Modern Economic Thought [Reprint 2016 ed.] 9781512808650

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MODERN ECONOMIC THOUGHT

Co-Authors E I L E E N APPLEBAUM

I N G R I D RIMA

A. ASIMAKOPULOS

MORGAN REYNOLDS

J E R E R . BEHRMAN

A L E S S A N D R O RONCAGLIA

RONALD G . BODKIN

WARREN J . SAMUELS

ARTHUR I. BLOOMFIELD

RICHARD T . S E L D E N

MARTIN

NANCY L . S C H W A R T Z

BRONFENBRENNER

PAUL DAVIDSON

G . L . S. SHACKLE

RICHARD EASTERLIN

KARL S H E L L

WILFRED ETHIER

EUGENE SMOLENSKY

D A N I E L A. GRAHAM

DOUGLAS VICKERS

DANIEL HAMBERG

MICHAEL L. WÄCHTER

M O R T O N I . KAMIEN

SUSAN M . W Ä C H T E R

J . A. K R E G E L

Ε . ROY WEINTRAUB

HYMAN P. MINSKY

PAUL W E L L S

IVOR F . PEARCE

OLIVER E . WILLIAMSON

MODERN ECONOMIC THOUGHT Edited by

SIDNEY WEINTRAUB

1

UNIVERSITY OF PENNSYLVANIA PRESS 1977

Copyright © 1977 by the University of Pennsylvania Press, Inc. Chapter 2 copyright © 1976 by G. L. S. Shackle Library of Congress Catalog Card Number: 76-20140 ISBN: 0-8122-7712-0 All rights reserved Printed in the United States of America

Contents χι

Preface I. From Marshall to Modernity

3

Introduction 1. Neoclassicism and Dissent, 1890-1925—INGRID ΚΙΜΑ

7

2. New Tracks for E c o n o m i c Theory, 1926-1939— G. L. S. SHACKLE

23

II. Keynesianism Introduction 3. Hicksian Keynesianism: Dominance and Decline—SIDNEY WEINTRAUB

41 45

4. Keynesian E c o n o m e t r i c Concepts: Consumption Functions, Investment Functions, and " T h e " Multiplier—RONALD G. BODKIN

67

5. Keynes' Disequilibrium Theory of Employment—PAUL WELLS

93

I I I . Equilibrium Systems Introduction 6. General Equilibrium Theory—E. ROY WEINTRAUB

105 107

7. Optimization and Game Theory—E. ROY WEINTRAUB

125

8. Input-Output and Linear Programming—DANIEL A. GRAHAM

137

9. T h e Sraffian Revolution—ALLESANDRO RONCAGLIA ν

163

Vi

CONTENTS

IV. Microeconomics Introduction 10. Firms and Markets—OLIVER E. WILLIAMSON

181 185

11. Financial Theory of the Firm—DOUGLAS VICKERS

203

12. Demand Theory, Consumers' Surplus, and Sovereignty—IVOR F. PEARCE

217

V. Money Introduction 13. Monetarism—RICHARD T. SELDEN

249 253

14. Post-Keynes Monetary Theory and Inflation—PAUL DAVIDSON

15. An " E c o n o m i c s of Keynes" Perspective on Money—HYMAN p. MINSKY

275

295

16. Money Wage Inflation: T h e Endogeneity-Exogeneity Issue—MICHAEL L. WÄCHTER AND SUSAN M. WÄCHTER

309

VI. Growth Introduction 17. Early Growth Theory: T h e Harrod-Domar Models—DANIEL HAMBERG

329 333

18. Neoclassical Growth Models—KARL SHELL

347

19. Post-Keynesian Growth Theory—A. ASIMAKOPULOS

369

VII. Distribution Theory Introduction 20. T e n Issues in Distribution Theory—MARTIN BRONFENBRENNER

391 395

21. Some Post-Keynesian Distribution Theory—J. A. KREGEL

421

V I I I . Special Topics Introduction 22. Welfare Economics: Or, When is a Change an

441

I m p r o v e m e n t ? — M O R G A N REYNOLDS AND E U G E N E SMOLENSKY

447

Contents

vii

23. Ideology in Economics—WARREN j . SAMUELS

467

24. Population: T h e Economics of the Long Run—RICHARD A. EASTERLIN

485

25. Technology: More for Less?—MORTON I. KAMIEN AND NANCY L. SCHWARTZ

501

26. International Economics—ARTHUR I. BLOOMFIELD AND WILFRED ETHIER

Index

517

27. Development Economics—JERE R. BEHRMAN

537

28. Radical Economics—EILEEN APPLEBAUM

559 575

"In matters of philosophy and science authority has ever been the great opponent of truth. A despotic calm is usually the triumph of error. In the republic of the sciences sedition and even anarchy are beneficial in the long run to the greatest happiness of the greatest number." William Stanley Jevons, The Theory of Political Economy (1871; 5th ed., reprint, New York: Augustus M. Kelley, 1965), pp. 2 7 5 - 7 6 .

Preface For many years I taught a graduate course on recent developments in economics. T h e course featured n e w monographs or journal articles which had not yet filtered into the standard curriculum. Ultimately, I had p l a n n e d to organize the cumulating notes into a critical survey of the analytical trends. After ceasing to offer the course nearly a decade ago, I prepared to sift through my earlier preoccupation with the ideas and to sort out the content of the evolving specialization. Sole authorship would at least provide a unified evaluation, for better or worse. Health considerations, however, compelled me to abandon the design of an individualized product. When it became apparent that I could not fulfill my contract, Director Robert Irwin and associate John McGuigan of the University of Pennsylvania Press readily consented that I act as editor of a collection of papers covering roughly the topics contemplated in the original prospectus. This was the genesis of the invited papers in this volume. As I read the chapters submitted, I confess that my t e m p e r e d expectations w e r e surpassed: a number of essays constitute eminent contributions. They transcend mere evaluation of the existing state of the art. I think the reader will benefit from an e n d product superior to what any o n e individual might practically accomplish in a discipline that has produced so massive a literature over the last quarter-century. As one who once had the energies to read, or at least to scan almost everything in the major economic journals and monographs, I shudder at the overwhelming task that faces the most dedicated and omnivorous reader in this day, w h e n professional output overwhelms even the most insatiable curiosity and exhausts the keenest sense of intellectual obligation and devotion. We can only sympathize with the formidable toils of our academic successors who must try to stay current while peering back at forerunners. I have also taught a fairly standard graduate course in the history of economic thought, adhering to the rule that the students must read the original works of the eminent authors of the longer past. In correspondence with the participants in this volume, I observed that such courses (by late cramming) barely completed Marshall, and then xi

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applied a quick porous brush to touch mostly fragments of the subsequent period. Clearly, the history of ideas has suffered sharp discounting in contemporary technique-centered Ph. D. programs. Over eighty-five years have elapsed since Marshall wrote. T h e time span is approximately that between Say (or early Malthus)—and preRicardo—and Marshall. In that earlier epoch, with only a handful of specialists, economics underwent a profound evolution from the "radical" doctrines of Adam Smith to the rigors of Ricardo, through the Senior and Mill "refinements," to the revolutionary volte-face of Marx, into the marginal utility uprising, and finally into the more placid and expansive neoclassical synthesis of Marshall. Replacing calendar time with f u n c t i o n a l time—a Marshallian residue—we have since his day traveled a second century in economic thought. The years since 1950 reveal an acceleration principle, measured in terms of quantity, and maybe public acceptance—if not always esteem—of economics as a concerted discipline. Economists have become identified as specialists with expertise in studies affecting the daily life of mankind—on this Marshall a n d surely Marx had a shrewd sense of what they were about in their writing. Marshall's very first chapter ventured the thought that through the study of economics poverty might be alleviated. The perception is old, and the problem is still acute and current, though perhaps with less of a pervasive sense of grinding futility in the affluent developed economies than in the economies of his day. As editor of this volume, I usually took the occasion to sketch what I thought was the appropriate coverage, beyond the obvious thoughts implicit in the assigned chapter title. Invariably my instructions were minimal; there was no need to pretend to lead w h e n the authors were identifiable masters of the terrain. I quote a few passages from my original statement of contents, not to preserve a model of communication, but to enable the reader to gauge what was intended and to judge how well it has been realized: In mind is as objective an assessment of the bulk-literature of the last quarter-century as economists, with predilections, can provide. The purpose is not advocacy but exposition. The chapter titles indicate that I am seeking to include views of major groupings of economists; this is the educational objective. Too, the collection is aimed toward students who will have had at least an intermediate economics course; I suggest the math-content be held to an elementary level (in most chapters), with short proofs relegated to footnotes, longer ones . . . referred to other sources. Chapters are to ran about 6,000 words. .. . To repeat, the writing is directed to students, not specialists.

Preface

xiii

I then offered this thought: Suppose yo« were asked to lecture on the assigned subject just next week at your university. What would be the significant themes that you would want to convey to students so that they could apprehend the modern directional tendencies? W h e r e were we in about 1950? How did the current position evolve? W h o ? Unresolved issues?

I confess that this last statement was more of a tantalizing strategem to entice ready acceptance! O f course, in the execution it is certain that more time was expended than most of us customarily allot to a weekly lecture, yet the statement at least conveys the flavor projected for the volume. As I read it, I think that teachers, and students, will generally concede that it fulfills the educational intent. Considering my own views on many of the subjects, I hope it will also be said that, within reasonable bounds of tolerance, I have tried to be fair over all, to incorporate under most headings the dominant "schools" conveying the salients from which economists approach the particular subjects. If I have indulged myself in some of the introductions I appeal to the charity of the reader, with the reminder that I once wanted to write the full volume. Obviously, the volume is topic-organized rather than calendarordered. Histories of thought, to be sure, are usually author-oriented. But this format would not serve what I had in mind. In the opening chapters it seemed appropriate to adopt a chronological setting for the drama before the climactic burst into modernity from about 1950 on. Beyond charting some directions of ongoing work in major theoretical areas, the bibliographical references offer guidance to students, and perhaps to new teachers, for additional reading. Most of the chapters are self-contained in the sense that they can be read without reliance on a previous chapter. Obviously, insofar as economics is unified, the whole is a connected piece. Generally, use of the volume need not abide by the chapter pattern that I thought best to pursue in organizing the book. It remains my pleasant task to thank all the contributors for their congenial partnership. Their competence made my task quite easy. I occasionally offered some constructive comments, or a word or a phrase which they were free to accept or reject. There were no unpleasant moments; quite the contrary. The entire experience was thus pleasurable and rewarding, to me at least. Maybe this is the supreme accomplishment, demonstrating that thirty one economists of diverse views can work harmoniously together toward a common education purpose—and deadline. I am indebted to John McGuigan for facilitating correspondence

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PREFACE

and always lending a sympathetic hand. Also to the Press editor, Miss Sandra Dechert, for her efficient amiability. I have used, as a reminder rather than a dedication, a passage from that t r u e intellectual " r e v o l u t i o n a r y , " William Stanley J e v o n s . Though I might today regard him as slightly "wrong-headed"—as he described Ricardo—his words still have a zing of vitality, especially in this conformist era when economists too often lean on "authority" to shape their views. Currently, w h e n our subject is vulnerable to attack for failing to grapple with serious problems, Jevons' message stays apt. More than ever we need the dissenters, rather than the submissive disciples of self-anointed Pollyannas who suggest that all is well. I would prefer to inscribe a dedication to those evocative and discerning free spirits, Joan Robinson and J. K. Galbraith. They should detect an appreciation in the passage selected from Jevons. I am an unreserved admirer of their individual and i n d e p e n d e n t efforts to release economics from the boring litany of in-house infallibility too often arrogated by establishment figures who stifle any innovative ideas which contradict their " m o d e l " blunders. My colleagues in this volume will not all share this view. Yet as editor, I have availed myself of the first word. Their innings follow. September

1976

SIDNEY W E I N T R A U B

I From Marshall to Modernity

Introduction In the beginning, as the monologist scanning the slide would say, there was Marshall. Alfred Marshall occupied the heights of the late Victorian economics to the e n d of World War I as firmly as Ricardo had been encamped b e t w e e n about 1820 and 1850, and as Keynes cornered the post-World War II period. To be sure, there were delicate finishing touches to the opinions of the masters, and there were rebellious streams. In the Marshallian age the pragmatic American empirical school made the d e e p e s t penetration, with the exemplary statistical studies of the disequilibrium cyclical economy under the skillful literary and technical wisdom of Wesley Clair Mitchell. Sustenance also came from the iconoclastic vim, overladen with a liberal dose of sarcasm, which flowed from the gifted pen of Thorstein Veblen, supported by the philosophic overtones of John Dewey. Historical and descriptive appraisals emerged from that other branch of American realism, namely the Institutionalists, who may even again, on a new set of issues, be poised to launch a new assault on irrelevant theorizing. The earlier aversion to rigid and outdated theorizing drew some of its inspiration from the ascendant German Historical school of the Hohenzollern empire. Professor Ingrid Rima, in an essay severely constrained by space limitations—for this period is not the focal subject of this volume— recounts some of the work that followed Marshall's great Principles. In England there were the mostly orthodox Marshall seminarians, led by Pigou but also including Hawtrey (with an individualistic monetary slant) and Lavington. Sir Sydney J. Chapman's condensed Outlines of Political Economy (London: Longmans, Green, 1917) made classroom study of Marshall more relaxed. Frank Taussig, with Carver and Bullock at Harvard, E. R. A. Seligman at Columbia in public finance, and Keynes himself, were mainly Marshallian offshoots of varying competence. In statistical studies, in history, and on labor markets, there were Bowley, Clapham, and the more institutionalist Sargant Florence in England. Too, there was that under-valued liberal skeptic John A. Hobson, and the "majority of one," E d w i n Cannan, a student of economic thought and a hard-headed analyst in money and 3

4

FROM MARSHALL TO MODERNITY

wealth. The Reverend Wicksteed commanded more perfunctory attention then. The most probing analytic mind in the United States belonged to Frank H. Knight, probably the founding father of the modern Chicago School—or at least present at its birth—though Knight was both too modest, and too independent, to belong to any movement, no matter how kind it was to him. A pervasive American figure, too, was that true theoretical genius, often eccentric but incomparably original and penetrating, Irving Fisher. T h e scales must balance well in registering his virtues. An individual, now more obscure, whose stout work on the ubiquitous nature of the price system in almost all human activity, ramifying beyond the usual interpretation of economics, was Herbert Davenport; he is only infrequently read and only rarely remembered today. The rich theoretical textbook by Fred Taylor can also be placed in the same category. Professor Rima looks beyond the American scene to comment on European writers, in Germany, Austria, Italy, and on those eminent Swedish economists, the immortal Knut Wicksell and, in his day, the more popular Gustav Cassell. In the 1930s—so long ago?—the textbook choice in "advanced" economics courses often settled down to Marshall or Cassell. Professor Rima has attached to her chapter a bibliographical list which should serve the student amply for extra reading, furnishing leads for the unsated curiosity on the undercurrent of ferment beneath the calm exterior of neoclassicism. Emeritus Professor G. L. S. Shackle traces the New Tracks to modernity. To Shackle belongs the distinction not only of christening the period " T h e Years of High Theory," but also of serving as our most knowledgeable guide and raconteur for the contemporary reader. This was the formative period of Professor Shackle's own education, during which he fashioned an incisive contribution to the exciting pre-1940 discussion. Since then, with a singular dexterity, he has sought to persuade economists buried in stationary or steady growth models of "perfect foresight" excluding uncertainty—the curious assumptions guaranteeing analytic stultification—of the spurious vitality of their illusory analyses. Several of Shackle's writings belong to the small shelf reserved for modern classics, comprising indispensable reading for an understanding of the operations of an economy in which anticipations dominate conduct, in which the expectations have an elusive vagueness, an unsureness, and thus an uncertainty in decision-making that escapes model-builders, who graft ill-fitting mathematical probability concepts onto essentially unique and nonrepetitive events. I suspect all readers will be indebted to Professor Shackle for reviv-

From Marshall to Modernity

5

ing the spirit of the "Emerging Age of Keynes," as some of us may regard it, or the "Years of High Theory," as Shackle named it. It is remarkable—speaking as an editor with student recollections of the era—at the way which Shackle conveys the essence of the epoch without detailed reference to the several prized pieces that were then on display and are now enshrined in our economic hall of fame devoted to the pioneers who forged our heritage. What should not be lost on the reader is the praise lavished on Gunnar Myrdal as being in the vanguard of interpretive insight. To too many moderns, Myrdal, who shared a 1974 Nobel prize, is patronizingly relegated to some status as a "sociologist" venturing into the economic idiom, rather than as a scholar who outgrew the bind that we seem to insist on as a price of fraternal membership. Professor Shackle has not provided us with a bibliography for the period of which he has distilled the essence. His modesty notwithstanding, Professor Shackle's exemplary volume on The Years of High Theory: Invention and Tradition in Economic Thought, 19261939 (Cambridge: Cambridge University Press, 1967) purveys delights not only in informational fare but also for its flourishes as a literary repast. The vital references abound, to Sraffa, Harrod, Joan Robinson, Chamberlin, Hicks, Hayek, Ohlin, Robertson, Kahn, Hawtrey, Robbins, Allen, Kaldor, Lange, Kalecki, Lerner, and many others. And certainly, overshadowing all, Keynes. A bibliography of writings in economic journals and monographs in that seething, squirming, swarming decade, when ideas abounded in the midst of the catastrophic depression, later shadowed by the menacing guns of war, can fill a good volume. There should be some interest in a book seldom referred to today, on taxonomic issues at least, by L. M. Fraser, Economic thought and Language (London: A. & C. Black, 1937). Some sparkling enlightenment, with leads and clues, is now available in The Collected Writings of John Maynard Keynes; two volumes merit particular notice: Volume XIII. The General Theory and After, Part I. Preparation and Volume XIV. Defence and Development, Part II (London: Macmillan St. Martin's Press, for the Royal Economic Society, 1973). It is certain that the publications of these volumes of Keynes will prompt much future research. Shackle's essay constitutes a perceptive excursion through what may ultimately prove to be a dense thicket of words—created more by interpreters (and detractors) than by Keynes.1 Ί speak as an unreconstructed, and impenitent, admirer despite the passage of time. I still see Keynes' article on "Why I Am A Liberal," in Essays in Persuasion (London: Harcourt Brace, 1930), as a remarkable feat of lasting prescience.

Neoclassicism and Dissent: 1890-1930 INGRID Η. RIMA Contemporary economists usually display little interest in developments of the early decades of the present century, the remarkable vitality of the scholarship of this period notwithstanding. Everyone, to be sure, "knows" Marshall (if only from secondary sources), but only cursory attention has been accorded other contributors, though the momentum of their intellectual activity comprised the prelude to the "Years of High Theory." The authority of the Cambridge school was so significant in shaping economics that inquiry into modern economic thought properly extends backward to 1890, with the first edition of Marshall's Principles. Marshall's fifth edition (1907) is the most enduring of the several works which conveyed the "grand manner" of the comprehensive treatise. There were others, notably Frederick Wieser's Natural Value (Vienna, 1893), Vilfredo Pareto's Cours (Torino, 1898) and Manuel d'economie politique (Paris, 1909), Knut Wicksell's Value, Capital and Rents (Stockholm, 1893) and Lectures on Political Economy on the Basis of the Marginal Principle (London, 1901), and Philip Wicksteed's Commonsense of Political Economy (London, 1910). After World War I, general treatises were less common as economists focused their inquiries on special problems. Theories of production and distribution were of particular concern; together with the 7

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INGRID Η. RIMA

theory of value, they comprise the substance of modem microstatics, containing the neoclassical paradigm which is generating its share of dissent even as its refinement continues. An extraordinarily large number of scholars working in four European countries, England, and America participated in the substantive evolution of the subject, posing obvious problems of selection. For the most part, developments in each country have been unique and have occurred in relative isolation for reasons more complicated and obscure than the impediment of communication. A more basic cause was their differing perceptions of scientific and economic inquiry. General points of mutuality can be captured by a grouping according to a more or less common intellectual heritage, subject to space limitations courting the danger of a parade of names. References and "Notes for Further Reading" provide some appreciation of the omitted details awaiting the reader in voluminous available sources.

The English Contribution Alfred Marshall's objective in writing his Principles was to update and generalize Mill's exposition of Ricardo. His efforts vastly surpassed this modest goal: the completed system incorporates major innovations which delineate Marshall from his classical forebears. Marshall's introduction of demand equations predicated on individual utility functions for the purpose of explaining the demand side in the determination of commodity values was a major innovation but one already in the air as demonstrated in the works of Augustin Cournot and Fleeming Jenkins. Marshall gave Mill's verbal presentation of demand (and supply) a schedule sense and an explicit functional character, establishing the link between utility and demand. 1 The demand side of the price problem was complemented by Marshall's inquiry into the connection between cost and supply, erected in terms of his celebrated "operational" rather than "clock-time" concepts. This analysis distinguished the instantaneous market period equilibrium of fixed stocks: the short run, which is compatible with output changes that can be achieved by altering variable (prime) costs; and the long run, during which costs (and supplies) can be completely adjusted to conform to changes in demand. Marshall classified costs as money and real, prime and supplementary (the latter two being equivalent to "variable" and "fixed" in modem terms). •Marshall's resentment of W. S. Jevons' claim of priority on marginal utility is documented in J. A. Schumpeter, History of Economic Analysis (New York: Oxford University Press, 1954), p. 826.

From Marshall to Modernity

9

Marshall's most controversial analytic case was that of long run decreasing cost: economies that are "external," in the sense that they are equally available to all firms, will enable many industries to experience decreasing supply price while preserving their purely competitive character. The controversy over Marshall's efforts to rationalize the compatibility of pure competition and decreasing supply price helped pave the way for the later theories of monopolistic and imperfect competition. 2 Marshall's position on income distribution was to regard value and distribution as different aspects of a single problem. Previously, wages, profits, and rents were viewed as incomes going to laborers, capitalists, and landowners, groups conceived of as social and political classes rather than as "factors" whose rewards tend to be related to their productive contributions. Today, the "classical" view associates income shares with the prevailing social and political milieu, while the "neoclassicist" descendants of Marshall associate income shares with the productivity of the "factors" commanding them. Unlike, Ricardian and Marxian predecessors, who envisaged costs wholly in objective terms, Marshall stressed the subjective sacrifices underlying the real costs of production. Indeed, Marshall's concern with the psychological factors of behavior in the marketplace imparted a quality of hedonism to the Principles which he tried, with limited success, to purge from successive editions and which, many contemporary critics maintain, is still pervasive in the discipline. From the perspective of post-Marshallian developments, Marshall's "partial e q u i l i b r i u m " p r e o c c u p a t i o n w i t h t h e d e t e r m i n a t i o n of real phenomena focuses on the allocation of resources, treating money essentially as an exchange medium (except in "crises of confidence") which exerts no perceptible influence on the determination of economic activity. This subsequently became one of the issues in the early macroeconomic controversies of the 1930s. Marshall was the great systemizer of his era. Neither Philip Henry Wicksteed nor Francis Y. Edgeworth, Marshall's contemporaries, produced a successful unified system. Wicksteed and William Smart, writing between 1870 and World War I, rejected classical cost theory in favor of the marginal utility theory. Wicksteed presented an elaborate statement of the relationship between price determination, production and distribution in his Commonsense of Political Economy (1910) which Lionel Robbins called " t h e most exhaustive nonmathematical exposition . . . of the so-called marginal theory of pure 2

A seminal article is Piero Sraffa, "The Laws of Returns under Competitive Conditions," Economic Journal 36 (December 1926): 536-550. Its main ideas appeared a year before in Annali di Economia 2 (1925).

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INGRID Η. RIMA

Economics which has appeared in any language." 3 However, in view of the limitations of his book on the theory of production, Wicksteed is mainly remembered today for posing the "adding up" theorem. 4 In the originality of his demonstration that marginal productivity theory is essentially a generalization of Ricardo's theory of rent, Wicksteed shares credit with J. B. Clark.5 The Marshallian A- W. Flux, however, identified the tie between Wicksteed's argument and Euler's theorem: the total product will be exhausted when all factors are paid the equivalent of their marginal products only if the production function is linearly homogeneous. 6 Although Francis Edgeworth, early editor of the Economics Journal, was a prolific writer of shorter notes and comments, except for Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences (1881; republished in 1925 in Papers Relative to Political Economy) and The Theory of Money (1897), Edgeworth's work receives only occasional attention, mainly from specialists. Yet Edgeworth often evinced profound originality and perception, demonstrating an awareness of average and marginal returns and handling it with more finesse than Marshall had.7 In The Pure Theory of International Values (1894), Edgeworth provided a deeper analytic probe of Mill's fundamentals. Arising out of his re-examination of the Cournot-Bertrand duopoly problem, Edgeworth's identification of the problem of bilateral monopoly was a genuinely new departure. The most durable priority, however, was in his invention of the indifference curve, introduced originally to disclose the indeterminacy of bilateral monopoly. The introduction of this curve antedates its use by Vilfredo Pareto, who, with Irving Fisher, gave wider application to this vital concept. 8 John A. Hobson's dissent from the Marshallian tradition is inseparable from his reformist zeal to alter the distribution of income and 3 Lionel Robbins, "Introduction" to Philip Wicksteed, Common Sense of Political Economy (London: George Routledge and Sons, 1933), p. xii. 4 Philip Henry Wicksteed, An Essay on the Coordination of the Laws of Distribution, 1894. 'John B. Clark, "Distribution as Determined by a Law of Rent," Quarterly Journal of Economics 5 (1890-1891): 289-318. 6Economic Journal 4 (June 1894): 305. 'George Stigler, Production and Distribution Theories (New York: Macmillan, 1941), p. 112-24. 'The indifference curve technique was revived in 1924 by A. Bowley in Mathematical Groundwork and subsequently popularized by John R. Hicks and R. G. D. Allen. There were excellent articles by W. E. Johnson, "The Pure Theory of Utility Curves," Economic Journal 23 (December 1913): 483-513, and also Ε. E. Slutsky, "On the Theory of the Budget of the Consumer," Giornate degli Economisti 51 (July 1915): 1-26, reprinted in Readings in Price Theory (Homewood, 111.: Irwin, 1952), pp. 27-56.

From Marshall to Modernity

11

w e a l t h in the industrial system. W h i l e contemporaries w e r e still c h i e f l y c o n c e r n e d with d i s c o v e r i n g the " l a w s " g o v e r n i n g the "norm a l " b e h a v i o r of the e c o n o m i c system, H o b s o n was coupling his analysis o f c y c l e s — t o a v e r y m i x e d academic r e c e p t i o n — w i t h prescriptions to increase wage-earner income w h i l e decreasing " o v e r s a v i n g s " via progressive income and inheritance taxes. 9 E d w i n Cannan, a L o n d o n School of E c o n o m i c s colleague, also e m p h a s i z e d the adverse e f f e c t s of inequality. 1 0 Arthur C . P i g o u succeeded to Marshall's chair in 1908; readers of K e y n e s mainly recall him as a "classicist" subject of criticism. Pigou's m a g n u m opus, Wealth and Welfare (1912) was subsequently republished and e x p a n d e d into Economics of Welfare (1932). Contemporary interest in social diseconomies or " e x t e r n a l i t i e s " has imparted n e w vitality to Pigou's perceptions of the "arrangements of resources" to m a x i m i z e the national d i v i d e n d . Contemporary concern with " s m o k y c h i m n e y s , ' ' congested cities, and polluted streams (i.e., with social costs not reflected in market prices) are the modern illustrations of P i g o u ' s i n c i s i v e separation of d i v e r g e n c e s b e t w e e n private and social product. L i k e Marshall, his master and mentor, Pigou typically argued that in industries characterized by decreasing supply price the output volu m e tends to b e b e l o w optimal because the marginal social product e x c e e d s the marginal private product. F r e e enterprise is therefore c o m p a t i b l e with e c o n o m i c w e l f a r e only if constant or decreasing returns p r e v a i l , with a prima facie case for a state p o l i c y to achieve o p t i m u m output under increasing returns. T h e P i g o v i a n m o d e l stimulated subsequent work by Richard Kahn, Harold H o t e l l i n g , and A b b a L e r n e r , w h o s h o w e d that t h e c a s e f o r p u b l i c i n t e r v e n t i o n is s t r e n g t h e n e d in industries in which marginal costs are b e l o w average cost o v e r a considerable range o f output because of a tendency toward m o n o p o l i s t i c or cartelized organization. 1 1 "J. A. Hobson, The Economics of Distribution ( N e w York: Macmillan, 1900); J. A. Hobson, Gold, Prices and Wages (London: Methuen, 1913). For a review of The Economics of Distribution by A. W. Flux, see Economic Journal 10 (1900), and for a review of Gold, Prices, and Wages by J. M. Keynes, see Economic Journal 23 (1913). 1 0 Edwin Cannan, " T h e Division of Income," Quarterly Journal of Economics 19 (1904-1905): 341-349. Cannan also wrote A History of the Theories of Production and Distribution in English Political Economy 1776-1848, London, 1893. T h e emphasis by a pair of American writers, W. T. Foster and W. Catchings, on the role of "oversaving" has much in common with Hobson's. See their Profits (Boston: Houghton Mifflin, 1925). " A b b a P. L e m e r , Economics of Control ( N e w York: Macmillan, 1944); Harold Hotelling, " T h e General Welfare in Relation to Problems of Taxation and Railway and Utility Rates," Econometrica 6 (July 1938): 242-269; R. F. Kahn, "Some Notes on Ideal Output." Economic Journal 45 (March 1935): 1-35.

12

INGRID Η. RIMA

While English economists generally paid little attention to the theory of the trade cycle between 1890 and World War I, both Part IV of Pigou's Wealth and Welfare (1912) and his later Industrial Fluctuations (1926) are devoted to this problem. Pigou attached particular importance to the causal role of "waves of optimism and pessimism," a psychological theme pursued by Frederick Lavington in The Trade Cycle (1922). In contrast, another Marshallian student, R. G. Hawtrey, conceived the business cycle as a purely monetary phenomenon tied to the price level. This view, put forward in Good Trade and Bad Trade (1913) and later works, was reflected during the 1920s in the monetary policy pursued by the English Treasury and the Federal Reserve system. In Industrial Fluctuations (1927), D. H. Robertson, who emphasized the source of cyclical instability in "real" investment fluctuations (as opposed to monetary and psychological factors), provided an alternative explanation of cyclical fluctuations. The analytical usefulness of the neoclassical (cash balance) income approach was exemplified in Hawtrey's Currency and Credit (1919). Keynes' commitment at this time, as evidenced in his first book, Indian Currency and Finance (1913) and in his later Tract on Monetary Reform (1924), was still essentially Marshallian. Not until the Treatise on Money (1930) did he maintain that an understanding of the pricemaking process requires bringing in "the rate of interest and the distinction between incomes and profits and between savings and investment." 12 The profession was thus on the brink of contemporary macrotheory by the end of the period under investigation.

Austrian and German Contributions Economic thought in Austria-Hungary and Germany often diverged despite the cultural affinity of the two nations. The Austrian (Viennese) school retained its commitment to theoretical doctrines; the historicists innately reflected the Romantic Spirit which had nurtured German nationalism and idealism. The dichotomy between the two schools, which originated in about 1875, derived not only from their dispute over methodology but also from the Austrian predilection toward laissez-faire. Historicism, however, was the dominant intellectual force in the German universities, and it was widely respected in Europe and America. But it could not halt the ultimate evolution of theoretical systems of thought, even in Germany, and the " J o h n Maynard Keynes, A Treatise 1930), 1:229.

on Money

(New York: Harcourt Brace & Co.,

From Marshall

to Modernity

13

Methodenstreit subsided. Continental thought strands during the period were therefore complex, for they reflected the continuing conflict between alternative conceptual ideas. Gustav Schmoller was the undisputed leader of historismus among those who yearned backward to the work of Miiller and List and, in part, Roscher. Schmoller's Outline (Grundriss, 1900) was the grand monument of "the younger historical school." Its two volumes treat a range of subjects historically, statistically, and, in a sense, analytically. Arthur Spietoff, once Schmoller's assistant, distinguished the "pure" theory of Ricardo, Johann von Thünen, and Carl Menger and the "observational" (anschauliche) theory of Schmoller and Weber. Likewise, there is a conjectural type of historical theory in the embracing themes of Werner Sombart and Max Weber to explain the rise of capitalism. In his business cycle studies, Spietoff drew on both the factual materials of the historical school and the statistical compilations of Clement Juglar to investigate general "overproduction," and to dismiss Say's law as "less a theory of explaining crises than a theory seeking to prove their impossibility, in complete disregard of all the facts." 13 Spietoff attributed "overproduction" partly to errors in forecasting market demand; he also demonstrated some perception of the independence of saving and investment as disturbing phenomena. Pure theory occupied the new generation of disciples of Menger's Grundsätze, namely, Frederick Wieser, Eugen von Böhm-Bawerk, Joseph Schumpeter (who spent most of his professional life in America), and two Swedish economists, Knut Wicksell and Gustav Cassel. Their contributions vastly extended the influence of the Austrian school. Wieser provided a most comprehensive espousal of marginal utility theory in his Social Economics (1914). His most significant idea, already present in an early essay, The Relation of Cost to Value (1876), was the "alternative-cost" principle, i.e., the cost of any good being the alternative output displaced by the use of the resources—the "modern trade-off." From this principle, Wieser proceeded to Zurechnung, or Menger's theory of "imputation," which attributes the value of goods of "a higher order" back to the utility of goods of a lower order for explaining factor incomes. This is essentially the theory of "derived demand." Böhm-Bawerk's capital and interest theory, which clarified the nature of "roundabout" processes and the "agio" commanded by "Schmoller's Jahrbuch (1903).

14

INGRID Η. RIMA

present goods and current income because of positive time preference, largely belongs to a slightly earlier period. 14 Wicksell's capital structure concept, with his inquiry into the effect of capital accumulation on distributive shares, was considerably influenced by Austrian capital theory. 15 His fame, however, rests on his pioneering effort to integrate monetary with real analysis via his analysis of the cumulative process involving price-level change. His argument that changes in the general price level take place indirectly in response to discrepancies between the "market" and "natural" rates of interest (rather than directly by the quantity of money) is well known. Wicksell's analysis, which emphasized investment demand, anticipated the Keynesian emphasis and established the traditions of the Swedish school, with Bertil Ohlin, Erick Lindahl, Eric Lundberg, and Gunnar Myrdal as eminent disciples. Wicksell's controversy with his countryman Gustav Cassel concerning the problem of value is also of interest. 16 Cassel, writing in German, helped to hasten the decline of historicism. Unlike either the Austrians or Marshall, Cassel argued from empirical demand premises, omitting the psychological premises of utility and proceeding immediately to market price determination. 17 Drawing heavily on Walras, generally without specific references to him, Cassel propounded a general equilibrium system of equations in order to show the market interdependence in the formation of prices. Joseph A. Schumpeter's place in modern economic thought is difficult to define. His work has an inner unity that derives from his vision of the socioeconomic process evident in his first book, Wesin und Hauptinhalt (1908), and subsequently given fuller expression in his exemplary Theory of Economic Development (1912). 18 He offered his theory of economic change in the conviction that it explained the "Eugen B'öhm-Bawerk, The Positive Theory of Capital, trans. William Smart (New York: G. E. Stechert and Company, 1923). "Wicksell's work was so little appreciated in the United States that a leading text of the period, W. A. Scott, Development of Economics (New York: Appleton Century Crofts, 1933), does not mention him. i e "Professor Cassel's Nationalökonomisches System," Schmoller's Jahrbuch 52 (1928): 771, published in Sweden in 1919. "Francis Edgeworth's review of The Theory of Social Economy, Economic Journal 30 (December 1920): 530-536, reveals the difference between Cassel's conception of price determination and that of Marshall. Herbert J. Davenport and Frank A. Fetter were among the American economists who also rejected the hedonistic approach of the earlier marginalists. Davenport, in particular, was skeptical of the usefulness of subjective real cost analysis. See his Economics of Enterprise (New York: Macmillan, 1913), p. 60.

"Joseph A. Schumpeter, Theory of Economic (Cambridge: Harvard University Press, 1934)

Development,

trans. Redvers Opie

From Marshall

to Modernity

15

capitalist world more satisfactorily than either the Walrasian or Marshallian apparatus. Schumpeter's theme was that capitalist economic development is necessarily discontinuous and lurching, inevitably imparting cyclical disturbances. The "circular flow" of the system is upset by the innovator-entrepreneur, who is followed by a host of imitators; it is magnified by the functioning of credit institutions. Schumpeter's theory thus breaks with the neoclassical "equilibrium" tradition which conceived of capital accumulation as being generally smooth and continuous.

The American Contribution Intellectual developments in America were the product of more diverse influences than prevailed in any European country. Although the Anglo-Saxon heritage was pronounced, Americans manifested an individualistic alertness to the doctrines of both the Austrian and Germanic schools; theoretical and pragmatic empirical exponents existed side by side. An impressive number of younger scholars were exposed to historicism while they studied in German universities. They were also interested in anthropology, psychology, and sociology to a degree which made intellectual conflict with the narrower neoclassical theory inevitable. On his return from studies in Germany, John Bates Clark initially repudiated the orthodox tradition. His Philosophy of Wealth (1885) urged a reconstruction of economic science along lines subsequently advocated by Thorstein Veblen and those of similar persuasion. But afterward, in the Distribution of Wealth (1899), Clark posited the "natural law" of income distribution, which held that every agent of production tends to receive the amount of wealth it creates. Clark's work, saturated with a natural order philosophy, became a pillar of neoclassical orthodoxy. The countervailing influence of dissident thinkers was considerable. Most shared an intellectual and philosophical legacy derived from European thinkers like Hegel, Marx, Darwin, and Spencer and from the works of the Americans, James, Pierce and Dewey, in which the concept of "becoming" (as contrasted with Newton's mechanistic idea of "being") is of particular importance. Darwin's Origin of the Species (1859) is the source of the evolutionary outlook which characterizes their institutional studies. 19 The chief aim of this movement "Methodologically, the dissidents were reacting against the influence of works like Keynes' Scope and Method of Political Economy (1890) which made economics an abstract science.

1 6

I N G R I D Η. RIMA

was to create a "cultural" science of economics grounded in anthropology, social psychology and sociology. 20 Early foes of economic orthodoxy were (in his early work) Richard T. Ely (a founder of the American Economic Association), Thorstein Vehlen, and Simon Patten. Their efforts were carried on by John R. Commons, Wesley C. Mitchell, a n d John Maurice Clark, thinkers w h o s u b s e q u e n t l y influenced Gardiner Means and Rexford Tugwell. Arthur Burns, current Chairman of the Federal Reserve System, is one of Mitchell's foremost students and disciples. Simon Kuznets, whose monumental work on national income earned a Nobel prize, is also a Mitchell student. While the early dream of the Institutionalist movement for reconstructing economics has not been realized, notable contributions are not absent. Mitchell's Business Cycles (1913) and Business Cycles: The Problem and Its Setting (1927) combine a unique blend of economic history, theory, and statistics. T h e 1927 volume was the result of many years of work at the National Bureau of Economic Research, which Mitchell founded; it is, perhaps, the crowning achievement of the Institutionalist school. J. M. Clark's Studies in the Economics of Overhead Costs (1923) focused on the significance of large investments in fixed capital equipment. This inquiry provided insight into the problems of unused industrial capacity, including the social overhead cost inherent in idle labor. Clark also established a nexus between unused capacity and monopolistic tendencies in industry. In his Strategic Factors in Business Cycles (1934), Clark saw changes in the ratio of the demand for consumer goods to the demand for captital goods—the acceleration principle—as a major factor in cyclical disturbance. John R. Commons' special interest in interpreting the American Labor movement helped shape the New Deal labor legislation and had ramifications for American politics. His conception of nonpartisan commissions for settling disputes became a prototype for contemporary state and federal industrial mediation. Following Commons' view that most disputes involve property rights, contemporary interest on the relation of property rights, externalities, transactions, and information costs has given renewed importance to Commons' insights into questions of economic justice. Property rights also occupied the profound and penetrating intellectual power of Frank Knight, perhaps the most thoroughgoing American neoclassicist (with several individualistic dissents) of the period. 4 0 See, e.g., Thorstein Vehlen, "Preconceptions of Economic Science," in The Place of Science in Modern Civilization (New York: B. W. Huebsch, 1919), p. 149.

From Marshall

to Modernity

17

In an often-cited dispute with Pigou concerning market failure through divergences between private and social marginal products, Knight argued that if government properly established property rights, the owners of a superior resource would charge a (Ricardian) rent equal to the differential surplus and the corrective tax prescribed by Pigou. 21 Knight's enduring reputation rests on his highly original doctoral dissertation, published as Risk, Uncertainty and Profit in 1926, which distinguishes between insurable risk and uninsurable uncertainty and links profit to uncertainty. Knight also viewed his theory of profit as repudiating Veblen's argument that "conspicuous consumption" violates consumer sovereignty. Not only is the consumer sovereign, according to Knight, but, in an uncertain world, the producer who correctly anticipates consumer preferences is rewarded with profit. Francis A. Walker and Irving Fisher were also among those committed to refining neoclassicism. Walker envisaged the entrepreneur as a "residual claimant." 22 Irving Fisher, responding to Böhm-Bawerk's agio theory, argued that "technical superiority" does not produce its effect independently of the psychological fact of "impatience." 2 3 Fisher conceived of interest as an index of the community's preference for a dollar of present over a dollar of future income. The rate is determined by the interaction of the "willingness principle," which governs the way in which individuals alter the time shape of their income streams, and the investment-opportunity principle. The resulting "real rate of interest" reflects the premium commanded by present (as opposed to future) income. 24 Fisher's Purchasing Power of Money (1911), an exemplary book by any standard, elaborated the celebrated MV = PT formula (on foundations laid by Simon Newcomb) for the Quantity Theory of Money. In "Frank Knight, "Fallacies in the Interpretation of Social Costs," Quarterly Journal of Economics 38 (May 1924): 582-606. An important contemporary statement of this position is Ronald Coase, "The Problem of Social Costs," The Journal of Law and Economics 3 (October 1960): 1-34. M F . A. Walker, The Wage Question, 1891. "Irving Fisher, The Rate of Interest (New York: Macmillan, 1907), p. 55. A particularly useful article on the "third reason" for a positive rate of interest is Guy Arvidisson, "On the Reasons for a Rate of Interest," trans. A. Williams, International Economic Papers, Vol. 6 (New York: Macmillan 1956), pp. 23-33. "Fisher's graphic demonstration of the way an individual adjusts to the real rate of interest introduced "willingness" curves (which are essentially "indifference" curves) drawn convex to the origin on the assumption that present income is preferred to future income. Fisher also constructed an "investment opportunity curve," an envelope of the most profitable investments among which an individual can choose, drawn concave to the origin to reflect diminishing returns. Cf. J. W. Conard, An Introduction to the Theory of Interest (Berkeley: University of California Press, 1959), ch. 4.

18

INGRID Η

RIMA

his Theory of Interest (1931)—far and away the most lucid and complete neoclassical formulation—he also distinguished between real and money rates of interest. Fisher reasoned that the money rate will reflect the behavior of the price level; this thesis remains as part of the modern monetarist doctrine. 25 His early work on index numbers, too, should be recalled. With these works and his Ph.D. thesis on Mathematical Investigations In the Theory of Value and Prices (1892), Fisher's claim to high (or highest) honors in American economics is secure. On the "laws of return," Allyn A. Young is often cited (most recently, by Nicholas Kaldor) for working out some of the implications of increasing returns, equilibrium, resource allocation, and Adam Smith's ideas on the division of labor as limited by the extent of the market. 26 The work of C. W. Cobb and Paul H. Douglas on the aggregate production function has also become a classic reference. 27 Herbert J. Davenport and Frank A. Fetter, writing on the psychological foundations of marginalist economics and the operation of the price system, also merit brief mention. 28 Davenport, like Cassel, discarded the subjective Marshallian real-cost analyses as unnecessary in explaining the price system.

Contributions to Italian Thought Italian economists adopted the mathematical method long before it became fashionable elsewhere. This appears to have been chiefly due to the influence of Maffeo Panteleoni on Vilfredo Pareto, an engineer and mathematician until he turned his attention to economics as successor to Walras at Lausanne. Pareto's substantive works are his Cours (1896-7) and the Manuel "Fisher, The Theory of Interest, ch. 19. Fisher's argument that interest is not simply a factor return like rent or wages, but the foundation of all incomes, is essentially an Austrian conception. The idea that the capital value of an income flow can be obtained by capitalizing it at a given interest rate appears in Frank Knight's conception of capital (cf. "Capital and Interest," in Readings in the Theory of Income Distribution, ed. W. Fellner and B. F. Haley (Philadelphia: R. D. Irwin, 1946), p. 384. However, the idea of capital as physical goods plays a smaller role in Knight's analysis than it does in Fisher's. Knight stressed the notion of capital as a fund. Cf. Nicholas Kaldor, "The Recent Controversy on the Theory of Capital," Econometrica 5 (July 1937): 201-233. "Allyn Young, "Increasing Returns and Economic Progress," Economic Journal 38 (1928): 527-542. "Charles W. Cobb and Paul H. Douglas, "A Theory of Production," American Economic Review 18 (1928): 139-165. ^Herbert J. Davenport, Economics of Enterprise, p. 60, and Frank A. Fetter, Economics (New York: The Century Company, 1913), 1915-1916.

From ( 1 9 0 9 ) . T h e P a r e t o o f t h e Cours Manuel

Marshall

to Modernity

19

is d i f f e r e n t f r o m t h e P a r e t o o f t h e

in at least o n e i m p o r t a n t r e s p e c t . T h e Cours

d e s p i t e its s o c i o l o g y . T h e Manuel,

is W a l r a s i a n ,

in contrast, d i s c a r d s t h e c a r d i n a l i t y

a s p e c t o f t h e W a l r a s i a n utility t h e o r y in f a v o r o f an o r d i n a l c o n c e p t o f ' o p h e l i m i t e , ' s u p p o r t e d b y an i n g e n i o u s use o f t h e i n d i f f e r e n c e c u r v e a p p a r a t u s . P a r e t o ' s i n d i f f e r e n c e s y s t e m , in t h e m a n n e r o f E d g e w o r t h , constituted the forerunner of the m o d e r n innovations by H i c k s and Allen. E n r i c o Barone, o n e o f Pareto's most important f o l l o w e r s , p r o b e d the nature o f g e n e r a l e q u i l i b r i u m u n d e r c o m p e t i t i o n ; his i n q u i r y i n t o h o w a p l a n n i n g board might duplicate the c o m p e t i t i v e solution remains a f a s c i n a t i n g c o n t r i b u t i o n ; it l e d S c h u m p e t e r to o p i n e that, l a r g e l y b e c a u s e o f t h e i n f l u e n c e o f P a r e t o , Italian e c o n o m i c s " w a s s e c o n d to n o n e b y 1914."

Notes for Further Reading Theo

S u r a n y i - U n g e r ' s Economics

in the Twentieth

Century

(New

Y o r k : W . W . N o r t o n a n d C o . , 1931) p r o v i d e s a c o m p r e h e n s i v e i n q u i r y i n t o t h e d e v e l o p m e n t o f e c o n o m i c t h o u g h t d u r i n g t h e first q u a r t e r o f this c e n t u r y , as d o e s B e n S e l i g m a n ' s Main nomics

Currents

in Modern

Eco-

( N e w Y o r k : G l e n c o e F r e e Press, 1962) S e e a l s o T e r e n c e W .

H u t c h i s o n , Review

of Economic

Doctrines

1870-1929

( N e w York: Ox-

f o r d U n i v e r s i t y Press, 1953). Joseph S c h u m p e t e r ' s History nomic Analysis

of

Eco-

( N e w Y o r k : C l a r e n d o n Press, 1953) is b e s t u s e d as an

e n c y c l o p e d i c r e f e r e n c e source o n this particular p o i n t . T h e l i t e r a t u r e on M a r s h a l l is m a s s i v e . T h e f o l l o w i n g g e n e r a l r e f e r ences also illuminate specific topics: C . W . G u i l l e b a u d ' s Introduction to Marshall's

Principles

of Economics,

9th e d . ( L o n d o n :

Macmillan,

f o r t h e R o y a l E c o n o m i c S o c i e t y , 1961); a n d G u i l l e b a u d ' s " M a r s h a l l ' s P r i n c i p l e s o f E c o n o m i c s in t h e L i g h t o f C o n t e m p o r a r y T h o u g h t , " Economica

Economic

1 9 ( 1 9 5 2 ) : 1 1 1 - 1 3 0 is p a r t i c u l a r l y r e c o m m e n d e d

to r e a d e r s f o r its m a c r o e c o n o m i c o r i e n t a t i o n . P a u l H o m a n ' s c h a p t e r o n A l f r e d M a r s h a l l in Contemporary

Economic

Thought

(New

York:

H a r p e r & R o w , 1928) s u r v e y s M a r s h a l l ' s C o n t r i b u t i o n . G e o r g e S t i g l e r e x a m i n e s M a r s h a l l ' s t h e o r y o f d i s t r i b u t i o n in Production bution

Theories,

Essays

in Biography,

and

Distri-

( N e w Y o r k : M a c m i l l a n , 1941), ch. 4. J. M . K e y n e s ' ch. 14, p r o v i d e s a b i o g r a p h i c a l a c c o u n t ; G . F .

29Enrico Barone, "The Ministry of Production in a Collectivist State" in F. A. von Hayek, ed., Collectivist Economic Planning: Critical Studies on the Possibilities of Socialism (London: G. Routledge and Sons Ltd. 1938).

20

INGRID Η. RIMA

Shove's essay, "Marshall's Principles in the Development of Economic Theory," Economic Journal 52 (December 1942) interprets Marshall's economics as generalizing Ricardo's value and distribution theory in contradistinction to the view that Marshall was seeking an eclectic compromise between marginal utility theorists and the classicists. See also the article by Jacob Viner on Marshall in H. W. Spiegel, ed., The Development of Economic Thought (New York: John Wiley and Sons, 1952.) A less than admiring appraisal of Marshall is presented by J. A. Schumpeter in "Alfred Marshall's Principles: A Semi-Centennial Appraisal," American Economic Review, 31 (June 1941), reprinted in Ten Great Economists (New York: Oxford University Press, 1951). T. W. Parsons examines the philosophical and psychological preconception of Marshall's work in "Wants and Activities in Marshall," Quarterly Journal of Economics, 1931. Jacob Viner's classic paper, "Cost Curves and Supply Curves," Zeitscrift für National-ökonomie (September 1931) develops the firm's "envelope" curve on the basis of Marshall's long-run analysis. The concept of industries of constant, increasing, or decreasing returns is examined by J. H. Clapham's paper, " O f Empty Economic Boxes," Economic Journal 32 (September 1922): 305-314, to which Pigou and Robertson responded in the issues of December 1922, pp. 458-465, and March 1924, pp. 16-31. An able account of Hobson's work appears in P. T. Homan's Contemporary Economic Thought. The article by Colin Clark on Pigou in The Development of Economic Thought puts both Pigou's early work and that which grew out of his differences with J. M. Keynes into perspective. Frederick Wieser's Natural Value (1893) is available in translation by A. Malloch (New York: Stechert, 1930). Francis Edgeworth's reviews of various Austrian publications of the period in his Papers Relating to Political Economy (London: Macmillan & Co., 1925) are useful for understanding the conflict between real cost and opportunity-cost theories. Gustav Cassel's Theory of Social Economy, translated by Joseph McCabe (New York: Harcourt, Brace and Co., 1924) enjoyed considerable success in America as a textbook. For an analysis of Schumpeter's system, see R. V. Clemence and F. S. Doody, The Schumpeterian System (Cambridge, Mass.: Addison-Wesley Press, 1950). Indispensable references on the American contribution to economic thought during the period are Allan Gruchy, Modern Economic Thought: The American Contribution (New York: Prentice-Hall, 1947) and the remarkably scholarly volumes by Joseph Dorfman, The

From Marshall

to Modernity

21

Economic Mind in American Civilization, vols. 3 - 5 (New York: Viking Press, 1949, 1959). Commemorative articles on Veblen, Commons, Mitchell, and J. B. Clark are included in Development of Economic Thought. P. T. Homan's Contemporary Economic Thought includes chapters on Veblen, Mitchell, and J. M. Clark. A recent reexamination of Veblen is available in Thorstein Veblen: A Critical Reappraisal, edited by Douglas F. Dowd. On the life and work of Irving Fisher, see William Fellner et al., Ten Economic Studies in the Tradition of Irving Fisher (New York: John Wiley and Sons, 1967). Among the successful American textbooks during the pre-1930 period, the most durable were Frank W. Taussig, Principles of Economics·, Frank A. Fetter, Economic Principles; Richard T. Ely, Outlines of Economics; and Frederick B. Garver and Alvin H. Hansen, Principles of Economics. Demaria's commemorative article on Pareto in Development of Economic Thought is r e c o m m e n d e d . Vincent Tarascio has written widely on Pareto; see his Pareto's Methodological Approach to Economics: A Study in the History of Some Scientific Aspects of Economic Thought (Chapel Hill: University of North Carolina Press, 1968). Also, W. Jaffe, "Pareto Translated: A Review Article," Journal of Economic Literature, December 1972. M. Allais and T. Parsons evaluate Pareto and his work in "Vilfredo Pareto," International Encyclopedia of the Social Sciences. The 1908 article by Enrico Barone, " T h e Ministry of Production in a Collectivist State," is available in translation in F. A. Hayek, ed., Collectivist Economic Planning: Critical Studies on the Possbility of Socialism (London: G. Routledge and Sons, 1938). For a more extensive treatment of many of these writings on a textbook level, see Ingrid Η. Rima, Development of Economic Analysis (Homewood, 111.: R. D. Irwin, 1972). Temple

University

2 New Tracks for Economic Theory, 1926-1939 C. L. S. SHACKLE

Rational Inter-active Choice In order to survive, to live enjoyably, to add to their possessions, men must use their circumstances according to reason. Some formal rules must be obeyed in their choices of conduct. To ignore these will be to get less far towards some goal than their circumstances would have allowed. When the conduct in question can be s u m m e d up in the word exchange, the renouncing or parting with one thing in order to possess another, the formal rules may take a prominent place. They can be seen as the architectural principles of a system where men of extremely diverse desires and e n d o w m e n t s can do the best for themselves that is possible when all alike enjoy an equal freedom with each other from force and fraud. Reason, in this light, seems to show how men should act. Cannot the analyst of their conduct then assume that they will thus act, and so claim, given details of their tastes and endowments, not only to understand but to predict their conduct? This is the claim made by the Theory of Value, which was established by the e n d of the nineteenth century as the central doctrine of political economy. It can be summarized by saying that self-interest induces 23

24

C. L S SHACKLE

men to live by reason, and that by doing his own reasoning from the tastes and circumstances of individuals, could he know them precisely, the analyst could know what they would do. Let us however inquire what we must mean here by circumstances. The circumstances which concern a man in choosing a course of conduct are those which will affect the sequel of that choice. Anything which, if it were itself different, would make a difference to the sequel, is relevant to his choice. Among such things are the actions which other people will be taking w h e n the sequel of his present choice is working itself out. Those actions of others will be the result of choices made by them, at the time when our chooser is making his choice, or in time to come. How can he know what actions they are choosing, or will choose? What they will choose in time-to-come he cannot know, if choice means what our unselfconscious use of language takes for granted. Can he even know what they are choosing " n o w " ? Only if we suppose that all the simultaneous choices are prereconciled. If each man made out a list of actions, one or other of which he would perform according to the actions promised by others, it is conceivable that when all the lists were collated, a set of actions could be found, one from each list, such that each man would choose that action out of his own list, given that each other man promised to perform the action prescribed for him out of his list. Such a set of pre-reconciled actions can be called a general equilibrium. It consists of actions all chosen at the same time. What of actions to be chosen in time-to-come? There must be no such actions. In order to have a general equilibrium, time-to-come must be abolished. The general equilibrium, where every person's action springs from fully informed reason, can exist only in a timeless world, a world of a single moment with no future. T h e notion of a general pre-reconciliation of choices is easier to entertain when the actions involved are confined to exchanges of goods between the members of the society. For then the business of pre-reconciliation need only find prices of goods in terms of each other, such that the total quantity of each good offered, and the total quantity of it asked for, are equal for every good. But the discovery of such prices is the business of a real existing institution, the market. It does not, however, pre-reconcile the offers of exchange made simultaneously in a timeless world. It works in the continuing stream of history. Moreover, the participants in the market are conscious that there will be market days in time-to-come, w h e n some of the goods now traded will still be in existence, so that any price agreed upon to-day will later be compared with prices which may prevail on any

New Tracks for Economic

Theory

25

such later day. Thus the market in durable goods, or in means of production intended to yield products on later days, will necessarily be speculative. T h e market in the real world of supposedly continuing history only pursues remotely the ideal of fully informed rational inter-active choices. Insofar as it approximates that ideal, however, it achieves a system which embraces all goods, including those means of production, such as the services rendered by human beings or by their possessions, the sale of which provides the members of society with incomes. These incomes consist of shares of the aggregate of goods and services which the members of society are collaborating to produce. Is it sure that the shares which they are individually able to claim will add up to a total neither more nor less than the aggregate which they have together produced? All will be well in regard to this, the famous adding-up problem, if we make some further stipulations. If production is so organized that a doubling, trebling, et cetera, of the numbers of workers, acres of land, and so on right through the list of factors of production, will precisely result respectively in a doubling, trebling, et cetera, of the quantity of product made per week or per year (the output); and if the pay of each person or other factor employed is equal to the difference which his presence or absence makes to the output of the product; and if the suppliers of productive services are paid their incomes in product and not in money, then the adding-up problem will come out right. However, in the real world, pay is in money and not in product. What further stipulation will ensure that this does not matter? It will not matter, if the product is made, and sold for money, by firms in perfect competition with each other. For then a change in any firm's own output will leave the price per unit of the product unaffected, and it will not matter w h e t h e r the annual quantity produced is measured in physical or in value units. What, then, is perfect competition?

Perfect Competition It is a dazzling piece of conceptual sleight-of-hand. We have to suppose the number of firms making some technologically defined product to "increase beyond all b o u n d s " (as a technique of thought, not as a piece of history). T h e total output of all these firms does not, however, in this purely abstract and formally conceived process, increase at all. Instead, each firm is d e e m e d to get smaller and smaller, so that its output "tends to zero" (without ever reaching zero). Each firm is thus of negligible size in relation to the industry, namely, to the entire

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collection of firms all making a technologically identical product. No practicable change in its own output will discemibly affect that of the industry as a whole, and thus it will sell its product at a market price which is uniform for the whole industry: it cannot charge more, it need not charge less. The unit price of the firm's product being thus invariant against changes of its output, that output can be measured either in dollars or in litres, kilograms, cubic feet, et cetera, and if, by deeming every factor of production to be as finely divisible as w e like, we ensure the sort of relation we have described above (called "constant returns to scale") between factor-quantities and output, then the adding-up problem comes out right no matter whether pay is in dollars or physical units.

Failure of the Rational Conception What picture of economic society and affairs does all this give us? In order to treat all conduct as guided by fully informed reason, it abolishes time, except for a single momentary flash of existence for the world; or, at the very least, a society which lives wholly in such moments, each entirely cut off from others and neither inheriting anything from the past nor bequeathing anything to time-to-come. In order to show how incomes are determined so as precisely to exhaust the total output, it assumes perfect competition, in which all firms are vanishingly small, and the consumers of goods do not mind from which individual supplier they get the commodities, each defined by physical characteristics, that they need. It was this picture of the economic world which, in the 1920s and, more dramatically, in the 1930s began to seem inadequate and even fundamentally wrong and misleading. The seeds of new thoughts had already been sown while the conception of perfectly competitive general equilibrium was establishing itself, and they had b e e n sown by one of the authors of that conception, Knut Wicksell, who in his Interest and Prices1 had shown that in a society which uses money in the full meaning of the word, money has a p o w e r f u l a n d essential influence of its own on affairs. In 1926 Sir Dennis Robertson (as he became) published Banking Policy and the Price Level, and in 1930 John Maynard Keynes, influenced by Wicksell and by his discussions with Robertson, published his Treatise on Money. Here Keynes used •The title given by Professor Lord Kahn to his translation of Geldzins preise.

und

Güter-

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a most powerful, simple, and fundamental invention of his own, which in an alternative form employed the principle concurrently and independently suggested by Wicksell's follower Gunnar Myrdal, expressed by him as the distinction between ex ante and ex post. Keynes nowhere explained his Fundamental Equations in these terms, failed apparently to see what their essential nature was, and in his The General Theory of Employment, Interest and Money, abandoned them in favor of an inappropriate resort to a quasi-equilibrium formulation. To Myrdal belongs the honor of liberating economic theory by an Alexandrine stroke from its assumption that the future and the past were meaningless words.

What Can Be Known? At the root of the false views and policies implicit in the Theory of Value, when this theory was consulted about the problems of the post-1918 world, was its neglect of the question: What can the maker of economic choices know? On the epistemic question, the Theory of Value had nothing to say, except for Edgeworth's (purely theoretical) proposal that the prices composing a General Equilibrium would be established by "re-contract" (i.e., by trial and error) and Walras' reference to essentially the same notion under the name of "tatonnements." (But the invention which performs at unthinkable speed a systematic procedure of trial-and-error was three quarters of a century away.) But the problem of discovering the measurements of a timeless equilibrium is at any rate not essentially, fundamentally, in the nature of the human condition and the Scheme of Things, beyond the reach of mortal man. Knowledge of the content of time-to-come is beyond it, if by choice we mean a human capacity and freedom to originate history. Suppose my employer, or some other compulsion, tells me to go from New York to Los Angeles, and suppose at the airport a notice gives me a list of flights and their respective destinations, one to Chicago, one to Montreal, one to Miami, and one to Los Angeles. I successfully reach Los Angeles, because I "chose" the right plane. If "choice" is a mere response to tastes and circumstances, both kinds being given and known, does "choice" originate anything? No. But if choice does originate something, if choice starts something new, something that was not implicit in the antecedents, then there is no foreknowing choice, and there is no knowing what time-to-come will make of present choices. In this foregoing paragraph I have gone far beyond any argument to be found in Keynes or in Myrdal. But if any

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such argument as the one I here propose concerning choice is accepted, then a frame of analysis such as Myrdal's ex ante and ex post, or the Fundamental Equations of the Treatise on Money, is indispensable and powerful.

Monetary Equilibrium Myrdal's English version, Monetary Equilibrium,2 appeared long after its Swedish and German versions, and still longer (some twelve years) after Myrdal's work in the later 1920s on his doctoral dissertation. Monetary Equilibrium is the record of an intense effort to give clear and sharply distinct form to Wicksell's discussion of the engenderment of inflation. An interest rate is a pace of proportionate growth of a debt. If one hundred dollars is lent today on condition of the borrower's promise to repay the lender one hundred and ten dollars one year from today, the debt is going to grow at ten percent of its initial amount in a year. This is a pace, so much per unit of time; and the "so much" is a proportion, ten percent. If the borrower thinks that what he can buy with the borrowed hundred dollars, or what he can make with what he buys or hires with it, will sell for one hundred and twenty dollars in a year's time, the borrowing will seem profitable. In order to make the loan, the lender may have refrained from himself buying something. Then, perhaps, the market will experience no increase of pressure. But there is a lender who can lend without foregoing any purchases. This is the banking system. If the banking system lends at a lower percentage per unit of time than the gain that businessmen think they can make with such loans, many businessmen will borrow in order to buy materials, build factories, hire labor. The prices of these will rise, the suppliers of them will be richer, they will themselves spend more than before, the prices of goods will rise again. And so on, and on. If the banks now raise the interest rate they charge so that it equals, on the whole, the rate of gain, whatever it may be, that businessmen now hope to make, it will no longer pay these businessmen, or seem to pay them, to expand continually their borrowing and their spending in attempting to expand their production. Thus, said Wicksell, the general rise of prices, the inflationary rise of prices, will stop. The general rise of prices, induced by a money rate of interest (the banks' lending rate) which is less than the natural rate of interest (the gain obtainable from industry and commerce) is a dis2 Hodge,

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equilibrium phenomenon, one which, so far from finding a new resting place, is spurred on by its own effects. If the two rates were kept equal, the inflationary process would never start. This theory, this theorem, was the inspiration of three men of very different experience, outlook, and natural tendency. It induced Myrdal to write the thesis which in English is called Monetary Equilibrium. It gave Keynes the clue for his Treatise on Money. It suggested to Professor Hayek the possibility of a neutral money, explained as one strand of Prices and Production, that prophetic warning given forty years before its time.

Investment and Saving What has all this to do with the 1930s? The problem then was catastrophic business depression and unemployment. Keynes' Treatise did not talk about unemployment, only about price levels. But it did talk about the relation between saving (leaving unbought some of the goods that were produced) and investment (producing goods intended for use by businessmen as such, not for consumers). Provided goods not bought by consumers were duly bought by businessmen as such, for use as tools, as means of further production, no one need be driven to fire his labor force by the fear that he could not sell his output. So long as investment absorbed all the output which was in excess of consumption, there would be no increase of unemployment. If this equality could be achieved and maintained for an output big enough to employ everybody who wanted to be employed, there need be no involuntary unemployment at all. Keynes decided to turn the Treatise argument in a new direction, to explain the size of output as a whole, and thus to explain the level of employment. The first Fundamental Equation of the Treatise on Money said that prices of consumers' goods in general ("the price level") would prove to have risen if it turned out, at the end of some period (a particular week or year) that the money spent in that period on investment had been more than the difference between the income earned in that period and the amount spent in it on consumption. But could those two amounts, investment and saving, differ from each other? They could, because the income in question was the income which had in total been expected at the beginning of the period by all those (including the businessmen themselves, the employers) who had collaborated in the production of goods during the period. The amount spent on investment goods, however, was not reckoned until the end of the

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period, it was a recorded fact, and its amount could be quite different from the excess of the formerly expected income over the recorded consumption-spending of the period. Money could be spent on investment which had been held in reserve, or which was borrowed from the banks as an addition to the pre-existing quantity of money; or investment could be less than saving, through money being put to reserve, or used to pay off bank loans. In short, the first Fundamental Equation treated income as a quantity reckoned before the event, ex ante facto, at the threshold of the period when the events would take place, but it treated consumption-spending and investment as quantities actually realized and recorded at the end of the period, ex post facto. Thus there could be a difference between (intended) saving and (realized) investment, and if the former fell short of the latter, more would be spent on consumption goods than people had reckoned on. Their prices would be higher than had, at the outset, been expected. And vice versa. Keynes did not use the expressions ex ante, ex post. These were Myrdal's introduction, and it was Myrdal, and by no means Keynes, who made explicit the vital difference of nature between what people envisage as the contents of a period of time-tocome and what they can record as its content when it is past. Yet this distinction is shown by Keynes' spontaneous implicit invention of it, and use of it, to be indispensable. When he had finished the Treatise, Keynes thought he "could do it better, and much shorter," if he were to start over again. The new version, The General Theory of Employment, Interest and Money, replaces a fragmentary and scattered account of the inducement to invest with a massive treatment occupying some forty pages. Yet it is one particular aspect of this treatment which is the truly essential contribution of the General Theory, the heart of Keynes' explanation of how unemployment can be involuntary. Keynes was very far from recognizing, in the course of writing the book, just what his ultimate conclusion was turning out to be. He left statements standing in the book which are incompatible with his ultimate theme. That theme is that we do not and cannot have knowledge of what will come about in time-to-come, not even a year or two ahead or (as recent events may have impressed on us in 1973, 1974, and 1975) a month or two ahead. Yet in Chapter 2, where Keynes attempts the obviously essential task of showing that "involuntary" unemployment is logically possible, he endorses the orthodox principle that the wage offered by an employer will be equal (under stress of competition from rival employers) to "the marginal product of labor," the difference which the presence or absence of one man would make to the value of output. In a time of

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deep business depression, w h e n all the foundations of confident expectation seem to have crumbled, what answer can a businessman give himself w h e n he asks: What difference does one extra man make to the value of an output which I have yet to sell, in a seemingly disintegrating market where nobody is buying anything he can do without? H e must reckon with the possibility that his output is already on a highly price-inelastic part of the d e m a n d curve, so that one extra man's output may actually make a negative difference to the total value of output. And there is a further question, to be put not by the businessman but by the analyst: What foundation is there in such a time for notions of definite and stable curves as descriptions of the situation facing a businessman? Keynes, in the Treatise, had shown that investment and saving were not identically equal, were not merely two names for the same thing. For they should be looked on as two distinct bodies of intentions, two sets of conjectures about time-to-come. But there is another possibility to be taken into account. May not these two quantities be brought into equality by some equilibrating influence? May there not be a price which makes demand for saving, namely investment, equal to supply of saving? What would this price be? It would be a rate of interest, if, as the orthodoxy of those days declared, the interest rate was itself determined at that level which brought investment and saving to equality. To show that investment could be unequal to saving and remain so, Keynes had to repudiate this theory of the interest rate and replace it with another. Liquidity preference, and the essential notion of liquidity itself, is the most original of Keynes' technical contributions.

Liquidity Preference A bond is a borrower's promise to pay to the lender stated sums at stated dates. The lender cannot tell, w h e n he hands over money as a loan to the borrower, at what date he may wish to repossess his money. If he should need it before the date w h e n the borrower has promised to complete his repayment, what will the lender be able to do? If there is a bond market, he can sell his bond for whatever sum, at the unknown date in time-to-come w h e n he may n e e d his money, it will fetch. In order to give himself some presumption that such a sale will at least restore, or complete, the restoration to him of the initial sum, the lender will require the borrower's promised payments to exceed, in total, the sum he lends. That percentage per unit of time which,

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when used to discount the borrower's promised payments, gives them a present value (a discounted value) equal in total to the initial loan, is the interest rate on this loan. It guards and compensates the lender for parting with a known sum of money in exchange for an unknown sum, it compensates him for his voluntary exposure to uncertainty. Interest is the price which lenders can exact for giving up a liquid asset, money, in exchange for one which is less liquid, a bond. What, then, in essence, is liquidity? Liquidity is the quality of that asset in which contracts for payment are made, and which, therefore, will ultimately be needed in order to make those payments. So long as the man who has contracted to make a payment (of wages, of a debt, et cetera) holds in his possession a suitable quantity of this payment-medium, he can feel sure of being able to pay. He will not be exposed to risk of loss of value, in terms of the payment-medium, of any asset he might hold instead. In "normal" times the most liquid asset, and the universal medium of contracts for payment, is money. Keynes said that there were three motives which might induce a man to hold money instead of an income-earning asset (land, houses, plant, company shares, or bonds). These were the speculative motive (fear of capital loss), the transactions motive (desire to be immediately able to make unforeseen payments), and the precautionary motive. The last of these, however, is superfluous. Assets held against the need for unforeseen payments could be incomeearning assets, were it not for the danger of capital loss in case of a precipitate sale. But to hold liquid assets against that danger is the speculative motive. What, then, is liquidity? It is a defense against uncertainty. The interest rate, or the system of rates on bonds with various terms to run to their extinction, plays a complex and somewhat deceptive role in the argument of the General Theory. It is shown there to owe its existence to uncertainty, and thus it fits well into an argument whose central theme is the blankness of time-to-come. It claims its place in the theory of the inducement to invest, since the value placed in today's market on an investment good (a petroleum-cracking plant, a ship, a housing block) rests on some hypothetical series of trading profits that this instrument is conceived to yield in future years. However, today's valuation would not, even if those future profits were guaranteed, be equal to their sum. For an amount less than that sum could be so lent today, various parts of it for various lengths of time, as to yield amounts equal to those supposed profits at the dates in question. The lower the interest rate used for this discounting, the higher would be the present value reckoned with it, the more easily that

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present value could out-top the cost of construction and make investment seem worthwhile. But if time-to-come is a matter so largely of blank unknowledge within wide bounds, will not the shifts of conjecture or ascribed possibility concerning the profits themselves far outweigh any fluctuations of the interest rate? Keynes ascribed a failure of businessmen to fill with an equal flow of investment the potential saving gap between output and consumption at full employment to a lack or breakdown of "confidence," a failure for the time being of the gambler's capacity for self-sustaining hope. Failure to fill the gap with investment deliberately planned will mean that it is filled at first, after a drop in such investment, by unintended investment in the form of unsold inventories of consumers' goods, and that later the gap itself will be reduced by a reduction of output, of employment, and thus of income. It is, unhappily, the mechanics of Keynes' conception of economic society, such features of it as the consumption function, which have c l a i m e d most a t t e n t i o n , distracting (or shielding?) m e n ' s thoughts from the vital proposition that enterprise is the daring, and desirable, pursuit of-imagination, not merely or mainly reason; that enterprise is imagination in action. T h e nature and source of a rate of interest was the problem which had engaged E u g e n von Böhm-Bawerk in writing his Positive Theory of Capital during the 1880s. His central ideas were given a refined mathematical expression by Wicksell and later intensely explored by Professor F. A. von Hayek. Böhm-Bawerk sought to explain interest as the reward claimed by those who contributed the productive services of themselves or their land long before the consumable product could emerge. T h e embryonic or instrumental products ("intermediate products") which stored up these services and carried them through the time-consuming productive process to consumable completion were the means of a more effective "division of labor" than the best available in a process leading more quickly from inputs to result; and the result, in each week or year, could therefore be permanently larger for the same input-amounts of the services of men and Nature. The intermediate products made up a mass of "capital" whose size, and whose efficacy as a whole in economizing productive services, increased with the "average period of production" which elapsed between inputs and output. This "waiting" between input and output was distasteful, and so its fruits, the tools which made labor and Nature more effective, were scarce, high-priced, and able to afford a compensation to those who performed it. Between increasing marginal distastefulness and decreasing marginal efficacy there would be a balance at some particular size of the capital stock, that is, of the

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"average period of production." However, there is a question here. We have to consider that everything that exists, exists now, in "the present." All goods which compose the capital stock exist simultaneously, and those individuals who are now supplying productive services can be paid now with the now existing results of earlier efforts. In a stable and constant capital stock, there is no inherent "waiting." It is only when the capital stock is being increased that the results of present effort must be looked forward to by individuals over a span of time. The notion of "roundabout production" in which an elaborate apparatus of "produced means of production," or "intermediate products," enables given quantities of "original means of production," labor and natural forces, to yield a larger output of the goods wanted by the ultimate consumers, can nowadays be illuminated by one more conceptual tool invented in the 1930s. In those years a scheme of thought was proposed whose purpose was to make possible the calculation of the changes of output of intermediate goods (the direct products of farming or mining, goods intended for further processing, tools of every kind, all sorts of instrumental systems and equipment) which would be called for in response to any change in any items of the list of d e m a n d e d quantities of final products ready for consumption. Leontief's input-output analysis is in fact a pragmatic picture of coexisting capital items, a picture of the techno-temporal structure of the capital stock. Leontief was concerned with the technical structure, but within this technical structure there is latent a temporal structure, residing in the fact that what exists today as yarn, and what exists today as cloth, and what exists today as finished garments, do not and never will belong in the same physical object, yet today's finished garment was at an earlier time cloth, and that cloth at an earlier time still was yarn. Leontief was not immediately concerned with the temporal structure, but if changes are made in the "bill of goods for final u s e " these changes will require time spans in order to have their full effects, and those time spans will reflect the technical capital structure of production. They are the reality of the time-structure of production. T h e Theory of Value and Distribution (that is, of relative prices and the sharing of income), the central doctrine of economic theory from late Victorian times until after the First World War, drew its ascendancy from its claim to be the logical consequence of a very few axioms easily recognized to be true. That ascendancy was destroyed during the 1920s and 1930s by its gross and fundamental incongruity with what was seen to be happening in the world. Far the most basic and incurable source of this incongruity, the essential reason for the

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failure and irrelevance of t h e doctrine, was its entire disregard of t h e question of what m e n could know. It assumed, without argument, that they could k n o w e v e r y t h i n g necessary for d e m o n s t r a b l y optimal choices of conduct. (Such demonstration would require a means of proving that the available knowledge was i n d e e d relevantly complete.) This total rejection and denial of the h u m a n condition, the fact of the void of future time which we can only fill with surmise a n d figment, left it helpless to explain the events of the early 1930s w h e n , for example, the income of the United States in money terms was halved. But even on its own terms the structure of the theory of value was defective. T h e notion of perfect competition, on which it rested, is internally inconsistent and even basically unintelligible. Its inconsistencies w e r e explained by Mr. Piero Sraffa in a classic article in the Economic Journal for 1926. If perfect competition lets firms expand output freely without reduction of price, and if economies of large scale make their unit costs lower the larger their output, what can prevent any one such firm " w h i c h gets a good start" from swallowing the whole market and destroying competition? This dilemma, p o s e d in essence by Alfred Marshall whose words I have just borrowed, a n d long before him by Cournot, b e c a m e in Mr. Sraffa's hands the signal for a great schism. Perfect competition was quite central and essential to t h e great encompassing, simplifying, and unifying Theory of Value, solver of the problem of income-sharing and foundation of the G e n e r a l Equilibrium. In the late 1920s and early 1930s, the move was m a d e by Harrod and Mrs. Robinson (among others) in Britain, by C h a m b e r l i n and Yntema in the United States, by Mehta in India, to abandon perf e c t c o m p e t i t i o n a n d c r e a t e a t h e o r y of I m p e r f e c t , or e l s e of Monopolistic, Competition. But it proved easier to destroy the old symmetry and simplicity than to replace it. To invent a n e w tool of thought, or show how an existing s c h e m e can be adapted from another discipline, can have as far-reaching an effect on our field as the proposal of n e w substantive propositions. In 1934 Sir John Hicks s h o w e d how an individual's division of his expenditure over different consumer's goods could be explained by means of indifference curves c o m b i n e d with a budget-line. Indifference curves, an adaptation to economics of the geographer's lines of e q u a l altitude or contour-lines, h a d b e e n i n t r o d u c e d by F r a n c i s Ysidro E d g e w o r t h in his book Mathematical Psychics in 1881. Vilfredo Pareto had u s e d a family of such curves as a " p h o t o g r a p h " of an individual's tastes, and E n r i c o Barone, in order to exhibit the effects of taxes, had a d d e d to Pareto's indifference-map a straight line w h i c h expressed both the prices of two goods in terms of each other, and the

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individual's income in terms of each good. Sir John Hicks used such a scheme to improve on Alfred Marshall's method of measuring the intensity of a consumer's desire for a small increment of his weekly (et cetera) supply of some commodity. Such a desire, Marshall said, could only be measured by seeing how much money, in given circumstances, the individual would pay for the extra weekly quantity. Chief among these circumstances was the size of his existing weekly supply. The larger it was, the less intensely he would wish for any extra. However, this diminishing marginal utility would not be quite accurately measured by the diminution of the money he was willing to pay, since the latter would be diminished also by his increasing shortage of money, as he considered buying a larger and larger weekly quantity of the good. Marshall's proposal was simply to ignore this effect of the increasing shortage of income and treat the marginal utility of income as invariant against changes in the amount of income still disposable. By means of the indifference-map and budget-line, Sir John Hicks was able to separate from each other the "substitution-effect" and the "income-effect." However, Hicks' real contribution, by his article in Economica of 1934, was to spread widely an appreciation of the indifference-map as a tool. It has been applied in scores of diverse contexts, with surgical effects on obscure economic enigmas. What has been called the "Cambridge method" in economic theory consists in a shuttling by the theoretician between the problem he at first sets out to solve and the conclusions at which, with great labor and many false trials, he eventually arrives. It may become obvious, when that solution is arrived at, that it could have been approached more easily, and can now be viewed more intelligibly, as the solution to a somewhat differently formulated problem from the actual starting point of the investigation. Then the argument is (very profitably and at a great gain in efficiency of insight) realigned on this somewhat different target. Closely linked with this practice is what may be called the encapsulating method. Difficulties which seem more tiresome than they are worth, obstructive of advance but not seemingly concerned with the essence of things, can be shut up in a black box which is then treated as a thing-in-itself, not to be inquired into but fitted, as a whole and unopened, into any scheme where its contents are broadly relevant. One such simplification is the capital-to-output ratio defined independently by Sir Roy Harrod and Professor Evsey Domar. It is essential to the notion of the regularly progressive economy, by which so dramatic a picture can be given of the workings of the business cycle, intractable unemployment, inflationary pressure of demand, and the inherent instability of economic systems.

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In t h e later 1920s and the 1930s, a great spasm of creative effort in e c o n o m i c theory r e s p o n d e d to the visible dissolution of the comparatively orderly Victorian world in w h i c h Marshall had b e e n able to discern t h e gradual perfectibility of industrial a n d social organization h i n t i n g at the perfectibility of h u m a n nature itself. T h e tranquillity had b e e n shattered, and the theory of e c o n o m i c life which reflected it n e e d e d to b e transcended a n d even wholly s u b v e r t e d . Not merely the detailed design of the economist's account of things n e e d e d to b e c h a n g e d , b u t its f u n d a m e n t a l assumptions, its p u r p o s e s and ambitions, what it claimed to do had to b e essentially reconsidered. Such a reorientation was hard to accept a n d is still mainly unaccepted.

II Keynesianism

Introduction Keynesian e c o n o m i c s d o m i n a t e d t h e t e a c h i n g world of macroeconomics from about 1950 to the mid 1960s. Ordinarily, what was done was to attach Keynes' name and prestige to an interpretation that first emanated substantially from the methods adopted by Professors Alvin Hansen and Paul Samuelson, and then later, in what were esteemed the more rigorous accounts, from the conceptual version of Keynes offered by Sir John Hicks. It is thus not inaccurate to describe the ideas that flourished in textbooks and economic journals, and penetrated the thought patterns of self-styled Keynesians, as Hicksian Keynesianism. Many of t h e m w e r e only t e n u o u s l y connected to Keynes' General Theory; they particularly violated his injunction to stick to the "wage-unit" as fundamental to the conduct of the analysis. Failure to h e e d the message has led to some abject confusion on what has emerged as the great issue of the last decade, perhaps of the future, namely, the torment of inflation compounded with growing unemployment and sometimes output recession. T h e "double trouble" has compelled the invention of the awkward "stagflation" and "slumpflation" names to describe the twin disaster. Lately there has been more awareness of the mischief perpetrated in the name of Keynes, and many of the erroneous thought currents promise to be corrected; but the price of the belated awakening has b e e n enormous damage to economic development, political systems, progress, and stability, by the bumbling loose play of "Keynesians" on the General Theory. Once the IS-LM model of Hicks became sanctified as Keynesianism, about the only serious subsequent modification in the system was its incorporation of the Phillips curves, to e m b e d the possibility of some inflation even before a state of full employment was achieved. After a contagious spectacle of faddish immersion in Phillips curve studies, the early ideas on the vaunted empirical " l a w " gave ground, followed by a flexible analytic concoction of "shifting" Phillips curves. Some still fail to see the anomalous intellectual caricature in this episode, even though it involved a 180-degree turn, to transform what was 41

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presumed to be a predictive law to an ex post description—or usually a post mortem on why predictions based on the predicated correlation went awry. Some aspects of the phenomena, and diverse evaluations, appear below. In the initial essay I have (after the failure of an assigned paper to appear) taken for granted student classroom experience of both the Hansen-Samuelson 45-degree line and the Hicks 1S-LM functions. After all, these fill our overstuffed textbooks in the first course, the intermediate course, the initial graduate school courses, and stops en route. My own exposition of the models is mainly to subject them to criticism, for I doubt that they can ever b e restored: more than a face-lifting is essential; a reconstruction from new foundations is necessary. While I think that my own version of the theory, emanating from Aggregate Demand and Aggregate Supply functions— and more definitely rooted in Keynes—is free of the Keynesian shortcomings, I have not pressed this opinion very far in my essay. Interested students can read further in Keynes and can peruse my frequent laments on the logical shortcomings and empirical i r r e l e v a n c e of c o n v e n t i o n a l Keynesianism. Beyond the simple models that passed for the Keynesian wisdom, the school is identifiable mainly by its technical baggage. T h e essential model components consist o f : (1) the consumption function, (2) the investment function, dependent on the marginal efficiency of investment, (3) the demand for money, as represented by liquidity preference, and (4) the multiplier, which explains the interaction between growing investment and growing income and e m p l o y m e n t . As a latter-day appendage, dating mainly to Sir Roy Harrod in his Trade Cycle volume, there is (5) the acceleration-principle. 1 All of these measurable concepts are derived from Keynes (with the acceleration principle included on a most generous textual appreciation of an occasional passage). Professor Ronald Bodkin undertakes the formidable job of surveying the content of what has become a voluminous specialized literature, with each concept capable of filling a small library section. The concepts figure prominently in the proliferation of computerized econometric forecasting models of the economy, where each concept has floated off to crystallize subdivisions, e.g., consumption functions for foodstuffs, for energy, for clothing, for autos, for consumer durables, etc. Likewise, the investment function has come to be drawn and quartered into housing, factory construction, equipment, inventories, and a variety of subcomponents. The »Roy F. Harrod, The Trade Cycle (Oxford: The Clarendon Press, 1936).

Keynesianism

43

resulting open concertina of equations has left the IS-LM model merely a collapsed accordion, poised at a moment of rest before being drawn out to accommodate a varying scale of identifiable notes. Bodkin has contributed to both the theoretical and applied Keynesian econometrics. Serving as senior editor in the construction of the 2049 equation Candide model for the Economic Council of Canada, he is also well-versed in United States models. The essay should be informative to students with only minimal exposure to Keynesian econometrics; Bodkin's interpretations will also evoke reflections even among specialist practitioners of what Keynes once called "the black art." Professor Paul Wells' essay is cast wholly in the theoretical mold. He too bears witness to aspects of the misguided Keynesian evolution. In the main, his view is consistent with my own position. Wells has effectively maneuvered Keynes' expectational attitude back on center stage (not unlike Shackle, Chapter 2 above). Wells also protests the analytic retreat involved in conceiving Keynes in a stationary framework, rather than apprehending that his theory opened the doors to the winds of change, the economic dynamics of growth, of cyclical oscillation, to an economy running down to severe unemployment or lunging forward to jobs for all. Professor Wells' paper is short but weighty. Although these three papers are included as a Keynesian unit, the classification is purely arbitrary, an act of editorial judgment on organization. Practically all of the papers that fall under Part V, on Money, could follow at this point. Some may prefer to read these essays immediately, as part of the Keynesian macroeconomic discussion. My arrangement is technical, not substantial: those who want to view monetary theory as independent of the Keynesian discussion may prefer the separation as not unnatural and as having some pedagogic advantages.

3 Hicksian Keynesianism: Dominance and Decline SIDNEY WEINTRAUB In an eloquent passage Keynes wrote that "Ricardo conquered England as completely as the Holy Inquisition conquered Spain." 1 Keynesianism likewise, often only tenuously connected to Keynes, dominated the post-World War II period until after 1968, when inflation and unemployment events exposed some hollowness in the paradigm.2 From a historical perspective, it is probably more accurate to describe the ideas that flourished and faltered as Hicksian Keynesianism in view of the pervasive influence of Nobel economist Sir John Hickr in conveying a thought scheme that was in critical ways at odds with the theory of Keynes. 3 In a plea for its abandonment, the present writer once denoted the Hicksian variety as Classical Keynesianism. 4 Joan Robinson has castigated the evolution as Bastard-Keynesl John Maynard Keynes, The General Theory of Employment Interest and Money (New York: Harcourt Brace, 1936), p. 32. ^Sidney Weintraub, "The Keynesian Light that Failed," Nebraska Journal of Business and Economics 14(Autumn 1975): 3-20. 3 The seminal article was J. R. Hicks "Mr. Keynes and the 'Classics'," Econometrica 5(1937): 147-159. 4 Sidney Weintraub, "Classical 45° Keynesianism: A Plea for Its Abandonment," in Classical Keynesianism, Monetary Theory, and the Price Level (Philadelphia: Chilton, 1961). Also "The Keynesian Theory of Inflation: The Two Faces of Janus?" International Economic Review 1 (May 1960): 143-155, reprinted in Classical Keynesianism.

45

46

SIDNEY WEI NT RAUB

ianism. 5 Axel Leijonhufvud has devoted a volume to spotlight the misconceptions in the Keynesian transcription of Keynes. 6 Space limitations p r e c l u d e a pursuit of this fascinating episode, in which Keynes' name was attached to the Hicksian anomaly. Rather than undertake another attempt to clarify the vital distinctions, this chapter will focus on the dominant textbook Keynesianism which prevailed until the inflation events disclosed its impotence and irrelevance to policy. U n r u l y p h e n o m e n a , r a t h e r than c o g e n t logic, t o p p l e d Keynesianism from its lofty perch. Western market economies (including Japan and Australia in the category), suffering from "stagflation" and "slumpflation" woes, have thus bedeviled Classical Keynesianism and left it in a state of disrepair, and they have aborted the Keynesian Revolution. Keynes, however, emerges as relatively unscathed. 7

Keynesian

Origins

Early Keynesianism was in great measure a creation honed by the late Alvin Hansen and by Paul Samuelson, the first U.S. Nobel laureate in economics, who popularized the doctrine in his enormously successful textbook. 8 Too, there had b e e n the exemplary statement by Lawrence Klein and a pioneering teaching exposition by Dudley Dillard. 9 As the early Hansen-Samuelson theory revealed an internal inconsistency, Keynesianism evolved in the 1S-LM functions of Hicks. Recently, Hicks has expressed disenchantment with the tradition he spawned. 1 0 It will undoubtedly take some time before 5 Joan Robinson, Economic Heresies ( N e w York: Basic Books, 1971), p. 90. Cf. also "The Second Crisis of Economic Theory," American Economic Review 62 (May 19721 e Axel Leijonhufvud, On Keynesian Economics and the Economics of Keynes ( N e w York: Oxford University Press, 1968). Beyond the excellent critique of Keynesianism, the author goes too far in imputing Walrasian general equilibrium concepts to Keynes. Ά . P. Lerner has remarked recently that in seeing the n e e d for control over moneywages Keynes was "often ahead of himself." S e e "From the Treatise on Money to the General Theory," Journal of Economic Literature, 12 (March 1974), p. 42. Similarly, Sir John Hicks, in the Crisis in Keynesian Economics ( N e w York: Basic Books, 1974) admits some failure to apprehend Keynes' use of "wage-units." Belatedly (by some 37 years) he enunciates Keynes' "wage-theorem," with money wages causing price level movements (pp. 59-60). Keynes can hardly be the one at fault for the colossal Keynesian misreading—mostly by secondary Keynesians accepting a standard interpretation. 8 A very lucid statement by Alvin Hansen, though by no means his earliest version, appears in Monetary Theory and Fiscal Policy ( N e w York: McGraw-Hill, 1949), ch. 5. T h e theory has b e e n widely disseminated in the various editions of the popular textbook of Paul Samuelson, Economics, lst-9th eds. ( N e w York: McGraw-Hill, 19481973). 9 Lawrence Klein, The Keynesian Revolution ( N e w York: Macmillan, 1947), and Dudley Dillard, The Economics of John Maynard Keynes ( N e w York: Prentice-Hall, 1948). 10 Hicks has remarked that he never expected the IS-LM analysis to b e "regarded . . . as complete." Cf. Hicks Crisis in Keynesian Economics, p. 6.

Hicksian

Keynesianism

47

other Hicksian Keynesians become aware of the recantation and alter their writings with the "muddles in the middle." 1 1 We shall consider, very briefly, the main fiscal policy precepts that e m a n a t e d f r o m t h e K e y n e s i a n s t r e a m . In s o m e v e r s i o n s Keynesianism, was a brand of fiscalism, with the theory providing a rationale for using the levers of government outlay and taxation. 12 The most original contributions in this context were A. P. Lerner's perceptive insights on Functional Finance. 1 3 More recently, Lerner has concluded that the propositions must be joined to Incomes Policy to prevent inflation. 14 Other fiscalists have usually been myopic on the distinction between fiscal policy to influence output and employment and the n e e d for money wage restraint for price-level objectives. An alternative version of Keynesianism in terms of Aggregate Demand and Aggregate Supply will be sketched briefly, with a comment on the public debt, a subject which can always provoke heated controversy.

The Hansen-Samuelson 45-Degree Keynesianism Hansen-Samuelson Keynesianism was built about the famous 45degree "cross," which was hailed as equal in significance to Marshall's equilibrium intersection of supply and demand. 1 5 We outline the spirit and essentials of this model, acknowledging that at times the equations were a bit more elaborate. 1 6 For consumption (C) there was the consumption function: C=C(Y,r),

(1)

w h e r e Y = real output or real income; r = interest rates, involving the interest structure and level. " C f . Sidney Weintraub, "Some Hicksian Revision and Recantation: A R e v i e w Article," Journal of Economic Issues 10 (1976). 12 As Hicks has remarked, "Keynesianism became fiscalism" because of the early belief in the impotency of lower interest rates in enlarging investment (Crisis in Keynesian Economics, p. 33). 13 An early statement by Lerner appears in The Economics of Control ( N e w York: Macmillan, 1944), ch. 24. A recent cogent statement can be found in his "Keynesianism: An Exaggerated D e m i s e and a Premature Funeral," mimeographed (paper delivered at the conference on the Relevance of the N e w Deal to the Present Situation, City University of N e w York, 2 3 - 2 5 June 1975). 14 Lerner, "On Keynes." "Paul Samuelson remarked that "the intersection C(Y) + / with the 4 5 d e g r e e line gives us our simplest 'Keynesian-cross,' which logically is exactly like a 'Marshalliancross' of supply and demand." S e e "The Simple Mathematics of Income Determination," Income Employment and Public Policy: Essays in Honor of Alvin H. Hansen ( N e w York: Norton and Co., 1948), p. 135. le H a n s e n , Monetary Theory and Fiscal Policy.

48

SIDNEY WEINTRAUB

Next, the investment (/) relation: / = Z(r),

(2)

where I = real investment. C = consumption outlay would increase with income. I would expand at lower interest rates. The liquidity-preference or money demand function (L) was written: L=L(Y,r).

(3)

Higher real income would elevate the d e m a n d for money to finance the larger v o l u m e of transactions. F u r t h e r , b e c a u s e of K e y n e s ' "speculative-motive,'' lower rates of interest would also enlarge money d e m a n d inasmuch as: (1) the interest sacrifice in holding money rather than owning government bonds would be reduced and (2) as interest rates fell, the fear of a subsequent rise would become more acute: an upward turn in interest rates would cut the capital value of bond holdings. At very low interest rates, at institutional minimums for bank lending, liquidity-preference would become absolute: the L-function would turn perfectly elastic as the demand for money in p r e f e r e n c e to bonds became nearly insatiable. This region was termed, after Dennis Robertson's expression, the "liquidity trap.'' The money supply, generally defined as currency and demand deposits, was held constant: Μ = Μ.

(4)

The money supply was interpreted as an exogenous creation of the central bank. Finally, the system was completed with the definitional equation to represent the equilibrium balance.

C +I =Y

(5)

By substituting (1) and (2) into (5) we have one equation and 2 unknowns. By equating Μ = L (Y, r) we obtain a second equation in the same unknowns. Thus (with proper restrictions on the form of the equations), the model was determinate.

Geometry of the 45-Degree

Model

The model was also amenable to a neat geometric statement. Figure 1 contains the ubiquitous 45-degree line; each point along its course

Hicksian Keynesianism C,I|

49

45° C+I

c

J Y * Y« f

0

• Y

Figure 1.

related C + I = Y so that t h e final e q u i l i b r i u m had to settle s o m e p l a c e along the 4 5 - d e g r e e track. A C - f u n c t i o n o f c o n v e n t i o n a l form also appears. S u p p l e m e n t e d by the v o l u m e o f real /-outlays, the i n t e r s e c t i o n o f C + / with the 4 5 d e g r e e line r e v e a l e d the e q u i l i b r i u m output position (as Y * ) and the associated e q u i l i b r i u m C + I real outlays. K n o w i n g the production function b i n d i n g e m p l o y m e n t (Ν) to real output, w h e r e Ν = N(Y), e m p l o y m e n t was implicitly d e t e r m i n e d . B y c o m p u t i n g t h e CFY ratio, e i t h e r g e o m e t r i c a l l y or from the mathematical C - f u n c t i o n , t h e average p r o p e n s i t y to c o n s u m e c o u l d b e derived. T h e C - s l o p e at e a c h Y l e v e l y i e l d e d the marginal propensity to c o n s u m e , ΔC/ΔΥ. F o l l o w i n g K e y n e s , t h e " l a w of the marginal propensity to c o n s u m e " e n t a i l e d 1 > AC/ΔΥ > 0: c o n s u m p t i o n w o u l d rise with more i n c o m e but in l e s s e r amount. F i g u r e 2 traces an I-function, with m o r e i n v e s t m e n t in r e s p o n s e to l o w e r interest rates. At rit t h e n i n v e s t m e n t w o u l d b e forthcoming. T h e 11 magnitude c o u l d b e s u p e r i m p o s e d on t h e C - f u n c t i o n in t h e 4 5 - d e g r e e diagram. As F i g u r e 1 shows, t h e ΔΥ i n c r e m e n t in Y w o u l d surpass the I - m a g n i t u d e , e m b o d y i n g t h e r e b y the K a h n - K e y n e s " m u l t i p l i e r " relation: i n v e s t m e n t outlay w o u l d i n v o l v e a m u l t i p l e i n c o m e growth.

Inflationary and Deflationary

Caps

E q u i l i b r i u m prevails at Y * in F i g u r e 1. I f Y/ d e n o t e s the full e m p l o y m e n t output v o l u m e , t h e n t h e d e f i c i e n c y Yf — Y * m e a s u r e s t h e "deflationary g a p . " S t e p s to raise C (through cutting personal i n c o m e taxes, for e x a m p l e ) or to lift I through b u s i n e s s tax amelioratives or

50

SIDNEY W E I N T R A U B

Figure 2.

through monetary policy to lower r would be prescribed. In a more complete model containing government expenditure outlay (G), higher direct outlays could supplement I to provide an analogous multiplier punch. If (somehow) the C + I intersection occurred to the right of Yf, there would be an "inflationary gap." Fiscal policy would contemplate steps to repress C, I, and G. Inflation and deflation (unemployment) were symmetrical; the fiscal faucet could run hot or cold. 17

The Liquidity

Function

Figure 3 is a typical diagram used to portray the determination of "the" interest rate. The demand for money was described as an amalgam of L (Y) and L(r), where L(Y) = the "transactions-demand" of Keynes with more output and employment requiring more money financing. This part of demand was (largely) interest inelastic. L (r) embodies the "speculative-motive,"associating interest rates and the demand for money: in the diagram the "speculative" interest-elastic portion of L is given by L — Lr = Ls. A "precautionary-demand" could be tied to Y or r, to include some contingency demand for money based as a reserve provision for unexpected outlays in the world of uncertainty. " O n e account of the "symmetry" of inflation and unemployment reads: "Depression and inflation are essentially opposites, the one a consequence of too little effective demand, and the other a consequence of too much" (Robert L. Bishop, "Alternative Expansionist Fiscal Policy," Essays in Honor of Alvin H. Hansen, p. 318). Needless to say, literally a legion wrote in the same vein.

Hicksian

ra

Keynesianism

51

Lt

ι

s

Μ

L

0

Μ Figure 3.

T h e supply o f m o n e y is given by the perfectly inelastic line M, with the magnitude d e c i d e d by the central bank. Outside the perfectly elastic liquidity trap w h e r e the L-function turns flat, changes in the m o n e y total would affect interest rates. I n s i d e the perfectly elastic segment, c h a n g e s in the m o n e y aggregate would leave the interest rate u n t o u c h e d .

Fiscalism As Keynesianism T o many, the formal apparatus o f Keynesianism provided an intellectual s u s t e n a n c e for fiscal policy. Others less c o n c e r n e d with the intellectual n i c e t i e s of theory saw Keynesianism as a useful rationalization for activist government programs. E i t h e r way, fiscalism, as Hicks rem a r k e d , ' c o m p o r t e d comfortably with K e y n e s i a n i s m . 1 8 E a r l y Keynesianism was often colored by the empirical b e l i e f o f the insensitivity o f investment to interest rate reductions. B e c a u s e the rate on long-term government bonds, as late as 1940, was 2.4 percent, with short-term rates at 0 . 0 1 4 percent, little scope existed for interest rate reductions, unlike the situation in 1975, for example, w h e n entries w e r e 8 and 7 percent. G o v e r n m e n t expenditure in the e a r l i e r K e y n e s i a n days s e e m e d to b e a b e t t e r m u l t i p l i e r stimulant than further monetary ease. L i k e w i s e , at the earlier m o n e y i n c o m e levels, tax cuts p r o m i s e d only m e a g e r opportunities for stimulating consumption. In the Ken18 See the cogent expression of this position by Walter W. Heller, New Dimensions Political Economy (Cambridge: Harvard University Press, 1966).

of

52

SIDNEY W E I N T R A U B

nedy years, at the higher tax and income levels, an important tax reduction was engineered. Also favoring G-outlays was the pithy observation of Galbraith that the world of affluence was marred by "private plenty and public squalor." In Galbraith's view, the public domain was starved by lack of ample outlay: government outlays thus transcended the virtues of tax cuts for more frivolous private consumption. 19 The precepts of fiscalism need not detain us in this overview of Keynesianism theory for the doctrines thrive on constant textbook reiteration. Much that is best in fiscal Keynesianism is captured in the terse formulation by A. P. Lerner on Functional Finance. Lerner observed that everything that government could do about employment could be collapsed into a few statements: it could (1) buy or sell, (2) lend or borrow, (3) pay subsidies or exact taxes. 20 Acting on each first item would enhance output and employment, while the alternatives would restrain production. There was also an early belief that inflation would cease as output contracted. In contrast to the views of conventional fiscal Keynesians, Lerner has been more explicit lately that the price level would only be stabilized by Incomes Policy.

Misgivings Over the 45-Degree Model We turn now to some misgivings over the 45-degree model: (1) Most mischievous was the simplistic view that the economy could experience either unemployment or inflation and that each was amenable to control by reversing the fiscal measures. The symmetry doctrine flourished despite Keynes' injunctions that the two states were not simple mirror images. Even as the Keynesian textbooks conquered the world, many countries, especially underdeveloped lands, were experiencing simultaneous inflation and unemployment. Yet they were being taught to raise C and I under unemployment and to cut C and I under inflation!21 The lack of contact of the theory with reality had to await the modern stagflation in the affluent countries before the Keynesian blunders were exposed. 19 J. K. Galbraith, The Affluent Society (Boston: Houghton Mifflin, 1958), chs. 18-22, especially. Galbraith, to his credit, also urged higher sales taxes if these were the only practical means to finance necessary communal projects. 20 A. P. Lerner, The Economics of Employment (New York: McGraw-Hill, 1951), p. 127. 21 It would be easy to cite cases of underdeveloped countries using Keynesian textbooks despite their utter irrelevance to the stagflation miseries.

Hicksian

Keynesianism

53

Some prominent Keynesians attributed all inflation to "excessdemand." To this day they edge off from ascribing money wage and salary excesses as the inflation incubus. 22 (2) One incongruity in the theory was skimmed over blithely. Examining the equations and the diagrams, we find all quantities expressed in real terms• the price level is wholly suppressed. Yet inflation was discussed—in a model lacking a price level! (3) Keynes had dwelt early and at length on the "wage-unit," interpreted for our purposes as the average money wage. For the most part of his analysis, Keynes assumed this to be constant. A change in the average money wage, up or down, would carry the price level in the same direction and to a degree practically proportional to the wage change. 23 Yet Keynesians insisted on working in "real" terms, deflating all quantities by price-level movements. On the choice of price versus money wage units Hansen believed that "fundamentally the matter is of no great consequence." 24 This may be so—if the money wage were somehow brought back into the analysis as an exogenous parameter. Usually, Keynesian theory simply missed the crucial significance of the money wage for price-level theory and the implications of money wage (and thereafter, price-level) variations for monetary policy. The failure to comprehend the "wage-unit" or the money wage in Keynes' scheme of things proved to be the ultimate straw that bent the Keynesians' back. 25 (4) Keynes had taught that the investment volume was motivated by "animal spirits" which overcame the attendant uncertainties: the will to act, not neat and deliberate calculations, spurred capital formation decisions. At a minimum, then, the I function would be written as I = I(r,(f>), where φ denoted expectations and the urge to act. It was through this channel that the climate of confidence entered as an economic impulse. Keynesians are prone to render investment a function of past output levels (an accelerator notion) or past profits, or other mechanical ties. (5) Keynes never intended to be interpreted as teaching that Μ would remain constant as Y and Ν ( = employment) advanced. Yet 22 With the attraction for Walrasian models, "excess-supply" would be a price-level depressant, and "excess-demand," a price-exhilarating factor. The sorry fact was that money wage aspects were rarely given prominence by Keynesian theorists—as Hicks acknowledged. " C f . Hicks, "Crisis," p. 59. M Cf. Alvin Hansen, A Guide to Keynes (New York: McGraw-Hill, 1953), p. 44. " T h i s has been my criticism since (at least) A General Theory of the Price Level (Philadelphia: Chilton, 1959), and through Keynes and the Monetarists (New Brunswick: Rutgers University Press, 1973).

5 4

SIDNEY

WEINTRAUB

Keynesian models of Μ = Μ abounded. In the Monetarist models, the same hypothesis is commonplace; changes in the money supply are regarded as an exogenous phenomenon; Keynes would have posited some endogeneity. (6) Income distribution aspects were virtually ignored. Keynes can also be faulted for this omission; disciples such as Joan Robinson and Nicholas Kaldor (and the present author) have tried to remedy this. 26 (7) Macrotheory became unnaturally divorced from microtheory: specialists pervade the one or the other. Yet it is possible to wed the theory of the economy to events in industries and firms. (See the development in Aggregate Demand and Aggregate Supply, below.)

Hicksian IS-LM Models It was on an internal logical inconsistency that the HansenSamuelson approach yielded to the Hicksian version. The contradiction can be put briefly. In the C + I diagram, the volume of I is superimposed on the C-function. Thereupon, Y is determined at the "cross." But to determine I, r must be known. But r depends on the L-function composed of L(Y) and L(r). To determine r, it is thus necessary to know Y, while to know Y it is necessary to know r! The Hicksian IS-LM apparatus provided ready succor to rectify the circular logic; the formal method was outlined in an early appraisal of the General Theory.2'' From the definitional equation ofY = C + S, where S = savings, the savings function S = S(Y, r) was derived. From the Keynesian identity of / = S (for Y = C + I and Y = C + S), the important IS equation quickly evolved. (6)

S(Y,r)=I(r). Also, after equating the L-function to the money supply, we have: L(Y,r) = M.

(7)

With the two equations in two unknowns the system is, in principle, solvable. In equation (6), r is taken as a parameter to derive an IS function; in (7), with Y as a parameter, the LM curve emerges. The intersection of the two functions yields a mutually compatible equilibrium solution. 2 6 For some discussion and further references, see my Keynes essays 8 and 9. " H i c k s , "Mr. Keynes and the 'Classics'," op. cit.

and the

Monetarists,

Hicksian Keynesianism

55

The functions are depicted in Figure 4. A changed /, S, or L function, or a change in M, would alter the curves, shifting them in the chart field. Ordinarily, the IS-LM version of Keynesianism was deemed so sophisticated that it was reserved for study only by "advanced" students and not regarded as suitable for introductory text books .

A Critique of IS-LM Hicksianism is vulnerable to the same critique as the 45-degree approach; only the internal inconsistency was terminated. It, too, lacked a price level and a connection to money wages. Stagflation (or slumpflation) experience was safely exorcised. Distribution forces could easily have been entered into the theory in deriving the IS function: Y

=

(8)

Hr)/S,

where s = S/Y, the average propensity to save.

(9) where W = the wage bill; R = gross "profits" (more aptly, nonwage income). Then, as ω = WfY for the wage share and π = RfY for the nonwage share, we h^ve: Υ = /(Γ)/ίκω+

(10)

sr π

r ι> LM

0

-"-r Y* Figure 4.

• Y

5 6

SIDNEY

WEINTRAUß

In (10), the distribution of income between wages and profits determines income so long as φ sr. In view of income disparities, s r > s,,,. In those simple versions of the theory where "wage earners spend all their income and capitalists save all their income," then s«. = 0 and sr = 1. Income then depends entirely on investment and the size of the profit share. 2 8

Phillips Curve Keynesianism Much IS-LM debate was preoccupied with the exact form of the functions. But this was an absorption with detail, considering the tight box into which the missing price level variable packed the theory. A remarkable paper by A. W. Phillips provided a promising rescue operation for Keynesians. Gathering empirical data for the U.K., covering the period 1861 to 1957, Phillips correlated unemployment with money wage changes, fitting a curve running southeast in a diagram which plotted Δ w / w against U, where w denoted the relative annual money wage changes and U denoted the rate of unemployment. Formally the relation was transcribed in a curve such as UP in Figure 5. With the Phillips curve, Keynesians acquired a plausible theory of inflation. 29 The Hicksian model yielded the employment level. By calculating unemployment and then going to the Phillips curve, Keynesians could extract the expected money wage change. With an equation linking the money wage to prices, the degree of inflation could be ascertained. One price level equation used in econometric models was the following: Ρ = ktv/A,

(11)

where w = the average money wage and salary; A = the average productivity of labor; k = the average mark-up of unit prices over unit labor costs (w/A) or the reciprocal of the wage share: k = l/w.30 M Cf.

Weintraub, Keynes and the Monetarists, essays 8 and 9. A. W. Phillips, "The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957," Economica 25 (1958). An early effort to apply the idea to the U. S. appeared in Paul A. Samuelson and Robert M. Solow, "Analytical Aspects of Anti-Inflation Policy," American Economic Review 50 (May 1960). 30 Cf. Weintraub, A General Theory of the Price Level. Also, Klein, The Keynesian Revolution, (rev. ed., 1966), p. 219. As Klein remarked in reviewing Keynesian theory, "we need to close the system by extending it in such a way that the price level is explained" (p. 194). 29 Cf.

Hicksian Δ W ti

Keynesianism

57

(J

W

Ρ

0 Figure 5.

In (11) suppose k = k: as an empirical fact k changes very little, either secularly or year-to-year. 31 A, the average productivity of labor, is derived from the production function inverse relation ofN = N(Q), for A = QfN. Hence, IS-LM Keynesianism determined Y(= Q), then looked to the production function for the employment level, thereafter to the Phillips curve for the money wage change at the attendant unemployment, and the price level was determined.

Phillips Curves and Keynesian Trade-Off

Complacency

Phillips curves conferred an ironic twist on Keynesianism: they engendered a new complacency in the presence of unemployment hardships, imparting respectability to the view that the economy had to endure both inflation and unemployment, and that it could suppress one only by ushering in more of the other. Talk of "trade-offs" of more unemployment and less inflation, or vice versa, was rife. The unpalatable alternatives were enunciated as an immutable "natural" law; we had to elect one or the other, or be burnt by both. Keynes' optimism on a stable economy was tarnished by the option of a "natural" choice among evils. Tossed between the devil and the deep blue sea, many "Keynesians" abandoned their commitment to full employment. Keynes had believed that human intelligence must be used to erase economic ills, and the Hicksian Keynesians deferred to Keynes, mainly in deploying 3 , F o r some international comparisons, see John Hotson, International Comparisons of Money Velocity and Wage Mark-Ups (New York: Augustus Kelley, 1968).

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the technical jargon of C, I, or L-functions, rather than in seeking the objective of full employment: jobs for all was no longer the moral— and economic—imperative that Keynes had envisaged, of an e n d to be pursued without violating the tenets of democratic freedom. Hicksian Keynesians were now impaled on the pike of c o m b i n e d unemployment and inflation. As a n o t h e r a n o m a l y , K e y n e s i a n s o f t e n b e c a m e a l i g n e d w i t h Monetarists in accepting tighter money and more u n e m p l o y m e n t as a c o u n t e r to inflation. Monetarist u n c o n c e r n w i t h u n e m p l o y m e n t afflicted the Keynesian stereotypes.

Shifting Phillips Curves Controversy ensued over the Phillips curve data. It also arose over the function, e.g., whether money wages w e r e not more crucially linked to profits inasmuch as u n e m p l o y m e n t was low during prosperity phases w h e n profits were high. 3 2 Others specified a tie to productivity improvements; others a link to union strength. 3 3 Undoubtedly, if the data continued to validate the southeast path of Phillips curves, there would be, by now, an eclectic formulation relating money wages to a multiplicity of variables. But much of the controversy was d i m m e d by events. After about 1968, in the U.S., U.K., Canada, Australia, and e l s e w h e r e , money wage moves ran counter to Phillips curve pronouncements. Higher money wages occurred with higher u n e m p l o y m e n t ! T h e Phillips curve points, rather than flying southeast, ran northwest—in unexpected and unpredictable directions. T h e "theory" of shifting Phillips curves was then born. 3 4 If higher money wages accompanied higher unemployment, then " t h e Phillips curve must have shifted." What was originally hailed as a significant empirical " l a w " became quickly transformed into an ad hoc ex post description. Phillips curves now provided post mortems, not predictions. 32 Cf. Nicholas Kaldor, "Economic Growth and the Problem of Inflation," Part II, Economica 26 (November 1959): 287-298. M For some variation in Phillips curve explanation, cf. Edwin Kuh, A Productivity Theory of Wage Levels—An Alternative to the Phillips Curve," Review of Economic Studies 34 (October 1967): 333-360. A. G. Hines, "Trade Unionism and Wage Inflation in the United Kingdom, 1893-1961," Review of Economic Studies 31 (October 1964): 221-252. "An influential article was that by E. S. Phelps, "Phillips Curves, Expectations of Inflation and Optimal Unemployment Over Time," Economica 34 (August 1967): 254281.

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Theoretical ingenuity led to the doctrine that the curves shifted because workers, or their union leaders, in making their wage demands, acted on "expectations of inflation." Expectations prompted higher money wage demands, so money wages mounted despite job losses. Rather than the doctrine sponsoring policies for money wage restraint, i.e., Incomes Policy, the usual counsel was for patience in waiting for "expectations" to change or, in a Keynesian reversal, for tempering "expectations of inflation" and "ultimately" curbing money wages by pressing for unemployment through monetary policy. The whole thought scheme was curious, for if money wages were the price culprit, it would seem that actions should be devised to check them and thereby alter "expectations": expectations alone could not lift prices without concomitant wage boosts, which drive up business costs and enhance consumer demand. 35 Phillips curve writings have lately dried up as the fad succumbed to the onrush of history.

"Ignore Inflation" and Indexation Keynesians Deprived of the Phillips curve pillar, some prominent Keynesians recommended that we ignore inflation and proceed ahead with the full-employment objective. 36 Their lack of a policy to contain inflation was obvious, as they also urged a "correction" for the inequities of 35 On the interdependence of "cost-push" and "demand-pull" as a result of a money wage increase, see my "Comment on Cost Inflation," Economic Journal 84 (June 1974): 379-382. 3e Cf. the presidential address to the American Economic Association by James Tobin. Tobin minimized the "social" cost of inflation against that of unemployment, and doubted that inflation would accelerate if substantially ignored. See "Inflation and Unemployment," American Economic Review 62 (March 1972), especially pp. 15-18. Also, for a greater acquiescence in inflation, which is viewed as an accompaniment of high-level employment, see E. S. Phelps, Inflation Policy and Unemployment Theory (New York: Norton, 1972). Likewise, three years later Walter Heller advocated full employment, belittling inflation fears because of unemployment! Walter W. Heller, New York Times, 30 June 1975, Op. Ed. Apparently, stagflation lessons since 1968 were unlearned despite the 65 percent price-level rise. In the United Kingdom, unemployment had mounted from about 0.5 to 5 percent, yet the inflation accelerated to over 25 percent per annum. Australia and Canada had parallel experiences, differing only in degree. Professor Hyman Minsky, observing the advice of Keynesians at the "summit" conference of President Ford in September 1974, characterized their performance as "futile." See "The Futility of President Ford's Economic Summit," mimeographed (Economics Department, Washington University, St. Louis, Mo., 25 September 1974). J. K. Galbraith refused to dismiss inflation in the superficial Keynesian way; he continued to recommend price-wage controls.

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inflation by padding Social Security payments, by issuing a fixed purchasing power government bond, by encouraging business firms to do likewise, etc. "Ignore inflation" thus merged with Indexation Keynesianism, for the "corrections" were to be linked, as a rule, to movements in the consumer price index. Interestingly, Indexation was also recommended by the most prominent Monetarist, so that the entente cordiale of Keynesians and Monetarists spanned the previous ideological gulf.37 Mostly, the appeals to corrections were long on casual rhetoric but short on specifics. Undoubtedly, the perennial defect of the private enterprise economy has been its incapacity for "corrections." Income disparities are an old sore, with one person's correction often appearing as another person's inequity. "Corrections" are hardly a simple matter; Keynesians (and Monetarists) bright enough to effectuate them should surely be wise enough to subdue inflation and prevent more people becoming wards of the government on the welfare dole. When the "Ignore Inflation" signals were originally emitted, inflation in the U.S. was hovering at the 5 percent per annum range. Apparently, it was felt that if the phenomenon was ignored, while vague comments on correction were uttered, the price surge would disappear. In some contradiction, there were expressions of dismay as double-digit inflation appeared in 1974. 38 It can hardly be supported that rational economic decision-making by consumers, business, and government is facilitated under random and haphazard high rates of inflation. Efficiency in resource allocation would benefit from a practically stable price level. Counseling businessmen to issue purchasing power bonds reveals an innocence of the facts of financial life. Business profitability for each firm depends on the firm's own sales prices, not on the "general" price level. In issuing bonds, it seeks to reduce some inherent interest payment uncertainties: the aim is to establish a scale of known, definite, fixed payments. Indexed bonds would compound the uncertainty, not alleviate it. Lenders, under indexing, would be engaged in a wager on whether individual firms would show prices moving faster (or slower) than the average, and so firms would be less (or more) vulnerable to default. Firms and lenders would thus be participating in a price-level lottery to decide their ultimate profit fate. 37 Cf. Milton Friedman, Monetary Correction: A Proposal for Escalator Clauses to Reduce the Costs of Ending Inflation (London: Institute of Economic Affairs, 1974). 38 Cf. James Tobin, New York Times, 6 September 1974, Op. Ed.

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Figure 6.

Ultimately, indexation is merely one way of deciding on the annual (or monthly) average pay hike. It might be described as an attempt to "catch u p " tomorrow to the events of yesterday by an agreement reached today. Only in fortuitous circumstances (of increases "ind e x e d " to yield a money wage improvement of 3 to 4 percent per a n n u m ) would the index corrections eradicate inflation and the attendant income inequities generated by the price moves. This dour assessment of indexation which flitted briefly on the Monetarist and Keynesian stage is not to be interpreted as critical of increases in Social Security payments or of government employee pay hikes in the years of inflation. Increases listed for these groups correspond to market increases in wages and salaries. Skepticism, however, extends to the concept of universal indexation for all incomes.

Aggregate Demand and Aggregate Supply An alternate version of Keynesianism, one more attuned to Keynes' money wage and price-level ideas, invokes Aggregate Demand and Aggregate Supply concepts. Although the approach is free of most of the objections to Hicksian Keynesianism, it has had far less attention. 39 In Figure 6(c), a (Marshallian) supply curve for industry A and industry B, each viewed as "representative" of typical industries, is 39 For some statement of the postulational basis of the theory, see my Approach to the Theory of Income Distribution (Philadelphia: Chilton, 1958), ch. 2. For a textbook use see Paul Davidson and Eugene Smolensky, Aggregate Supply and Demand Analysis (New York: Harper and Row, 1964). Also (with some modification in output units) Miles Fleming, Introduction to Economic Analyses (London: Allen & Unwin, 1969), Part III.

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drawn. At a price of P, there are the respective Q, outputs in A and B. Multiplying each PQ we can arrive at %PQι = Pxa + Pi6 + . . . , with XPiQi thereby representing the aggregate of industry proceeds expected at supply prices Ρι. Similarly, we can find the employment total implicit at each Q t from the underlying industry production functions Ν = N(Q). In Figure 6(a), we can therefore specify the employment level attached to each total expected proceeds level 1PQ. At each aggregate proceeds level (written as Z=PQ) we can, in effect, go out to industry supply curves and ascertain the output and implicit employment levels. One restrictive hypothesis is involved, to wit, that any aggregate proceeds sum is unequally allocated among industries. Hicksian and Hansen-Samuelson analyses use an even more restrictive hypothesis in supposing that the output composite is unchanged: all outputs are assumed to vary proportionately whenever changes in Y occur. For the Aggregate Demand curve, we can ask: "How much output will be demanded when the industry produces QI,Q2, . . . etc. along the course of each industry supply curve?" Thereby the intended volume of outlays at each supply price can be ascertained, permitting us to derive a "D-O" demand outlay curve in each industry, as indicated in Figure 7b. This is, in effect, a cross-cut of the ordinary de-

(a)

Figure 7.

(b)

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mand curves of price theory, in which each demand is drawn on the assumption of "given" income or "given" employment. For example, in Figure 7(b) a quantity CV is wanted, at an outlay of P, a Qi ad , at a supply price P, a and output CV5. By aggregating such intended purchase outlays over the full economy, we can build an aggregate demand curve as in Figure 7(a). It is to be noted that at each N-level, exactly the same prices are embedded in Aggregate Demand (D) as in Aggregate Supply (Z). Both D and Ζ are joined in Figure 8. At the intersection we have the equilibrium balance, this time representing total employment and total proceeds (or Gross Business Product). Ordinary industry supply curves are erected on two major hypotheses: (1) given factor prices, and (2) given factor productivity, meaning the input-output production function. The dual hypotheses yield the supply curve for the industry; the supply curve also presupposes competitive markets. In (2), for short-period macrotheory, labor is the essential variable factor. Every time the money wage alters, the industry supply curves will shift. Inevitably, there will be a parametric shift in the Ζ and D functions, illustrated in Figure 9 where Di and Z t are contingent on the money wage wlt and D 2 and Z2 on w2, where w2 > wj. As drawn, the higher money wage acts to diminish the equilibrium employment, as

Figure 8.

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F i g u r e 9.

in the conventional pre-Keynes conclusion; we know now that it follows only under some restrictive monetary conditions.40 By parametric boosts in w, we can trace out a demand curve for labor representing the connection between money—not real—wages and employment. The same apparatus could be extended to the theory of growth; it could also be used to illuminate issues in the theory of money and income distribution.41 The apparatus builds in a price level from the start; micro- and macrotheory are also joined. With the collapse of the IS-LM doctrine, this alternate version of Keynes' theory may enjoy wider use.

The National Debt Largely, fiscal Keynesianism accepted the prospects of deficits by the federal government, or of a mounting national debt, with equanimity. With the positive influence of government outlay on employment regarded as a social benefit, any tax burden by way of interest payments on the debt depended on the ratio of interest charges compared to income growth. 40Although the conclusion is pre-Keynes and pTe-General Theory, many economists still write as if the interpretation is unassailable. Cf. Weintraub, Approach to the Theory of Income Distribution, ch. 6 4, Cf. Sidney Weintraub, A Keynesian Theory of Employment Growth and Income Distribution (Philadelphia: Chilton, 1965). Also, Paul Davidson, Money and the Real World (London: Macmillan & Co., 1973).

Hicksian

Keynesianism

(Interest on the National Debt/National Income) = Interest Burden of the National Debt

65

(12)

It followed that so long as the national income rose faster than interest payments, the debt " b u r d e n " would be alleviated: the net tax cost of carrying the debt would be reduced. Likewise, in (12), so long as interest was counted as income, the ratio had to be unity or less: there would always be enough "income" to cover the debt charges. Furthermore, there was the other contention that on the other side of debt were bonds held as an asset by bondholders. If the government " o w e d , " then the people " o w n e d " the bonds. Having financial assets in the form of government bonds would impart favorable wealth effects for consumption; in the case of businesses, borrowing would be easier for firms owning bonds offered as collateral. Debt could, of course, be reduced by higher taxes, but, apart from the deleterious effects on consumption outlay of taxes, the redemption of the bonds by government would leave individuals feeling poorer: they would pay higher taxes to have the Treasury buy the bonds back from them and, in the process, personal assets would be destroyed. So skepticism was attached to reducing the national debt in other than special circumstances. To those who argued that government borrowing shifted the debt " b u r d e n " to future generations, it would be countered that "future" citizens would also inherit bonds and financial assets. Furthermore, that there was no way to shift a real " b u r d e n " to the future; if the present generation was smart enough to do it, future generations would be equally bright. Most of the national debt, in any event, occurred during wartime and periods of unemployment; hardships and real burdens occurred at those times and could not be shifted out in time. This was the position that emerged from Keynesian thought. While this controversy is never over, there has been at least one lively exchange on the issue by academic economists; non-Keynesians held that in paying taxes individuals are "compelled" to give up purchase claims on output and real resources. In buying bonds "voluntarily" they sacrifice nothing now and receive interest receipts in the future at the expense of those who have to pay taxes. 42 Much of the debate is 42 Fora Keynesian view of the debt burden, see Evsey C. Domar, "The Burden of the Debt and the National Income," American Economic Review 34 (December 1944): 798-827. Also, A. P. Lerner, "The Burden of the National Debt," Essays in Honor of Alvin H. Hansen. For views on the public debt as a burden, see James M. Buchanan, Public Principles of Public Debt (Homewood, 111.: Richard Irwin, 1958) and James E. Ferguson, ed., The Public Debt and Future Generations (Chapel Hill: University of North Carolina Press, 1964).

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confusing in loose references to "inflation," associated with deficits, even when prices are not rising.

Whither Keynesianism? With Hicks' admission of the theoretical inadequacy of the IS-LM model, and with the shortcomings of Keynesian inflation policy, it is an understatement to describe Hicksian Keynesianism as being in a state of disrepair: its inflation slip is showing. We have traced the several stands. In each stance new straws were grasped, each creating a new brand of Keynesians. Within a 15-year span, the parade marched first to the 45-degree banner, then to the IS-LM flag; it stepped to Phillips curve tunes, waltzed to Shifting Phillips curve notes, sang "Ignore Inflation" songs and murmured Indexation chants. Still, an illusion persists in textbooks that all is coherent, "scientific," and successful. 4 3 Nonetheless, only few believe that Keynesianism is the assured, unassailable, formidable system that dominated the 1950s. Most of Keynes, however, can withstand the criticism heaped on Keynesianism. The reconstruction toward such systems should carry the analysis closer to what Keynes tried to say—although too many Keynesians refused to read.44 The mourning period for Keynesianism, considering its inadequacy, can be brief, for the rendition had mainly form without a foundation. University of

Pennsylvania

"Cf. Walter W. Heller, "What's Right with Economics?", American Economic Review 65 (March 1975): 1-25. "Thus, on Keynes' General Theory, Galbraith has remarked: "All economists claim to have read it, only a few have" [Money: Whence It Came, Where it Went (Boston: Houghton Mifflin, 1975), p. 218], Chapters 14-21 of the General Theory seem to be uncut pages for too many Keynesians.

4 Keynesian Econometric Concepts: Consumption Functions, Investment Functions, and "The" Multiplier RONALD G. BODKIN*

Consumption The modern theory of aggregate consumption functions begins with the monumental work of John Maynard Keynes. Keynes postulated, as a fundamental building-block of his system, a functional relationship between aggregate consumption and aggregate income, both deflated in terms of wage units. 1 In a survey, only several salient points can be discussed. First, it is interesting to note that the deflator selected by Keynes was the money wage rate. Later students and developers of the Keynesian system have, with rare exceptions (such as Sidney * I wish to thank Eric Davis, A. Asimakopulos, and S i d n e y Weintraub for their comments on this paper. I confess that I have s h a m e l e s s l y consulted four other surveys of consumption functions, those by Robert Ferber, T h o m a s Mayer, Irwin A. Shapiro, and J a m e s Tobin. As I have consulted u n p u b l i s h e d versions of the latter two surveys, my debts are compounded. 'John Maynard Keynes, The General Theory of Employment, Interest and Money ( N e w York: Harcourt, Brace & Co., 1936). 67

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Weintraub 2 ) modified this deflator to be " t h e " aggregate price level. 3 Second, the only principle concerning the shape of this function on which Keynes was willing to commit himself strongly was that the marginal propensity to consume (the slope of this function) had to lie between zero and unity. H e thought it quite likely that the average propensity to consume declined with rising community income and he perhaps believed as well that the marginal propensity to consume also declined with rising income. 4 But only the basic assertion was elevated to the status of a "fundamental psychological law." Third, it is worth noting that Keynes' discussion was quite intricate, with a n u m b e r of the qualifications, at least in embryonic form, which we often associate with later writers. Keynes specifically mentioned six "objective" factors and eight "subjective" factors that might shift his consumption function. Two of the objective factors may be specifically mentioned: (1) "windfall changes in capital-values not allowed for in calculating net income" (Keynes considered these to be among the major factors that could produce short-term disturbances in his consumption function, as " t h e consumption of the wealth-owning class may be extremely susceptible to unforeseen changes in the moneyvalue of its wealth." 5 ); and (2) "changes in expectations of the relation between the present and the future level of income." It must be admitted, however, that Keynes did not think the second influence very important for the community as a whole, however strong a role it might play in the case of particular individuals. Yet there is the germ of a "wealth hypothesis" in the former objective factor and the suggestion of a p e r m a n e n t income hypothesis in the latter. 2 See, e.g., An Approach to the Theory of Income Distribution (Philadelphia: Chilton, 1958). 3 Keynes himself implied that the price level is more or less proportional to the money wage rate, particularly at a given employment level, and thus the difference might appear to be purely one of style. Weintraub has argued, on a number of occasions, that there is more to the issue than this, and indeed there are some passages in Keynes that would appear to support him. In discussing the effects of a change in the wage unit, Keynes also stated that under some circumstances one must take account of the effect of a change in the wage unit on the distribution of income between entrepreneurs and rentiers. See The General Theory of Employment, Interest and Money (New York: Harcourt, Brace and Company, 1936). 4 This guess about Keynes' view of this matter is perhaps corroborated by a study of his numerical example on pp. 125-128 of The General Theory. In this example, a consumption function with a declining marginal propensity to consume is presented for illustrative purposes. 5 General Theory, pp. 92-93. Keynes took up this theme some 200 pages later (in his General Theory, ch. 22, "Notes on the Trade Cycle"). There he explained the downward shift of the consumption function in the U.S.A. during the 1930s in terms of the decline of share prices in the stock market.

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Early Empirical

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Findings

Keynes' work spawned a plethora of attempts at empirical verification, and Keynes himself attempted to check his theoretical constructs against the early work of Simon Kuznets (for the U.S.A.) and Colin Clark (for the U.K.). T h e later empirical researches of Kuznets and Goldsmith established several important generalizations, at least for the U.S. economy.® First, although the cyclical consumption function was as Keynes had suspected (with the proportion of income consumed declining with rising income), the secular or long-term consumption function apparently displayed no such tendencies. Au contraire, it appeared to be suitably described as a ray through the origin with a slope slightly greater than 0.9 (when consumption was expressed as a function of disposable income, not national income, as Keynes had first suggested). Thus the marginal and average propensities to consume appeared to be equal as a long-term tendency, with neither displaying any tendency to decline secularly with rising income. On the other hand, a large n u m b e r of cross-section studies suggested that the consumption function for individual households was like the aggregate cyclical consumption function, with a positive intercept and a relatively flat slope, so that the average propensity to consume declined with rising income. (In some studies, so did the marginal propensity to consume.) How could one reconcile these apparently diverse findings? One of the earliest reconciliations was that by Smithies, Livingston, and Mosak. 7 Using annual data for the U.S.A. for the interwar period, Smithies et al. explained real (price-deflated) consumption per capita in terms of real disposable income per capita and a time trend which was found to have a significantly positive regression coefficient. In the short run, the estimated marginal propensity to consume (MPC) was fairly low, at 0.76. Thus the cyclical consumption function had the expected appearance. Moreover, the positive time trend could be interpreted as an upward-shifting constant term, and so the cyclical consumption function could be thought of as continually moving upwards over time. In consequence, a judicious cross-cut of the cyclical consumption functions could explain Kuznets' long-term results. (See Figure 1. The vertical and horizontal axes represent real consumption and real disposable income respectively, and the implied secular cone See Simon Kuznets, National Product Since 1869 (New York: National Bureau of Economic Research 1946), and Raymond W. Goldsmith, A Study of Saving in the United States, 3 vols. (Princeton: Princeton University Press, 1956). 'Arthur Smithies, S. Morris Livingston, and Jacob L. Mosak, "Forecasting Postwar Demand: I, II, and III," Econometrica 13, no. 1 (January 1945): 1-37.

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F i g u r e 1.

Yd

sumption function is indicated by the dashed lines.) Also, this explanation shortly appeared satisfying because it explained another body of data: for cross-sections of comparable American households, the consumption function that was higher in the field (i.e., the one which predicted more consumption at a given level of real disposable income) was invariably the one with the later date of collection of the data.8 Smithies, Livingston, and Mosaic's time trend, which could be interpreted as reflecting the development of tastes for new luxuries, appeared to give a satisfactory rationalization of this phenomenon.

The Duesenberry Past-Peak Hypothesis The explanation by Smithies et. al. was soon challenged by James S. Duesenberry, who adduced some evidence that, for individual households, consumption depends on percentile position in the income distribution (relative income) rather than absolute income. 9 (This was an alternative rationalization of the aforementioned Bradye See, e.g., Dorothy S. Brady and Rose D. Friedman, "Savings and the Income Distribution," Studies in Income and Wealth, vol. 10 (New York: National Bureau of Economic Research, 1947), pp. 247-265. e In "Income-Consumption Relations and Their Implications," in Income, Employment and Public Policy, Essays in Honor of Alvin H. Hansen (New York: W. W. Norton & Co., 1948), pp. 54—81, and Income, Saving, and the Theory of Consumer Behavior (Cambridge: Harvard University Press, 1949).

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Friedman evidence from two cross-sections separated in time. In the aggregate, Duesenberry asserted that the consumption-income ratio (or its complement, the savings-income ratio) could be explained in terms of a linear regression, with the ratio of current income to previous peak income as the sole explanatory variable. T h e connection between the model for the aggregates and the model of individual household behavior was not made explicit, but presumably standards for the representative consumer of the economy would be set by previous prosperity levels of income, rather than by current experience in a depressed economy. Several points may be made in reviewing Duesenberry's work. First, it is to be observed that this function both fitted the long-term data and explained the relative flatness of the aggregate consumption function in the recession; under these circumstances, consumption acts itself as a sort of built-in stabilizer. 10 (See Figure 2, in which the axes have the same labels as Figure 1. Here the dotted line indiciates the implicit cyclical consumption fu v t i o n . ) Second, it may be noted that the argument for previous peak income as part of the explanation of variations in the consumption-income ratio easily leads to a more intuitively plausible use of previous peak consumption as a generator of consumption standards in a depressed year. Τ. E. Davis followed up this intuition and showed that the Duesenberry model could be improved as a result. 11 Franco Modigliani had a similar model. Because this model is quite close to Duesenberry's, however, (and also because Modigliani might prefer his later model), this similarity will be merely mentioned en passant.12 10 In Figure 2, the cyclical consumption function is extended beyond its intersection with the secular consumption function. This might be rationalized by arguing that, during a long depression (such as that of the 1930's), the level of earlier peak income might no longer represent a full-employment level. In consequence, during a cyclical recovery, real disposable income could shoot past its previous peak at a higher rate of growth than would be sustainable in the Jong term. If this occurred, the cyclical consumption function could extend beyond its intersection with the secular consumption function (the appropriate ray from the origin). The supposed behavior of consumption still acts as a built-in stabilizer against inflationary pressures emanating from excess aggregate demand. ""The Consumption Function as a Tool for Prediction," Review of Economics and Statistics 34, no. 3 (August 1952): 270-277. Using Canadian data, Τ. M. Brown noted a similar improvement when previous peak consumption was substituted for previous peak income. However, as we shall see presently, Brown discarded this form of the consumption function. See Brown, "Habit Persistence and Lags in Consumer Behaviour," Econometrica 20, no. 3 (July 1952): 207-233, especially pp. 208-213. I2 See Franco Modigliani, "Fluctuations in the Saving-Income Ratio: A Problem in Economic Forecasting," Studies in Income and Wealth, vol. II (New York: National Bureau of Economic Research, 1949), pp. 371-443. The discussion on p. 80 of the later article by Ando and Modigliani, cited in footnote 18 below, suggests that Modigliani may well prefer his current formulation.

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The Tobin Modification Shortly after the appearance of Duesenberry's work, James Tobin pointed out that a modified absolute income hypothesis could provide an alternative explanation for most of the phenomena for which Duesenberry invoked his theory. 13 Tobin's modification involved the suggestion that consumption could be regarded as dependent both on disposable income and on wealth, or net worth. If one takes the view that permanent savings (i.e., saving never consumed during the life time of the saver) is motivated principally by the desire to pass on an estate, then the size of net worth already possessed would appear to be a relevant determinant of the allocation of current disposable in1 3 Tobin, "Relative Income, Absolute. Income and Saving," in Money, Trade and Economic Growth, Essays in Honor of John Henry Williams (New York: Macmillan, 1951), pp. 135-156.

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come b e t w e e n saving and consumption. For example, the fact that cross-section studies appeared to indicate that blacks consume less (i.e., save more) at given levels of income had been employed by Duesenberry to buttress his theory, on the reasonable contention that black communities had lower mean incomes, and so a given absolute income for a black family would mean a higher relative income. Such a family would thus be less subject to emulative pressures to consume than a white family with the same absolute income. 14 Tobin pointed out that, at given levels of real income, the net worth of a typical black family might be expected to be lower than that of the typical white family, and this could provide an equally satisfactory explanation of the higher savings propensities of blacks. The application to the aggregative consumption function, once the matter is regarded in this fashion, is obvious. Over time, a growing society experiences increasing levels of wealth as well as increasing levels of real income. Accordingly, the partial relationship between consumption and disposable income (the short-run consumption function) can shift upward, driven by increasing levels of real net worth, which stimulate consumption by obviating the need for saving at any given level of disposable income. Again, as in Figure 1, the secular consumption function becomes a cross-cut of judiciously selected points on the short-term relationships, which are thus considerably flatter (have lower Μ PCs) than their long-run analogues.

The Brown

Modification

The difference between long-run and short-run consumption functions was also central to the pioneering research of Τ. M. Brown. 15 Brown studied various versions of a consumption function describing the Canadian economy during the interwar and immediate postwar years, after which he e m b e d d e d his final variant in a small model of the Canadian economy. In the final variant, real consumption expenditures d e p e n d e d upon real disposable income (separated into its wage and nonwage components), the level of consumption expenditures during the preceding year, and a shift dummy. This shift dummy indicated that, at given levels of the economic explanatory variables, real consumption was significantly higher during the postwar years; but no economic explanation of this shift was given. Brown also exI4 The nonblack, popular mind appears to have given this effect a rather simpliste interpretation in terms of intrinsic racial characteristics, if one can judge from the pejorative word "niggardly" in the English language. 15 See Brown, "Habit Persistence and Lags in Consumer Behaviour."

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perimented with previous peak income, previous peak consumption, and lagged income as alternative explanatory variables (in place of lagged consumption), but all of these were inferior to the version Brown finally retained in which real disposable income was separated into wage and property income components. Brown interpreted his work as indicating a type of "habit persistence." Previous levels of consumption were regarded as setting a sort of standard to which current possibilities would be compared. 1 6 Of course, such standards do not exist in perpetuity; the influence of previous levels of consumption gradually dies away, which is the indicated effect when the previous year's level of consumption is employed as one of the exp l a n a t o r y v a r i a b l e s . As B r o w n also e s t i m a t e d the r e g r e s s i o n coefficient of lagged consumption to be small, but significantly positive, the short-run marginal propensity to consume will be somewhat smaller than the corresponding value of this parameter in the long run. (In this sense, there is an analogy to the situation depicted in Figure 1.) For the Canadian economy, Brown found an MPC out of labor income in the short run equal to 0.61, while in the long term this parameter was estimated to rise to 0.77. For property income, the MPCs were calculated to be 0.28 and 0 . 3 6 respectively. 1 7

Permanent Income

Theories

Two final theories to be considered in explaining the difference between the short-term and secular consumption functions are the life cycle theory of Modigliani-Ando-Brumberg and the permanent income theory of Milton Friedman. 1 8 Farrell and many others have rel e More recently, H. S. Houthakker and Lester D. Taylor have constructed a theory of consumption (primarily but not exclusively a theory of expenditures on consumption categories) in which the notion of a stock for durable goods is generalized to the concept of a state for all types of consumption goods (or for total consumption itself). This "state" notion can be interpreted as a residuum of all previous consumption experiences relevant to the category under consideration. Of course, this stock of previous experiences gradually wears off, or "depreciates," analogously to a concrete physical stock. Thus there is more than a passing resemblance to the concepts developed in Brown's earlier work. See Houthakker and Taylor, Consumer Demand in the United States: Analyses and Projections, 2d ed., enlarged (Cambridge: Harvard University Press, 1970). 1 7 The parameter estimates given in the text are based on simultaneous equations estimation techniques (limited information maximum likelihood estimation), which are quite close, however, to ordinary least squares estimates. 18 Albert Ando and Franco Modigliani, " T h e 'Life Cycle' Hypothesis of Saving: Aggregate Implications and Tests," American Economic Review 53, no. 1 (March 1963), reprinted in A.E.A. Readings in Business Cycles, vol. 10, ed. Gordon and Klein (Homewood, 111,: Richard D. Irwin, 1965), pp. 398-426; Franco Modigliani and Richard Brumberg. "Utility Analysis and the Consumption Function: An Interpretation of Cross-Section Data." in Post Keynesian Economics, ed. Kurihara (New Brunswick, N.J.: Rutgers University Press, 1954), pp. 388-436; and Milton Friedman, A Theory of the Consumption Function (Princeton: Princeton University Press, for the National Bureau of Economic Research, 1957).

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garded these two theories as similar, as each takes as its point of departure the contention that consumption adjusts to an income concept considerably longer than the conventional accounting period (such as a quarter of a year or even a full year). 19 Nevertheless, important differences exist, and e v e n in a survey a separate treatment w o u l d appear to be justified. For the life cycle hypothesis, Modigliani and his two collaborators make the strong assumption that consumption will be planned over a lifetime horizon; if one adds the almost equa'ly strong assumption of an absence of estate motivation, it follows that the typical consumer unit w i l l adjust its consumption to average income expected over its remaining lifetime. In the aggregate, w e obtain what Farrell has called the "Rate of Growth Hypothesis": a static society w i l l generate no net savings (by households), as the dissaving of the elderly retired will just be matched by the saving of the economically active. H o w ever, if the population is growing (so that there are proportionately more economically active members or if real income is growing (so that the young have a higher lifetime income than the elderly dissavers), then net personal saving will result. Moreover, it can be shown that the ratio of saving to disposable income will be proportional to the rate of growth of real income. 20 In the permanent i n c o m e hypothesis of Milton Friedman, the sharply defined focus of lifetime budgeting is softened, and the horizon over which the typical consumer unit plans its consumption outlays becomes an empirical matter. (Friedman argued that three years is a reasonable estimate of the length of the horizon for a typical 19 A good summary of some of the distinctive features of these theories appears in the review article by Farrell, " T h e N e w Theories of the Consumption Function," Economic Journal 69 ( D e c e m b e r 1959): 678-696, reprinted in Α.Ε.Λ. Readings, pp. 379397. Recently, W . H. Somermeyer and R. Bannink have attempted to generalize the life cycle theory of consumption behavior by eliminating the strong simplifying assumptions of Modigliani and his collaborators, at the cost of some increased complexity in the analysis. See Somermeyer and Bannink, A Consumption-Savings Model and Its Applications ( N e w York: Elsevier, 1973). 2 0 In " T h e ' L i f e Cycle' Hypothesis of Saving," Ando and Modigliani derived this rate of growth hypothesis in a slightly different manner from Farrell. First, employing rather severe assumptions about the underlying distributions, they aggregated the household consumption functions over the entire economy in order to obtain a homogeneous consumption function in which the level of consumption depends upon initial net worth and current and expected future income from labor services, but which has a zero value for the constant term. T h e authors demonstrated how their model will generate a dynamic equilibrium (in the absence of differential movements in asset prices) in which real income, wealth, and saving are all growing at the same rate, and in which the savings rate is proportional to this common rate of growth. Ando and Modigliani e v e n drew a graph similar to Figure 1, in which the slope of the consumption-labor-income relationship is considerably flatter than its long-run analogue, which in dynamic equilibrium becomes a ray through the origin.

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American household during the first half of the twentieth century.) Disposable income is divided into "permanent" and "transitory" components: the permanent component is comprised of income emanating from factors considered to be more long-lasting than the horizon; transitory income is considered the resultant of factors whose effects will be exhausted within the income horizon. Thus the theory requires the representative consumer to look beyond the horizon. It is postulated that, aside from stochastic error (transitory consumption), consumption depends only on permanent income. Friedman's assumptions prevent transitory income from having any systematic relationship to total consumption: they imply a zero marginal propensity to consume all income whose generation will be exhausted within the period of the horizon. Equally severe is the assumption that consumption (aside from its transitory component) is simply a constant multiple of permanent income. 21 Friedman estimated this proportion to be roughly 0.9 for American households during the first half of the twentieth century. Friedman tested his theory against a wide variety of evidence. 22 Three critical points may be noted. First, Friedman's theory gives a particularly simple explanation of the divergence between the shortterm and the secular consumption functions. Aside from aggregation effects, the long-term consumption function could be expected to be the mirror image of the household propensity to consume permanent income. Its approximate constancy becomes, in this view, a mere corollary of the postulate that permanent consumption is a simple proportion of permanent income. On the other hand, variations in disposable income during the business cycle are (virtually by definition) ridden with transitory elements, and in consequence the cyclical 21 In theory, this constant proportion is not truly invariant but may depend parametically on the market rate of interest, the ratio of household net worth to total income (in Friedman's words, "the ratio of nonhuman wealth to permanent income"), and any other variable (such as age of the unit) relevant to the tastes of the unit in the consumption-saving decision. The point on which Friedman insisted is that this ratio is independent of the level of permanent income itself. However, in most applications, this refinement is regarded as being of secondary importance and is not usually pursued. Farrell has criticized this so-called "proportionality hypothesis," arguing that even in Friedman's framework there is no reason why permanent consumption has to be related to permanent income in such a simple manner. However, in the view of the present author, such a proportionality relationship is more than an unnecessary appendage of the basic theory: if the so-called "proportionality hypothesis" is rejected, it would appear to be difficult to explain the approximate long-term constancy of the ratio of savings to disposable income. " A good discussion of these tests may be found in Farrell's evaluative article, "The N e w Theories of the Consumption Function"; in Thomas Mayer's exhaustive discussion, Permanent Income, Wealth and Consumption (Berkeley and Los Angeles: University of California Press, 1972); and, of course, in Friedman's work itself.

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Μ PC is considerably lower, b e i n g a w e i g h t e d average of the longterm parameter and a much l o w e r propensity (zero, in F r i e d m a n ' s strict formulation) to c o n s u m e transitory income. 2 3 S e c o n d , applying the model to time series data, F r i e d m a n a s s u m e d that aggregate p e r m a n e n t i n c o m e is a weighted sum (with geometrically d e c l i n i n g weights) of current and past levels of disposable inc o m e . As L a w r e n c e Klein pointed out almost c o n t e m p o r a n e o u s l y , in such a formulation the lagged level of consumption can serve as a shorthand method o f capturing this kind o f effect, with the additional virtue o f conserving d e g r e e s of freedom in a statistical analysis o f time series with few observations. 2 4 Accordingly, the work of Brown can b e said to have anticipated the aggregative implications of F r i e d m a n ' s theory, e v e n though the theoretical interpretation is somewhat different. Finally, to anticipate the discussion of the multiplier c o n c e p t , w e may note that in F r i e d m a n ' s theory the numerical value of this measure is rather low. T h i s is true b e c a u s e F r i e d m a n ' s M P C is not the structural value o f this paramerter (the " t r u e " proportion o f p e r m a n e n t i n c o m e consumed), but rather the cyclical value, which is r e d u c e d b y the e x i s t e n c e o f a zero propensity to c o n s u m e transitory i n c o m e . F i s cal policy stimulants such as temporary tax cuts will be particularly weak, as the associated variation in disposable i n c o m e will b e comprised almost entirely o f transitory i n c o m e . 2 5 T h e e x i s t e n c e of a strict zero propensity to c o n s u m e transitory inc o m e would not appear to b e essential to a " p e r m a n e n t theory o f e x p e n d i t u r e . " I f h o u s e h o l d s ' expenditures are constrained by t h e i r small holdings o f liquid assets, t h e r e may b e good reasons why positive transitory i n c o m e may b e associated with i n c r e a s e d consumption expenditures. T h o m a s M a y e r has argued that all o f the valid e v i d e n c e 23 An analogous explanation holds for the relatively low MPCs observed in crosssection studies. Households with high observed incomes will, in general, be enjoying positive transitory income, as part of the explanation of their high observed incomes would be favorable temporary income experience. The same argument holds in reverse for households with low observed incomes. Hence, as measured income varies from households with the lowest observed incomes to those with the highest, permanent income will vary by a smaller magnitude. Again, the observed marginal propensity will be a weighted average of the "true" value of this parameter and the zero propensity to consume out of transitory income. "Lawrence R. Klein, "The Friedman-Becker Illusion, "Journal of Political Economy 66, no. 6 (December 1958): 539-545. 25 It should be noted that in Friedman's theoretical framework most of the expenditure on consumer durables is classified as saving, as only the part of the stock actually consumed within the period is defined to be consumption. Of course, if temporary tax cuts can induce "investment" in consumer durables (or, for that matter, in residential construction), they may well have beneficial effects on output and employment in an economy with less than fully employed resources.

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that Friedman marshals for his theory is equally consistent with Mayer's "standard income theory," in which the marginal propensity to consume transitory income is positive (but smaller than that out of permanent income). Some years ago, Roger C. Bird and the present author argued that the American National Service Life Insurance dividends of 1950 were most nearly explained by a "loose" permanent income hypothesis in which the marginal propensity to consume transitory income was positive (but again less than the MPC out of permanent income). 26 Harold Watts, in a fine study of Norwegian households, has also adduced some convincing evidence that the marginal propensity to consume unexpected income changes is strictly positive, particularly when these income changes are gains and not losses. 27 A number of studies with time series aggregates have suggested a positive marginal propensity to consume (measured) transitory income, although this parameter is estimated to be significantly smaller than the MPC out of permanent income. 28 In brief, the strict assumption of a zero marginal propensity to consume transitory income seems to be refuted by the ensemble of a number of pieces of evidence. 29

Real-Balance Effects First A. C. Pigou, and later Don Patinkin, rewrote the consumption function with absolute income as a key explanatory variable to include new liquid claims of the private sector on the government as an additional determinant. 30 Consumption was envisaged to increase, ceteris paribus, with a higher level of real net liquid assets; early commen26 Roger C. Bird and Ronald G. Bodkin, "The National Service Life Insurance Dividend of 1950 and Consumption: A Further Test of the 'Strict' Permanent Income Hypothesis," Journal of Political Economy 73, no. 5 (October 1965): 499-515. 27 "An Analysis of the Effects of Transitory Income on Expenditures of Norwegian Households," Cowles Foundation Discussion Paper No. 149 (Presented at the Pittsburgh meetings of the Econometric Society, December 1962). M See, e.g., James M. Holmes, "A Direct Test of Friedman's Permanent Income Theory," Journal of the American Statistical Association 65 (September 1970): 11591162. M In the life cycle theory, the propensity to consume temporary income gains is always positive. It is at least equal to the propensity to consume out of existing net worth at the beginning of the period. For details, see Farrell, "The New Theories of the Consumption Function." 30 A. C. Pigou, "Economic Progress in a Stable Environment," Economica, n.s., 14 (1947): 180-188, reprinted in A.EA. Readings in Monetary Theory, ed. Lutz and Mints (New York: The Blakiston Company, 1951): and Don Patinkin, "Price Flexibility and Full Employment," American Economic Review 38 (1948): 543-564, reprinted with corrections and modifications in A.EA. Readings (1951), pp. 252-283, and Money, Interest, and Prices, 2nd ed. (New York: Harper & Row, 1965).

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tators termed this the "Pigou Effect" or, as Patinkin had it, the "realbalance effect." The net liquid assets of the private sector were envisaged as the sum of "outside" money, namely money for which there is no corresponding private liability (thus most commercial bank deposits would be excluded) and of interest-bearing government debt. However, because of the possibility that the public may anticipate future tax liabilities required for the servicing of such debt, some writers have argued that government debt should be either largely (or completely) eliminated from the relevant net liquid claims on the government. Patinkin argued that the impetus given by large real balances to consumption can be interpreted as a short-run manifestation of a wealth effect, as in the short run the stock of real capital (and its valuation) will be constant and all other private assets and liabilities will cancel out, in a closed economy. Patinkin has used this approach primarily in the context of monetary theory, while Pigou introduced the idea in the debate over the theoretical possibility of aggregative equilibrium of the economy at a position of less than full employment. 31 J. Ernest Tanner has tested for the importance of a real-balance effect and has found evidence that such a factor is both present and nontrivial, using postwar Canadian data. 32 The consideration of a real-balance effect leads to the question of whether the aggregate consumption function (under an absolute income hypothesis) is more properly specified with liquid assets or net worth as an important secondary explanatory variable. As James Tobin and Walter Dolde have pointed out, there has been a tension in macroeconomic theory and practice for some time between "wealth" and "liquidity" theories of consumption and saving. 33 On the one hand, Lawrence R. Klein obtained excellent results with liquid assets as an important subsidiary explanatory variable, in cross-section analyses of the determinants of savings and durable goods expenditures. 3 4 31 Patinkin's 1948 article, as amended when it was reprinted in the 1951 Α. Ε A. Readings in Monetary Theory, gives a fair presentation of both sides of this debate. Recent work in disequilibrium dynamics may have reduced the practical (as distinct from the theoretical) importance of this issue. See, e.g., Axel Leijonhufvud, On Keynesian Economics and the Economics of Keynes: A Study in Monetary Theory (New York: Oxford University Press, 1968). 32 "Empirical Evidence on the Short Run Real Balance Effect in Canada,"Journal of Money, Credit and Banking 2, no. 4 (November 1970): 473-485. '"Tobin and Dolde, "Wealth, Liquidity and Consumption," in Consumer Spending and Monetary Policy, Monetary Conference Series no. 5 (Boston: The Federal Reserve Bank of Boston, 1971), pp. 99-146. ""Statistical Estimation of Economic Relations from Survey Data," in Katona et al., Contributions of Survey Methods to Economics (New York: Columbia University Press, 1954).

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Moreover, many macroeconometric models utilize liquid assets as one of the explanatory variables in the fitted consumption function (or functions), possibly because this variable is much more easily obtained than a constructed series of the wealth of the personal sector. 35 But Tobin has long argued against such a specification on the theoretical g r o u n d s that an u l t i m a t e d e t e r m i n a n t of b o t h the c u r r e n t consumption-savings decision a n d the portfolio decision of t h e household must be net worth rather than liquid assets. 36 A study by John J. Arena provided some interesting evidence on these points. 37 From U.S. data, Arena found that the liquid assets variable was significant only when the net worth of the personal sector was not included as an explanatory variable; liquid assets thus appeared to be simply playing a proxy role. For the postwar regressions, however, liquid assets of the household sector seemed to have an independent influence and did not vanish in importance when net worth was included as an explanatory variable. Tobin and Dolde have recently gone far to resolve the apparent contradictions in these two approaches. The authors have made the distinction b e t w e e n liquidity-constrained and non-liquidity-constrained households: the former are those whose income prospects would justify a higher level of consumption expenditures than they can finance either out of current income or else out of loans from imperfect capital markets. 38 (A young family headed by a promising but impecunious medical student could serve as an example of a liquidity-constrained household.) To the extent that this phenomenon is widespread, a liquid assets variable would appear to be justified in a fitted consumption function, either as a substitute for, or in addition to, a variable measuring household net worth. 39 35 An early illustration is the Klein-Goldberger model of the U.S. economy; see Lawrence R. Klein and A. S. Goldberger, An Econometric Model of the United States, 1929-1952 (Amsterdam: North Holland, 1955). 3e James Tobin, "Asset Holdings and Spending Decisions," American Economic Review, Papers and Proceedings 42, no. 2 (May 1952): 109-123, and "The Consumption Function," mimeographed (Extended article prepared for the International Encyclopedia of the Social Sciences, c. 1964). 37 "The Wealth Effect and Consumption: A Statistical Inquiry," Yale Economic Essays 3, no. 2 (Fall 1963): 250-303. 38 Tobin and Dolde, "Wealth, Liquidity, and the Propensity to Consume," Cowles Foundation Discussion Paper no. 314, mimeographed (New Haven, Conn., 1971), and "Wealth, Liquidity and Consumption." 39 In the context of most time series analyses, the intercorrelation between a liquid assets variable and household net worth would probably prevent the inclusion of both of these variables as meaningful determinants of aggregate consumption (or of personal savings). As Tobin pointed out in his survey, "The Consumption Function," to the extent that an intercorrelation exists (and is reasonably strong), the practical import of this issue may not be very great.

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The Rate of Interest Another interesting issue concerns the role of the rate of interest in the aggregate consumption function. Does this theoretically relevant variable have a practical significance, and if so, what is the direction of the effect? Skepticism about the influence of interest rates on consumption and savings began with Keynes, who asserted that the effect was small. 40 In particular, Keynes argued that the main channel by which a fall in interest rates increased aggregate consumption out of a given level of income was to increase the dissaving of the elderly, as such a change would make an annuity more attractive relative to straight interest income. The second controversy can be traced at least back to Alfred Marshall, who attributed to Sargant the possibility of target savings, in which case a rise in the interest rate could conceivably reduce the rate of saving. 41 Marshall regarded this outcome as an anomaly. A later generation, raised on income and substitution effects, would argue that the standard substitution effect of a rise in the interest rate would be to increase future consumption (and hence saving) at the expense of current consumption, although there might exist circumstances in which the substitution effect could be overwhelmed by a stronger income effect. Curiously, there appears to be some empirical evidence on the side regarded as unusual or perverse by the economic theorists. Warren E. Weber, in two recent papers based on a life cycle model of consumption, presents results from U.S. data indicating that a rise in the rate of interest will induce an increased level of consumption. 4 2 The same conclusion, namely a negative direct effect of the treasury bill rate on personal savings, results as a by-product of Tanner's study of the real-balance effect in Canada. 43 But Somermeyer and Bannink report the more conventional positive effect of a rise in the interest rate in the context of an aggregate savings function for the Dutch economy, although the effect is not statistically significant. 44 The fact that it is difficult to resolve the second issue suggests that Keynes was probably right about the first one. 40

Keynes, General Theory, pp. 93-94. Alfred Marshall, Principles of Economics, 1890, 8th ed., 1920 ( N e w York: Macmillan, 1948), p. 235. 42 "The Effects of Interest Rates on Aggregate Consumption," American Economic Review 60, no. 4 (September 1970): 591-600, and "Interest Rates, Inflation, and Consumer Expenditures," American Economic Review 65, no. 5 ( D e c e m b e r 1975): 8 4 3 858. 43 It must be admitted that the direct effect could conceivably be offset by the indirect wealth effect of a rise in interest rates, which reduces the value of the nondiscounted amount of the government debt held by the public and so increases the rate of savings, in Tanner's final equation. 41

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Income

Distribution

A final issue to be considered is the influence of the distribution of income on the level of aggregate consumption. This is a vast subject of which we can only scratch the surface. If the different socioeconomic classes have different marginal propensities to consume, then a redistribution of income toward the socioeconomic group (generally assumed to be wage-earners and/or low income groups) with a high MPC will obviously raise the aggregate consumption function. Keynes mentioned such possibilities, and Nicholas Kaldor has constructed a whole theory of the distribution of income in the aggregate on the postulate that the marginal propensity of capitalists to save (property income recipients) far outruns the MPS of workers. 45 Weintraub has made the differing Μ PCs of three major socioeconomic groups (workers, rentiers, and profit-income recipients) one of the central themes in his theory of the aggregate income distribution. 46 Weintraub's theory is nevertheless general-equilibrium in character, integrating marginal productivity considerations and nonconsumption aggregate demand components as well. Τ. M. Brown's final consumption function for the Canadian economy allowed for a much higher propensity to consume labor income than property income. Along similar lines, the Klein-Goldberger econometric model allowed for differing MPCs out of disposable income for three socioeconomic groups: farmers, nonfarm business owners, and (nonfarm) wage and salary recipients, with the MPCs increasing in the order delineated above. 47 On the other hand, Harold Lubell provided an early expression of skepticism as to the quantitative importance of this phenomenon. 48 He argued that any conceivable redistribution of income would have had at most a minor impact on the aggregate consumption func• " S e e A Consumption-Savings Model and Its Applications, ch. 7. In " S o m e E v i d e n c e o n the Interest Elasticity of C o n s u m p t i o n , " American Economic Review 57, no. 4 (Sept e m b e r 1967): 8 5 0 - 8 5 5 . C o l i n Wright p r e s e n t e d e v i d e n c e of a negative i n f l u e n c e of the interest rate on aggregate U.S. c o n s u m p t i o n . T h i s e v i d e n c e is largely irrelevant to the s e c o n d issue, h o w e v e r , as it c o m e s from a m o d e l in w h i c h the interest rate as an explanatory variable is a measure of only the substitution effect. N o o n e e v e r d o u b t e d the direction of the substitution e f f e c t alone, although Wright takes s o m e pains to demonstrate that this substitution e f f e c t is nontrivial in magnitude. 45 N i c h o l a s Kaldor, "Alternative T h e o r i e s of Distribution," Review of Economic Studies 23, no. 2 ( 1 9 5 5 - 1 9 5 6 ) : 9 4 - 1 0 0 . An extreme Kaldorian position w o u l d b e the assumption that capitalists save all of their i n c o m e , w h i l e workers save n o n e of theirs. 46 S e e Weintraub, An Approach to the Theory of Income Distribution. 47 S e e Brown, "Habit Persistence and Lags in C o n s u m e r Behaviour," and Klein and Goldberger, An Econometric Model of the United States. 48 "Effects of Redistribution of I n c o m e on C o n s u m e r s ' Expenditures," American Economic Review 37, no. 1 (March 1947): 1 5 7 - 1 7 0 .

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tion. Moreover, Duesenberry argued that the effect of greater equality in the distribution of income might be to lower the aggregate consumption function. This outcome could result if the MPCs of the various households were interdependent (not independent) and if such a change weakened (almost universally) emulative pressures to maintain consumption standards. Tobin attributed to Houthakker the view that the distribution of income has an effect across societies, with societies with high shares of property income also being ones with high savings ratios. 49 This author's feeling is that the same influence could work within a single country over time as well, but that because of the great stability of income shares within an economy over moderately long periods; it is of second-order importance in a short-run analysis or even a medium-term study. 50

The Investment Demand Function The concept of an investment function, as distinct from the staticd e m a n d for capital as a factor of production, again goes back to Keynes' monumental work. The discussion in this section will be brief. Dale Jorgenson has prepared an excellent summary of the recent literature, generally evaluated from his own point of view. 51 Keynes introduced a concept called "the marginal efficiency of capital," a rate of discount which just served to equalize the stream of anticipated net revenues (net of direct costs but not of depreciation or finance charges) from an investment project to the supply price of the capital good or project. As each project could be evaluated (in principle) by such a calculus, it was possible to trace out an investment 49 In "The Consumption Function," Tobin held that societies with high property income shares and high savings rates are also societies with high interest rates. However, the discussion of the preceding subsection suggests that this implies far too strong an influence of the interest rate in inducing savings, e v e n if the (noncompensated or gross) effect of a rise in the interest rate is assumed to be in the direction of inducing more (not less) savings, on the margin. 50 Probably more important than the gross share of national income going to property income recipients is the proportion going to independent businessmen, as this socioe c o n o m i c group tends to be composed, in the U.S.A. at least, of disproportionately high savers. On this point, see Lawrence R. Klein, "Entrepreneurial Saving," in Proceedings of the Conference on Consumption and Saving, vol. 2 (Philadelphia: University of Pennsylvania Press, 1960). ' ' " E c o n o m e t r i c Studies of Investment Behavior: A Survey," Journal of Economic Literature 9, no. 4 ( D e c e m b e r 1971): 1111-1147. A vigorous discussion of Jorgenson's controversial assertions may be found in Lawrence R. Klein, "Issues in Econometric Studies of Investment Behavior," Journal of Economic Literature 12, no. 1 (March 1974): pp. 4 3 - 4 9 , and in Robert Eisner, "Econometric Studies of Investment Behavior: A Comment," Economic Inquiry 12, no. 1 (March 1974): 91-104.

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demand schedule for an entire industry or even for the entire private sector of a particular economy. The concept has been widely applied in current theoretical systems, including econometric models of modern economies. Several comments may be proffered in connection with Keynes' investment demand function. First, it should be noted that the concept was expectational in character. Because there was thought to be no completely airtight basis on which to estimate future revenues or costs of any particular investment project, entrepreneurs' feelings about prospective investment decisions were regarded as important, even critical, in the process. Keynes himself stressed the importance of this factor. Most, p r o b a b l y , of our d e c i s i o n s to d o s o m e t h i n g p o s i t i v e , the full conseq u e n c e s o f w h i c h w i l l be d r a w n out o v e r many days to c o m e , can only b e undertaken as a result of animal spirits—of a spontaneous urge to action rather than inaction, and not as the o u t c o m e of a w e i g h t e d a v e r a g e of quantitative benefits m u l t i p l i e d b y quantitative probabilities. 5 2

Second, as it rested on such uncertainties, the investment demand function was envisaged as subject to considerable variation. This fluctuating function, in conjunction with the multiplier implications of a stable consumption function, was viewed as inducing great variations in employment and output in a modern economy. Third, by making expected net revenue a function of a number of possible variables (e.g., the level of national income itself, the rate of unemployment, the state of the stock market), a very flexible form of the investment demand function will result, as we shall observe later. Fourth, the rate of interest was a relevant and nontrivial explanatory variable for the level of investment expenditures demanded, although it is equally clear that fluctuations in actual investment demand were viewed by Keynes as reflecting principally fluctuations in the marginal efficiency of capital, variations more important than those in the complex of interest rates. Finally, it would appear that new capital goods (the investment projects under consideration) are differentiated in some manner from old capital goods, or from the initial stock of capital in general. This distinction may result from technological progress embodied in new investment goods, or simply because there are psychic and/or financial costs to the act of adjusting the firm's capital stock, so that an adjustment of actual capital stocks to desired levels will not take place instantaneously. For such reasons, Abba P. Lerner has suggested that Keynes' concept, the marginal efficiency of capital, be renamed "the " K e y n e s , General Theory, p. 161.

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53

marginal efficiency of investment." By making such a distinction, w e are led more easily to consider the existing stock of capital as a relevant a r g u m e n t in the investment d e m a n d function. Following R. G. D. Allen, we can formalize these notions. 54 Let a,„(t;I ,Κ,α) be the net r e v e n u e of the marginal investment project at time t; we assume that this net r e v e n u e is always positive but will d i m i n i s h with either increased investment (/) in the present period or a larger initial stock of capital (K).55 T h e shift parameter α is left abstract but could represent the level of national income, the rate of u n e m p l o y m e n t , or some factor (such as the state of the stock market) influencing expected future profits. T h e parameter thus corresponds to Keynes' expectational elements. This revenue stream is p r e s u m e d to last for Τ periods into the future. Τ is the time horizon for such i n v e s t m e n t calculations, and any scrap value from the e q u i p m e n t (or plant) of the investment project is s u b s u m e d in am(T;I,K, a ). Finally, let V be the present valuation of the marginal investment project and let r* be the marginal efficiency of investment. T h e n , by definition, w e have: (1)

We may derive an investment d e m a n d function by making two additional assumptions. Let us denote the supply price of the marginal i n v e s t m e n t project as P, and let us suppose (due to capacity limitations in t h e capital goods industry for example) that this variable rises with increasing gross investment, I + R, w h e r e R is replacement investment. If we again suppose that replacement investment is a simple increasing function of the initial stock of capital K, we have: Ρ = P(I

+ R) = Ρ (I +

f(K)).

(2)

If we now equate the supply price of t h e marginal investment project to its p r e s e n t valuation (substituting a market rate of interest i for the marginal efficiency of investment), we obtain: (3) 53

Abba Lerner, The Economics of Control (New York: Macmillan, 1944). Macro-Economic Theory: A Mathematical Treatment (New York: Macmillan, 1967), especially pp. 108—112. Allen treats time as continuous, thereby avoiding the arbitrariness in the choice of a period if one deals with time on the basis of discrete intervals. Nevertheless, in this chapter the author employs a discrete treatment in order to simplify the mathematics slightly. "Such an assumption avoids the well-known problem of obtaining multiple roots in the calculation of the marginal efficiency of investment. Multiple roots would impart indeterminacy to the analysis. 54

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Equation (3) is an implicit function for the determination of the level of investment demand, given the other relevant determinants. By t h e w e l l - k n o w n implicit function t h e o r e m of mathematical analysis, w e may (in principle, at least) write our investment demand function explicitly as follows I = I ( i , K , a ) .

(4)

1

The investment demand function will then behave as w e might expect: the level of investment expenditures will vary negatively with the rate of interest and with the initial stock of capital and positively with any other determinant which, acting through the parameter a, raises the marginal efficiency of investment. 57 Finally, we may briefly contrast this formulation with a much more rigorous (but also more rigid) model. Dale Jorgenson has d o n e pathbreaking work on a new "neoclassical" theory of investment demand, a theory now widely incorporated in econometric models. M Jorgenson set up an expression for the discounted value of the net receipts, calculated indefinitely into the future, of a typical enterprise. M I n particular, if we assume that all the functions are at least twice differentiable, then the sufficient condition for the local existence of the implicit function is that

0, where

Ol

F ^ Ρ (I +/(K))

But

ol

= P' -

- Ι

.

> d?" / (1 + i f , and this expression is strictly positive under our asdl /

sumptions, as P ' > 0 and

da dl

< 0, for all t. Η ence the sufficient condition is met.

" T h e signs of all of these partial derivatives can be established by implicit partial differentiation. For example, to obtain dl/di, we differentiate equation (3) with respect to i as an independent variable. We obtain:

ρ

=

JiV_

θί

dl

di

di

where

-fr=i-W 0, etc.

(4)

Such a definition of course d e p e n d e d only on system (2) and did not utilize any dynamic adjustment process. For a single market, with linear demand and supply schedules, it simply reduced to the elementary statement that slope of demand curve < slope of supply curve,

(5)

i.e., the supply curve cut the demand curve from below. Samuelson followed a well-established literature in mathematics to formulate the definition of stability with reference to a given dynamic system: an equilibrium was stable if it was "attracting," if that is, perturbations from the equilibrium were, by the dynamic laws of motion, eliminated. To equilibrium conditions like (2), one thus had to a p p e n d a dynamic model like the tatonnement: •4&-=klEl 0; i =j), then Hicks' and Samuelson's definitions are equivalent. It is important to recognize just how limited this set of propositions was. First, the propositions dealt with "given excess demand functions," as in (6). They did not use any economic hypothesis to cut down the number of possible functions £,; consequently, there was still not too much in the economics of the problem, except perhaps strong gross substitutability, to provide even a potential stabilizer. Furthermore, the assumption that excess d e m a n d functions were linear was crucial to the "true" dynamic stability characterization. n

A . Smithies, "The Stability of Competitive Equilibrium," Econometrica 10 (1942): 256-257; and Lloyd A. Metzler, "Stability of Multiple Markets: The Hicks Conditions," Econometrica 13 (1945): 277-292.

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Of course, stability was defined for arbitrary processes like (6); results, however, could only be obtained for linear systems like (8). Although this was useful since instability for (8) entailed instability for (6), the important problem was to develop economic assumptions which entailed stability of (6). Such theorems were not easy: it would be almost fifteen years before economists could provide any rigorous proof.

The Arrow-Debreu Model The current approach to general equilibrium theory might be dated to 1954, for in that year Kenneth J. Arrow and Gerhard Debreu remodeled the Wald system by introducing production sets to replace the restrictive "fixed-coefficient" technology, and preference structures to replace utility functions with "nice" properties.12 Their method of proof was distinct from that of Wald. To discern the changes that had occurred over the years, some discussion of how economists proved that a competitive equilibrium could exist is interesting. The existence problem is rather easy to state: is there a set of non-negative prices, one for each market, such that if consumers and producers were to optimize taking those prices as given, the demand and supply quantities which would result would yield prices in those markets identical to those taken as given? Phrased in this manner, the problem has a very straightforward heuristic for a proof. Consider a non-negative price vector p. For these prices, a solution of the optimization problem for consumers and producers, yields, via the excess demand relations, an excess supply or an excess demand in each market. If the former obtains in the t'th market, reduce the i th component of p; if the latter, raise that component. Under what conditions will the "fudging" of ρ terminate? Are there reasonable economic restrictions on consumer and producer behavior that produce a price vector which will clear the markets simultaneously?13 "Kenneth J. Arrow and Gerhard Debreu, "Existence of an Equilibrium tor a Competitive Economy," Econometrica 22 (1954): 265-290. 13 The observation that each agent, optimizing individually, entails a coherent social outcome is directly traceable to Adam Smith. As Dobb observed, following Schumpeter, "Smith's 'principle of Natural Liberty,' which he enunciated as early as 1749, was the empirical assertation that.. . 'free interaction of individuals produces not chaos but an orderly pattern that is logically determined'—a pattern which, accordingly, could be elucidated in rational terms" [Maurice Dobb, Theories of Value and Distribution Since Adam Smith (New York: Cambridge University Press, 1973), p. 139.J

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Arrow and Debreu phrased the problem with the aid of an equilibrium notion derived in the context of an n-person game, and they established the competitive equilibrium as an analogue of the Nashequilibrium for such games, (a notion of "best, given the responses of everyone else")· In the same year, Lionel W. McKenzie used the Kakutani fixed-point theorem to establish existence of an equilibrium.14 Briefly, that theorem states that if one takes a point in a set with nice geometric properties (compact, convex subset of Euclidean η-space) and maps that point in a smooth manner (by an upper semicontinuous mapping) back into the set from which it came, then at least one point from the set gets "sent to itself." A less general version of this theorem, the Brouwer fixed-point theorem, was used by David Gale in 1955 to establish the existence of a competitive equilibrium in a Wald-type model. 15 Almost simultaneously, Hukukane Nikaido and McKenzie used the Kakutani theorem to establish existence of a competitive equilibrium for generalized Arrow-Debreu models. 16 Recalling the economic interpretation of the method of proof discussed above, the McKenzie argument noted that economic assumptions entailed a linear dependence among the η-prices from Walras' Law, and degree zero homogeneity of demand. If the dependence is written Pi + p2 + · · · + p„ = 1, then any non-negative price vector remains within a compact, convex subset of Euclidean η-space, specifically the unit n-simplex. Consider one such vector. The process by which individuals optimize, given that price vector, is an upper semicontinuous map from a price vector to a quantity vector (a small price change produces only a small quantity change). The quantities themselves, in the market, produce new prices in the original set in a continuous manner. Thus an initial p° yields a q° which yields a p1 which yields a q 1 , etc. . . . "Lionel W. McKenzie, "On Equilibrium in Graham's Model of World Trade and Other Competitive Systems," Econometrica 22 (1954). See also Shizuo Kakutani, "A Generalization of Brouwer's Fixed Point Theorem," Duke Mathematical Journal 8 (1941): 457-459. 15 The original statement of this theorem was by L. E. J. Brouwer, "On Continuous Vector Distribution on Surfaces," Amsterdam Proceedings, vol. 11, 1909. Modem use, and proofs, are often based on B. Knaster, C. Kuratowski, and S. Mazurkiewiez, "Ein Beweis des Fixpunktsatzes fur n-dimensionale Simplexe," Fundamenta Mathematica 14 (1929): 132-137. See also David Gale, "The Law of Supply and Demand," Mathematica Scandinavica 3 (1955): 87-101. le Hukukane Nikaido, "On the Classical Multilateral Exchange Problem," Metroeconomica 8 (1956): 116-126; and Lionel W. McKenzie, "Competitive Equilibrium with Dependent Consumer Preferences," in Proceedings of the Second Symposium in Linear Programming, ed. H. A. Antosiewicz (Washington: National Bureau of Standards, 1955).

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The Kakutani theorem then says that there is some p* such that p* yields q* which yields precisely p*. Such a price vector p* is a competitive equilibrium. On the credo of some mathematicians that " i f problem χ is the subject of a textbook exposition, then problem χ is a dead issue for research," the appearance in 1959 of Debreu's Theory of Value closed down investigation of the "existence of competitive equilibria." 17 In only 102 compact pages of text, Debreu presented a full axiomatic development of consumer behavior, firm behavior, and existence of equilibrium (using the Kakutani theorem). Furthermore, he showed that the competitive equilibrium produced an allocation of goods and services that was Pareto-efficient: any reallocation would make at least one economic agent worse off. Finally, Debreu established that state-of-the-world uncertainty about the future would make no difference in the problem if there were a sufficient number of futures markets for the goods and services.

Stability Theory With the existence problem "settled" by the late 1950s, mathematical theorists turned their attention back to those problems of dynamic adjustment raised by Hicks, Samuelson, Metzler, et al. in the early 1940s. T h e research quickly focused on the problems of: (1) taking an Arrow-Debreu representation of the Walrasian system, (2) modeling the tatonnement adjustment process, and (3) finding the economic assumptions which would guarantee stability under the tatonnement rules. As with the existence problem and its solution via fixed-point theorems, stability theory relied on an old mathematical technique which was new to economists, the "second" or "indirect" method of Liapunov. 18 Consider, for example, the differential equation χ = / ( * ) , *(0) = x „ .

(9)

Here χ is a real number, χ is dxldt, and f is a very well-behaved (differentiable), function of time. An equilibrium is a function of time 17 G. Debreu, The Theory of Value: An Axiomatic Analysis of Economic Equilibrium, Cowles Foundation Monograph no. 17 ( N e w York: John Wiley, 1959). 18 A Liapunov, " P r o b l e m e general de la stabilite du movement," Annales de la Faculte des Sciences de l'Universite de Toulouse 9, no. 2 (1907). For a discussion of this approach see Joseph LaSalle and Solomon Lefschetz, Stability by Liapunov's Direct Method ( N e w York: Academic Press, 1961).

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Ε. R O Y W E I N T R A U B

or a state, xe(t), such that xe(t) = 0; alternatively, it is a root or zero of the function f(x). To find out whether a given equilibrium xe(t) is stable, one needs to examine whether other "nearby" motions of the system "get close" to xe(t). We are thus led to consider: (1) an equilibrium of a system like (9); (2) a representation of the distance between arbitrary motions of the system and the equilibrium; and (3) a study of whether, over time, the distance between an arbitrary motion and equilibrium grows smaller; if so, then the system's rules mean that nonequilibrium states approach equilibrium, and thus that the equilibrium is stable. For the tatonnement of equation (8), if p, is the deviation of the ith price from equilibrium, one obtains the system, for ρ = ( ρ j , . . . ,p„) T , where " T " indicates the transpose operator, ρ = KBp

(10)

with ρ = 0 the equilibrium. Now certainly Vzp • ρ measures half the square of the distance from ρ to equilibrium. It thus behaves like distance itself. But d/dt(Yzp • p) = Vi(prρ + pp r ). Using ρ from (10), then

dt

(distance) = Vi(pTKBp +

p^fCp)

Sufficient conditions for stability are then sufficient conditions that d/dt (distance) < 0, but these are simply conditions that the quadratic form

be negative definite. Because Κ represents speeds of adjustment, and Β is the Jacobian of the excess demand matrix, whatever conditions on Κ and Β ensure that the quadratic form is negative definite will be economic conditions sufficient to guarantee stability of the tatonnement system given by (10). Use of the indirect Liapunov method quickly provided a number of sufficient conditions for tatonnement stability. Papers by Arrow and Hurwicz, Hahn, Negishi, McKenzie, and Nikaido and Uzawa were all

General Equilibrium

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11 7

19

written in a comparatively short period. Arrow, Block, and Hurwicz, for example, proved that system (6) was "globally asymptotically stable" provided that the excess demand functions were difFerentiable and homogeneous of degree zero in prices; that they satisfied Walras' Law; and that all goods were strong gross substitutes for each other. 20 These results were soon shown to be about as much as could be hoped for when Herbert Scarf produced a range of interesting classes of "reasonable" economic systems which were unstable.21 These examples " s u g g e s t . . . [that] instability seems to be a universal phenomenon in competitive economics, rather than an exceptional one, whereas global stability [can be] expected to prevail only in very well-behaved systems." 22 Also around 1960 theorists began to examine some expressly nonWalrasian adjustment mechanisms. In particular Uzawa, Hahn, and Hahn and Negishi began the study of what are now termed nontatonnement processes. 23 This is not a very descriptive characterization of a wide variety of adjustment mechanisms which explicitly permit trading to occur at nonequilibrium states of the system. For such processes, it was not difficult to show that "reasonable" rules which constrained the actual trading process would lead to a final allocation that would be Pareto-efficient. 24 By the early 1960s, there was thus a reasonably well-understood model of a decentralized private-ownership economy for which a "Kenneth J. Arrow and Leonid Hurwicz, "On the Stability of the Competitive Equilibrium, I," Econometrica 26 (1958): 522-552; Frank H. Hahn, "Gross Substitutes and the Dynamic Stability of General Equilibrium," Econometrica 26 (1958): 169-170; Takashi Negishi, "A Note on the Stability of an Economy Where all Goods and Gross Substitutes," Econometrica 26 (1958): 445-447; Lionel W. McKenzie, "Stability of Equilibrium and the Value of Positive Excess Demand," Econometrica 28 (1960): 606-617; Hukukane Nikaido and Hirofiimi Uzawa, "Stability and Non-Negativity in a Walrasian Tatonnement Process," International Economic Review 2 (1960): 50-59. 20 Kenneth Arrow, Herbert D. Block, and Leonid Hurwicz, "On the Stability of the Competitive Equilibrium, II"Econometrica 26 (1959): 89-109. "Herbert Scarf, "Some Examples of Global Instability of the Competitive Equilibrium," International Economic Review 1 (1960): 157-172. "Hukukane Nikaido, Convex Structures and Economic Theory (New York: Academic Press, 1968), p. 337. 23 Hirofumi Uzawa, "On the Stability of Edgeworth's Barter Process," International Economic Review 3, (1962): 218-232; Frank H. Hahn, "On the Stability of Pure Exchange Equilibrium," International Economic Review 3 (1962): 206-213; and Frank H. Hahn and T. Negishi, "A Theorem on Non-Tatonnement Stability," Econometrica 30 (1962): 463-469. "We could require that successive allocations of goods to the traders during the adjustment period result in a net utility gain for those agents who had engaged in trade, so that the process could be considered to be a gradient process in utility.

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Pareto-efficient competitive equilibrium could be shown to exist. The model was stable under a generally accepted set of price adjustment rules. The microeconomic research program of general equilibrium theory was in a fairly settled state, and future investigations, it then appeared, would be concerned with extensions of the basic model to problems involving noncompetitive price formation, uncertainty, externalities, and public goods. To be sure, such investigations dominated the mainstream literature on general equilibrium theory during the first part of the 1960s. T w o major developments, however, have shifted the focus of the theory somewhat over the past dozen years. First, the resurgence of interest in monetary theory has induced a re-examination of the microfoundations of macroeconomic theory, and that study has been drawn inevitably to the general equilibrium method of analysis. Second, the continued study by mathematical economists of the theory of n-person games has provided an elegant new approach to multi-agent interaction, which was previously identified with general equilibrium theory. Each of these developments will be discussed in turn, although the research on game-theoretic approaches to Walrasian theory will be more completely examined in the next chapter.

Microfoundations of Macroeconomic Theory The Lange-type macroeconomic concerns for general equilibrium theory proceeded hand in hand with the more elegant formal analyses during the 1950s and reached their culmination in Don Patinkin's Money, Interest, and Prices.2* Patinkin integrated real money balances into the excess demand structure of the partially disaggregated system of: (1) goods markets, (2) money markets, (3) labor markets, and (4) bond markets. The four-way "disaggregation" undoubtedly cast fresh light on the Keynes-Classics controversy. This neoclassical synthesis produced a number of classical monetary theory implications, such as a revised full-employment quantity theory, a version of monetary "neutrality," and the assessment of Keynesian Theory as a special case of the general neoclassical theory characterized by disequilibrium behavior in one, or in several, markets. Patinkin's reintegration of value theory (general equilibrium theory) with monetary theory was questioned by a number of econoa D o n Patinkin, Money, 1966).

Interest,

and Prices,

2d ed. ( N e w York: Harper and Row,

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mists from a variety of perspectives. This essay must skirt those issues of monetary theory proper raised by Patinkin's work.2® Likewise, it is not possible to pursue the numerous diverse intellectual currents emanating from it that compelled economists to re-examine other theoretical issues in the context of Money, Interest, and Prices. For present purposes, it need only be noted that the presence of money was not necessarily compatible with the Arrow-Debreu treatment of uncertainty, futures markets, expectations, speculation, and decentralized optimization-cum-centralized-auctioneer price adjustment. T h e search for compatibility between models of optimization behavior without money as an asset (i.e., money serving as numeraire only) and models in which the decision structures and transactions structures are related to uncertainty about the future set of transactions has dominated recent work in general equilibrium theory. 27 T w o major concentrations of research effort can be identified to support this thesis: (1) a very detailed, and rapidly growing, literature on " m o n e y " and/or "transactions costs," and/or "uncertainty" and general equilibrium theory based on the Arrow-Debreu static structure; and (2) a variety of investigations focusing on disequilibrium adjustment processes which attempt to handle the information problems brought on by uncertainty about other agents' behavior and from which "asset m o n e y " evolves. Extensions of the Arrow-Debreu framework to incorporate uncertainty were treated in a paper by Roy Radner, w h o showed that uncertainty about the future states of the world could be handled in the standard model, provided there did exist a complete set of futures markets in conditional contracts. 28 Such analysis led Radner, in later work, to formulate the concept (attributed to Hicks) of temporary equilibrium in sequence economies in which one could "investigate the possibility of consistency among the expectations and plans of the various agents" and define an extension of the Arrow-Debreu equilibrium concept as "a set of prices on the current market, a set of common expectations for the future, and a consistent set of individual plans, one for each agent, such that, given the current prices and price expec-

2 e For some indication of this literature, see Axel Leijonhufvud, On Keynesian Economics and the Economics of Keynes ( N e w York: Oxford University Press, 1968), and E. Roy Weintraub, "Uncertainty and the Keynesian Revolution" History of Political Economy 6, no. 4 (1976). " S e e the excellent discussion of these issues in Frank H. Hahn, On the Notion of Equilibrium in Economics (Cambridge: Cambridge University Press, 1973). M R o y Radner, " C o m p e t i t i v e Equilibrium Under Uncertainty," Econometrica (1968): 31-58.

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tations, each agent's plan is optimal for him, subject to the appropriate sequence of b u d g e t constraints." 2 9 This idea of temporal sequences of Arrow-Debreu economies was used by Hahn, Kurz, and Starrett to examine the technology by which transactions might b e effected over the sequence, and the role that assets like money might play in delineating transactions rules which could lead to efficient allocations. 30 Similarly, recent work by Grandmont and Younes, Sonderman, and others exhibits concern for institutional features of monetary economies and for the manner in whcih they might b e incorporated into general equilibrium analysis. 3 1 For example, Jerry Green was able to identify a particular institution, the collateral-loan market, which appears inefficient in the context of an Arrow-Debreu economy with a sufficient number of futures markets to eliminate state-of-the-world uncertainty. 32 Current research on disequilibrium adjustment has its roots in the non-tatonnement mechanisms described earlier. Without the auctioneer, H a h n noted, " w e are faced with the necessity of specifying precisely the forces which shape producers' demand for goods, and in particular how this d e m a n d reacts to these signs. 33 Such questions have received a great deal of attention in recent years. Fisher, Diamond, Hey, Iwai and others have examined different assumptions about market search, bid behavior, informational decentralization, and their interplay with money's role in the adjustment processes. 3 4 2e Roy Radner, "Problems in the Theory of Markets Under Uncertainty," American Economic Review (May 1970): 458-459. 30 Frank H. Hahn, "Equilibrium with Transaction Costs," Econometrica 39 (1971): 417^439, and "On Transactions Costs, Inessential Sequence Economies and Money," Review of Economic Studies 40 (October 1973): 449-463; Mordicai Kurz, "Equilibrium in a Finite Sequence of Markets with Transaction Cost," Econometrica 42 (1974): 1-20; David Starrett, "Inefficiency and the Demand for Money in a Sequence Economy," Review of Economic Studies 40 (October 1973): 437^449. 31 J. M. Grandmont and Y. Younes, "On the Efficiency of Monetary Equilibrium," Review of Economic Studies 40 (April 1973): 149-167, and "On the Role of Money and the Existence of a Monetary Equilibrium," Review of Economic Studies 42 (July 1975): 355-373; see also the papers by both Grandmont and Dieter Sonderman in Jacques Dreze, ed., Allocation Under Uncertainty, Equilibrium, and Optimality (London: Macmillan & Co., 1973). 32 Jerry Green, "Temporary General Equilibrium in a Sequential Trading Model with Spot and Future Transactions," Econometrica 41 (1973): 1103-1124. ^Frank H. Hahn, "Some Adjustment Problems," Econometrica 38 (1970): 1-17. " S e e , e.g., F. Fisher, "On Price Adjustment Without an Auctioneer," Review of Economic Studies 39 (January 1972): 1-17 and "Stability and Competitive Equilibrium in Two Model of Search and Individual Price Adjustment," Journal of Economic Theory 6 (October 1973): 446-471; Peter A. Diamond, "A Model of Price Adjustment," Journal of Economic Theory 3 (June 1971): 156-169; John D. Hey, "Price Adjustment in an Atomistic Market," Journal of Economic Theory 8 (August 1974): 483-500; Katshuhito Iwai, "The Firm in Uncertain Markets and its Price, Wage, and Employment Adjustment," Review of Economic Studies 41 (April 1974): 257-277.

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Overall, the "monetary revival" has enriched the discourse and concerns of general equilibrium theorists to a considerable extent. T h e past decade has been characterized by considerable extension (and some redirection) of general equilibrium theory. Certainly treatments of the subject which suggest that Debreu's Theory of Value represents the culmination of general equilibrium theorizing are only half correct: while it " e n d e d " less rigorous modeling attempts, it simultaneously provided a beginning for serious study of a general equilibrium theory sufficiently rich and flexible to deal with the evershifting concerns of economic theory. 35

The Core of a Competitive Economy An alternative approach to multi-agent, multi-good analysis can be traced directly to F. Y. Edgeworth's Mathematical Psychics written in 1881, roughly contemporaneously with Walras' 1874 Elements.36 For Edgeworth, the process of contracting to reallocate goods, and subsequent recontracting by the agents (without actual trading) to improve their position, was at the heart of market processes. H e was able to provide a heuristic proof of the proposition that as the number of agents increased relative to the number of traded commodities, there would exist a unique allocation of goods to traders, an allocation on which no group of traders could improve. This allocation was in fact the competitive allocation, or the goods-assignment that would have been arrived at had all traders passively optimized with respect to given prices. This Edgeworthian insight, which certainly provided an alternative path to the study of the existence of competitive equilibria, was revived and formally modeled by Martin Shubik in 1959.37 Shubik established the Edgeworth conjecture that the set of viable allocations diminished as the number of traders increased. This " l i m i t T h e o r e m " was the subject of papers by Debreu and Scarf, and then Aumann, and

35 In this regard, it might be noted that the path-breaking treatise by Walter Isard, a pioneer in Regional Science, is based on the Debreu model. See W. Isard, General Theory: Social, Political, Economic and Regional with Particular Reference to Decision-Making Analysis (Cambridge: Massachusetts Institute of Technology Press, 1969). 3 e F. Y. Edgeworth, Mathematical Psychics (London: Kegan-Paul, 1881). 37 Martin Shubik, "Edgeworth Market Games," in A. W. Tucker and R. D. Luce, eds., Contributions to the Theory of Game, IV, Annals of Mathematics Studies, no. 40 (Princeton: Princeton University Press, 1959).

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Vind.38

Their methods were all based on Shubik's treatment of the Edgeworth problem as an n-person game and on the use of the concept of the "core" as the appropriate solution concept for such economic games. This alternative route to the study of general equilibrium systems necessitated at least partial replication of existing results for the Walrasian model in order to claim generality for the new approach. Current work, however, provides some indication of the power of the game-theoretic point of view in unraveling the complex behavioral interactions at the heart of traditional Walrasian conundrums like the role of external diseconomies.39

Conclusion General equilibrium theory, in the mid-1970s, is itself in a "healthy" state. The research program that followed from the work of Hicks and Wald in the 1930s has been fruitful, leading to a better understanding of how decentralized mechanisms for resource allocation may lead to orderly market outcomes. The theory has been responsive to changes in the way economists have viewed current problems, and this responsiveness has facilitated the use of general equilibrium analysis in many areas of applied economics. This two-way interaction is probably the best indicator that the concerns of Smith, Cournot, Walras, Pareto, and Edgeworth are still alive, and lively, today.

An Approach to the Literature There are a variety of good references for readings on general equilibrium theory that can serve as some introduction to the sources cited in the footnotes. The list is intended only as a sample set for a directed study program on the subject. For relatively limited mathematical preparation, Vivian C. Walsh's Introduction to Contemporary Microeconomics ( N e w York: McGraw-Hill, 1969) and E. Roy Weintraub's General Equilibrium 38Gerhard Debreu and Herbert Scarf, " A Limit Theorem on the Core of an Economy," International Economic Review 4 (September 1963): 235-246; R. Aumann, "Markets with a Continuum of Traders" Econometrica 32 (1964): 39-50; and Karl Vind, "Edgeworth Allocations in an Exchange Economy with Many Traders," International Economic Review 5 (1964): 165-177. 3e See, for example, Lloyd S. Shapley and Martin Shubik, "On the Core of an Economic System with Externalities," American Economic Review 59 (September 1969): 678-684.

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Theory (London: Macmillan & Co., 1974), both available in paperback, provide an introduction and survey of current concerns. To grasp the technical issues, see the first essay in Tjalling C. Koopmans' Three Essays on the State of Economic Science (New York: McGraw-Hill, 1957), and Chapter 13 of Robert Dorfman, Paul Samuelson, and Robert Solow's Linear Programming and Economic Analysis (New York: McGraw-Hill, 1958). For upper-level undergraduates, who have courses in intermediate level price theory, some calculus, and some linear algebra, see the clear exposition by J. Quirk and R. Saposnik, Introduction to General Equilibrium Theory and Welfare Economics (New York: McGrawHill, 1968). The essay by Frank H. Hahn, On The Notion of Equilibrium in Economics (Cambridge: Cambridge University Press, 1973) conveys the problems inherent in the Walrasian approach to monetary theory. Also, although it requires some familiarity with issues in macroeconomic theory, B. Hansen's A Survey of General Equilibrium Systems (New York: McGraw-Hill, 1970) repays study. At the more advanced study level, there is now the treatise by Kenneth Arrow and Frank H. Hahn, General Competitive Analysis (San Francisco: Holden Day, 1971); this will carry the reader up to stateof-the-art journal literature. Good substitutes are lacking. Duke

University

7 Optimization and Game Theory E. ROY WEINTRAUB

The neoclassical revival of the 1930s, based on the analytic work of John R. Hicks and R. G. D. Allen and the methodological critique by Lionel Robbins, placed emphasis on the choice-theoretic underpinnings of most economic reasoning. When these developments were brought together by Paul Samuelson in Foundations of Economic Analysis, the substructure of applied theorizing could be considered well-identified. In its most compact form, neoclassical analysis assumed that economic agents could be modeled as individual entities which had given desires or preferences over outcomes. Such preferences would lead the rational agent to select the best outcome from among all available outcomes. T h e outcomes that are available, however, are subject to the constraints that scarcity entails, and it is the essence of economic choice that scarcity be recognized. 1 The structure of an economic problem, then, could be identified once agents were recognized, their preferences modeled, and the constraints on their choices fully specified. The problem became one of constrained optimization, alternatively called optimization subject to constraints. A solution of the particular economic problem would consist of an object of choice that, among all objects which could b e 'See Lionel Robbins, An Essay on the Nature and Significance (London: Macmillan & Co., 1932). 125

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chosen (and did satisfy the constraints), was the most preferred, given the preferences of the agent.2 Formally, one required a set of objects, S, and agent, a; a preference relation for a on S, R a ; and constraints which served to define some subset C C S. The economic problem was for a to choose some object χ eC C S such that χ was maximal with respect to R„ on C. To solve this problem concretely, one needed (1) economic assumptions to structure the choice set S; (2) economic assumptions to specify a well-defined preference relation R„; (3) economic assumptions which modeled the constraints to yield C; and (4) a methodological proviso that the agent could indeed be treated as if he were a rational chooser in the sense of the problem.

Varieties of Optimizing Problems To be sure, economists had long understood that demand functions could be obtained by maximizing a utility function subject to a budget constraint. The new analysis showed that this logic was exceedingly general and could serve to unify economic theory by treating many problems symmetrically.3 Older economists had "fleshed out" the structure of the problem by assuming that (1) objects of choice were real numbers; (2) preferences could be modeled by continuously differentiable real-valued functions; (3) constraints were linear equalities (e.g., budget lines); and (4) each agent acted as a "homo economicus." The standard technique for solving a static constrained optimization problem realized as (1) through (4) was by means of Lagrange multipliers, variables which when multiplied by the constraint, were added to the objective function to tum the constrained problem into an unconstrained optimization exercise. For such problems, well-known techniques existed to identify the optimal solutions, generally by examining "potential" solutions provided by necessary conditions (or first-order conditions) that a solution existed. In a dynamic setting, the technique used was the calculus of variations; objectives would be some integral (with respect to time) of 2 For an excellent exposition of this basic choice-theoretic framework, see Vivian C. Walsh, Introduction to Contemporary Microeconomics (New York: McGraw-Hill, 1970). Constrained optimization techniques are currently the substance of courses titled Microeconomic Theory (intermediate). 3Paul A. Samuelson's Foundations of Economic Analysis (Cambridge: Harvard University Press, 1947) certainly hammered this point home.

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instantaneous objective functions, and the constraints w o u l d b e given by " p a t h s " or solutions of differential equations. T h e goal was the path that optimized the objective functional. 4 O n e of the difficulties of both static a n d d y n a m i c constrained optimization, in the continuous or calculus setting d e s c r i b e d above, is that specific objective functions are n e e d e d to get specific answers. Generally, nonspecific functions suffice for economic problems w h e r e the interest lies solely in qualitative properties of t h e solution. If, however, one desires to model a concrete real p r o b l e m , unspecified utility functions just won't do. D u r i n g and after the Second World War a n e w approach to optimization with constraints was d e v e l o p e d to solve practical problems. Part of the m e t h o d entailed computation of t h e o p t i m u m values t h e m selves provided: (1) the objective function was linear in the objects of choice, and (2) the constraints w e r e linear inequalities. This m e t h o d , called linear programming (or activity analysis), m a d e its mark in economic theory by providing a m e t h o d for b r i n g i n g together, in the theory of the firm, two decisions formerly thought to b e separate, n a m e l y t h e c h o i c e of t e c h n i q u e a n d t h e c h o i c e of t h e profitmaximizing output. 5 For situations in which the objective function could not b e m o d e l e d by a linear function, the theory of nonlinear p r o g r a m m i n g was developed to imitate the linear analysis. 6 For d y n a m i c problems, d y n a m i c programming and optimal control theory have essentially replaced the calculus of variations as the t e c h n i q u e of t h e day. Optimization theory can b e v i e w e d as a distinct sub-branch of mathematics, or as a collection of tools the working economist needs to do sensible applied work; currently, it is not economists b u t colleagues in operations research and m a n a g e m e n t science who are most responsible for refining t h e s e 4 An excellent older example of this technique is found in Frank P. Ramsey's "A Mathematical Theory of Saving," Economic Journal 38 (1928): 543-559. 5 The current literature is, of course, immense. For economists, the older sources which gave impetus to study included: Robert Dorfman, Application of Linear Programming to the Theory of the Firm (Berkeley: University of California Press, 1951); A. Charnes, W. W. Cooper, and A. Henderson, An Introduction to Linear Programming (New York: John Wiley, 1953); and Tjalling J. Koopmans, ed., Activity Analysis of Production and Allocation (New York: John Wiley, 1951). The introductory essay by Koopmans provides a good historical background to the analytic method. By the mid1950s, economists had the elaborate treatise by Robert Dorfman, Paul Samuelson, and Robert Solow, Linear Programming and Economic Analysis (New York: McGraw-Hill, 1958). "The major reference here, before texts, is simply H. W. Kuhn and A. W. Tucker, "Nonlinear Programming," in Jerzy Neyman, ed., Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (Berkeley: University of California Press, 1950).

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techniques, which were developed to answer questions phrased with more specificity than economic theory would wish. Economic theory is still a qualitative or logical discipline.

Came Theory: The Early Stages In its early development, game theory was properly viewed as a generalized theory of optimization with the notion of two or more agents having preferences over outcomes, and constraints on their choices. The intrinsic difference from standard theory, however, was the recognition of agent interaction and the potential for interagent conflict. This extension was modeled by the objective function, which specified payoffs given the choices, but the payoff of an agent depended not only on his own choices but also on the choices made by other agents. 7 From this point of view, applications to economics focused on those economic problems, like bilateral monopoly or oligopoly, in which explicit recognition of the interfirm rivalry had brought traditional theory to the impasse of indeterminate outcomes, of "anythingcould-happen," or of ad hoc explanations. Game theory could, it seemed, cut through the knot of complicated ceteris paribus arguments, in which everyone recognized that "ceteris" was unlikely to be "paribus." The theory of games has grown to have an importance in economic theory quite different from the expectations of its early devotees, and it has moved away from its beginnings as a theory of interdependent optimization. In order to explain how game theory became an investigative logic of the social sciences, it is necessary to develop a taxonomy of the field and a sense of the limitations of various subcategories of the theory; it is to such matters that we now tum.

A Taxonomy of Games The simplest way to distinguish among games is to classify them by the number of players who are making the choices which lead to ' T h i s view of g a m e theory is not central to current applications, nor even to its current mathematical development. It was, however, the explicit impetus for the subject. " I f two or more persons exchange goods with each other, then the result for each one will d e p e n d in general not merely upon his own actions but on those of others as well. T h u s each participant attempts to maximize a function . . . of which he d o e s not control all the variables. . . . T h i s kind of problem is n o w h e r e d e a l t with in classical mathematics . . . and it is this problem which the theory o f ' g a m e of strategy' is mainly d e v i s e d to m e e t " [John von Neumann and Oscar Morgenstern, Theory of Games and Economic Behavior, 2 d ed. (Princeton: Princeton University Press, 1947), pp. 11-12],

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payoffs. Although some authors phrase stochastic optimization problems for one agent as a one-person game (played against Nature, which has no choices), a proper taxonomy begins with two agents, three agents, and so on. (A further refinement here would also permit Ν to be infinite.) Within the structure of the theory, it turns out that the jump from two to three players is highly significant in a way that the introduction of a sixth player is not. This anomaly is produced by the possibility of collusion, or coalitions, as soon as more than two players (with potentially conflicting interests) are present; going from two to three players introduces coalitions, whereas going from five to six simply increases the number of potential coalitions. A second way to distinguish among games is by means of the payoffs to the players. In some games it may be possible to model a problem as having a constant payoff: for one set of choices by the agents, the fixed payoff is split one way; with another set of choices, it is divided another way. Such games can be normalized to have a total payoff to all players represented by "zero," with some players receiving positive payoffs, others negative, in such a way that the sum of all payoffs to players is zero. Such games are called zero-sum games and capture " I lose, you win or I win, you lose" elements; they are really pure conflict situations with no cooperative aspects. Finally, consider some non-zero-sum game of two or more players in which one sum of payoffs to players' choices is larger than a second. In that case, one of the players might like to " b r i b e " another to make the choice which would yield the first sum. The bribe, of course, can only be paid out of the eventual payoff, and consequently the payoff must be in terms of some object which is transferable between players (like "money," unlike "power"). We may thus speak of games with, and without, side-payments dependent on whether or not the payoffs are freely transferable.

Two-Person Zero-Sum Games Games of total conflict between two players are theoretically uninteresting because a well-defined solution exists for all of these problems. Such games did, however, provide the impetus for two developments in economic theory, namely, measurable utility and noncooperative equilibria. Analysis of the structure of payoffs requires that they be measured in some way; payoffs should represent outcomes of strategy choices by agents and should reflect, in a well-defined sense, the agents' preferences over those outcomes. Consequently, it was necessary for game

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theorists, in the early development of the subject, to grapple directly with the old cardinal-ordinal utility controversies among economists. It is a matter of historical record that the solution of this problem was provided by mathematicians for game theory. 8 Briefly, given agents' preferences over outcomes, and given that the preferences satisfied certain reasonable conditions like transitivity and completeness, it could be proved that there existed a continuous positive real-valued function defined on outcomes which assigned larger numbers to more preferred outcomes. Such a function could be termed a utility function: utility was inferred from preferences. Furthermore, the function was not unique, but was as a scale, like temperature, which only preserved relative differences. The old conundrums about utility were settled by the recognition that: (1) yes, utility could be measureed, but (2) only essentially ordinal properties were analytically meaningful. In any event, economists no longer had to feel shy about using real-valued utility functions in choice-theoretic exercises. The second contribution of such simple games was the refinement of the notion of equilibrium, traditionally a chimera to economists. An equilibrium strategy for an agent in two-person zero-sum games was a strategy that provided the largest minimum payoff to the agent against any potential strategy of the other player. It was a conservative notion, for the agent was not to choose that strategy which yielded the largest payoff against a stupid choice by his opponent, but rather to select a strategy that could maximally ensure against loss by an omniscient opponent. The sort of reasoning behind this max-min equilibrium provided an analytically rigorous approach to older duopoly problems which forced the firm to ignore the behavior of its rival. 9 Each firm was best off if it assumed that its rival could take any action at all, and each would thus act to maximize the minimum gain that could be obtained from each available strategy. In short, an equilibrium choice could be extended naturally from a situation in which A s payoff depended only on A's choice to a situation in which A's payoff depended as well on choices made by B. This was a concrete progressive step in econom8 There is really little to dispute here, except perhaps by economists embarrassed at how quickly first-rate mathematicians can solve "insolvable" economic problems. See von Neumann and Morgenstern, Theory of Games, Appendix, pp. 617-632, and Israel N. Herstein and John Milnor, "An Axiomatic Approach to Measurable Utility," Econometrica 21 (1953): 291-297. 9 For these intricate problems, see the extremely cumbersome taxonomy utilized by an analyst as gifted as Ragnar Frisch in "Monopole-Polypole—La notion de force dans l'economie," Nationalkonomisk Tidsskrift, April, 1933, trans, in International Economic Papers, vol. 1 (New York: Macmillan, 1951), pp. 23-36.

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ics, for it showed that equilibrium itself was a situationally d e p e n d e n t concept and not necessarily wedded to supply and demand.

Two-Person Non-Zero-Sum Games Once payoffs to the players are permitted to b e nonsymmetric, so that A's gain is not necessarily B's loss, elements of cooperation intrude upon the strategic interaction. Two types of such games in particular have commended themselves to economists seeking to understand real phenomena: the Prisoners' Dilemma and the bargaining problem. T h e salient feature of the Prisoners' Dilemma is that each player, A or B, has two strategies, a cooperative one (c) and a noncooperative one (NC), so that there are four possible outcomes of simultaneous strategy choice: Bc

B.\c

Ac

4,4

1,5

Ave

5,1

3,3

On the basis of individually rational choice, A would choose strategy A,vC rather than Ac because noncooperation is better against any choice by Β; and Β would take a similar course. A and Β each receive the equilibrium payoff of 3. However the choice Ac> Bc leads to a Paretoimprovement with payoffs 4,4: individually rational behavior leads to a socially "irrational" outcome. 1 0 This model was studied early in game theory's development and led to various attempts to model economic problems—numerous examples were created to suggest that market outcomes were based on individually rational behavior, but such outcomes were socially inefficient and necessitated state (or institutional) intervention in agent choice to lead to Pareto-superior outcomes. In short, the Prisoners' Dilemma entailed a sprain of the "invisible h a n d " and thus provided an explanation for a variety of real institutions which, in opposition to l0 This game is attributed to A. W. Tucker. The best single reference on the game, from a psychological viewpoint, is Anatol Rapoport and Albert Chammah, Prisoner's Dilemma (Ann Arbor: University of Michigan Press, 1965). Its relevance to social choice was well-documented in William J. Baumol, Welfare Economics and The Theory of the State (London: Longmans, Green, 1952).

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laissez-faire dogma, could be justified because they facilitated efficient outcomes. 11 The bargaining game reflects the concern with the potential cooperation that characterizes non-zero-sum situations. In matrix form, it could be represented by: B.

B2

Ai

0,2

-2,1

A2

-4,-4

2,0

Here there is no clear-cut, individually rational strategy for either A or B, but A could choose A 2 , forcing Β to have at most a zero payoff, while Β could choose B 2 , giving himself at least a non-negative payoff. IfA and Β could agree to alternate in some sense between (A u B,) and (A2, B 2 ), they would both be better off. If such alternation were modeled by a probability, we could graph the result as in Figure 1.

The line segment in the first quadrant of Figure I represents Paretoefficient outcomes with respect to all potential outcomes on the payoff quadrilateral. T h e question, then, is where on the segment " T h i s explanation is sketched in William Riker and Peter Ordeshook, Introduction Positive Political Theory (Englewood Cliffs, N.J.: Prentice-Hall, 1973).

to

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(0,2)-(2, 0) the parties will agree. Once it is realized that A, and B2 represent potential "threat strategies" guaranteeingA no less than —2, and Β no less than 1, it is clear that such games can model the power that the agents have to enforce outcomes. Various equilibria have been developed by theorists for such games. For economists, however, interest in the bargaining game is primarily a result of the fact that many economic phenomena are essentially negotiated outcomes. Consequently, the theory of such games can provide "negotiating variables" which can narrow the range of economic equilibria resulting from efficiency arguments alone. 12

N-Person Cooperative Games With more than two players, games become immensely rich, as coalitions can form to achieve cooperative gains. T h e primary tool used to investigate such situations is the characteristic function which assigns a payoff to every coalition in such a way that a coalition receives a larger payoff than the sum of the payoffs to its individual members. The game itself is then completely defined once the characteristic function is given. The questions of interest deal with the notion of an equilibrium outcome, or an outcome that cannot be improved on by the formation or dissolution of any coalition. More precisely, if some allocation of gains to players can be realized with a specific coalition structure, another allocation is said to dominate the given one if there exists a coalition which, by its own actions, can improve the lot of its members. The core is the set of allocations which are undominated: the core is thus an equilibrium concept. T h e r e are, of course, other equilibrium notions which can be created. We call a set of allocations a von Neumann-Morgenstern solution if, for any two allocations in the set, neither dominates the other, and if any allocation outside the set is dominated by at least one member of the set. It is only in the past decade or so that the theory of N-person games has begun to play a role in economic theorizing, and this is a result, primarily, of the slow development of the theory up to the work done to define the core as a solution concept for such games. The core is an economic concept because it represents an outcome that cannot be improved on by any coalition of agents. It is a generalization of a 12

An elegant application, which reviews the Nash bargaining theory, can be found in George de Menil, Bargaining: Monopoly Power versus Union Power (Cambridge: Massachusetts Institute of Technology Press, 1971).

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Pareto-efficient allocation, as it is characterized by the condition that not only is it impossible for the coalition of all agents to be bettered, but no subcoalition can improve its lot by taking a permissible action. The core is thus related to the notion of contractual freedom, or competition, and many economic analyses of market problems can be set up in terms of a market game. For such games it is often possible to show that the core bears some definite relationship to the competitive equilibrium, if both exist. 13 Of potentially greater interest to economists, however, are those economic problems which can be modeled as N-person cooperative games for which a core does not exist. Intuitively, the core is constructed by looking first at the set of all allocations, then throwing away those dominated by the all-agent coalition (Pareto-inefficient allocations), then discarding those dominated by the η Ν—I agent coalitions, and so on. By elimination, we are left with core allocations. If too much is discarded, the core may not exist. Consequently, it is a "strong" concept of equilibrium in which interest attaches to economic problems without a core solution as such situations correspond to a failure of market liberty to reconcile the potentially conflicting desires of the market participants.14 Because the core is defined as those allocations which simultaneously satisfy all the various coalitional action constraints, nonexistence of the core can lead to inferences about the relative strength or reasonableness of the scheme (game) which defines the core constraints. Hence the core is a useful tool for evaluating the a priori coherence of a given set of economic institutions to solve a particular market problem.

Came Theory and General Equilibrium Although the fact is not often recognized by workers in areas of 13 The literature on this sort of application to partial equilibrium analysis is growing rapidly. Most authors acknowledge the horsemarket analysis of Bohm-Bawerk as seminal. For a state of the art exposition see Lester Telser, Competition, Collusion, and Game Theory (Chicago: Aldine, 1972). 14 For an application to problems of externalities, see Lloyd S. Shapley and Martin Shubik, "On the Core of an Economic System with Externalities," American Economic Review 59 (September 1969):678-684; regarding public enterprise problems, see George R. Faulhaber, "Cross-Subsidization: Pricing in Public Enterprises," American Economic Review 65 (December 1975): 966-978. The Arrow Impossibility Theorem of welfare economics has a core-theoretic argument at its heart: see Robert Wilson, "The Game Theoretic Structure of Arrow's General Possibility Theorem," Journal of Economic Theory 5 (1972): 14-20.

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applied economics, general equilibrium analysis has been completely rewritten from a game-theoretic perspective over the last decade. 15 The new approach begins with a large number of traders, their preferences and endowments, and firms who also are engaged in choice. The economy is considered to provide freedom of contract, or liberty to form coalitions which improve the well-being of the various agents: economizing (or optimizing) is thus subsumed in the question of coalition formation for reallocative efficiency. For such economies, it is well known that the competitive equilibrium lies within the core. In other words, an allocation of goods to traders that, for some price system, is optimal for the constraints, is also a core allocation. Furthermore, allocations which award similar payoffs to similar traders are in the core. 16 More importantly, as the market becomes more "competitive" in the sense that each agent's influence over market events becomes smaller, the core shrinks, although it continues to contain the "competitive" allocation. In the limit, as the number of traders becomes infinite, the core approaches the competitive allocation. Such analysis brings the role of competition into sharp focus: the existence of a general equilibrium is thus a consequence of a rigorous definition of competition, alternatively, competition is a natural concept, not one which has to be defended by ad hoc arguments. As an assumption, competition can be examined in terms of the conclusion such models produce—the size of the core.17 I5 See Kenneth Arrow and Frank H. Hahn, General Competitive Analysis (San Francisco: Holden Day, 1971), especially ch. 8. " T h e modern literature begins with Martin Shubik's "rehabilitation" of Edgeworth in "Edgeworth Market Games," in Contributions to the Theory of Games, vol. 4, ed. A. W. Tucker and R. D. Luce, Annals of Mathematics Studies, no. 40 (Princeton: Princeton University Press, 1959). The literature on "limit theorems" was defined, for economic purposes, by Gerhard Debreu and Herbert Scarf, "A Limit Theorem on the Core of an Economy," International Economic Review 4 (September 1963): 235-246. The modem, or measure-theoretic treatments, were initiated by Robert Aumann in two papers, "Markets with a Continuum of Traders," Econometrica 32 (January 1964): 39-50, and "Existence of Competitive Equilibria in Markets with a Continuum of Traders," Econometrica 34 (January 1966): 1-17. This treatment has been extended by Werner Hildenbrand in "On Economies with Many Agents," Journal of Economic Theory 2 (June 1970): 161-189, and his recent treatise Core and Equilibria of a Large Economy (Princeton: Princeton University Press, 1974). See the references in any of these works for a key to the bargaining literature. " F o r an analysis of the way this literature may provide a link between microeconomics and macroeconomics, see E. Roy Weintraub, "Microfoundations of Macroeconomics: A Critical Survey," Mimeographed (Durham, N.C.: Duke University, 1976; for a contrary view, see Martin Shubik, "The General Equilibrium Model Is Incomplete and Not Adequate For the Reconciliation of Micro and Macroeconomic Theory," Kyklos 28, no. 3 (1975): 545-573.

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Other Solution Concepts The core is a cooperative concept. It is a result of coalition behavior which entails cooperation for mutual gainoncooperative games, one is forced back to generalizations of individually rational behavior. The Nash-equilibrium captures this essence and forces the individual agent to assess his potential best, given the actions (potentially harmful) of other agents. Many problems of imperfect information, "wrong" expectations, etc., can be well posed in this context.18 Furthermore, even in cooperative games there is no a priori discussion of payoffs to individual agents. Rather, the behavior of coalitions leads to coalition payoffs with the distribution of payoffs within the coalition left unexamined. A family of solutions, based on the characteristic function, has been developed to investigate such problems: they are variously called "values" of the games to the participant. Intuitively, the Shapley value of an N-person game represents the average (considering all coalitions of which the player is a member) of that player's marginal contribution to the coalition payoff. Although this concept has been extensively applied by political scientists in the context of voting and committees, it has only recently been used by economists to examine problems in both partial equilibrium theory (e.g., duopoly) and general equilibrium analysis.19

A Note on the Literature There is a dearth of text material to structure a reading program in Game Theory and Economics. At present, the only elementary exposition for economists is E. Roy Weintraub, Conflict and Cooperation in Economics (London: Macmillan, & Co., 1975). At the intermediate level, see the older exposition in Duncan Luce and H. Raiffa, Games and Decisions (New York; John'Wiley, 1957). Finally, at a more advanced (and modem) level, see the forthcoming volume by Lloyd S. Shapley and Martin Shubik, Game Theory and Economics. Various chapters of this book are available from RAND as reports R-904/ 1,2,3,4, and 6. Duke University 18 For a strong defense of the Nash-equilibrium's applicability to economics, see Shubik, "The General Equilibrium Model." '"See Steven Brams, Game Theory and Politics (New York: The Free Press, 1975); and Robert J. Aumann and Lloyd S. Shapley, Values of Non-Atomic Games (Princeton: Princeton University Press, 1974).

8 Input-Output and Linear Programming DANIEL A. GRAHAM

Historical Overview Future historians of economic thought may well label the period beginning roughly with the Second World War as "the age of linear economics." The volume of research and the importance accorded it can hardly be overstated. Three main "fronts" have been involved: game theory (the subject of the previous chapter), input-output analysis, and linear programming. Input-output analysis appeared earlier than linear programming. Itshistorical beginnings may be found in the writings of Francois Quesnay (1694—1774), a court physician to Madame Pompadour and Louis XV, and to his Tableau Economique, which represented the flow of products among the three classes of society: farmers, landowners and manufacturers. Karl Marx's analysis of the capitalistic process of reproduction also contained elements of input-output analysis. The real credit for the development of modem input-output analysis belongs to the American Nobel economist W. W. Leontief, who first explained the method in 1936 and gave a full exposition in 1941.1 'W. W. Leontief, "Quantitative Input and Output Relation in the Economic System of the United States," Review of Economic Statistics (August 1936): 105-125, and The Structure of American Economy, 1919-1939 (Cambridge: Harvard University Press, 1941). 137

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Input-output analysis dealt originally with a completely closed economic system—all produced goods were regarded as potential inputs to some other part of the system. Consumer goods, for example, were regarded as inputs needed to produce labor services. With the advent of World War II, interest shifted to the open model, which relaxed the requirement that all goods be intermediate goods, admitting the possibility of both primary factors (goods such as land which are productive but cannot b e produced) and final products (goods such as motion pictures which may be produced but cannot be used to produce other goods). In this analysis, the amounts of primary factors and the pattern of final demands were regarded as exogenously determined (determined outside the system) and input-output analysis was used to find the output levels consistent with the specified final demands. Inputoutput analysis was applied in this form to such problems as mobilization planning for war, i.e., determining how a shift of final demands from " b u t t e r " to "guns" would affect resource allocation in the various sectors. The basic idea of input-output analysis is that quantities of inputs are linearly related to the quantities of output to be produced. The analysis deals almost exclusively with production; demand theory plays little or no role. Second, the analysis emphasizes general equilibrium phenomena through the interdependence of the production plans of the many industries which constitute an economy. Third, input-output analysis is designed for empirical investigation. The empirical aspect distinguishes it from the work of Walras and later general equilibrium theorists. The comparative simplicity of the inputoutput model is the feature that makes empirical analysis possible—at a cost of encompassing fewer phenomena than the general equilibrium model. A fourth attribute lies in its close relationship to linear programming; the input-output model's "best allocations" are obtained by solving an appropriately formulated linear programming problem. The d e v e l o p m e n t of linear programming is due principally to George B. Dantzig. 2 Developed in 1947 as a technique for planning the activities of the U.S. Air Force, linear programming has subsequently b e e n applied to managerial planning and to economic theory generally. 3 2

George B. Dantzig, "Maximization of a Linear Function of Variables Subject to Linear Inequalities," in T. C. Koopmans, ed., Activity Analysis of Production and Allocation (New York: John Wiley & Sons, 1951). 3 Robert Dorfman, Paul Samuelson, and Robert Solow, Linear Programming and Economic Analysis (New York: McGraw-Hill, 1958) is a classic reference on the application of linear programming to a wide range of economic problems.

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Input-Output Analysis The Transactions Matrix Leontief s input-output model can be illustrated by considering a simplified economy in which there are two industries—agriculture and manufacturing. Each industry directly requires the primary factor labor as an input, as well as the output of the other industry. Table 1 provides a representation of this economy not unlike the Tableau Economique.

T a b l e 1. T r a n s a c t i o n s Matrix. Sector

Inputs to Agriculture

Inputs to Manufacturing

Final Demand

Total

Agriculture Manufacturing Labor

20 10 20

10 10 20

30 10 0

60 30 40

There is a row for each type of good. Reading across a row shows what happens to the total output of that good. In manufacturing, for example, a total of 30 units of manufactured goods are produced per year, divided evenly among agriculture, manufacturing, and final demand. Similarly, the last row indicates that of the 40 units of labor available per year, 20 units are employed in agriculture with the remainder in manufacturing. While it makes sense to add across rows, because all entries in any given row are measured in the same physical units, it would be nonsense to add down a column, as the physical units vary. Any given column, taken as a whole (or as a vector) does have meaning, however. Columns one and two give points from the production functions of the corresponding industries. Column one, for example, indicates that with the input of 20 units of agricultural produce, plus 10 units of manufactured goods and 20 units of labor, it is possible to produce 60 units of agricultural produce. The economy represented in Table 1 can be viewed as a black-box capable of transforming the available 40 units of labor into a net output of 30 units of agricultural produce and 10 units of manufactured goods available for final consumption. It remains to determine what other menus of final consumption are possible.

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The Input Requirements Matrix Table 1 is a purely descriptive device. To convert it into an analytical tool requires several assumptions. Calling agriculture "industry 1," manufacturing, "industry 2 , " and giving labor the subscript " 0 , " Table 1 can be rewritten as indicated in Table 2. Table 2. Sector Industry 1 Industry 2 Labor

Inputs to Industry 1

Inputs to Industry 2

Final Demand

in

111 lit

Ci Ci

*01

0

Xgs

Total X, X2 Xo

Production functions can then be written as X, = f l ( x

*oi);

Leontief makes the strong assumption that the production functions take the special form

Xu *21

On

*01 Ö21 ' Ooi

*12

*22 J E * . ) ,

a i2 ' a22 αa0022 /

where a„ is the required minimal input of commodity i per unit of output of commodity j . 4 A little thought should convince the reader that this assumption implies constant returns to scale, i.e., multiplying each Xy by a constant implies that the corresponding Xj will be multiplied by the same constant. The isoquant surfaces corresponding to these "fixed proportion" production functions have right-angle corners. To obtain the a^s from Table 1 we need merely to divide the entries in the first column by the first row total, and those in the second column by the second row total. Thus

"flu a 12 a = Ö21 Ö22 .001 Ö02-

4

~y3 -

y3"

Ve y3

_y3

The notation min(x, y, z) means the smallest of the numbers x, y, z.

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completely describes the technology of the economy under the Leontief assumption. This matrix is called the input-coefficient or inputrequirements matrix.

The Consumption Possibility

Frontier

Having described the technology of the economy, we may tum to the question of what alternative menus of final consumption are possible, given the available labor input. To produce one unit of commodity 1 requires a minimum input ofön units of commodity 1, α21 units of commodity 2, anda 01 units of labor. To produce X t units of commodity 1 must then require a l t X! units of commodity units of commodity 2, and a0iX! units of labor. Production ofX 2 units of commodity 2 similarly requires at least aiaX2 units of good 1, a 22 X 2 units of good 2, and aoaX2 units of labor. Adding these input requirements yields altK t + a12X2 = total input requirement for good 1; α2ιΧι + a 2a X 2 = total input requirement for good 2; a0jX, + 002X2 = total labor requirement. We have the obvious requirement that no more of a commodity be used than is available. fliiX 1 + 013X2 + Ci — Xi;

a2iX1 + aiaX2 + c 2 s X 2 ; α 0ί Χ, + a 02 X 2 +

Ϊ£ X 0 .

Rearranging, these constraints can be rewritten as

V C2

_


[/ - a]~' = b + ba + ba2 + ba3 + ... T h e last expression is easily recognized as the sum of the direct primary factor requirements, plus first round indirect requirements, plus second round indirect requirements and so forth. Note that to produce one w i d g e t you need as much labor as the direct requirement, plus as much labor as is required to produce the other inputs needed to produce a widget, plus the labor needed to produce the inputs used to produce the inputs, etc.

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times a vector representing direct and indirect labor requirements. In this case prices are directly proportional to the labor "embodied" in the comodities, and a simple labor theory of value holds. T h e next generalization of the input-output model to be considered is called the Leontief model with alternative techniques. In the case of this model, producers can choose from alternative methods or activities for producing a given good. In Figure 3, for example, production of one unit of the j t h product could be accomplished by any of the input combinations labeled A, B, or C. Moreover, because constant returns to scale are again assumed, it is possible to produce V2 unit by the input combination halfway from Ο to B, and V2 unit by the input combination halfway from Ο to C. Combining, we see that point D, halfway from Β to C, also represents a feasible input combination for producing one unit. Clearly, other "convex combinations" of activities are also feasible, and any input combination within the shaded area of Figure 3 suffices to produce one unit of the j t h product. T h e general specification of the alternative techniques model is straightforward. Let αϋ represent the amount of the tth good required to operate thej'th activity at unit intensity and let djj represent the amount of the tth good produced when t h e j t h activity is operated at

inpu

A

0 a

lj

B

D a

lj

a

lj

Figure 3.

a

^ lj

input 1

148

DANIEL Α G R A H A M

unit intensity. Here d j equals one if the j'th activity produces the ith good, and zero otherwise. If du

d 12

.du

2

·

•

dls

"1

1

1

0

0 "

•

(k5_

0

0

0

1

1_

for example, then the first three activities produce the first good, and the fourth and fifth activities produce the second good. Here it is assumed that there is no joint production; each activity produces only one good—the number one occurs only once in any given column of the d matrix. Let Xj represent the level of operation of the j t h activity, then gross outputs associated with intensity levels χ = (χ,, . . . , xr)T are given by dx. Similarly, input requirements for produced commodities are ax and primary resource requirements are bx where bu now represents the amount of the ith primary resource required for unit operation of the j t h activity. Equilibrium in production, zero excess supplies/ demands, is summarized by dx = ax + c, or (d - a)x = c,

(6)

while resource constraints require that bx < s.

(7)

These two sets of conditions again determine the consumption possibility frontier for the economy. Price equilibrium requires: (1) that any activity actually used to produce a given good make zero profits; and (2) that any activity not used be no more potentially profitable than one which is used, i.e., all other activities would make either zero profits or losses. Again, letting ρ denote the prices of produced goods and w the prices of primary resources, w e have pd s pa + wb with equalities holding for at least one activity for each industry (the activities to be used). That is, letting d, a, and b represent matrices composed of one " e m p l o y e d " activity for each industry, w e have pd = pä + wb or ρ = wb(d— a)'1. A collection of activities, one for each industry, is called a technique. T h e fact that many such collections of activities are possible gives rise to the term " L e o n t i e f model with alternative techniques." As w e shall see in the next section, the actual choice of technique can often be v i e w e d as a linear programming problem. T h e neoclassical model is a natural extension of the Leontief model with alternative techniques. Constant returns to scale are assumed, and producers are able to select an activity for producing the jth good

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149

f r o m t h e infinite c o l l e c t i o n d e s c r i b e d b y 1 = β(αί}, . . ., ('nji · · • . bmj). T h e a,·/s again r e p r e s e n t input r e q u i r e m e n t s for prod u c e d goods and the foj/s are input r e q u i r e m e n t s for primary factors. T h e only d i f f e r e n c e is that an infinite n u m b e r of alternative activities is now possible; the Leontief model with alternative t e c h n i q u e s admitted only t h e possibility of a finite n u m b e r . T h e case for η = 2, m = 0 is illustrated in F i g u r e 4. Any input combination along the unit isoquant for t h e first good can b e selected as t h e activity for p r o d u c i n g good 1 (e.g., point A), and any point along the unit isoquant for the second good as the activity for p r o d u c i n g good 2 (e.g., point B). T h e neoclassical model is thus a " s m o o t h " version of t h e Leontief model with alternative t e c h n i q u e s and could b e regarded as a limiting approximation for most purposes. T h e final m o d e l specification to b e c o n s i d e r e d is t h e activity analysis model. T h e modification of the alternative t e c h n i q u e s model is slight—simply relax the r e q u i r e m e n t that there b e no joint produc-

Figure 4.

150

DANIEL Α. G R A H A M

tion. Recall the d matrix where d^ equals one if the ith good is produced by thejth activity, and zero otherwise. We previously required that there be only one 1 in any given column of this matrix. We now relax this requirement and admit the possibility of more than one nonzero entry in each column. For example, 1

1

.0

17

1 0

2

d =

12

1

1

depicts a case in which activities 2, 3, and 5 produce goods 1 and 2 jointly. 12 Joint production makes a considerable difference in analysis. It makes possible, for example, the study of environmental pollution problems where "bads" are produced jointly with "goods," and of other cases involving externalities. 13

Linear Programming Geometrical

Considerations

A frequent problem in input-output analysis involves the search for that allocation of resources which maximizes the value of final demand (national product) at specified prices. Using the notation of the Leontief model with several primary factors, we are interested in maximizing pc subject to the resource constraints expressed in equation (4) and the obvious non-negativity restriction that c s 0. This problem involves maximizing a linear function of the choice variables, the c, 's, subject to a number of linear inequality constraints involving these choice variables. Linear programming is a device for solving such problems. To understand linear programming, it is quite useful to grasp the "standard form" of the linear equation. Consider a simple example: 4xt + 3x2 = 30, or, in matrix notation, [4, 3]

= 30 *2

1J It is not in general possible to require all entries to be zeros or ones because that level of operation of an activity which produces one unit of one good may not produce one unit of another good. ,3 See, for example, Kart-Göran Maler, A Study in Environmental Economics (Baltimore: Johns Hopkins University Press, 1974).

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and Linear Programming

151

T h e solution set of this equation, the set of all ordered pairs (x1; x2) which satisfy it, can be described as a line which is perpendicular to the direction of vector (4,3) and lies a directed distance from the origin equal to 30/V4 2 + 3 2 = 6. This is illustrated in Figure 5. First, plot the point corresponding to the coefficient vector of the equation—the ordered pair (4,3)—and think of this vector as an arrow with its tail at the origin and its head at the coordinates (4, 3). This arrow is the hypotenuse of a right triangle with sides 4 units long and 3 units long, respectively, and has length equal to V4 2 + 3 2 = 5. Next, divide the length of the coefficient vector, 5, into the constant term of the linear equation, 30, to obtain 6. Measuring out from the origin in the direction of the arrow, point A is located a distance of 6 units from the origin. Now, construct a line through A perpendicular to the direction of the arrow. This line is the solution set of the equation: the coordinates of any point along this line, when multiplied by the coefficient vector (4,3), will yield exactly 30.

Figure 5.

152

DANIEL Α. G R A H A M

Consider the equation with a larger constant term [4,3]

= 35.

Following the same procedure, we divide the length of the arrow, 5, into the constant term, 35, to obtain 7. Point Β is located 7 units from the origin in the direction of the arrow. The line through Β perpendicular to the arrow is the solution set of the new equation. Alternatively, if the equation were [4,3]

= 0, *2.

we would construct a line through the origin (0/5 units from the origin) perpendicular to the arrow. Finally, if the equation had a negative constant term, e.g., [4,3]

= -10, 1X2.

we would need to measure 2 units from the origin in the opposite direction of the arrow to locate the perpendicular line. This is the meaning of the term "directed distance": positive distances are measured in the direction of the arrow, negative distances are measured in the opposite direction. This standard way of considering linear equations extends to higher dimensional spaces. Indeed, this is its prime virtue. In 3-dimensional space, for example, we might have an equation such as [2,3,4]

Xi

*2

= 7.

*3 Again, plot the arrow given by the coefficient vector, measure its length, V29, and divide this into 7. Measuring from the origin 7/V29 units in the direction of the arrow ( + sign) we locate a point, and through this point we construct a plane perpendicular to the arrow. This plane is the solution set of the equation. The same procedure is involved in n-dimensional space. Given an equation of the form

Input-Output

and Linear

( a „ a2, . . . .a«)

Programming

153

= b,

we calculate the length of the coefficient vector, Μ

.

ί=1

and divide this into the number b. The solution set of the equation is a hyperplane orthogonal to the coefficient vector and lying a directed distance of b/\a\ from the origin. The term "orthogonal" is simply the η-space equivalent of "perpendicular" (the hyperplane is perpendicular in each of the η — 1 directions in which it is possible to be perpendicular). The term hyperplane comes from the fact that it bears the same relationship to η-space as a plane does to 3-space, e.g., it divides the space into two "half-spaces" (there is no way to move from one side of the hyperplane to the other without passing through it). Given these observations, the solution set for a linear inequality

(a„ a2

, an)

Xi *2

< b

will be recognized to be one of the half-spaces formed by the hyperplane ax = b, i.e., the solution set of the inequality consists of all those points lying on or to one side of the hyperplane. In Figure 5, for example, the solution set for [4,3]

30 L*2.

consists of all those points on or below the hyperplane (line) through point A. 14 Reversing the inequality yields all those points on or above this hyperplane.

Graphical

Solution

Half-spaces are particularly nice sets from a mathematical point of view because they are convex (a line segment connecting any two I 4 A line is a hyperplane in 2-dimensional space; a point is a hyperplane in 1-dimensional space. Notice that the dimensionality of the hyperplane is always one less than the dimensionality of the space.

154

DANIEL Α. G R A H A M

points in the set belongs entirely to the set) and closed (the set contains all its limit points). T h e y also form the basic ingredient of linear programming. To see this, consider the form of a standard linear programming problem: max «ιΛ··Λ

^T ßjXj j=l

subject to i = 1,. . . , m

AjjXj < r, j=l and

j = 1, . . . , η

0

w h e r e the gjS, the Aus, and the r,s are all given parameters of the problem, and the x,s are to b e determined. In obvious matrix notation, this problem is: max X s.t. AjX s r,

ex i = 1, . . . , m

χ > 0 Each of the linear inequality constraints, Atx ^ riy has a solution set which is a half-space. Similarly, each of the constraints, Xj s 0, has a solution set which is a half-space, as can be seen by writing these constraints as Xi [1,0,. ..,0]

0 Xv

[0,1,...,0]

*1 Xi

> 0

and so forth. The xs which simultaneously satisfy all the inequality constraints are those xs which simultaneously belong to all the associated half-spaces, i.e., to the intersection of all the half-spaces. Now the intersection of a n u m b e r of closed and convex sets is itself closed a n d convex; it represents t h e x ' s which satisfy all the constraints and is

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Programming

155

called the feasible set.15 An example for η = 2, m = 2 is illustrated in Figure 6. The feasible set is given by the region bounded by points 1,2,4, and 6 and represents the intersection of η + τη = 4 half-spaces. T o solve the linear programming problem, w e need to find that χ belonging to the feasible set which makes the objective function, ex, as large as possible. Consider an iso-value contour of this objective function: ex = constant. As w e already know, this is the equation of a hyperplane orthogonal to e and passing a directed distance from the " N o t e that the intersection—the feasible set—may be empty. This is the case of a poorly posed problem which simply has no solution.

156

DANIEL Α. G R A H A M

origin proportional to the constant. If the constant equals 0 the hyperplane passes through the origin; increasing the value of the constant shifts the hyperplane upward and outward, generating an entire "family" of parallel hyperplanes. Examination of the example illustrated in F i g u r e 6 reveals that the constant associated with the hyperplane through point 2 is smaller than the constant for the one passing through point 6, which, in t u m , is smaller than the constant associated with the hyperplane passing through point 4. Each of these hyperplanes is successively "further out." Consider the iso-value contour represented by the hyperplane through point 4. Only one point from the feasible set lies on this contour, namely, point 4. All other feasible points, moreover, lie on lower iso-value contours. Point 4 is therefore the solution to the example problem. T h e general solution is just as simple; one searches for that χ which is feasible and which lies on that objective function hyperplane which is furthest out. 1 6

The Simplex Algorithm T h e fact that the objective function is linear means that the solution to a linear programming problem will always occur on the boundary of the feasible set; a preferred contour can always be reached by moving away from any interior point toward the boundary. Also, a solution can always be found among t h e vertices (corners) of the feasible set. If a contour of the objective function coincided with an edge of the feasible set, such as 4-6 in Figure 6, either of the vertices given by point 4 or point 6 would be as good a solution as any point along the edge b e t w e e n points 4 and 6. This means that the search for an optimal solution can be restricted not only to the boundary of the feasible set b u t also to its vertices. Since there are a finite number of vertices, the restriction represents a considerable computational advantage. Still further computational gains are possible. Toward this end it is u s e f u l to d e f i n e t h e n e w " s l a c k v a r i a b l e s " xn+i = r, — A,x i = 1,. . . , m and the n e w "canonical problem" max

(e | 0)x

I

s.t. (A

\I)x = r

χ> 0 le

In a minimization problem, the search is for the iso-value contour which is closest in. In both cases the existence of an optimal solution depends upon the feasible set being bounded, i.e., upon the impossibility of pushing the objective function contours indefinitely outward (in the case of a maximum problem) or indefinitely inward (in the case of a minimum problem). Outward and inward, of course, refer to the direction extablished by the coefficient vector of the objective function.

Input-Output

and Linear Programming

157

w h e r e χ n o w has η + η c o m p o n e n t s ; the objective coefficient vector has b e e n a u g m e n t e d with 0s in the places c o r r e s p o n d i n g to the n e w xs and the A matrix has b e e n a u g m e n t e d with an τη χ m identity matrix (ones on the diagonal and zeros elsewhere). Clearly, this n e w formulation of the problem is completely e q u i v a l e n t to the original. What is the interpretation of the n e w slack variables? If x„+, equals zero, then Atx = r, so that a slack variable b e i n g zero implies that the corresponding constraint is b i n d i n g (holds as an equality). Moreover, χ,,+ι greater than zero implies that Α, χ < η . Consider the example (n = 2) illustrated in F i g u r e 7. H e r e x' depicts a feasible solution in w h i c h the t'th constraint is not b i n d i n g (holds as a strict inequality). Of course, the definition of x,l+, implies that A f x' = r, Xn+i with Xn+i > 0 . Notice that A,x — r,· is the equation of a h y p e r p l a n e which passes a directed distance from the origin equal to OD = rj A,· . Likewise, A,x = rf — x„+, is the equation of a h y p e r p l a n e parallel to

Figure 7.

158

DANIEL Α. G R A H A M

the first but lying OC = (r, — Xn+^/jA,! from the origin. This means that the solution, x', lies a distance: CD

= OD - OC = rj|A,| - (r, - x„+,)/|A, =

Xn+i/|A(|

from the constraint. Thus the value of a slack variable is seen to be proportional to the directed distance of the solution from the constraint associated with the slack variable. Consider now the entire set of constraints for the canonical problem, (A\I)x = r. These constraints form a system of m equations in η + m variables. We know that we can always express r, an m-vector, as a linear combination o f m linearly independent columns of (A|/).17 We may, therefore, pick any m linearly independent columns ofA, set the x,s corresponding to the columns not chosen equal to zero, and solve uniquely for the remaining x/s. Such a solution, with at most m Xj's not equal to zero, is called a basic solution. If it also happens that all the x/s in such a solution are non-negative, then the solution is called a basic feasible solution. Geometrically, basic solutions correspond to intersections of constraint hyperplanes. Basic feasible solutions correspond to vertices of the feasible set. For the problem illustrated in Figure 6, there are six basic solutions. Table 3 Χι point point point point point point

1 2 3 4 5 6

0 0 0 + + +

0 + + + 0 0

*3 (1st slack)

Ϊ4 (2nd slack)

+ + 0 0

+ 0

-

0

-

0 0 +

Notice that points 1 , 2 , 4 , and 6 are the only basic feasible solutions; all the others involve x/s which assume negative values. Point 3, for example, is characterized by the fact that xx = 0 and x 2 > 0 (read directly from Figure 6), while x3 = 0 (point 3 is zero distance from the first constraint), and x4 < 0 (point 3 is a negative "wrong way" distance from the second constraint). 17Any m linearly independent vectors form a basis for m-space. See for example, H. Nikaido, Introduction to Sets and Mappings in Modern Economics (New York: North Holland/American Elsevier, 1970), pp. 48-57.

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We are now ready to examine the simplex method. Having observed that with m = 2 and η = 2 there are

ways of choosing m = 2 linearly independent columns, we note that in general there will be

( basic solutions. T h e simplex algorithm is simply a method or procedure for systematically examining a subset of the basic solutions in order to find the solution to the linear programming problem. Starting with a basic feasible solution, the simplex algorithm is an iterative method that determines which column vector to bring into the basis and which to remove from the basis in order to assure movement to an optimal solution. Geometrically, the simplex algorithm can b e shown as follows. First, we n e e d a basic feasible solution. Notice that in our problem and in all typical maximum problems the origin is a ready-made basic feasible solution, i.e., Xj = 0 *7i+i - r{

i = 1, . . . , η i = 1, . . . , m

In the example of Figure 6, this means that we start off at point 1 with the third and fourth columns of A„

A 12

1

0

A21

A22

0

1

(A|J) = forming the basis. T h e value of the objective function at this point is, of course, e, • 0 + e2 • 0 + 0 · r, + 0 · r 2 = 0. T h e problem now is to determine which column to bring into the basis. Should we allow x, or x 2 to b e c o m e positive? Suppose w e increase X] from 0 to 1. This would improve the objective function by β\. Alternatively, if we increased x 2 from 0 to 1 we would improve the objective function by e2• In the example eι > e2, and making x t positive promises greater improvement than making x 2 positive. We accordingly determine to bring the first column of (A|J) into the basis. 1 8 " N o t i c e that in the product (A|/)x, x, is essentially a weight for the tth column of (A|/). choosing to make Xj positive, then, is equivalent to choosing to add the ith column of (AI/) to the basis.

160

DANIEL Α. G R A H A M

Another way of seeing the alternatives is to turn Figure 6 so that the objective function coefficient vector (eu et) points straight up and the line perpendicular to it and passing through the origin forms the horizon. We have two choices in moving away from the origin: we can move up the x r axis or we can move up the x2-axis. From the point of view of the artificial horizon generated by the objective function, the x^axis is the steeper ascent direction, and we choose it. We now have to determine which of the variables x3 or x4 to set equal to zero, or, equivalently, which of third or fourth columns of (A|J) to delete from the basis. Examination of Table 3 suggests that deleting the third column would move the solution to point 6; deleting the fourth column would move it to point 5. Notice that the choice of which column to delete comes down to the choice of how far to move along the x^axis. Staying in the feasible set dictates that we stop at the first intersection; we accordingly delete the third column and arrive at point 6. Time to begin again. We are at the basic feasible solution corresponding to point 6 with columns one and four in the basis, and there are two feasible directions in which movement is possible. We may travel back down thexj-axis toward the origin by choosing to bring the third column back into the basis, or we may move along the edge 4-6 by choosing to bring the second column into the basis. By consulting the artificial horizon of the objective function, we determine that the route back down the x^axis goes down (reduces the value of the objective function), while the route along edge 4-6 gains altitude. Choosing the latter direction, we bring the second column of (A|/) into the basis. Deciding which column to delete again comes down to the decision of how far to move in the given direction; deleting the fourth column leads to point 4, while deleting the first column lead to point 3. Feasibility again requires that we stop at the first intersection, and the fourth column is deleted. The basic feasible solution now involves columns one and two of (A|/) and corresponds to point 4 in Figure 6. There are now two feasible directions in which to move: along edge 2-4 or along edge 4-6. The former would involve bringing column three into the basis, and the latter would involve bringing column four into the basis. Consulting the artificial horizon, we determine that both routes lead down; the value of the objective function cannot be improved by movement in any feasible direction. We conclude that an optimal solution to the linear programming problem has been reached. The simplex algorithm is thus a method for climbing up the edges of the feasible set along directions of steepest ascent until an optimum

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161

has been found. Its chief virtue is that its iterative procedure can be broken down into simple rules suitable for computer programming. Armed with these instructions, computers can solve large and incredibly complicated linear programming problems. 19

Duality Corresponding to the original linear programming problem max

ex

X s.t. Ax < r χ > 0,

there is a closely related "dual problem" min

wr

w

s.t.

wA ΐ e

w > 0. Much recent work has been devoted to exploring the relationship between these two related problems. The results have been surprising and important: it turns out, for example, that if x* is the optimal solution to the original problem and tu* is the optimal solution for the dual problem, then ex* = w*r, the optimal values for the objective functions of the two problems are identical. Moreover, if the ith slack variable for the original problem is positive in the optimal solution (the ith constraint is not binding), then Wj* is zero in the optimal solution to the dual problem. Alternatively, if w * is positive, then the ith constraint in the original or primal problem must be binding (must hold as an equality). These considerations lead to the interpretation of Wj* as the "shadow price" associated with the ith constraint, i.e., wt* indicates how much the optimal value of the objective function in the primal problem would increase if r, were increased by one unit. Recalling the Leontief model with several primary factors, if we pose the linear programming problem

19 R. Read, A Mathematical Background for Economists and Social Scientists (Englewood Cliffs, N.J.: Prentice-Hall, 1972). Ch. 16 contains a more algebraic discussion of the simplex method.

162

DANIEL Α. G R A H A M

max

pc

c

s.t.

a]~1c

-

< s

c > 0 then the optimal w*s from the dual problem min

ws

w

s.t.

wb[I

-

α] - 1

> ρ

w > 0

become the equilibrium prices of primary resources associated with product prices p. If the e n d o w m e n t of the ith primary resource increased by one unit, national product (pc*) would increase by wf*. T h e reader will recognize the constraints from the dual problem as the equilibrium condition that no industries make profits [expressed orig20 inally in equation Duke University (5)].

20 The interested reader might wish to examine the discussion in M. Intrilligator, Mathematical Optimization and Economic Theory (Englewood Cliffs, N.J.: PrenticeHall, 1971), ch. 5.

9 The Sraffian Revolution ALESSANDRO RONCACLIA Piero Sraffa's main work, Production of Commodities by Means of Commodities, was published in 1960. Since then there has been a growing interest in Sraffa's analysis of prices. In some countries, such as Italy and Japan, Sraffa's analysis of prices of production is considered (especially by Marxist economists) to be at least as important as Keynes' theory of employment. In other countries, such as the United States, the esteem in which Sraffa is held by some theoreticians is not matched by a widespread interest in the analysis of his work. 1 Such a disparate appreciation of Sraffa's analysis may be accounted for by the deep disagreements over its interpretation. 2 Some maintain that Sraffa has done nothing but expound a linear model of price determination. 3 A linear model would have been considered a fundamental contribution in the 1920s, when Sraffa's model was conceived, but it was largely surpassed at the date of its actual publication. 4 To •Paul Samuelson, for example, speaks of "this age of Leontief and Sraffa" [Paul A. Samuelson, "Understanding the Marxian Notion of Exploitation: A Summary of the So-Called Transformation Problem between Marxian Values and Competitive Prices," Journal of Economic Literature 9 (1971): 400], Note also the title of A. L. Levine's article, "This Age of L e o n t i e f . . . and Who? An Interpretation," Journal of Economic Literature 12 (1974): 872-881. 2 For the most recent contributions to this debate, see E. Burmeister, "A Comment on 'This Age of L e o n t i e f . . . and Who?' "Journal of Economic Literature 12 (1975): 454457; and A. L. Levine, '"This Age of Leontief. . . and Who?' A Reply," Journal of Economic Literature 13 (1975): 457-461. 3 See, e.g., R. E. Quandt, "Review of Production of Commodities by Means of Commodities ," Journal of Political Economy 69 (1961): 500; and M. W. Reder, "Review of Production of Commodities by Means of Commodities," American Economic Review 51 (1961): 688-695. 4 See Piero Sraffa, Production of Commodities by Means of Commodities (Cambridge: Cambridge University Press, 1960), p. vi. 163

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others, Sraffa's contribution is fundamental, even now, in offering a solution to weighty analytical problems and in implying basic conceptual changes in value theory.5 Among advocates of this latter view, some stress the criticisms to the role of an independent measure of capital in the marginalist theory of distribution, criticisms which are implicit in Sraffa's work; others emphasize Sraffa's positive contribution to the theory of prices.® In order to form a reasoned opinion of the various interpretations, it is not necessary to translate Sraffa's work into the language of matrix algebra, for a direct knowledge of Sraffa's writings is sufficient to this task.7 Indeed, it is much more important to understand the conceptual framework in which Sraffa's work is to be placed. The irreconcilable differences between his conceptual framework and the prevalent theory of value explain the many misunderstandings about Sraffa's theory.

T h e Sraffa theory The main analytical results presented in Production of Commodities by Means of Commodities can be briefly summarized. Sraffa starts his analysis by demonstrating that in a system of subsistence production "which produces just enough to maintain itself," and where "commodities are produced by separated industries . . . there is a unique set of exchange-values which if adopted by the market restores the original distribution of the products and makes it possible for the process to be repeated; such values spring directly from the methods of production."8 In an economy that produces as outputs just the quantities and types of commodities that are required as inputs for their production, relative prices are determined by conditions of production alone. 5 S e e , e.g., Maurice H e r b e r t D o b b , " T h e Sraffa System and Critique of the Neoclassical T h e o r y of Distribution," De Economist 143 (1970): 347-362, and Theories of Value and Distribution since Adam Smith ( C a m b r i d g e : C a m b r i d g e University Press, 1973), pp. 248-266; R. L . M e e k , " M r . Sraffa's Rehabilitation o f Classical E c o n o m i c s , " Scottish Journal of Political Economy 8 (1961): 119-136; E. J. N e l l , " T h e o r i e s of Growth and T h e o r i e s o f V a l u e , " E c o n o m i c Development and Cultural Change 16 (1967): 15-26; and Joan Robinson, " P r e l u d e to a Critique o f E c o n o m i c T h e o r y , " Oxford Economic Papers 13 (1961): 53-58. e S e e , e.g., M e e k , " M r . Sraffa's Rehabilitation." ' F o r matrix algebra interpretation, see P. N e w m a n , " P r o d u c t i o n of Commodities by Means of C o m m o d i t i e s , " Schweizerische Zeitschrift fur Volkswirtschaft und Statistik 98 (1962): 58-75; and L . Pasinetti, Lezioni di teoria della produzione ( M i l a n : II Mulino, 1975). 'Sraffa, Production of Commodities, p. 3.

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If the economy produces a surplus (an excess of commodities produced over commodities used up in the production process and as workers' subsistence), then "the distribution of the surplus must be determined through the same mechanism and at the same time as are the prices of production." 9 If the wage rate is allowed to be higher than the subsistence level, relative prices and one of the distributive variables (wage rate or rate of profits) may be simultaneously determined, given the technology and the other distributive variable.10 That is, in an economy producing a surplus of outputs over inputs, the relative prices are determined by conditions of production and by the manner in which the surplus is distributed between wages and profits. In a system in which a surplus is produced, and in which the wage rate is not limited to the subsistence level, the surplus is distributed between wages and profits; and (apart from particular cases of joint production) the higher the wage rate, the lower the rate of profits. We have thus an inverse relationship between the two distributive variables—the so-called wage-profit curve, describing all possible combinations of a non-negative wage rate and a non-negative rate of profits—from the one corresponding to a maximum rate of profits and a zero wage rate, to the one corresponding to a maximum wage rate and a zero rate of profits. Sraffa then analyzes "the key to the movement of relative prices consequent upon a change in the wage." As the classical economists and Marx already knew, this "lies in the inequality of the proportions in which labour and means of production are employed in the various industries.... If the proportions were the same in all industries no price-changes could ensue," but "it is impossible for prices to remain unchanged when there is inequality of'proportions.' " 1 1 In this framework, Sraffa restores the classical distinction between necessary (or basic) commodities and luxury (or nonbasic) commodities. The first are commodities directly or indirectly necessary for production of output in all industries; the nonbasics are used as means of production only for themselves or other nonbasics, or they are not used at all. If the method of production of some basic commodity changes, its variation has a general repercussion on the set of relative prices and on the wage-profit relationship. If the change relates to nonbasics, its influence is limited to the exchange ratios between the nonbasic commodities involved and all other commodities. Exchange «Ibid, p. 8. 10 Ibid., pp. 9-11. " I b i d . , pp. 12-13. 1 2 Ibid„ pp. 7-8.

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ratios between basic commodities, and the wage-profit relationship, are not modified. 12

The Standard Commodity For a better understanding of the relationship between prices and distribution, Sraffa works out a special device, the "standard commodity." It is a composite commodity produced by a system in which "the various commodities are represented among its aggregate means of production in the same proportions as they are among its product." 13 This is the "standard system," a purely mental construction derived from the real system through appropriate changes in the levels of output in the various industries. 14 The concept has remarkable similarities to von Neumann's system of proportional growth, but in Sraffa's scheme it is a simple auxiliary device, deduced from the properties of the standard commodity. 15 Sraffa uses it to tackle an ancient problem that much worried classical economists, especially David Ricardo: how does one determine the ratio of aggregate profits to aggregate capital when there are changes in the distribution of income? To overcome this problem, classical economists tried to express the rate of profits as a ratio of purely physical quantities. 16 Now, by measuring the wage rate in terms of standard commodity, profits in the standard system are automatically measured in the same way, while means of production in the standard system consist (by definition) of a certain quantity of the same composite commodity. Therefore the rate of profits appears, within the standard system, as a ratio between two different quantities of the same composite (standard) commodity. 17 Thus, with the "standard commodity," Sraffa shows the conditions required for determining the rate of profits 13 Ibid.,

p. 19. See ch. 4 on the "standard commodity." "Ibid., ch. 5. 15 See J. von Neumann, "A Model of General Economic Equilibrium," Review of Economic Studies 13 (1945): 1-9. '"See Piero Sraffa, "Introduction," in David Ricardo, Works and Correspondence, 10 vols. (Cambridge: Cambridge University Press, 1951), 1: xxxi-xxxiii. " T h e standard commodity is also said to be an "invariable measure of value," in the limited sense that its price in terms of its means of production does not change when distribution changes. This property of the standard commodity is obviously related to the one put forward in the text. Their link has a parallel in the link which, as Sraffa shows, runs between the Ricardian analysis of the rate of profits and a particular aspect of the Ricardian problem of seeking an invariant measure of value. (See Sraffa, "Introduction," pp. xlvi-xlix). Thus the standard commodity is relevant for understanding both these aspects of the Ricardian theory of value and distribution.

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as a ratio of physical quantities. We may consider this as a "physical analogue" to Sraffa's general solution which, as seen above, requires the simultaneous determination of the rate of profits and the set of relative prices.

The Choice of Techniques As for the quite separate problem concerning the choice of techniques of production, Sraffa shows that one technique may yield maximum profitability at two different rates of profits, even if at intermediate rates another technique may be more profitable. 18 This phenomenon, called "reswitching of techniques," makes it impossible to construct a measure of capital which satisfies the condition that when the rate of profits (the "price of capital") rises, the techniques chosen present a decreasing "capital intensity" (a decreasing "quantity of capital" per worker). 19 The analysis of prices of production is completed by the examination of the case of joint products and, within this category, of fixed capital goods; and of scarce, nonreproducible means of production such as land. 2 0 But these cases do not require substantial modifications to the simplified scheme expounded in Part I of Sraffa's book. 2 1

The Various Interpretations With these basic results in mind an assessment of the various interpretations of Sraffa's work can be made. T h e necessity, or non-necessity, of the constant returns assumption is the main battlefield for Sraffa's interpreters. Sraffa himself stresses, in three places on the very first page of his book, that his analysis presupposes "no changes in output a n d . . . no changes in the proportions in which different means of production are used by an industry . . . so that no question arises as to

18

Sraffa, Production of Commodities, ch. 12. The "reswitching of techniques" is at the base of the recent debate on capital theory. For the history of this debate, see Geoffrey Colin Harcourt, Some Cambridge Controversies in the Theory of Capital (Cambridge: Cambridge University Press, 1972). See also "Symposium on Paradoxes in Capital Theory," Quarterly Journal of Economics 80 (1966): 503-583. 20 Sraffa, Production of Commodities, chs. 7-11. 21 See also B. Schefold, Mr. Sraffa on Joint Production Theorie der Kuppelproduktion (Basel, 1971). 19

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the variation or constancy of returns. 2 2 Some commentators, overlooking Sraffa's explicit statements, deem it necessary to assume "constant returns to scale," especially for the construction of the standard system. 2 3 However, as has been stressed, those passages in the book which seem to contradict the author's statements imply "purely mental manipulations leaving technical conditions unchanged," without any actual changes in output levels. 24 That Sraffa has spent much time working on this problem can be seen by looking at the development of his work. The transition from the articles of his youth to the work of his maturity is marked by Sraffa's rejection of the idea that some assumption about "retums-toscale" is necessary for the analysis of prices. In 1925, Sraffa criticized the Marshallian theory of the firm, questioning the theoretical "laws" of increasing and decreasing returns, as used by Marshall for his theory of value in a regime of perfect competition. As Sraffa reminds us, in classical political economy the law of diminishing returns was associated mainly with the problem of rent (theory of distribution), while the law of increasing returns was associated with the division of labor, i.e., with general economic progress (theory of production). Marshall and other neoclassical economists, attempted to merge these laws in a single law of nonproportional returns, utilizing it in the field of price theory to establish a functional connection between costs and quantity produced. Thus a law of supply in individual markets was made available, and it could be coordinated with the corresponding law of demand. Sraffa admits that changes in the level of output in an industry may cause variations in its average unit costs, but these variations will be of the same order of magnitude as the variations in costs in any other industries, for they stem from the same cause—the existence of some scarce factor of production for decreasing returns, and economies of production on a large scale for increasing returns. 2 5 Therefore, "these 22 Sraffa, Production of Commodities, p. v. Immediately before this passage, Sraffa says that the reader may adopt the assumption of constant returns "as a temporary working hypothesis," but he states that "no such assumption is made." And in the same page he adds: "The investigation is concerned exclusively with such properties of an economic system as do not depend on changes in the scale of production or in the proportions of 'factoring.'" " S e e Quandt, "Review," and D. A. Collard, "The Production of Commodities," Economic Journal 73 (1963): 144-146. M A Bose, "Production of Commodities: A Further Note," Economic Journal 74 (1964): 728. "Variations in cost in an individual industry can be considered in isolation only in those unrealistic cases in which the scarce factor is only utilized in that industry, and in which economies of production are peculiar to the industry under consideration but external to individual firms. Economies internal to individual firms are contradictory with the assumption of perfect competition.

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causes of variation of cost, highly important from the point of view of general economic equilibrium, must of necessity be considered to be negligible in the study of the particular equilibrium of an industry. From this point of view, which constitutes only a preliminary approximation of reality, we must then concede that, in general, commodities are produced under conditions of constant costs." 26 The suggestion of constant returns is very cautious. Sraffa does not deny the existence of a link between cost and quantity produced. This link cannot be rigorously analyzed, however, when examining partial equilibria. Constant returns are therefore only a first approximation; and however useful this first approximation might be, price theory cannot be limited to it. Having acknowledged, as early as 1925, the limits of the attempt to attribute general importance to the case of constant returns, Sraffa was faced, it would appear, with only two possible alternatives: (1) either to take into account the interrelations among industries by considering them all together in a full general equilibrium system; or (2) to drop the assumption of perfect competition, stressing the real and omnipresent limitations to it. In his 1926 article Sraffa makes a probe in the latter direction.27 But as early as 1930, in another paper published in the Economic Journal, Sraffa drops both the hint to the constant returns assumption and the suggestion to abandon the assumption of perfect competition. He concentrates on direct criticisms ("negative and destructive," Keynes wrote) of the Marshallian analysis of partial equilibria. No mending is possible, the theory is either incoherent or unreal, and in either case it must be discarded.28 It would seem, therefore, that only the third direction, i.e., the analysis of general economic equilibrium, remains open. In point of fact, many economists interpret Production of Commodities by Means of Commodities as an attempt in this direction, fully consistent with the conceptual framework of marginalist theory. If Sraffa's analysis is interpreted in terms of equilibrium between supply and demand, the assumption of constant returns is necessary to separate the determination of prices from the determination of levels of output. This (and not the hypothetical changes in levels of output necessary to construct the standard system) is the underlying reason why so many interpreters impose the assumption of constant returns. Sraffa himself, in present2e Piero Sraffa, "Sulle relazioni fra costo e quantita prodotta," Annali di Economia 2 (1925): 328. Unfortunately, there is no English version of this article. The ideas developed in it are briefly summarized in the opening pages of Piero Sraffa, "The Laws of Returns under Competitive Conditions," Economic Journal 36 (1926): 535-550. "Ibid. M Piero Sraffa, "A Criticism" and "Rejoinder" in "Symposium on Increasing Returns and the Representative Firm," Economic Journal 40 (1930): 89-93.

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ing the results of his long struggle to escape the traditional schemes of economic analysis, recognizes this: "Anyone accustomed to think in terms of the equilibrium of demand and supply may be inclined, on reading these pages, to suppose that the argument rests on a tacit assumption of constant returns in all industries." 2 9 It is hardly necessary to reiterate that this is not Sraffa's assumption.

Abandoning Demand and Supply Sraffa did not, in fact, follow this third direction of general equilibrium analysis; he opened a new path by completely dropping the abstract concepts of supply and demand curves. The contraposition of cost and demand is a hybrid of objective and subjective elements, which are irreconcilable. As Wicksteed recognized, the subjective elements, once introduced through demand functions, necessarily tend to dominate the theoretical scheme, superseding the objective e l e m e n t represented by the supply function. Supply curves disappear and costs re-emerge as opportunity costs (the utility that might be obtained in uses alternative to the one considered). 3 0 T h e rejection of the subjectivist approach leads Sraffa to the opposite pole—"objective" approach of classical economists, ranging from Sir William Petty to Ricardo and Marx. From this viewpoint, demand plays no direct analytical role in price determination; price theory is f o u n d e d on "physical production costs," i.e., on the quantities of the various means of production (labor included) required to obtain a given quantity of product. 3 1 T h e abandonment of the concept of prices as determined by supply and demand curves calls for the abandonment of the marginalist concepts of general or partial equilibrium, as well as the marginalist attempt to determine equilibrium prices and quantities simultaneously. Here, too, Sraffa initiates a return to classical political economy. In Sraffa's analysis, as in that of classical economists, the condition of equilibrium for prices of production (classical economists' "natural prices") simply consists of the equality of the rate of profits in the ^Sraffa, Production of Commodities, p. v. ^Philip Henry Wicksteed, The Common Sense of Political Economy and Selected Papers, ed. Lionel Robbins (London: G. Routledge, 1934). Wicksteed is considered by Sraffa (Production of Commodities, p. v.), probably on this account, "the purist of marginal theory." The importance of Wicksteed's views was stressed in Sraffa, "Sulle relazioni," pp. 294-295. 31 The criticism of the utilization of demand as an analytical tool appeared early, in Sraffa, "Sulle relazioni," pp. 294-295.

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different sectors; it no longer requires the stricter condition of equality between supply and demand in all sectors. 32 Moreover, the assumption of a uniform rate of profits for all sectors recalls the classical (and Marxian) concept of competition founded on freedom of entry of new firms into any sector. Under such conditions, no sector can perpetually reap a profit rate higher than the average one, as the potential higher returns would attract new firms toward that sector; as a consequence, productive capacity and output would increase, thus causing greater difficulties of realization for all firms, and eventually causing a decrease in the price of the product. This concept of competition is rather different from the marginalist idea of competition, in which individual firms are unable to influence the price of their products. T h e marginalist idea also requires small (almost infinitesimal) size of firms as compared to the size of the industry, and a high (infinite) number of firms. Assumptions such as these are unnecessary for the classical concept of competition, which simply requires the assumption of no technological discontinuities depending on the size of plants, and no legal (or generally, institutional) obstacles to movements of capital from one sector to another, obstacles which might create "barriers to entry" to new producers. 3 3 The two concepts of competition can thus be distinguished by their analytical implications. The classical idea corresponds to the simple assumption of a uniform rate of profits in all sectors. T h e marginalist idea (which can be used in partial analysis, i.e., for an industry considered in isolation) corresponds to the assumption of prices considered as data by each firm. As we have seen above, this marginalist contention is precisely the assumption which Sraffa criticized in his 1925 article. Finally, Sraffa rejects the marginalist attempt to determine equilibrium prices and quantities simultaneously. This stems from the possibility of eliminating demand from a direct analytical role in price determination. In this respect, Sraffa's analysis suggests a return to Marx. In Das Kapital the problem of demand is subdivided into two 32

Obviously, the tendency to a uniform rate of profits comes true if we take into account, sector by sector, the greater or smaller difficulties of "realization" (in the Marxian sense of realization by sale on a market). See Alessandro Roncaglia, Sraffa e la teoria dei prezzi (Rome: Laterza, 1975), pp. 32-36. 33 The theory of competition implicit in Sraffa's scheme appears to have the same conceptual basis as the theory of oligopoly developed by Joe S. Bain and Paolo Sylos Labini [Bain, Barriers to New Competition (Cambridge: Harvard University Press, 1956); and P. S. Labini, Oligopoly and Technical Progress (Cambridge: Harvard University Press, 1962)]. While the analytical results independently reached by the two authors are analogous, the link between these results, and the classical conception, is stressed by Sylos Labini alone.

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parts: the problem of the levels of output and the "realization" problem. Neither problem is tackled by Sraffa. From a logical viewpoint, levels of output (which are data in Sraffa's analysis) are uphill of the price problem, while realization is down-dale, for it concerns the relationship between quantities produced and quantities sold, between prices of production and market (real) prices. Considering levels of output as data of the problem, and distinguishing prices of production from market prices, Sraffa succeeds in isolating the problem of prices of production without jeopardizing the analysis of the two remaining factors, namely, levels of output and levels of realization.34

Some Classical Revival As seen above, Sraffa's position is in many respects similar to that of the classical economists. Their conceptual framework can thus be used in general for the Sraffian analysis. In simple terms, this use implies the following: prices are determined, at any given moment, according to the prevailing technology. This datum is valid only for the moment under consideration, for technology undergoes continuous change (widening of markets, increasing division of labor). Analytically, the situation of a certain economic system is considered as it might appear from a "photograph" taken at a given moment. All economic magnitudes which are not the object of the analysis may be considered as data, and the theoretician can concentrate his attention on the virtual (hypothetical) movements of magnitudes, and on their mutual relationship which appear as "isolated in vacuo." In the case of Production of Commodities by Means of Commodities, Sraffa has chosen the relationship between production prices and distributive variables (rate of profits and wage rate) as the objects of the analysis. All other variables (technology, levels of output, firm structure of all industries, etc.) are taken as data of the problem. It must be stressed, however, that this choice does not imply an a priori refusal of the possibility of analyzing the problems of technological development, levels of output, strategy of the firms, etc. This choice simply stems from the necessity of analyzing the different problems one by one, and each in isolation. The necessary assumptions and methods of analysis are not necessarily identical for all problems; for each of them only what is relevant should be included, 34 As a consequence of this, Sraffa's theory is compatible with the rejection of "Say's law." It is also compatible with the Keynesian theory of employment based on the principle of "effective demand."

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leaving aside those e l e m e n t s which, as Ricardo said, simply " m o d i f y " the analysis but do not change it substantially. 3 5

The Marginalist Critique Having briefly e x a m i n e d the conceptual framework of Sraffa's work, it is now easier to examine Sraffa's explicit, or implicit, criticisms of marginalist theory. First of all, there is the criticism to the neoclassical concept of capital as a m a g n i t u d e m e a s u r a b l e i n d e p e n d e n t l y of distribution. This criticism, based on the " r e s w i t c h i n g of t e c h n i q u e s , " (see above, par. 1), was dealt with in t h e 1960s, in t h e lively d e b a t e on capital theory. H e r e it is only necessary to recall that Sraffa's criticism refers not only to t h e " a g g r e g a t e production f u n c t i o n " (as CobbDouglas), b u t also to any attempt (including Walras' in the framework of a multi-sector model) to d e t e r m i n e a uniform rate of profits. It is, in fact, a criticism of the attempt to solve the problem of long-run distribution b e t w e e n wages and profits as part of price theory, on the basis of such data as technology, availability of resources, a n d consumers' tastes. 3 6 Here, too, the rejection of marginalist theory corresponds to a return to the attitude of classical economists (like Mill) to w h o m the problem of distribution is analytically distinct from the p r o b l e m of prices. From this perspective, it b e c o m e s possible to explain distribution without ignoring those political and social e l e m e n t s which could b e s y n t h e t i z e d in a f o r m u l a of " p o w e r r e l a t i o n s h i p s b e t w e e n capitalists and workers." A particular feature of this criticism of the marginalist concept of capital is the proof, given by Sraffa in the c h a p t e r on " r e d u c t i o n to 35 See David Ricardo, Works and Correspondence, ed. Piero Sraffa, 10 vols. (Cambridge: Cambridge University Press), 4: 318, 7: 337. Sraffa's methodological position, implicit in Production of Commodities, is completely different from the marginalist one, as exemplified by Lionel Robbins or Paul Samuelson [Robbins, An Essay on the Nature and Significance of Economic Science (London: Macmillan & Co., 1932); and Samuelson, Foundations of Economic Analysis (Cambridge: Harvard University Press, 1947)]. The marginalists tend to build a general theory. That is, they identify economics with one general problem (optimal allocation of scarce resources between alternative uses) and all specific problems (from international trade to the theory of the firm) are considered as particular aspects of the general problem. They attempt to find a method for solving the general problem. The method will then also give the solution for any particular problem. On this, see Roncaglia, Sraffa e la teoria dei prezzi, ch. 6. 3e Sraffa's criticisms are developed with reference to the various forms of marginalist theory in P. Garegnani, II capitale nelle teorie della distribuzione (Milan: Ciuffre, 1960). Garegnani shows that the aggregate concept of capital is necessary for all marginalist theories wishing to explain long-run equilibria, i.e., wishing to determine a uniform rate of profits.

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dated quantities of labor," of "the impossibility of aggregating the [production] 'periods' belonging to the several quantities of labor into a single magnitude which could be regarded as representing the quantity of capital." 37 This criticism refers to the "average period of production" d e v e l o p e d by the Austrian school, and particularly by Böhm-Bawerk, to measure the capital intensity of production techniques independently of distribution, and hence suitable for the foundation of a marginalist theory of capital.38 Finally, and more generally, a criticism of the marginalist theory of value and distribution is implicit in Sraffa's rejection of the very structure of that theory. Having distinguished the problem of the determination of prices from the problems of distribution and of the levels of output, Sraffa is able to study prices of production with a theoretical scheme independent of the main analytical tools of the marginalist theory, such as "marginal product," or "marginal cost," and "marginal utility." This is an "external" criticism to marginalist theory, consisting in the proposal of an alternative theory, logically coherent and placed in a completely different analytical and conceptual framework.

The Alternative Theoretical System W e have seen that deep disagreements exist over the interpretation of Sraffa's work. These disagreements do not concern the analytical results (summarized earlier) as such, but rather the conceptual framework in which Sraffa's analysis is to be placed—as observed in the discussion over the non-necessity of the constant returns assumption. Once this point is established it is easier to recognize the main characteristics of Sraffa's analysis: the rejection of the subjectivist viewpoint of marginalist economic theory in favor of classical economists and Marx's " o b j e c t i v e " viewpoint; the rejection of the marginalist conceptions of price, equilibrium, perfect competition, in favor of their classical and Marxian counterparts. Thus, beyond sketching a conceptual Production of Commodities, p. 38. Eugen von Böhm-Bawerk, Kapital und Kapitalzins, 1884, and Knut Wicksell, Über Wert, Kapital und Rente, 1893. Sraffa's criticism was misunderstood by Sir Roy Harrod, who tried to defend the "average period of production" by recalling that it can be computed, for any given rate of profits [Harrod, "Review of Production of Commodities by Means of Commodities," Economic Journal 71 (1961):783-787]. As Sraffra showed in his reply, Harrod did not realize that, even if computed, the average period of production could no longer be used to explain income distribution, because it remains crucially dependent on the profit rate [Piero Sraffa, "Production of Commodities, A Comment," Economic Journal 72 (1962): 477-479]. It thus remains useless as a measure of a "quantity of capital," independent of distribution. 37Sraffa,

3e See

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and methodological framework of reference for SrafFa's analysis, w e have seen SrafFa's direct criticisms of some fundamental aspects of the marginalist theory of value and distribution. W e may then c o n c l u d e that SrafFa's analytical apparatus within a classical and Marxian conceptual framework makes it possible to abandon the marginalist viewpoint without being left with any alternative system.

Bibliography T h e interpretation of Sraffa's thought presented here is drawn from my recent book Sraffa e la teoria dei prezzi, which also contains an extensive bibliography of Sraffa's writings and of the writings on Production of Commodities by Means of Commodities. In addition to the bibliography given here (particularly Sraffa's 1 9 2 5 and 1951 works and Dobb's and Garegnani's books), the works of the classical economists (particularly Ricardo's Principles) and of Marx (particularly Capital and Theories of Surplus Value) are useful for an understanding of Sraffa's analysis of prices. Bain, J. Staten. Barriers to New Competition. Cambridge: Harvard University Press, 1956. Böhm-Bawerk, Eugen von. Kapital und Kapitalzins. Innsbruck, 1884. Bose, A. "Production of Commodities: A Further Note." Economic Journal 74 (1964): 728. Burmeister, Ε. "A Comment on 'This Age of Leontief. . . and Who?' "Journal of Economic Literature 12 (1975): 454-457. Collard, D. A. " T h e Production of Commodities." Economic Journal 73 (1963): 144-146. Dobb, Maurice. " T h e Sraffa System and Critique of the Neoclassical Theory of Distribution." De Economist 143 (1970): 347-362. Reprinted in A Critique of Economic Theory. Edited by Ε. K. Hunt and J. G. Schwartz. Harmondsworth, Middlesex: Penguin, 1972. . Theories of Value and Distribution Since Adam Smith. Cambridge: Cambridge University Press, 1973. Garegnani, P. II capitale nelle teorie della distribuzione. Milan: Giuffre, 1960. (The English reader may use Garegnani's Ph. D. thesis, 1959, available at Cambridge University Library.) Harcourt, Geoffrey Colin. Some Cambridge Controversies in the Theory of Capital. Cambridge: Cambridge University Press, 1972. Harrod, Sir Roy. "Review of Production of Commodities by Means of Commodities." Economic Journal 71 (1961): 783-787. Keynes, John Maynard. "Editor's Note." Economic Journal 40 (1930): 79.

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Levine, A. L. " 'This Age of L e o n t i e f . . . and Who?' An Interpretation." Journal of Economic Literature 12 (1974): 872-881. . " 'This Age of L e o n t i e f . . . and Who?' A Reply. "Journal of Economic Literature 13 (1975): 457-11. Meek, R. L. "Mr. Sraffa's Rehabilitation of Classical Economics." Scottish Journal of Political Economy 8 (1961): 119-136. Reprinted in Meek, R. L. Economics and Ideology and Other Essays. London: Chapman and Hall, 1967. Nell, E. J. "Theories of Growth and Theories of Value." Economic Development and Cultural Change 16 (1967): 15-26. Reprinted in Capital and Growth. E d i t e d by G e o f f r e y Colin H a r c o u r t and N. L a i n g . Harmondsworth, Middlesex: Penguin, 1971. Neumann, J. von. "A Model of General Economic Equilibrium." Review of Economic Studies 13 (1945): 1-9. N e w m a n , P. " P r o d u c t i o n of Commodities by Means of Commodities.'' Schweizerische Zeitschrift für Volkswirtschaft und Statistik 98 (1962): 58-75. Pasinetti, L. "A Mathematical Formulation of the Ricardian System." Review of Economic Studies 27 (1960): 78-98. Reprinted in L. Pasinetti. Growth and Income Distribution. Cambridge: Cambridge University Press, 1974. . Lezioni di teoria della produzione. Milan: II Mulino, 1975. English edition; New York: Columbia University Press, forthcoming. Quandt, R. E. "Review of Production of Commodities by Means of Commodities," Journal of Political Economy 69 (1961): p. 500. Reder, M. W. "Review of Production of Commodities by Means of Commodities." American Economic Review 51 (1961): 688-695. Ricardo, David. Works and Correspondence. Edited by Piero Sraffa. 10 vols. Cambridge: Cambridge University Press, 1951-1955. Robbins, Lionel Charles. An Essay on the Nature and Significance of Economic Science. London: Macmillan & Co., 1932. Robinson, Joan. "Prelude to a Critique of Economic Theory." Oxford Economic Papers 13 (1961): 53-58. Reprinted, with addendum, in Robinson, Joan. Collected Economic Papers, vol. 3. Oxford: Blackwell, 1965. Also r e p r i n t e d in A Critique of Economic Theory, e d i t e d by H u n t and Schwartz. Roncaglia, Alessandro. Sraffa e la teoria dei prezzi. Rome: Laterza, 1975. English edition; New York: Wiley, forthcoming. Samuelson, Paul A. Foundations of Economic Analysis. Cambridge: Harvard University Press, 1947. . "Understanding the Marxian Notion of Exploitation: A Summary' of the So-Called Transformation Problem between Marxian Values and Competitive Prices ."Journal of Economic Literature 9 (1971): 399-431. Schefold, B. Mr. Sraffa on Joint Production (Theorie der Kuppelproduktion). Basel, 1971. Sraffa, Piero. "Sülle relazione fra costo e quantitä prodotta." Annali di Economia 2 (1925): 277-328.

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. " T h e Laws of Returns Under Competitive Conditions." Economic Journal 36 (1926): 535-550. Reprinted in Readings in Economic Analysis, vol. 2. Edited by R. V. Clemenee. Cambridge, Mass.: Addison-Wesley Press, 1950. Also reprinted in Readings in Price Theory. Edited by G. J. Stigler and Κ. E. Boulding. London: Allen and Unwin, 1953. . "A Criticism" and "Rejoinder" in "Symposium on Increasing Returns and the Representative Firm." Economic Journal 40 (1930): 89-93. . "Introduction." In Ricardo, David. Works and Correspondence, vol. 1. Cambridge: Cambridge University Press, 1951. . Production of Commodities by Means of Commodities. Cambridge: Cambridge University Press, 1960. . "Production of Commodities: A Comment." Economic Journal 72 (1962): 477-479. "Symposium on Paradoxes in Capital Theory." Articles by Pasinetti; Levhari and Samuelson; Morishima; Bruno; Burmeister and Sheshinski; Garegnani; Samuelson. Quarterly Journal of Economics 80 (1966): 503-583. Sylos Labini, Paolo. Oligopoly and Technical Progress. 1st ed., 1956. Cambridge: Harvard University Press, 1962. Wickseil, Knut. Über Wert, Kapital und Rente. Jena, 1893. Wicksteed, Philip Henry. The Common Sense of Political Economy and Selected Papers. Edited by Lionel Robbins. London: G. Routledge, 1934. University

of Perugia,

Italy

IV Microeconomics

Introduction The theory of the firm and industry, and their market relations, has been the orthodox vital center of economics, with value and distribution theory comprising the analytic field. E d g e d aside by Keynesian macroeconomics, the old theory was reborn u n d e r the fresh baptismal name of microeconomics. For many of the early postwar years it was treated as s o m e t h i n g of an u n w a n t e d o r p h a n c o m p a r e d to macroeconomic pronouncements which promised economists an opportunity to participate in the play of public policy on major issues of concern: full employment precepts and prescriptive advice for growth enabled economic practitioners to carry their attache cases into the highest realms of public service, and with unadorned success—at least until the late 1960s in the affluent Western economies. Lately, a reversal in emphasis can be detected. Several reasons may be adduced: (1) the disenchantment with Keynesian attempts to stop the i n f l a t i o n - u n e m p l o y m e n t d u e l ; (2) t h e b i t t e r m e d i c i n e that monetarists have been eager to dispense to unwilling, and skeptical, public audiences; and (3) the signals of environmental and ecological disorders, in water pollution, air impurities, and environmental damage. Not least has been the energy shortfall in an economy that has been devouring its oil resources. Coupled with the Arab boycott, turmoil in the Middle East, and the futility of macroeconomic attempts to resolve the "stagflation" plight, microtheory has gained n e w favor. T h e price mechanism is again being scrutinized for its part in a rational solution to sectoral problems. There is apparent some throwback to Pigou's ideas (earlier delineated by Marshall and still earlier by Sidgwick 1 ) of distinguishing b e t w e e n private costs experienced by the firm and the corresponding social costs b o m e by society in mitigating messy by-products in costs such as outlays for purifying the waters, or preventing food contaminants or carcinogenic substances. The literature, if not yet wholly codified, contains some of the most useful work performed by economists today. On autos, congestion, pollution, 'Cf. Henry Sidgwick, The Principles Co., 1883), Book III, ch. 2.

of Political 181

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and resource depletion, in health care, in land use, in broad and narrow ecology and environmental concerns, there is a prophetic sense of involvement with matters that affect mankind—as Marshall might have expected and approved. Professor Williamson has been one of the most prolific and respected contributors to the modem theory of the firm, especially of its hierarchical dimensions. While his chapter focuses strongly on organizational structure, the implications for markets are transparent, involving the validity of the theory of competition, oligopoly, and even countervailing power. As a unit warranting study, it was in the 1930s that the firm was literally "discovered" (as against Marshall's nondescript "representative" firm, neither average nor typical in the usual sense). Thereafter, the theory rushed off into Joan Robinson's imperfect competition variety or into the differentiated Chamberlin product of monopolistic competition; a keen market struggle for ideas prevailed. To both, and aptly expressed by Mrs. Robinson, the theory of "monopoly" would "swallow" competition. Whether the morsel can be fully digestible is still controversial, unrelieved by ideological fevers. Professor Douglas Vickers was early to detect a soft spot in the conventional theory of the firm. Economists have envisaged the firm as the organizing vehicle for productive factors engaged to produce physical outputs in our industrial system. Omitted, more often than merely neglected, was the most basic ingredient of all in a capitalist economy, namely, money—or finance—to hire labor and pay wages, to purchase raw materials, and to finance the layout of plant and equipment in which industrial chemistry transformed the inputs collected into market end-products. On the necessary theory of financial flows, Professor Vickers has developed ideas which constitute an indispensable microfoundation consistent with the post-Keynesian theory of money. Professor Vickers draws on Marshall—as did Keynes—in his skepticism of bolting the volatile financial market developments down on the stationary Walrasian general equilibrium mat. This, too, resembles Keynes' own release. What I find most interesting, considering the enormous theoretical attention to tatonnements inducing "ultimate" equilibrium, is Professor Vickers' perception that in financial "layering," with " d i s e q u i l i b r i u m " agreements, the commonplace tatonnement trials are potentially disorderly, carrying scant conviction of final equilibration. This contrasts with opinions that in product markets the equilibrium is unlikely to be deflected. The Vickers essay reveals a broad compatibility with the persistent emphasis of Professor Shackle on the quintessential uncertainty in-

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volved in determining the evolution of economic life and activity. The theme also fits comfortably with the monetary ideas outlined from a macrotheory angle in the essays by Professors Davidson and Minsky below. "Real Market" theorists who ignore financial market "layering of claims" court the peril of omitting the most fundamental decision processes troubling the entrepreneurial hierarchy. Consumer d e m a n d theory has engaged the highest mathematical talents of the profession since early days, certainly after Hicks and Allen and the momentum generated by the original work of Paul Samuelson. To nonspecialists the modern theory has become a subtle, intricate, and confusing maze; contributions have come thick and fast, marked by higher rigor and succinctness. Professor Ivor Pearce, an important innovator in this field, combines clarity, technical skill, and judgment in sifting "big from small." Even those with a minimal of mathematical skills should be able to absorb the fundamental drift of the theory. To lift some bafflement for budding specialists is his reminder of the many roads to Rome, of the "many different ways of proving known results," and a n u m b e r of "elegant tricks" in extracting important theorems.

ΊΟ Firms and Markets OLIVER E. WILLIAMSON

The period between 1950 and 1975 has been an exciting one for the study of firms and markets. Neoclassical theory has been both refined and extended. A number of new approaches to the study of firm and market organization have b e e n advanced. Probably the most significant development is that the firm is no longer considered mainly as a building-block necessary to motivate the study of markets; it has come to b e regarded as a distinctly interesting economic entity in itself. If, realistically, many firms are large hierarchical structures of considerable internal complexity, maintaining fictions of atomistic organization may be unhelpful. To the extent that the attributes of the firm in hierarchical respects (including organization form as well as internal control and incentive instruments) are believed to have nontrivial economic consequences, the internal organization of the firm becomes an interesting object of investigation. The discussion of firms and markets is developed in three parts. T h e first describes alternative (not necessarily mutually exclusive) approaches to the study of firm and market organization. The second is concerned with specific applications. Additional remarks on markets appear in the third section. Given space limitations, a number of topics are necessarily omitted. The more important of these are indicated in the bibliographic notes at the end of the chapter. 185

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Alternative Approaches Neoclassical

theory

T h e theory that dominates most intermediate microtheory texts and constitutes the core to which recent variants are contrasted is the neoclassical theory of the firm. The firm is characterized here by a production function to which a profit maximization objective has been assigned. Internal efficiency assumptions of two kinds are featured. First, it is assumed that the firm operates on its production function, whence the maximum output of the product is realized from each feasible combination of factor inputs (mainly labor and capital). Failure to operate on the production frontier would imply wasteful use of inputs; this is assumed away. Second, given factor prices, it is assumed that the firm chooses the least-cost factor combination for each possible level of output. The total cost curve, from which average and marginal cost curves are derived, is constructed in this way. Whether the competitive or monopolistic model of the firm is more appropriate depends on whether economies of scale are large in relation to the market. But whichever model is employed, the prevailing behavioral assumption is one of profit maximization. T h e nature of the firm with respect to what it will make and what it will buy is normally taken as given; matters of internal organization (hierarchical structure, internal control processes) are likewise ignored. Conformably, competition in the capital market issues rarely surface, much less are probed in depth. That many interesting problems of firms and markets are suppressed or bypassed by reducing the firm to a technological entity wholly lacking in goal variety should come as no surprise. T h e past twenty-five years have witnessed the extension of the basic static model in a n u m b e r of directions, only two of which will be mentioned here. One of these concerns the economic implications of imperfect information. George Stigler's work on the economics of information and applications thereof is the entering wedge. 1 Search behavior, which is anomalous in a world of perfect competition, appears on this account. Another variant, which has important implications for the study of labor markets, is job market signaling, of which Michael Spence's work is illustrative. 2 Given that individuals differ with respect to their productivity attributes, and that this can b e discerned 'George J. Stigler, "The Economics of Information, "Journal of Political Economy 69 (June 1961): 213-25. 2 A. Michael Spence, Market Signalling (Cambridge; Harvard University Press, 1974).

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only imperfectly ex ante, how do signals and wage schedules interact to achieve a job market equilibrium, and what are its economic properties? A second important line of investigation has been to study the behavior of the firm under uncertainty. It is often necessary for this purpose to characterize the firm's attitude toward risk. Risk aversion is usually assumed, though risk-neutral and risk-preference conditions have also been examined. Agnar Sandmo studies the behavior of the competitive firm under price uncertainty, while Hayne E. Leland extends the analysis to deal with imperfect competition. 3 Uncertain demand implies, among other things, that the firm's selection of price and output is not invariant to changes in fixed costs.

Natural

selection

Powerful support for the profit maximization hypothesis is afforded by the economic natural selection arguments of Armen Alchian and Milton Friedman. 4 What businessmen purport or appear to do is unimportant if economic natural selection processes are reasonably effective. Non-profit-maximizing behavior will not be viable if there is requisite variety among firms in their choice of decision rules. Those firms which, by c h a n c e or otherwise, choose rules of a profitenhancing kind will acquire resources and grow relatively. Deviants will be forced to imitate or face extinction. 5 Sidney G. Winter has expressly taken issue with natural selection arguments on the grounds that the assumptions needed for selection on profit to go through are very severe. 6 Interactions between decision variables within the firm (and with rivals), as well as the nature of the stochastic disturbances to which an industry is subject, all influence the efficacy of the selection process. This is consistent with Herbert Simon's contention that much more attention to the process and mechanisms of adaptation is needed. 7 Although Winter's subsequent 3Agnar Sandmo, "On the Theory of the Competitive Firm under Price Uncertainty," American Economic Review 61 (March 1971): 65-73; Leland, "Theory of the Firm Facing Uncertain Demand," American Economic Review 62 (June 1972): 278-91. 4Armen Alchian, "Uncertainty, Evolution and Economic Theory," Journal of Political Economy 58 (June 1950): 211-21; Friedman, Essays in Positive Economics (Chicago: University of Chicago Press, 1953). s The simple analytics of the argument have been set out by Gary S. Becker, "Investment in Human Capital: A Theoretical Analysis," Journal of Political Economy, Supplement, 70 (October 1962): 9-44. eSidney G. Winter, "Economic Natural Selection and the Theory of the Firm," Yale Economic Essays 4 (Spring 1964): 225-72. 'Herbert Simon, "Theories of Decision-Making in Economics and Behavioral Sciences," American Economic Review 49 (June 1959): 253-83.

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work, which introduces Schumpeterian innovation issues, is somewhat more sanguine regarding the selection process, serious doubts nevertheless remain that selection will reliably operate in the manner postulated by Alchian and Friedman. 8

Managerial

models

Managerial models of the firm trace their origins to Berle and Means' 1930s argument regarding the separation of ownership from control. 9 To this is a d d e d the assumption that managers do not behave in a purely instrumental stewardship fashion but, like other economic agents, they act in ways which promote their own interests. Maximizing assumptions, however, are maintained. The questions then are: what is maximized, subject to what constraints, and with what testable implications? Both William J. Baumol and Robin Marris have addressed these issues. Baumöl s original treatment of the problem postulated that managers operate firms in a sales-maximizing fashion subject to a minimum profit constraint; he subsequently reformulated the argument in a dynamic context by expressing the objective of the firm in growth-maximizing terms. 1 0 Marris likewise c h a r a c t e r i z e s the firm's o b j e c t i v e as one of growth maximization subject to a rate of return constraint. 1 1 Although behavior qualitatively different from that of profit maximization is claimed, Robert M. Solow's subsequent work on this concludes that growthoriented and profit-oriented firms would respond in qualitatively similar ways to parameter changes in factor prices or in variations of excise or profit tax. 12 An alternative way to characterize the firm's objective is to postulate a managerial utility function of a more general kind. Oliver E. Williamson's managerial discretion models assume that managers make trade-offs b e t w e e n "slack" and profitability. 1 3 In the static version, slack can take the form of either excessive administrative staff or man8 S e e , e.g., S i d n e y G. Winter, "Satisficing, S e l e c t i o n and the Innovating Remnant," Quarterly Journal of Economics 85 (May 1971): 2 3 7 - 6 1 . 8 A. A. Berle and G. C. M e a n s , The Modern Corporation and Private Property (New York: C o m m e r c e C l e a r i n g H o u s e , 1932). '"William J. B a u m o l , " T h e T h e o r y of E x p a n s i o n of the Firm," American Economic Review 52 ( D e c e m b e r 1962): 1 0 7 8 - 8 7 ; a n d Business Behavior, Value and Growth (N'ew York: Macmillan, 1970). " R o b i n L. Marris, Economic Theory of Managerial Capitalism (London: Macmillan, & Co. 1964). l2 Robert M. S o l o w , " S o m e Implications of Alternative Criteria for the Firm," in R. Marris and A. Wood, eds., The Corporate Economy ( L o n d o n : Macmillan & Co., 1971). 13 OHver E. W i l l i a m s o n , The Economics of Discretionary Behavior ( E n g l e w o o d Cliffs, N.J.: Prentice-Hall, 1964); a n d Corporate Control and Business Behavior (Englewood Cliffs, N.J.: Prentice-Hall, 1970).

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agerial e m o l u m e n t s (corporate personal consumption). In the dynamic-stochastic version, slack takes the form of internal inefficiency, which is akin to what Harvey Leibenstein refers to as X-inefficiency. 14 Behavior that is qualitatively different from that of profits and sales (or growth) maximization is obtained from these discretionary models, though aspects of this have been disputed as well. 15

Behavioral models Behavioral models of the firm trace their origins to the work of Richard M. Cyert and James G. March. 16 These models drop any pretext that the firm is operated in a maximizing way. The internal decision process is studied instead. The firm is assumed to seek a satisfactory level of performance (referred to as satisficing) because managers lack the wits to maximize. An aspiration-level mechanism is introduced for purposes of setting target levels of performance. Attention is focused on the operating parts of the enterprise (production, sales, finance, etc.) and the subgoals associated therewith. Overall performance is the outcome of an internal bargaining process and the external environment. Search is a central element of the theory and can take any of three forms: local, exploratory, and strategic. Local search takes place in response to failure to satisfy suhgoal targets. A "fire department" model of the firm obtains in which putting out fires preoccupies the attention of the management of the functional units. Exploratory search takes place in a serendipitous way as the firm interacts with the environment and new opportunities "avail themselves." Strategic search is an effort by the firm to position itself favorably with respect to strategic opportunities. This last, however, is not a well-developed aspect of behavioral theory and borders on maximization. Behavioral theory, as developed by Cyert and March, relies extensively on computer simulation. The implications of interdependent decision rules (rules of thumb) are permitted to "unfold" as the firm operates in a feedback relation with the environment. Baumol and Richard E . Quandt likewise rely on simulation to explore the properties of decision rules and adaptations thereof. 17 They argue that l 4 Harvey Leibenstein, "Allocative Efficiency vs. X-Efficiency," American Economic Review 56 (June 1966): 3 9 2 - 4 1 5 . " S e e , e.g., R. Rees, "A Reconsideration of the Expense Preference Theory of the Firm," Economica 41 (August 1974): 2 9 5 - 3 0 7 . 1βΑ Behavioral Theory of the Firm (Englewood Cliffs, N.J.: Prentice-Hall, 1963). "William J. Baumol and Richard E. Quandt, "Rules of Thumb and Optimally Imperfect Decisions," American Economic Review 54 (March 1964): 2 3 - 4 6 .

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although bounded rationality limits the feasibility of neoclassical optimization (which entails continuously equating marginals), a high order of rationality can nevertheless be associated with relatively crude decision rule adaptation mechanisms. Recent work in the behavioral tradition has been of a more analytical kind. Several studies are noteworthy. Winter and Roy Radner both examine the implications of simple decision rules for the cost behavior of the enterprise and set out the conditions under which rules such as "allocate all of your effort to the imput which promises the largest expected cost reduction" have viability properties. 18 Richard Nelson and Winter have examined evolutionary models in which search and selection processes are prominently featured and certain primitive investment rules obtain 19 Although qualitative results consistent with neoclassical theory are derived (e.g., an increase in the wage rate induces an upward shift in the capital-labor ratio) the fact that Nelson and Winter expressly set out the process is noteworthy. The neoclassical model, by contrast, simply posits maximization and competitive equilibrium. Analytical results derived from much more plausible behavioral assumptions naturally reinforce one's confidence that confirmation by the data is not accidental.

Property

rights

T h e economics of property rights literature is concerned with the way in which alternative assignments of property rights (including ambiguous assignments or nonassignments of such rights) give rise to differential economic behavior. Alchian was among the earliest to identify the property rights approach as a distinctive one and he has contributed importantly to its systematic development—both in general and with respect to the theory of the firm, including the theory of the regulated enterprise. 20 18 Sidney G. Winter, "Cost Reduction and Input Proportions," Discussion Paper, Institute of Public Policy Studies, University of Michigan, Ann Arbor, August 1974; Roy Radner, "A Behavioral Model of Cost Reduction," Bell Journal of Economics 6 (Spring 1975): 196-215. '•Richard Nelson and Sidney G. Winter, "Toward an Evolutionary Theory of Economic Capabilities," American Economic Review 63 (May 1973): 440-86; and "Factor Price Changes and Factor Substitution in an Evolutionary Model," Bell Journal of Economics 6 (Autumn 1975): 466-86. 20 Armen A. Alchian, "The Basis of Some Recent Advances in the Theory of Management of the Firm, "Journal of Industrial Economics 14 (February 1965): 30-41; Alchian, "Corporate Management and Property Rights," in H. G. Manne, ed., Economic Policy and Regulation of Corporate Securities (Washington, D.C.: American Enterprise Institute for Public Policy Research, 1969): Alchian and Reuben Kessel, "Competition, Monopoly and the Pursuit of Pecuniary Gain," Aspects of Labor Economics (Princeton, N.J.: Princeton University Press, 1962).

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The issues have been developed by Ronald H. Coase and Harold Demsetz in connection with externalities and the efficient adaptation thereto. Applications to nonprofit organizations, government bureaus, and socialist firms illustrate the range of issues to which this approach can fruitfully be brought to bear. 21

Transaction Costs Even more than in the property rights approach, the transaction-cost approach focuses on microanalytic detail of a kind that is usually ignored in more conventional theories of the firm. Following John R. Commons, the relevant unit of analysis is the transaction, and the interesting economic problem is to organize transactions in such a way as to promote efficiency. 22 The transaction-cost approach draws extensively on the market failure literature together with aspects of organization theory. 23 The importance of bounded rationality and the proclivity of human agents to behave opportunistically, which involves self-interest seeking with guile, are both prominently featured.24 Alternative modes of contracting are accordingly assessed with respect to their properties for economizing on bounded rationality and attenuating opportunism.25 Both market and internal modes of contracting are examined. Market modes include complex contracts involving contingent claims, incomplete long-term contracts, and recurrent spot contracts. Internal modes include peer group organization, simple hierarchies, and complex hierarchies of various kinds. A comparative institutional orientation is maintained, and the efficacy of contracting is evaluated by examining the frictions associated with alternative modes rather than by reference to an abstract (frictionless) ideal. Also, organization form 21 Ronald H. Coase, "The Problem of Social Cost," Journal of Law and Economics 3 (October 1960): 1^44; Harold Demsetz, "Toward a Theory of Property Rights," American Economic Review 57 (May 1967): 347-59; Mark V. Pauly and Michael A. Redisch, "The Not-for-Profit Hospital as a Physician's Cooperative," American Economic Review 63 (March 1973): 87-99; Ronald N. McKean, "Property Rights within Government, and Devices to Increase Governmental Efficiency," Southern Economic Journal 39 (October 1972): 177-86; Erik G. Furubotn and Svetozar Pejovich, "Property Rights and the Behavior of the Firm in a Socialist State: The Example of Yugoslavia," Zeitschrift für Nationalökonomie 30 (1970): 431-54. " S e e John R. Commons, Institutional Economics (New York: Macmillan, 1934). ^See, e.g., Kenneth J. Arrow, "The Organization of Economic Activity," in The Analysis and Evaluation of Public Expenditure: The PPB System, Joint Economic Committee, 91st Congress, 1st Session (Washington, D.C.: Government Printing Office, 1969), pp. 59-73. "Herbert A. Simon, Models of Man (New York: John Wiley & Sons, 1957); Irving Goffman, Strategic Interaction (Philadelphia: University of Pennsylvania Press, 1969). "Oliver E. Williamson, Markets and Hierarchies: Analysis and Antitrust Implications (New York: The Free Press, 1975).

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matters. Transferring a transaction out of the market into the firm is not sufficient; the manner in which the internal transaction is organized hierarchically and subjected to internal control processes is also germane. The range of applications of the transaction-cost approach is indicated in the following discussion.

Applications The Employment

Relation

Studies of the employment relation of two main types can be distinguished. One of these picks up from the economics of information literature and applies it to labor markets. Stigler formulates the problem as one of search: workers search for wage offers and employers search for wage demands until the expected marginal returns and costs are equlized. 26 Spence's work on job signaling is a variant of this tradition, as is that of Joseph E. Stiglitz, although the latter is closely related to the contractual approaches discussed below as well. 27 A classic contribution to the study of the employment relation is Simon's comparison of the properties of sales and employment contracts. 28 Sales contracts entail an agreement to perform a specific task, while employment contracts involve use of an authority relationship in which the parties, within limits, leave the details to be specified as events unfold. Adaptability is thus the key element in the employment contract. For tasks which involve execution under uncertainty and for which complex contingent claims contracts are prohibitively costly to write, the employment contract has obvious advantages over the sales contract, ceteris paribus. Alchian and Demsetz argue, however, that it is a delusion to characterize the relation between the employer and employee by reference to authority. 28 Their view of the employment contract is that it is explained by technological nonseparabilities. Given the impossibility or the prohibitive cost of evaluating the marginal product of workers 2 ®George J. Stigler, "Information in the Labor Market, "Journal of Political Economy 70 (February 1962): 94-105. 27 Spence, Market Signalling; Joseph E. Stiglitz, "Incentives, Risk, and Information: Notes Towards a Theory of Hierarchy," Bell Journal of Economics 6 (Autumn 1975): 552-79. ^Herbert A. Simon, "A Formal Theory of the Employment Relation," Econometrica 19 (July 1951): 180-96. M Araien Alchian and Harold Demsetz, "Production, Information Costs, and Economic Organization," American Economic Review 62 (December 1972): 777-95.

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engaged in team tasks, a boss is created whose function it is to monitor the performance of workers. Furthermore, the boss has claims against residual product that exceeds prescribed amounts. What the authors refer to as "the classical capitalist firm" results. Williamson, Wächter, and Harris take the position that the classical capitalist firm (defined in this way) is relatively uninteresting, because technological nonseparabilities can at best explain small group organization. 30 They emphasize that the employment relation should be assessed less in technological than in transaction-cost terms when the tasks in question involve recurrent contracting and the jobs of interest are those for which learning by doing is important. T h e efficiency issue is to organize such jobs in a way that promotes cooperative adaptation to changing market and technological conditions. T h e "internal labor market" literature can be interpreted in this way. 31 Individualistic market contracting for such jobs gives rise to recurrent bargaining, which is itself costly and impedes effective adaptation. Internal labor markets represent a systems solution in which wage rates attach mainly to jobs, rather than to workers. An internal due process apparatus to settle disputes is put in place. Collective bargaining and internal organization are thus joined in a way that, by intent, attenuates subgoal pursuit, thereby to promote transactional economies.

Vertical

Integration

McKenzie addresses the problem of vertical integration in the context of ideal output. 3 2 T h e issue here is what are the efficiency effects of supplying an intermediate good or service on monopolistic terms when the item in question is subsequently combined in variable proportions with competitively supplied factors. T h e incentive of the downstream firm to use inefficient factor proportions, where this is expressed in real-cost terms, is avoided if the monopoly supply and intermediate use stages are joined. T h e argument has since b e e n made by others, and Frederick Warren-Boulton has extended it to 30

Oliver E. Williamson, Michael L. Wächter, and Jeffrey E. Harris, "Understanding the Employment Relation: The Analysis of idiosyncratic Exchange," Bell Journal of Economics 6 (Spring 1975): 250-78. 31 Peter Doeringer and Michael Piore, Internal Labor Markets and Manpower Analysis (Lexington, Mass.: D.C. Heath, 1971). 32 Lionel McKenzie, "Ideal Output and The Interdependence of Firms," Economic Journal 61 (December 1951): 785-803.

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include an assessment of the effects of integration on final product markets. 33 Stigler's treatment of vertical integration is concerned with reported life cycle tendencies for integration to appear at an early stage in an industry's development, become less prevalent later, and reappear when an industry passes into decline. 3 4 T h e analysis employs conventional cost curve apparatus and relies on Adam Smith's theorem that the division of labor is limited by the extent of the market. However, the underlying rationale for the behavior reported by Stigler appears to be transactional. 35 The argument is closely akin to that set out in connection with the employment relation. In cases influenced by small numbers supply conditions and learning by doing, autonomous market contracting poses bargaining hazards. Without these, specialization by one or a few firms to the mutual benefit of all would presumably be characteristic of supply conditions at both early and late stages in an industry's life cycle. Put differently, technology is no bar to contracting; rather, transactional considerations are decisive. It is not sufficient, however, merely to transfer a transaction out of the market and locate it in the firm instead. The internal management of transactions also matters. The issues are illustrated by John Buttrick's interesting examination of the "inside contracting system" which developed among New England manufacturing plants after the Civil War and was supplanted by more comprehensive forms of internal control. 36 Whereas the "inside contracting system" provided for consolidated ownership of plant and equipment, department heads retained considerable autonomy. They not only hired their own workers and supervised the work force, but they also negotiated annual piece rate compensation with the company. A number of problems developed, most of which reduce to conflicts between the owner and the inside contractors over adapting efficiently to unanticipated market changes. These conflicts were transactional in nature, attributable to the incompleteness of contracting, due to bounded rationality, and to the proclivity of inside contractors to exploit their idiosyncratic 3 3 John M. Vernon and P. A. Graham, "Profitability of Monopolization by Vertical Integration," Journal of Political Economy 79 (July-August 1971): 924-25; Richard L. Schmalensee, "A Note on the Theory of Vertical Integration," Journal of Political Economy 81 (March-April 1973): 4 4 2 - 4 9 ; Frederick Warren-Boulton, "Vertical Control with Variable Proportions,"Journa/o/Po/ifica/Economy 82 (July-August 1974): 783-802. ^ G e o r g e J. Stigler, " T h e Division of Labor is Limited by the Extent of the Market," Journal of Political Economy 59 (June 1951): 185-93. 3 5 S e e Williamson, Markets and Hierarchies. 3 e John Buttrick, " T h e Inside Contracting System," Journal of Economic History 12 (Summer 1952): 205-21.

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information and skill advantages opportunistically. Transforming the relationship from quasi-autonomy to one in which department heads b e c a m e employees (who no longer had claims over individual profit streams) was necessary to overcome these adaptational disabilities.

Oligopoly William Fellner's sensitive treatment of the oligopoly problem is classic. He contends that it is impossible to deduce determinate prices and outputs for oligopoly markets on the basis of demand and supply functions derived from technological data and utility functions. 3 7 Rather, fewness carries with it a range of indeterminacy. Although received price theory is useful for establishing the region o f indeterminacy, notions of "conjectural i n t e r d e p e n d e n c e " are n e e d e d to ascertain how choice is made within these limits. A variant of the recognized interdependence approach is entrybarrier analysis, which has evoked considerable theoretical and policy interest. This approach is traceable to Joe S. Bain and Paolo SylosLabini and has b e e n elegantly summarized by Franco Modigliani. 3 8 Firms already in an industry are assumed to maximize profits subject to the condition that the price charged does not induce new entrants to appear. T h e theory leads to a number of testable implications in which the excess of price over minimum costs is expressed as a function of scale economies, size of market, and demand elasticity. Almarin Phillips and Williamson have turned to the organization theory and social psychology literatures on small group behavior to secure insights into the oligopoly problem. 3 9 Communication and the factors which bear on the effectiveness thereof play a prominent role. An interesting implication of the dynamic interfirm approach is that the degree of successful collusion will vary directly with the condition of the environment, so that conspiracies are expected to unravel under conditions of slack demand and excess capacity. Stigler takes as given that oligopolists wish, through collusion, to maximize joint profits, and he attemps to establish the factors bearing "William Fellner, Competition Among the Few (New York: Knopf, 1949). M J o e S. Bain, Barriers to New Competition (Cambridge: Harvard University Press, 1956); Paolo Sylos-Labini, Oligopoly and Technical Progress, trans. Elizabeth Henderson (Cambridge: Harvard University Press, 1962); Franco Modigliani, "New Developments on the Oligopoly Front," Journal of Political Economy 66 (June 1958): 2 1 5 32. 39 Almarin Phillips, Market Structure, Organization, and Performance (Cambridge: Harvard University Press, 1962); Oliver E. Williamson, "A Dynamic Theory of Interfirm Behavior," Quarterly Journal of Economics 79 (November 1975): 579-607.

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on the efficacy of such aspirations. 4 0 While h e admits that colluding firms m u s t s o m e h o w reach a g r e e m e n t u p o n t h e price structure, Stigler's analysis is focused entirely on the problem of policing such a collusive agreement. A price structure of some complexity, one which makes "appropriate" provision for heterogeneity among products and buyers, as well as for the hazard of activating potential entrants, is simply imputed to oligopolists. Because an audit of transaction prices reported by sellers is unlawful (and in any event may b e unreliable), transaction prices paid by buyers are n e e d e d to detect secret price-cutting. Stigler contends that statistical inference techniques are the usual ways in which such price-cutting is discovered. In particular, the basic method of detecting a price-cutter is that h e is getting business that he would not otherwise obtain. Among the implications of this statistical inference approach to oligopoly are: (1) collusion is more effective in markets in which buyers correctly report prices tendered (as in government bidding); (2) collusion is limited if the identity of buyers is continuously changing (as in the construction industries); and (3) elsewhere, the efficacy of collusion varies inversely with the n u m b e r of sellers, the number of buyers, and the proportion of new buyers, but directly with the degree of inequality of firm size among sellers. A more general approach to the study of oligopoly is to treat it as a contracting problem. 4 1 An agreement between two or more parties will be attractive in the degree to which: (1) the good, service, or behavior in question is amenable to specification in writing; (2) joint gains from collective action are potentially available; (3) implementation in the face of uncertainty does not occasion costly haggling; (4) m o n i t o r i n g t h e a g r e e m e n t is not costly; a n d (5) d e t e c t e d noncompliance carries commensurate penalties at low enforcement exp e n s e . A s s e s s i n g t h e t r a n s a c t i o n a l p r o p e r t i e s of o l i g o p o l i s t i c agreements in this way discloses that, except in rather special circumstances, oligopolistic collusion is difficult to effectuate. The prospect of writing, executing, and enforcing complex interfirm agreements of a joint profit-maximizing kind is impaired by considerations of b o u n d e d rationality (the necessary complex contract with appropriate provisions for adaptations to uncertainty is infeasible or prohibitively costly to write). It is also hindered because agreements are not self-enforcing. Individual parties will defect w h e n it suits their purposes, and they can b e disciplined only by resort to market 40 George J. Stigler, "A Theory of Oligopoly,"Journal of Political Economy 72 (February 1964): 44-61. 41 See, e.g., Richard A. Posner, "Natural Monopoly and Its Regulation," Stanford Law Review 21 (February 1969): 548-643; and Williamson, Markets and Hierarchies.

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retaliation—which f u r t h e r impairs collusion. T h e u p s h o t is that oligopolistic industries ought not uncritically to b e regarded as dominant firm or monopoly equivalents. T h e monopolist has neither the need to engage in complex contracting nor the need to use market processes to bring deviant members of a conspiracy into line. These are differences of no little moment. Cyert and DeGroot have employed Bayesian models of the decision process to reformulate the duopoly problem. 4 2 Rather than impute simultaneous myopic optimizing rules to each duopolist, as is characteristic of Cournot models and elaborations thereof, Cyert and DeGroot a s s u m e that p a r t i c i p a n t s m a k e d e c i s i o n s in a l t e r n a t i n g periods and follow the same decision rule for two periods, and that each participant makes the decision which maximizes his total longrun profit if the other participant behaves similarly. Bayesian learning is then introduced to reach a cooperative solution.

Conglomerates The structural phenomenon referred to as the conglomerate form of organization has constituted a public policy anomaly for all of twenty years. The failure on the part of received microtheory to regard the internal organization of the firm as interesting explains the puzzlement. The issues can be put in perspective by recognizing that the conglomerate is merely a diversified variant of the multidivisional structure initially devised in the 1920s as a means by which to secure control over—and supply affirmative incentives within—the large corporation. Rather than organize the enterprise along functional lines (production, marketing, finance, etc.) and experience the subgoal pursuit which predictably obtained in large firms, the corporation was split instead into semi-autonomous operating divisions in which division managers were held responsible for divisional performance. T h e progressive transformation of the large corporation from a functionally organized to a multidivisional structure is set out in Chandler's classic book. 4 3 Lawrence Franko describes the spread of this organizing mode to Europe in the 1960s. 44 "Richard M. Cyert and Μ. H. DeGroot, "Bayesian Analysis and Duopoly Theory," Journal of Political Economy 78 (September 1970): 1168-84; and "An Analysis of Cooperation and Learning in a Duopoly Context," American Economic Review 63 (March 1973): 24-37. •'Alfred D. Chandler, Jr., Strategy and Structure (New York: Doubleday, Anchor Books, 1966). "Lawrence G. Franko, "The Growth, Organizational Efficiency of European Multinational Firms: Some Emerging Hypotheses," Colloques International Aux C.N.R.S. 549 (1972): 335-66.

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Successful divisionalization requires that strategic and operating decisions be separated. Strategic resource allocation decisions among the divisions are assigned to the general office; operating decisions are assigned to the divisions. The general office in this way takes on functions ordinarily associated with capital markets. Indeed, the conglomerate variant of the multidivisional structure is usefully regarded as a miniature capital market. Although its investment opportunities are limited, its knowledge with respect to each is very deep. 45

Regulation The last ten years have witnessed a strong renewal of interest in the study of regulation. This resurgence is partly attributable to work by Harvey Averch and Leland Johnson, who demonstrated that the resource allocation effects of rate of return constraints could easily be investigated using the neoclassical model. 46 Such constraints induce the firm to use a more capital-intensive technology than is consistent with least-cost supply. A number of extensions of the model have been made, notably by Alvin Klevorick and Elizabeth Bailey. 47 As Paul Joskow points out, however, the Averch-Johnson model and variants do not get at the essence of the regulatory process.48 Attention to institutional detail of a kind that is difficult to capture with neoclassical apparatus is missing. The policy relevance of A-J models is accordingly uncertain. Stigler sets out what purports to be a supply and demand theory of regulation in which industries are held to be demanding regulation to promote their interests, and in which government is the supplier.49 Although this approach has generated considerable interest, it is instructive that the implied supply and demand diagrams have yet to appear. Possibly this is because the axes have never been expressly 45 A refined development of this strategic resource allocation concept of the corporation is provided by William F. Hamilton and Michael A. Moses, "An Optimization Model for Corporate Financial Planning," Operations Research 21 (May-June 1973): 677-92. The economic implications have been examined by Joseph L. Bower, "Planning within the Firm," American Economics Review 60 (March 1970): 186-94, and, with special emphasis on antitrust policy, by Williamson, Markets and Hierarchies. 4e Harvey Averch and Leland L. Johnson, "Behavior of the Firm Under Regulatory Constraint," American Economic Review 52 (December 1962): 1052-69. 47 Alvin K. Klevorick, "The Behavior of a Firm Subject to Stochastic Regulatory Review," Bell Journal of Economics 4 (Spring 1973): 57-88; Elizabeth Bailey, Economic Theory of Regulatory Constraint (Lexington, Mass.: D.C. Heath, 1973). •"Paul L. Joskow, "Inflation and Environmental Concern: Structural Change in the Process of Public Utility Price Regulation,"Journal of Law and Economics 17 (October 1974): 291-328. 4e George J. Stigler, "The Theory of Economic Regulation, Bell Journal of Economics and Management Science 2 (Spring 1971): 3-21.

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defined and the shift parameters associated with supply and demand curves have never been identified. Joskow notes that the conceptual models in this area leave much to be desired. A contractual approach to the problem of regulation has b e e n suggested by Demsetz, who contends that net beneficial consequences can often be realized by supplanting regulation with franchise bidding. 5 0 What is needed is to push the contracting process "back to the beginning." Conventional analysis is flawed by a failure to distinguish between the number of ex ante bidders and the condition of ex post supply. Even though scale economies may dictate that there be a single ex post supplier, large numbers competition may nevertheless be feasible at the initial bidding stage. Where large n u m b e r s of qualified parties enter noncollusive bids to become suppliers of the decreasing cost activity, the resulting price need not reflect monopoly power. Repeating the bidding process at regular intervals permits successive adaptations to be made and maintains the benefits of competition. Posner endorses the franchise bidding approach to regulation and specifically suggests that it be used in conjunction with cable television services. 51 A microanalytic examination of the contracting problems associated with franchise bidding, both in general and with respect to CATV, reveals, however, that this organizational mode is beset with much more severe problems than its supporters have acknowledged. 5 2 For one thing, the efficacy of scalar valued bidding for many public utility services is of doubtful merit or feasibility. Additionally, difficult issues of defining and monitoring service quality need to be addressed, and adaptational arrangements during the execution period of the contract need to be considered. Finally, learning-by-doing advantages accrue to incumbents and difficult physical asset valuation problems are posed if incumbents are to be displaced at contract rebidding intervals. Confidence in bidding competition, once the initial award is made, is therefore impaired. These objections are not merely objections in principle. Franchise bidding, in practice, is typically encumbered with an administrative apparatus of considerable complexity, the purpose of which is to mitigate these difficulties. The purported dichotomy between "regulatory controls" on the one hand and "natural economic forces" on the other is accordingly strained. Among the more recent approaches to the study of regulation, the 50

Harold Demsetz, "Why Regulate Utilities?," Journal of Law and Economics 11 (April 1968): 55-56. "Richard A. Posner, Economic Analysis of Law (Boston: Little-Brown, 1972). 52 See Oliver E. Williamson, "Franchise Bidding for Natural Monopolies—in General and with respect to CATV," Bell Journal of Economics 7 (Spring 1976): 69-88.

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behavioral approach and a neoclassical reformulation of the regulatory problem in duopoly terms show considerable promise for the future. 53 Joskow's behavioral study focuses on organizational structure, regulatory instruments, and operating procedures, with special attention to the way in which these are adapted to encompass significant changes of economic and political kinds. Spence's neoclassical approach recognizes that utility service has both price and quality aspects. Reaction curves are set out in which the regulatory agency optimizes with respect to price and the firm adapts with respect to quality. Both Cournot solutions and leadership positions are characterized. Rate of return regulation is shown to offer prospective gains over price regulation under plausible assumptions.

Markets Although the above sections are more expressly concerned with firms than with markets, to conclude that markets have been neglected would be to miss one of the more significant developments in the firm and market literature since 1950. Firms and markets not only can be but have been treated as alternative modes of organizing transactions. Furthermore, they bear symbiotic relations to each other. The basic argument, to recapitulate, is this: in circumstances where markets arguably incur nontrivial frictions in completing complex transactions, a shift of these transactions out of the market into the firm warrants consideration. Internal labor markets thus arise as a way of mitigating the transaction costs that afflict autonomous market contracting for idiosyncratic jobs; vertical integration serves to internalize failures of intermediate product markets; conglomerate organization assumes functions normally associated with capital markets. The upshot is that firms and markets are and should be examined in active juxtaposition to one another. This is to be contrasted to the usual tradition, which treats firms and markets as "natural" analytical entities, the boundaries for which, as if by fiat, were preassigned and could be taken as given. 5 4 T h e progressive refinement of the market failure literature reveals this artifice to be unhelpful; comparative inω Ρ . L. Joskow, "Inflation and Environmental Concern"; A. M. Spence, "Monopoly, Quality and Regulation," Bell Journal of Economics 6 (Autumn 1975): 417-29. 54 A notable exception to the traditional approach is Ronald H. Coase. See "The Nature of the Firm," Economica, N.S. 4 (1937): 386-405, reprinted in G. J. Stigler and Κ. E. Boulding, eds., Readings in Price Theory (Homewood, 111,: Richard D. Irwin, Inc., 1952).

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stitutional approaches to the study of firms and markets have b e e n elaborated more recently. 5 5 Although the concurrent (comparative institutional) study of firms and markets is prominently featured in the very recent firm and market literature, significant d e v e l o p m e n t s of strictly market-related kinds warrant acknowledgment as well. Arrow's pioneering work on contingent claims markets and the extensive ramifications thereof for the study of risk bearing is especially notable. 5 6 Subsequent theoretical contributions include those by Gerard D e b r e u and Roy Radner. 5 7 James Meade usefully avails himself of this literature in his insightful treatment of indicative planning. 5 8 A perhaps u n i n t e n d e d but yet important byproduct of this work is that it has permitted a more systematic assessment of the limits of markets to be made. Without an explicit statement of the strong assumptions n e e d e d for a complete set of futures markets to exist and perform their ideal allocative functions, critiques of the fiction that markets are ubiquitous were, perforce, conjectural. Significant developments in the study of competitive equilibrium and Pareto optimality using the mathematical theory of linear spaces also warrant acknowledgment. 5 9 Work of this kind has gone off in a rarified general equilibrium direction, and some of its import has been seriously questioned. 6 0

Concluding Remarks Although the foregoing survey of developments in the study of firms and markets during the past twenty-five years is necessarily selective, it reveals that this has b e e n an area of intense interest and more than a little progress. Neoclassical theory has demonstrated its robust qualities, but other approaches have m a d e obvious progress in helping to "See Arrow, "The Organization of Economic Activity." 5e For a statement of the theory, which was first reported in 1952, together with a number of applications, see K. J. Arrow, Theory of Risk-Bearing (Chicago: Markham, 1971). "Gerard Debreu, Theory of Value (New York: Wiley, 1959); Roy Radner, "Competitive Equilibrium under Uncertainty," Econometrica (January 1968): 31-58; and Radner, "Problems in the Theory of Markets under Uncertainty," American Economic Review 60 (May 1970): 454-60. 5e James E. Meade, The Controlled Economy (Albany, N.Y.: State University of New York Press, 1972). 59 Tjalling C. Koopmans, Three Essays on the State of Economic Science (New York, 1957). 60 R. A. Gordon, "Rigor and Relevance in a Changing Institutional Setting," American Economic Review 66 (March 1976): 1-14.

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understand problems for which neoclassical theory is inherently limited. The comparative institutional study of the efficiency properties of alternative modes of contracting is one example. The study of institutional process in a behavioral context is another. The prospect that neoclassical, transactional, and behavioral approaches will each develop in interesting and complementary ways during the next decade is distinctly promising.

Bibliographical Note A number of books and survey articles have appeared recently which, in ways that are mainly complementary, develop or emphasize somewhat different aspects of the firm and market literature than that attempted here. Among the survey articles that should be consulted are the following: Herbert A. Simon, "Theories of Decision-Making in Economics and Behavioral Science," American Economic Review 49 (June 1959): 253-80; F. Machlup, "Theories of the Firm: Marginalist, Behavioral, Managerial," American Economic Review 57 (March 1967): 1-33; M. Shubik, "A Curmudgeon's Guide to Microeconomics," Journal of Economic Literature 8 (June 1970): 405-34; J. J. McCall, "Probabilistic Microeconomics," Bell Journal of Economics and Management Science 2 (Autumn 1971): 403-33; and Richard M. Cyert and C. L. Hedrick, "Theory of the Firm: Past, Present, and Future, "Journal of Economic Literature 10 (June 1972): 398-412. Books of interest include Monopolistic Competition Theory: Studies in Impact, ed. R. E. Kuenne (New York: Wiley 1967); The Corporate Economy, ed. R. L. Marris and A. Wood (London: Macmillan & Co., 1971; and M. A. Crew, Theory of the Firm (New York: Longman, 1975). University of

Pennsylvania

11 Financial Theory of the Firm DOUGLAS VICKERS The problem of time, if we are to understand Marshall's Principles correctly, stands like a riddle at the core of economic theory. Marshall's representative firm and his trees of the forest, along with Pigou's optimum size of the firm, were intellectual constructs designed to accommodate the realities of economic behavior in historic time to what was to become a timeless and static theory. 1 It is one of the ironies of the history of economic thought that in subsequent neoclassical microeconomics Marshall's grand design of "studying a recognizable economy in a particular phase of its historical development" 2 was submerged in analyses based on timeless equilibrium thought forms; and many latter-day advances have stemmed from a retrieval of the intertemporal and disequilibrium perspectives which Marshall's vision had encompassed. Marshall's insistence on "the great importance of the element of time . .. the source of many of the greatest difficulties in economics" 3 was transmuted in the 1930s in the manner of Joan Robinson's influential Economics of Imperfect Competition: " T h e technique set out in this book is a technique for studying equilibrium positions. No refer'Cf. Joan Robinson, The Economics of Imperfect Competition, 2d ed. (London: Macmillan & Co., 1969), pp. v-vi. Robinson refers to her "shameless fudge . . . [with] comparisons of static equilibrium positions . . . dressed up to appear to represent a process going on through time" (p. vi). Cf. also Joan Robinson, Economic Heresies (New York: Basic Books, 1971), p. 27. 2 Joan Robinson, History versus Equilibrium (London: Thames Polytechnic, 1974), p. 6. 3 Alfred Marshall, Principles of Economics 8th ed. (London: Macmillan & Co., 1920), pp. 347, 109. 203

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ence is made to the effects of the passage of time . . . no study is made of the process of m o v i n g from one position of equilibrium to another. . . ." 4 Subsequently, with uncommon candor, Professor Robinson has been most prominent in emphasizing the need to inject a time perspective. Although Marshallians "examined the existing world in a spirit of respect," 5 Marshall's own caution substantially evaded the model builders. " W e cannot foresee the future perfectly. The unexpected may happen; and the existing tendencies may be modified before they have had time to accomplish . .. their full and complete work." That the unexpected may happen was "the source of many of the difficulties that are met with in applying economic doctrines to practical problems." 8 Keynes, to be sure, had grasped the pervasiveness of uncertainty in the Knightian sense: " H e brought the argument down from timeless stationary states into the present, here and now, when the past cannot be changed and the future cannot be known." 7 That uncertainty in this residual, nonquantifiable sense lies at the heart of Keynes' work has lately received renewed attention; Paul Davidson noted Keynes' protest of models where "at any given time facts and expectations were assumed to be given in a definite and calculable form. The calculus of probability . . . was supposed to be capable of reducing uncertainty to the same calculable status as that of certainty itself. I accuse the classical economic theory of being itself one of these pretty, polite techniques which tries to deal with the present by abstracting from the fact that we know very little about the future." 8 The proper attitude is that "risk can, via probability statements, be reduced to certainty, uncertainty cannot." 9 Shackle's poetic conception of "the human being's endless journey into the v o i d of t i m e " clinches the point and dramatizes the problem. 10

4Robinson, Economics of Imperfect Competition, p. 16. Also the perceptive arguments in G. L. S. Shackle, The Years of High Theory (Cambridge: Cambridge University Press, 1967), pp. 47-48, 59-60. "Shackle, Years of High Theory, p. 47. •Marshall, Principles of Economics, p. 347. 'Robinson, Economic Heresies, p. ix. "John Maynard Keynes, cited in Paul Davidson, Money and the Real World (London: Macmillan & Co., 1972), pp. 10-11. See also, E. Roy Weintraub, "Uncertainty and the Keynesian Revolution," History of Political Economy 7 (Winter 1975): 530-548. •Davidson, Money and the Real World, p. 142n. '»Shackle, The Years of High Theory p. 149.

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Walrasian Models For the theory of the firm, meshed in the theory of optimum economic behavior, the timeless, static, stationary, equilibrium mold implied a neo-Walrasian orthodoxy, dropping a potentially richer Marshallian tradition. For Walras, the world at a given point in time is described by a system of simultaneous equations in which the economic endowments, factor supplies, knowledge, preferences, and tastes of economic decision-makers and optimizers are given. Uncertainty is handled by the probability reduction methods which Keynes, a student of probability theory, had rejected. Indeed, in the application of the Walrasian analysis to the theory of finance, the assumption is generally made, as part of "the capital-asset pricing model," that participants approach financial markets with homogeneous expectations about the means, variances, and covariances of asset rates of return. Eugene F. Fama and Merton H. Miller, for example, in an elegant neoclassical statement, develop their theory of finance on perfect market Walrasian postulates. 11 The contemporary consolidation of the financial theory of the firm in neo-Walrasian analysis contrasts with the methods of both Marshall and Keynes. Indeed, it is a remarkable feature of the present state of economic theory that while we are witnessing a retreat from the strong neoclassical resurgence in the areas of money, production, capital, labor markets, and distribution, attempts should be made to base financial theory on Walrasian postulates and on assumptions of market perfection. 12 Robert Clower, for example, has declared that "either Walras' Law is incompatible with Keynesian economics, or Keynes had nothing fundamentally new to add to orthodox e c o n o m i c theory." 1 3 Axel Leijonhufvud has commented: " I t would be incongru"Eugene F. Fama and Merton H. Miller, The Theory of Finance (New York: Holt, Rinehart and Winston, 1972), ch. 7. Also J. Hirshleifer, Investment, Interest and Capital (Englewood Cliffs, N.J.: Prentice-Hall, 1970), and Jan Mossin, Security Pricing Theory and its Implications for Corporate Investment Decisions (Morristown N.J.: General Learning press, 1972), pp. 2, 3. The textbook application of the Walrasian type financial decision-making is explored in Harold Bierman, Jr. and Jerome E. Hass, An Introduction to Managerial Finance (New York: Norton, 1973), ch. 14. ia In addition to Paul Davidson, Money and the Real World, see Robert Clower, "The Keynesian Counterrevolution: A Theoretical Appraisal," in F. H. Hahn and F. P. R. Brechling, eds., The Theory of Interest Rates (London: Macmillan & Co., 1965); Axel Leijonhufvud, On Keynesian Economics and the Economics of Keynes (New York: Oxford University Press, 1968); Herschel I. Grossman, "Theories of Markets without Recontracting," Journal of Economic Theory 1 (December 1969): 476-479; and A. G. Hines, On the Reappraisal of Keynesian Economics (London: Martin Robinson, 1971), and references there cited. 13Clower, "The Keynesian Counterrevolution," p. 110.

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ous, of course, to combine the 'imperfect' markets for current output and factor services with so-called 'perfect capital markets' in the same model." 1 4 This anticipates the argument and conclusions that follow. 15 T h e backdrop of current financial market theory can be summarized briefly in the Fama and Miller postulates. Markets for consumption goods and investment assets are assumed to be p e r f e c t . . . consumers and firms are assumed to be price takers in frictionless markets.... Equilibrium at the beginning of period 1 is assumed to be reached through a process of tatonnement with recontracting: that is, investors come to market with their resources and tastes, and firms bring their production opportunity sets. A tentative set of prices for consumption goods, labor, and shares is announced, firms make tentative production decisions, and investors offer their labor to firms and begin bidding for consumption goods and investment assets. Prices and decisions are tentative; it is agreed that no decisions are executed until an equilibrium set of prices, that is, a set of prices at which all markets can clear, has been determined. Our treatment of this model concentrates on the nature of equilibrium in the capital market; that is, we take equilibrium in the markets for labor and consumption goods as given. 16

Against these assumptions, two critical issues d e m a n d f u r t h e r evaluation. First, it is assumed that no transactions are consummated in the money capital market at nonequilibrium prices, or that, in the words of Sir John Hicks, no "false trading" occurs. 17 The question needs to be confronted, however, as to how the assumption of smooth and rapid Walrasian equilibration in financial markets accords with possibly pervasive false trading in the real markets supporting the financial markets. Jan Mossin, for example, invoking the Walrasian auctioneer, remarks that "the floor trading in actual security markets resembles closely this process. Because of the unusually rapid flow of i n f o r m a t i o n , s e c u r i t y m a r k e t s are p r o b a b l y more e f f e c t i v e in eliminating discrepancies between demand and supply than any other market." 1 8 That may be so. But the question of the efficiency with which information emanating from the real markets is disseminated in the financial markets is not the sole or even the principal point at issue. T h e larger question relates to the quality, the ease of availability, and 14

Leijonhufvud, On Keynesian Economics, p. 57n. "Douglas Vickers, "Finance, and False Trading in Non-Tatonnement Markets," Australian Economic Papers 14 (December 1975): 171-186. le Fama and Miller, Theory of Finance, pp. 277-278. "John R. Hicks, Value and Capital (Oxford: Clarendon, 1946), p. 129. 18 Jan Mossin, Security Pricing Theory, p. 2.

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the efficiency of dissemination of information in the real markets themselves. F o r the possibilities of the generation of precise or inaccurate equilibrium or disequilibrium information in goods markets, labor markets, and real-asset markets influence the manner in which new information develops for lateral transmission to the security market, as well as its effective dissemination there. Here we are confronting the need to be aware of the relevance for the financial theory o f the firm of the Marshallian respect for history and the significance of the consummation of real-world transactions with which our concern began. A supplementary controversy in the modern theory of financial markets relates to the assumption that a viable theory of finance can be established on the supposition that all of the firm's factor and commodity markets are already in equilibrium. T h e need exists to establish lines of interconnection between the real markets and the financial sectors of the economy when the former exhibit demonstrably d i s e q u i l i b r i u m characteristics. 1 9 A question which must e m e r g e prominently in the financial theory of the firm concerns the extent to which equilibrium conditions of the money capital market provide valid decision criteria for firms which are in demonstrably disequilibrium postures. Acutely, as Joan Robinson has insisted, we n e e d to distinguish equilibrium models from historical models. 2 0 Part of the analytical problem lies in sorting and sifting the two. Joan Robinson is correct when she says, quite bluntly, that " i t is not legitimate to introduce an event into a system of simultaneous equations." 2 1

Early Financial Theory In the progress toward a fully developed financial theory of the firm, considerable significance must be accorded Oskar Lange's dissent in 1936 from the then received traditions. 2 2 Lange argued that the theory of the firm was based on the extremely unrealistic assumption that the firm, in making its optimum production and factor use decisions, did not face any shortage of money capital. Lange's analysis, which was unfortunately confined mainly to the case of a single period circulating capital investment, rested on the clear "distinction b e t w e e n 19 Cf. Douglas Vickers, "Disequilibrium Structures and Financing Decisions in the Firm, "Journal of Business Finance and Accounting 1 (Autumn 1974): 375-387. 20 Davidson, Money and the Real World, p. 25. "Robinson, History versus Equilibrium, p. 5. 22 Oskar Lange, "The Place of Interest in the Theory of Production," Review of Economic Studies 3 (June 1936): 159-192.

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money capital and real capital.... We prefer to speak simply of money capital as a sum of money invested in the purchase of factors of production and of real capital as a mere alternative term to denote equipment co-operating with labor in production." 23 The same distinction, vital for a microtheory of finance, was adopted in the later work of Andre Gabor and Ivor F. Pearce, who recognized that while real capital should properly enter as an argument in the firm's production function, money capital was not a factor of production: "the exclusion of money capital from the production function is the cornerstone of our approach." 24 For Lange, the dichotomy was pivotal. "The equations of the traditional theory of production are based on the tacit assumption that there is always available the money capital necessary to enable all firms to choose the best method of production." 25 This, Lange observed, implied "a theory of production in a state of perfect saturation with capital," and against this he developed "a theory of production subject to a shortage of capital." 26 From the latter analysis, Lange constructed his theory of the rate of interest. These seminal ideas have recently been developed into a formal theory of the firm which sets against the conventional assumption of "money capital saturation" the realities of enterprise decision-making subject to a "money capital availability constraint." 27 The firm, it is argued, confronts a trilogy of interdependent decision problems in production, asset investment, and finance. The conditions on which money capital is available to the firm exert significant effects on its optimum production level and factor employment decisions, determined principally by the "money capital intensity" of the various production factors employed, or the extent to which factor usage decisions give rise to "money capital requirements." These effects follow from the need to impute to the factors of production the "marginal money capital costs" as determined by each factor's "money capital requirement coefficient" and the money capital cost imputation rate. The imputation rate is shown to be specified by the marginal productivity of money capital in the firm. The production structure of the firm *»Ibid. p. 178. M Andre Gabor and I. F. Pearce, "The Place of Money Capital in the Theory of Production," Quarterly Journal of Economics 72 (1958): 537-557. See also John R. Moroney, "The Current State of Money and Production Theory," American Economic Review 62 (May, 1972): 335-343. "Lange, "The Place of Interest in the Theory of Production," p. 177. M Ibid., p. 190. "Douglas Vickers, The Theory of the Firm: Production, Capital, and Finance (New York: McGraw-Hill, 1968), p. 133 and ch. 6 on "The Issues in Historical Perspective." On financial investment and the degree of risk, see the pioneering article by Michal Kalecki, "The Principle of Increasing Risk," Economica 4 (November 1937): 440-447.

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(notably, its optimum degree of real capital intensity) depends directly on the conditions of availability of money capital. T h e "cost of capital" to the firm is the " f u l l marginal cost of relaxing the money capital availability constraint," and there are reasons to b e l i e v e that decision-makers will react to a higher marginal cost of money capital by adopting production structures w h i c h e c o n o m i z e on m o n e y capital-intensive factors. 28 It is possible to specify conditions under which interdependences between the firm's production, investment, and financing decisions do not obtain, so that "separation theorems" can be invoked. Separation theorems, which hold that a firm's financing decision is independent of its production decision, or that the financing mix is independent of the investment decision, have been described as "the major result of capital structure theory." 2 9 But the cost in realism and relevance is high. As Hirshleifer acknowledges, " t h e assumption of perfect markets turns out to be critical," as is "the standard assumption. . . that markets are both complete and perfect, so that equilibrium is instantaneously and costlessly attained." 3 0 This illustrates the dependence of contemporary theory on the Walrasian postulates, as already noted. On another level, the stringency of the assumptions necessary to avoid the production-investment-financing interdependence is indicated in the Fama and Miller application of the "capital asset pricing m o d e l , " which assumes that the firm is a perfect competitor, that it "is in a given risk class, and its only decision is to choose the optimal scale of activity." 3 1 In Fama and Miller's analysis the firm's investment has become production scale-changing only, with the critical factor proportions problem ignored entirely. This assumption, that real investment activities are scale-changing and risk-class-preserving only, resembles the seminal Modigliani and Miller analysis to which w e refer below. 3 2 Attempts have been made to generalize investment decision criteria away from this essentially nondiversifying characteristic. Yet the factor proportions problem has not been integrated into these analyses. Mossin, for example, has endeavored to show that the properties of the general equilibrium capi28See Douglas Vickers, The Theory of the Firm·, also "The Cost of Capital and the Structure of the Firm," Journal of Finance 25 (March 1970): 35-46, reprinted in L. R. Amey, ed., Readings in Management Decision (London: Longman, 1973). "Fama and Miller, Theory of Finance, p. 152. Cf. also J. Hirshleifer, Investment, Interest, and Capital. ^Hirshleifer, Investment, Interest, and Capital, pp. 14, 312. 31Fama and Miller, Theory of Finance, p. 311. 32F. Modigliani and Μ. H. Miller, "The Cost of Capital, Corporation Finance and the Theory of Investment," American Economic Review 68 (June 1958): 261-297.

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tal market model can be used to specify an investment decision criterion for any marginal investment, whatever its kind. 33 Unfortunately, the assumptions appear to render Mossin's criterion quite unusable, for it presupposes that a covariance matrix can be defined, specifying the covariance relationship between the income stream of the existing firm and that of its proposed marginal investment and, more seriously, the covariances between the marginal project of that firm and the earnings streams of all other firms in the investors' opportunity set. Similarly, Harold Bierman and Jerome E. Hass, in the spirit of the Walrasian market model, invoke assumptions that "(1) the (securities) market is currently in equilibrium (2) the market will move toward equilibrium if a disequilibrium condition sets in and (3) the market finds out about the [firm's real investment] decision immediately it is made." Thereupon, the authors conclude that "the relevant risk consideration" (in making a real investment decision) is "the relation of the risk of the investment to the market risk. The firm's risk position is not relevant." 34 It is questionable whether in actual fact a firm's individual investment projects are empirically and permanently separable as independently viable entities in the manner necessary to make these assumptions and implied decision criteria relevant.

Risk and Capital Structure In a work which consolidated opinion and gave direction to the subject Ezra Solomon summed up the questions to be examined: " H o w much capital should an enterprise commit? In what form should the commitments be made? H o w should the required funds be raised?" 35 In practical terms the questions concerned the size of the firm's balance sheet and the optimum structure of its assets and liabilities sides. Theory from this standpoint continued to avoid Lange's sharp money capital real capital dichotomy and his concern for what was in due course christened the "money capital availability constraint." This meant that no sustained treatment was accorded the firm's factor proportions problem, which has only lately entered the financing question. Important questions were the firm's project investment decision ^Mossin, Security Pricing Theory, p. 14. " B i e r m a n and Hass, Introduction to Managerial Finance, p. 230, and "Capital Budgeting under Uncertainty: A Reformulation," Journal of Finance 28 (March 1973): 127. 35 Ezra Solomon, The Theory of Financial Management ( N e w York: Columbia University Press, 1963), p. x.

Financial

Theory of the Firm

211

criteria, its cost of money capital, and its optimum financing mix. 36 The most serious logical deficiency of the theory as it developed in the 1960s was its focus on a project-by-project analysis of the firm's investment decisions, to the neglect of many more important interdependencies. 3 7 The investment decision criterion was expressed in two different forms. It was conceived that the future expected stream of cash-flow benefits attributable to a project could be discounted to the present, and that the project could be considered acceptable if the present value exceeded the money capital outlay necessary to make the project operational. Future cash flows were to be valued at a discount factor equal to the firm's "cost of capital." In an importance sense, however, this fudged the issue by begging the other critical question of how the cost of capital was to be specified. Second, it was argued that a "true rate of profit" on an investment project could be calculated as that discount factor which rendered the present discounted value of the future expected periodic net cash inflows equal to the required capital outlay. The project would be acceptable if this rate of profit exceeded the firm's " c o s t " of capital. For a normal investment project involving a cash outlay in exchange for a series of positive future net cash inflows, both the "present value" and the "rate of profit" criteria would yield the same answer to an accept-or-reject decision. But many problems remained to be canvassed: (1) reinvestment rate assumptions for purposes of recovering the capital outlay or maintaining capital intact; (2) comparing the relative attractiveness of projects of differing economic life horizons; (3) possible multiple solutions to profit rate calculations in cases whose project cash flows assumed negative values in certain future time periods; (4) consistent ranking of mutually exclusive projects; (5) the selection of an optimum subset of projects from a larger candidate set. 38 Considerable attention has ^Solomon summarized the state of the theory in an influential volume of readings, The Management of Corporate Capital (Chicago: Glencoe Free Press, 1959). 3, Cf. two widely used books of the time, Harold Bierman and Seymour Smidt, The Capital Budgeting Decision, Economic Analysis and Financing of Investment Projects, 2d ed. (New York: Macmillan, 1966), and A. J. Merrett and Allen Sykes, The Finance and Analysis of Capital Projects (New York: Wiley, 1963). Each was preoccupied with individual project analysis. 38Among suggestions for optimizing programming approaches to project set selection, cf. Clement G. Krouse, "Optimal Financing and Capital Structure Programs for the Firm," Journal of Finance 27 (December 1972): 1057-1071; L. J. Merville and L. A. Tavis, "A Generalized Model for Capital Investment," Journal of Finance 28 (March 1973): 109-118; Stewart C. Myers, "Interactions of Corporate Financing and Investment Decisions—Implications for Capital Budgeting," Journal of Finance 29 (March 1974): 1-25.

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been given also to: (6) the relative superiority of present value versus rate-of-profit rules; (7) the incorporation of utility function analysis into choice-theoretic approaches; and (8) the proper treatment of uncertainty, or the appropriateness of reducing uncertainty to risk or to "certainty-equivalents." 39 But the problems which continue to occupy most attention in the financial theory of the firm are threefold: (1) the specification of the firm's cost of capital; (2) the dependence of this datum on risk; and (3) the existence or nonexistence, in the light of the cost of capital analysis, of an optimum financial structure for the firm.40 A dominant opinion that the judicious use of relatively lower-cost debt financing in conjunction with owners' equity funds could lower the average cost of capital to the firm (and thereby increase the firm's market value and enhance the owners' wealth position) was controverted by the Modigliani and Miller ( M - M ) model, which implied a constant average cost of capital, independent of the financing mix.41 The authors concluded that security market arbitrage forces would cause firms in the same "risk class," but of differing debt-equity financing structures, to exhibit the same total market value of their capital securities. The M-M doctrine held that the weighted average cost of money capital to the firm was invariant with respect to the financing mix, so that a singular capital cost datum applied as the firm's investment decision criterion. It was acknowledged that the tax deductibility of interest on debt capital favored a "maximum" debt capital financing. The traditional theory maintained that equity capital investors would not lift their "required rate of return" or the "equity capitalization rate" in response to the technically increased risk exposure implied by a moderate amount of debt financing; as a result, the average cost of capital would be lowered. Excessive debt commitments, on the " O n questions of capital structure, see Stephen H. Archer and Charles A. D'Ambrosio, The Theory of Business Finance: A Book of Readings ( N e w York: Macmillan, 1967). 4 °The extensive controversies in these areas have stemmed from the papers by Modigliani and Miller and by William F. Sharpe, "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk," Journal of Finance 19 (September 1964): 425-442. Sharpe's contribution, which underlies the contemporary neoWalrasian capital market model, is summarized in two articles in the Autumn 1972 issue of The Bell Journal of Economics and Management Science, by Michael C. Jensen, "Capital Markets: Theory and E v i d e n c e , " and Eugene F. Fama, " P e r f e c t Competition and Optimal Production Decisions under Uncertainty." See the latter's "Risk, Return and Equilibrium: Some Clarifying Comments," Journal of Finance 23 (March 1968): 29-40, and Marshall Blume and Irwin Friend, " A N e w Look at the Capital Asset Pricing M o d e l , " Journal of Finance 28 (March 1973): 19-33. 41 On the main issues in the controversy, see Solomon, Theory of Financial Management·, for evaluative arguments, see Bierman and Hass, An Introduction to Managerial Finance.

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213

other hand, could be expected to increase investors' required rates of return and thereby increase the overall cost of capital. Considered as a function of the debt-to-equity or the "financial l e v e r a g e " ratio the cost of capital was thought to be U-shaped or to resemble a somewhat shallow saucer. T h e debt-to-equity ratio at which the function was at its minimum described the firm's optimum financing mix. T h e overall cost of capital thus envisaged was understood as the weighted average of the firm's debt and equity capital costs, where each capital cost was weighted by the relative importance of the corresponding type of capital, measured at market values, in the firm's total capital structure. 42 It has become recognized, however, that the weighted average cost of capital is not a valid investment decision criterion in a straightforward sense. Considerations of production-investment-financing interdependencies have made it clear that the average capital cost is relevant for financial decisions only when the firm is in an "optimum optimorum" operating, asset, and financing posture. At such a razoredge condition, if the analysis is to b e locked into its equilibrium mold, no further investment would be contemplated. T h e only situation in which the average cost of capital is valid is thus one in which it would not have to b e used! 4 3 In the full optimal posture, the weighted average cost of capital would equal the "full marginal cost of d e b t " and the "full marginal cost o f equity," or, in short, the "full marginal cost of relaxing the money capital availability constraint," irrespective of the financing source employed to introduce additional money capital to the firm.44 In general, as E n r i q u e Arzac has shown, the operative cost-of-capital criterion (assessing risk exposures from both operating and financing structures) is the full marginal cost of the financing source employed.

Current Impasse and Future Reconstruction T h e recognition of the principal results and difficulties of the neoWalrasian model, as applied to the decision criteria of the firm, returns the assessment to its starting point. T h e need still remains for a more realistic premise that decisions and transactions occur in historic time. 42 The continuing relevance and survival of the weighted average cost of capital is demonstrated by the exchange of views in the Journal of Finance 30 (June 1975). •"Cf. Douglas Vickers, "The Cost of Capital and the Structure of the Firm," and Enrique R. Arzac, "Structural Planning under Controllable Business Risk," Journal of Finance 30 (December 1975): 1229-1237. " S e e Arzac, "Structural Planning," on the Vickers theorems and their relation to general asset market equilibrium theory.

214

DOUGLAS VICKERS

This must enter into the most important aspect of the theory, which concerns the market's "required" yield, or rate of return, on a specified firm's common stock, i.e., on its (risky) ownership equity. The capital asset pricing model is "very much in the classical tradition . . . formally it is a model of pure exchange," and "being a pure exchange model it takes as given the firm's investment and financing decision." 4 5 The assumption is generally made that investors are mean-variance efficient portfolio optimizers, being risk averters who optimize their risky asset portfolio selection against utility functions defined in terms of expected return and of the variance of return on the assets. Homogeneous investor expectations, market perfection, and absence of transactions costs are also generally stipulated. Of course, homogeneous expectations, or investor agreement on the objectively given market opportunity set, do not imply homogeneous utility functions or subjective attitudes against which different investors evaluate the externally agreed market opportunities. Different utility functions do yield different subjectively acceptable risk-return trade-offs. But the theory does imply that in security market equilibrium all investors will settle at points on risk-return indifference curves at which their marginal rates of substitution between risk and return are equalized, as all traders adapt their holdings to the slope of an objectively attainable risk-return trade-off denoting the market price of risk. This principal result of the instantaneous equilibrium model furnishes direct contact with the financial theory of the firm. It can be shown, on the assumptions of the theory, that in equilibrium the required yield on a risky asset is equal to the attainable yield on a risk-free asset plus a risk premium. The magnitude of the premium depends on two derived data: first, the equilibrium market risk premium, or the excess over the risk-free rate of the weighted average required rate of return on all the securities in the risky opportunity set; and second, the correlation between the market return and the return on the specified asset. The acute and unresolved problem is precisely the extent to which the equilibrium data can be imported as decision criteria to actual financial decision situations. 48 Principally, it is alleged that the equilibrium specification of the risky asset's required yield on a firm's shares of equity capital can be taken as the firm's cost of capital for decision-making purposes. If, notwithstanding the cautions we have raised, the concept of the weighted average cost of capital is relied 45 4e

Mossin, Security Pricing Theory, p. 2. S e e Vickers, "Finance, and False Trading in Non-Tatonnement Markets."

Financial

Theory of the Firm

215

upon, it is proposed that this equity capital cost can enter the weighted average computation. T h u s , it is s u p p o s e d , the firm's capital budgeting decision criterion is appropriately specified. 4 7 But the financial theory of the firm has still to grapple satisfactorily with precisely this point. Meaningful decision rules derived from the Walrasian capital market theory b e c o m e suspect simply because of the fact that w e do not live in a Walrasian world. Market equilibration, in the real commodity and productive factor markets and in the financial markets of the economy, does not exhibit Walrasian infinite price velocities. False trading occurs. Transactions take place in historic time, and at nonequilibrium prices. Expectations, utility functions, and behavioral reactions are affected as a result. Rigidities, inelasticities, market imperfections, weaknesses in information transmissions, and the sheer changes that lend excitement to economic life complicate simple rules of action. It w o u l d be a pity if the social relevance of economics were betrayed by a mistaken insistence on artificial concepts contrary to facts. University

of Western

Australia

" B i e r m a n and Hass, Introduction

to Managerial

Finance, p. 230.

12 Demand Theory, Consumers' Surplus, and Sovereignty IVOR F. PEARCE

Until recently, economists said little on the subject (of consumer demand) because they really had not much to say that was not the common property of all sensible people. Alfred Marshall, in Principles of Economics, 1890.

Not surprisingly, since economics is about life as it is, most people have a d e e p instinctive knowledge of what we now call the theory of consumer demand. Indeed, it seems likely that words which distinguish between the money price (exchange value) of an object, its cost of production (labor content), and its utility (intrinsic value) have b e e n in common use in all parts of the world as long as markets have existed. It is a serious mistake to imagine, as many commentators do, that the theories of value in use, and value in exchange, of Adam Smith and David Ricardo differ in any material way from those of W. S. Jevons and Carl Menger or even Alfred Marshall. 1 It is not, for example, true that Smith subscribed to a cost (or labor) theory of value i n d e p e n d e n t of demand. The Wealth of Nations, in Book I, chapter 7, differentiates sharply between market price and natural price (long-run cost). T h e r e is a quite explicit statement that "when supply falls short of effectual 'See, e.g., Smith, The Wealth of Nations, 1776; Ricardo, Principles of Political Economy and Taxation, 1817; Jevons, The Theory of Political Economy, 1871; Menger Principles of Economics, English translation (Glencoe, 111.: Glencoe Free Press, 1950); and Marshall, Principles of Economics, 1890. 217

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IVOR F. PEARCE

demand at the natural price, some [persons]... will be willing to give more [than the natural price]." Nothing in modern textbook accounts of the part played by market price in equating supply and demand would surprise Smith, except possibly the frequency with which it is today thought necessary to illustrate the process with a diagram. At the other end of the scale, Jevons was well aware that the "final degree of utility" (marginal utility), which he showed to be a measure of value in exchange, is itself dependent upon quantity supplied (consumed). The relationship thus established between sales and the final degree of utility is, of course, the Marshallian demand curve. Again, we might note that John Stuart Mill had a clear conception of the margin we now call "consumer surplus," even though he must have been writing contemporaneously with Jules Dupuit who is usually held to have pioneered the idea. Mill, moreover, laid no claim to originality; he bases his argument explicitly on that of Thomas De Quincey. 2 If any doubt remains that some contemporary equivalent of the idea of a demand schedule has been present in the minds of men as long as prices have existed, this might be dispelled by recalling that, almost a century before the publication of The Wealth of Nations, Gregory King actually estimated, implicitly, the elasticity of demand for wheat. Richard Cantillon, also, traced a schedule concept. 3 And it seems hard to believe that Venetian accountants, faced a century and half earlier with the same pressing necessity as King, did not think of the same thing, just as Joseph-bar-Jacob probably did during the seven years of wheat rationing in ancient Egypt.

Modern Mathematical Demand Theory Modern demand theory is about "value in use." The age-old understanding that the value in use of any commodity depends upon how much one has of it, as well as of other commodities, is nowadays expressed by writing a utility function. U=U

(x,, . . . , x j ,

(1)

'Mill, Principles of Political Economy, 1848, Book III, ch. 1. Cf. Dupuit, "De la Mesure d'Utilite des Traveaux Publics," Annales des Ponts et Chausees, 1844, trans, in International Economic Papers, no. 2 (London: Macmillan & Co., 1952). See also de Quincey, Logic of Political Economy, 1844. 3 King, "Natural and Political Observations upon the State and Condition of England," in Two Tracts by King, ed. G. E. Bamett (Baltimore: Johns Hopkins University Press, 1936); and Cantillon, Essai sur la Nature du Commerce en General, 1732.

Demand

Theory

219

where x, is the quantity of the ith commodity consumed. Explicit references to such a function in the literature begin towards the end of the nineteenth century. 4 From there, it is but a short step to the idea that consumers will try, in the market, to maximize U subject to a budget constraint y = Σ Λ*

i

where y is total spending power and pf is the price of the ith commodity. T h e necessary conditions for maximum U subject to the constraint y are U

i

= k p

i

(3)

( i = l , . . . , n)

where (7, is the so-called marginal utility of the ith commodity (Jevons' final degree of utility). Since p, is measured in money per unit of the ith commodity, and [/,· is utility per unit, it is logical to call λ the marginal utility of money. Thus equation (3) expresses the classical understanding that the utility of an object [t/,/λ] is the extreme limit of its exchange value, p,.5 T h e η equations (3) may be reduced to η - 1 equations of the form, Ui/U;

= Pi/Pi

(j *

i),

(4)

eliminating λ. Thus (4) and (2) may be solved for the η unknowns x, to yield the demand functions X, = Xj(pi, . . . , p„,y)

(i = 1, ...

,n)

(5)

which underlie the classical theory of value in exchange. Actually, there is no unique measure of utility which can be derived from the equations (5) defining market behavior, for, if w e wrote F(U) for U, where F is any function, maximizing F yields precisely the same behavior equations (5) as maximizing U. Observed consumer behavior cannot distinguish between U and any F(U), nor is there any other available way to measure utility other than in an ordinal sense.® T h e claim that a cardinal measure of utility might be deduced from observation of behavior under uncertainty rests upon unjustified assump4 See Vilfredo Pareto, Manuel of Political Economy (London: Macmillan & Co., 1972), and "Ophelimity in Non-Closed Cycles," English translation in Preferences, Utility and Demand, ed. J. Chipman et al. ( N e w York: Harcourt Brace Jovanovich, 1971); Irving Fisher, "Mathematical Investigations in the Theory of Value and Prices," Transactions of the Connecticut Academy of Arts and Sciences, vol. 9, 1892; Francis Y. Edgeworth, Mathematical Psychics (London: Kegan Paul, 1881). 'Mill, Principles, Book I I I , ch. 2. e H. A. John Green, Consumer Theory (Harmondsworth, Middlesex: Penguin, 1971), pp. 220-226.

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IVOR F. PEARCE

tions.7 The utility of a lottery ticket, like all other utilities, is not necessarily independent of the quantities of other goods possessed. The fact that the existence of U is not easily confirmed by experiment has generated a great deal of debate. Almost as soon as the first utility functions were explicitly formulated, Vilfredo Pareto was seeking to measure "ophelimity" by the integration of market clearing functions.8 If the demand equations (5) are inverted to obtain market clearing functions Pi = Pi(xι,

• • • , *n,y)

«

=

1, . . . , n ) ,

(6)

then, by (3), λΣρ ( dxf = dU, and in the special case where dU = 0, we have dx, = 0

(7)

Because the functions pf are observable, Pareto argued that by integration of the differential equation (7) he could obtain observed "indifference lines," i.e., contours of the function U. A similar argument was put forward by Fisher.9 Pareto seems even to have gone further, supposing that by integrating the differential equation £p(

dx,

= dF

(8)

in a general way, he might obtain a measure F of utility itself. It was quickly pointed out that this is not the case.10 Unless we begin by assuming the existence of U, we have no reason to believe that the observed functions in (7) and (8) are integrable at all. To be integrable the functions pf must satisfy a special integrability condition.11 In this case, and in this case only, it will be possible to find an integrating factor μ, which, when multiplied through (7) and (8), converts the functions p, into functions μρι which satisfy the conditions dpxpi) dx}

=

9(μρ]) dXj

' S e e J. von Neumann and Oscar Morgenstern, Theory of Games and Economic Behavior, ( N e w York: W i l e y , 1947). 8 See Pareto, " O p h e l i m i t y , " originally published in Giornale degli Economisti 33 (November 1906). ®In "Mathematical Investigations." l 0 Vito Volterra, " L ' E c o n o m i a Matematica ed il nuovo Manuale del prof. Pareto," Giornale degli Economisti 32 (April 1906), trans. A. P. Kirman in Preferences, Utility and Demand, ed. Chipman et al. n P a u l A. Samuelson, Foundations of Economic Analysis (Cambridge: Harvard University Press, 1947).

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221

Obviously, the marginal utility of money λ is just such a factor, but the function λ is not observable, and i n d e e d we have no reason to suspect its existence unless we circularly assume what we wish to prove. The classical demand functions (5), or alternatively the market clearing functions (6), stripped of their utility scaffolding, tell us how people behave but not why they behave the way they do. Recall also that behavior is the same under any F(U) as it is u n d e r U, but from (3) we observe that the function λ is different in each case. Despite the obvious intuitive appeal, and the long-established acceptance of the idea of value in use, the difficulties noted caused some worry, particularly to those who were disturbed by the growth of a welfare economics based upon utility. 12 Vigorous attempts were made to introduce purely behavioral hypotheses which would be sufficient to establish the existence of U. In particular, attention was for some while concentrated upon the so-called revealed preference theory developed by Paul A. Samuelson. 1 3 This theory rests upon an assumption, which may be interpreted as a restriction on either the functions (5) or (6) as desired, and which is best explained as follows. Let p° b e a vector of prices, and x° b e the corresponding chosen vector of commodities u n d e r (5) or (6). If (p°, x°) > (p°, x 1 ), (x° φ χ 1 ), where (p°, x°) is the inner product Σρ,°χΛ t h e n the c o m m o d i t y vector x° is said to h a v e b e e n " r e v e a l e d preferred" to the commodity vector* 1 : we write the relation x® Rx1. x° is revealed as preferred because it was chosen w h e n x 1 could have been chosen. We now introduce, as a testable restriction on demand or market clearing functions, the hypothesis if x° R x1, then not x1 fl x®,

(9)

1

that is, x will never be chosen w h e n x° is available. This seemingly innocuous assumption made it possible to prove quite simply a great many of the fundamental results which can be deduced from the utility hypothesis. But it did not, in the end, prove sufficient to establish the necessary existence of a utility function. T h e flavour of the argument at this point is well reflected in W. M. Gorman's work. 14 The motivation for the axiom of revealed preference is obvious. If the consumer had in mind some consistent complete ordering of ls See, e.g., I. M. D. Little, A Critique of Welfare Economics, 2d ed. (Oxford: Oxford University Press, 1957). 13 See "Consumption Theorems in Terms of Overcompensation Rather than Indifference Comparisons," Economica 20, no. 77 (1953), and Foundations, ch. 5. 14 See Gorman's "Preference, Revealed Preference and Indifference," written in 1955, in Preferences, Utility and Demand, ed. Chipman et al.

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IVOR F. PEARCE

commodity bundles χ1, then he would never choose a bundle lower in the ordering when something higher is available. W e would like the revealed preference axiom to imply the existence of just such an ordering. But to do this, it is not sufficient simply to be able to order all pairs such as x° and xl. It is necessary also to impose a condition of transitivity, i.e., it must be assumed that if x°Px1 and χ1 Ρ x2, then x ° P x 2 where Ρ means "higher in the ordering." Unfortunately, the revealed preference relation need not be transitive. A simple two-dimensional example of an intransitive revealedpreference relation can be constructed even when a utility function exists. Accordingly, a new strong axiom of revealed preference has been proposed as follows. A commodity bundle x° is said to be indirectly revealed-preferred to a bundle x", ( x ° R * x " ) , if there exists a chain x°Rx1, x1Rx2 . . . x"~1R χ". The strong axiom of revealed preference now says i f x ° R * χ", then not x" R* x°

(10)

Historically, the strong axiom seems to have been inspired by an attempt to trace out a consistent "indifference surface" with a revealed preference chain.15 Indeed, it is true that for each price vector in a chain, the largest expenditure (such that the most preferred commodity bundle available is not preferred to the bundle immediately before it) maps out an indifference curve—if the chain is sufficiently long. With hindsight, on the other hand, the logic of indirectly revealed preference can be much more easily demonstrated. Suppose that an individual is asked to state his most preferred commodity bundle in a chain x°Rx1Rx2. The weak axiom suggests that it would be illogical to point to any bundle other thanx 0 ; for i f x 2 is chosen before x1, this contradicts x 1 R x2 (by the weak axiom), and i f x 1 is chosen, this contradicts x ° R x 1 (also by the weak axiom). There is, therefore, a powerful sense in which the weak axiom is consistent only with the idea that i f x ° R * x 2 , then n o t x 2 R x ° . It seems but a very short step from this to a claim that the weak axiom implies the strong axiom (10), but we cannot take this step. D. Gale has presented an example of a set of continuous demand functions, with the usual properties, which satisfy the weak axiom for all non-negative prices, yet they do not satisfy the strong axiom.16 T h e reason why such an example can be found is easy to see. 1 5 See H. S. Houthakker, " R e v e a l e d Preference and the Utility Function," Economica 17 ( M a y 1950): and Jean Ville, " T h e Existence Conditions o f a Total Utility F u n c t i o n , " trans. P. K. N e w m a n , Review of Economic Studies 19 (1951-52). ' " S e e Gale, " A N o t e on R e v e a l e d P r e f e r e n c e , " Economica 27 ( N o v e m b e r 1960).

Demand Theory

223

We have already noted that even when a utility function exists we may readily find examples where x°RxlRx2, but not x°Rx2. (At the 2 same time, we should expect not x Rx° by the argument already given.) Reversing the order, not x2Rx° does not imply not x2R*x°. Therefore, the weak axiom does not imply the strong. However, the strong axiom is a logical extension of the weak in a powerful sense. T o see this, suppose (contrary to the strong axiom) that x2R* x°. We then have the chain x°R* x2 R* x°. Now, the consumer, asked to choose his most preferred bundle from the whole set in the constructed chain, cannot answer without appearing to contradict the weak axiom. Any bundle xf, including x°, alleged to be most preferred, is somewhere preceded in the chain by a different bundle which has already been revealed-preferred to it. Note that, as long as not more than two bundles are offered, a choice can be made without contradicting the weak axiom. It will not surprise the reader to learn that it can be proved that the strong axiom properly in context, together with certain continuity assumptions, is both necessary and sufficient for the existence of a consistent (transitive) preference ordering of all bundles. 1 7 T h e weak axiom is necessary but, by Gale's example, not sufficient. At the same time, it is intuitively obvious that, given only a finite number of bundles, it is easy to select a utility function U(x) such that χ' Ρ xi i m p l i e s U(x') > U(x*), and for x' = xk in the o r d e r i n g U(x') = l/(x*). T h e existence of an ordering is the same thing as the existence of a utility function. A continuity assumption is sufficient to deal with the case in which the number of bundles is infinite. 18 It is natural to wonder why the theory of consumer choice, required to establish the existence of a utility function, needs to be restricted to choices made under market conditions. Does not the paraphernalia of revealed preference simply dig for us an unnecessary hole? T h e answer is yes, it does. T o be quite sure of the existence of a utility function, it is necessary only to suppose: (1) that an individual faced with a choice b e t w e e n x° a n d * 1 will be able to say either x°Px1 or not x°P x1, where Ρ means "would be chosen with certainty," (i.e., not at random); (2) that Ρ χ 1 and χ 1 Ρ x 2 implies Ρ χ 2 ; and "See, e.g., Hirofumi Uzawa, "Preference and Rational Choice in the Theory of Consumption," in Mathematical Methods in the Social Sciences, ed. Kenneth J. Arrow, S. Karlin, and P. Suppes (Stanford, Calif.: Stanford University Press, 1960). 18 See Gerard Debreu, "Representation of a Preference Ordering by a Numerical Function," in Decision Processes, ed. R. M. Thrall, C. H. Coombs, and R. L. Davis (New York: Wiley, 1954): and Ivor F . Pearce, A Contribution to Demand Analysis (Oxford: Oxford University Press, 1964).

2 2 4

I V O R F. P E A R C E

(3) that the resulting ordering should be continuous (for any bundle x1 not equal in the ordering to a bundle x°, there exists a neighborhood Ν of x° such that every bundle in Ν is closer in the ordering to x° than is x1). The whole of the theory of demand follows from these three assumptions. Notice also that the relation R * satisfies (1) and (2) above if we assume the strong axiom. It can be shown also that it satisfies (3). 19

Qualitative Restrictions on Demand Functions From its beginning, the theory of demand was developed with at least three aims consciously or subconsciously in view. The objectives were: first, to explain the formation of market prices; second, to make qualitative or quantitative statements about the relation between market price and the volume of sales; and third, to define a measure of utility based on observed behavior designed to make possible qualitative or quantitative statements about policy and welfare. So far, we have established the existence of a demand schedule in equation (5) above. Assuming that supply is related to cost in a quite independent way, and that bargaining takes place so as to equate price and cost and supply and demand, we have sufficient equations to determine market prices. T h e first objective of demand theory has been attained. The next step is to seek to make qualitative statements about the demand function (5). To this end we differentiate the equations (2) and (3) totally, writing in matrix form the system of equations ~UU

p-

p'

0.

"

dx

-d\_

kdp dy - x'

dp

(ID

where Uu is the matrix of second partial derivatives (Hessian) of the utility function (1), and where other symbols represent row or column vectors or scalars in an obvious notation. 20 Multiplying (11) through19 For a more intuitive, less exact, but fuller account of the theory, see Pearce, Demand Analysis, pp. 16-43. A first-rate elementary treatment can be found in Green, Consumer Theory, chs. 2, 3, 6, and 7. For the more technically oriented, Chipman's Preferences, Utility and Demand is an important collection of essays, and D. W. Katzner's Static Demand Theory (New York: Macmillan, 1970) is an excellent and in some ways original text. i0 This way of writing the basic equation of demand theory was first suggested to the author by P. J. Dhrymes long before it came into common use.

Demand

Theory

225

out by the inverse of the first matrix on the left-hand side, which w e shall designate σ ru = σ'

0

and choosing the elements of the vector of the right-hand side appropriately, w e obtain the fundamental results -I

5

dps

-= W

- χ>σ„

(12)

where σ, is the t'th element in the vector σ occuring in Γ ϋ ; and =

(13)

Despite appearances in (12), w e know, from (4) and (5) and the argument following, that both dx,/dps and dxf/dy are independent of λ, because behavior is independent of the chosen utility index. T o reconcile this with (12) and (13), it is easy to prove, by direct methods, that σ-j is independent of λ, that is not independent of λ, but that λ σ ξ is, which is what w e have to expect. 21 Accordingly, w e write σ 0 = \σ% and (12) in virtue of (13) becomes = σ „ - χ, - P - . dy

dPj

(14)

Next, w e recall that the inner product of the elements of any row of a determinant and a corresponding column vector of alien co-factors is always zero. Applying this to Ty,1 w e note from (11) that Σ V Pα = 0 ι

(15)

2

(16)

or, in v i e w of (3), i

= 0.

This last result suggests that w e should interpret σ^ as the change in the quantity of the tth commodity due to unit change in the j'th price after total spending y has been increased just sufficiently to compensate for the price rise. For this reason, it is usual to refer to the terms au and —xjidxj/dy) as the substitution effect and the income effect, respectively, o f the price change. It should be noted that xh when 21Pearce,

Demand

Analysis,

p. 53.

2 2 6

I V O R F. P E A R C E

thought of as multiplied by unit change in p}, is the sum of money just sufficient to allow the consumer to buy precisely the same commodity bundle as before the price rise, so that it is a genuine compensation. Notice now that the matrix r,j is symmetric so that συ = σ Η

(17)

and, of course, Σ PPis = 0.

(18)

j

Again, we recall that because the utility function U is at a maximum subject to the budget constraint Χρ(χ, - y = 0, the bordered Hessian matrix on the left-hand side of (11) has bordered on-diagonal blocks whose determinants alternate in sign. By Jacobi's theorem, relating the values of the minors of a determinant with values of the minors of the adjugate, 22 sign conditions are imposed upon συ as follows: < 0

0, and so on.

(19)

er«

In addition, from (18), it is clear that the final determinant in (19), which includes all cr(J, is always equal to zero. dxf/dy will ordinarily be expected to be non-negative: one would not be expected to buy less of any commodity as total expenditure rises. It follows, therefore, from (14) and (19), that dxi/dpl will ordinarily be negative in sign. This is the commonplace classical downwardsloping demand schedule. By differentiating SpjXj — y = 0, we may write

(20) (21) Inspection of equations (4) and (2) reveals at once that demand functions must be homogeneous of order zero in prices and expenditure so that ι

dps

(22)

dy

22 On Jacobi's theorem, see A. C. Aitken, Determinants Oliver & Boyd, 1946).

and Matrices

(Edinburgh:

Demand Theory

227

Equations (14), (15), (17), (18), (19), (20), (21), and (22) exhibit the principal qualitative restrictions imposed upon demand functions by the utility hypothesis. 2 3 T h e r e is an alternative way of looking at the whole problem. Instead of studying the properties o f the demand functions in terms of the partial derivative of equations (5), we could have inverted (5) to form price equations, or market clearing functions Pi = P,Ui, · · · , Xn,y)

(23)

directing attention to the partial derivatives dpjdxj. But for an accident of history the whole of economic theory might have been developed this way. Consider the income effect -xjidxf/dy) of the partial θχ,/öpj. In a pure mirror image theory we should expect to see a term ~pj(dpi/dy) in the partial d p j d x j . What, by analogy, could be the meaning of the "compensation" pj? Obviously, it is not in any sense a compensation, because an increase in the consumption of one commodity (all other quantities constant) cannot reduce utility whatever change in expenditure occurs. However, a change in money expenditure of p, might very well be interpreted as a kind of " e n a b l i n g " expenditure increase, as it is the amount of money which would just " a l l o w " the purchase of the new commodity bundle at the old prices. Furthermore, in the aggregate, the offer for sale of an extra unit of a commodity usually generates the income necessary to buy it. This is Say's law. 2 4 Now notice that the function (23) must be homogeneous of order one since doubling expenditure for the same commodity bundle must double all prices. Thus we have ψ dy

= ^

y

(24)

and it is open to us to write = «ο ~ Pi or aXj ay S3 Among those contributing to the earliest known mathematical formulation of these results were: W. E. Johnson, " T h e Pure Theory of Utility Curves," reprinted in Precursors in Mathematical Economics, ed. W. J. Baumol and S. M. Goldfeld (London: London School of Economics Press, 1968); G. B. Antonelli, "Sulla Teoria Matematica della Economia Politica," trans. J. S. Chipman and A. P. Kirman, in Preferences, Utility and Demand, ed. Chipman et al.; Eugenio Slutsky, "On the Theory of the Budget of the Consumer," English translation in Readings in Price Theory, ed. G. J. Stigler and Κ. E. Boulding (New York: Macmillan, 1952); and J. R. Hicks and R. G. D. Allen, "A Reconsideration of the Theory of Value, I and I I , " Economica 1 (February 1934 and May 1934). 2 4 S e e Mill, Principles.

2 2 8

I V O R F. P E A R C E

4 a .

dXj

c,. - -

=

(25)

PiPj/y

in analogous fashion to equation (14). T h e second term is the "income-enabling" effect and the first term is the "price-substitution" effect. Differentiating Ut/X = p( with respect to Xj reveals at once the presence of the income-enabling term. 25 Analogous to (15), we have Σ

(26)

= ο

and to (19), 0

< Pi

0

p,

p2

Pi

Su

Sl2

Pi

«21

S22

p, 0

^ 0, and so on.

(27)

«Ii

T h e sign of sit is not certain except in the case where the utility function is homogeneous in the commodity vector x, (i.e., homothetic). T h e price-substitution effect su is not symmetric, although the income enabling term is: dpjdy is positive corresponding to d x i / d y . Σ * - § * · = i;

corresponding to (20) and (21). 28 Suppose that instead of the extra " e n a b l i n g " expenditure being added to form the price-substitution effect s u , we imagine the sum taken away. Once again, there is no compensation in any sense because the expenditure reduction is offset by price changes which leave the consumption pattern unchanged by definition. However, as U, = \pj, Pj would have been a compensating penalty if prices did not change. For the moment, therefore, we define a generalized Antonelli price substitution effect as - „ JLEL= ν - "n dp.

Α. ^

dxj

" P e a r c e , Demand Analysis,

Pl

dy

Su

2P'

dy •

p. 60.

" T h e r e is a close relationship between these results first published by Pearce, in chapter 1 of Demand Analysis, and the so-called Antonelli price-substitution effect, which dates from at least 1886. See Antonelli, "Sulla Teoria Matematica."

Demand Theory

229

The income-enabling term now appears twice: it was taken away and it was initially imbedded in dpjdx,.27 Notice that it is not true that A,j = Aji unless Sjj = s}i, which is certainly not true in general. On the other hand, it is often said that the Antonelli matrix of substitution effects is symmetric. It is easy to see the reason for this apparent contradiction. Suppose there was no money, only commodities. Define the Jcth commodity to be a numeraire (commodity money). The commodity money, unlike bank notes, enters directly into the utility function and the marginal utility of money is Uk. Hence, Pj would be Uj/Uk. We then have (dpjdxj) - p/dpi/dy), interpreted as

d{U,/Uk) _ dxj

Uk

( i W ) , dxk

which is easily seen to be symmetric in i,j. This is the Antonelli symmetry theorem. In general, however, A,j = A^ only if the utility function is homogeneous, in which CäS6 S(j — Sji and for that matter

dpt/dxj = dpj/dxj.28

Finally, because of symmetry of the income-enabling term, both Ajj and dpf/dxj also satisfy the sign conditions (27). 29

Measuring Demand—Specialized

Utility

Functions

The qualitative restrictions on demand worked out in the previous sections are little enough. The practice in so-called "partial equilibrium analysis" of ignoring cross-partial derivatives (assuming them to be negligible) has generated an exaggerated notion of the value in economic analysis of the condition σΗ < 0. It is, therefore, worth emphasizing the triviality of such a simplification. If all dxt/dpj (j τ* i) were zero in (21), we should have (pj/xj) ( d x j / d p ) ) = — 1. No estimation of demand elasticity would ever be necessary; money expenditure on each commodity would be constant, whatever the price charged. A monopolist would offer for sale the smallest perceivable quantity of the monopolized product. Observe that (21) also implies that, however small the individual cross-partial derivatives may be, their sum is of the same order of magnitude as the slope of the direct Marshallian demand curve, the center of our attention. There is an urgent need to be able to measure the direct and all crosselasticities of demand in (21). 27 Pearce, Demand Analysis, p. 60. »Ibid., p. 227. 2eProofs, if these are needed, are given in Demand

Analysis.

2 3 0

I V O R F PEARCE

Attempts to estimate demand functions (5) by econometric methods are complicated by the multiplicity of independent variables. I f every price had to enter into every equation, it would be impossible to obtain sufficient observed data to calculate separate effects. Research, therefore, has concentrated upon specific hypotheses, based upon introspection, to reduce the number of parameters to be estimated or to establish some known relationship between them. A number of apparently different approaches along these lines seem based on the same essential idea and have converged to the same result. First, there is the everyday notion of the degree of substitutability or complementarity between different commodities. Substitutes provide alternative ways of satisfying the same need. Complements do not satisfy any need unless they are used together. Earlier economists sought to use their intuition to impose sign restrictions either upon elements of the utility function or upon demand functions. Vilfredo Pareto and Irving Fisher characterize goods i a n d j as substitutes if Ujj < 0, and as complements if υ ί } > 0, i.e., acquisition of a substitute diminishes the marginal utility of the ith good, complements increase it. 3 0 Unfortunately, the sign of Uu is not independent of the chosen index of the preference ordering. For example, FU(U) = {dF/dU)Ujj + {d2F/dU2) (L/, φ , so that Fu is not necessarily of the same sign as Uu. T h e natural way to escape this difficulty is to concentrate attention, not upon Uiy but upon the difference between the change in marginal utility of good i and the change in utility of a quantity of a good j of equal value, when the quantity of g o o d j consumed is increased, i.e., dU,

dXj

ipAdUj

V f)j ) dxj

= Uu - ( ^ U j j .

(30)

If i a n d j are good substitutes, this expression should be zero since the effect on marginal utility of the two equal-value perfectly substitutable quantities should be the same. For complements, the first term should be positive and large, and the second negative and large. We have, in the expression (30), a continuous measure of complementarity running from zero to infinity, the zero being independent of both units and the utility index chosen. A measure of curvature of the 3 0 See Paul A. Samuelson, "Complementarity—An Essay on the 40th Anniversary of the Hicks-Allen Revolution in Demand Theory," Journal of Economic Literature 12 (1974).

Demand Theory

231

constant utility (indifference) curve b e t w e e n x, and with all other commodity quantities constant, is given by a w e i g h t e d average of the degree of complementarity between i and j and b e t w e e n j and i as given by formula (30). 31 T h e s e simple ideas yield one of the most fruitful notions introduced into demand theory in recent years. Suppose that w e wish to compare the degree of complementarity not b e t w e e n i and j , but b e t w e e n i and a third commodity w, and j and w . W e then write C,J1(. = Uiu. — (U,/Uj)UJir, or U, ]Uj

Uiu. UjU.

where CUw is the measure w e require. If w is a better substitute for i than for j, then C , < 0. I f it is less substitutable than for j, then Q ju . > 0. T h e r e w i l l be many groups of three commodities in which ι and./ have no special relation with w . T h e y are neither complements nor substitutes. W e should expect to have CUw identically zero which is a very p o w e r f u l restriction on the utility function. T h e same result is suggested if w e ask whether the ratios of marginal utilities Uj/Uj would be left unaffected by an increase in consumption of u;. F o l l o w i n g up this idea it was proved that U,

UIU

σ,

= 0 implies U,

uh

ο-,,,.

= 0, for all w

(31)

Oj

and vice versa, where cr, = dxjdij and aiw is the Slutsky substitution term. 32 This is the most general theorem uniting all that is known about a possible property of utility functions now called "separability." R. G. D. A l l e n chose the sign of the Slutsky term as his immediate criterion for complementarity. 3 3 This has c o m e to be w i d e l y accepted, the argument b e i n g that if, after compensation, a rise in the price of/ induces a decrease in the consumption o f i , then i a n d j must be complements. If there is an increase in the consumption o f i , then i is substituted for j. But w e know that σ υ can never be a measure of complementarity b e t w e e n i and j , since its magnitude is equally de31 Pearce,

Demand Analysis, p. 144. p. 212. 3 3 See Allen, "A Comparison Between Different Definitions of Complementary and Competitive Goods," Econometrica 2 (April 1934). 32 Ibid.,

232

IVOR F. PEARCE

pendent upon the degree of substitutability between i and j and all other commodities. A suitable measure of complementarity between i and j alone involving a s has been developed: Ci}

(32)

- - σ 0 (σ,ί + cry) / = ylL = y

yV(l±.. y )

On these assumptions it is illuminating to study the properties of the function * = * (p, · · · Pn, (v = H, (p. · · ·

Pn, y)

·•• ( l / ^ ) )

(35) (35)a

on the assumption the t//y remain constant. Naturally, one would wish to know the values of the derivatives θχ,/θif of (35) in order to take account of income redistribution, even though this might often not be important. T h e Wold/Jureen example proves that, in general, (35)a need not show restrictions consistent with the existence of a well-defined preference field for the community as a whole. Aggregate substitution effects need not be symmetric. 4 3 42 See Paul A. Samuelson, "Social Indifference Curves," Quarterly Journal of Economics 70, no. 1 (1956). 43 Note especially that the simple two-commodity examples suggested by J. R. Hicks {A Revision of Demand Theory (Oxford: Oxford University Press, 1956), ch. 6] and Green (Consumer Theory) do not reject the symmetry hypothesis. They prove only that the implied commodity preference ordering need not be convex. See Pearce, Demand Theory, p. 109.

Demand

Theory

237

Despite Wold/Jureen, however, only a very weak condition is necessary to reinstate all the restrictions of individual demand theory on the functions ( β δ ^ . 4 4 A necessary and sufficient condition for the existence of an implicit preference ordering for the community (subject to a given income distribution) and a sufficient condition for that ordering to be convex is (36) A number of special cases of (36) can be found in the literature. Some authors have also sought more stringent conditions under which the function Hf might be written so that x, might be independent of any change whatever in income distribution satisfying Σιf = y. It is both necessary and sufficient in this case that every derivative dXjIdtf of (35) should be the same (i.e., Engel curves should be parallel for all individuals for all income distributions). This condition will immediately satisfy (36) because dHj mi. = dy

γ / dx, γ ΐ Ji_ £ y dtf

_=

dXj dtf

_=

dXj etc dy> ' e i c -

Hence parallel Engel curves for all individuals imply that aggregate demand functions satisfy all the usual restrictions, as for the individual. 45 More special cases of this have been identified. Engel curves arc parallel, for example, when preference orderings and income distributions are identical for all individuals, or when Engel curves are straight lines passing through the origin. As such cases are highly unlikely, little interest is attached to them. On the other hand, the conditions (36) are relatively weak and might be approximately satisfied. If any uniformities appear in aggregate data, they are likely to emerge when we abstract from income redistribution—as in (35)a—or in the context of observations redistribution is random with respect to slopes of Engel curves. 4 6 On the matter of aggregation over commodities, we may note that composite commodities can always be formed when components are taken in fixed proportions or as long as the relative prices of the elements remain constant. 47 By the same token, the aggregate error remains small as long as relative prices stay fairly constant or proportions remain fairly fixed. See Pearce, Demand Theory, p. 118. See H. A. John Green, Aggregation in Economic Analysis (Princeton: Princeton University Press, 1964). ^ S e e D. W. Katzner, "A Simple Approach to Existence and Uniqueness of Competitive Equilibria," American Economic Review 62, no. 3, (June 1972). 44

45

238

IVOR F. PEARCE

Otherwise, w e must choose both a price index and a quantity index for the composite commodity, indices such that demand functions remain invariant under changes in the composition of the elements of the aggregate (prices or quantities). Of course, this applies only in rare cases. Not surprisingly, however, it can be shown that when utility functions are separable, commodities may be aggregated to some degree if the pattern of separability is followed. In most of these cases, it is necessary to use separate price indices for the income part and the substitution part of the demand partials.47 Finally, inquiry has shown that in a general way aggregation over commodities is not possible and that it is indeed common sense that it should not be. 48 The proper answer to all aggregation problems is not to aggregate. Where it happens to be either necessary or convenient to aggregate, w e should not ask "is it correct?" but "how much error is involved?"

Time, Money, and Quantities in Utility Theory It would be wrong to leave the subject of demand without asking in what units w e measure, what is meant by a commodity bundle, and to what time period does utility refer. These problems are discussed at length in A Contribution to Demand Analysis, Chapter 1. Clearly, utility must mean utility per period of time, i.e., a flow of accruing utility. On the other hand, because w e are investigating purchases of commodities "across the counter," it is tempting to identify the commodity bundle χ in a set of demand functions simply with purchases, even though in some cases durable commodities are involved. This is a confusion. T h e most logical approach is to define χ as the commodity bundle in use during the time period of the utility function. Hence χ does not include purchases for stock, although it does include all single-use commodities used up during the time period. This definition at once raises further questions. T h e price of commodities in use must now be defined as their rental per time period, as opposed to their across-thecounter price. This presents no difficulty, as w e have the simple relation rental = rp/( 1 - e~rl), where r is the rate of interest and I is the life of the commodity in use, given its intensity of use.49 47 Cf. A. P. Barten and S. J. Turnovsky, "Some Aspects of the Aggregation Problem for Composite Demand Equations," International Economic Review 7 (1966). •"See Green, Aggregation. 4 e See Pearce, Demand Analysis, p. 41.

Demand

Theory

239

All that w e need to do n o w is to relate the across-the-counter purchases to the desired quantity in use, as represented by the demand function. Purchases b e c o m e simply x, — plus percentage of stock reaching the end of life. T h e s e considerations suggest that, as an integral part of his utilitymaximizing behavior, the c o n s u m e r will b e making a number of choices over and above the simple selection of his desired pattern of commodity usage. In particular, the consumer has an income, y, stocks of financial and real assets ivt not "in u s e " in a utility sense, each with an expected selling price, wf, at the end of the time period (including any property income accruing), an e x p e c t e d future income yf, and an expected inflation rate, dp/p. As w e l l as choosing commodities in use, he must decide additions to assets (i.e., saving). T h u s w e might write the utility function in the form ' ' *n> Mi·.

( χ

^uw,,.)],

(37;

w h e r e uif/Wj is the e x p e c t e d percent change in value (including income) of one dollar's worth of the ith asset wt; yf is the present value of expected future income; dp/p is the expected rate of change of the general price level; and Σ , Σ ^ α ^ υ » is the variance of the deviations of the expected value of the portfolio of assets from the actual, vu b e i n g the covariances of the individual assets. ( T h e last term is a suitable measure of risk.) yf, dp/p and wf/w( are parameters. T h e choices to b e made are of wt and Xj subject to the constraint X Pi*i + X^i η f

= y + w

w h e r e w is the initial stock of wealth and y is current income (as opposed to expenditure). Note that w e now have w*/w(, yf, dp/p, and risk, and all enter as p a r a m e t e r s of the d e m a n d f u n c t i o n s . By i t s e l f , this c a u s e s no difficulty, but it has b e e n pointed out that the p r e s e n c e of yf and dp/p in the utility function could be destructive of all the qualitative properties of demand functions so far established.50 dp/p is, in fact, an index of inflation upon w h i c h the consumer bases his expectations of the future purchasing p o w e r of his current stock of financial and other assets. W h e n w e ask h o w the d e s i r e d stock of consumption goods in 5 0 I b i d . , ch. 2; and Don Patinkin, Money, Harper & Row, 1965).

Interest

and Prices,

2d ed. (New York:

240

IVOR F PEARCE

use will change in consequence of a current price rise, we have to take into account the effect of this upon the parameter dp/p of the utility function. Every demand function will now have an extra term, in addition to income and substitution effects, measuring the change in consumption d u e to the impact of the current price change on the inflation rate index. There could even be a fourth term if expected future income is also affected. Furthermore, it is not possible to put an a priori sign on the extra term. A rise in one price reduces the realwealth stock, but it also reduces real consumption. There will be a desire to replace the lost wealth but there will also be pressure to replace lost consumption. Fortunately, it is not unreasonable to expect that the utility function (37) would, for most people, be separable in commodities x, which refer to current goods in use, and the remaining variables and parameters which are relevant only to future consumption. On this assumption, all of the difficult·'^ disappear; with separability between current and future enjoyments, it is possible to replace the current income variable, and all other variables relating to saving and wealthstocks which occur in current demand equations, with a single variable "expenditure." The theory of current demand for nonwealth goods then reverts precisely to that outlined in the earlier parts of this chapter. A distinct set of demand functions for financial and other assets not in use appear with the asset parameters as arguments. Aggregating these, we obtain a savings (consumption) function which relates consumption (= y + tv - Σ/· Wj = Σ ρ,χ,) to current income, expected future income, expected property income, the inflation rate, and risk. 51 An alternative approach is to include into the utility function not only current consumption b u t also future p l a n n e d consumption, period by period, for the whole of the expected lifespan of the consumer. 5 2 We do not develop the subject here, as a theory explicitly involving planned expenditure seems hardly operational. Theory should be about the interrelationships between observable variables in which we are immediately interested. It is doubtful whether consumers ever have precise plans for future consumption beyond an intent to have a certain sum of spending money available. "For a more detailed account, see Pearce, Demand Theory, ch. 2; Green, Consumer Theory, ch. 15; and the very considerable literature on portfolio analysis which forms a separate subject. s2 For an account and summary of the literature in this area, see Green, Consumer Theory, Part IV.

Demand Theory

241

Consumer Surplus, Index Numbers, and Consumer Sovereignty The third and final object of demand theory is to devise, if possible, some observable index of utility. Indeed, it might be said that this is the central purpose of all economic theory. To decide whether a policy is " g o o d " or "bad," it is necessary to say whether the probable change in utility is positive or negative. We begin our study from the simple observation that because Expenditure — y = ZpiXt, then 2 Pi dxi =

% dp(

+

dy.

(38)

The left-hand side of (38) can be thought of as an index number of the change in real consumption due to a policy change (or any other cause). This is the change in consumption valued at base prices p, commonly used as an indicator of the change in real national product. The word "real" implies an attempt to measure utility. To defend this idea, we recall that λρ,· = U(, so that λΣ ρ, cfx, = Σ I/,· dxi — dU. The fact that Σt/ s dx, is not more than a first approximation to dU has indirectly generated a great deal of debate. It was quickly noticed that Σ,(ρ, + dpt) dx* has just as powerful a claim to be called an index of utility (quantity index) as Σρ, dx,. The two are known as Paasche and Laspeyres indices and the diligent reader of Fisher will discover many more varieties of combination. 5 3 The problem is that it is just as easy to choose a case where Σρ, dx, > 0 b u t d l / < 0 as it is to choose a case where Σ(ρ, + dp,) < 0 but dU > 0. 54 Of course, if the change dx is small enough, anomalies cannot be observed but the possibility of error is sufficiently great to have provoked the suggestion that a more proper index would be, in vector notation, (39) where the p, in the vector ρ are taken to be the inverted demand functions (23), the arguments of which are Xj. The definite integral is 53

See Irving Fisher, The Making of Index Numbers, 1922. The reader is advised to consult a comprehensive review article by Paul A. Samuelson and S. Swamy, "Invariant Economic Index Numbers and Canonical Duality: Survey and Synthesis," American Economic Review 64 (September 1974). 54

2 4 2

I V O R F. PEARCE

taken over the range x° to x', the before and after policy patterns of consumption. 55 It was quickly pointed out that the function p( need not be exactly integrable even though it is assumed to be derived from a utility function U. (Some normalizing procedure would also be needed if ρ is to be allowed to change over the path of integration. Otherwise, the integral may be made as large as we please for the same real policy by allowing both prices and expenditure to rise proportionately). The measure (39) is not independent of the path of integration, or of the degree of inflation over the path; it is therefore quite ambiguous (meaningless) even if a number could be found by numerical methods for the path integral. For independence of the path of integration, it is necessary that the utility function should be homothetic and that y, for example, should be kept constant.56 If one wishes to find an integral like (39), it is essential, if the answer is to make any sense at all, to seek an integrating factor which w e call λ (because the marginal utility of money is just such a factor). Then, multiply (39) by λ and integrate Xt7, dx, = dU over the range. This integral will be both path-independent and independent of aggregate spending. The problem is indeed precisely that discussed at length above. As w e wish to recover some cardinal measure of ordinal utility from the observed behavior implied in (39), w e have to develop some way of observing not the true marginal utility of money—for this is impossible—but some representation of it which will allow us to order social states, however close in the ordering they may be. T o integrate (39) over a path is to assume that the integrating factor is identically unity, a patently false assumption.57 McKenzie and Pearce have recently suggested a way in which one integrating factor might be found and expressed in terms of a Taylor series.58 If a sufficient number of terms in the Taylor series are taken, a cardinal measure of ordinal utility may be written in terms of partial and higher order partial derivatives of demand functions, exact as we like to make it. Any two policies may be precisely ordered. Up to two terms, the Pearce/McKenzie formula is du=

- Σ * dPi - V2 2 2 ( J * - X i f ^ ) dp, dPi +dy -

dV.