Money, growth, and stability

Money, Growth and Sta bi I ity
Frank Hahn

The MIT Press
Cambridge 1 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
forrn 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


Contents

..

Acknowledgements
Introduction
In Praise of Economic Theory
1
2
3
4
5

PART I

vu

1
10

MONEY

Money and General Equilibrium
The General Equilibrium Theory of Money: A Comment
The Rate of Interest and General Equilibrium Analysis
Equilibrium with Transaction Costs
On Transaction Costs, Inessential Sequence Economies

and Money
PART II

NON-WALRASIAN EQUILIBRIA

6 On Non-Walrasian Equilibria
7 Exercises in Conjectural Equilibria
PART III

STABILITY

8 On Some Propositions of General Equilibrium Analysis
9 On the Stability of Pure Exchange Equilibrium
10 A Theorem on Non-tatonnement Stability
With Takashi Negishi

11 Uncertainty and the Cobweb

31
46
56
75

105
131
159
183
192
202
21O

Contents

V1

PART IV

GROWTH

231

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
Growth Model
17 On Some Equilibrium Paths

301
322

18
19
20
21

341

348
364
377

PART V

MISCELLANEOUS

Savings and Uncertainty
Exe ss Capacity and Imperfect Competition
On Optimum Taxation
On Equilibrium with Market-dep nd nt Information

Index

243
261
278

388


Acknowledgements

The publishers acknowledge with gratitude permission to repro­
duce the fallowing texts:

'Money and General Equilibrium' from the Indian Economic
Journal, 23, 109-22 (Special Number in Monetary Economics,
Oct.-Dec. 1975). 'The General Equilibrium Theory of Money: a

Comment' from The Review of Economic Studies (1952-3), 19,
179-85. ·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, 1-17. '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 Takashi Negishi frotn 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 ( 19 70) 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 Opti1num Taxation' from The Journal of Economic Theory ( 19 73), 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
Jevons 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
a worthwhile activity.
In the remainder of this introduction I briefly comment on the
papers which follow.
I

MONEY

My interest in monetary theory derives largely fro1n the difficulty
one has in incorporating it into classic theories of the econo1ny

which in other respects seem satisfactory. It is, of course, widely
known that Arrow-Debreu theory will not allow such incorpora­
tion at all. But recent work on models of overlapping generations
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


Introduction

2

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


Introduction

3

to consider that this abstraction is satisfactory both intellectually
and for the study of actual economies. To take just one exa1nple,
it seems that the fraction of UK GNP spent on advertising was for
long comparable to that spent on education. Such a dissonance
between theory and gross observation would certainly give pause
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 fro1n 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 co1nments on papers 8 , 9 and 1 0 . In 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 produc­
tion by Fisher (1983). Even so, we are a long way from under­
standing 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 intellec­
tually 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, 1976). I took my result to show that
warranted paths of the economy as defined by Harrod did not in

Introduction

6

general seek t h e steady stat e . I t never o ccurred to m e t hat anyo ne
\Vould \Vish to posi t perfect foresight o ver t he infinite fut ure . But
I \Vas \Vro ng : such a post u late is now co mmo nplace . It still strikes
1n e as d o tt y . O n the t e chnical sid e , d evelop 1nent s since I wro te
have sho\v n t hat \vith m an y co n su mptio n go o d s ( I assu m ed o nly
o n e su ch go o d ) t h ere \vo uld be a co ne of p aths which approach
t he stead y sta t e . These result s make my own no n-co nvergen ce
pro po si t io ns less d ra m atic but raise t he n ew pro blem o f t he non­
u niqueness of perfect fo resight paths. The relevan ce of all o f this
to t he rat io nal expectatio ns lit erat ure will b e clear.
I n pa pers 1 5 a nd 1 6 I study sta b ility not of equilibrium paths
b u t o f a ctual paths. In the first of these I postulate certain
resp o n ses to an e x cess d ema n d fo r fin ish ed go ods and for inputs.
Ho wever, a s S argen t ( 1 96 2 ) po int ed o ut later, I paid too little
att en tion to w ho go t \vhat \vhen the economy is out of equi­
librium . No ne the less, certa in o f the insights may b e of interest .
I n paper 1 6 I loo ked a t a situatio n no t too d ifferent fro m t he
'fix-price' literature o f recent years . By postu lat i ng a su b st it u tio n
t h eo rem eco nomy I co uld determine relat ive steady-st a te prices
as a fu n ct io n of the int erest rate and independently of excess
d emand . I then assumed a price fo rmatio n pro cess which pro­
ceed ed ind epend ently o f e x cess d em and a n d was governed largely
by expecta tio ns. I showed that it co nverged u nder cert a i n assu1np­
tio ns. On t he o ther h an d , ex cess demands at sub st it u t io n theore1n
prices w ere met o ut o f inventories. The a ccum ulation a nd d e­

cumu latio n o f the latter were go verned by a ' flexible a ccelera tor'
mech anism . I showed t hat t he stead y-state equ ilibrium was sta ble
in t he small und er t h is m echanisn1 . A short co 1ning o f t h e paper
is certainly that it assu n1 ed labo ur never to be in short supply ; b ut
it seem s to m e t h at it may no ne the less be a pro 111 ising beginn ing .
In paper 1 7 I use d uality t h eo ry to cxa111 i nc the behaviour o f
eq uil i b ri u m paths. I t he n pro ceed t o exa111 i n c a suggest i o n of S hell
and S t ig l i t z ( 1 9 67 ) that inelastic expectatio n s ( i . e . no n-ratio n a l
e x pect at ions ) a r c sta bi l i z i ng . It t urns o u t t hat t h i s i s b y n o 1ncans
always t he case .
V

MISC E LLAN EOUS

The fo u r p a p ers in t h is last part a rc on vario us to p ics . Pa per 1 8
was o cca sioned by o ne b y Lcvha ri a n d Srin ivasa n ( 1 9 6 9 ) . I t deals
w i t h t h e q uest io n o f w he t h er a n increase i n the un certai n ty o f t he


In troductio n

7

future productivity o f capital would lead to an in crease 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 o ptimum accumulation under un certainty .
Paper 1 9 was inspired by Hicks ( 1 9 5 4) . It is co ncerned with
excess capacity and entran ce d eterrence. It , o f course, does not
have the benefit of recent advan ces in the appli catio n of game

theory to these pro b lems. But Hicks 1nad e the important point
that the story rather d epends on the preferen ces of the people
who run firms. This point is not much d iscussed in current work
and it may be import ant .
Pap er 20 was written to clarify (partly to myself) the well­
known taxation results of Diamo n d and Mirrlees ( 1 9 7 1 ) . It pro­
ceeds slightly more generally than they did . Ho wever, 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 wa s required for the Diamo nd-Mirrlees results.
Paper 2 1 was also an attempt to understand . Joe Stiglitz had
given a preliminary versio n of the famous Ro thshild-Stiglitz
( 1 9 7 6) paper at a Cam bridge seminar . I could not then put my
finger on j ust what feature of the example was responsible for the
no n-existence of an equilibrium. Paper 2 1 was an attempt to do
so . This has sin ce been studied mo re deeply and satisfactorily by
Dasgupta , Hammond and Maskin ( 1 97 9) .

ACKNOWLEDGEMENTS
I am very grateful to Mr K. Gatsio s o f the Fa culty of Econo1nics
and Politi cs at the University o f Cambridge for proofread ing. My
intellectual debts will mostly b e o bvious . But one of these may
not be . For twelve years Teren ce Gorman and I \Vere co lleagues.
Many o f the papers here reprinted I discussed with him . He usually
went to the heart o f 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 a chieve.

REFERENCES
Cass , D . and Shell, K. ( 1 976 ) . ' The St ructure and St ability of Competitive

Dynamical Syst ems', Journal of Econon1 ic Theory , 1 2 , 3 1 -70 .


8

In troduction

Dasgupt a , P. , Ham mon d , P. and Maskin , E . ( 1 979), ' The l1n plementati o n o f
Social Choice Rules : Som e General Results i n I ncen t ive Co1npat ibilit y ' ,
R eview of Econom ic Studies , Symposium o n Ince n t ive Co1npatibility , 4 6 ,
1 83 -2 1 5 .
Deb reu , G . ( 1 9 70), ' Econom ies wit h a Finite Set o f Equili b ria', Econometrica,
3 8 , 3 8 7-92 .
Diam on d , P. and Mirrlees, J . ( 1 9 7 1 ) , 'Optin1al Taxation and Public Pro duc­
t i o n ' , A nzerican Econom ic R eview, 6 1 , 8-2 7 and 2 6 1 -7 8 .
Dreze , J . ( 1 9 7 5 ) , 'Existe nce o f Equ ilibrium u nder Price Rigidity and Quant i t y
Rationi ng' , International Econom ic R eview, 1 6, 3 0 1 -20 .
Fishe r , F. ( 1 983 ) , Disequilibriurn Foundations of Equilibriunz Economics ,
Oxfo rd Unive rsi t y Press .
Foley , D. ( 1 9 70). ' Economic Equili b rium wit h Costly Marketing', Journal of
Econom ic Theory , 2 , 276-9 1 .
Gal e , D. ( 1 982), Money : In Equilibriu1n , Cambridge Universi t y Press and
Nisbet , Cain b ridge Economic Ha ndbooks.
Gale , D. ( 1 983), Money: In Disequilibrium , Cam b ridge Universi t y Press and
Nisbe t , Cam b ridge Economic Handbooks.
Hart , 0 . ( 1 983) , 'Monopolistic Com pet i t ion in the Spirit of Chamberlin' and
'General Model and Special Results', ICERD Discussion Pa pers n o . 8 2 and
8 5 , Lo ndo n School o f Economics .
Helle r, W. and St arr , R. ( 1 976), 'Equil ib rium with No n-c o nvex Transaction
Costs : Monetary a n d Non-mo neta ry Economics' , R eview of Econon1ic

S tudies , 4 3 , 1 9 5 -2 1 5 .
Hicks, J . R. ( 1 9 54), ' The Process o f Imperfect Competition', Oxford Eco­
nom ic Papers , 6, 4 1 -54 .
Kurz , M . ( 1 968), ' The General Instability o f a Class o f Com pet i t ive Growth
Processes' , R eview of Econom ic Studies , 3 5 , 1 5 5 - 74 .
Kurz, M . ( 1 9 72), ' Equilibrium i n a Fin ite Sequence o f Marke t s wit h Transac­
t io n Cost s' , St a n fo rd Unive rsi t y , I nstitute of Mathemat ical S t u dies in t he
Soc ial Scie nces , Technical Report no . 5 1 , Januar y , Stan ford , Cal i fo r ni a .
Levhari, D . a n d Srin ivasa n , T . N . ( 1 969), 'Opt imal Savings Und e r Uncer t ai n t y' ,
R eview of Econo,n ic Studies , 3 6 , 27-3 8 .
M a ko wski , L. ( 1 9 8 3 ) , ' " Ra tio nal Co nj e ct ures" a re n ' t Ra t i o n a l and "Reaso n­
a b le Conjectures" a re n ' t Reaso nable ' , SSRC Proj e c t o n ' Risk , I nformation
and Quantity Sign als in Eco nomics', Ca m b ridge Un iversit y Discussio n
Pa per no . 6 6 .
M a l i nva u d , E . ( 1 9 7 7 ) , The Theory of Unenzploynzen t R econsidered, Basil
Blackwe l l , O x fo rd .
Marsh a k , T . a n d S e l te n , R . ( 1 9 79), A GenC'ral h'quilibriu,n Model with Price­
makinK Firms, Spri nger , New Yo rk .
Ncg ish i , T . ( 1 96 1 ) , ' M o no pol ist ic Co m pe t ition and General Eq uilibrium ' ,
R eview of h'c onom ic ,S'tudies , 2 8 , 1 96-20 I .
Pa t in k i n , D. ( 1 96 5 ) , Muney, Interest and Prices (2nd edn), Harper and Ro w ,
New Yo rk .


Introduction

9

Rot hshild , M . and Stiglitz, J . ( 1 976), 'Equilib rium in Comp etitive Insurance
Markets : An Essay on the Economics of Imperfect Information', Quarterly

Journal of Economics , 90, 6 29- 49 .
Sargent , ( 1 96 2), ' The Stability o f Growth Equilibrium : Com ment ' , Quarterly
Journal of Economics , 304, 494-50 1 .
Shell, K. and Cass , D. ( 1 976), ' Th e St ructure and Stability of Competitive
Dynamical Systems', Journal of Economic Theory , 1 2, 3 1 -7 0 .
Shell, K. a n d Stiglitz, J . ( 1 967), ' Th e Allocation o f Investment i n a Dynam ic
Economy', Quarterly Journal of Economics, 8 1 , 5 9 2-6 1 0 .
Smale, S . ( 1 9 7 5 ) , 'An Approach t o the Analysis o f Dynamic Processes in
Economic Systems', in Equilibrium and Disequilibrium in Economic
Theory , ed. G. Schwoohauer, Reidel, Boston.
Starrett , D. ( 1 973), ' Inefficiency and t he Deman d fo r Mo ney in a Sequence
Economy', Review of Economic Studies, 40, 437- 4 8 .

B


I n Pra i se of Eco n o m i c Th eo ry

I con1e before you today to blow the tru1npet for econo1nic theory
large ly because it is so often under attack and so often misunder­
stood. But I have not come to da1nn other e ndeavours in eco­
no1nics. This is not entai led by praising theory and ,votdd be odd
in a Jevons Lecturer. J evons ,vas both a theorist and an applied
econo1nist and on occasions e x cel led 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�o lly. But there is another reason ,vhy, if it had not bee n too

latc , 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 sha ll want to argue that the variety
of co1npcting econo n1ic theories is nn1 ch s111aller than popular
opi nion takes it to be. But I do not want to start ,vith either that
question or t h at argu111 ent. For what I a1n centrally interested in
is the enterprise of the9riz ing in econo 111ics . By t his I 1nean the
undertaking to gai n understanding of the particu lar by reference
to generalizing insight s and in the light of certain abstract unifying
princ i pl e s.
I want t o c 1nphasi zc the word · u nd e rstand ing' and tha t i t is not
din; ct ly re lated to posi t i vist predi ct ion. Fo r instance , we under­
stand tlH� cau se o r c�1 rthq u �1 kes hut canno t at t he 111on1ent pred ict
the m. We can u 11 d c rst �1 1Hl wlty two peo p le arc seen to e xchange
without bt: ing able to pred i ct tha t they wi ll d o so. So1newhat 111ore
so p h ist i catedly, we 1nay be ab le to u nderstand an a llocation of


In Praise of Econo,nic Tlz eory

11

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 clai1 n '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 abilit y 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 argu1nent to show that , while chocolate, lipstick , cars, etc. , are intrinsic
goods, understanding of the world needs justification in tenns of


12

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
n1ig ht w ant 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 unify ing
prin ciples'. It is th is 1nore particular n1ode of proceeding which
I want to convince you is worth y of praise.
Let 1ne call 'the abstract unify ing principles' axion1s and dis­
tinguish th ese fron1 assun1ptions. A th eory will typically h ave
a logical structure derived fron1 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 on e starts w ith observation
one requires at the very least an axion1 of induction b ut in general
a much richer array. One of n1y first reasons for praising theory ,
at least in its n1od ern 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 w hat somewhat mysteriously is called the 'real'
world , they constitute claims about this world so widely agreed as
to make fu rther argu n1ent unnecessary. Indeed , often i n axion1ati z­
ing a theory one is atten1pti ng to see \Vhether its propositions are
ded ucib le from cle 1nentary agreed features of the world . For
i n stance , the von Neun1ann axion1atization of expecte d utility
includes the 'sure thing principle'. It appeals to our intu ition and
it appeals to what we know about ourselves.
The best known and rnost in1 portant axiom is, of course, th at 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 i losoph ical debate on th e 1ncaning of "rat ional' . It also arouses
hosti l ity arnong th ose rorna n t ical l y incl ined :
A levelli ng rancoro us ra tional so rt of rn incl
That never looked o ut of t he eye of a sa int
Or o ut of a dru n k ard 's eye

( Yeats, Seven So ngs)


J,1

Praise of Econon1ic Theory

13

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 charac­
teristics 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 fe\v assu1nptions - for instance,
the symmetry of the substitution tern1 s, the excess burden of non­
lump-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 founda­
tion 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 follo\v the Friedmanite

route whose singleminded concern with prediction I have already
disclai1ned. The 'as if ' argun1ent is in any case shaky . I t does not
allo\v one, for instance, to distinguish bet\veen agents who act on
their O\vn preferences and those \vho are con1pelled t o act on the
preferences of a hypnotist. For purposes of ·understand ing ' , the
status of the axio1ns n1atters a great deal.
In the first instance, then, I \Vant to 1n aintain that the pa rt 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 a l l .
Between any A and B fron1 a rich do1nain he can either not put


14

In Praise of Econornic Th eory

t he111 in to a ny preferen ce relation or not understand what is meant
\vhen he is asked to do so. This person \vould h ave 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.
Eve n if his actions 'revealed' preferences, \Ve could not invoke
these to underst and the a ctions. I n short, he \vould be an ani1nal
a nd not a perso n ; for aniin als can give no reasons for their actions
and neither can this someone. In the first instan ce, then, the
axion1 says that economic agents are persons.
But, of course , it is stronger than that. For instance, persons
1n ay make n1istakes in their preferen ces and they 1nay have no

preferen ces over parts of the domain in \Vhich they are not offered
choices. It n1ay be the case that a person's preferen ces are not
t ransitive. There are t\vo things to be said here. First, mu ch of the
theory can proceed \Vith a weaker version \vhich does not postulate
transitivity. For this I refer you to a fa1nous paper by Son nenschein
( 197 1) . Second , \Ve \vould expect that a person would re-exa1nine
his preferen ces 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 a ctions. However , at the end we shall
have to agree that the ge n uine axion1 , persons have so111e prefer­
en ces, has been idealized and strengthened by theorists beyond the
point at \Vhich it con1111ands u niversal conse nt .
The sharpening and idealizatio n o f agreed fea tures o f the \Vorld
is one of t h e d i stin ctive 1narks of theorizing. On e atte1npts to
und e rstan d eve n ts in the lig h t of refined descriptions of con11non­
place reg u la ritie s and their logical cn taihne nts. One u ndersta n d s , in
so far as o n e ca n give no reaso n why the sharpening a nd idealiza­
tion of the ag reed axio n, sho uld n1islead on e .
Take a s a n exan1 p lc t h e case o f a Giffe n good , tha t is, a good
t h e de1n a n cl fo r whic h va ries positively wi th price. Our axio1n has
l ed us to a distin ctio n b e t we en su bstit ution a n d i n co1nc effects.
We u n d ersta nd t ha t a r ise in price of t h e good will cause co nsu 1ners
t o see k a su bstit u t e while a sig n i ficant d e cline in rea l w ealth result­
i n g fro In t h l' p ricc 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 i t is o f a k i n d t h �, t low-wealth peo ple h ave to co nsu 1nc
pro po rt io n a t e ly , n o rl' o r . W h l' n I say we u n lk rsta n d I 1n ean two
t hing� . Firs t, t h e o bse rva tio n of �, Giffe n good case fi t s into the
t h t.:o ry , a n d t h e exp la n a tio n co n fo rn1s wit h w hat we kno\v of
ou rse lves a n d o t h l'rs. B u t I rnean so 1n ething e l se as we l l : we can

In Praise of Econo,nic Th eory

15

explain to son1eone surprised by the deviation of a Giffen 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 under­
stood 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 co111puta­
tional ability. Knowledge and computation are themselves objects
of choice, and that seems to leave the theory dangling by its boot­
straps.
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 so111e­
what 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


16

In Praise of Econonzic Th eory

\v het h er tha t n1e ant t hat they ahvays con sun1e d the san1e things
i n d e pe n d e ntly of prices or inco1ne . H e was not ,villing to agre e
to th a t. A fter son1e ti1ne it se en1ed t hat ,ve could agree that
con sun1ers h ad a h ab itual response to income and p r ices , at \vh ich
point I could not forbear to t ranslat e t h is into : Consun1 ers h ave
rat h er stable pre ference s . In exactly t h e sa1ne \vay can Sin1on's
critique b e used to d ee p e n un d erstanding of what we already have .

A consun1 er buys a good at a price h igh er t han p revails for an
i d entical good else \v here . Ho,v d o we u n d erst and that , and w hy is
there som e t h ing h e re w h i c h ,ve need to underst and ? We h av e
a p rin1a facie puzzle b ecause t he pure t h eory d oes n ot account for
the event . Sin1on rea 1 1y con1 es to its aid by proposing t hat the
con sun1 er n1 ay not k no,v of the ch eaper good and that he ,votdd
have to e xpe n d e ffort to find out. He will sp end tha t e ffort i f h is
asp irations not to b e t aken for a rid e are ser iously in1paired , i. e.
w he n he b elieves t he gain fro1n searc h large e n oug h .
I d o not. of course , wish t o argue that a ll roa d s lead back to t he
te xtbook th eory. \Vhat I d o wan t to 1na i n ta i n is t hat it has n1ad e
possible an ord erly and coh ere n t d eepening of und erstand ing .
I need only ren1 ind you o f the recent tlowering of t h e econo1nics
of i n fo nn ation to 111 a k e th is poi n t. T h e i n i t ial th eory, once
d igest ed . threw a k in d of searchlight on the u n e x plained : Why can
s i1n ilar good s sell at d i ffere n t p r ices? How are potent i al e xch a nge
po ss i b ili t ie s n1 ad e k now n , a n d is i t possible t h at u n satis fact ory
s t a t es where t h ey a re not a 11 k now n can persist? How is the 1narket
for loa ns a ffe cted by 111ora l hazard , a n d how is that connected
w it h son1e ratio n i ng or cred i t ? O n e can go on and on to d e 111on­
stra t e how t h eo ry ge nerate s the question a n d prov i d e s the la nguage
fo r att e 1n pted a n s\ve rs . Wi t h out t hat a bs t ra ct t h eory we wou l d
k n ow n e i t h er w he n t o ask ·why' n o r how t o proceed wh e n ,ve d o
a sk.
I ha ve spe n t a lo ng t i 111 c on t h is n1o st co n t ent i o us a sp e ct of
t h eo r iz i ng , t h e ra t io n a l a g e n t . T h e re are o t h e r d irectio n s to
e x plo re. I l oweve r , b e fo re I d o t h�1 t t wo o t h e r aspe c t s d ese rve so n1 e
CO 111 111 C ll t .
T h e fi rst o f t hese i s e�1 sily a nd q u i c k ly d is c u ssed . O p pone n t s of
t h eo ry o ft e n arg u e t h a t it is t �1 u t ologo u s b e ca u se i t co nsist s of

log i c a l d ed uct io ns fro 111 a x io 1n s a n d ass u 1n p t io ns. I f o ne is k i n d to
such crit ics o n e i n terpre t s t h e n1 as sign a l l i ng t h a t t h ey do no t care
fo r t h ese a x io 111 s a nd t h ese a ssu 111 p t io ns. I n a ny case , a ll t h eo ry i n
all �u bj c c t s p ro ceed s i n t h is 1na n ne r . I n t h e p rese n t co n t e x t o ne
so 1n e t i rne � h ears i t 111:.i i n t a i n ed t ha t t h e t he o ry of cho ice s i 1nply


In Praise of Econonzic Th eory

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 refrain 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 unfa111iliar
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


18

/11 Praise of Econonzic Th eory

use ful. Y e t j ust 110\v in Britain it also see1n s dangerous. Indeed ,

onl y t h e other day a politician warned against it at the Conserva­
tive conference . Certainly if what Mr Lawson asserts is taken to be
economic th eory , th en 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 th em \Ve treat as an axiom , while universal perfect con1peti­
tion , for inst ance , 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. B u t 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 empiricisn1 . That n1anagers have pre ferences is an axion1 :
that they take a particular fonn - for instance that they are linear
in e xpected profit - is an ass u 1nption \vhich both si1nplifies and
seen1 s not implausible in the light of experience . Whatever it is ,
a theory suggests that \Ve und erstand . that understanding is con­
tingent on both the axioms and assu 1nptions . It certainly is also
contingent on the logical entailn1ent of the proposi tions of the
theory by the assu 1nptions and a xio1ns .
Consider a fashionable cxan1ple . The proposal that \Ve should
take it that an agent \Vhose forecasts of future events are syste 1nati­
cally disappointed \vill change his forecast se e1ns to n1e a xiomatic.
I t is d ifficult in t he light of introspection and experience to deny
it , although I have no d ou bt that one can find exceptions. But
that an agent will nonn ally have l e a rned to n1ake forecasts which
arc not systen1atically disappointed is hardly a self-evident truth .
M ore seriously, there arc great difficu lties in und erstand ing ho\v
the agent cou ld reach this satisfacto ry state ; for the learning of

agents a ffects what there is to be learned . Sterling pioneering \vork
on this rnatter by such econo 1nis t s a s M argaret Bray ( 1 9 8 2 )
illustrates this . H e nce the proposition that a gents have rational
expectations is an assu 1np tion. Cerli. 1 in not very care ful people
have tho ught that this a ss un1 ption is i1nplicd by \vhat I have
granted as an axio1n : viz . , that peop le will no t persist in an
erroneo us b e l ie f. S u c h a step is j ust wrong . It is not 1na d c right by
rationa l cxpcct�1tions ccono111etrics wit h good fits . That is so
beca use we cannot und e rstand why it s h o u ld fit well. As I hav�
a rgued e lsewhere , t h e evid ence fo r 111 i raclcs at Lourd es is stronger
tha n is this ccono111ctrics . Y et without understanding it does not
pe rsuad e .


In Praise of Econon1ic Th eory

19

What a rational expectations theory provides is an understand­
ing 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 spe cial infonnation. 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 expect ations theorizing be cause 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 t heoretical point of
view, the rational expe ctations story, even when tak en as a useful
'Gedank en 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 extrava­
gance 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 : t h at theory is
powerful in saving us from cranks and witches only if it is taken
seriously. For who can understand the precisely forn1u lated 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 e conon1ies. 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 sophis­
tication to understand what one is about in equilibriu1n theorizing.
I want here to praise the giants of equilibrium theory, Arro\v
and D ebreu. 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 designa t ed as an
equilibrium. In particular, this left 1nany possible states which

were not equilibriu1n stat es and one needed to prove tha t there are