Theory of Markets

129 Pages·1989·7.224 MB·English

by  Michael Allingham (auth.)

THEORY OF MARKETS
By the same author
EQUILffiRIUM AND DISEQUILffiRIUM
GENERAL EQUILffiRIUM
RESOURCE ALLOCATION AND ECONOMIC POLICY (editor with M. E.
Burstein)
VALUE
THEORY OF MARKETS
Michael Allingham
Professor of Economic Theory
University ofK ent
Palgrave Macmillan
ISBN 978-1-349-10267-9 ISBN 978-1-349-10265-5 (eBook)
DOI 10.1007/978-1-349-10265-5
© Michael AUingbam 1989
Softcover reprint of the hardcover 1s t edition 1989
AU rigIUs ~ For information. write:
Scbolarly and Reference Division.
SI. Martin's Press,Inc., 175 Fifth Avenue,
New YOIt, N.Y. 10010
First published in the United Stares of America in 1990
ISBN 978-0-312-04062-8
library of Congress Caraloging-in-PubHcation Data
AUingham. Michael.
Theory of markets / Michael AIIingham.
p. CID.
Inchldes bibliographical references.
ISBN 978-0-312-04062-8
I. Marltct&-Mathematical models. 2. EquiHbrium (Economics)
I. Tide.
HFS470.A45 1989
332.()4.-(Jc20 89-29088
CIP
Contents
Preface vii
1 Introduction 1
2 Traders 4
Preferences 4
Utility 10
Demand 16
3 Economies 23
Excess Demands 23
Decomposability 25
Quasi-economies 33
4 Equilibrium 36
The Market Correspondence 36
An Aigebraic Approach 39
A Differential Approach 46
5 Smooth Economies 51
The Equilibrium Manifold 51
The Natural Projection 55
An Excess Demand Approach 58
Index Analysis 61
6 Close Economies 65
Revealed Preference 65
Uniqueness, Stability and Scarcity 68
Substitutes 76
v
vi Contents
7 GoocIs aud Assets 82
Real Economies 82
Financial Economies 84
Mixed Economies 93
8 AUocations ')7
Efficient Allocations 97
Core Allocations 102
Approximation 104
Replication 108
Glossary 115
Bibliography 116
Index 119
Preface
Adam Smith's famous invisible hand, through which the individual'by
pursuing his own interest frequently prornotes that of society more
effectually than when he really intends to promote it', operates through
the market system. This book explores the workings of this system;
how prices are formed, how they change and how they affect people.
Tbe markets which affect people most directly are those for real goods
and services, such as food, shelter and labour. Yet the markets which
are most active are those for financial assets and instruments, such as
stocks, bonds and currencies. Tbe currency markets in London alone
are over twice as important, in terms of value, as the labour markets
in the entire world. This book develops a unified theory of markets
which integrates markets for real goods with those for financial assets.
As the questions considered are quite deep the treatment is necessarily
somewhat technicaL However, all the mathematics required is available
in the standard treatments of mathematica1 methods in economics; an
excellent summary may be found, for example, in the first chapter of
Andreu Mas-Colell's The Theory 0/ General Economic Equilibrium.
Although employing technical arguments the book is essentially
about markets rather than technique. It thus differs from Mas-Colell's
work, which is 'a book on technique, and technique is, undoubtedly,
its raison d'etre'. In the same way it differs from a related book, Yves
Balasko's Foundations 0/ the Theory 0/ General Equilibrium, which is
'devoted to a presentation of the theory that takes advantage of the
differentiability assumptions'.
Indeed, the technical requirements are kept as simple as possible; in
particular, no use is made of topology on dimensionless spaces, or,
beyond its most basic concepts, of measure theory. However, this does
mean that certain topics are omitted; there is little discussion of spaces
of preferences, or of economies with infinitely many traders.
Tbis book developed from aseries of lectures which I gave at the
School of Advanced Studies in Social Science in Marseilles, and
developed further at the Institute of Advanced Studies in Vienna. I am
grateful to colleagues in both institutions for many valuable discussions,
and to the University of Kent at Canterbury for the period of leave in
vii
vüi Preface
which the book was written. I am also grateful to members of the Man
group in London, New York and Hong Kong for an invaluable insight
into the workings of markets in practice.
MICHAEL ALLINGHAM
1 Introduction
In the course of a few hours on 'Black Monday' in October 1987, and
in the absence of any significant iII news, the value of the entire
productive wealth of society, as measured by its price on the stock
market, fell by something of the order of a quarter.
Tbis book explores the workings of the market system which
produced such an apparently extreme change: how prices are formed,
how they change and how they affect people. It does this by developing
a theory of markets.
Tbe basis of such a theory is an analysis of the behaviour of the
people in the market, or traders (this is discussed in Chapter 2). Traders
have preferences about the various commodities (food, stocks and so
forth) in the market; they also have given bundles of commodities, or
endowments, which they may trade. Given a system of prices, one for
each commodity, they plan, on the basis of their preferences and
endowments, how much of each commodity to buy and how much
to seil.
The economy, or market system, is specified by the characteristics
that is, the preferences and endowments - of the various traders
(Chapter 3). Given some price system the excess demand ror a
commodity is the difference between total planned purchases and total
planned sales. Provided that traders' preferences are reasonably orderly
these excess demands will be continuous, in that a small change in
prices will bring about only a small change in excess demands. Indeed,
this is (effectively) the only property which excess demands must
have: the relation between excess demands and prices may take any
continuous form.
The central concept of the theory is that of equilibrium - that is, a
system of prices at which each trader's planned purchases and sales
can actually be made, or equivalently at which the excess demand for
each commodity is zero (Chapter 4). And the central result of the theory
is that there a1ways is such an equilibrium. However, there may be
infinitely many equilibria, and these may change substantially when
the characteristics of the agents change only marginally.
If, as is typically the case, the preferences of the various agents are
'smooth' (in a technical sense) then the theory becomes more specific
(Chapter 5). Tbere may still be infinitely many equilibria, but this
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