EQUILIBRIUM AND DISEQUILIBRIUM IN ECONOMIC THEORY

THEORY AND DECISION LIBRARY

AN INTERNATIONAL SERIES

IN THE PHILOSOPHY AND METHODOLOGY OF THE

SOCIAL AND BEHAVIORAL SCIENCES

Editors:

GERALD EBERLEIN, University of Saarland

WERNER LEINFELLNER, University of Nebraska

Editorial Advisory Board:

K. BORCH, Norwegian School of Economics and Business Administration

M. BUNGE, McGill University

J. S. COLEMAN, University of Chicago

W. KROEBER-RIEL, University of Saarland

F. SCHICK, Rutgers University

A. RAPOPORT, University of Toronto

A. SEN, University of London

W. STEGMULLER, University of Munich

K. SZANIA WSKI, University of Warsaw

L. TONDL, Prague

VOLUME 13

EQUILIBRIUM

AND DISEQUILIBRIUM IN

ECONOMIC THEORY

PROCEEDINGS OF A CONFERENCE ORGANIZED BY THE

INSTITUTE FOR ADVANCED STUDIES, VIENNA, AUSTRIA

JULY 3-5, 1974

Edited by

GERHARD SCHWODIAUER

Institute for Advanced Studies, Vienna, Austria

D. REIDEL PUBLISHING COMPANY

DORDRECHT-HOLLAND I BOSTON -U. S.A.

Library of Congress Cataloging in Publication Data

Main entry under title:

Equilibrium and disequilibrium in economic theory.

(Theory and decision library; v. 13) Bibliography: p. Includes index. 1. Economics-Congresses. 2. Equilibrium

(Economics)-Congresses. 3. Statics and dynamics (Social sciences)-Congresses. I. SchwOdiauer, Gerhard. II. Institut fiir hahere Studien und wissenschaftliche Forschung, Vienna. HB21.e69 330'.01'8 ISBN-13: 978-94-010-1157-0 DOl: 10.1007/978-94-010-1155-6

77-25391 e-ISBN-13: 978-94-010-1155-6

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TABLE OF CONTENTS

PREFACE

INTRODUCTION

LIST OF PARTICIPANTS

PART 1 / EQUILIBRIUM

IX

XI

XLIX

K. VIND / Equilibrium with Respect to a Simple Market 3 D. GALE and A. MAS-COLELL / On the Role of Complete,

Transitive Preferences in Equilibrium Theory 7 C. WEDDEPOHL / Equilibrium in a Market with Incomplete

Preferences where the Number of Consumers May Be Finite 15 W.P. HELLER / Continuity in General Nonconvex Economies

(with Applications to the Convex Case) 27 H. KEIDING / Are Core Allocations Obtainable as Exchange

Equilibria? 39 P. VAN MOESEKE / Equivalence of Competitive and Relative-Core

Allocations on a Measure Space of Economic Agents 47 V. BOHM / Non-Stable Cores of Exchange Economies 53 M. J. BECKMANN / Does Perfect Competition in Spatial Markets

Maximize Welfare? 67 W.E. DIEWERT / Walras' Theory of Capital Formation and the

Existence of a Temporary Equilibrium 73

PART 2 / CRITIQUE OF EQUILIBRIUM THEORY

M. ALLAIS / Theories of General Economic Equilibrium and Maximum Efficiency 129

H. ABELE / Towards a Neo-Austrian Theory of Exchange 203 M. SHUBIK / Competitive and Controlled Price Economies: the

Arrow-Debreu Model Revisited 213

VI TABLE OF CONTENTS

PART 3 / EXTENSIONS OF EQUILIBRIUM THEORY­IMPERFECT COMPETITION, UNCERTAINTY, AND MONEY

T. HANSEN and A. S. MANNE / Equilibrium and Linear Comple­mentarity ~ an Economy with Institutional Constraints on Prices 227

R. R. CORNWALL / Marketing Costs and Imperfect Competition in General Equilibrium 239

A. R. G. HEESTERMAN / Oligopoly and Its Macroeconomic Implications 255

G. TINTNER / Risk and Uncertainty. Their Importance for the Homogeneity of Demand and Supply Functions and the Dicho-tomy between Real and Monetary Economies 277

G. HEAL / Notes on the Economic Consequences of Uncertain Product Quality 295

M. KING / Corporate Policy, Uncertainty, and the Stock Market 315 A. ULPH and D. ULPH / Efficiency, Inessentiality and the 'Debreu

Property' of Prices 337

PART 4/ PROBLEMS IN DYNAMICS

S. SMALE / An Approach to the Analysis of Dynamic Processes in Economic Systems 363

K. NAGATANI and P.A. NEHER / On Adjustment Dynamics~An Exercise in Traverse 369

W.A. BROCK and J.A. SCHEINKMAN / On the Long-Run Behaviour of a Competitive Firm 397

N. GEORGESCu-RoEGEN / Dynamic Models and Economic Growth 4 t 3

PART 5 / DISEQUILIBRIUM AND MACROECONOMIC THEORY

P. W. HOWITT / The Qualitative Effects of False Trading 453 P. G. KORLIRAS / Non-Tiitonnement and Disequilibrium

Adjustments in Macroeconomic Models 463 T. NEGISHI / Existence of an Under-Employment Equilibrium 497 J.-P. BENASSY / A Neokeynesian Model of Price and Quantity

Determination in Disequilibrium 51 I

T ABLE OF CONTENTS VII

D. M. JAFFEE / The Specification of Disequilibrium in Flow of Funds Models 545

R.J. BARRO and H. I. GROSSMAN / Consumption, Income, and Liquidity 565

D.A. STARRETT / A Model of Dynamic Keynesian Equilibrium 593 T. RADER / Many-Good Multiplier Analysis under Traditional,

Classical and Neo-Keynesian Conditions 611 C. AZARIADIS / Stochastic Disequilibrium in a Labor Contracts

Economy 651 G. D. DEMOPOULOS / Expectations, the Real Rate of Interest, and

Labor Market Behavior in a Macromodel 671 R. BRITTO / Optimal International Adjustment for a Country in a

State of Fundamental Dynamic Disequilibrium 691 S. W. ARNDT / International Trade and Payments when Markets

Fail to Clear 705

INDEX OF NAMES 723

INDEX OF SUBJECTS 728

PREFACE

This volume is the result of a conference held at the Institute for Advanced Studies, Vienna. There is still a gap reflected both in fundamental meth­odological differences and in the style of analysis between the Walrasian (and Edgeworthian) tradition of general equilibrium theory and the theo­retical and policy problems raised in the framework of Keynesian and post-Keynesian macroeconomics. The conference succeeded in bringing together economic theorists working in fields ranging from abstract prob­lems of mathematical equilibrium analysis to applied macroeconomic theory, and it is hoped that the present volume will contribute to bridging the above-mentioned hiatus.

As organizer of the meeting and editor of its proceedings I want to thank the Institute for Advanced Studies for providing facilities and funds. I am also sincerely grateful to all my colleagues from the Institute for their generous help, in particular to Mrs Monika Herkner without whose assistance and organizational talent the conference would certainly not have been the success it in fact - in the opinion of all participants - turned out to have been. Furthermore, I wish to express my gratitude towards all participants in the meeting and contributors to the volume whose patient support of the whole enterprise proved indispensable. To Mrs Elfriede Auracher I am deeply indebted for her skillful and effective general management of the editorial work and her invaluable assistance in compiling the indexes.

GERHARD SCHWODIAUER

INTRODUCTION

Economic Equilibrium and Disequilibrium from a Dynamic Point of View *

The theory of general economic equilibrium, or, rather, the collection of general equilibrium models (for there certainly does not yet exist such a 'theory' in the stronger sense established in the physical sciences), can nowadays rightly be considered the theoretical basis and core of economic science. Characteristic for any type of modern general equilibrium theory - and what distinguishes its research program from certain variants of 'macro-theorizing' - is its 'methodological individualism': General equilibrium theory explicitly recognizes that at the bottom of every collec­tive, social phenomenon are the actions of individual human decision makers, and argues that, for this reason, the modeling of individual deci­sion making plays an indispensible role in the analysis and explanation of economic macro-phenomena. This means neither that the program of general equilibrium theory is opposed to empirical macroeconomics - on the contrary, for purposes of making theoretical concepts operational, testing theoretical hypotheses, and practical policy applications, cluster­ing and aggregation, and a certain loss of structural information, are un­avoidable (the general equilibrium theorist would only argue that macro­economic concepts and relations are of a derived nature and are to be deduced, by means of explicit aggregation rules, from their microeconom­ic counterparts) - nor that the analysis of individual behavior is thought sufficient for the explanation of the social consequences resulting from individual actions. As Hayek [24, p. 39] has pointed out,

it is a mistake, to which careless expressions by social scientists often give countenance, to believe that their aim is to explain conscious action. This, if it can be done at all, is

* Contributions contained in this volume are referred to in the introduction by using small capital letters for the respective name(s) of author(s) while all other references are listed alphabetically and numbered correspondingly, their respective numbers being put in brackets in the text.

XII INTRODUCTION

a different task, the task of psychology. For the social sciences the types of conscious action are data .... The problems which they try to answer arise only in so far as regularities are observed which are not the result of anybody's design. If social pheno­mena showed no order except in so far as they were consciously designed, there would indeed be no room for theoretical sciences of society and there would be, as is often argued, only problems of psychology. It is only in so far as some sort of order arises as a result of individual action but without being designed by any individual that a problem is raised which demands a theoretical explanation.

Indeed, the transformation of individual actions by institutional arrange­ments like the market into collective outcomes unforeseen and undesired by the individual decision makers is one of the perennial themes of economic theory, whether this phenomenon was hailed as a benevolent 'invisible hand' by Adam Smith or regarded as a symptom of alienation by Karl Marx. The observation that society and economy are the result of human action but not of human design, and the wonder at the apparent fact that decentralized economies which comprise vast numbers of auton­omous decision-making units pursuing their own interest do as a rule not engender total chaos but are, on the contrary, quite capable of pro­ducing a coherent pattern of economic activities serving the well-being of its members much better than most of the historically known centrally planned economies do (though there may be characteristic deficiencies as, e.g., more or less regular fluctuations in employment), have been the prime intellectual motivations for general equilibrium analysis. It has to be stressed once more that the theory of general economic equilibrium is at least as much interested in understanding and modeling the institutional socio-economic arrangements controlling the interaction of the economic agents as in analyzing their individual goals and choice possibilities (sec also [18]). Using game-theoretical terminology [49; SHUBIK]: In positive economics, the theorist's task is to specify a game (in extensive form given by the set of players, i.e. economic agents, their so-called payoff functions describing their valuations of the outcomes of the game, i. e. states of the economy, and a full description of the information conditions and all se­quences of moves leading to these outcomes) whose solutions (e.g., non­cooperative equilibrium points) correspond most closely to the regularities observed and to be explained. In normative, or welfare, economics, the task is to compare various conceivable rules of games, keeping, e.g., play­ers, payoff functions, physical and technological conditions constant, but varying the extensive form with respect to institutional conditions, and

INTRODUCTION XIII

jUdging them on the basis of the solutions they yield (we may, e.g., re­commend rules generating equilibrium points that give higher payoffs for all players or all members of a certain group of players than other con­ceivable rules). We see that a 'mathematical-institutional economics' (Shubik [56]) is not only no contractio in adjecto but, on the contrary, is in full accord with the central problems of a well-conceived theory of general economic equilibrium.

The so-called Walrasian general equilibrium model as most elegantly formulated, e.g., by Debreu [9], which, as was recently pointed out once more by Clower and Leijonhufvud [8], bears only rather distant resem­blance to Walras's [57] original conception ofthe working of a capitalist economic system, describes an economy consisting of a finite number of households and firms (which are the only categories of economic agents) dealing in a finite number, say m, of different commodities. The value (in exchange) v(x) of a commodity bundle x E IRm is defined as v(x) = px, and P E IR~* (the non-negative orthant ofthe space dual to IRm) is called a price vector or price structure. Since two different commodity bundles x and y can be exchanged if and only if px = py, two price vectors p und q with q = AP, 0 < A E IR, may be regarded as essentially equivalent, mean­ing that in this context only price ratios and not price levels matter. If the total quantity of each (produced or unproduced) commodity supplied at a given price structure p is subtracted from the respective total demand at that price vector, we obtain the so-called (market) excess demand Zk(P) for that good; z(p) E IRm is the corresponding, not necessarily uniquely determined, excess demand vector. An equilibrium is usually defined as a price vector p* and an associated collection of individual demands and supplies such that

Z(p*) ~ 0

and pt Zk(P*) = 0 for k = I, ... , m. The 'market' is pictured as a sort of analogue computer solving this system of inequalities.

Some basic concepts of systems theory (see, e.g., [2]; also SMALE) will help to elucidate this problem and will be useful in interpreting and putt­ing in perspective the above notion on general economic equilibrium.

A (dynamic) system is a pair (S, {LdiEl) where {LdiEI is a family of mappings L i : S --4 S from a non-empty set S into itself. S is called the set of states, Li a law of motion, and I the set of inputs (or parameters) of

XIV INTRODUCTION

the system; while L j is the special law of motion ruling when input i is effective, {LJ j E I may be considered the general law of motion an alter­native formulation of which would be the mapping L: I x S _ S, in which case the system is given by (S, L). A system is called determinate if the mappings L j are functions; if they are correspondences (or, functions from S into 2S ) the system is called indeterminate. It is obvious that only for determinate systems we can associate with any state So E S a unique trajectory (or, path)

{so,sJ, ... ,sn,···},

where Sn = L?(so) = Lj (L? -) (so)), L? (so) = so, n = 1, 2, .... An equilibrium state, or simply equilibrium, of a determinate system (S, {LdjEI) for the transformation L j is a state s* E S with the property

For an indeterminate system, an equilibrium may be analogously defined as a state

In this place, it should be pointed out that possessing an equilibrium (or equilibria) is not a feature of the real world but a characteristic of a system which is a theoretical description of certain real world phenomena. Furthermore, this notion of equilibrium is completely stripped of any normative (and, of course, ideological) connotation, and, since it is defined with respect to a certain law of motion L j describing the course of events also outside equilibrium states, is an intrinsically dynamic concept. Formally, an equilibrium is obviously a fixed point of the mapping L j ,

sufficient conditions for the existence of an equilibrium can therefore be found in the well-known fixed-point theorems of Brouwer (if S is a non­empty, compact and convex subset of IRm, and L is a continuous function from S into itselfthen there exists a fixed point s* = L(s*) E S) and Kaku­tani (if S is a non-empty, compact and convex subset of IRm, and L is a correspondence from S into itself such that L(s) is non-empty and convex for all s E Sand {(s, s') I s' E L(s), s E S} is closed in 1R 2m, then there exists a fixed point s* E L(s*), s* E S).

Let us consider a determinate system with an equilibrium s* = Lj(s*) and a mapping D: S - S describing a displacement (or, disturbance) of

INTRODUCTION xv

the system. We then call the state of equilibrium s* of the system with transformation Li (asymptotically) stable under displacement D if

lim L7(D(s*») = s*. n~oo

If a dynamic system does not possess a state of equilibrium there may at least exist some proper subset E ~ S which is closed under the transfor­mation Li and is called an equilibrium region. For a determinate system a state of equilibrium is the (only) element of a singleton equilibrium region. Another special case of an equilibrium region is a cycle, i.e. a sequence of states

C = {Sb LUSk), ... , Ll (Sk)} ,

\with Sk = Li (Ll(Sk») = Ll+ 1 (sd for some I ~ 1. The dynamic system underlying the Walrasian general equilibrium

model is a pair (S, L) with a set of states

S=Px Z,

where P = {p E IR~ * 12:k' = 1 Pk = 1} is the so-called price simplex and Z c IRm is a non-empty, compact and convex subset of the commodity space, and a law of motion

L: P x Z --. P x Z,

where L((p, z») = {(pi, zl)lz l E '(pi) C Z} and

I Pk + max [Ak(z), Bk(p)] p k = --''-'==--_--'''-='-'--'----'c:.c.::..-'--''-_=_

1 + 2:;'=1 max [Adz), Bdp)]

for all k = 1, ... , m. The functions Ak : Z -.IR and Bk : P --. IR are continu­ouswithsgnAk = sgnzk's gnBk = - sgnPk. The correspondence ,: P--. Z which associates with every price structure p a set of excess demand vectors z is called excess demand correspondence. Thus, the system (S,L) is indeterminate. Only in the special case of, (p) being a one-element set for each pEP so that we can define an excess demand function z: P --. Z with '(p) = {z(p)}, the system is determinate; all investigations of the stability of Walrasian equilibria deal with this special case where, in addition, the set of states may be reduced to S = P and the law of motion L: P --. P with L(p) = pi is given a continuous formulation in terms of a system of differential equations (see, e.g. [47]). Determinateness

XVI INTRODUCTION

can only be achieved by assuming strict convexity of consumer preferences (i.e., strict quasi-concavity of utility functions) and of production possibil­ity sets (which excludes not only increasing but also constant returns to scale even within some range). The law of motion of the above specified type L represents the Walrasian principle of'tatonnement' (a simultane­ous rather than Walras's original successive tatonnement [57; 48] ac­cording to which the 'market', or the fictitious auctioneer, raises the price of any commodity if the respective excess demand is positive, and reduces the price if there is some positive excess supply (i.e., negative excess demand), but not below zero. The fundamental characteristic of the tatonnement principle is that the redistribution of commodities among the agents due to the transactions made along a path of price vectors de­scribed by L has no impact on the excess demand correspondence' and, therefore, does not influence the speed and direction of the process of price adjustment. This feature of a tatonnement process may be inter­preted institutionally as meaning that any transaction outside equilibrium is only tentative and will be cancelled in case some of the markets do not clear at the given price structure p and a new vector of prices pi has to be announced.

Whether we can be sure about the existence of an equilibrium of the system (S,L) obviously depends upon the properties ofthe excess demand correspondence ,. If , can be replaced by an excess demand function z it will be sufficient for the existence of an equilibrium p* E P, according to Brouwer's theorem, that z: P _ IR is a continuous function (where Z may be taken as the image z[P] under the mapping z). In the general case of an indeterminate system (S,L), the upper-semicontinuity of the excess demand correspondence' mapping the compact and convex set P into some compact subset Z c IRm (i.e., the closedness of its graph) and its convex-valued ness satisfy the conditions of the Kakutani theorem and, therefore, suffice to establish the existence of an equilibrium. A pair con­sisting of a price structure p* E P and an excess demand vector z* E '(p*) is an equilibrium state of the system (S, L) if and only if z* ~ 0 and pt zt = 0 are fulfilled for all k = 1, ... , m, which is tantamount to the de­finition of general competitive equilibrium not relying on systems theory but just formulating necessary and sufficient conditions for the mutual compatibility of the individually optimizing actions of the economic agents facing a given set of prices. The usual assumptions made with

INTRODUCTION XVII

respect to the behavior of households and finns - in particular, closedness and convexity of consumption and production possibility sets, maximiza­tion of profits by firms, and preference preorderings of the households that are continuous and convex (which is equivalent to continuous and quasi-concave utility functions) and do not possess a satiation point -yield an excess demand correspondence with the properties desired (see, e.g., [1] and [9]). Thus, the standard assumptions secure the existence of a Walrasian competitive equilibrium. It has to be pointed out, however, that in case of an indeterminate system (where the agents' individual optima are, because of 'flat' indifference curves and constant returns to scale in production, not uniquely determined) a decentralized manage­ment of the economy by means of price signals only will not be possible -the 'auctioneer' must also select suitable quantities of which he has tc infonn the economic agents.

The paper by Karl VIND studies a pure exchange economy (i.e., an economy without production) where the preference relations -<h of the trading households h E H are not defined on their consumption possibility sets but on the sets Q h = {x E IRml x + Wh ~ O} of their feasible net trades, where Wh E IR~ is household h's vector of endowments. In such an economy one can, as VIND points out, introduce market institutions, i.e., a set of new agents and sets of actions pennissible for new and old agents. Further­more, for each such economy with market institutions equilibrium con­cepts can be defined. Thus, if no new market agents are introduced, but we allow the households to reallocate their initial endowments among themselves in any way they want, the set of (Pareto) optimal net trades seems to be a natural set of equilibria; it we also pennit reallocation with­in all subsets of households the core (see Section II of this introduction) emerges as a possible equilibrium concept. In the Walrasian model, a new agent is introduced as a market agent who selects a price vector p and then lets all other agents choose any net trade X h E Q h with PXh ~ O. A corresponding equilibrium concept is the Walrasian competitive equilib­rium which, in this framework, is defined as a collection of net trades {Xh} hER with LhERXh = 0 and a price vector p* such that p* X h = 0, h E H, and Xh -<hY imply py> O. VIND proves that the generalization where {x E IRm Ipx ~ O} is replaced by an arbitrary subset Me IRm with M + M c M and 0 E M, which he calls a simple market, leads to almost the same set of equilibria.

XVIII INTRODUCTION

In the Arrow-Debreu-style Walrasian model the preference relations ofthe consumers are taken to be complete quasi-orderings: The 'rational' consumer is assumed to be capable of ordering all possible states of the world so that confronted with two such states he will either be able to decide which one he prefers or else express indifference between them; furthermore, his preferences are supposed to show consistency by being transitive. These conditions are among those which are sufficient to yield upper-semicontinuous demand functions ofthe households. On the other hand, however, they seem rather unrealistic if, e.g., one thinks of an eco­nomic agent as an organized group of persons, rather than a single indi­vidual, with a collective decision rule specifying that a state is preferred to another only ifit is preferred by all members (or, at least by one while the others may be indifferent) in which case the group will not display a complete preference ordering even if its individual members are 'rational' in the above strong sense. But also the individuals themselves rarely show a choice behavior that can correctly be represented by a complete and transitive ordering of alternatives. Thus, it would be important to de­monstrate that the central result of the Walrasian theory, namely the existence of a competitive equilibrium, can be obtained under less restric­tive conditions on household preferences. Building upon results showing the existence of equilibria in markets with continua of traders, WEDDEPOHL proves the existence of an equilibrium in a market with a finite number of consumers whose behavior is characterized by incomplete preferences. GALE and MAS-COLELL show that neither completeness nor transitivity of preferences are necessary to establish the main results of Walrasian equilibrium analysis: Their only assumption is that for any state of the world xa household h is able to specify the set of states Ph(x) which he prefers to x where the only ordering condition retained is irreflexivity, x ¢ Ph (x). As in the traditional model, the convexity of Ph (x) is indispen­sable, and a continuity and a non-satiation condition have to be imposed.

Convexity of production and consumption possibility sets and of pref­erences is one of the most important and most heroic assumptions necessary to obtain an upper-semicontinuous and convex-valued excess demand correspondence. The mathematical tool for dealing with non­convexities is a theorem by Shapley and Folkman (see, e.g. [25J; also [1 J) saying that any point in the convex hull of the sum of n arbitrary (i.~., not necessarily convex) non-empty subsets Xi c: IRm can be constructed as

INTRODUCTION XIX

the sum of points in the Xi except for at most r points that have to be taken from the convex hulls of the respective sets Xi (where r does not depend on n). Thus, the standard method for treating non-convexities is to convexify the problem, i.e., to replace production, consumption, and preference sets by their convex hulls, assume (or establish economically meaningful conditions under which) these convex hulls are closed sets, and obtain an equilibrium (p*, z*) for the convexified economy which can be shown (by virtue of the Shapley-Folkman theorem) to be not too far away, in terms ofthe gap between the convexified excess demand z* ~ 0 and the true excess demand z* E ((p*) which need not be ~ 0, from the so-called approximate equilibrium (p*, z*) of the non-convex economy. For a non-convex economy with a large number of agents of more or less equal size, its approximate equilibrium will be virtually indistinguishable from the convexified economy's equilibrium in the sense that calling a price vector p* will, for all practical purposes, allow market clearing in the original economy. The approach proposed in HELLER'S paper is not to convexify the production, consumption, and preference sets but to establish the continuity of the original excess demand correspondence, and then convexify it. For this purpose, some general propositions are provided which are useful in securing continuity in the absence of con­vexity. It is an advantage of this approach that assumptions made on the true sets rather than the convexified sets are easier to be interpreted. Moreover, one also obtains more satisfactory approximations to equili­brium.

II

A concept which has gained considerable importance in general equili­brium analysis is that of the core of an economy. The notion of core was originally introduced by Edgeworth [11] under the name of contract curve and was also used, independently of Edgeworth, by Bohm-Bawerk [6] in his theory of marginal pairs; under the influence of the theory of games [49] it underwent a thorough generalization. The core theory is remarkable for the smooth transition it provides from the problem of isolated exchange between two traders (bilateral monopoly) to that of exchange in an economy with arbitrary numbers of agents and commo­dities.

xx INTRODUCTION

Let us consider a pure exchange economy (without production) with a finite number oftraders h E H characterized by consumption possibility sets X h C IR~, initial endowments Wh E X h, and the usual preference pre­-orderings ::$h' An allocation of resources in such an economy is given by a matrix A a row of which describes the distribution of a certain commodity among the traders, while a column ah E IR~ stands for the corresponding trader's allotment of goods. By d = {A = (ah) I LheHah ~ ~ LheHWh, ah E X h, hE H} we denote the set of all feasible allocations. The fundamental supposition of the Edgeworth theory is that exchange can be understood as a redistribution of resources among the traders in a way which, starting from the allocation A = (whheH, increases at least one agent's utility without diminishing the other traders' welfare, and, moreover, that each subgroup T c H may form a trading coalition reallo­cating its resources among its members.

We say that an allocation A dominates another allocation A' via coalition T, denoted by A domT A', if all traders in T", (() strictly prefer A to A', i.e., if for all columns ah of A and a~ of A', hE T, a~ -<hah, and, moreover, Lh e T ah ~ Lh e T Who Let us adopt, for the sake of convenience, the following notation:

DomTA = {A'E dlA domTA'},

DomA = UTcHDomTA,

DomTll = UAd/CA DomTA,

Domll = U TcH DomTll.

In case of full freedom to trade with anyone, i.e., freedom for every trader to join any coalition, we may expect no trader to be satisfied with his allot­men t ah in an allocation A ifhe is able to find partners offering better terms. We call an economy (or, rather, the behavior of traders) competitive - in contrast to collusive behavior - if every trader is always willing to desert any coalition for the prospect of some increase in utility in another trading arrangement. Consequently, competition can be regarded as the process of eliminating dominated allocations by contracting and recontracting [11] which may be conceived of as a fictitious tatonnement-like procedure or may, under certain rather restrictive assumptions of stationarity, take place in real time. In terms of systems theory, the competitive process of

INTRODUCTION XXI

recontracting can be described by an indeterminate dynamic system (S, L) with S = d and a law of motion L: d -. d where

L(A) _ {ff = {A' Ed lA' domTA for some T c H} if ff =f. 0, {A} if ff = 0.

Thus, an allocation is a state of equilibrium in which the process of re­contracting stops, if and only if it is undominated. The set of all equili­brium states, i.e. the set of all undominated allocations f(l = d \ Domd, is called the core of the (pure exchange) economy.

One of the main attractions the concept of core has held for general equilibrium theorists is its intimate and peculiar relationship to the notion ofWalrasian competitive equilibrium whose underlying 'price dynamics' is in some sense dual to the 'allocation dynamics' of the Edgeworthian theory. Under the usual assumptions made on preferences, consumption sets and endowments it can be shown that each allocation A* = (anheH

corresponding to a Walrasian equilibrium (p*, z*), where z* = LheH

(at - Wh) E ((p*), is an element of the core, i.e. cannot be improved upon by any coalition of economic agents. This property at the same time constitutes a proof of existence of equilibria for the recontracting process, i.e., of a non-empty core. Moreover, under certain conditions the core 'shrinks' with increasing numbers of traders and converges to the set of Walrasian equilibrium allocations; for continuum economies as the limiting case of 'large' economies the core coincides with the set of Walrasian equilibrium allocation [31 J.

While the notion of core is usually considered a precise statement of in particular Edgeworth's ideas, Hans KEIDING argues that the concept of exchange equilibrium developed by Vind is closer in spirit to Edgeworth's and Jevons's thoughts. An exchange is defined as a function e: H x H -.[Rm

with e(h, h') = - e(h', h) for all h, h' E H. It is called feasible if Lh'eH

e(h, h') = X h is a net trade of agent h for all hE H and, moreover, the net trade matrix (xhheH is feasible, i.e., LheHXh = O. We say that a feasible exchange e can be improved upon if there is a coalition T cHand a feasible exchange e' such that e' (h, h') = e(h, h') or e' (h, h') = 0 for all hE T, h' ¢ T, and X h -<hX~ for all hE T (where Xh, x~ are the net trades of the households generated by the exchanges e and e'). An exchange equilibrium is a feasible exchange that cannot be improved upon. The

XXII INTRODUCTION

result of KEIDING'S paper is however that, except for very special situa­tions, it does not matter whether we use the concept of exchange equili­brium or that of the (net trades) core. He demonstrates that given any allocation in the core of a finite economy an exchange equilibrium can be found which results precisely in that allocation. By slightly altering the definition of exchange equilibrium he gets a restriction on the class of core allocations obtainable as exchange equilibria. Finally, KEIDING

shows that similar results hold for economies with a measure space of agents.

So far we have only dealt with the core of a pure exchange economy. The core theory can, however, be extended to the case of economies with production though there are different approaches to taking productive activities into account. One analytical possibility is to associate a pro­duction technology set with each coalition of traders without introducing firms, profits, etc. [31]; another approach is to specify an economy with a certain number of production possibility sets shares of which are owned by the individual consumer-traders who remain the only decision-making units [1 J. A third way is chosen by VAN MOESEKE: Studying an economy with a measure space of households and endowing each coalition, i.e., each element of a a-algebra r on H, with a production possibility set, he also introduces prices and a (measurable) profit function on H whose integral over T E r yields the maximum profit attainable by coalition T at a given price vector p. VAN MOESEKE calls an allocation competitive at p if each consumer maximizes his preferences given his budget con­straint (determined by his profit income), total profits are maximized over the set of production plans available to the grand coalition H, and excess demand is zero. The core relative to p is then defined as the set of un­dominated allocations where an allocation is said to dominate another one via some coalition T if it is weakly preferred by all and strictly preferred by at least one member of T and can be afforded by T at the given price vector p. VAN MOESEKE proves that an allocation is competitive at prices p if and only if it is an element of the core relative to p.

However attractive the notion of core may appear to the general equilibrium theorist it must not be overlooked that it suffers from a serious conceptual deficiency. The theory of games seeks to define, prove the feasibility of, and compute rational behavior in multi-person decision making situations involving conflict and cooperation. As is argued in

INTRODUCTION XXIII

[44], a satisfactory, or at least acceptable, concept of solution (i.e., rational behavior) ought not to be invalidated by the knowledge of the theory on part of the agents - it should be immune against 'theoryab­sorption'. Since there are, in general, allocations outside the core which are not dominated by any allocation belonging to it, the core does not satisfy this condition: In the process of contracting and recontracting, traders may be played off against each other and manoeuvred into core allocations with which they are worse off than with certain allocations outside the core. Thus, for some traders it proves profitable to stop the process of recontracting at some dominated imputation which they are able to agree upon. These considerations can be expressed in the follow­ing, somewhat paradoxical, statement [44]: If the traders are rational (in the sense of always choosing the preferred alternative) and if they know that a stable outcome of the bargaining process can only be an ele­ment ofthe core -- and what the core looks like - then, in general, no allo­cation in the core will be stable. Thus, if we define collusion as the prac­tice of stabilizing dominated allocations by means of 'combinations' (as Edgeworth [11] called the cartel-like precontracts between traders not to recontract without the consent of all), we are led to conclude that competition can only be expected to prevail if the behavior of the traders is characterized by a peculiar mixture of rationality, complete information about the opportunities the market offers, and short-sightedness.

Combinations may be conceived of as exogenously given - as part of the rules of the game, so to speak. It seems that Edgeworth [11] had in mind this sort of combinations when he was inquiring into the possible imperfections of competition that prevent the contract curve (core) from shrinking when the number of traders increases. In this case, a combina­tion is viewed as existing irrespective of the actual distribution of benefits among its members, it is treated as a separate agent, and the introduction of combinations into the model of an economy amounts just to a reduc­tion of traders. Recently, also Aumann [3] has treated the phenomenon of collusion by studying the core of a market game (with side payments) in which a certain subgroup of traders is regarded as a single agent, term­ed 'syndicate', and no coalition is considered that contains some but not all members of the syndicate. This approach yields the paradoxical result that syndication may be disadvantageous in the sense that when a sub­group T of traders is syndicated, there are imputations in the core that

XXIV INTRODUCTION

are worse for T than the core imputation which is the most disadvantage­ous for the traders in T when they are unsyndicated. In reality, however, we observe cartels, unions, etc. to disintegrate when certain conditions of equitable distribution of benefits are not met. Thus, another, more sophisticated and realistic approach to the analysis of collusion is to look upon combinations as coalitions which may be viable as long as the utility payoffs appear satisfactory to each one of their members but will break up if the distribution of the proceeds does not appeal to some of them [44]. The solution concept originally propounded by von Neumann and Morgenstern [49] for cooperative games with side payments, the so-called stable-set solution, overcomes the difficulties encountered by the core. A stable set of allocations!/' c d is defined by the two proper­ties

!/' n Dom!/' = 0, and

!/'uDom!/' = d,

or, in one expression, by

!/' = d \ Dom !/'.

In other words, a stable set of allocations is both internally stable (allo­cations in !/' do not dominate each other) and externally stable (any allocation not in !/' is dominated by at least one element of !/'). If a stable set exists - which need not be the case since, on the contrary, games have been found that do not possess stable set solutions - it always contains the core. The core itself is obviously internally but not necessarily exter­nally stable, which is exactly the deficiency discussed above. It can be argued [44] that a stable set is a rational standard of behavior specifying not only those allocations which are equilibrium states in case of com­petitive behavior - the core CC -, but also those which both provide an incentive for collusion (by not being dominated by any allocation in CC) and enable some combinations to uphold them - the set of collusive allocations!/' \ CC. There may be economies for which the core is stable in which case it is the unique stable set of allocations. In the classical side-payments case there is, e.g., the class of convex games - dis­playing a snow-balling or band-wagon effect according to which the in­centive for any agent to join a coalition increases with increasing size of

INTRODUCTION xxv

coalition - for which the core is always stable. BOHM in his paper, besides giving examples which show that, in general, the core of an exchange economy will not be stable, tries to find sufficient conditions for stable cores by introducing a natural generalization of the notion of convex games for the non-side-payments case. His result is essentially a negative one: Although the question of equivalence of core and unique stable set is left open as unsolved, it is shown that convexity is a cardinal concept which can be destroyed by some monotonic transformations of utilities and that convexity cannot be easily generated by imposing some natural conditions on the economy, even in the special case when it can be re­presented as a side-payment game.

III

As Maurice ALLAIS, in his critical review of contemporary theories of general economic equilibrium and maximum efficiency, rightly points out, the formulation given to the general equilibrium problem by Arrow, Debreu, and others [1; 9] veils, because of its generality and abstractness, a lot of concepts - like saving and investment, the distinction between durable goods and their services, the rate of interest, the notion of the value of any durable good as being equal to the sum of discounted present values of its future services, etc. - which are indispensable for economic theory. It is, however, rather easy to make the above mentioned concepts, and besides these a host of others, explicit by simply defining in closer detail what we mean by a 'commodity' [9]: A commodity is a material good or service characterized by its physical properties, the date of its availability, the location of its availability, and, possibly, the uncertain event on the occurrence of which its availability is conditional. If we focus on the location of availability we obtain a spatial interpretation of the Walrasian model (for a special problem in spatial economics see BECKMANN). The temporal interpretation of the Walrasian model is of particular interest. In thi~ framework we may define the concept of inter­est rate by considering ratios of prices of the 'same' commodity delivered at different dates - there will be as many 'short-term interest rates' (not to be confused with monetary rates of interest) as there are commodities, defined by characteristics other than time, and elementary periods in the economy; the corresponding longer-term interest rates are implied by,

XXVI INTRODUCTION

and can be calculated from, the short-term rates (see, e.g., [26, pp. 141ff.J, [9J and [5J). The elementary time periods to be taken into account are defined in accordance with the time structure of production. While in the general Arrow-Debreu version of the model the production possibil­ities of the firms fE F are described by closed and convex (besides some other properties) sets Yf c IR m an element of which, a feasible production plan Yf' is a vector specifying the net amounts (flows) of goods and services used (negative numbers) and produced (positive numbers), the temporal interpretation of the model suggests the introduction of production technology sets Crt c lR;q for each period t (where q is number of different types of goods apart from dates of availability). An elementary produc­tion plan (at> bt + 1) E Ct (for the sake of simplicity we drop the index f) contains the non-negative vector of inputs at the beginning of period t (including stocks), at, and the resulting non-negative vector of outputs at the beginning of period t + 1 (again including stocks), bt + l , such that bt - at = Yt is a feasible net input-output vector of goods available at date (the beginning of period) t according to the production plan Y [39; 5J. This so-called von Neumann method [29; 45J of describing production processes implies, of course, the enlargement of the list of different types of goods by all the intermediate products and capital goods of all vin­tages made visible in this sequential stock model of production (which yields, among other things, a general and elegant theoretical treatment of the problem of depreciation of capital goods). The description of pro­duction possibilities over time by sequences Cft of production technology sets for each firm also enables us to take into account (but hardly to explain!) all possible kinds of technological change - the emergence of new goods (which have to be contained, of course, in our list of q types of goods but are made available as natura(resources or technologically feasible products only from a certain point of time on) as well as the emergence of new processes; the practical economic usage and disappear­ance of technologically available products and processes may be explain­ed on grounds of profitability. Moreover, there is no need to assume that the production possibilities Cft be given independently of each other. A plausible formulation would be to regard the Cfr's as correspondences

Cft : X Cft ,(.) --+ lR!q t'<t

where Cjt(a l , b2 , ... , at - b bt ) describes the production techniques avail-

INTRODUCTION XXVII

able to firm f in period t in case it had chosen the production plans (aJ' b2), ... , (at-J, bt) in the past. This formulation allows the modeling of irreversibilities and of adjustment costs due to changes of technique in the course oftime [5; BROCK -SCHEINKMAN], and of certain kinds of endogen­nous (e.g., 'learning-by-doing') technical progress. Endogenous technical progress will in many cases be experienced by the firm as an external effect which may be described by the further generalization

Cft : X [X Cft ,(.)] ~ Riq • feF t'<t

As long as we do not take into account transactions cost, short-run and long-run profit maximization by firms are equivalent if and only if the firms' production technologies are independent over time. In any case, the model of balanced (semi-stationary) growth [5; 27; 45; NAGATANI­NEHER] is thus just a very special case of the temporal interpretation of the Walrasian model. On the other hand, there can be no doubt that the intertemporal Walrasian model- though its conceptual apparatus covers, at least in principle, a considerably broader domain than the traditional growth models or even the von Neumann model and its extensions [45] - does not provide an adequate representation and explanation of all the evolutionary phenomena involved in economic development which have been stressed by GEORGESCU-ROEGEN (see also [14]).

The methods of explicitly dating the commodities in an Arrow-Debreu model yields for at least two reasons only a rather sterile concept of time. One reason is that because of the peculiar 'dynamics' of the tatonnement procedure which does not take place in real, historical time measured, e.g., by the elementary periods of production - exchange and the formation of prices remain essentially timeless. The other reason - complementary to the first one which makes exchange completely surprise-free - is that the traditional Arrow-Debreu-type Walrasian theory precludes any endogenous economic uncertainty from the model. The extension of the model to the case of (exogenous) uncertainty as pioneered by Arrow and Debreu [9] is based on the concept of contingent commodity. A contin­gent commodity is defined not only by its physical properties, location and date of availability but also by the states of the world in which it is available. It is assumed that at each point of time there will be a family of elementary observable events, represented by a partition of all possible states, so that an elementary contract consists of the purchase or sale of a

XXVIII INTRODUCTION

certain quantity of some commodity to be delivered at a specified location and date in case a specified elementary event occurs. For each contingent commodity the Walrasian 'auctioneer' calls a price that is known with certainty to all economic agents. By this construction, the firms' present values and the net worth of each consumer (i.e., his budget constraint) remain magnitudes known with certainty so that no problems of indivi­dual credit-worthiness and bankruptcy arise, and there is no point in trading shares.

Thus, even if exogenous (environmental) uncertainty is incorporated by employing the concept of contingent commodity, the Arrow-Debreu equilibrium continues to be a 'full equilibrium over time' in the sense of Hicks [26]. In reality, however, the crucial assumption of the existence of a 'perfect' market for each contingent commodity is seldom fulfilled. The recognition ofthis fact leads to the Hicksian [26] concept of 'tempo­rary equilibrium' where the 'auctioneer' only calls the prices of some goods and services, e.g. those presently available and some futurecommod­ities for which forward markets are assumed to exist, while for the prices of all the other commodities the economic agents possess generally diver­gent, and possibly probabilistic, expectations. In all other respects, the typical Walrasian characteristics are retained, in particular the tatonne­ment dynamics whose state space now includes, of course, only the prices generated by the 'market' in the present period while all the price expecta­tions are inputs to the dynamic system. This distinction between prices known with certainty at which contracts can be made now and prices just anticipated (either with subjective certainty or uncertainty) creates the dichotomy between the present and the future which is obscured by the full-equilibrium analysis. It should be recalled, however, that it had been Walras himself who in his treatment of capital formation and credit [57, Part V] presented for the first time a relatively complete model of tempo­rary equilibrium. By distinguishing carefully between the purchasing (or stock) prices and the rental (or flow) prices of durable goods Walras succeeded, as DIEWERT points out, in introducing a rudimentary model of the stock exchange. DrEwERT'S paper takes up Walras's approach in a modern analytical framework. While he sticks to the postulate that expectations about future prices are held with certainty he assumes them to depend in a continuous way on present prices which covers not only Walras's case of static expectations but also adaptive and rational

INTRODUCTION XXIX

expectations. Furthermore, DIEWERT indicates how by introducing vintages of capital goods and making depreciation dependent upon the utilization of durables, Walras's original assumptions of constant depre­ciation rates and measuring depreciated durable goods in units of the respective undepreciated goods can be relaxed. DIEWERT also touches upon the question of which data would have to be collected in order to implement a macro-econometric version of Walras's model of capital formation. For a long time, capital theory has been treated in an exclusively stationary or semi-stationary (,steady-state') full-equilibrium context; DIEWERT'S contribution is a step towards a short-run, temporary equilib­rium theory of capital and investment (see also [5]) which, in combination with an adequate theory of money, would be an integral and fundamen­tal part of a satisfactory theory of industrial fluctuations [20; 21; 22; 29].

It is the exclusion of uncertainty or the Arrow-Debreu treatment of uncertainty by means of contingent commodities and conditional con­tracts which, in Mervyn KING'S qpinion, also accounts for the failure of the traditional general equilibrium model to capture the essence of the modern corporation with its complex interaction between labor force, management and shareholders. In his view, in an economy where there are fewer securities than states of the world the stock market is not only a market for assets which determine hedging opportunities but also the arena where individuals and groups are fighting for the control of parti­cular companies. The questions KING poses are: What is the nature and aim of firms? And, is it reasonable to suppose that firms maximize the market value of their shares, or are there other objectives to be investigat­ed? KING demonstrates that unanimous agreement among shareholders in matters of corporate policy is a very special case which cannot provide a satisfactory basis for a theory of the firm in a stock-market economy with an incomplete set of markets. He also shows that the market-value maximization criterion may yield policies different from those which minimize the risk of being taken over. TINTNER surveys a variety of approaches to dealing with anticipated prices in general equilibrium models. 'Risk' (i.e., the case of known probability distributions) and 'uncertainty' (i.e., the case where the probability distribution is unknown but some a priori probability distribution exists) are discussed in the context of a simple portfolio selection model. TINTNER shows that homo-

xxx INTRODUCTION

geneity of supply and demand functions is preserved in the case of' risk' but not always in the case of'uncertainty'.

An example of exogenous uncertainty is considered by HEAL whose analysis is motivated by the observation that a consumer is often un­certain about the quality of a product which he intends to buy at a given price. HEAL studies several simple partial equilibrium models shedding some light on the effect of uncertainty about product quality on the behav­ior of consumers and producers. As long as we assume that each trader's preferences can be scaled in terms of utility and subjective probability so that, according to the expected utility hypothesis, each economic agent may be characterized by a subjective probability measure on the set of complete histories of the environment (states of the world), exogenous uncertainty, i.e. uncertain expectations concerning future environmental events, does not raise any further conceptual problems: given their in­formation at any date about the history of the environment up to that date, the agents' conditional subjective probabilities of future events are well defined [53; 55]. The assumptions on which this approach to deal­ing with exogenous uncertainty rests are, however, rather strong and may appear implausible in many cases. This holds in particular for the promise that the individuals have full knowledge of the set of all possible histories of the environment (although they do not know which state of the world will be realized), an assumption that excludes what may be termed evolu­tionary uncertainty or 'true' surprise from the picture. For this and relat­ed reasons, many economic theorists - among them Keynes [33, pp. 148ff.] and Mises [42, pp.105ff.] - have rejected this approach to un­certainty as irrelevant for the description of decision-making problems facing the economic agents. But even if we accept the subjective proba­bility approach to environmental uncertainty as a first approximation this does not solve the problem of how to deal with endogenous uncertain­ty, i.e. the economic agents' uncertain expectations about the realization of events that are the outcome of other individuals' actions. In fact, this is exactly the type of problem for the treatment of which the theory of games has been invented [43; 49; 56; SHUBIK]. In the framework of Walrasian theory where the price signals set by the 'market' are exclusive in guiding the price-taking individuals' optimizing behavior, the problem for each trader reduces to forecast the future market-clearing prices given his information about the history of the environment up to the present

INTRODUCTION XXXI

date and about the sequence of temporary equilibria realized so far. There are several possible approaches to describing theoretically how the economic agents solve this problem, i.e. how their anticipations are formed and revised over time. One is the so-called rational expectations hypothesis (or, perfect foresight approach) which postulates that the individuals "be able to forecast, in some sense, the equilibrium prices that will prevail in the future under all alternative states of the environ­ment". [55, p. 62; also 54] Apparently, this approach demands of the economic agents" a capacity for imagination and computation far beyond what is realistic" [55, p. 62], and it has been argued that it is precisely the main advantage of a decentralized market economy that it does not re­quire of its members such superhuman abilities [23]. Thus, a limited rationality, adaptive expectations hypothesis according to which the traders' planning horizons (and memories) are bounded and their expecta­tion formation follows some rule of thumb may be more adequate for a dynamic temporary equilibrium theory [15].

IV

As mentioned above, the short-run dynamics leading to a temporary (Walrasian) equilibrium is of the Ultonnement type. It is, however, not difficult in principle to devise a dynamic system which describes the suc­cession of temporary equilibria over time. An element of the state space of such a dynamic system is a vector whose components are the price structures realized up to the present date; its dimension equals the num­ber of observations relevant to the formation of expectations about future prices. The system's law of motion shortens each of these vectors by the first component and adds the new temporary equilibrium price structure. Obviously, the dynamic system will be determinate if and only if there exists a unique temporary equilibrium for each period. An equilibrium of such a system is called a stationary temporary equilibrium. The exis­tence and stability of such equilibria has so far been investigated only under rather special and restrictive conditions (see, e.g. [15] and the literature quoted there), about other properties of systems of this type - for example, the existence and stability of cycles which would be of importance for the microfoundations of the theory of industrial fluctua­tions - hardly anything is yet known. There are two principal variants

XXXII INTRODUCTION

oftemporary equilibrium dynamics: the Hicks [26J and the Lindahl [38J theory. In the original Hicksian approach it is assumed that anticipations of future prices do depend on the current temporary equilibrium prices that are yet to be formed by the usual tatonnement procedure. By virtue of this construct, the individuals' expectations themselves are in each period subjected anew to the fictitious, essentially timeless tatonnement dynamics, and are thus virtually formed afresh, simultaneously with the current temporary equilibrium prices, at the beginning of each period. The upshot of this Hicksian formulation is that it fails to effectively link the individual periods and thus lacks - for the same reason as the so­called instantaneous Keynesian multiplier does - an essential element of 'true' dynamics. By contrast, the Lindahl theory which is in this respect nowadays preferred by Hicks himself [27J assumes that only past prices at which transactions had already been concluded effect the economic agents' expectations about future prices on the basis of which current equilibrium prices form. The dynamic system whose trajectories corres­pond to sequences of temporary Walrasian equilibria bears certain features of a non-tatonnement process in so far as transactions are actu­ally carried out over the trajectories at prices that turn out to be in dis­equilibrium from a long-run point of view.

While there may be severe fluctuations in employment over such sequences of temporary (Walrasian) equilibria, there will never be in­voluntary unemployment in a technical sense since by definition markets always clear at the prices called by the 'auctioneer'. Only if we adopt the 'fixprice method' [27J of describing the economic process, i.e. if we assume that at the beginning of an elementary trading period a price structure exists at which all transactions have to be carried out but which is an historically given, not necessarily market-clearing price vector, phe­nomena that are typical of Keynesian economics may emerge. Along these lines, HOWITT analyzes the consequences of trading at 'false' prices for consumer demand in terms of a 'cash-constraint effect' - which describes the effect of the rationing experienced in the previous period on the trader's cash holdings, and thus his net demands, in the current period -and a 'spillover effect' which works through the impact of experienced rationing constraints on expected current and future rationing quotas and prices. KORLIRAS examines the nature and main characteristics of the 'disequilibrium' or non-tatonnement methodology in the context of

INTRODUCTION XXXIII

macroeconomic theory. Economists have come to identify the concepts of 'equilibrium' and 'Walrasian (t<1tonnement) equilibrium' to such an extent that often any situation in which markets do not clear for demands and supplies derived from individual optimization at given prices is termed 'disequilibrium' [34]' In a technical sense, however, in which 'equilibrium' is just the property of a certain dynamic system such a situation need not necessarily be a disequilibrium but may very well be a state of equilibrium which does not change under the law of motion of the respective system. If prices are rigid and markets do not clear if only price signals are taken into account, traders on the long side of the market have to be rationed according to some rationing principle. A host of differ­ent rationing schemes are imaginable (first come, first served; uniform rationing; rationing proportional to individual excess demands; queu­ing rules; etc.), and different rationing schemes may be used in different markets being part of the institutional arrangement of the economy. The quantities which the traders on the long side are allowed to buy or sell, respectively, may be thought of as being chosen, in accordance with the rationing rules that apply, by the 'market' or the counterpart of a Wal­rasian 'auctioneer' in a quantity-tatonnement process such that actual transactions will take place only when a set of mutually compatible rationing prescriptions have been found [10].

This implies an information process which, like the Walrasian tatonnement, functions apart from the trading process itself, but relates to quantities, not to prices. Households are informed of their real income before trade takes place. There are no false purchases of consumption goods. If generalized to all markets, this would imply an instantane­ous multiplier. [37, p. 74-75].

The demand and supply functions derived from individual optimization that is not only constrained by the usual budget hyperplane derived from endowments and price signals but also by the rationing signals perceived in all markets have been termed 'effective' demands and supplies, respec­tively, by Clower [7J in order to contrast them with the 'notional' de­mands and supplies of traditional Walrasian theory (in fact, Clower de­fined the effective excess demand for a certain commodity as the result of an optimizing behavior taking into account all the perceived constraints except the rationing in the market for the commudity under considera­tion). It has to be pointed out that Clower's concept of 'effective' excess

XXXIV INTRODUCTION

demand functions and Keynes's [33, pp. 23ff.] notion of' effective demand' are not identical. Still, in so far as in Keynes's General Theory [33] - contrary to the model employed in his Treatise [32] - "the Marshallian ranking of price - and quantity-adjustment speeds is reversed" [37, p. 52] central results of the rationing-tatonnement analysis and important as­pects of Keynes's theory, in particular his consumption function, are related in spirit so that calling the equilibria of the dynamic system describing the quantity tatonnement at fixed prices Keynesian equilibria [4] is not wholly unjustified. The perceived rationing constraints which enter the economic agents' optimization problems provide the vehicle for the spillover effect of trading at non-market-clearing prices that is neither present in the more traditional non-tatonnement models [47; 48; 12; 13; 19] - which only consider a distributional income effect and as­sume that each time prices have changed (because markets did not clear) traders again expect being able to buy or sell any quantity they wish - nor has been treated in a fully satisfactory way by Patinkin [52] in his attempt to marry neoclassical and Keynesian economics. Again, the intra-perIod rationing-tatonnement can be converted into an intertemporal process by setting up a dynamic system whose state variables consist of price profiles and corresponding rationing signals for as many periods as are relevant for the economic agents' expectation formation. Under the system's law of motion a state vector is shortened by the components pertaining to the earliest period while a new price structure and a set of (momentary) equilibrium rationing signals are added. The new price structure may be chosen according to the rule that prices are raised if and only if binding rationing constraints on the demand for the respective commodities have been observed in the previous period and are left un­changed if and only if no rationing constraints were binding. Obviously, such a dynamic system whose trajectories correspond to sequences of so-called Keynesian temporary equilibria will be determinate only if there exist unique short-run (Keynesian) rationing equilibria for each period - which is even more unlikely than unique Walrasian temporary equilibria. The crucial question concerning dynamic economic systems of this type is not so much the problem of the existence of equilibria - if all prices are flexible in the long run as postulated above then equilibrium states will show all the characteristics of Walrasian (full-employment) stationary temporary equilibria - but the question of the stability of

INTRODUCTION xxxv

equilibria: It is typical of neoclassical economics, even of neoclassical 'Keynesians', that they attribute the persistence of underemployment situations exclusively to some long-run price rigidities (e.g., long-run downward rigidities of nominal wages) - if we incorporate such no­change rules for certain prices even when markets do not clear into the dynamic law of motion of the system we may arrive at underemployment equilibria, or equilibria with so-called repressed inflation, or both -whereas Keynes [33, pp. 257ff.] definitely doubted the ability of the sys­tem to reach a full-employment equilibrium even if complete longer-run flexibility of all prices, including wages and interest rates, were secured (quite on the contrary, he went so far as to recommend stabilization of money wages as a remedy against a further drop in the level of economic activity!). In his paper, KORLIRAS analyzes the structure and implications of Clower's [7] 'dual decision hypothesis', and establishes certain propo­sitions concerning the validity of Walras's law which, in terms of 'effec­tive' excess demands, does not generally hold. Furthermore, he examines the adjustments occurring in 'disequilibrium' situations in the context of a period-analysis framework with discrete time intervals (Hicksian weeks) which lead, under a variety of simplifying assumptions, to equilib­ria that may involve both unemployment and inflation. RADER investigates short-run underemployment equilibria of effective-demand systems with flxed prices and wages, and, alternatively, with variable price levels but still fixed relative prices and real interest rates. In this context, he studies comparative-static properties and possible government stabilization policies. The contribution by BARRO and GROSSMAN mainly focuses on the behavior of households within a simple aggregative framework in­volving labor services, consumer goods, and fiat money. Firms employ labor services to produce non-storable consumption goods, and the government creates and destroys money by transfer payments and taxes, respectively. After sketching the behavior of households under general­market-clearing conditions, BARRO and GROSSMAN turn to their principal analytical goal of stud"ying household behavior in situations where the prevailing wage rate and price level generate excess supply of labor ser­vices. Because money serves as a store of value consumer decision-making remains an intertemporal problem (in spite of the non-storability of produced goods), and the choice of consumption and savings time paths depends not only on the current employment constraint but also on the

XXXVI INTRODUCTION

expected future constraints. It is assumed that the expectations consumers hold concerning their profit income are consistent with the anticipated employment opportunities. This yields effective demands for commodities and real money balances which are functions of the level of employment. The marginal propensity to consume out of current income obtained in this model when working with a lifetime budget constraint is implausibly low; BARRO and GROSSMAN show that it would be considerably higher and more in the range required for significant multiplier effects if a li­quidity constraint, i.e. a condition that real money balances must always be non-negative, were introduced. Non-market-clearing phenomena may also play some role in financial markets. JAFFEE introduces a theo­retical basis for modeling disequilibria and spillover effects in such markets and develops an econometric approach to estimating the proposed dis­equilibrium specification from flow-of-funds data. The papers by STARRETT, AZARIADIS, and DEMOPOULOS concentrate on some specific problems of dealing with the labor market in macroeconomic models. STARRETT challenges the monetarist view that with rational economic agents money is neutral in the long run and that there is no long-run stable Phillips curve on which economic policy could be based. He de­monstrates that money can be non-neutral even in a model where indi­viduals are rational maximizers exhibiting no money illusion, and shows that this result leads, if one drops the assumption that wage adjustments were instantaneous, to a Phillips curve trade-off. AZARIADIS analyzes an economy where, under conditions of technological uncertainty, the services of risk-averse workers are employed to produce one consumption good. Labor contracts arising out ofthe dual role of firms as both employ­ers and insurers react to random shocks by varying employment and the distribution of factor payments rather than varying the wage rate and leaving distribution unchanged. In the market for current output equilibrium will then prevail only on average. Consequently, if contracts are not instantaneously renegotiable, non-zero excess demand for labor will be sustainable and, under a variety of non-price rationing rules, be closely related to temporary deviations of income distribution from its competitive level. DEMOPOULOS'S paper develops a macroeconomic model which, contrary to the traditional IS-LM analysis, explicitly in­corporates labor market behavior in terms of a preference function, acquisition of information, expectations, search costs, and speeds of

INTRODUCTION XXXVII

adjustment. The labor market is then linked to the output and money markets, and the adjustment of output and prices to a 'normal-employ­ment output' is studied in the context of the recent history of change in aggregate demand. ARNDT develops a model of an open economy com­posed of markets for goods, bonds, and money and examines its behavior under non-tiHonnement conditions when markets fail to clear at prevail­ing prices and when price and quantity adjustments are not instantaneous. The distinction between constrained and unconstrained demand and supply functions on the micro level implies an analogous dichotomy for macroeconomic aggregates. Thus domestic and foreign balance functions, with and without constraints, are introduced and their behavior in dynamic adjustment is studied. It is shown that the variability in pro­ductive capacity - ARNDT'S model is insofar a medium-term one as it takes the capacity effects of investment on macroeconomic adjustment into account - has important implications for the path of dynamic ad­justment, thereby affecting stabilization policy. Finally, the role of buffer stocks in determining the proportion of adjustment which is achieved by price changes and that which results from output changes is examined. BRITTO in his paper investigates the problem of the optimal adjustment to be made by a country finding itself in a state of fundamental disequilib­rium the extent of which is unknown to the decision-maker, i.e. the mone­tary authorities. and changing over time. Under specific assumptions on the stochastic law the equilibrium exchange rate is following and from the costs of holding, obtaining and depleting international reserves, BRITTO derives the decision rule specifying how the optimal adjustment to be made in a certain period depends on the level of reserves, the expect­ed values of current and future changes in reserves, the discount rate and the parameters of the cost functions.

Although, in the variety of 'disequilibrium' models examined so far, the Uitonnement or recontracting assumption concerning prices has been dropped, the fiction of an 'auctioneer' or the 'market' setting consistent quantity-rationing signals and adjusting the prices from period to period while the economic agents behave as price-takers has been upheld. How­ever, as NEGISHI argues, even in a competitive market the demand curve perceived by each individual seller cannot be infinitely elastic beyond the quantity currently demanded when total supply exceeds demand and no one can sell larger quantities at the prevailing price. Nevertheless, the

XXXVIII INTRODUCTION

individual seller - a buyer is, of course, in an analogous position - may still perceive an imperfectly elastic relation between the demand for his pro­duct or service and the price he offers or accepts, taking the reactions of his competitors into consideration. Although this market 'imperfection' has got nothing to do with monopolistic [48; 1] or oligopolistic market structures [HEESTERMAN] in the narrower sense but is due exclusively to deficiencies of effective demand (or supply, respectively), it leads to similar analytical consequences. In particular, instead of just assuming price rigidities, e.g. as institutional constraints [HANSEN and MANNE], inde­pendently of the behavior of the traders, rigidities in prices may be ex­plained as the outcome of the agents' optimizing behavior in the face of certain expectations about price elasticities on grounds analogous to kinked-demand-curve effects in oligopoly theory. Thus, a situation appearing as disequilibrium from the viewpoint of infinitely elastic per­ceived demand (or, supply) curves may be considered an equilibrium if a perceived finite elasticity of certain magnitude is taken into account. NEGISHI chooses· this approach to analyze wage rigidities and to show the existence of an under-employment equilibrium where unemployment is involuntary in the Keynesian sense of being abatable at unchanged real wages by an increase in effective demand. In the traditional Walrasian general equilibrium model the behavior of price-taking individuals at non-market-clearing prices is not well-defined [SHUBIK] - for this reason it is also necessary to put further constraints on consumption and pro­duction possibility sets when constructing the law of motion of the tatonnement dynamical system by means of the excess-demand corres­pondences [1; 9]. The introduction of a tatonnement-like quantity­rationing mechanism is one remedy. Much more plausible and satis­factory from both an empirical and theoretical point of view (and also much more in line with Keynes's theory of effective demands) is however, to do completely without the fiction of an 'auctioneer' and to have prices announced by agents internal to the economy such as specialized traders [12], or firms, or just sellers of commodities and services. In the last analysis, this approach leads to formulating the economic process as games (in extensive form, or as sequences of games in strategic form) and to studying non-cooperative equilibria of such games [SHUBIK; 56]. BENASSY, in continuation of his earlier work [4], introduces the concept of a monopolistic Keynesian equilibrium as one where no monopolistic

INTRODUCTION XXXIX

price-maker shows a tendency of changing his price because the perceived constraints and other information he received in this situation lead him to choose the current price. He then studies in a simple one-period model comprising two aggregated agents (households and firms), three goods (labor, output, and money) and two markets (since labor and output are only exchanged for money) the problems of quantity determination, efficiency of Keynesian equilibria, and of monopolistic price-setting paying particular attention to the main types of Keynesian equilibria corresponding to regimes of stagflation, deflation, and inflation.

v

In the Arrow-Debreu theory money plays no role whatsoever, and in most of the 'disequilibrium' models monetary institutions are invoked in a rather ad-hoc manner. A theory of money ought to be able to account for at least two phenomena: the existence, in the real world, of specialized media of exchange and the holding of certain amounts of money from period to period by the economic agents even if the substance used as money is more or less worthless. The reason why the traditional Walrasian model of general economic equilibrium cannot cope with these problems is that it views exchange as a completely anonymous and cost less sub­stitution, by each individual, of preferred commodity bundles x E IRm the values of which are given by px for bundles y in their possession whose values are sufficiently high, py ~ px. A fictitious central market-clearing agency is responsible for setting some equilibrium price vector p and for effectuating the 'exchanges'. Since marketing activities are costless and all commodities, even those which are not delivered 'now' but at some later date (if we choose to give the model a temporal interpretation), are equally marketable there is no need for a special medium of exchange, and there can be no problem of liquidity (there are, of course, also no parti­cular money rates of interest). It has often been claimed in the literature that Walrasian models are not adequate for describing the working of a monetary economy because they are models of barter. In fact, the Arrow-Debreu theory does not offer a satisfactory model of a barter economy either. It is rather a model of an ideal accounting economy which may also be called a perfectly integrated economy [ULPH and

XL INTRODUCTION

ULPH] since there is, from an institutional point of view, only one market place - as ALLAIS emphasizes, it describes a 'market economy' instead of an 'economy of markets' - and each individual faces only a single financial constraint expressed in accounting units. Thus, in addition to viewing exchange as a resource-conserving activity (while consumption is regarded as a commodity-absorbing process and production is analyzed as a process oftransforming goods into commodities of different qualities and/or dates of availability), the traditional approach obscures the character of exchange as a sequence of 'bilateral bargains and trades' [ABELE J. One of the essential functions of money is to serve as a medium of exchange. But even in a barter economy there exist as a rule commod­ities that are used as media of exchange. Commodities may be exchang­ed only to be consumed at once after delivery, or in order to be used as inputs in the production of consumption goods made available at some later date (induding stored consumption goods and consumer durables) - if two commodities are traded for these reasons we speak of direct exchange. On the other hand, there is the possibility that a commodity is purchased also for the purpose of being exchanged for some other commodities; in this case we speak of indirect exchange and call the commodities bought and resold media of exchange [42; pp. 395-475J. Whether and to which extent the economic agents make use of the opportunities of indirect exchange depends on the structure of trans­actions costs since indirect exchange will replace direct exchange only if this is found advantageous by the individual traders. Even if certain commodities are intrinsically worthless for an individual because their consumption does not enhance the individual's satisfaction and his pro­duction technology does not allow their conversion into useful things either, they will cease to be without value to the economic agent - and he may be willing therefore to keep certain quantities ofthese commodities in store - if there are markets where they may be traded for directly useful commodities at a bearable transactions cost. Following earlier investiga­tions by Hahn [16; 17] and Kurz [35; 36], ULPH and ULPH analyze a model of general equilibrium which differs from the usual Arrow-Debreu model only in that it endows each economic agent with a specific trans­actions technology for each market describing his feasible purchases and sales there as well as the transactions costs involved, i.e. the resources used up in the process of exchange. A barter economy in a wider sense is

INTRODUCTION XLI

one where there is a separate market (with a transactions technology for each individual) for each pair of goods and each pair of economic agents and which is, moreover, completely segregated in the sense that for each market separately the value of an individual's sales must not exceed the value of his purchases. The segregation assumption does not hinder the granting of credit among economic agents (by means of forward con­tracts), it only rules out the availability of a universal unit of account such reflecting the absence of a central market-clearing agency responsible for organizing multilateral trading arrangements. Transactions costs arise because the traders, before they are able and willing to exchange ownership titles for commodities, have to find each other, have to com­municate and to higgle over the terms, the goods have to be inspected, measured and marked (when they are physically existent which might be the case only some time after the transaction took place), and, especi­ally in case offorward contracts, the reliability and trustworthiness of the respective trading partner have to be examined (and/or secured by establishing sanctions mechanisms), the transfer of ownership may have to be recorded, contracts may have to be drawn up, the law or the cir­cumstances may require a particular procedure for the transfer of owner­ship, etc. Thus, a good deal ofthese transactions costs have to be incurred independently ofthe eventual volume of transactions. For this reason, the assumption of convexity is particularly implausible for transactions technologies, and fundamental non-convexities arise out of the set-up character of many transactions costs [25; CORNWALL; HELLER]. The transactions technologies represent above all the level of commercial organization and development of the economy under consideration, all its social arrangements and conventions, and its legal system in so far as these institutions are related to the organization of exchange operations and the protection of property rights [36; 50]. Hence, also the differences in transactions costs incurred by different individuals in different markets at different points of time are probably only to a minor degree caused by differences in the physical nature of the commodities traded. Of course, the quality of some goods can be inspected and tested, or demonstrated, respectively, more easily than that of other commodities which will with­out doubt reduce exchange costs in the markets where they are traded. But much more important in accounting for variations in transactions technologies are factors such as the different extent to which the various

XLII INTRODUCTION

markets are efficiently organized, the varying degrees of trustworthiness attached to traders by their potential partners (which may be purely sub­jective, based more or less on personal experience, or, e.g., be motivated by the different severity of obligations and restrictions imposed on the traders by legal institutions), the different legal formalities prescribed for transactions in different commodities between different individuals, the varying degree of protection granted by the law for exchange activities in the various goods (possibly also varying with respect to the potential transactors and transaction periods), etc. A barter economy (in a narrower sense) is, as a reflection of its low level of commercial development, characterized by a set of relatively undifferentiated transactions techno­logies and, as a consequence, by the use of a variety of media of exchange for different purposes among different groups of economic agents. If a commodity - because of the relatively lower transactions costs its use in indirect exchange involves - is employed as a medium of exchange by almost all individuals (or, at least, within an important group of economic agents, e.g. all business firms) in almost all transactions it is called money. Hence, a monetary economy can be described as a barter economy (in a wider sense) with a high degree of differentiation in transactions techno­logies as far as traders (see also CORNWALL) and commodities are con­cerned. For certain analytical purposes, a monetary economy may be considered as the limiting case of a barter economy where trade in one distinguished commodity - the money commodity - is completely cost­less [50; 51]' This approach differs somewhat from ULPH and ULPH'S

conception of a monetary economy in which money is just an additional instrument, "a kind of transferable debt-credit account", that helps in overcoming the effects of market segregation. It ought to be pointed out, however, that either approach is at most able to provide a theoretically more explicit and adequate description of the structures underlying ex­change activities in a given monetary economy but not suitable for·ex­plaining the existing monetary institutions which are the product of socio-economic evolution [41]. Historically, for reasons rather obvious from the above interpretation of transactions technologies, the evolution of monetary institutions has been thoroughly intertwined with the develop­ment of new forms of property in means of production (e.g., joint-stock companies), new methods of transferring free capital and of financing the public debt, and with the evolution of banking institutions. Even

INTRODUCTION XLIII

before the existence of a modern banking system debt contracts, e.g. bills of exchange, circulated to a limited extent as money substitutes within certain groups of traders; with a full-grown commercial banking system transactions costs for trading in certain debt contracts issued by banks (demand deposits) became low enough - because of the particular trust­worthiness of well-known banks and of the efficient clearing arrange­ments offered by the banking system [28] - for these debt contracts to be used as a medium of exchange. This evolution of credit money has further loosened the connection between saving and investment, and has laid the basis for the type of industrial fluctuations termed credit cycles [58; 59; 42; 46; 20; 21; 22].

The second function usually ascribed to money - besides its accidental role as a standard of value, i.e. the unit in which prices are expressed, for which also other commodities or abstract units of account may and have been used - is that of a store of value. This function of money is intimately related to the question why economic agents are willing to hold certain amounts of money even if the thing itself that serves as money is useless for consumption or production purposes. For Keynes money is even primarily an asset -

the importance of money essentially flows from its being a link between the present and the future .... So long as there exists any durable asset, it is capable of possessing monetary attributes and, therefore, of giving rise to the characteristic problems of a monetary economy. [33; pp. 293-294J

In general, however, it is not possible for the whole economy to store value by hoarding money, only individual economic agents whose actions are of negligible influence on prices are able to transfer purchasing power into the future by means of money balances - money as such is not a store of value in use (as consumer durables or durable means of production are) but just of value in exchange. Nevertheless, the determinants of the indi­viduals' money-holding behavior are of utmost importance since in a monetary economy fluctuations in cash balances may give rise to situa­tions of general excess demand for or excess supply of all non-monetary goods and services. As Wicksell has pointed out: "Any theory of money worthy of the name must be able to show and why the monetary or pe­cuniary demand for goods exceeds or falls short of the supply of goods in given conditions." [59; p. 160] In a model of the Arrow-Debreu type where the economic agents are assumed to possess perfect foresight and

XLIV INTRODUCTION

trading occurs only at given equilibrium prices, e.g. in a model like that of ULPH and ULPH, only a transactions demand for money balances is conceivable. It arises, e.g., because fixed transactions costs make the temporal clustering of certain exchange activities for consumption and production purposes profitable without synchronizing purchases and sales while, for the same reason, the continual buying or selling of inter­est-bearing assets may be too costly. Trading at disequilibrium prices with money as the only non-rationed commodity [see, e.g., BENASSY J would provide an additional reason for the accumulation or decumula­tion of money balances.

But it could not be said that there was a "demand for money for transactions purposes" in the sense of a voluntary demand, like the demand for commodities, .... There would indeed be a volume of money outstanding ... but how much it was would depend upon the pattern of transactions conducted [28, p. 14].

Or, in the words of Hayek,

money would enter into the plans, not in the quasi-independent character of command over things in general ... , but only as a transitory item representing the definite quan­tities of commodities for the purchase of which the particular amounts of money are held. [22. p. 29]

This corresponds to the concept of a full equilibrium over time or a station­ary temporary equilibrium in which no longer any uncertain expectations exist and to the classical idea of money as a mere veil over the real econom­ic forces [46, p.10; 48, pp. 247-263]. But in the actual world there is no perfect foresight and "money is largely held because the decision as to when to buy or to pay for something is deliberately postponed; ... money ... is ... something which confers on its holders the chance of taking ad­vantage of unforeseen opportunities" [22; p. 29]. Thus, a theory of monetary economies has to be a theory of temporary equilibria [33; p. 293: 38; 46J, and it may be recalled that even the classical quantity theory did not claim a 'neutrality' of money in the short run; on the contrary, it explicitly recognized real effects ('Cantillon effects') of fluctuations in the quantity of money. It maintained, however, that an economy disturbed in its stationary equilibrium by an influx of an addi­tional quantity of money would eventually, via a sequence of temporary equilibria, return to its original stationary equilibrium. This classical conception of the non-tiitonnement response of an economy to monetary

INTRODUCTION XLV

disturbances presupposes a determinate dynamical system with a unique, globally stable equilibrium. Patinkin's quantity theory of money [52J differs from the classical theory in the dynamics postulated: Patinkin describes a tatonnement response to monetary disturbances yielding, under rather restrictive assumptions, a neutral effect of changes in the quantity of money even with respect to the short-run-equilibrium price structure (see also [15 J). The 'flexibility' [30, pp. 31 ff.J or 'plasticity' [40J, i.e. the high degree of reversibility of the portfolio decision, which marks the holding of wealth in the form of money balances - what is also called the 'liquidity' [32; 33J of money - is due to its medium-of-exchange character. Any other asset can only be exchanged for a preferred asset at, as a rule, a prohibitive transaction cost or has, also at a relatively high transaction cost, first to be exchanged for money. There may be, however, particular (usually, financial) assets which, because of the existence of highly organized markets, can be converted into money at especially low transactions costs. These assets may be considered money substitutes (' near-monies ') as far as the store-of-value function of money is concerned. Although the role of money as a store of value is a derivate of its being the dominant medium of exchange it is, in a world of uncertainty and sur­prise, of central importance not only just for the planning of individual economic agents but also for the welfare ofthe whole economic communi­ty. On the one hand, the use of money as a store of value introduces a criti­cal element of variability into intertemporal economic decisions, i.e. into investment and capital formation (by allowing 'uncommitted' savings), thus being responsible for a good deal of the unsteadiness of economic development in monetary economies, in particular for the short-run fluctuations ('business cycles') in output and employment. On the other hand, in a world in which economic decisions have to be taken on the basis of incomplete and uncertain information, the chance of avoiding ill-considered actions that could only be amended at a high cost which is provided by the possibility of holding assets in liquid form, i.e. as money balances or portfolios of highly liquid money substitutes, ought not to be underrated in its contribution to an efficient use and allocation of resour­ces in decentralized economic communities. In this sense, monetary institutions save resources not only because they render exchange less costly but also because they reduce the resource-absorbing consequences of all the errors in individual economic planning that are as such inevi-

XLVI INTRODUCTION

table so long as foresight is not perfect. This might even well have been the most important' selection advantage' of monetary institutions in the process of socio-economic evolution.

GERHARD SCHWODIAUER

BIBLIOGRAPHY

[1] Arrow, K. 1. and Hahn, F. H., General Competitive Analysis, Oliver & Boyd/ Holden Day, Edinburgh - San Francisco 1971.

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translation: The Positive Theory of Capital, Macmillan, London 1891 (reprint, Stechert, New York 1923).

[7] Clower, R., 'The Keynesian Counterrevolution: A Theoretical Appraisal', The Theory of Interest Rates (F. H. Hahn and F. P. R. Brechling, eds.), Macmillan, London-New York 1965, pp.t03-125.

[8] Clower, R. and Leijonhufvud, A., 'The Coordination of Economic Activities: A Keynesian Perspective', American Economic Review 65 (Papers and Proc.), 1975, pp.182-188.

[9] Debreu, G., Theory of Value, Wiley, New York 1959. [to] Dreze, 1. H., 'Existence of an Exchange Equilibrium Under Price Rigidities',

International Economic Review 16 (1975),301-320. [11] Edgeworth, F. 1., Mathematical Psychics, London 1881 (reprint, Kelley, New York

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(1977), 535-572. [16] Hahn, F.H., 'Equilibrium with Transaction Costs', Econometrica 39 (1971),

417-439. [17] Hahn, F.H., 'On Transaction Costs, Inessential Sequence Economies and

Money', Review of Economic Studies 40 (1973), 449-461. [18] Hahn, F. H., On the Notion of Equilibrium in Economics, Cambridge Univ. Press,

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Third World Congress of the Econometric Society, Toronto, August 1975.

INTRODUCTION XLVII

[20] Hayek, F.A. V., Prices and Production, Routledge, London 1931 (2nd ed., 1935). [21] Hayek, F. A. V., Profits, Interest and Investment, Routledge, London 1939 (reprint,

Kelley, New York 1969, 1975). [22] Hayek, F. A. V., The Pure Theory of Capital, Routledge & Kegan, London

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Costs: Monetary and Non-Monetary Economies', Review of Economic Studies 43 (1976), 195-215.

[26] Hicks, J.R., Value and Capital, Clarendon Press, Oxford 1939 (2nd ed., 1946). [27] Hicks, J.R., Capital and Growth, Clarendon Press, Oxford 1965. [28] Hicks, J.R., Critical Essays in Monetary Theory, Clarendon Press, Oxford 1967. [29] Hicks, J. R., Capital and Time, Clarendon Press, Oxford 1973. [30] Hicks, l.R., The Crisis in Keynesian Economics, Blackwell, Oxford 1974. [31] Hildenbrand, W., Core and Equilibria of a Large Economy, Princeton Univ. Press,

Princeton 1974. [32] Keynes, J. M., A Treatise on Money, Harcourt, London 1930. [33] Keynes, J. M., The General Theory of Employment, Interest and Money, Mac­

millan, London 1936. [34] Kornai, J., Anti-Equilibrium, North-Holland, Amsterdam-London 1971. [35] Kurz, M., 'Equilibrium with Transaction Cost and Money in a Single Market

Exchange Economy', Journal of Economic Theory 7 (1974), 418-452. [36] Kurz, M., 'Equilibrium in a Finite Sequence of Markets with Transaction Cost',

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Econometrica 21 (1953), 233-268. [40] Marschak, J., 'Money and the Theory of Assets', Econometrica 6 (1938),311-325. [41] Menger, c., 'Geld', Handworterbuch der Staatswissenschaften, Vol. 3, lena 1892. [42] Mises, L, V., Human Action. A Treatise on Economics, Hodge, London 1940. [43] Morgenstern, 0., 'Vollkommene Voraussicht und wirtschaftliches Gleichge-

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Amsterdam-London 1972.

XLVIII INTRODUCTION

[49J Neumann, 1. v. and Morgenstern, 0., Theory of Games and Economic Behavior, Princeton Univ. Press, Princeton 1944 (3rd ed., 1953).

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[59J WickseJl, K., Lectures on Political Economy, Vol. I I: Money, Routledge & Kegan Paul, London 1935 (first German edition 1906).

LIST OF PARTICIPANTS

Hanns ABELE (Universite de Fribourg, Switzerland) Sven W.ARNDT (University of California, Santa Cruz) Costas AZARIADIS (Brown University, Providence, R.T.) Robert J. BARRO (The University of Chicago) Martin BECKMANN (Technische UniversiHit Miinchen-Brown Univ.,

Providence, R. I.) Jean-Pascal BENASSY (CEPREMAP, Paris) Bernhard BOHM (Technische Universitat Wien) Volker BOHM (CORE, Heverlee, Belgium - Universitat Bonn) Richard CORNWALL (University of California, Davis) George DEMOPOULOS (Rochester Institute of Technology) Erwin DIEWERT (The University of British Columbia, Vancouver,

Canada) Helmut FRISCH (Technische Universitat Wien) Erhard FURST (Institute for Advanced Studies, Vienna) David GALE (University of California, Berkeley) Nicholas GEORGESCu-RoEGEN (Vanderbilt University, Nashville) Heinz GLiicK (Institute for Advanced Studies, Vienna) Herschel I. GROSSMAN (Brown University, Providence, R.I.) Franz HASLINGER (Universitat Regensburg) Geoffrey HEAL (The University of Sussex) A. R. G. HEESTERMAN (The University of Birmingham) Walter P. HELLER (University of California, La Jolla) Norbert HENTSCHEL (Wirtschaftsuniversitat Wien) Peter W. HOWITT (University of Western Ontario, London, Canada) Dwight JAFFEE (Princeton University - University of Stockholm) Hans KEIDING (University of Copenhagen) Mervyn KING (University of Cambridge) Tjalling C. KOOPMANS (Yale University) Panayotis KORLIRAS (University of Pittsburg, Pa.) Wilhelm KRELLE (UniversiHit Bonn)

L LIST OF PARTICIPANTS

Harold W. KUHN (Princeton University) Mikulas LUPTACIK (Technische Universitat Wien) Adam LASCIAK (School of Economics, Bratislava, CSSR) Kazimierz LASKI (Universitat Linz, Austria) Axel LEIJONHUFVUD (University of California, Los Angeles) Egon MATZNER (Technische Universitat Wien) Lionel W. McKENZIE (Center for Advanced Study in the Behavioral

Sciences, Stanford, Calif.) Allan H. MELTZER (Carnegie-Mellon University, Pittsburgh, Pa.) Paul van MOESEKE (Universite de Leuven, Belgium) Takashi NEGISHI (University of Tokyo) Philip A. NEHER (University of British Columbia, Vancouver, Canada) Jiirg NIEHANS (The Johns Hopkins University) Ewald NOWOTNY (Universitat Linz, Austria) Heinrich OTRUBA (Technische Universitat Wien) Jean-Pierre PONSSARD (Ecole Polytechnique, Paris) Trout RADER (Washington University, St. Louis, Missouri) Abdur RAHMAN (Institute for Advanced Studies, Vienna) Kurt ROTHSCHILD (Universitat Linz, Austria) Jose SCHEINKMAN (University of Chicago) Ingo SCHMORANZ (Institute for Advanced Studies, Vienna) Uwe SCHUBERT (Wirtschaftsuniversitat Wien) Gerhard SCHWODIAUER (Institute for Advanced Studies, Vienna) Stephen SMALE (University of California, Berkeley) David A. STARRETT (Stanford University) Gerhard TINTNER (Technische Universitat Wien) Alistair and David ULPH (University of Stirling, Scotland) Karl VIND (University of Copenhagen) Michael WAGNER (Institute for Advanced Studies, Vienna) H. N. WEDDEPOHL (CORE, Heverlee, Belgium) Georg WINKLER (Universitat Wien)