltltend to bid u p a tiifle the price3 of factors of production 111 prod~tcinqOqy lathe1 than Oqi. This would affect all firms in the industl\, firm I inclucled, raising their cost curles a trifle and tllerebj leading eat11 ot the otlre~films to reduce output a trifle. These chanqes will be negligil~leto each i n d i r i d t ~ ~ i l firm if there are supposed to be manv finns, but the aqgreg.dte effect on the employment of factors by all firms is of the same o r d ~ of i n ~ ~ ~ y n i t uas c l ethe increased ernplojment of factoi s b\ firm 1 I11 consequerite, tlle increase in price of factols due to exparlsion b) filrn 1 is eaen less than might 'lequired ' I~ecaicqe the distribution of the output :imong tllc intlitidual fir~iisma\ i ~ o t1)c the \ ; ~ m c ;i t trill depend on the arrarlgelnerits \\heiel)y t!le c~uantitj-OQ is "l.ntiolied" amollg slippliers eager to produce a larger quar~tity.

100

PRICE THEORY

significance, sirice it shows the pressure on the market at nonequilibrium prices. T h a t is, from the market demand and supply curves, it would appear that maintenance of a m-inimum price of O P would require rationing production "quotas," as it were, aggregating O Q anlollg producers clesirous of producing OQ', so that QQ' measures the "excess supply" or "excess capacity" with which the "rationing authority" would have to contend. I n fact, however, the "excess supply" with which the "rationing authority" would have to contend is not QQ' but QQ". This point is of more than academic interest. I t explains why attempts to "rig" or "peg" prices frequently are subjected to considerably greater pressure than was anticipated, and why the abandonment of such attempts frequently produces less of a change in actual output than the pressure against them ~i-oulcllead one to expect. (One example is the allocation of crop quotas under one or another of our agricultural programs.) Figure 5.1 1 illustrates the same point for the case iri wliich external economies affecting marginal cost curves are sufficiently important to yield a negatively sloping supply cunre to the industry. Let SS be this supply curve, DD the demand curve, ant1 O P the minimum price legally enforced. Since at this price the amount tlemanded, ; i s shown by the tlcmand curve (OQ), is cgreater than the amount supplied, as shown by the cupply 'curve (OQ'), it might appear that there is no prol~lelnof rationing the amount demanded anlong suppliers eager to proctuce a larger amount a t the legal price. This is, liowever, false, as can be seen 11). slrp~~osirlg, tentatively, that only O Q ' is produced. In this case, tlie price ~roultlnot 1)e OP but OP", since the eager demanders would bid up the price. B I I ~if, output of the industry is OQ', the ilidividual firms will be trying to atljltst in the light of the marginal cost curves that correspond to the teclmical contiitions and conditions on the factors markets associated ~,i-itllpoint Y' on SS. T o each separately, this marginal cost curve rises, ant1 so the sum of these marginal cost curves (ChfC') will rise. Accordingly, if the industry's output were OQ' and market price were OP", intlividual firms would try to produce more than OQ'. T h e sum of what they individually t l ~ i n kthey want to produce under these conditions would he P"K' or RR' in excess of the amount demanded-and ",MCf is the "virtual" or "slladow" supply curve. T h e attempts of individual firms to expand output to P"R' xvo~~ld have two effects: the actual expansion in output ~ v o t ~ (l 1d) lower price because of conditions of demand and (2) change the technical conditions and conditions 011 tile factor market in such a fashion as to slliit the marginal cost curves to the right. Illhen price had fallen to the legal minimum, OP, output would be OQ. But at this output, technical co~lditionsand conditions on the factor markets are those associated with point N on tlie sup. ply curve, and the "shadow" supply curve would be fRIC. Xccorctingly, individual firms "think" they would like to produce an output of OQ", ant1 there remains the problem of "rationing" an outp11t of O Q among suppliers eager to produce OQ". T h e market point would be M, on the de-

Relatiorashzpc Betscecn S u p p l y anrl Cost Cu?z~cr

101

IMG'

Quantity per u n i t time

mand curve, and there tvould I-emain tlo~unr\~ard pressure on the minimum price. This analysis illustrates Ilo~vit is that w1lere;is to e;tcll individual proclucel- sep;~~-;~tely, his supply ~.III-1.c slio~vstlie n?ilrinili?n a~nourlthe ~ v o ~ l l d t specified price, a 1leg;ttively sloping curye for 1)e ~villirigto 1,l.otlrlc.e ; ~ the ;ul inclustr) pi.oducet1 by external ecoilonlies sllows the ? r r i n i ~ n ~qr~antity ~uz that would be sul~plietlat each price. Tllis point i, at once so irnportarit ancl so puz7ling that it may be woi-tll illustratiilg it for yet ;trlotller case. 111Figure 5.12, let OP I)e a legal 1n;rsinlurn ~ x i c e l\'llat . will Ile the actual point achieved in tlic m:irket so long ;is we ,r~pposet l ~ esuppl) curve to be sloped negatively e\ery~vliere?TIie ariswer is an output of zero, i.e., tlic point P. I t is clear that no output Price

D

S

P

0

Q"

Q

Q'

Q u a n t i t y per unit time

102

PRICE THEORY

greater than OQ would be possible at the price OP since it could not be sold. But if, tentatively, OQ is supposed to be the output, tlle relevant nlargil-la1 cost curves are those associated with point N' on SS, the sum of xvhich is given by the curve labelled PMC'. But if suppliers were to try to adjust their output in the light of these marginal cost c u r x s , they would try to produce OQ" at a price of OP, or less than OQ. As thej- tried to d o so, cost curves would rise and their desired output would fall. There is n o end to this process short of an output of zero, so long as we insist on supposing the supply curve negatively inclined tl~rougllout.Of course, if, as might well happen, the supply curve had a positively sloping segment (as i n Figure 5.13), the final solution would be at an output of OQ".

One waj of cornbininq this nnd the pieceding example is to 5llo~ion the r l d but '11so the nlen of att,ilrrfigure not 0111) tile s u p p l ~and d e ~ l l ~ ~culres able points, as in Figme 7 14. T h e ale'l indic'lted 1n \eltical sliatling l i att,riilablc so fa1 as tontlit~oniof 5ul)pl) aloire ,Ilr contelnetl, tlic ~llenintlic'ltecl b j hoiizontal sh,rding is ,~ttainableso fai n i tontiitions of clern,~lltl alone nl e concei ned; 0111) poiiits in tlie c I osi-llntclretl ,Ilea (,it10 a1 e tonsistent with conditions of both suppl\ m t l tlemnnd Tlle pllte to~reipontl ing to d (OP) is thus the lonest piice consistent nit11 tlli5 iilduiti\ ,5.It iila! Ile xt-01-th noti!~gt!inc !!?is an:lIysis in !'?IXC of "at:ai~?al~lca l t ~ \ ' ;r\o!\ci ' in a sarisfactouy \ray the cluestion of stablc \elsus unstablc c~qailil~riurn pocitions, 11-hich has been m11cil tlisrn\\etl ill tlic literatine i n tei-ms of all alleged conflict t)et~veenthe "IValras" an(! "hlarslinll" conditions. I t turn, out that .rthal determii~cctile stabilit? of ccluilihrir~mis not I\-liether tlic mal-kct p1.oc.es.; is al.l~it~al.ily supposed to p~oceetlaltelnag cotisrant o r q~iantitiescon\tant, but xihetlier a negatively sloped t i ~ e l yby l ~ o l d i ~ lprice\ stcppl) cur\e is "back\\ ai-cl bctldi~ig"or. "forrt-a~tl falling." If it is "l~ack\carcli)eniling," s t a h i l i t ~rcc111ires that the s u ~ ~ p cl yu n c c a t tlic deiira~ldcui.vc fl.0111 al~ove;if it is "for wart1 falling," from below, as i n Figure 5.14.

Relationships Between Supply and Cost Curves

103

Price

FIGURE5.14

Quantity per unit time

T h e Firm So far we have taken the notion of a firm for granted. This notion is sur1-ourlded by difficulties, and a tl~orouglilysatisfactory definition of a firm or a thoroughly satisfactoi-y theory explaining the determinants of the number or structure of firms does not exist. Fortunately, many of these difficulties are not relevant for the present purpose, so we can beg the really t1~ouhlesomeqrlestions. Rut some~vhatinore discussion of the meaning of the fil-rn is tlesirable. Let us tlliilk of all resources (factors of production) as owned by indii-id11;ils. Let us suppose furtlier that t l ~ cindividual can derive iricome from :In)-resources that he own slloultl the eupected iesidual income differ f ~ o mthe eul~ectetltontract~i,ilincome? T\'1-1) sllould it cliffel for some oxvnels of le,omces in one diiection 'rnd f o ~otheii t exp1,~ininq in the opposite direction; T\'liat fact015 are most i m p o ~ t a n ln s u ~ ldifferences? l For our purposes, it is enotlg.11 to sa\ that sllth cliffeiencei betneen euand expected contiactual income will aii5e. not pected ~ c s i d ~ l aincome l o n l ~ as , tempola1 y diffelences a1 iiinq from illa~Let impel fections o~ moclisequilibrium, I I L I ~also as l ~ e ~ l n a n e differences nt consistent with ment,~~ ) "stable" equilibrium. 1Z7elllust st~pposet l u t expec tctl icsidual inconle will exceed eupec ced coilt~actual iiic onle fol 5oine ~ r i t litluals i~ ,111el toll\ el selr toi o t h e ~ s ,antl tllnt chanyes in fac to1 and p ~ o d u c t111 ices nil1 affect s ~ ~ c h diffeiences antl so lend to cl~anges1r1 the nliml~eiof film5 It seem4 both poisible , ~ n dtlesil ,ible to suppose that "lli~etl' ie5oulces (or their seirices) call be defined i n phrsicnl terms in sutli a war tllat diffelent lrriits of wllat 1s c'illed "'i fac to1 of pioduction" can be I egnlclecl as peifect substitutes in 111 oduction i egditlless ot v 110 ov xis them 01 of tlie quantity of that or otliei I'tcto~s emplorcd, xzheie,ts uriits of "tfifferent" t e sp~odrlclesoulces cannot be ~eg'lldcdAS uniforml~perfect s ~ ~ l ~ s t i t u111 tion. Our emphasis on the possible dil el geilce I ~ e teen ~ i tlie cxpectetl i esid~tal intorrle ant1 eupec ted conti nctllal iiicome of ail om rle~of 1 esotu te5 me'ins th'it n e cannot specif) completel) the ie3orllces onnet1 11) 'In ~ n t l i ~ i d u a l simply b) listlrig the nunll~erof untts of eacli crpe of leionlce Ile owns, ~ v h e nthe units ale c,~lculatetlas if the iesoulces w o e all icnted out to otllela If this rieie a complete spccific.rtio11, ~t w oultl tien\ tlie pors~bilitr of 't permanent dilergence betx\.cen expectecl iesid~t,ilincome and eupected t onti actual income; it ould 11e ~t matic1 of l~itiiffelrrlce hetl-iel the le3ouices were " h i ~ e d "or nsetl b~ "films" and we sllould be tll~owing linked to a price index of the product produccd or of products in general; there may he bonuses dcpcnding 011 gross or nct vccriptu; tlvo o~ nlarly o ~ \ n c r sof resources rnav form a partucrship anti share residual incol~ie;ant1 so on at1 in/initlc111.Brit I h e l i e ~ cthat no essential generality is lost, xvllile much is gained in simplici~yot eupositio11, b! restrictillg discussiotl to the "pure" t!I)es above.

Relationships B e t w e e n Supply a n d Cost Curves

103

out the feature 1i7eintroduced to explain the existence and formation of "firms." There is therefore implicit in tile view we are atlopting the notion that each intlivitlual can, as a formal matter, be regartled as o~vningtwo types of resources: (1) His resources viewetl exclusively as "llired" resorircesivhat his resources would he if lie were not to form his own firm. These resources can be viewed in physical terms arld can be coin1)ined with similar resources o~vnedby others to give supply cur\-cs of all resources viewed sole1~-in terms of their productivity if used as hired resources. If an indi\~iclualdoes decide to be a residual income recipient, he must be viewed as hiring these resources from I~imself,and he must consider their market price as a cost identical in kind ~i-it11the cost of other hired resoui-ces.7 (2) X resource tliat 1,eflects the difference between the protluctivity of his resources viewed solely as llircd resources and their productivity when owned rial or some by his firm-we may call this M Y . X's e n t ~ ~ p ~ e n e z ~capacity similar term. This resource is specific to each individual; by definition, it has no value to any otller firm. TVhether it is lised or not will depend on the price of the final product and the price^ of hiretl resources or on the demand for the final product and the supply curve of hired resources, if the 11roduct ant1 factor market are not competitive. For some sets of prices it ~villbe s~~ppliccl in its entirety; for otller sets of prices, not at all. For this . ~ slrpply 1nc;ins a statement of the kind of factor, then, givcn r o n d i t i o ~ zof economic char;~cteristicsof the firms-or of tlie "entrepreneurial capacities" of the fou~ldersof the firms-that ~vouldbe forrned under all possible sets of prices. It should be emphasized tliat this distinction between the two types of resources is purely formal. Giving names to our ignorance may be useful; it does not dispel the ignorance. A really satisfactory theory would do more than sa)- there must be something other than hired resources; it would say ~ v h a tile t essential cliaracteristics of the "something other" are. tinder our assumptions, the entvepreneurial cap;tcity available to a firm is liinitecl to that owned by the intlividual ~ v h odecides to become a resiclual incorllc recipient. Insofar as the "quantity" of entrepreneurial capacity can be conlpared between firms, it ]nay differ from firm to firm. For any one firm, however, the quantity it owns sets a maximum to the quantity it c a t use. This introduces ;I limitation on a factor or an "indivisibility," sufficierlt to explain ~ i h ythere are limits to the size of individual firms. Anti it is, of course, pl-eciseiy because we 1,j-antto rationalix ol~servectpl-ie'7. T h e resources hc owns ma!, Ilorce~cr,differ from others in that he may have to rise all of his own 1.csources in his oxen fir111 if he uses any (e.g., it may not he feasible for Iiirn to divide his 1al)or porcer hetrvecn his fir111 and other firms.) This difference need not, Ilo~vevcr,arise. It may be perfect11 feasit)le for hitll to divide his resources in any fashion hctween his own firm and use as "hired" resources by other finlls. '\Ve shall suppose this in general to be tile rase i11 01-der to avoid certain d-iscontinuities that might other~ciseoccur.

nomena that suggest that the size of firms is not capricious or arbitrary or irrelevant that we have introduced this unknown sometlling, which we have christened entrepreneurial capacity.

T h e Formal Economic Specification of "Entrepreneurial Capacity" For simplicity, let us suppose that theie are no nonpecuniary factors entering into an individual's decision whether to form his own firm or to rent out all the resources he owns.8 For simplicity, also, let us suppose that the individual's entrepreneurial capacity, if used at all, will be used in the industry under discussion, so that we can beg the choice of what product to p r o d u ~ e . ~ Tlle indi~idual'sentleplerleurial capacity can then be specified by a production function, showing the maxiinum quantity of p ~ o d u c the is cap~ conditions wi tll gix en quantities of "llil ecl" able of producing under g i en resources (including any he "hires" from himself) T h u s if x, replesents the quantity of product produced by incli\idual i, and a, b, c, the quantities of tarious factors he uses, we can concei~eof x,= f, (a, b, c, .) as the plocluctiorl function attached to the indi\idu,~l T h i i plocluctlon function will not in geneial be homogeneous of the fil st deglee in .I, h, c, . for all values of a, h, c, . . since it does not contain ~ 1 the 1 ~ a l i a b l e sthat affect output but only those tltat the intli~itlualentrepseneus can control I11 particular, entrepreneurial capacity is supposed to be not greater than the amount he owns, and there may be additional \aliablec, Ile cannot control (e.g., distance between cities for raihoads, etc ) Indeed, if the production function wele homogeneous of the filst degree in a, 11, c. , this nould imply that entrepreneurial capacity ic, not import'lnt in this in5tance and t11'1t thele is no limit to the si7e of the firm. I t is concei~ablethat the production function coulci 11e identical for t n o . . ) - f, (a,l~,c,. ) = 0 f o ~all 'I, h , c, indiliduals; i e., that. y a ~f,, (a,l~,c, I n this case these two incli~iclualswould h n ~ eidentical mtrcplc~leulialcapacity. If this M ele true fol a n inclefinitel) lalye nllrnl~elof i~lclixitluali, i t would be e q u i ~ a l e n to t a supplj culve of entrepreneulial capacit~that T V ' I ~ perfectly elastic at a price, g i ~ e no u ~assumptions, of reso (since IVC h ' l ~ e 8. T h i s i n v o l ~ e sn o e5scntial losi of ::cnei.ality. Sonpecuniary returns can Ije hanclled 11)- including n nioncy c q u i ~ , s l c n tin tile cost5 :hc tii.m ili'trgr\ itielf for the irwrclces i t o w l s o r b y regarding the fi1-tn as producing two prod~icts,the p r o t l ~ ~ markctetl ct ant1 thc norrpecuniavy advantages o r disatlvantages of entrepreneurship. 9. T h i s too involvei ]lo esscrltial losr of g e ~ ~ e l a l i tFor v . $\en conditions in other in, highest possil~leretrlrn to each intli~itlualfrom dustries he might consider e n r e ~ i n g the entering one of those induitries ~ v i l lhe a e If the ;tr el age i ex cnue cui.ie is aerywhele belor$ the arerage ,~~ial,le cost ( u i \ e , the film nil1 add more to its corts br p~otlucing sonletl~ingtllarl i t will ~ d to d i t s ~e ceipts, and it v ill therefole be better off to pi oduc e notllinq If the 'txe1 age lerenue culr7e is above the arei;lge ~ a r i a b l ecost c m r e ,it one 01 mole points, it will be prefeiable to produce at one of these points lathel than not to produce at all. Given that the firm is to produce something, the o p t i ~ n u mamount to produce is gi.ien by a comparison of the maryinal lerenue and malginal cost curves. If for any output, marginal revenue is greatel than n ~ ~ ~ r q i n a l cost, more will be added to total receipts than to total costs br ploducirlq a little more; hence it pays to produce a little more Coilr enel\, if maiginal t ~ flonl total lere.i7enue is less than marginal cost, less \till be s ~ bacted ceipts than f ~ o mtotal costs h j producing a little leis: hence it pnxs to produce a little less. Tlie optimum output is therefole th'lt ,it mhich tnargilial revenue equals marginal cost.16 If we neglect the possibilitx that the firm produces nothinq, equations (1) can be extended to include the firm's output deci5ion and to destrihe the general equilibrium of the firm 131 eliminatinc the ie.;triction to a p a ticular output and addin? the requllcinent that malginal cost equals marginal re1 enue. The! then become: 16. Note that this output -\vill necessm-ily bc one of those for rchicl~a\c.rage revenue e ~ c e c d saverage ~ a r i a h l ecost. ant1 that this condition is alrcatly iimplicit in those rtatetl above, as call be seen from thc georneLl-\ of the lelntion bet-\\-cen the average and mavginal curves.

R e l u t i o n s h i p ~Between Supply a n d Cost Czrrz~ec - -1 hIFC, ' - hfC x = fi (a, b, . . .)

MPP, - MPP,, AIFC,,

' '

117

1 -

1"lR

rvhere hIC is marginal cost ant1 MR marginal relVenuc. For a given tlemand curve and given conditions of cost, the optimtin output is clearly a nllinber. T o get a function relating the optimum output to the demand curve it woulcl be necessary to tlcscribe the demand curve by some list of parameters and then expl-ess the optimum output as a function of these parameters. For example, if one could restrict oneself to straight-line demand curves, the optimum output, for given cost conditions, could be expressecl as a function of the lieight and slope of the demand curve. A particularly important special case in which it is possible to describe the demand curve by a single pal-;]meter is that of competition, in wllich the demand curve for the firm's product is taken to be a horizontal line. This demand curve is then completely descril)etl by its height, which is tlle n optimum output to tlle mal-ket price of the protluct. T h e f ~ ~ n c t i orelating denland curve can then be describctl a s relating optimum output to price. I11 this special case, the average revenue curve and the marginal revenue curve b e ~ o m eidentical and equal to price. T h e firm nrill protluce nothii~g unless price is above nliriimum average variable costs; if price is above this level, it will produce an output that \\-ill make price equal to marginal cost. T h e loctis of optililum outputs for 1.arious prices is stin~marizedin Figlire 5.19 for the cost curves for case I)' in Figure 5.18(d). At a price bcPrice I

I

L

I - - - - - - - - - -0unit utput . . per t~me

low Op, the optimlnn output is zero, so the soiid part of the v axis is the locus of optimum outputs; n t a piite a b o ~ eOp, the solid part of the malg i n d cobt curve is the locur of optim~[ruoutput At Op, tlrere is a discontinuit); the lloiizontal dashed line connects two altelnative points, but no

point on it is an optimum. This discontinuity is not present in cases A, B, and C of the pieceding section. In cnse A (ant1 A') of the preceding section, the optimum o u t p ~ l is t infinite foi an) p i c e , ~ b o ~ tile e (constant) maiginai cost, ~ v h i ~ i> 1 1the leason wily this case is incompatible with competition.

( 2 ) T h e firm's supply curve I t will be recalled that a supply curae of a pal ticular group for a particular coinmodity was defined as "the boundar) line between those points that are and those that are not nttalnahle under the g i ~ e nconditions of suppl)" and that points mere defined as attainable if "the suppliers would be ~ i l l i n gto supply the indicated qunntity at the indicated price." One fuithel point must be made explicit before we can use our cost curaes to dlam a supply curie as so defined: I n askirlg avhethei the suppliers would be mlll~ngto supplj tlie indic'lted qudrltity at the indicated price, what a l t e ~ r l a t i ~ edo s we suppose llinl to hale? There are two main possibilities: (1) IVe might suppose him to haxe onlj the alternntile of shutting tlownme might consider him faced with an all-or-nothing ploposition. (2) We might suppose him to h,r\e the alteinative of supplying the indicated amount or any smaller amount t all-or-riothing c,tse-tllc a\ erdge T aiiable cost curpe i n the f i ~ s c'tse-the cle u-1~is the boundar) line between attLti~lnl)le and unattainable points T h e film wollld plefer an\ point a b o e~ t11e a\ el ,cge x ariable cost curl e to the alternntive of plod~tcinynothing nrld ~vouldpiefel to ploduce notlling iatliel t h m to accepL a point I~elox\the ~LLeiage~ar1,ll)leco5t culre. T h e second case-in 1.i hi( 11 the dltelnatir es include suppl) ing lei4 than the iriclic~ttetlamount-i5 much the more useful of the two arltI is the one geneiall\ intended when s u p p l ~ crnr es ale ch,~xvn I n this case, the hounclniv lme I)et~reenthe attairldble ant1 ~in,rttniil~ihlc points is sliglltl) rriorc t o ~ n ~ ~ l i c a tFor e d .LII) output, the nlinimum supplb pilce is the 01dll e curie 01 the maryinal cost culxe, ii'ite of either tile alelaye ~ d l i a l ~ cost is highel, tlle suppll c m l e is tllen t!le locus of these minim~rm ~vliicl~e\ei in Figule i20 foi case D'. suppl) piicei. This con;,,,a11d x (i = 1, . . . , k). If, however, the solutions of equations (2), (3), and (4) satisfy tlie inequality,

k

Xj

Px < 2 "ij pai + Cj, i=l

the equilibrium values are given by (2)' xj = 0

(i=l,.,.,k)

(3)' aij = 0 (4) aij = ?iij

( i = k + l , . . . , m).

THE DEMAND AND SUPPLY OF FACTORS

If tliere are n potential firms, the total amount of each factor demanded is given by n (i = 1 , . . . , m). a, 78 aij J=1 T h e supply of tlie variable factois to the industry can be described by

Relationships B e t w e e n S u p p l y and Cost Curues

129

where gi may also depend on prices of other products and the like, variables that are taken as fixed to the industry. No supply equations for the fixed factors need be inclucled, since, by virtue of equations (4), they ~vouldbe itleiitical with equations ( 5 ) for i = k + 1, . . . , m. THE S U P P L Y OF THE PRODUCT

Finally, the total supply of the product is given by

THE NUMBER OF VARIABLES A N D EQUATIONS

IVe may now count the number of ~ a r i a b l e sand equations to check for completeness. T h e variables are as follows:

V a ~ i Oales Symbol

Name

Output of the industry Output of each firm Total quantity of each factor Quantity of each factor emplojed by each firm Price of the product Price of the 1ariable factors

hTumber

x x J ( j = l , . . . , n) a, (i = I , . . . , m ) alJ(i= 1, . . . , m) ( j = l , . . . , n)

1 n m mn

I'x

1

pa, (i = 1, . . . , k)

k

Total number of variables

2 +k

+ n + m + mn

T h e equations are as follows:

Equations

N u m be?

(Z), (3), (4), or (2)', (3)', (4)

n(m

+ 1)

(5)

m

(6)

k 1

(7) Total number of equations

1+ k

+ n + m + mn

There is one mole \ariable than equations. M'e can therefore eliminate all lariable5 except, say, x and p,, and be left with one equation. If we solve the resulting equation for x to yield, say

this equation is the supply curve of the industry.

The Law of Variable Proportions and a Firm's Cost Curves

M'e have just gone through in a formal way tlle ~ a r i o u tjpes s of supply conditions that may obtain. \lie have seen that the suppl) conditions depend on the cost curves of the individual fiml. We now turn to tlle firm, to examine the conditions underlying its cost curves. Our interest here is, of course, not in the firm per se but rather in a fuller understanding of the factors determining the supply conditions in an industry. \lie must remember that a suppl) curTe is a meaningful concept only for a competiti~e industry. Otherwise, price alone does not describe completely the conditions of demand facing the individual firm. \Ire must also remember that in going from cost curves to supply curves we have to be on the lookout for the possible existence of external economies or diseconomies--economies or diseconomies external to the firm hut internal to the industry and hence affecting the supply curve of that industry.

T h e Lazu of Variable P ~ o p o r t i o n s W e may regard the firm as an intermediary between factor markets, wherein it buys resources, and product markets, wllereirl it sells products. For the firm, the demand conditions for the product it produces are summarized in the demand (or average revenue) curve for its product. T h e supply conditions on factor markets are sumi~larizedin the supply curves of factors of production to the firm. T h e technological conditions governing the firm are summarized in the production function, which shows the (maximum) quantity of product it can produce for given quantities of each of the various factors of production it uses.

The Law of Variable Proportions

131

One of the properties assigned to this production function is generally described as "the Law of Diminishing Returns." This terminology is closely connected with the explanation of the so-called law in terms of fixed and variable factors of production. At bottom, however, the issue in question has little or no relation to this distinction between fixed and variable factors; it is rather concerned with the effect of varying the proportions in which different factors are employed, and all factors enter i n completely symmetrical fashion. Accordingly, it will perhaps avoid misunderstanding to call it "the Law of Variable Proportions." A hypothetical production function designed to illustrate this law is given i n tabular form i n Table 6.1 and in graphic form in Figure 6.1. For this example, let us suppose that only two factors of production, say A and B, are used to produce the product. Column 1 gives selected values of the number of units of B per unit of A, i.e., of the ratio in which the factors

X

B -

XA

X

A

A B

0

w

0

Ind.

1/16

16

1

16

1/8

8

4

32

1/4

4

9

36

1/2

2

18

36

1

1

25

25

2

1/2

36

18

4

1/4

36

9

8

1/8

32

4

16

1/16

16

1

02

0

Ind.

0

;\TOTE:

X

4-

i

A )

ax

A )

a($)

1

16

Ind.

3

48

16

5

40

4

9

36

0

7

14

-11

11

11

-7

0

0

-9

-4

-1

-5

- 16

-2

-3

Ind.

0

-

A ( $ )

4-

ax x=z B

-1

I n d . \tand\ for intleterminate.

Verbal de5criptions of column headings: (1) S o , of urlils of B per urlit of .I (2) S o . of u11it5 of A per ~ ~ r lofi lR 13) Product per unit of A (4) Product per unit of R (5) Change i n product per unit of X

(6) Change in no. of units of R per unit of A (7) LIai-ginal product of B 18) Change in product per unit of B (9) Change in no. of unit5 of A per unit of B (10) Marginal product of A

T h e Lam of Vuriable Ptoportions

133

are supposed combined. Let us skip column 2 for the moment. Column 3 sho~vsthe number of units of output per unit of .A for each ratio of B to ,4. For example, it says that if one-sixteenth as man): units of B as of A are used, then one unit of product will be produced for each unit of X employed; if equal number of units of B and of A are used, then 25 units of product will be produced for each unit of A employed. Now the mere possibility of p a k i n g statements of this kind already says a great deal about the character of the production function. For it might be, say, that one unit of B and one unit of A would produce t~venty-five units of product, but two units of B and two units of A would produce either more or less than fifty units. I n that case, the knowledge that equal numbers of units of A and B were employed would not be enough to determine the output per unit of A; in addition, one would have to k n o ~ v the absolute number of units. Output per unit of A will be a function solely of the ratio of the factors of production if and only if the production function has the property that multiplying the quantities of all factors by a constant will multiply output by the same constant-e.g., that doubling quantities of all factors ~villdouble the output. Functions having this functions of the first degree, and property are by definition hornogeneo~~s our illustrative table is drawn for such a function. I't'e shall discuss the meaning and significance of this property later. For the moment, it will suffice to say that we Tvant ultimately to distinguish between two sets of considerations affecting the costs of an individual firm: the proportions in which it combines factors and the scale on wllicll it operates. T h e law of variable proportions deals with the first set, and we can best abstract from the influence of scale by provisionally supposing it to have no influence; this is precisely what is involved in supposing the firm's production function to be homogeneous of the first degree in A and B, and A and B to be the only two factors of production involved. We shall see, further, that the influence of scale can itself be viewed as the result of the operation of the law of variable proportions, so we are making a less special assumption than might at first be supposed. Given that the production function is homogeneous of the first degree and that only two factors are involved, a pair of columns like 1 and 3 describes it completely if the entries are sufficiently numerous. For consider the general question: how much X can be produced if there are a, units of A and b, units of B? T h e answer can be obtained by computing !?L en2. --1

tering it in column 1, finding the corresponding entry in column 3, and multiplying the result by a,. This is what we mean by saying that in this case everything depends only on the proportions in ~vhichthe different factors are combined. It follows that all the rest of Table 6.1 can be obtained from columns 1 and 3, and examination of the column headings will confirm this: column 2 is simply the reciprocal of 1; column 4 is

equal to column 3 divided by column 1 or multiplied by c o l ~ m n2; and so 011. One reason for entering both columns 1 and 2 is to enable us to translate this table readily into terms of variable and fixed factors. Suppose the firm must use one unit of A, but can use varying amounts of B. T h e n column 3-or product per unit of A-is "total" product; column 4-or product per unit of B-is "average product" of the "variable" factor; and column 7-marginal product of B-is "darginal pl-oduct" of the "variable" factor. Similarly, if the firm must use one unit of B but can use varying amounts of A, we can take column 2 to sho~vtlie amount of A used. IZ'e shall then, of course, want to read the table from the bottom up, since this will correspond to increasing amounts of the "variable" factor. Column 4-or product per unit of B-is then the "total product," colurnn 3 -product per unit of A-tlie average product of the "variable factor"; and column 10-marginal product of A-the "marginal" product of tlle variable factor. Let us noxv turn to the numerical values in the table and tlle grapli. This particular example is set up so as to illustrate most of tlie cases that are arithmetically possible within the framework of a two-variable llonlogeneous production f ~ ~ n c t i oofn the first degree. Not all cases are aritlimetically possible; for example, average product cannot increase as tlle relevant variable increases alld at tlie same time 11e greater than tlle corresponding marginal proclllct. I n checking for this kind of internal conbe kept in rnind that X derreases relative to sistency in tlie figure, it slio~~lcl B as one goes from left to right, and, llence, in interpreting tlie A curves they sllould be read "back~vards,"as i t Tvere. T h e terms i n r ~ e n s i n g1-etlr~n.~ and diminishing 1.ellirn.s are sometimes used to refer to marginal returns and sometinles to average returns, so i t will be best to indicate explicitly which is intended. Flu-thermore, they always refer to the behavior of returns as tlle quantity of the corresponding factor increases. Alarginal returns to B increase at first, thereafter diminish, and ultimately become negative. Average returns to B increase over a longer range (until a ratio of 1 / 4 of a unit of B per ~ l n i tof A if Tve stick only to the designated points and avoid interpolation), are the same at a ratio of B to A of 1/2 as at 1/3, and then diminish. A behaves, of course, in the same Tvay, as we shall see most readily if Ive read from the bottom of tlie table up, or from the riglit of the g r a p l ~to the left, Alarginal returns to A increases to somewllere bet~ceen1/16 and 1/8 of a unit of ,4 per unit of B, then decline, and ultimately become negative. Average returns increase to 1/4 of a unit of A per unit of B, are tlle same at 1 / 2 as at 1/4, and then diminis11.l 1 . T h e first and last entrie\ in the table de\el.\e a ~ r o r dof explanation. T h e product per. unit of .\ is set at 0 for R/;\ = 0;this implies that B is 311 "essential" factor in the sense hat 110 o~ltprltis possible ~vitlloutsome B. Sirlce column 4 is column 3 divided by

T h e Law of Variable Proportions

135

T h e table and graph supposedly summarize the technological conditions governing the production of the product in question. T h a t is, they are designed to answer the technological question: given specified amounts of the two factors of production, what is the maximum amount of product that can be produced? Let us now see how we would use this information; in the process, we can also test whether all the arithmetically possible cases they contain are economically or technologically relevant. Suppose, for example, that we have 8 units of A and 64 units of B. T h e table shows an output of 32 per unit of A when the ratio of B to A is 8 to 1, which would mean a total output of 256. But is this really the best we can do? Further examination of the table suggests that it is not. If it costs 110thing to "throw" B away-not to "use" it-we can get an output of 36 per unit of A, or 288 in all, simply by using only 16 or 32 of our units of B, that is, either 2 or 4 units of B per unit of A. If the table had more entries, perhaps some number between 2 and 4 would be even better. Obviously, the situation is the same for any larger number of units of B per unit of A, so n o matter how plentiful B is, it will not be sensible to use more than 4 units of B per unit of A. Similarly, suppose we had the same 8 units of A but only 1 unit of B. T h e entry under a ratio of B to A of 1 / 8 shows an output of 4 per unit of A or 32 i n all. But again this is not really the best we can do. Suppose we were to "throw" away, i.e., not use, 4 of the units of A. 12-e should then be operating with a ratio of B to X of 1/4, for which the output per unit of A is 9; multiplied by the 4 units of A being used, total output is 36. I n consequence, no matter how "scarce" B is, it is not sensible to use less than l / 4 of a unit of B per unit of A-or stated in reverse, no matter how plentiful A is, it is not sensible to use more than 4 units of A per unit of B. Suppose now that the ratio of B to A is between 1 / 4 and 4, say 8 units of A and 8 units of B, or a ratio of 1, does anything similar occur? Clearly it does not. By using all of the X and all of the B, output per unit of X is 25, total output is 200. By using less of the A, say only 4 units, output per tmit of A can be raised to 36, but since only 4 units are used, total output is reduced to 144; similarly, by using less of the B, say only 4 units, output per unit of B can be raised to 36, but only at the expense of reducing total output to 144. These examples sho~vthat the three regions marked off in Figure 6.1 according to the behavior of average returns have very different meanings and significance. I n the first region, average returns to B are increasing and nT>.erage returns to A4aye diminishing; in the second region, average returns to both X and B are diminishing. T h e third region is the counterpart of the first-average returns are increasing to one factoy, i n this case A, and column 1, the cor~.espondingproduct per unit of B is 010, hence indeterminate. It is possil~lethat some product could be p r o d ~ ~ c ehy t l use of h alone. In this case, the first entry in column 3 ~vouldbe finite. 3 1 1 ~ 1in column 1 a.Similar remarks apply to the last entry.

diminishing to the other. Kow our exa~nplesshow that the fix-st and third regions are ones to be shunned. Put differently, the figures entered i n our table for these regions, while a ~ i t l ~ n z c t i r a l lpossible y uncle]- our assumptions, are technologically inconsistent with those entered else~vhere.T h e table purports to sho~vthe maximum output technologically possible for different combinations of factors. B u t it does not do so, for, as we have seen, when the ratio of B to 4 is 8 to 1, there is a way of using the factors that will produce an output of 36 per unit of X and hence of 4 11'2 per unit of B, whereas the table sho~vsan output of only 32 antl 4 respectively. In other wortls, on tecllnological grountls alone, the table is wrong, given the assumptions that the production function is l~omogeneousof the first degree and that A and B are perfectly divisible (this point is discussetl below). For B / A = I / 16, the entry in columll 3 illould he 2$4, in c o l ~ ~ m4,n86; for B / A = 1/8, the entry in column 3 should be 4p,, in column 4, 86; for B/.4 = 8, the entry in column 8 \hould 11e 86, in column 4, 4%; for B / A = I f , the entry in column 3 should be 86, in column 4, 2%. This then is the law of variable proportions relevant for economics: insofar as possible, production will take place 11y the use of such a combination of factors that the a1,erage returns to each separately will diminish (or at most remain constant) with an increase in the amount of that factor used relative to the amounts of other factors. And this "law" is not a fact of t is tlemonstrated nature, in the sense that nothing else is possible, or t l ~ a it by repeated pllysical experiments: it is a maxiin of rational contluct. I t may seem some\vhat paradoxical that "increasing returns," ~vllicll sound like something gootl, shoultl be something to be avoided. This appearance of paradox may be reduced by noting that in both the table antl the figure, the region of increasing average returns to one factor coincides with negative marginal returns to the other factor. T h i s is no accident; it is a necessary consequence of the fact that the production function is 110mogeneous of the first degree, as can reatlily he demonstrated. Suppose that 1 unit of A plus B, units of B protluce X, unitr of product and that this is a region of increasing average returns to A. T h e n 2 units of A plus B1 units of B will produce more than 2X1 units of protluct, say 2X1 AX ~vllereAX > 0. But because of homogeneity of first degree, 2 units of .A plur 2B,, units of B will produce only 2X, units of product. Hence the adtlitional units of B have diminislled output, so B must 11;1ve a negative marginal product. T h e common saying, "There's no llse going furtlier because you'1.e already reached the point of diminishing return," is highly misleading. T h e point not to be exceeded is the point of vanishing (marginal) returns; the prudent man will seek to exceed the point of diminishing (average) return^.^

+

2. Note that the equi~alencebetween increasing axerage returns to one factor and negati\e marginal returns to the other is Lalid only for a homogeneous function of the

The L a w of Vnrinblc Proportions

137

Can entries like those in the first ancl third regions of Table 6.1 and Figure 6.1 ever be relevant? There are two sets of circumstances under which they can. T h e first is trivial and involves only a verbal exception: Suppose that "using" a factor is paid for, i.e., involves a negative cost, as, for example, when it involves using laborers who are learning a trade and are willing to pay for it. I t may then be worth going into the region of increasing return to the other factor and negative return to this one. But in that case, the firm is really producing two products, the output entered in the table ancl education, and the table is not a complete summary of production conditions. Another example of the same case is where it costs something to "throw away" a factor, but again this must mean that there are other factors of production or other products involved. T h e more important case is suggested by the qualification insofar as possible in the statement above of the law of variable proportions. I t may not be possible for a firm to get into the region of diminishing returns for either of two reasons: 11ecause the quantities of relevant factors of production are outside of its control or 11ecause of indivisibilities. Let us postpone the first reason for the time being ancl consider only the second. Suppose factor A is land, plus labor, etc., in fixed ratios to the amount of land; factor R, services of a tractor in cultivating it; ancl the product is, say, wheat. Suppose, further, that tractors come in two sizes, one of which, size 11, can be regarded as "twice" as much tractor as the other, or size I . For a given amount of Factor A, it may well be that totcrl output is less with one tractor of size I1 than with one tractor of size I , because the smaller tractor does enough work per unit of time to cultivate the given area with the given other factors, while the only additional effect of the bigger tractor is to trample down more of the wheat. This means that with the bigger tractor, we are in the region of negative marginal returns to tractors and increasing average returns to land. Yet if only the bigger tractor is available it may be better to use it than to use no tractor at all. I n this case, it is not physically possible to throw "half" the tractor away, thougll it would be desirable to do so. Note that this effect does not come from owning the tractor rather than renting it; the same effect arises if a tractor can be rented by the hour, say, but the only tractor that can be rented is one of size 11. Using this tractor half the time may not be equivalent to using a tractor of size I all the time. T h e number of "tractor clays" of service that can be used may be perfectly continuous, yet indivisibility may be present. first degree. Suppose the plotluction function is homogeneous but not of the first degree and contains onlv ~ T V Ovariahles. Tf the degree of the function is less than one, then increasing returns to one factor ilnplies negatibe tnarginal returns to the other, but the converse does not Ilold: negative tnarginal leturns to one factor are consistent with diminishing average returns to the other. If the degree of the function is greater than one, negatibe marginal I-eturns to one factor implv increasil~gaverage returns to the other, hut the converse does not hold: increasing average returns to one factor are consistent with positive marginal returns to the other.

Note also that the indivisibility of one factor means increasing average returns to the other factor, not to the first. I n the particular example, the indivisibility could presumably be removed on the market by selling the larger tractor and buying a small one. But it is clear that this may not be possible, since there will be some minimum size or scale of tractor made. Ultimately, most such indivisibility traces to the indivisibility of the human agent (the absence of the "halfsize man" to drive or make the "half-size tractor").

Translation of the Law of Variable Proportions into Cost Cur.i)es Let us now turn to the determination of cost curxes from a production function like that summarized in Table 6.1. Suppose, first, that there are no indivisibilities and that the firm is perfectly free to hire any number of units of either of the factors of production. There is now no definite number of units of each factor of production axailable. Instead, the firm is limited by the price (or under monopsony, the supply curve) of the factors of production. Assume competition in the factor market, and suppose the price of B is zero. This is analogous to an unlimited amount of B being ax ailable, and obviously the optimum combination of B to A \\.ill be betlveen two and four units of B per unit of A. This will mean an output of P thirty-six per unit of A or a cost of &per unit of product, where Pa is the 3t)

price per unit of A. Clearly, under the gixen assumptions, this cost is independent of output, so the cost curves will be horizontal, as in Figure 6.2.

Cost per u n i t

I

Q u a n t i t y per unit of time FIGURE6.2

Similarly if P, were rero, but P, (the price per unit of B) were not, the P cost would be - L a n d two to four units of A would be used per unit of B. 36 Suppose, now, that neither price is zero. IZ'e k n o ~ vfrom our earlier analy-

T h e Law of Variable Proportions

139

MPP MPP,. For sis that the optimum combination will be given by 3= pa p, example, suppose P, = $1.40, P, = $1 .lo; then the optimum combination would be between one and two units of B per unit of A, For one unit of A to one unit of B, the cost per unit of product would be 1 0 ~for ; two units of B per unit of A, lo$; for four units of B per unit of A, 16 1/9$. Again the marginal and average cost curves would coincide as in Figure 6.2. T h e analysis until now has shown that if all factors were perfectly divisible and obtainable by the firm at a constant supply price, then the optimum combination of A / B would be the same for all levels of output. T h e marginal and average cost curves would then be coincide~ltand their height would be determined by factor prices. This case is not, however, the only relevant one, or even the most significant. I n the first place, horizontal cost curves would imply either monopoly (if the height of the cost curve were lower for one firm than for others) or complete indeterminancy of the size of firms.(if several or many firms had curves of the same height). 111 the second place, it is not useful in analyzing different "runs," which are disti~lguishedprecisely by the different possibilities of changing the amounts of various factors. TVhat this case does bring out is that for llolnogeneous production functions of the first degree, rising cost curves, hence linlitatiorls on the sire of firms, must be sought in limitations on the firm in the possibility of varying the amounts of some factor or other. Suppose that the supply of A is fixed to the firm at one unit-either temporarily for a short-run problem or permanently. T h e firm can then vary its output only by varying the amount of B en~ployed.Its cost conditions can then be derived directly from Table 6.1, together with 1) the price of B and (2) knowledge whether the unit of A is divisible or not. Table 6.2 and Figure 6.3 give the results when the price of a unit of B is $1.10. TZ7hetheror not A is indivisible makes a difference only for small amounts of B, for clearly R is taken to be divicible: when large amounts of B are supposed employed, there is clearly nothing to prevent some of the R from not being used. For smaller amounts of B, when A is indivisible, the figures in the original Table 6.1 are relevant; when A4is divisible, the revised figures take account of the possibility of not using some A, i.e., of not letting the ratio of B to A in use fall below G . T h e marginal costs can be calculated in either of t ~ v oways: by dividing the increment in column 4 by the corresponding increment in column 2 or 3, or by dividing the price of a unit of B by its marginal product as shown in column 7 of Table 6.1, for A indivisil~le-or in an appropriately revised column, for A divisible. \\7hen R/A is between 1 and 2, we have the combination that turns out ,

Ol~tpl~t

9 0 . of units of B emfiloyed

A indivisible

0

0

-

A divis ible

Total wariable cost ( I ) X $1.10

0

0

Alarginal cost

1/8 1/4

A indinisible

A divisible

Ind.

.031/18

.06 7/8

.03 1/18

.03 7/16

.03 1/18

-

9.06 7/8 1/16

A divisible

A indinisible

Average wariahle cost

2 1/4

1 4

41 / 9

9.03 1/18

$0.06 7/8 .027/24

.031/18

.02 3/4

.03 1/18

0.13 6/8 0.27 4/8

.03 1/18 .03 1/18

1/2

18

0.55

.03 1/18 .07 6/7

1

25

1.10

.04 2/5 .10

2

36

2.20

.06 1/9

to be optimum in our earlier example of both factors variable wllen Pa = $1.40 and P, = $1.10. Since the price of B is assumed the same in this example, the marginal cost, for that combination of factors, is, of course, the same as before, 10g per unit. T h e dashed lines in Figure 6.3 are for A indivisil~le.T h e indivisibility produces a decline both in average variable costs and marginal costs, the counterpart of increasing average returns to B and negative marginal protluct to A. T h a t it is no advantage for marginal costs to decline, or even for it to be lower for a segment than the marginal cost when A is divisible, is clear from the higher average variable cost during this interval when A is indivisible than when it is divisible. For A divisible, the marginal cost and average variable cost are horizontal (and therefore coincide) initially. This is because the limitation on A is irrelevant for this interval; this is essentially our earlier case, when A was a free good, because in this interxal it is not worth while employing all of A. T o put this in other terms, the supply curve for A is taken to be as in Figure 6.4. For low o~itputs,the horizontal segment of the supply curve of A is relevant.

T h e Law of Variable PI-oportio,l.r

Price of A

Quantity o f A per unit time

141

H o m o g e n e o ~ lFlrrt-Deg,.ee ~ P ) otlztcfton F u n c f z o n ~ . T h e P ) oblenl of Scale T h e examples just discussed indicate that tlle use of a production function that is homogeneous of the first degi-ee is compatible xvith almost any kind of cost conditions-with declining average variable costs if there are indivisihilities, xvitll rising average variable costs if there are limitatiorls on the quantity of one factor employed. Indeed, it begins to look as if a homogeneous production function of the first degree can be vielved not as an empirically special kind of function but as a manner of speakirlg about all functions, as a framework of 1-eference,or tautology. This is one wa!- of viexving it, and an extremely useful way of doing so. Fi-om this point of view, the concept of a llomogeneous furlction of the first degree can he considel-ed equivalent, on the one hand, to the concept of a conti-olled experiment, ant1 on the othei-, to tlle concept that the units c1io"sen for measuring quantities are il-relevant (the principle of relativity). Fundanlerltal to science is the conception that if an experiment is repeated under identical conditions, it lvill give identical results. Rut is not clouhling the quantity of eztcll of the factors equiv;~lentto 1-epeating an experinlent? If the initi;il 1)undle of factors yieltled X units of o u t p l ~ t , must not an identical I~unclleunder the same contlitions yield X al5o? Hence, must not the two 1111ntllestogether \ieltl 2X? Or if the two b ~ ~ n t l l e s together yield 2X, while it is said that one 1)untlle alone yields less than X , must not that mean tllztt the corlditions ~verenot the same and the experiment rras not really the same expel-iment? If the one-b~mtlleexperiment were a precise replica of tlle txvo-bundle experiment in all details, to the except uniformly on half the scale, must it not yield XI Or to t~u-11 other ax-gunlent-from tlimensions-can anything 11e considered changed if Tve look at objects through telescopes 01- microscopes? If we change units from 1-atesof flow per week to rates of flow per montll? If xve think of homogeneity of the first degree a5 a tluis~u,it cannot, of l'et certain ol~viousexamples seem to contl-adict it, corn-se,be co~~tratlicted. such ar the pal-able of the fly, which, it is said, if i t lvere rep-otlucecl accun-ately on a larger scale ~votlldbe uixrble to support its 01~11weight. Tlle anslver is, of course, that there must he some "relevant" factor of production that has not been increased in scale along wit11 the fly's dimensionsin this case, presuma1)ly tlle ail- pressure and the force of gal-iry. In tile same vein is Pal-eto's answei- to someone xvho said that doubling the subway s!-sten1 of Paris ~vouldnot yield t~vicethe return (01- pel-haps involve tlvice the cost). For honlogeneity of tlie first degree to lje relevant, he said, tllel-ewould have to be t ~ v oParises. T h e ~lsefulnessof this tautology depends on tlie value of tlle classification it suggests of the things that may affect cost conditions. I t leads to a

T h e Law of Variable Proportions

143

classification into (1) those that operate through explicit changes in the proportions among the factors of production, the chief of which are prices (or conditions of supply) of factors of production; (2) those that operate througll limiting the quantities of some factors of production available to the firm-these account for rising cost curves and include the existence of conditions affecting cost (size of cities, amount of coal in the ground, constant of gravity, etc.) outside the control of the individual firm, limitations imposed by contractual arrangements, and those largely anonymous conditions concealed in the notion of "entrepreneurial capacity;" and (3) those account for the possibility of decreasthat produce indivisibilities-these ing cost curves and in most cases can be ultimately traced back to the indivisibility of the human agent, as is suggested by the fact that the gains from division of labor and specialization of function are all included under this heading. Conceiving of the underlying production function as homogeneous of the first degree does not imply that the production function as v i e w e d by t h e fil-nz is Ilomogeneous of the first degree. T h e firm is only concerned with those factors of production, or other conditions affecting costs, over wllich it has control. I11 consequence, the production function to the firm can be regarded as a cross-section of the underlying production functionthat is, as obtained from the underlying production function by giving to the variables over which it has no control the constant values which they have for the problem in question. Indeed, it is precisely this step that enables us to conceive of rising long-run cost curves for individual firms and hence to rationalize the existence of limits to the size of firms. This is what Tias meant earlier by the remark that the "scale" of firms can itself be regarded as rationalized by the law of variable proportions. Slalislical Cost Czriur Stzrdlrs a n d Olilf1z1t Flexibility

,Iconsiderable number of empirical studies of cost curves of indiyidual firms have been made within the past tTio decades. These have been mainly concernetl Tiit11 estimatirlg short-run curyes, hlost of them suggest that short-run marginal cost curves are horizontal over the usual range of output, wllereas the preceding analysis would rather suggest rising marginal cost because of the existence of limits to the amounts of some factors of production, eyen in the loyg run ant1 certainly in the short run. I n an excellent discussion of these studies and some of their inlplications, Hans Alpelpoints out that the statistical evidence for this conclusion is quite limited and not particularly representati~e.?I~n particular, much of the evidence is for periods in wllich output was relatively low, so there might 3. "hlarginal Cost Cont~.o\er.s)-ant1 Its Itiiplications," Americslrl Econo?rlic Rez~ieu) (l>ecembcr.1948): 870-85.

have been "unused capacity:" i.e., in terins of our preceding analysis, there miglit Iiave been periods in ~vhicliit was possible to keep tlie ratio of factors fixed xchen output wirs increased despite the limited quantities of some factors, 1)ecause it had previously been rational not to use part of the latter factors. But it is not at all clear that the results can be entirely explained in this way. I n any event, consideration of these statistical results led George Stigler to suggest a force, Ilitherto neglected, tliat might make horizontal short-run marginal cost curves a deliberate objective of maximizing beliavior.4 This force is the desire to obtain flexibility. 12'11e11 a plant is huilt, it is not expected tliat precisely a single output will be produced year in and year out. I t is known that there will be fluctuations in demand and in tlesired output. The prol~lem,in other ~vords,is not to minimize the cost of a given output steadily and regularly to be produced 11ut to ~ninimizethe cost of a probability distribution of outputs, indicating the fraction of time each output will be produced. Tlle relevant variable to measure along the horizontal axis is not "tlie" output but the "average" output, taking full account of variations from tliat output. For example, consider the average variable cost curves sllorvn in Figure 6.5. llethod of production A is a rigid method, xcliich is highly efficient for a particular output but not for any other. T h e A curve shows tlie average cost if precisely the output indicated on the horizontal axis is produced day after day. T h e A' curve sliow~the average cost if the horizontal axis is regarded as the average output over tiine and actual output is regarded as fluctuating from day to day about this average in some given fas1lion.T T h e two cni-ves B anti B' have tlie corresponding meanings for a "flexible" method of protluction. For the figures as drawn, it is clear that the better method of prod~lction for a given unchanged output is A ; for a distril~utionof outputs varying from day to (lay around x,, B. P

P

Method A

XI

Method 0

X~

4. " P ~ o d u c t i o n :~nd1)istrihutiorl i n the Short Rl.in," J o r ~ v l a lof Politicnl Eroiioir:y ( J u n e 1030): 312-22. 3 . Yote that A' need not i,e above .clcl-v~vhcl.e I as ill thi5 graph. It1 geilcral, .I' \\ill be al,o\e -4. tile \amc a s :\, or 11elo\\ .\ a t a n \ point acco~tlinga s .I is conca\e u p \ \ a r d , linear, or conLa\ i. d o ~ n ~ v a r cfor l , the 1-elelallt region abo1.1t this point.

T h e Law of Variable Proportions

145

Comment on S t n t i ~ t i r c lCost l Curves*

I have great sympatlly with Caleb Smith's conclusion that the right questions have not been asked of the data on the costs of firms of different sizes. My quarrel with him is that he does not go far enough. I believe that cross-section, contemporaneous accounting data for different firms or plants give little if any information on so-called economies of scale. Smith implies that difficulty arises because the observed phenomena do not correspond directly ~ v i t hthe theoretical constructs because there is no single, homogeneous product, and so on. I believe that tlle basic difficulty is both simpler ancl more fundamental; that the pure tlleory itself gives no reason to expect that cross-section data will yield the relevant cost curves. Some of the bases for this view are syggested by Smitll in his cliscussion, but lle stops short of carrying them to their logical conclusion. YO SPECIALIZED FACTORS O F PR0DI:CTION

Let us consider first the simplest theoretical case, when all factors of procluction are unspecialized so there are numerous possible firms, all potentially alike. This is the model that implicitly or explicitly underlies most textbook discussions of cost curves. For present purposes, we may beg the really troublesome point about this case-why there is any limit to the size simply assume that there is some resource (entrepreof the firm-and neurial ability) of which each firm can have only one unit, that these units are all identical, and that the n u m l ~ e rin existence (though not the number in use) is indefinitely large, so all receive a return of zero. In this case, the (minimum) average cost at ~vhiclla particular firm can produce each alternative hypothetical output is clearly defined, independently of the price of the product, since it depends on the prices that the resources can conlmantl in alternative uses. T h e average cost curve is the same for all films ant1 independent of the output of the industry, so the long-run supply curve is horizontal and hence determines the price of the product.Vn the absence of mistakes or changes in conditions, all firms ~voulclbe identical in size and could operate at the same output and the l d determined by condisame average cost. T h e number of firms ~ ~ o u be Page? 1 4 6 5 1 are reprinted from my "Comment" on Caleb -4. Smith'? "Survey Co?:centrntion and Price of thc Empirical Evidence on Economies of Scale," in I3:~sine.i~ Policy (Princeton I.ili\crsity Press, for the r a t i o n a l Bureau of Economics Research, l9,5,5), p p . 230-38, b! permission of the publi?her; copyright 1055 by Princeton University Press. 6. T h i s i~eglccts?ome minor qunlifications, of which two may deserve explicit mention: Grit, the irrelevance of the output of the industry depends ?on~ewhato n the prec i ~ eassrlmpticin? about the Yorlrce of an! increased demand; second, strictly speaking, the \upply c u r l e n:aY have tiny \cn\es in it attributnhle to the finite number of finns. On the first point, see Richard Rrumberg, "Cetrvis Pnrihus for Supply Curves," E:cnomic J o : ~ n t n(June l 1953): 462-63.

tions of demand. I n this model, the "optimum" size firm has an unambiguous meaning. Suppose this model is regarded as applying to a particular industry. Differences among firms in size (however measured) are then to be interpreted as the result of either mistakes or changes in circumstances that have altered the appropriate size of tlle firm. If "mistakes" are about as likely to be on one side as the other of the "optimum" size, the mean or modal size firm in the industry can be regarded as the "optimum"; but there is no necessity for mistakes to be symmetrically distributed, and in any event this approach assumes the answer that cross-section studies seek. What more, if anything, can contemporaneous accounting data add? Can we use them to compute the average cost curve that was initially supposed to exist? Or even to determine the size of the firm with minimum average cost? I think not. Consider a firm that made a "mistake" and is in consequence, let us say, too large. This means that the average cost per unit of output that would currently have to be incurred to produce the firm's present output by reproducing the firm would be higher than the price of tlie product. I t does not mean that the current accounting cost is higher than the price of the product--even if there have been no changes in conditions since the firm was established, so that original cost corresponds to reproduction cost. If the firm has changed hands since it was established, the price paid for the "good will" of the firm will have taken full account of the mistake; the original investors will have taken a capital loss, and the new owners will have a level of cost equal to price. If the firm has not changed hands, accounting costs may well have been similarly affected by write-downs and the like. I n any event, cost as computed by the statistician will clearly be affected if capital cost is computed by imputing a market return to the equity in the firm as valued by the capital market. I n short, differences among contemporaneous recorded costs tell nothing ahout the ex ante costs of outputs of different sizes but only about the efficiency of tlie capital market in revaluing assets. I n tlle case just cited, data on historical cost would Ije relevant. However, their relevance depends critically on the possil3ility of neglecting both technological and monetary changes in conditions affecting costs since the firms were established. A-lmore tempting possil~ilityis to estimate reproduction costs. This involves essentially depa.1-ting from contemporaneous acrounting data and using engineering data instead, in wllirh case there seems little reason to stick to the particular plants or firms that happen to exist as a result of llistoriral accidents. Under the assumed conditions, the unduly large firms would be converting themselves into smaller ones, the unduly small firms into larger ones, so that all would be converging on "the" single optimum size. Changes over time in the distribution of firms by size might in this way give some indication of the "optimum" size of the firm.

T h e Law of Variable Proportions

147

SPECIALIZED FACTORS OF PRODUCTION

T h e existence of specialized factors of production introduces an additional reason why firms should differ in size. Even if output is homogeneous, there is no longer, even in theory, a single "optimum" or "equilibrium" size. Tlle appropriate size of firm to produce, say, copper, may be different for two different mines, and both can exist simultaneously because it is impossible to duplicate either one precisely-this is the economic meaning of "specialized" factors. Or, to take another example, Jones's special forte may be organization of production efficiently on a large scale; Robinson's, the maintenance of good personal relations with customers; the firm that gives appropriate scope to Jones's special ability maybe larger than the firm that gives appropriate scope to Robinson's. It follows that in any "industry," however defined, in which the resources used cannot be regarded as unspecialized, there will tend to be firms of different sizes. One could speak of an "optimum distril~utionof firms by size," perhaps, but not of an "optimum" size of firm. T h e existing distribution reflects both "mistakes" and intended differences designed to take advantage of the particular specializetl resources under the control of different firms. Tlle existence of specialized resources not only complicates the definition of optinzzim size; even more important, it makes it impossible to define the average cost of a particular firm for different hypotlletical outputs independently of conditions of demand. T h e returns to the specialized factors are now "rents," at least in part, and, in consequence, do not determine the price, but are determined 1)y it. Take the copper mine of the preceding paragraph: its cost curve cannot be computed without knowledge of the royalty or rent that must he paid to the owners of the mine, if the firm does not itself own it, or imputed as royalty or rent, if the firm does. Rut the royalty is clearly dependent on the price at which copper sells on the market and is determined in sucll a way as to make average cost tend to equal price. T h e point at issue may perhaps be put in a different way. T h e long-run conditio~lsof eq~iilil~rium for a competitive firm are stated in the textbooks as "price equals marginal cost equals average cost." Rut with specialized resources, "price equals marginal cost" has a fundamentally diffrom "price equals average cost." T h e ferent meaning and sig~lifica~lce fil-st statement is a goal of the firm itself; the firm seeks to equate marginal cost with price, since this is equivalent to maximizing its return. Tlle second statement is not, in any meani~lgfulsense, a goal of the firm; indeed, its avoidance could wit11 more justification I)e said to be its goal, at least in the meaning it would be likely to attach to average cost. Tile equality of it; of price to average cost is ;I result of equilibrium, not a determi~la~lt it is forced on the firm by the operation of the capital market or the market determining rents for specialized resources.

Consider a situation in ~ l h i c la~group of competitive firms are all appropriately adjusted to existing conditions, in which there is no tendency for firms to change their output, for new firms to enter, or for old firms to leave-in short, a situation of long-run equilil~rium.For each firm separately, marginal cost (long-run and sllort-run) is equal to price-otherwise, the firms would be seeking to change their outputs. Suppose that, for one or more firms, total payments to hired factors of production fall short of total revenue-that average cost in this sense is less than price. If these firms could be reproduced by assembling similar collections of hired factors, there would be an incentive to do so. T h e fact that there is no tendency for new firms to enter means that they cannot be reproduced, implying that the firms own some specialized factors. For any one firm, the difference between total receipts and total payments to hired factors is the rent attrillutable to these specialized factors; tlle capitalized value of this rent is the amount that, in a perfect capital market, ~vouldhe paid for the firm. If the firm is sold for this sum, the rent weuld show up on the hooks as "interest" or "di\~idends."If it is not sold, a corresponding amount .rzrould he inlj ~ ~ ~ as t e ad return to the "good-will" or capital value of the firm. T h e equality between price and average cost, in any sense in ~vhic11it is more than a truism, thus reflects competition on the capital market and has no relation to the state of competition in product or factor markets. For simplicity, the preceding discussion is in terms of a competitive industry. Clearly, the same anal!sis applies to a monopolistic firm wit11 only minor changes in wortling. T h e firm seeks to equate marginal cost ant1 marginal revenue. T h e capital market values the firm so ;is to make average cost tend to equal price. Indeed, one of the specialized factors that receives rent may be whatever gives the firm its monoj~olisticpower, be it a patent or the personality of its owner. It follows from this analysis that cross-section accounting data on costr tell nothing about "economies of scale" in any me;iningful sense. If firms differ in size because they use different specialized resources, their average costs will all tend to be equal, provitiletl they are properly computed so as to include rents. TVllether actually computed costs are or are not equal can only tell us something about the state of the capital market or of the accounting profession. If firms differ in size partl! because of mistakes, the comments on the preceding simpler nlotlel appl!; historical cost data might be relevant, but it is dubious that current accounting cost data are. And how do we know whether the differences in size are mistakes or not? T H E D E F I N I T I O N O F COST

T h e preceding discussion shares with most such discussions the defect of evading a precise definition of the relation between total costs and total receipts. Looking forward, one can conceive of defining the total cost of producing various outputs as equal to the highest aggregate that the re-

T h e Law of C'uric~blrP ~ o p o r t i o n s

149

sources required could receive in alternative pursuits. Total cost so estimated need not be identical ~ v i t harlticipatecl total revenue; hence ex ante total cost, so defined, need not equal total revenue. Rut after tlle event, how is one to classify payments not regarded as cost? Does some part of receipts go to someone in a capacity other than as owner of a factor of production? All in all, the best procedure seems to me to be to define total cost as identical with total receipts-to make these the totals of two sides of a clouble-entry account. One can then disti~lguishbetween different kinds of costs, the chief distinctio~lin pure theory being betwee11 costs that clepe~ld on what the firm does but not on how its actions turn out (contractual costs) and the rest of its costs or receipts (noncontractual costs). T h e former represent the cost of factors of production viewed solely as "hired" resources capable of being rented out to other firms; the latter represent payment for whatever it is that makes iclentical collections of resources different when employetl by different firms-a factor of production that we may formally designate ~ n t r e p v e n e lvli c l l c a p a c i t y , recognizing that this term gives a name to our ignorance rather than dispelling it. Actual noncontractual costs can obviously never Ile known in advance, since they will be affected by all sorts of accidents, mistakes, and the like. It is therefore important to distinguish further betxveen espected ancl actual noncontractual costs. Expected noncontractual costs are a "rent" or "quasi-rent" for entrepreneurial capacity. They are to be regarded as the motivating force behind the firm's decisions, for it is this ancl this alone . h e difference 1,etTveen espected and that the firm can seek to m a s i m i ~ eT actual noncontractual costs is "profits" or "pure profits"-an unanticipated residual arising from uncertainty. Definitions of total costs that do not require them to equal total receipts generally equate them either ~ v i t hcontractual costs alone or with expected costs, contractual and noncontractual, and so regard all or some payments to the entrepreneurial capacity of the firm as noncost payments. Tlle difficulty is, as I hope the preceding tliscussion makes clear, that there are no simple institutional lines or accounting categories that correspond to these distinctions. Snlitll mentions the possibility of relating cost per dollar of output to s i ~ e Presumably . one reason why this procedure has not been follo~vedis that it brings the problems ave haye been discussing sllarplp to the surface and in consequence makes it clear that notlling is to be learned in this Tvay. If costs e x p o s t are defirletl to equal receipts P X pcst, cost per dollar of output is necessarily one dollar, regardless of size. Any other result must imply that some costs are disregarded, or some receipts regarded ar noncost receipts. Generally, the costs disregarded are capital costs-frequently called p,.ofit.r. T h e study then simply shoaj~shoav c;ipital costs vary with size, avllich may, as Smith points o~ct,merely reflect systematic clifferences in factor combinations according to size. One could, with equal validity,

study wage costs or electricity costs per unit of output as a function of size. T h e use of physical units of output avoids so obvious an objection; clearly it does not avoid the basic difficulty and, as Smith points out, it introduces prohlems of its own. T h e heterogeneity of output means that any changes in average cost with scale may merely measure changes in the "quality" of what is taken to be a unit of outpllt, Insofar as size itself is measured by actual output, or an index related to it, a much more serious hias is introduced tending toward an apparent decline of costs as size increases. This can most easily be brougllt out by an extreme example. Suppose a firin produces a product the demand for ~ v l ~ i chas h a known t~vo-year cycle, so that it plans to produce 100 units in year one, 200 in year two, 100 in year three, etc. Suppose, also, that the hest way to do this is by an arrangement that involves identical outlays for hired factors in each year (no "variable" costs). If outlays are regarded as total costs, as they ~vouldbe in studies of the kind under discussion, average cost per unit will ol~viously be twice as large when output is 100 as when it i s 200. If, instead of years one and two, we substitute firms one and two, a cross-section study ~vould sho~vsharply declining average costs. TZ'lien firms are classified by actual output, essentially this kind of bias arises. T h e firms with the largest output are unlikely to he producirig at an unusually low level; on the average, they are clearly likely to be producing at an un~rsuallyhigh level, and conversely for those that have the lowest output.' SIZE DISTRIBCTION O F F I R M S

I t ma? nell be that a more promising source of information than crosssection accounting data would he the temporal h e h a ~ i o rof the d ~ s t r i l ~ u tion of firms 11? sire. If, oler time, the distril~utiontends to 11e lelati\el\ stable, one might conclude that this is the "equilibrium" distribution and defines not the optimum scale of firm but the optimum distril~utionIf the distlibution tends to become increasingl) concentrated, one might conclude that the extlemes represented mistakes, the point of concentration the "optimum" scale, and similarl? ~ v i t hother changes TZ7hether,in fact, sucll deductions nould be just~fieddepentis on how leasonal~leit is to ~-ocliictio~l: th:it i i , rhc i r i tlifference c1irL.e (or tn.;ulsfoi-rnation c~trve)slio~ving-tlle ~ ~ ; l r i o ucombinas tions of, say, S aritl I' that can be producetl \\.it11 an!- given quantities of arid R will he a straight line as i n Figure 8.1 for 100 units ol A ant1 100 units of R. Clearly, X ancl 1-must. sell for the s ; ~ m price ~ in a free market, :rnd similarly for the other comnloclities. n o matter xvlnat q11;tntities of them are pro-

T h e Theor) of Distribution zoith Fixed Proportions

167

Quantity of Y

duced. T h e relative demands for them ~villdetermine the quantities produced 11ut will have no effect on their price. T h e fact that there are different commodities, therefore, is unimportant on the side of demand for factors of production. Since their relatil~eprices are always rigidly fixed, it is as if there were only one commodity, say Z. This simple case illustrates ail important general point, namely, that substitution in production is an alternative to substitution in consumption and vice versa. Let us now construct a derived demand curve for factor R along the lines of orlr joint demand analysis. T o do so, we need the demand curve for Z and the supply curve of A. How shall TVC draw the de~nantlcurve for Z, the single co~nmodityin the community? Our analysis is concerned wit11 relative prices, not al)solute prices, since we have inti-oduced no "ruoney" into the economy, so this question involves decidiilg on the "numeraire" in terms of which to express prices. Since our f u ~ l d a ~ n e n t aproblem l is the tlivision of the total output among the cooperating factors, and since, thanks to fixed relative prices among final proilucts (wliicli justifies our treating them all as a sirigle product), there is no prol~lemh o ~ vto measure o l ~ t p u t it , seems convenient to express the prices of factors of p r o d ~ ~ c t i o n in rcrms of the final product: i.e., to take Z a s a nninei-aire. Rut tlleil the price of Z in terms of itself as numei-aire is c1e;rrly rlnity by definition, no inatter 1 1 0 ~mltcll ~ or little Z there is. But this means that (hp defiuitioil) the clemarld curve for Z is a 1101-izontal line at a price of unity, as in Figure 8.2. l\:llat of the supply c ~ ~ r vofc -41There is presumal,ly some ~naximuin flo~rof X that can he ~ u a d eavailable to the production of this commodity, s 2 ~ 100 jlei i ~ i l i i ttime. If we stick riqorously to the assumption that Z is tlie onl! final pi-oduct, there is nothing else that tliese services can be used for, and llerlce they \trill be availal~lefor this use at any price, i.e., the supply crlrr-e of A ~villbe perfectly inelastic for any 13ositix.e price, and perfectly elastic at a price of zero. It is drawn as OFG in Figure 8.2. (The elasticity of tlie supply curve of factors to the market as n xvhole rcflccts the existence of ilonmarket uses of productive services, here ruled out by definition.)

Price relative to the price I of Z

I/

Supply o f A

per unit time per unit time

By our preceding analysis, the demand for B is given b y tlle vertical difference between the demand curve for Z and tlle supply curve of A, which yields a demand curve for B as in Figure 8.3. Note that this demand curve is nearly identical with the value of the marginal product curve for B. Given 100 units of A, the niarginal product of B is unity so long as the quantity of B is less than 100, 0 thereafter. T o get the equilibrium price of B, we need to know the supply curve of B. As in the case of A, it will I)e perfectly inelastic at any positive price, so it can be tlescribctl hj. a single e r nnits of B available per unit time is less number. Suppose the n ~ ~ r n b of than 100. T h e supply curve of H (S,, in Figure 8.3) will then intersect tlle demand curve for B at PI or at a price of 1, so the equilibrium price ~ v i l he l equal to unity for B, ~cl-liclimeans, of course, 0 for A (as can be sllown directly- by carrying through the snrne analysis for it). If tlle irrpply of R is greater tllan 100 (S'B in the above diagram), the supply curve intersects the demand cur\-e at P,, implying a price of 0 for B and of unity for A. Price relatlve to t h e price of Z

I

S~

I

S'B

T h e T h e o r y of Distribulzon with Fixrd Pioportions

169

These two cases are relatively simple and straightforward. If one or the other of the factor5 is so plentiful relative to tlre other that not all of it can be used, then in the absence of combinatiorl (implicitly ruled out in drawing our supply curves) it will I)e a "free" good. But what if the quantity of B available is precisely the same as that of A, i.e., 100 in the example? T h e supply and demand curves will then be as in Figure 8.4. Clearly any price Price r e l o t i v e t o price of Z

i Supply of B I

1

... . ..... . . ...... ............... .... 0 100

Quantity of B per u n i t t i m e Demond f o r B

of B not greater than 1 01 less than 0 is consistent with equilibrium. G i ~ e n the p i c e of B, i a j P,,, the plite of A will cleailv 11e P, = 1 - P,, since the total amount to be di~ideclbetween li-\ ant1 1B is one unit of Z, the amount they produce. This solution is unclerstandable: we have no way of determining the separate contributions of X ant1 B to the total l~roduct,lience no way on grounds of their marginal contril>utions of determining their separate economic value. Only ;I bundle of an A plus a B is an economically rneaningful unit. T h e product of such a unit is 1, so PA + P, = 1. Any values of PA and P, such that they add up to unity will do. There are an infinite number of values that are compatible with this type of equilibrium. Economic forces as such do not dictate a unique pair of values for PA and P,. They merely set u p limits, i.e., that PA P, = 1. T h e actual values of PAY and P, depend on other factors. If no "noneconomic" considerations are relevant, it is irrelevant how the total of unity is divided between a partnership of an A and a B, for only the combined unit is significant, just as it is of little significance what part of a man's wages is to be attributed to his right hand and what to his left. Tlie problem of the division of the product between A and B is significant only if there are noneconomic considerations that make the distinction of an A from a B significant. I n this case, these noneconomic considerations will completely determine the division; we will have the relative returns determined by "pure bargaining," as it were.

+

We have introduced pure bargaining to explain the division of the product between A and B only when their supply curves coincide. But, it may be asked, may we not also have to introduce it when the supply curves do not coincide, because the implicit assumption that there is no coalition among the A's or among the B's will be invalid? If, say, the quantity of A available per unit time is 150, but of B only 100, cannot the owners of A (call them A's) secure a return above 0 by forming a coalition? Suppose, for a moment, they do, agreeing to divide equally among themselves any amount they get, and suppose for the moment that they succeed in getting 9/ 10 of the product for themselves, so each of tlle 100 units of B (who do not, we suppose, form a coalition) gets 1/10 of a unit of Z, while the coalition of 150 units of A gets 90 units of Z. Is this a stable position? Clearly not, so far as economic considerations are concerned. Each A separately is receiving 6/ 10 of a unit of Z, each B, 1/ 10 of a unit of Z. Clearly there is an incentive for an A and a B to get together outside the coalition. T o each A separately, it appears that if he leaves the coalition wllile the others stay, he can bribe a B to depart from the coalition and still have sometlling more left for himself, since the total product of the A and B partnership outside the co;tlition will be 3/ 10 of a unit greater than the sun1 of their returns so long as the coalition is unbroken. This means that the coalition of the A's is unstable, and that economic forces will be perpetually tending to dismpt even if it once is established. So far, we have considered a world in which tile proportions of factors of production are not only fixed in each intlustry but also the same in all industries. Let us now suppose that while fixed in each industry separately, they are not the same in all industries. As the simplest case, tve may s~1ppose two sets of industries. Call tile (composite) product of one set X, the other Y, and assume that it takes one unit of A plus one unit of R to produce one unit of X, 2nd one unit of A plus t ~ v ounits of B to produce one unit of Y. These pl-otluction conditions will ~ i e l t al l~rocluctionpossibility curve like that in Figure 8.5 for 100 units of h antl 150 tlrlits of 13. Except at P,, not all units of X or of R are used. Between Y, and P I , some units of A are unemployetl, between P, and X I , seine units of R . Clearly in either of these sectors, we are back i;l our earlier problern. Betxz7cenI', ancl PI, the price of -4 will be zero, the rate of substitution of X for Y rvill be fixed by the number of units of R requiretl and will be t ~ v o units of X for one unit of i',so :he price of 'li will be tivice the price of X. Bet~veenPI antl X I , tlie price of B will be zero, the rate of sul~stitt~tion of X for Y will 11e fixed 11). the number of units of X required and will be one unit of X for one unit of Y , so the price of X ~villequal tlie price of Y. \ZT1iether tlie final e c ~ u i l i l ~ r iwill ~ ~ mbe in one of these sectors will depend on co~ltlitionsof demantl. If .rve suppose Figure 8.5 to be for one inclivitlual (in a society, say, of itlentical individuals), we c.zt11 superimpose on it tlle

The Theory of Distribution with Fixed Proportions

171

Quantity of Y

'I;

0

50

100

Quantity of X

consumption indifference curves of the intli\itlual, u ~ h i c hyields the three possibilities summarized in Figure 8.6.

I n (I), tlie point of eqnilihrium in\ olves tlie uriemplo!-merit of sonic '4, 1ienc.e a price of zero for .I;in ( I I ) , tlie ~ ~ l i e m p l o ) - n ~ofe nsome t B, llencc a price of zero for 13. Tlicse are escnti:rlly the same ;IS o u r earlier case. 111(I), it is as if we h a d one coinmotlit), tlie quantit) of ~ v l i i c w;ts l ~ obtninetl 11)t r e a t i l ~ gt ~ v o11rlit~of X ;IS cq~l;tlto one unit of Y; i n (11). as if Tve hilt1 one c o m m o t l i t ~ ,the q l ~ a n t i t yof ~vliicliwas ohtained 1)y treating one unit of X as e q ~ i n to l one u n i t of IT.In either of thebe c;tses, tlelnantl, as it were, determiiles only the relative quantities o f X ant1 Y, ;tnd p i - o d ~ ~ c t i oconclin ions deicrlllll~erelatii-e price$. T h e interesting case is (111). I-lel-e pl.otluctioil conditions cleterrnine rclntive quantities a n d demand conditioi~si.elative price. T h e price of 'k' is sornewl~ei-ebetween tlie price of X and t~vicctlie 111-ice of X, tlie exact point depending o n ~t-llatprice ratio ~ v i l lind1lc.e tllc public to consume thc same amount of X as of Y. Suppose tli~ltit took ;r price of 1-thar was 1.6 times the price of X to irlduce the public to consume tlic sitme amount of X as

of Y. Let p,, p,, pa, p,,, he the price of X, Y, A, and B respectively. I t urould then follow that:

or, substractingequation (1) from equation ( 2 ) ,

which, from equation (I), means

These prices are equal to the maryinal product of A and R iespectixel~a t the malgin. If a unit of A is added, it can be emploved b j procit~c~ng one fewer units of Y, ~vllichwill release one unit of A and two units of R, and two additional units of X, which xi11 require the two units of A a i d two units of B a~ailable.T h e maiginal product of h is tlie~eforetwo units of X minus one unit of Y, 01 in ~ a l u eterms, 211, - p, = 4 p , Sirnilall), tlie marg-inal product of B is one unit of Y minus one unit of X, or, in kalue terms, p, - p, = .6p,. Mole generally, we can deli\? tlie ma1 qinal protluct of e'lcli factoi aild the \slue of the inaiginal product f o ~different amounts of it, i e , me c,tn deiixe marginal produc titity cutves, whicli in this c'isc will also be demand tulles for the fact01 Considel, fi~st,the marqinal p ~ o d u c tof A, giver1 that theie ale 150 units of B If we think of adtling- units of A to the 150 units of B, we hale a choice n1ie11 we use the first unit of 4 wlletliel to combine it with 2 R to produce one unit of 1' oi witli 1 B to p~otluceorle unit of X, or partly one and pnl tl) the other Since, 11ndei these coritlitions, the late at which Y can be 5nbstituted foi X is one to one (since B is supelabundant), the plice of X and of Y uoulcl h n ~ to e be the same if both ale to he ploduced. By our cor~ventionof taking the pilce of X as the numerai~e, the price of both will be equal to 1 arld so will total income NOT+,tt tliese prices and this income, coilditions of demand ("~~tilitx functions") will tletermir~eh0J4, the first unit of X mill be d i ~ i d e dhet~veerl~,rotluctionof X and of Y. At one extleme, consumeis might prefe~0111) Y,at tlie o t h e ~ , onl) X. I n either of tliese extieme cases, the price of onl) oilc of the products %ill be defined, but exen when t l i ~ sis the price of Y, it will be simplest. anti xnlicl, to regard it a\ equal to 1 \lore yeneralll, the consurners will distribute their unit irlcome among both products, so hot11 will be produced. I n all t h e e cases, howeler, the marginal product of X is unity at the outset. Let us continue to add units of A. FOI a time, it is clear, everything is the same as when the first unit is applied to the 150 units of B. B is supere the marginal product abundant, so X and Y ale equal in price, the ~ a l u of

T h e Theory of Dictribution with Fixed Proportions

173

of a unit of X is unity, the physical product being divided between X and Y in proportions dictated by demand. How many units of A must be added before a point is reached at ~.rrl~ich B is no longer superabundant. hence no longer a free good? Clearly this depentls on conditions of demand. If at a price of unity for both, X is in much greater demand tlian Y, so the bulk of each increment to total output is composed of X, then B will not become a "limitational" factor until close to 150 units of A have been added to the 150 units of B available. At the other extreme, if at a price of unity for both, Y is in much greater demand than X, so the bulk of each increment to total output is composed of Y, then R will become a "limitational" factor when slightly more than 75 units of A have been added to the I50 units of B a\ ailable. T o be concrete, let 11s sllppose that demand conditions are summarized by

This "demand cuire" iinplies that the iatio of Y to X depends only on the piice ratio of the two produt ts ant1 not on the absolute level of income If p, = the ratio of X to Y is 518, whit11 means tirat in the initial pha?e, as urilts of A ale added, 5/ 13 of eat11 unit is used to prod~ice5/ 13 of a unit of X; 8/ 13 of each unit to pi otluce 8/ 13 of a unit of Y. So long as this coiitinues, the amount of R iequired is g i ~ e nby

~vllelea is the 'imount of A ernplojed, b the amount of B required. Tliis can continue so long as the a m o ~ i nof t B required is less than 150, i.e., until

'it ~tllicllpoint 35 5 / i units of X antl 57 1/7 units of Y ale being procl~~ced.

Once this point has been ieacheci, furtller units of A can no longei he emploIed in this fashion. An extra unit of 4 tan be employed only b j producing one unit fewer of \/, antl using the unit of 1 and 2 units of B theielq relensed togethe1 ~ i t l the i ,idclitional unit of X to produce two units of X. In ph\sic,il terms, then, the marginal product of A becomes two runits of X minus one unit of Y. At the prices of X and Y prevailing when this point is reached, namely p, = p, = 1, the 1 alue of the marginal product 1. T h e set of utility furlctions that will yield this demand curve is given by 8

V = ~ ( x y z )where , F'

> 0.

is 2p, - p, or unit) as before. But as additional units of A are added, the prices of Y and X cannot remain the same, for the quantity of Y is declining ielative to the quantit) of X, so the price of Y must rise relative to the price of X in order to induce consumers to buy Y and X in the proportions in which they are being made available, which means that the value of the marginal product of A declines. Additional units of A will be used to produce two additional units of X and one fewer units of Y so long as the >slue of this combination is positive, i.e., so lollg as the price of one unit of Y is less than the price of two units of X. \\'hen p , 1)ecomes equal to 2p,, tlle value of the marginal pioduct of A is zero, and additional units of A I\ ill not be used at all. I n our special case, when a 2 92 6/7, the amount of X produced will be equal to

Inserting equations (7) and (8) into equation (3), the price of Y will be

(9) so that

(10) Value of marginal protlt~ct= 213, - p,

11 2700 This xvill be equal to zero when a = -- = 103 -. 26 13

Tile 1.esulting value of marginal product curve is given in Figure 8.7. T h e valne of the margirlal 1j1.otluct is unit) when the quantity of .I is 92 6/7 01- less, declines at an inc.1-e;rsing rate from 92 ( i i 7 to 103 11/ 13, and is 0 thereafier. If tllc alllourit of X av;iilable is 100, as earlier assumed, the price of .1is :I, as shown 11). the intersection of tile supply curve arid tile value of marginal prodnct c11rve. This curve is of course valid only if b is equal to 150. By exactly tlle same procedure, the v;tlue of marginal protll~ctof B can be derived, and you will find i t a useful exercise to go tl~roughthe ai-ithmetic of deriving it. T h e indeterminac) that arose \\.hen the proportions were botlr fixed and the same in different industries is entirely clinlinatcd 1)): the existence of 2. These equations ran he checked most rcadilv 1,y noting that they refer to the int e r ~ a lin ~vllichall units of ;\ and of H are used. T h e amount of A used is given by s 'y r a; the aniouilt of R b y x 1 27 = 150, in the case i n cluestion. Solving these two e q ~ ~ a t i o gives n s (7) and (8)directly.

T h e Theory of Distributzon with Fixed Proportions

175

Value of the m a r g i n a l product of A r e l a t i v e to t h e p r i c e of X

two alterriati-ce ploportion5 in wl~iclithe factois can be combined, as can be see11 f ~ o mthe preceding figu~e.If the quantity of '2 is less than 92 6/7, its price is unitv (the p ~ i t eof B is relo): if the quantit) of '1 is greater than 103 11/ 13, its plice is 0 (tile piice of B is unity); if the quantit\ of A is be2700 - 26a tween 92 617 and 103 l l / 13, its price is given by or the ordi5(150 - a ) ' nate of the cur-ce plotted in Figure 8.7 There no longer remains any scope for a "pure bargaining" theory of wayes.

The Theory of Marginal Productivity and the Demand for Factors of Production

Tlie case just considered-of fixed proportions zunong tlle factors of production in each industry sep;lrately-is a special case of tile general theory of marginal productivity. In that special case, an increase in the supply and coiisequeilt reduction in price of a particular factor increases the quantity of the factor demanded solely through st~1)stitutioiiin consumption: the lowered price of this factor makes the products in wllose production it is relatively important cheaper reli~tiveto otller products, and this leatls coilsumers to substitute them for tlie other protlucts. More generally, also take place in protlt~ctiori.For each product sepasubstitution ~~vill rately, protluccrs will l1:i~ean incentive to substitute tlie relatively clieaper factor for others, arlcl in general it is possible to tlo so, at least to some extent. T h e "theory of marginal productivity" is sornetimes described as the "tlieory of distribution." This statement is inisleatling. T h e tlieory of marginal productivity at most analyzes the factors affectirig the demaild for a factor of production. T h e price of the factor depends also oil coilditioils of sul~ply.Tlie tendency to speak of a "marginal productivity theory of distribution" arises because in many problems and contexts it is useful to think of the supply of factors of production as given quantities, as perfectly inelastic. This is particularly relevant if the problem concerns hot11 market and norlmarket uses of factors of prodtlction. I n sllcll cases, there is a sense in which supply conditions determine only the quantity of the

T h e Theory of 'Lfarginal P)oducti.ciity

177

factors, while demancl collditions (sun~inarizedin the phrase marginal p~oducti-ciit?~) determine price. But note that ever1 in this case a change in supply-in the fixed amount of a factor-will change the price of the factor, unless tle~nandis perfectly elastic. So it will be better in all cases to regard the theory of marginal productivity as a theory solely of the demand for factors of protluction. X complete theory requires a theory of 11otl1the demand for and the supply of factors of production. I n tlle main, the marginal productivity theory is a way of organizing the considerations that are re1ev;int to the demand for a factor of production. I t has some, but not very much, substantive content. This is reflected in our ability to speak of an abstract factor of protl~~ction-factors A or R, etc.-without having to specify it any further. T o say that wages are equal to the value of tlie marginal prodrict, for example, sals relatively little in and of itself. Its function is rather to suggest what to look for in further analysis. Tlle value of tlle rnarginal protluct is not a single number tleterlniiled by forces outside the control of intlividuals or society; it is rather a schedule or function of many varia1)les. I t will depend on the quality and quantity of workers, the quantity of capital they have to work with, the quality of the management organizing their activities, the institutional structure of tlie markets in \\-llicll they ai-e hired and the product soltl. etc. I n concrete applications, the basic substantive issue is likely to be what tletcrmines tlle ma]-gin;tl protll~ctivityand how the changes under corisiileration will affect it. Tlle analysis of tile demaild for factors o f p r o d ~ ~ c t i oisn closely relatetl ro thc analysis of tlle supply of products, and, indeed, is really only another .rv:ry of looking a t or organi7ing the same material. Iri analyzing the supply cli1.T.e of a protiuct, Ice ar-e interejtecl in tracing the effect of cllanges in the dcn1;intl for it rintler given conditions on the factor markets. hl conse) ~ the i t firm or inclustry ant1 take quence, we direct attention to tlle o ~ 1 ~ 1 of tor ::]-anted tlie clzanges in the quantity of the T-ariorisfactors of protluctioin employetl and in tlleii- prices as clemand for tile p~odrtctand ~vit!lit oittput of the protluct change. Ti1 tlistriljutiori t11eo;l.y~our interest centers in t l ~ e factor ~n;irkets,;ind so T\-econc-entrirte atterltion on a tliffercnt facet of the saine ;idjustme~it1)y t l ~ efirm. 7-0 p u t it dinerently, the statement that ir. fil-nl seeks to equate mal-ginal f;ictor cost to marginal valae protluct is anot11er -iva)- of baying that it seeks to equate nlargiual reyenue t o ~rl;tigin:il cost rather til;ill a n ;ttlditional contlition or1 the equi1il)riun of the firm. ; 2 ~ tile i!li.o:~, 0,E 5::t-.1J1:, o[ p r ~ < ! ~ c [ iherc ,, 32-6.i-i-~y,~.l cliffr:rfy;r li.;y;'? of an:!l)sl\, :tilt1 the clernand c1iri.c ~ i i l lchniigt- :I, we shift our point of 1-iewfrom the rc;lctions of the firm to tile reactions of an inclustry. ;Znd in this case, there is also a tllirtl le~.eltllat is significant, the economy as a \z,llolc, bince rrran)- iliffei.eilt ind~istrie,may employ crhat for any p:ir?icu1ar problem it is useful to regnrcl ;is ;i sirigle factor of production. T h e clemand curve for a factor of production by a particular group of

demanders (which may as a special case be a single firm) shows the maximum quantity of the factor that will be purchased by the group per unit of time at each price of the factor, for given conditions. As in previous problems, there is some uncertainty how it is best to specify the "given condi"state of the tions." They clearly include (1) technical knowledge-the arts" or the production functions of actual and potential firms; and (2) the conditions of demand for the final producst. Tile uncertainty attaches primarily to the handling of other factors of production. One proceclure is to take as given (3) the supply curves of other factors of production to the group of demanders considered. T h e problem with item 3 is that at least for the economy as a whole, constant supply curves for other factors may mean an increase in the total resources of the community as we move along the demand curve for this factor in response to an increase in its supply. T h e alternative is to take tile "total resources" of the community, appropriately defined, as fixed, and thus to regard changes in the supply of this factor as changes in its supply relative to other factors but not in the total resources of the community. Mre shall for the most part beg this question, since most of our discussion wold be unaffected by its resolution. I t should be noted that the precise meaning of items 2 and 3 as stated above depends on the particular group of demanders considereti. T o a firm selling its product on a competitive market, item 2 is equivalent to holding the price of the product constant; to an industry producing a single product, it is equivalent to holding the tlemand function for the product constant. T o a firm, item 3 is equivalent to holding constant the p r i r ~of . r other factors that it buys on competitive markets, and the szlpply r ~ ~ r o eof factors. I n particular, it is equivalent to holding constant the amorlilt of "fixed" factors. T o an industry, item 8 may still be equivalent to hol(1ing constant the price of some factors, namely those of u~hichthe industry as a whole buys only a small part of tlle total, so that tlie supply curve of tlie factor to the industry is effectively Ilorirontal. T o the economy as a wliole, especially if this is regarded as including tlie nonmarket as well as the market sector, item 3 may be equivalent to holtling tlle quantities of otlier factors constant (though this obviously depends critically on how the uncertainty about itern 3 is resolved). Note also that the difference between short- and long-run demand curves is in the precise content of items 2 and 3. Finally, the list of "other things" is not exliausti\,e for all prol~lems.For many problems, for example, it xvill be desirable to give special cc)rlsiileration to closely related factors of production. T h e Indi-oidllnl Firm In analyzing tlie denland for factors of production 11.r the individual firm, Me ma) again start with the fundamental equations tlefining its equilibri~inlposition:

The Theory of Marginal Productivity

(1)

1 - MPP, lClR - MFC,

-

179

MPP, MPP, - 1 - -- . . . MFC, MFC, MC

If there is competition on the product market, MR will, of course, be equal to the price of the product or p,; if a factor is purchased on a competitive market, its marginal factor cost will, of course, be equal to its price. For the time being, we may suppose that any factors are either purchased competitively, so that we can replace their marginal factor costs by their prices, e r are "fixed" to the firm, so that we can regard the quantity (or maximum quantity) available as given. T h e shorter the run, the larger the number of factors the available quantity of wllicll are to be regarded as given, ant1 conversely. Indeed, as we saw in the discussion of supply, this is essentially the definition of lerlgth of run. From a purely formal point of view, the demand curve for a factor of production by an individual firm can be derived immediately and directly froin equations 1 and 2. Let the firm be selling on a competitive market, let factors A, B, . . . be purcllased competitively, and A', R', . . . be the factors ~vhosequantities are fixed to the firm for the run considered. Then the demand curve for, say, factor A, will be given by

w11ei-e a', G', . . . stand for the fixed quantities of these factors available to the firm. Now this equation is simply a rearrangement of equations 1 and 2. For any given set of values of the independent variables in equation 3, equations I and 2 can be solved to give the quantities of the various factors employed and tlle quantity of product produced. This car1 therefore be clone for every set, ant1 the quantity of X employed can be expressed as a function of these varial~les,as in equation 3. If tlie product market is not competitive, p, in equation 3 is replaced by tlie demand curve for X; if the factor market for B is not competitive, p, is replaced by the supply curve of R to the firm, etc. TZ'e shall, llowever, gain insight if we proceed more slo~vlyand less forinally to this final result. I t is helpful to rexvrite equation 1 in the following form:

If xve have competition on both factor and product market?, these reduce px * MPP,, = p,,, I'r ' ;ZIPP, = p,,,

o r the familiar equations that marginal value protluct of a factor equal its marginal factor cost, in the general case, o r value of tlle marginal product of a factor equal tlte price of the factor, i n the c.onlpetitive c.asc. Consider the first of equ;rtions 5. T h i s shows a relation I~etrveenthe price of A a n d its quantity: for each price of A, it sho~vstlie quantity of A that would have a marginal product whose \,slue woultl be equal to that price of A. I t is tempting to interpret this as tlie dellland c u r r e of the firm for A, antl, indeed, the demantl curve for h is often loo5ely descril~edas given by the value of marginal procluct curve for A. But this is strictly col-rect only in one special case: tltat i n whicll the firm is not free to vary the quantity of any factor other than A, i.e., all other factors are "fixed." In that case, the only adjustment the firm can make to a change in the price of A is to change the quantity of A employetl: a11 eql~zitionsotlirr than tlie first i n 5 become irrelevant a n d are replaced by eqrtations of the form: b' = 6'.T h e firm will move along the marginnl protluct curve foi- X until the value of the marginal protl~icti5 equal to tlie new price of A antl this curve will be its tlemand curve. Suppose, llowever, that not a11 other fat tors are fixed, that, for example, B can be varied ant1 is purchased competitively. Hypothetically, stlI,l,ose the price of A to fall a n d tlie firill to make its first adjustment along the marginal protluct curve for A, so that it in(.]-eases tllr einployn~entof .l until the margin;rl procl~ictfalls enorigh to satisfy tlie first of the ec111;rtions 5. T h e I-emaining eqnations are now n o longel- satisfied, tleipite tlie fact that they initi;tlly were a n d that tlte quantity of o t h e ~factors . is, 11). assumljtion, the s;tnle as initially. T h e reaso~l,of course, is that the m;~rgin:tl l ~ r o d u c of t the other factors tlepeiltls on the amount of h emp1o)etl. Some t ~ iA: t e tlte s ~ ~ l a r g i r tprotl~lct al of these other factors ~ v i l lbe close ~ ~ ~ l ~ s t i for l will be reduced by the increased employment of A. Othel- f;lctors ~ v i l tend to have their marginal protll~ctiricre;~setl11). inc.re;isctl e~nplo)rrientof A. since in effect there is less of then1 per unit of .I.I n general, we niay expect r o u r earlier tliic ~ission tlie latter effect to doniiiiate, as shoultl I)e c l e ; ~ [I-om of :!ie IRXV of variable proportions. Tlie firm ~ v i l lt11er.efol.e want to c.1iange e nthose t the ainorlnt of other factors employetl, reducing tlie e ~ r ~ p l o y ~ nof xsllose rilarginal product i5 now less than initially anti inc.reairly: the eml~loylnentof the otliers. Rut these ;rtljl~strnents~ v i l lirr turn cliange the marginal prodt~ctix'it)o f A, tencling to increase it for e;rcll quantity of A; 110th tlie reduction in quantity of competitive factors antl the i~icr-e:~sc in q ~ i ~ ~ ~oT t i others it) operate in genera! in tl?i.: direct i o r ? T h e 6n:iI position will be one at wllicll the equations 5 are satisfiecl. At thir final positiori, tllc price of A is equal to the value of its niarginal product, J e t this point is not ct T11e essential p o i ~ is ~ ttliat o n tile initial valtle of nlarginztl p ~ . o t l ~ icurve. the lnarginal product curve is t1ra.ia.n for fixed quaittitier of other fac.to1.s: the tlemand curve, in o u r special case, for fixed prices of ~ : i r i a l ~f;lcton. le Figure 9.1 summarizes the situation. Tlle solid lines nre v;~lueof rnar-

T h e Theory of ~ZfarginalProductivity

Price o f A, Value o f marginal product of A

b. b ,

b=b,

b=b,

b=b,

b=b.

1

181

product cur& for A for given p r i c e product.

Demond curve for A by individual f i r m for gtven for ~ t sproduct ond given prices of other actors. Quontity of A per u n ~ ttime

ginal product curves for different amount of B (used here to stand for all other factors). T h e dashed line is a demand curve for A by the individual firm. Since competition is assumed on both product and factor markets, the price of the final product and of otller variable factors of production is the sairle at all points on it. But, as seen, the quantity of B is not; it varies in sucll a way as to keep equations 5 satisfied. Accordingly, the demand curve cuts through the 1-alueof marginal product curves, in general going through successively higher cnrves as tlle price of h falls. If demand for the product is not competitive, given demand conditions irnply different prices as tlie output varies. Marginal value product diverges from value of marginal product and is the quantity relevant to the inclivitlual firm. 1ITit11this change in nomenclature, Figure 9.1 can summarize the situation, except that there is no longer any presumption that the quantities of otller factors in general will increase as the price of . I falls or that the demand curve will pass tlirougli nlarginal value product curves for successively higher quantities of 11. T h e reason is that while an increase in the quantity of .I employed in response to a decline in its price would in general raise the rllargirial physical product of given quantities of the otlier factors, it will also mean an increare in output, a decline in the price of the product, ant1 perhaps also a decline in marginal revenue. This inay offset or more t l ~ a noffset the rise in the marginal pllvsical product of the other factors arid so lead to a decline in the quantity of those employed. 127e shall meet an analogous effect again when we combine competitive firms ant1 examine the demand curve of an industry. If the market for factor A is not competitive, so that the firm is a monopsonistic purcllaser of A, how much the firm would employ at various prices is no longer a meaningful or relevant question, since the firm affects the price by its action and determines the price and quantity simultaneously.

T11e correspollding question is then the leaction of tlre firm to changes in the supply of the factoi, and these cllanges cannot be summarized b j the sltlgle pnrnmeter, price of the factor, as they can when the inarket for A ic competitive \\'hat would othelwise be the "demand curve" for factor A still etai ins significance I t sllows the quantit) that w o ~ ~ be l d pu~chasedat lalious m ~ i ~ g l n nfactor l costs. H o ~ i e ~ eIn r , so intelpreting it, it must be l general I l a ~ edifferent markept 111 mind that a single supply curie w ~ l in gindl fdctor costs f o ~different qunntities supplied, arld that many different supply curves call have the same marginal factor cost for the same quantity supplied. (This case is cli~cussetlmore full) in the follotving pages ) I n the above analjsis we ha\e taken '1s our (hypothetical) first approxi of 11vit11 fixed q u n t i t i e s of otliel factors nl'rtion the cluange in qrlrium, ant1 so ;ill tllree pass througll it. T h e steepest ptrrcllase if it kepi o u t (at P) slio~vsthe amoutlt of .It h a t the firm 11~)~ild put c.onst;tnt; the next steepest sllo~vsthe amourlt of LA it ~ i ~ o r ~ l~t nl r c l ~at ase given protluct prices if it kept the amount of other factors employed constant; the flattest sllo~vsthe amount of A it wot~ltlpl1rcll;ise at given pro(lnct price arid gil-en prices for otllel- factors. You will find it instructive to check and pro1.e statements made abo11t 111e order of these curves; to sllow that rnol~opolyon the product market

T h e T h e o r y of ~ZlarginnlProductivity

183

Price o f A

Demand curve for A Value o f marginal product curve Constant output curve

Quantity of A per u n i t time

car1 change the order of these curres; , ~ n dto translate the abore in terms of ~ x o d t ~ c t i oirldiffelence n culres.

T h e C o m p e f i f i u eI r ~ d u s t r y 111 reacting to contlitions on the product 'ind factoi maikets as the) see them, irldiridual fiiills obrio~-ices. 'rhe effect on the average price of a l l rrsourccs (inrluding A) relative to tile a v e r q e p1.ice of final gootls and services tiepcnds to sorne extent on o i i i - initial nssrm1i)tions allout the source of the increase in tile suppl? of .A that pl.oiiiicei the decline it1 its price (i.e., ailout the ~near~irig of g i ~ e ncolitlitio~~s of suppi: of res3arces). i f the incrensp ic supply of is :::ken t o be \(>!elb. ;I:: l i r crease in relative supply compensated by a decrease iri the supply of ;ill other factors sufficient to keep total resotlrcer available ~inchangetlin a n appropriate sense, then in that same sense aggregate output will be unchanged, and Ilence the average price of all resources ~villrem;:in MIchanged relative to the ayerage price of gootls ant1 services. This, ho~vever. means that (lie average price of resources other tlian X rises relatibe to the

T h e T h e o r y of .14arginal Productiuity

187

average price of final goods and sell ices If the increase in supply of A is supposed to be a net addition to the total resources of the communitj, with the supply of other resources unchanged, then it obviously pelinits a greater agglegate output It is not clear what effect this will have on the average price of all lesources relative to the price of final goods and sen7ices; it is clear, howe~er,that tlie alerage price of all resources other than A will rise lelative to the average price of final qoods and services, as in the preceding case.1 T h e impor tant thing throughout is to recoqnize that we cannot speak about changes in "price" for the economy as a whole without defining the base relative to which price is measured As just noted, according to at least one possible interpretation of "yiven conelitions of supply of factors of procluction," total output must in one sense remain the same despite the ieduction in the rel,iti~cprice of A. Yet we saw in the precediny qection that, if we took account on11 of the reactions within a single industry, tlie decline in the p i c e of A would lead to an inclease in output in each industr) separately Olxiousl~,there must be some external effects that re\ er se this result for some or manv industries External effects l i a the prices of particular resources highlv competitive with or complementar~,to A may do so. Xlore qenerallv, however, the external effect that is import,lnt in this conncctiorl is on the lelatiae prices of final goocls and ser~icesand the associated substitution in consumptionthe effect that lie saw xvorking in pure foinl iii the case of fixed proportions In the plecetlinq section, we took account of the cllnnqe5 in resollrce p~ices that each inclustiy pxoduced b\ its own reactions Rut these clianqes impose external effects on other inclust~ies As we san in the pxelious paragraph, a decline in the p i c e of A mems that the piice of other resotilces in qenerdl rises r el,~tiveto tlie price of Z ;111tlnlw I e l a t i ~ e to the el aye price of all resource5 and to the 'lvel,lye price of final yoocls ,111tl set rice5 Fot product5 poduced preclominantl~ ~ v i t hthese other f'tc tors, this lise in their price nil1 more t h i n ottset tl-ie fall ill tlie p~ice of A T h e cost of 1x0d t i c i n ~S I I C ~ I p l o d u c t ~wr1: tllc~efolelise and their cupplv ctutec cliift to tile left Tllii occu~sfoi these 1ritl:istries ,i result not ~t their o'iin le'action5 to thc retluced piice of \ 13utI~ecnltseof eute~n,:lefiects imposetl oil tt 111ern 1n tlie leactloils o.f otlic~iridustlies T h e out1,iit of silcl~i i i d ~ ~ sies u ill tend to decline, tllol~yhtheir elllplo~merlt of ma\ not, foi , like other intli~stties,tbe~,ha\e an i n t e r l t i ~ eto sul~stituteZ foi otllct Fac to15 Rut the clecli~le111 output m,ia Ile ellougli to 111oducc ,tlso ;r decline irl errlp1oln:cnt si '1 1 ;:I:.,, l ~ l ; l l e i11e ~Le~n