Money, growth, and stability

2 The General Equilibrium Theory of Money: A Comment 46 3 The Rate of Interest and General Equilibrium Analysis 56 5 On Transaction Costs, Inessential Sequence Economies PART II NON-WA

Money, Growth and Sta bi I ity

Frank Hahn

The MIT Press Cambridge1 Massachusetts

First MIT Press edition, 1985

© Frank Hahn 1985

First published 1985 Basil Blackwell Ltd

108 Cowley Road, Oxford OX4 IJF, UK

All rights reserved Except for the quotation of short passages for the purposes of criticism and review, no part of this publication may

be reproduced, stored in a retrieval system, or transmitted, in any

f orrn or by any means, electronic, mechanical, photocopying, recording or

otherwise, without the prior permission of the publisher

Library of C::ongress Cataloging-in-Publication Data

Hahn, Frank Money, growth and stability Bibliography: p

Includes index

1 Money 2 Equilibrium (Economics)

I Title HG221.3.H28 1985 339.5 85-15132 ISBN 0-262-08156-3

Typeset by Unicus Graphics Ltd, Horsham Prin tcd in ,reat Bri lain by Bell and Bain Ltd, Glasgow

2 The General Equilibrium Theory of Money: A Comment 46

3 The Rate of Interest and General Equilibrium Analysis 56

5 On Transaction Costs, Inessential Sequence Economies

PART II NON-WALRASIAN EQUILIBRIA

6 On Non-Walrasian Equilibria

7 Exercises in Conjectural Equilibria

PART III STABILITY

131

159

8 On Some Propositions of General Equilibrium Analysis 183

9 On the Stability of Pure Exchange Equilibrium 192

10 A Theorem on Non-tatonnement Stability 202

With Takashi Negishi

V1 Contents

1 On Two-sector Growth Models

I Equilibrium Dynamic with Heterogeneous Capital

Goods

14 On Warranted Growth Paths

15 The Stability of Growth Equilibrium

16 On the Disequilibrium Behaviour of a Multi-sectoral

19 Exe ss Capacity and Imperfect Competition 348

21 On Equilibrium with Market-dep nd nt Information 377

Oct.-Dec 1975) 'The General Equilibrium Theory of Money: a

Comment' from The Review of Economic Studies (1952-3), 19,

1 79-85 ·The Rate of Interest and General Equilibrium Analysis'

from The Economic Journal ( 1955), 65, 52-66 (Cambridge University Press) 'Equilibrium with Transaction Costs' from

Econometrica (1971), 39, 417-39 'On Transaction Costs, Inessen­ tial Sequence Economies and Money' from The Review of Eco­ nomic Studies (1973), 40, 449-61 'On Non-Walrasian Equilibria' from The Review of Economic Studies ( 1978), 45, 1-1 7 'Exer­

cises in Conjectural Equilibria' from the Scandinavian Journal of Economics ( 1977), 79, 210-26 'On Some Propositions of General

Equilibrium Analysis' from Economica ( 1968), 35, 424-30 'On

the Stability of a Pure Exchange Equilibrium' from the Inter­ national Economic Revieiv ( 1962), 3, 206-13 'A Theore1n of

Non-tatonnement Stability' with Tak as hi Negishi f rotn Econo­ n1etrica ( 1962), 30, 463-9 'Uncertainty and the Cobweb' from

The Review of Economic Studies ( 1955-6), 35, 65-75 'On Two

Sector Growth Models' from The Review of Economic Studies

( 1965), 32, 339-46 'Equilibriun1 Dynamics with Heterogeneous

Capital Goods' fro111 The Quarterly Journal of Econonzics ( 1966),

80, 633-45 © The President and Fellows of Harvard College 'On

Warranted Growth Paths' from The Revie,v of Econo1nic Studies

( 1968), 35, 175-84 'The Stability of Growth Equilibriu111' from

The Quarterly Journal of Econo,nics ( 1960), 74, 206-26 © The President and Fellows of Harvard College 'On the Disequilibriu111

Behaviour of a Multi-sectoral Growth Model' frotn Tlze Quarterly

111 Acknowledgements

Journal of the Royal Economic Society ( 1963), 73, 442-57 (Cambridg University Press) 'On Some Equilibrium Paths' from

Jod l of Economic Growth, ed J A Mirrlees and N H Stern

(Proceedings of a Conference held by IEA at Jerusalem), pp

193-_06 Sa ings and Uncertainty from The Review of Economic Studies ( 1970) 37, 21-4 'Excess Capacity and Imperfect Compe­

tition from Oxford Economic Papers, new series volume 7, no 3,

October 1955 (Oxford, Clarendon Press), pp 229-40 'On

Opti-1num Taxation' from The Journal of Economic Theory ( 1973), 6, 96-106 © Academic Press, New York and London 'On Equi­

librium with Market-Dep ndent Information' from Quantitative Wirtschaftforschung, pp 245-54

Introduction

The papers which follow are more technical than those of the pre­

vious volume, Equilibrium and Macroecono,nics (Basil Blackwell;

Oxford, 1984 ) But they should be accessible to anyone familiar with a n1odern text By way of introduction I have included my

J evons Lecture, 'In Praise of Economic Theory' In it I discuss what I think we are doing when we theorize and I argue that this is

in which money appears are equally unsuitable as long as it is the only asset, and when it is not it raises all sorts of difficulties Some

of these are quite old in the literature Someti1nes it seen1s as if the world is coming to the aid of the theorist Thus, interest-paying current accounts are beco1ning 1nore \Videspread and thereby one old puzzle is sidestepped But this pheno1nenon also shows that the theoretical puzzle has real substance: there is a tendency for other assets to drive out 'sterile' money In paper 1 I give an account, of a rather non-technical kind, of the way general equi­ librium theorists have tried to incorporate non-interest-bearing, intrinsically worthless, money into their theorizing

In the 1950s the most notable atten1pt in this direction was that

of Patinkin (2nd edn, 1965) In son1e of his early papers he failed

2 Introduction

to n1odel adequately the essential intertemporal aspect of money

In paper 2 I pointed out why that was wrong Of course, it was only a slip on Patinkin's part, and I reprint it only because it 111akes the point concerning the central importance of the inter­ ten1poral aspect rather sin1ply

In the 1950s also the battle still raged between 'loanable funds' and 'liquidity preference' theories of the rate of interest This episode is now, deservedly, almost forgotten But the bad habits

of the debate have persisted in other contexts In particular, there

is the habit of writing that some price is 'determined' in one particular market without giving this clai111 the precision it needs

to be meaningful; examples are 'Inflation is a Monetary Phenome­ non' and 'Investment determines Savings' This means that paper

3 may still be of interest since it is an attempt, in a particular context, to sort out this sort of muddle

The next two papers represent my most serious attempt to fashion a general equilibrium theory in which money can find a place The first of these is not easy or pleasant reading because the con1plications of an econo1ny with transaction technologies are rather large Foley ( 1970) had pursued the same line at the same time and independently However, he did not examine the inter­ temporal problems which gave rise to the possibility of inefficient equilibria This came as a surprise to n1e, since the inefficiency in question is relative to the transaction technology Starrett' s example ( 1973) is a beautifully clear one, and readers interested in these matters should read it as a companion piece to paper 5 Kurz ( 1972) made further clarifications possible, and the \Vhole rnatter has recently been rnagisterially discussed by Gale ( 1982) I do think that this whole episode has i111proved our understanding of monetary theory But there are still large gaps The 'transaction

technology' is ad hoc and not properly grounded, as it should be,

in inforn1ation theory Moreover, although Heller and Starr

( 1976) huve relaxed the assurnption sornewhat, it is still the case that we cannot deal at present with the likely significant non­ convexity of transaction technologies Clearly, one needs to dig more deep!� to the level at which the infonnation of exchanging agents can be studied

II NON-WALRASIAN EQUILIBRIA

Perfectly cornpetitive econornies arc now understood rather well

I have, however, been puzzled by the many econo1nists who seern

to, say, physicists, but not to n1any economists, who are apt to mun1ble something about looking for lost keys under a street light

or appealing to the metaphysics of 'as if' Even if somehow this odd stance could be defended, it would still be highly peculiar not

to be interested in the challenge of studying economies in which agents must act strategically In any case, for the last ten years or

so I have been much interested in departures from Walrasian economies, although I cannot claim to have advanced far along this difficult road

The Belgians led by Dreze ( 197 5) and the French led by Malinvaud (1977) went, as it \Vere, to the other extreme and studied econo1nies with exogenously given prices and consequent rationing They considered what in paper 6 I called 'orderly equilibria', that is, equilibria where only the 'short side' in any market is rationed This was the basis of the dynamic process studied by Negishi and myself (see paper IO below) In the first part of paper 6 I was interested in an existence proof for a Dreze equilibrium I found it useful to study an associated economy with coupon prices as rationing devices for this purpose But the aim of that paper was to move beyond exogenously given prices For that purpose I introduced the term 'conjectures' to describe theories of firms of the reaction of the economy to their own actions Of course, this was related to Negishi's ( 1961) perceived de1nand curve but was rather more general Paper 7 considers so1ne examples of conjectural equilibria

In the theory which I develop in paper 6 I introduced the notions of rational and of reasonable conjectures The first of these was badly christened since it triggers a \Vrong reaction in game theorists (see Makowski, 1983) I should have named the1n

correct conjectures, and even that tenninology needs further elaboration The idea is this Agents have theories of what will happen to, say, their profits if they deviate fron1 so1ne given status quo I considered only small deviations and implicitly supposed that the direct consequences of such a deviation would be spread over many agents I did not have a duopoly or oligopoly ga1ne in mind I therefore took the consequences of a sn1all deviation by a single agent to be calculable from the equilibriu111 of the rest of the

4 Introduction

econo1ny after the deviation and when all other agents keep to

their conjectures This becomes clear in the examples of paper 7

I certainly \vas not thinking of dynamics, nor of games in extensive form No agent is playing against another who reacts to his devia­ tion by calculating the best responses Rather, any one agent has

an anonymous opponent - the rest of the economy - and for 1ny purposes the agents who constitute that economy need not know

\vho has deviated and may indeed regard the ne\v signal as being due to some change in the state of the economy

I hope it is clear f ro1n this that n1y intention was not to take

a shortcut through the intricacies of rationality in an economy­

\vide ga1ne As far as I kno\v, game theory and general equilibrium theory have met only in circumstances in which a perfect competi­ tive equilibrium is the outcorne Moreover, those studies seem to have all been concentrated on pure exchange The main exception

to this is the book by Marschak and Selten ( 1979), which proceeds

in a manner not markedly dissimilar from the one \vhich I fol­ lo\ved (It preceded my own work, but I only became aware of it later.) In any case, I have to confess that I have some doubts that

it \vill prove possible to bring about a marriage of recent rather beautiful advances in game theory and economy-\vide analysis Certainly when I wrote my papers I knew that it was beyond

me I accordingly opted for what is essentially a Chamberlinian approach (see Hart, 1983) I will not be surprised if it transpires that that was a wrong move

III STABILITY

I can be brief in m y co 1n men ts o n papers 8 , 9 and 1 0 I n the first

of these I am concerned rather less with stability than with the existence of equilibriu111 I showed how, in an econorny with the gross substitutability property, one could develop an existence proof by induction (and so without a fixed point theore1n)

I needed gross substitutes because I needed equilibriu111 to be unique for every way of fonning a certain co1nposite con1n1odity out of two con1n1odities I now believe that it n1ay be possible to carry out the same proof with only the postulate that the economy

is always regular (Debreu, 1970) But I have not tried to do this since there arc more interesting things to do instead

Both the ren1aining papers concern a price adjustn1ent process for a pure exchange econon1y in which trading takes place at all

Introduction 5

dates when it can take place It turned out that non-tatonne1nent was easier to analyse than was tatonnement and that it yielded stability without special restrictions on the forms of the excess demand functions This was further studied in a 1nuch more general setting by Smale ( 197 5) and extended to include produc­tion by Fisher (1983) Even so, we are a long way from under­standing the operation of any actual price mechanism (The currently fashionable procedure of simply postulating prices to be

at all times market-clearing can have no attraction to the intellec­tually fastidious.)

Paper 11 was written a long time ago and probably shows it

But it considers a question which is rarely discussed but which seems important: How is uncertainty related to stability? I study this in the context of a simple cobweb The idea is that the more uncertain the expectation of future price, the less responsive an agent will be to deviations of current price fron1 its equilibrium value This in turn has implications for cobweb behaviour My guess is that there is further \VOrthwhile work to be done on this class of problems in the light of what we have learned in the intervening thirty years

IV GROWTH

Growth theory is now less fashionable than it was in the 1960s which was its period of boom None the less, n1uch current work (e.g the new macroecono1nics) relies rather heavily on it My own interests were two-fold: to study growth in the fra1nework of general equilibrium analysis, and to exa1nine the stability of growth equilibrium

In paper 12 I use straightforward general eq uilibriu1n theory in the attempt to impose some order on the many anecdotal results which were being produced at the time The main issue \Vas the uniqueness of temporary equilibrium \Vhich was required for a straightforward analysis of a sequence of such equilibria It turned out that this could best be studied by the use of the Weak Axiom

of Revealed Preference in a particular formulation

Papers 13 and 14 show why with certain assu1nptions the steady state was a saddle-point in a certain subspace There has been

a good deal written on this since (e.g Shell and Stiglitz� ! 967:

Kurz, 1968: Cass and Shell, 197 6) I took my result to show that warranted paths of the economy as defined by Harrod did not in

6 Introduction

general seek the steady state It never o ccurred to me that anyone

\Vould \Vish to posit perfect foresight over the infinite future But

I \Vas \Vro ng : such a postulate is now commonplace It still strikes 1ne as dotty On the technical side, develop1nents since I wrote have sho\v n that \vith many co nsumption goods (I assumed o nly one such good) there \vould be a cone of paths which approach the steady state These results make my own non-convergence propositions less dramatic but raise the new problem of the non­uniqueness of perfect foresight paths The relevance of all of this

to the rational expectations literature will be clear

In papers 1 5 and 1 6 I study stability not of equilibrium paths but of actual paths In the first of these I postulate certain responses to an excess demand for finished goods and for inputs However, as Sargent ( 1 962) pointed out later, I paid too little att ention to who got \vhat \vhen the economy is out of equi­librium None the less, certain of the insights may be of interest

I n paper 1 6 I looked at a situation not too different from the 'fix-price' literature of recent years By postulating a substitution theorem economy I could determine relative steady-state prices

as a fun ction of the interest rate and independently of excess demand I then assumed a price formation process which pro­ceeded independently of excess demand and was governed largely

by expectatio ns I showed that it converged under certain assu1np­tions On t he other hand, excess demands at substitution theore1n prices were met out of inventories The accumulation and de­cumulation of the latter were governed by a 'flexible accelerator' mechanism I showed t hat the steady-state equilibrium was stable

in the small under this mechanisn1 A shortco1ning of the paper

is certainly that it assun1ed labo ur never to be in short supply ; but

it seems to me that it may no ne the less be a pro111ising beginning

In paper 1 7 I use duality theory to cxa111inc the behaviour of

eq uilibrium paths I t hen pro ceed to exa111inc a suggestion of Shell and Stiglitz ( 1 967 ) that inelastic expectations (i.e non-rational expectations) arc stabilizing It turns out that this is by no 1ncans always the case

V MISCE LLANEOUS

The four papers in this last part arc on various topics Paper 1 8 was occasioned by one by Lcvhari and Srinivasan ( 1 969) It deals with the q uest io n of whether an increase in the uncertainty of the

In troduc tio n 7

future productivity of capital would lead to an increase or decrease

in the optimal amount of savings In writing this paper I gained much from conversations with Jim Mirrlees, who had written a celebrated thesis on optimum accumulation under uncertainty

Paper 1 9 was inspired by Hicks ( 1 954) It is concerned with excess capacity and entrance deterrence It, of course, does not have the benefit of recent advances in the application of game theory to these problems But Hicks 1nade the important point that the story rather depends on the preferences of the people who run firms This point is not much discussed in current work and it may be important

Paper 20 was written to clarify (partly to myself) the well­ known taxation results of Diamond and Mirrlees ( 1 97 1 ) It pro­ ceeds slightly more generally than they did However, I did not pay sufficient attention to the fact that knowledge of the distribu­ tion of characteristics of agents on the part of government was all that was required for the Diamond-Mirrlees results

Paper 2 1 was also an attempt to understand Joe Stiglitz had given a preliminary version of the famous Rothshild-Stiglitz ( 1 97 6) paper at a Cam bridge seminar I could not then put my finger on just what feature of the example was responsible for the non-existence of an equilibrium Paper 2 1 was an attempt to do

so This has since been studied more deeply and satisfactorily by Dasgupta, Hammond and Maskin ( 1 979)

ACKNOWLEDGEMENTS

I am very grateful to Mr K Gatsios of the Faculty of Econo1nics and Politics at the University of Cambridge for proofreading My intellectual debts will mostly be obvious But one of these may not be For twelve years Terence Gorman and I \Vere colleagues Many of the papers here reprinted I discussed with him He usually went to the heart of the matter aln1ost before I had tin1e to tell him what I was about He set an intellectual standard which

I could ai1n at but not achieve

REFERENCES

Cass, D and Shell, K (1 976) ' The Structure and Stability of Competitive Dynamical Systems', Journal of Econon1ic Theory, 12, 3 1 -70

85 , London School of Economics

Heller, W and Starr , R ( 1 976), 'Equilibrium with Non-convex Transaction Costs : Monetary and Non-monetary Economics' , Review of Econon1ic Studies, 4 3 , 1 9 5-2 1 5

Hicks, J R ( 1 954), ' The Process o f Imperfect Competition', Oxford Eco­ nomic Papers, 6, 4 1 -54

Kurz, M ( 1 968), ' The General Instability of a Class of Competitive Growth Processes' , Review of Economic Studies, 3 5 , 1 5 5-74

Kurz, M ( 1 972), 'Equilibrium in a Finite Sequence of Markets with Transac­ tion Costs' , Stanford University, I nstitute of Mathematical Studies in the Social Sciences, Technical Report no 5 1 , January, Stan ford , California Levhari, D and Srinivasan, T N ( 1 969), 'Optimal Savings Under Uncertainty' ,

R eview of Econo,nic Studies , 36, 27-3 8

Makowski , L ( 1 983), ' "Ra tional Conjectures" aren't Rational and "Reason­ able Conjectures" aren't Reasonable', SSRC Project on ' Risk, Information and Quantity Signals in Eco nomics', Cambridge University Discussion Paper no 66

Malinvaud , E ( 1 977 ), The Theory of Unenzploynzen t Reconsidered, Basil Blackwell, Oxford

Marshak, T and Selte n , R ( 1 979), A GenC'ral h'quilibriu,n Model with Price­ makinK Firms, Springer, New York

Ncgish i , T ( 1 96 1 ), 'Monopolist ic Competition and General Equilibrium', Review of h'conomic ,S'tudies, 28, 1 96-20 I

Pa t inki n , D ( 1 965), Muney, Interest and Prices (2nd edn), Harper and Row ,

New York

Introduction 9

Rothshild , M and Stiglitz, J ( 1 976), 'Equilibrium in Competitive Insurance Markets : An Essay on the Economics of Imperfect Information', Quarterly Journal of Economics, 90, 629- 49

Sargent , ( 1 962), ' The Stability o f Growth Equilibrium : Comment', Quarterly Journal of Economics, 304, 494-50 1

Shell, K and Cass, D ( 1 976), 'The Structure and Stability of Competitive Dynamical Systems', Journal of Economic Theory, 1 2, 3 1 -70

Shell, K and Stiglitz, J ( 1 967), ' The Allocation of Investment in a Dynamic Economy', Quarterly Journal of Economics, 8 1 , 592-6 1 0

Smale, S ( 1 975), 'An Approach t o the Analysis of Dynamic Processes in Economic Systems', in Equilibrium and Disequilibrium in Economic Theory, ed G Schwoohauer, Reidel, Boston

Starrett , D ( 1 973), ' Inefficiency and the Demand for Money in a Sequence

B

I n Praise of Econom ic Theory

I con1e before you today to blow the tru1npet for econo1nic theory largely because it is so often under attack and so often misunder­ stood But I have not come to da1nn other endeavours in eco­ no1nics This is not entailed by praising theory and ,votdd be odd

in a Jevons Lecturer Jevons ,vas both a theorist and an applied econo1nist and on occasions excelled as both There 'are 111any mansions ', and in concentrating on one I do not wish to be taken as in1 plying anything about the others

In thinking what I should say on this occasion it soon beca111e clear that I had chosen a so1ne,vhat unsatisfactory title , if for no

other reason than that it re1nincls one of Eras111us and his In Praise

of f�olly But there is another reason ,vhy, if it had not been too

la tc , I wou Id have changed it to · I n Praise of Theorizing in Eco­ nomics' For to announce praise for ccono1nic theory leaves one open to the q uestion, which of a nu1nber of theories one intends

to praise As a n1atter of fact, I shall want to argue that the variety

of co1npcting econon1ic theories is nn1ch s111aller than popular opinion takes it to be But I do not want to start ,vith either that question or t hat argu111ent For what I a1n centrally interested in

is the enterprise of the9rizing in econo111ics By this I 1nean the undertaking to gain understanding of the particu lar by reference

to generalizing insights and in the light of certain abstract unifying princi ples

I want to c1nphasizc the word ·understanding' and that it is not din;ct ly related to posi tivist predict ion For instance, we under­ stand tlH� cause o r c�1 rthqu�1 kes hut cannot at the 111on1ent predict them We can u 11dcrst�1 1Hl wlty two people arc seen to exchange without bt:ing able to pred ict that they wi ll do so So1newhat 111ore

so ph ist icatedly, we 1nay be able to understand an a llocation of

In Praise of Econo,nic Tlzeory 1 1 resources as one of a nun1ber of possible equilibriu1n allocations without being able to predict which equilibriu1n will be observed

in any one case In the first instance the clai1n 'I understand' does not logically imply that I also assert that I can predict

But what does it imply? I a1n aware that these are deep Wittgen­ steinian waters, in which however I do not propose to splash or drown It see1ns to me that there are at least three necessary condi­ tions that a claim to understand an event or a series of events must satisfy First, I must have a theory which co1nprises the event or events; second, the event or events 1nust not contradict the theory; and third, the theory must be in the public do1nain, by which

I mean that it should be con1municable to others in a language and grainmar that is common If you have a theory which cannot be communicated to others, then others can give no n1eaning to your claim that you understand

I do not, as I have already said, want to argue for this view in any detail The first desideratum is, I suspect, not controversial The second is really the possibility of ex post prediction : n1y

theory includes the possibility of that event and it would have been in the support of any probability distribution of events allowed by my theory The third I have already partly justified It does not mean that 'truth' is a 1natter of sociology, but rather that uncommunicable truths or modes of understanding concern the inner processes of an individual and not the theory of a subject

In any case, I shall consider theorizing in econo1nics to be an ongoing search for understanding in this sense

There is one further n1ethodological matter which I can get out

of the way now Understanding does not i1nply the ability to 1nanipulate events, although understanding 1nay be a necessary precondition It is not at all the case, for instance, that if one believes that one understands the causes of une1nploy1nent one must then also know how to cure it It is often believed that understanding which does not facilitate 1nanipulation is a useless luxur>'· This must however be wrong For understanding can certainly aid us in recognizing futile or misdirected atte1npts at 1nanipulation For instance, \Ve cannot change the orbit of the n1oon by praying to the sun, and we cannot cure poverty by mini1num wage legislation Indeed, one of the great uses of under­ standing is that it is a line of first defence against 1nad 1nen and witches But even if that were not so, I have never seen an argu- 1nent to show that, while chocolate, lipstick , cars, etc , are intrinsic goods, understanding of the world needs justification in tenns of

1 2 In Praise of Econonzic Theory

other things G E Moore's chapter on the 'Naturalist Fallacy' can easily be adapted to den1onstrate the confusion of such a view Con1ing no\v to n1y topic, one recognizes that theorists are not the only economists in the quest for understanding � indeed, one n1ight want to argue that almost all acade1nic econo1nists at least are thus engaged That is why earlier I added 'by reference to generalizing insights and in the light of certain abstract unifying prin ciples' It is this 1nore particular n1ode of proceeding which

I want to convince you is worthy of praise

Let 1ne call 'the abstract unifying principles' axion1s and dis­ tinguish these f ron1 assun1ptions A theory will typically have

a logical structure derived f ron1 axion1s To some econon1ists axion1atic-logico-deductive theory is anathen1a : for instance, that

is the case for Professor Kornai and Lord Kaldor However, it seems to me that any coherent general propositions are decon1pos­ able into this forn1 For instance, if one starts with observation one requires at the very least an axion1 of induction but in general

a much richer array One of n1y first reasons for praising theory ,

at least in its n1odern mode, is that it co1nes clean on both its axiorns and its assu 1nptions They do not need to be searched for

by back\vard recursion from propositions In this theorists sho\v not only an engaging 1nodesty but also honesty

Axio1ns are not plucked out of thin air, and far fron1 distancing the theorists from what somewhat mysteriously is called the 'real' world, they constitute claims about this world so widely agreed as

to make further argu n1ent unnecessary Indeed, often in axion1atiz­ ing a theory one is atten1pting to see \Vhether its propositions are ded ucible from cle1nentary agreed features of the world For instance, the von Neun1ann axion1atization of expected utility includes the 'sure thing principle' It appeals to our intuition and

it appeals to what we know about ourselves

The best known and rnost in1 portant axiom is, of course, that of the rational agent and I shall now d iscuss that axion1 in so1ne detail

The nornenclature is son1cw hat unfort unate because it invites

ph ilosoph ical debate on the 1ncaning of "rational' It also arouses hostil ity arnong those rornantically inclined :

A levelling rancorous rational sort of rn incl

That never looked out of the eye of a saint

Or out of a drunkard's eye

(Yeats, Seven Songs)

J,1 Praise of Econon1ic Theory 1 3

as Yeats has it, and I an1 sure I do not need to quote Ruskin to you But economists mean so1nething quite precise and far less offensive The rational agent knows what he wants, and from a1nong the alternatives available to him chooses what he wants

By 'knowing what he wants' we mean that he has a proper preference ordering over a relevant do1nain This do1nain may be large and complex It n1ay include beef and 1nutton and the happiness of one's grandn1other For 1nany purposes, of course, one will be interested only in the projection of this do1nain on to

a smaller one (one with lo\ver di111ension) For instance, we will neglect the grandmother's happiness when studying the choice between beef and mutton but not when we consider the choice

of homes in different locations This cutting down of the domain will be the role of assumptions The description of the don1ain is important For instance, our axio1n 1nay have more po\ver in

a theory of advertising if we consider preferences over charac­teristics of goods rather than over goods themselves

There is little doubt that even at this level of generality the axion1 yields a rich harvest with f e\v assu1nptions - for instance, the symmetry of the substitution tern1s, the excess burden of non­lump-sun1 taxation, a notion of efficiency in the allocation of goods and an understanding of what it is we do when \Ve make cost of living index numbers On general do1nains it is the founda­tion of Arrow's Impossibility Theore1n \vhich stands like a granite tower in the othenvise indistinct and shado\vy landscape of political theory Certainly all of this is achieved \vith great econo111y

of means and \vith elegance, so let us at least give it so111e marks for that

But I am more ambitious, since I \Vant to argue in favour of the axiom itself That is, I do not propose to f ollo\v the Friedmanite route whose singleminded concern with prediction I have already disclai1ned The 'as if' argun1en t is in any case shaky It does not allo\v one, for instance, to distinguish bet\veen agents who act on their O\vn preferences and those \vho are con1pelled to act on the preferences of a hypnotist For purposes of ·understanding' , the status of the axio1ns n1atters a great deal

In the first instance, then, I \Vant to 1naintain that the part o r the axion1 for which agents have preferences is the claitn that they are persons If so, then this is sufficiently agreed to be so as to make it acceptable as an axion1

Suppose there is so1neone without any preferences at all

Between any A and B fron1 a rich do1nain he can either not put

14 In Praise of Econornic Theory

the111 into any preference relation or not understand what is meant

\vhen he is asked to do so This person \vould have no reasons for his actions \vhenever they can be the subject of choice Reme1nber that he is not indifferent between all elements in his do1nain - rather, he has no views on them at all There \vould be no way to describe this son1eone other than by his physical characteristics Even if his actions 'revealed' preferences, \Ve could not invoke these to understand the actions In short, he \vould be an ani1nal and not a person ; for aniinals can give no reasons for their actions and neither can this someone In the first instance, then, the axion1 says that economic agents are persons

But, of course, it is stronger than that For instance, persons 1nay make n1istakes in their preferences and they 1nay have no preferences over parts of the domain in \Vhich they are not offered choices It n1ay be the case that a person's preferences are not transitive There are t\vo things to be said here First, much of the theory can proceed \Vith a weaker version \vhich does not postulate transitivity For this I refer you to a fa1nous paper by Sonnenschein (197 1 ) Second , \Ve \vould expect that a person would re-exa1nine his preferences if their intransitivity \Vere pointed out to hi1n This

\vould be the case particularly if su ch intransitivity n1ade it i1npos­ sible to give reasons for his actions However, at the end we shall have to agree that the genuine axion1, persons have so111e prefer­ ences, has been idealized and strengthened by theorists beyond the point at \Vhich it con1111ands universal consent

The sharpening and idealizatio n of agreed features of the \Vorld

is one of t he d istinctive 1narks of theorizing One atte1npts to understand eve nts in the light of refined descriptions of con11non­ place regularities and their logical cntaihnents One understands, in

so far as one ca n give no reaso n why the sharpening and idealiza­ tion of the agreed axion, should n1islead one

Take as an exan1plc the case of a Giffen good , that is, a good the de1nancl for which varies positively with price Our axio1n has led us to a distin ctio n between substitution and inco1nc effects

We understa nd t hat a rise in price of t he good will cause co nsu1ners

to seek a su bstitute while a significant decline in real wealth result­

i n g fro In t h l' p r i cc rise 111 a y le ad t h c 111 to co n s u 111 e 111 o re o f i t bl'cause it is of a k i nd t h�,t low-wealth people have to consu1nc pro portio nately ,norl' or Whl'n I say we unlkrsta nd I 1nean two

t hing� First, the observa tio n of �, Giffen good case fits into the tht.:ory, and t he expla natio n co n forn1s wit h what we kno\v of ourse lves a nd o t h l'rs But I rnean so 1nething else as well : we can

In Praise of Econo,nic Theory 1 5

explain to son1eone surprised by the deviation of a Giff en good observation fro1n observations common for other goods how both kinds of observation can be traced back to a common account of choice This we can do only by making the axiom sufficiently precise But we can also argue that there seen1s no argun1ent which would, by, say, considering mistaken preferences, make our explanation invalid For we understand everything we do think we understand by just such an abstraction No two chestnuts are alike

in every particular but we speak of the property of chestnuts, and

no couples love in the same way and yet \Ve claim to understand something about love We may often think that we have under­stood when we have not, but we shall never understand anything

if we neither generalize nor idealize

But perhaps I protest too n1uch I shall admit that and turn it to

my advantage

Simon ( 195 5) has drawn attention to the fact that the theory of the rational agent is seriously inco111plete in failing to distinguish between what this agent knows and \Vhat in principle he could know In addition, if we forswear Friedman, the theory often makes quite implausibly large demands on an agent's co111puta­tional ability Knowledge and computation are themselves objects

of choice, and that seems to leave the theory dangling by its boot­straps

Who can deny that Si1non has a good point? But who also can deny that 'satisficing' does nothing much to 1neet it? The only economist who to 1ny knowledge has given this notion a serious run for money is Radner (1980) The work shows that periods of routine will be punctuated by periods of search when aspiration levels are breached It is quite easy to translate this into a so111e­what richer model of rational choice than the one of the textbook But paradoxically, what Simon has done is to appeal to our intuition of what constitutes rational choice and in particular \Vhat

is an appropriate don1ain of preferences It is not reasonable to suppose that time and effort spent in discovering the set of possible choices is not itself an element of this do1nain The san1e goes for the trouble, etc , of self-scrutiny involved in having complete and consistent preferences Simon's argu1nent gains \Vhat force it has

by the existence of the pure theory which he finds wanting

Above all, ho\vever, I want to praise econo1nic theory for providing the language in which proposals like those of Si1non can

be discussed I recall arguing with Sraff a when he clai1ned that consumer behaviour was entirely a n1atter of habit: I asked

1 6 In Praise of Econonzic Theory

\vhet her tha t n1eant t hat they ahvays con sun1e d the san1e things independe ntly of prices or inco1ne He was not ,villing to agree

to that A fter son1e ti1ne it seen1ed t hat ,ve could agree that consun1ers had a habitual response to income and prices, at \vh ich point I could not forbear to t ranslate this into : Consun1ers have rat h er stable pre ferences In exactly the sa1ne \vay can Sin1on's critique be used to d eepen understanding of what we already have

A consun1 er buys a good at a price higher t han prevails for an identical good else\vhere Ho,v do we understand that , and why is there some t hing here which ,ve need to understand ? We have

a prin1a facie puzzle because t he pure theory does not account for the event Sin1on rea 1 1y con1 es to its aid by proposing t hat the consun1er n1ay not k no,v of the cheaper good and that he ,votdd have to expend effort to find out He will spend that effort if h is aspirations not to be taken for a ride are seriously in1paired , i.e

w hen he believes t he gain fro1n search large enough

I do not of course , wish to argue that all roads lead back to t he textbook theory \Vhat I do want to 1naintain is t hat it has n1ade possible an ord erly and coherent d eepening of understand ing

I need only ren1 ind you of the recent tlowering of t he econo1nics

of i n fonn ation to 111ake this poi n t The init ial theory, once digested threw a k ind of searchlight on the unexplained : Why can si1nilar good s sell at d ifferen t prices? How are potent ial excha nge possibili t ies n1ad e k nown , and is it possible t h at unsatisfactory states where t h ey are not a 11 k nown can persist? How is the 1narket for loa ns a ffected by 111oral hazard , and how is that connected wit h son1e ratio ning or cred i t ? One can go on and on to de111on­strate how t heory ge nerates the question and provides the language for atte1n pted a ns\ve rs Wit hout t hat a bstra ct t heory we would

k now neit her w he n to ask ·why' nor how to proceed when ,ve do ask

I ha ve spen t a lo ng t i111c on t h is n1ost co nt ent ious aspect of

t heo rizing , t he ra t io nal agen t There are ot her d irectio ns to

ex plore I lowever, befo re I do t h�1 t two o t her aspects deserve so n1e

CO 111 111 C ll t

The first o f t hese i s e�1 sily a nd q u ickly d iscussed Opponents of

t h eo ry o ft e n argue t h at it is t �1 u t ologo us beca use i t co nsist s of logical d ed uct io ns fro 111 a x io 1ns a nd assu1n p t io ns I f o ne is k ind to such crit ics o ne i n terpre t s t he n1 as signa l l ing t hat t h ey do no t care

fo r t h ese a x io 111s a nd t h ese assu 111ptio ns I n a ny case , all t heory in all �u bjccts proceed s i n t h is 1na n ner I n t he p rese n t co ntex t o ne

so 1net irne � hears it 111:.i i n t a ined t hat t he t heory of cho ice si1nply

In Praise of Econonzic Theory 17

says that a person will do what he prefers and that there is no way

of falsifying that But that is to misunderstand the theory An

agent whose preferences are continuously in flux is like an agent without any preferences at all The theory thus postulates that this is not the case, and so the charge that our understanding is not tested by observation is false Connected with this is the endless ref rain of some that most of our preferences are socially determined If I understand that correctly, then I can only answer :

Of course they are It is however a puzzle why this observation should, for instance, affect my analysis of Giffen goods unless once again it is proposed that social forces are continuously leading to a change of preferences

The second matter is more co1nplex and I can only touch on it This is the observation that the rational agent and the theory he supports is a powerful tool in the discussion of many policy issues One does not need to be a utilitarian to agree that the preferences and welfare of individuals are relevant to policy debates They need not of course be decisive The theory constructed by eco­ nomists provides a subtle and elegant language in which this aspect

of policy can be discussed Any economist who has been on com­ mittees with non-economists will be conscious of the advantage which he has in discussion even of such imponderables as the allocation of research money between astronomy and dentistry The theory allows him to organize his thoughts and to recognize what is relevant Nor is it true, as economists gone sour with public responsibility so1netimes argue, that only the most ele1nentary and obvious ideas such as opportunity cost are involved Questions of the appropriateness of market prices and interest rates in calcula­ tions of such costs arise, and I would not trust anyone unf a111iliar with quite sophisticated theory to get it right I would agree that theorists son1etimes write as if all of 1noral philosophy \Vere embodied in a Benthamite calculus They also often forget the importance of the lack of 1narkets for future goods and the relative

paucity of insurance n1arkets But then the proper theory is avail­

able and a certain diffidence in questions of the 'good' can be instilled in some However there can be no doubt that, without the economic theory \Vhich we have, very 1nany matters of policy would literally not be discussable, \vhich means that they could not be subjected to any coherent thought I think that this is

a matter for praise

These last re1narks suggest that econon1ic theory not only seeks understanding, which is its own re\vard, but is also on occasions

1 8 /11 Praise of Econonzic Theory

useful Yet j ust 110\v in Britain it also see1ns dangerous Indeed, only the other day a politician warned against it at the Conserva­ tive conference Certainly if what Mr Lawson asserts is taken to be economic theory, then the case is proved But this is all \Vrong, not just in a rather obvious \Vay but also in an interesting \Vay

I have suggested earlier that we need to distinguish between axiorns and assu1nptions That people have preferences and try to satisfy them \Ve treat as an axiom, while universal perfect con1peti­ tion, for instance , must count as an assumption By this I n1ean that neither introspection nor observation n1akes it self-evident up

to an acceptable 1nargin of error that agents are price-takers in all n1arkets But assun1ptions are no n1ore capriciously i1nposed than are axion1s They serve to sirnplify - that is, to 1nake argument possible - and they also often atten1pt to encapsulate a sort of casual em piricisn1 That n1anagers have preferences is an axion1 : that they take a particular fonn - for instance that they are linear

in expected profit - is an assu1nption \vhich both si1nplifies and seen1s not implausible in the light of experience Whatever it is,

a theory suggests that \Ve understand that understanding is con­ tingent on both the axioms and assu1nptions It certainly is also contingent on the logical entailn1ent of the proposi tions of the theory by the assu1nptions and axio1ns

Consider a fashionable cxan1ple The proposal that \Ve should take it that an agent \Vhose forecasts of future events are syste1nati­ cally disappointed \vill change his forecast see1ns to n1e axiomatic

It is difficult in t he light of introspection and experience to deny

it, although I have no doubt that one can find exceptions But that an agent will nonnally have learned to n1ake forecasts which arc not systen1atically disappointed is hardly a self-evident truth More seriously, there arc great difficulties in understanding ho\v the agent could reach this satisfactory state ; for the learning of agents affects what there is to be learned Sterling pioneering \vork

on this rnatter by such econo1nists as M argaret Bray ( 1 982) illustrates this Hence the proposition that agents have rational expectations is an assu1nption Cerli.1in not very careful people have tho ught that this assun1 ption is i1nplicd by \vhat I have granted as an axio1n : viz , that people will no t persist in an erroneo us belie f S uch a step is j ust wrong It is not 1nadc right by rationa l cxpcct�1tions ccono111etrics with good fits That is so beca use we cannot und erstand why it should fit well As I hav� argued elsewhere , t he evid ence fo r 111 iraclcs at Lourd es is stronger tha n is this ccono111ctrics Yet without understanding it does not

pe rsuad e

In Praise of Econon1ic Theory 1 9 What a rational expectations theory provides is an understand­ing of an imagined economy which satisfies the assu1nption As such it may be of great use For instance, it allows us to study pathologies which cannot be traced to expectational mistakes Or, again, it leads to an understanding of how 1narket variables, by revealing information to the uninformed, reduce (or negate) the benefits of special inf onnation Or, yet again, it allows us to grasp the informational disturbances introduced by an u nkno\vn monetary policy It is a vulgar misunderstanding of theory and its aims to dis1niss rational expectations theorizing because of its assumptions I repeat again that I do not hold this view on 'as if' grounds

But it ought to be en1phasized that, fro1n a theoretical point of view, the rational expectations story, even when taken as a useful 'Gedanken experiment', is pretty shaky For instance, there is in general a continuum of rational expectations equilibria over finite time To get rid of this one needs to suppose that people have rational expectations over the infinite future Even that extrava­gance often does not suffice, and one must cook the story to yield

a long-run stationary state which is also a saddle point We have robust examples of an infinity of rational expectations equilibrium cycles I am not here concerned to dot the i's of this argu1nent My concern is to document what I claimed earlier: that theory is powerful in saving us from cranks and witches only if it is taken seriously For who can understand the precisely forn1ulated theory

of rational expectations equilibrium and claim that he understands

it as description? At the very best, the new macroecono1netricians are like someone who noticed that beans gre\v better \vhen kitchen waste was dug into their soil That is an observation and not a theory I want to emphasize here 'at best'

Exactly the same problen1s arise with equilibriu1n theory in general It takes a little sophistication to see \vhy the study of economics in equilibrium is an important step in understanding actual econon1ies For instance, even if we kno\v nothing of detailed dynamics, disequilibriun1 is an occasion for change and so

an explanation of change But it see1ns to take 1nuch 1nore sophis­tication to understand what one is about in equilibriu1n theorizing

I want here to praise the giants of equilibrium theory, Arro\v and Debreu In the first place they deserve praise for \vriting do\vn precisely, and beyond the power of 1nisunderstanding of a nonnal person, what state of the econo1ny was to be designated as an equilibrium In particular, this left 1nany possible states which were not equilibriu1n states and one needed to prove that there are

20 In Praise of Econonzic Tlzeory

son1e \Vhich \Vere In doing this it beca111e clear that \Vithout certain assun1ptions it \vould ahvays be possible to describe an econo1ny of the kind \Vhich they considered for which no equi­ libriun1 existed No a111biguity of \Vhat it is that is being done is possible \Ve are concerned with the existence of a particular state

of the economy in \Vhich the best choices of individuals are mutually con1patible \vhen these choices are entirely determined

by preferences, technology, endo\vments and 1narket prices There

is nothing here to tell us that any given econon1y \Vill be in that state or that it tends to that state The theory is \Vhat it is and not sornething else

In giving us this precise fonnulation and these existence proofs, Arro\v and Debreu vastly increased our understanding of \Vhat had gone before and laid the foundations for a great deal 1nore As

I have argued else\vhere, they provided the first essential step in any serious discussion of the Invisible Hand \vith its task accon1plished� The elegant definition of a good made it clear to the naked eye that the market structure \VOtdd have to be n1uch richer than in fact it is if an actual econon1y in eq uilibriun1 should correspond to theirs The funda1nental theore1n of welfare economics then underlines the n1essage that, even if acttial econon1ies are in equi­ libriun1, they n1ay be inefficient It becan1e clear that econon1ies with n1oney would have to be n1odelled in a special way and that that special \Vay was connected with having too fe\v rnarkets It also becan1e possible to connect equilibriun1 concepts of ga1ne theory with market eq uilibriurn and thus to bring about a n1uch deeper understanding of the postu late of perfect competition Who can read the Core theore1n without even a flicker of pleasure

in the beautiful and not obvious role of the Arro\v-Debreu equi­ libriurn? \Vho can read the1n without finding their understanding

of market power and the role of 1narkets deepened ?

The Arrow-Debreu theory has been \Videly 1nisundcrstood and misused One of the coarsest criticis1ns is to say that if used in

a co1npara tive statics \Vay it has generally very lo\v, or no, predic­ tive power : 'anything' , it is said , 'can happen' Exactly so The theory is crystal cle�1 r as to its foundations - the funda1nental axio rns which I have already discussed I r you want 1nore out you have to put 1nore in, t hat is, you n1ust supple1nent those axio1ns

\Vith assurnptions, e.g., that prod uction functions are Cobb­ Dougla� What the theory provides is a coherent rnanner of study­ ing the i 1nplications of these assu1n ptions for equilibriu1n Most oth er criticis1ns have turned on its lack or rcalis1n, but the ain1 is

In Praise of Econo111ic Theory 2 1 not realism but aid to understanding Think of externalities, of imperfect competition, of increasing returns and n1any other 'realistic' phenomena, and ask how \Ve \Vould fit them into our comprehension without the ideal reference point provided by Arrow-Debreu We understand a basic problem with public goods because of our understanding of the private goods case We can for the same reason give some precise meaning to significant and insignificant increasing returns The work which has gone before pinpoints precisely where there will be difficulties with equilibrium

of an imperfectly co111petitive economy Is our understanding of Keynesian claims not deepened and n1odified by n1aking the connection to missing 111arkets? If we did not have the Arrow­Debreu theory it would be priority number one to construct it : for, while it does not describe the world , it is a solid starting point for the quest for understanding it

But of course there are influential economists who take a version

of the theory as descriptive For instance, they hold the view that the British labour market in 1 984 can be understood as a Walrasian market in equilibrium

Let us notice straight away that there is no axion1 to the effect that an economy is in eq uilibriun1 at all tin1es If there were, then Arrow and Debreu certainly wasted their time For it would be exceedingly odd to accept this axiom and prove at the san1e ti1ne that equilibrium exists It also, of course, does not further under­standing to answer Adam Smith's funda1nental question, Can

a decentralized econon1y with self-interested agents have a coherent allocation of resources?, with the affirmative ans\vers in the f orn1

of an axiom By adopting the axion1 these econo1nists re111ove

a major part of any problen1 from the possibility of understanding This of course is still true if the 'as if' interpretation were put on the axiom

In fact, t here have been atten1pts to justify this procedure by

an appeal to the fundamental axion1 of rationality First , it is said that a rational agent will always act to his best advantage given the opportunities which he faces Thus all actions are eq uilibriu111 actions This indeed is part of the require111ent of Arrow-Debreu equilibrium and it is also a proper use of the fundan1ental axio111 But what of the other require1nent of equilibriun1 that t he individual actions of agents should be co111patible econo1ny-wide? The answer given is this If they were not co111patible then� ,vould

be Pareto-improving n1oves which have not been exploited But that is not rational Hence the equilibrium actions n1ust be con1-

In Praise of Econonzic Theory

patible That this syllogisn1 does violence to the foundations of

a theory of decentralized choices see111s to n1e so obvious as not

to require discussion I ref er you to the Prisoner's Dilemma as

3 vivid exa1nplc of this observation The justification of an axion1

of perpetual equilibrium can be dismissed

But that is just as \Vell ; for if we accepted it in this forn1, a vast range of economic phenomena, as I have already said, would at once be removed fro1n enquiry and so fro111 the reahn of under­ standing One would have a theory \Vhich closes rather than opens doors I want to en1phasize that this does not apply to a proper version of the axion1 that all actions are equilibriun1 actions - that, after all, is just the axiom of rationality which I have defended By

a 'proper version' I n1ean one which properly states the informa­ tion and expectations of the agent in the light of which the equi­ librium action is undertaken This leads us back to rational expectations \V hich I have already discussed

But I have come to praise theory, and here I seem to be found attacking it Not so To make this clear I have once again to return

to the beginning

The economists I have been discussing might be taken to be

engaged in the following progran1me : to enquire ho\v far observed events are consistent with an econon1y \vhich is in continuous

\Valrasian equilibrium Such a program111e would be of consider­ able value For we might find that events \vhich we had explained

as being due to disequilibriun1 or, indeed, to trade unions and monopolists could be accounted for without these That surely

\Vould be valuable for understanding; but it \vould not be true that \Ve understood the events For we would not understand how continuous equilibrium is possible in a decentralized econon1y, and we do not understand why a \Vorlcl with trade unions and monopolies behaves like a perfectly competitive one Theorizing in econornies, I have argued, is an atten1pt at understanding, and

I now add that bad theorizing is a prc111ature clai111 to understand

What has happened in this instance is that "as if' prediction n1ethodology has taken over Recall Fricd111an's cxa111plc : leaves

o n a pla n t orientate the111selvcs as if the plant were 1naxin1izing the surface area of leaves exposed to the sun This 111ay well predict the orienta tio n or leaves, but it is not an acco unt which we under­ stand, precisely because we know t hat plants arc not, as Fried1nan notes, capable or any calcula t io ns So we do not leave n1atters

t here We invest igate chen1ical feedback 111cchanis111s wh ich account for the observation and wh ich we understand They fit into what

In Praise of Econonzic Theory 23

we know generally about chen1ical substances in quite different contexts and into what we quite generally stipulate about causal processes All the economists I have been discussing are n1uch more concerned with 'as if' than with understanding, as their numerous econometric exercises testify There is nothing wrong with this predictive progran1me But all theory could claim is that this and this is not inconsistent with an econon1y in perpetual Walrasian equilibrium, and not that lhis and this is explained by such an equilibrium They would have to be that modest because

of the n1any things left unexplained

I now leave these central but son1ewhat abstract arguments to call Jevons to my aid, although, as \Vill be seen, not exactly in

a straightforward manner

In a review of the sixth volu1ne of J evons' papers and corres­pondence edited by Collison-Black, Stigler ( I 983) pokes fun at Jevons' sunspot theory He reports that recent American investiga­tion into that theory had to conclude that Granger causality analysis showed the American econo1ny as having a significant impact on sunspots and not the other \Vay round Stigler also says : 'All his life Jevons played with numbers' and that he was "not by instinct a formal theorist'

The Granger causality result makes us s1nile because, coming back to my old refrain, there is no way in which we can under­stand it That, of course, does not establish that it is wrong For that, other theoretical arguments are required which show that there could be no influence on the sun from Arnerican econon1ic activity, with which, we may note, economic activity all over the world is probably correlated Far less does the Granger causality test establish that sunspots exert no influence on economic activity The trouble with J evons' sunspots was not that he could never clinch it with numbers, but that he would never clinch it with theory ; that is, he could never bring it into consonance with the existing understanding of the working of an econo1ny In fact, unlike some current macroecono1netricians, I cannot see ho\v any economic argument \Vhich we do not understand can be clinched without misunderstanding

J evons was a practitioner of what Keynes called 'the black inductive art', but he also provided the first English axion1atic formulation of econo1nic theory In the n1atter of sunspots the black art was at the forefront, although he did atte1npt to provide

an understanding of \Vhat he claiined to be the case by an appeal

to Indian harvest fluctuations But it is clear that this \Vas what

� 4 In Praise of Econunzic Theory

one n1 igh t cal l 'casual t heorizing' Certain ly no precise or detailed picture of internat ional econon1 ic relations is to be fou nd in this

\Vork of Jevons No con nect ion was made, as Keynes notes, \Vith his O\v n earlier analysis of the role of durable goods in t he under­sta n d ing of fluctuations Above all, Jevons seen1s to have believed

t h at his sin1ple explanation could be tested by si1nple means,

a sure sign t h at he did not fully grasp t h e difference between plausible hypothesis a nd serious t heory

I t h erefore \Va n t to \vay t hat it is a n1 isu se of language to say that Jevo ns had a sunspot t h eory of econon1ic fluctuations What

he had was a h ypothesis w hich he tried to confirn1 fron1 data

A hypot h esis is not a t heory , alt hough in co1nmon parlance t hese

t wo are often used indifferen tly I do not ' u nderst a nd' econo111ic fluct uat ions by being told t hat t hey are correlated \vit h su nspots

I do not u ndersta nd t he fonnat ion of prices by being told t hat t he price level a nd so111e n1easure of n1oney are correlated At best ,

su ch observat ions a nd such hypotheses 1nay cau se one to re­exa1nine n1at ters alread y filed away as und erstood

B u t Jevons' su nspots a re back i n t he t heoret ical literat u re, a nd

t h is t in1e, although t hey are only nan1ed so 1netaphorically , we do

h ave a t heory or how t hey 1nigh t be related to lluct uat ions I refer here to t h e \vork by Azariades ( 198 1 ) , Cass and Shell ( 1 983),

\Voodf ord ( 1984) a nd others on overlapping generations 1nodels of

t he cconon1y The t heory is si1n ple , although t here is so1ne co1n­

p lex ity in i t s fu ll cl evelo p1nen t I t is t hat , if agen ts condit ion t heir expect at io ns of ccono1n ic variables on su nspots or indeed any other sta te of nature whatever, t hen t hese sun spots \Vi i i have a n

i n lluence on t he evolu t ion of t he econo1ny Co nd it ion ing expecta­

t ions on a n i n trinsically cycl ic state helps in genera t i ng cycles But

t h eory a nd u ndersta ndi ng do not stop here ; for it is sho\vn t hat

ea ch age n t in t he e co no 111 y a ct s r a t i o n a 11 y a n d est i 111 �1 t es rut u re eve n t s ra tionally I n pa rt icu lar , t he fluct uat i ng e cono1ny is at a l l

t i 1nes in rat iona l expecta t ions eq ui libriu 1n I f asked , 'Why do you

ta ke not ice o r su nspots in fann ing yo ur ex pecta t io ns?' 1ny ra t ional

a nswer is, 'beca use ot hers d o ' I o ught t o a dd t hat G ra nd 1nont

( 1 98 5 ) has shown t ha t ra t io na l ex pect a t io ns cq uilibriu1n cycles arc

a lso possi h k in a detenn inist ic wo rl d

I ho pe t h at t h is ex�11n ple w i l l co nvi nce t hose w ho need convin c­ing o r t he use fu lness or t h eoriz i ng The work w h ich I have just report ed does not d e part fro 111 t he fu nda1nen t a l rat ionality axio1ns,

or ind eed fro1n a n y or our t rad itio na l rnodels of underst a nd ing,

a nd �o acco u n ts for so 1net h i ng h it herto u nco nsidered in a la nguage

In Praise of Econo,nic Theory 25

we already understand It is not tied to actual sunspots The saine

account will do if the deus ex ,naclzina is the pronounce111ent of

c1 guru or, I am tempted to add, the numbers for M3 And notice

why it is important that the theory has the form it has: we do not have to invoke individual irrationality verging on madness to explain what we want to explain That means that we do not need

to invoke something we know nothing aboµt to understand what

is involved It is a gain in understanding to know that irrationality need not be involved and all will see that this is not the same thing

as claiming that people everywhere and always are rational

Lastly, of course, it is now a matter for empirical research to see

whether, in forming their expectations, people are influenced by events to which we can assign no direct econo111ic role or signifi­ cance

I now \Vant to conclude \Vith much simpler matters These turn

on some of the most frequent criticisms one hears of current modes of theorizing

The 1nathe1natical f orn1 of 1nuch of 111odern theorizing is

frequently under attack Slack and intellectually lazy obiter dicta

of Marshall and Keynes are often invoked Walras noted how son1e people found it offensive to their vie\v of hun1anity to see it studied in symbols It is very difficult to consider a criticis1n appealing so much to sensibility and so little to reason For instance, consider the pronouncement of Marshall (I believe) that one must always translate mathematical propositions into words

to 1nake sure that they make sense It seen1s to view 111athen1atical reasoning like automatic writing, not guided by volition In any case how, to take an example, do you translate into English that certain economic processes can be represented by equations \Vith complex roots which give rise to cyclical behaviour? Even if son1eho\v translated, \Vhat is gained? Or there is the view that

mathematical reasoning ipso facto n1akes theory unrealistic and

irrelevant - a view surely not worth discussing

As far as I can see, there are only t\VO possible coherent argu­ ments One is that the use of mathen1atics 1nakes a theorist ignore matters \Vhich cannot be thus captured The other is that the search for rigour inhibits creative thinking \Vhich in its first stages may be far fro1n rigorous I believe that there is so1nething to both objections and perhaps especially to the second one Certainly,

a mathematical fonnulation is not a necessary feature of acceptable theorizing But when I consider ho\v much our understanding owes to n1athematically 1ninded theorists, how they have liberated

26 In Praise of Econo,nic Theory

us fro1n argun1ents by arithmetical exan1ple as for instance in Boh1n-Ba\verk, Marx and Ricardo, ho\v they have produced definiteness and con1prehension \vhere there was flabby hand­

\Vaving, and ho\v they have forced us to specify rather exactly the basis of any pronouncement, these objections becorne insignificant Indeed, let us praise 1nathematical econo1nics for these achieve- 1nents Let us also fors\vear the sentence, 'this is n1athen1atics and not econo1nics' , unless \Ve can say \Vhat it rneans For instance, the study of sufficient conditions \vhich \vill ensure that aggregate den1and functions are differentiable is largely 1nathen1atical in nature : but \vhy is it not economics? That is, \vhy is it not relevant

to things \Ve \vish to say about the econo1ny?

The other grand objection to theorizing I have been really discussing throughout That is of course that it is unrealistic, like

a chess gan1e in fact, and of no use to a nyone I have never been able to understand this objection What exactly is realistic eco­ nomics? I think what is frequently 1neant is that someone through practical experience and knowledge clairns to have direct kno\v­ ledge of ho\v an econo1ny \Yorks but appeals to 'his judgement' for authority But in any case ask , Why is theory often such an in1perf ect mirror of the \vorld? The ans\ver is not love of obfusca­ tion or of abstraction but the li1nits on \vhat \Ve are capable of understand ing I recall here n1y earlier requiren1ent that under­ standing must be publicly accessible Of course, theorizing leaves out much of interest and i1nportance and there are 1nany pheno­ n1ena it ca nnot account for adequately, but that is not so by devilish design but by the li1nitations of our capacity to forn1

a unified and coherent account of the \vhole econo1nic world For the recognition or this li1nitation we should praise rather than cond en1n theorists

Of course, there are silly theories and there are also silly ques­ tio ns on wh ich son1eti1ncs too 1nuch effort is expounded But listening and read ing t he 'practical' econo1nists does not suggest tha t living in t he world is a guarantee or sense

Indeed, it is o ne o f the great virtues of theorizing in econon1 ics that it leaves the practit ioner wit h c1 suspicion that , \Vha t I suppose was once a progra111 1ne for econo1n ics, 1n�1y be i1npossihle to carry out It goes o f co urse without s�1 ying th�1t econo111 ics is not like physics But I rather th i n k i t 1n�1y not be 1nuch like 1neteorology, either The law of la rge nu 1nlH.:rs docs not self-evidently operate in the social world in wh ich custo 1ns and views of s01ne conta1ninatc tho�e or others It is not just t hat there are 1nany va riables and

In Praise of Econo,nic Theory 27 complex interactions: it is that the constraints on what is possible seem much weaker than is the case with physical processes studied in meteorology A theorist then will be surprised if there are 'laws of economies', in the sense of propositions holding universally, to be discovered He will be surprised if deep know­ledge of 'affairs' were to reveal some fundamental or invariant structure of an economy He will know better than many who profess the modern version of 'political econon1y' the inco1nplete­ness and partial nature of what we have and what it seems we may ever have Of course, he hopes to illuminate the darkness, but few, unlike so many practical men, would claim to have turned it into daylight, and some, myself included, may have the view that shadowy mists may be the best we can ever hope for

Lastly, I turn to the matter of there being many contradictory economic theories This, of course, is a cause for merriment and conte1npt to journalists and men of judgement We have only ourselves to blame The display of certainty by many economists

in discussing matters of economic policy is not only lacking in honesty but extren1ely harmful to the subject In any case, I hold the view that it is not the case that there are many rival and contradictory economic theories And I 1nean theories, and not the beliefs of, say, Mr Lawson or Mr Benn

Take monetarism in any of its fonns as an exa1nple In the 'language of theory', as Debreu puts it, it is quite clear that certain

of the new macroeconomists' propositions concerning rational expectations Walrasian equilibria can be correct Certainly in deriving these they and, say, I follow the same steps and the sa1ne theory Where we part co1npany is that they take the construction

as descriptive and as immediately applicable while I do not One of the reasons why I do not is because I can use the sa1ne theory to deduce valid propositions quite contrary to theirs The difference

is not one of theory but rather in the evaluation of what theory

is about and what it can deliver Another difference is, of course, the mysterious belief so many monetarists have in the confinnatory power of their econometric exercises But I want to e1nphasize that one is not here concerned with rival theories at all in the sense

in which I have used the term

I would, if there were time, argue that even Marxian econo1nics and neoclassical economics are not rival theories where they study the san1e problem and where no logical mistakes are made Let 111e only note that it is neoclassical econo1nics which 1nade so111e sense of the labour theory of value and it was Marx \vho built one

/11 Praise of Eco11on1ic Theory

of the first miniature general equilibrium models On 'the laws of history', \Vhatever that means, there is no dispute since neoclassical econo1nists have not proposed any

\Vhat I an1 arguing, then, is that it is hard to find rival theories but easy to find contradictory opinions The contrary itnpression steins f ron1 a n1isunderstanding of theorizing and of course f ron1 the \vilful obfuscation of those \vho seek power and influence or

\V ho are driven by 1nillennial drean1s

At the end of it all, I \Vant to praise theorizing in economics because it is one of the high\vays to understanding and because it has already provided a good deal of it I \Vant to praise it for its n1odesty and honesty and also for the occasional excite111ent and beauty which it provides Above all, I want to praise it for this:

no one \vho has seriously theorized can be enslaved by the slogans and shibboleths of practical n1en and women who have not No one accuston1ed to the discipline of coherence and proof \Vill fall a victin1 to such pepole If \Ve were all theorists, it just 1night

be a better world

REFERENCES

Azariades, C ( 1 9 8 1 ), 'Self-f u l fllling Prophecies', Journal of Econonzic Theory ,

25

Bray , M ( 1 982), 'Learning Estimation and the Stability o f Rational Expecta­

tions', Journal of Econornic Theory, 26

Cass, D and Shell, K ( 1 983), 'Do Sunspots M atter?', Journal of Political Economy , 9 1

Grandmont, J M ( 1 985), Forthcoming art icle in Econonzetrica

Rad ner, R ( 1 980 ), 'Collusive Behaviour in No n-cooperative E psilon-Eq u ii ibria

of Oligopolies with Long But Fin ite Lives' , Journal of Economic Theo1J' ,

22

Sim o n , I I ( 1 95 5), 'A Behavioural Model o f Rat ional Choice', Cowles Com­

m ission Papers, New Series, no 98, Chicago

Sonnenschein, I I ( 1 9 7 1 ), 'Demand Theory withou t Transit ive Preferences with Appl ications to t he Theory of Competitive Equilibrium', in Ch ipman ,

J , I lurwicz , L , Richter, M and Sonnenschein , H (eds) Preferences,

Utility and /Jcnwnd, I larcourt Brace J ova novich , New York

Stigler, D ( 1 983), ' Review o f Black (R D Collison) (ed ) Papers and Cor­ respn11dcncc uf Williwn Stanley Jevons, Vol VI I , Papers 011 Political Econon1y' , Econon1ic /011r11al, 9 , 3

Wood ford , M ( 1 984), ' I nd e t e rmina cy o f Equ ilibrium i n the Overlapping Generations Model : a Survey', mimeo , Columbia University

Part I Money

1 Money and General Eq u i I i bri um

I INTRODUCTION The Arrow-Debreu model describes a world in which none of the problems which interested Keynes can occur Nor is it the case that this 1nodel can acco1nmodate n1oney in any interesting or essential way Many theorists now working on n1onetary and related problems have therefore found that they are really engaged

in a reconstruction of the only fully understood foundation of our subject Not unnaturally, they are n1uch at sea This present paper discusses son1e of this work but also contains some new material Before I start there are several preluninary ren1arks I should like to make

What fallows is in no way meant to be a comprehensive survey

of recent 1nonetary theory; indeed, I shall be only partly concerned with the work of others I have picked out for discussion 1natters which interest 1ne and which are relevant to n1y topic It is not an i1nplication therefore that studies which are not discussed are regarded as unin1 port ant or as inferior

In particular, I shall only 1nake occasional references to 'rnonetarists' or what The Tinies called 'n1odern 111onetary theory'

This is due partly to the difficulties I have had in discovering a precise state1nent of this theory and partly to the fact that 1nany n1onetarists see1n to base the1nselves on empirical induction rather than on theoretical propositions which are my pri1ne concern here But Professor Pearce recently announced in a letter to The Tinzes that 'an increase in the quantity of money is a necessary and sufficient condition for a rising price level.' So there see1n to be theore1ns, and when their proofs become available they will have

to be taken seriously

The second preliminary remark is 1notivated by the fear that,

as on a previous occasion, I n1ay inadvertently give co111fort to

J\Joney

those who arc the encn1ies of 1nodern 1nathen1atical econo1nics

\Vhen, as I shall do, I criticize this or that construction or point to great areas of ignorance, I do not \Vant to be taken to 1nean that there is son1c alternative available which either does better or

\Vhich co111n1ands respect Indeed, I a1n daily 1nore convinced that the only serious battle no\v being \Vaged against our considerable ignorance is by those who are fa1niliar also \Vith the theoretical achieven1ents of the last generation They at least are constructing

a raft of sorts: the 1nan of judgen1ent and the pundits are prepared

to walk on the waters I have nothing to say which they would find of interest, and l 1nuch hope that they will find nothing to coin fort then1

+ , t he nu1nbcr of households (II ), their consu111ption sets

Xh, their ordering ( t> on X11 anJ their c ndow1ncnts ih E R� It is then taken for grantcJ that there arc kno\vn tenns of exchange in prices, one price for each good and the sa1nc price for each agent , and tha t any act ion wh ich satisfies t he budget constraint at these prices is feasible for an agent

But certainly an old question is, Why is there a 1ncdiun1 of exchange? /\nd an old way of answering it is to consider an econo1ny which d oes not have one A l though the question and answers arc old , it has only recent ly been possible to rnake then, precise I an1 th inking here o r the work o r Nichans and Starr and

of Ostroy and S tarr as well as the various 111odcls of exchange processes such as t hose or Uzawa, Ncgishi, I J ahn, I Iurwicz, Radncr and Reiter I return to this later and wri te down

1l1011ey and General Equilibrizun 33

Question 1 (a) How do we supplement the traditional description

of the economy in order to co1npare an econo1ny with a mediu1n

of exchange to one without one? (b) What do we learn when we have done that?

To this we can straight away add a further question, which as yet has not been answered and which seems important One of the traditional advantages claiined for a monetary over a barter econo1ny is that the farmer permits a far greater division of labour than does the latter But this raises two related difficulties If we want to make sense of this proposition with classical convex production sets, then a barter equilibrium will have to be Pareto­inefficient and the tem1s at which goods exchange will have to differ between agents or some other iinportant feature in the description of an equilibrium must be missing Alternatively,

if, as I believe, the advantages of the division of labour are to

be understood as stemming from important increasing returns

to scale to specialization, then we face well known proble1ns

In particular, it is not clear that Starr-like approximation methods

of dealing with the1n will not throw out the baby with the bath water In any case, I write

Question 2 How do we study the connection claimed to exist between the 1nethod of exchange and the division of labour?

It is possible to bypass the questions posed so far and to start with an economy which already has a medium of exchange But even so practically oriented an economist as Keynes felt bound to ask why we have the particular mediu1n we do have Indeed, as I shall argue later, this is an e1ninently practical question His answer, given in a largely incomprehensible chapter, turned on the relative stability of wages in tem1s of different potential media As far as I know, no one has succeeded in making this into a theory Nor do I know of any satisfactory 1nodern discussion of the question In any case, I pose it

Question 3 What essential features of an econo1ny 1nust be captured by a model if it is to account for the use, or exclusive use, of a particular 111edium of exchange?

This question too has often been bypassed and the analysis started

at the point where the 1nedium of exchange is an intrinsically worthless one, i.e fiat money To do this, Patinkin, for instance, and latterly Clower and his n1any followers have simply stipulated

34 i\lloney

that 'only n1oney buys goods.' This beco1nes an axiom of the 111odel and it is not a hannless one In particular, it should be rather sharply distinguished fro111 t he related but basically quite different axio1n that the ability to acquire goods is conditional

on the ability to dispose of goods It is not the case that the distinction bct\veen effective and notional demand depends logically on a particular, or indeed on any, 1nediu1n of exchange

By accepting the procedure of axio1natizing the use of fiat 1noney, this 1nust still be 1nade consistent with a theory of the econo111y and this theory cannot be Arrow-Debreu For unless

\Ve have a theory in which exchange takes place at each date,

it will be difficult to account for the holding of the \vorthless 1nediu1n of exchange at each date Nowadays we say that we

111 ust study a sequence econon1y

There are still 1nany unsolved conceptual and technical proble1ns

to be solved in the fonnulation of such an econo1ny Foley, H ahn, Kurz, Heller, Starrett and others have studied the sequential structure as arising f rorn transaction costs, while Radncr has given the more fundamental interpretation in tenns of the differential information available to agents Not a great deal of progress has

so far been 1nade with allowing for the intrinsic non-convexities

of transaction costs or for the intrinsic pu blic good aspect of at least so1ne in fonnation But these 111atters, while iinportantly related , arc not at the centre of the 111onctary stage, and once again they can be, at least partly, bypassed by si111ply postulating a sequential structure, i.e by a priori cnu1nerating the markets on which trade can take place But I return to son1c of these 111attcrs when I d iscuss the ideas of l iq u id i ty

As far as l k now, seq uence cconornics were first stud ied by the Swedish econo1nists in the 1 930s and then given a general

cq u ilibriu1n fonnulation by H icks /\t a certai n level we know what we arc a bout when we 1nodel thc1n, while at another we still seem 111uch a t sea I pose son1e of the 1nost irnportant questions here and leave certain other, inorc technical, ones u ntil later

The 1no1ncn t we stud y seq ucncc ccono1n ies we 111 ust su 1nen t the descrip tion o r agents given so far by thei r ex pectations

pplc-Of course, in the A rrow-Debreu description or co111 1nod itics, t,;x pcctat ions in the sense of probability d istri bu tion over states of

n ature a rc included in the notion of p re ferences So the novelty,

as far as that 1nodel is concerned , is that we rnust adjoin at least expecta t ion!-> concern ing future tenns at wh ich trade can take place These wil l be condi tional ex pectations One very non-

/Honey and General Equilibriu,n 35 Keynesian proposal is to take the expected price to be conditioned

by the state of nature and so independent of observed prices Sonderman, Green, Grandmont and others have studied 1nodels where the expectations are a map from observed prices into a suitable space of probability distributions of prices In any case,

a more or less uncertain future casts a shadow over the present, and not only are we closer to Keynes but, 1nore importantly,

to reality

The precise fonnulation of this class of 1nodels has revealed technical proble1ns which are more than technical For instance,

to name just two, there is a difficulty arising fro1n the possibility

of unbounded actions, e.g borrowing and lending, as well as difficulties with bankruptcy One says: no one can borrow more than a certain a1nount at any price as a n1atter of co1nn1on sense, but is left with the task of modelling this as a 1natter of rational choice There is also the question of what 1nanagers of firms whose shares may be held by agents with diverse expectations exactly are supposed to do Although recent work by Diamond , Stiglitz, Dreze, Wilson, Radner and Leland has cast some light, 1nuch is still in darkness But there are heroic assu1nptions, so1ne of the 1nost heroic, I fear, in Arrow-Hahn, which at least allow one

to proceed

Once a sequence fonnulation of the Walrasian econon1y has been achieved, new equilibriu1n concepts become available In particular, one would wish to distinguish between the equili­brium of an econo1ny at a n10111ent in time-temporary equilibriu111 and equilibrium through tune The definition of the latter is not now obvious since the underlying randomness, say, of the states

of nature, co1nbined with spot trading at each date, will at best generate a price distribution Radner has done so1ne pioneering work here, but other sources of randomness, e.g of tastes of endow1nents and an associated equilibriu1n concept, have been studied by Hilden brand t, M alinvaud and others For 111 y present purposes I shall however concentrate largely on the short period and so only write

Question 4 Has it been possible to construct a logically consistent model of short-period Walrasian equilibriu1n � i.e , does such an equilibriu1n exist? How palatable are the assu111ptions?

But we want more In particular, we wish to accon11nodate 1noney

in this construction and so want to ensure that, in any short­period equilibrium there n1ight be, 1noney has a positive exchange