The Social Viability of Money: Competitive Equilibria and the Core of Overlapping Generations Economies

208 Pages·1991·7.606 MB·English

by  Dr. Joan Esteban (auth.)

Lecture Notes in Economics
and Mathematical Systems 372
Editorial Board:
H. Albach, M. Beckmann (Managing Editor)
P. Dhrymes, G. Fandel, G. Feichinger, W. Hildenbrand
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Managing Editors:
Prof. Dr. M. Beckmann
Brown University
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Prof. Dr. W. Krelle
Institut fUr Gesellschafts- und Wirtschaftswissenschaften
der Universitat Bonn
Adenauerallee 24-42, W-5300 Bonn, FRG
Joan Esteban
The Social Viability
of Money
Competitive Equilibria and the Core of
Overlapping Generations Economies
Springer-Verlag
Berlin Heidelberg New York
London Paris Tokyo
Hong Kong Barcelona
Budapest
Author
Dr. Joan Esteban
Institut d' Analisi Economica, CSIC
Universitat Autonoma de Barcelona
Bellaterra, E-08193 Barcelona
ISBN-13: 978-3-540-54649-8 e-ISBN-13: 978-3-642-46755-4
DOl: 10.1007/978-3-642-46755-4
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© Springer-Verlag Berlin Heidelberg 1991
Typesetting: Camera ready by author
42/3140-543210 -Printed on acid-free paper
CONTENTS
Foreword
PART I Introduction
Chapter I The Viabil ity of Fiat Money 3
PART II The Overlapping Generations Model of an
Exchange Economy 25
Chapter II Dynamic Efficiency 29
Chapter III Competitive Equilibria in a Barter,
Overlapping Generations Economy 53
Chapter IV Monetary Equilibria 77
PART III The Core in Overlapping Generations Economies 103
Chapter V A Characterization of the Core 105
Chapter VI Competitive Equilibria and the Core.
One agent per generation 131
Chapter VII Competitive Equilibria and the Core.
Many agents per generation 161
References 195
Foreword
IX
The content of this book has developed along a fairly
extended period of time. It was Teo Millan who by October 1981
drew my attention to overlapping generations models, when
conducting a workshop on this topic at the Universitat Autonoma
de Barcelona. This workshop was attended by Xavier
Calsamigl ia, Isabel Fradera, Andreu Mas-Colell, Clara Ponsati
and Pep Oliu. It was there were I first presented my initial ideas
on the core of an overlapping generations economy with one agent
per generation, which finally became what now is the SUbject of
Chapters V and VI, in Part III.
An initial version of the material contained in these
Chapters was published at the Working Papers series of the
Department and was later converted into two articles: "EI nucleo
en Economias de Generaciones Sucesivas", Revjsta Espanola de
Economja, 2 (1985), 3-17, and "A Characterization of the Core in
Overlapping-Generations Economies", Journal of Economjc
Theory 39 (1986), 439-456. The extension of the model to
generations with many agents was initiated as a joint work with
Teo Millan during the first half of 1983 and has now become
Chapter VII of this book. It has been previously published as
"Competitive Equilibria and the Core of Overlapping Generations
Economies" Journal of Economic Theory 50 (1990), 155-174, co
authored with Teo Milich
The development of my research has shaped the
structure of the book. Except for an intrOductory Chapter, it is
organized in self -contained units. Each Chapter begins with an
introductory section, containing the motivation and review of the
relevant related work. This is followed by the formal description
x
of the model, as well as the definitions and assumptions that will
be used in the Chapter. Finally, chapters end with a section
discussing the main implications of the results. In order to help
the reader not familiar with the Overlapping Generation model I
have included Chapters II, III ad IV, Part II of the book, which give
a rigorous but not highly technical presentation of the model.
I wish to aknowledge my debt to the colleagues and
friends who have read different bits of my research in previous
versions. I have benefited from helpful comments by Jordi
Andreu, Salvador Barbera. Dave Cass, Suchan Chae, Luis Corch6n,
Isabel Fradera, Jean Fraisse, John Geanakoplos, Birgit Grodal,
Roger Guesnerie, Tim Kehoe, Jean-Jacques Laffont, Antonio
Manresa, Andreu Mas-Colell, Michel Moreau, Heraklis
Polemarchakis, Ferran Sancho, Jose Scheinkman, Karl Shell, Hugo
Sonnenschein, Juan Urrutia, Fernando Vega, and Neil Wallace. I
wish to give special thanks to Teo Millan, Xavier Calsamiglia,
David Bevan, Jim Mirrlees and Nick Stern. They have discussed
with me virtually every point and have been for me a constant
source of stimulus.
Financial support from the Fl.lndacidn del Banco
Exterior for the completion of this research is gratefully
acknowl edged.
PART I
INTRODUCTION
Chapter 1 The Vjabil jty of Fjat Money
1.1. Introductjon
In this book we analyse overlapping generations economies
from a game theoretical point of view. We are concerned with the
social acceptability of consumption allocations in infinite horizon
models of pure exchange economies with agents with finite lifetimes
who behave cooperatively. Specifically. we study the core of such
economies and its relation with competitive equilibria.
The overlapping generations model poses a number of
specific theoretical problems. The fundamental difference with
r,espect to the standard Arrow-Debreu model is the description of
the population of consumers. In the overlapping generations model
time is defined as an indefinite sequence of periods. In each period a
new generation is born and a generation dies. Let us suppose that
periods are so defined that every generation lives for two periods.
Generation t when young will overlap with old generation t-1 and
when old with the then new young generation t+1. This specific
demographic structure imposes an exogenously 'given interdependence
among consumers. Exchanges involving future del iveries against
present goods can only be agreed under the certainty that the future
unborn generation will accept to carry out the delivery which in turn
requires the certainty that the generation after will in turn make a
compensating delivery. and so on.
Samuelson [50] was the first to give an example of an
overlapping generations model in which the walrasian equilibrium
4
was not Pareto optimal. Since then there have been many
contributions towards explaining why the competitive mechanism
may fail in bringing about efficient allocations. Amongst the most
significant ones we have Cass and Yaari [14], Shell [55], Gale [27],
Balasko and Shell [4] and Okuno and Zilcha [47]. The fact that the
First Fundamental Theorem of Welfare Economics does not apply to
overlapping generations economies makes plain that some walrasian
allocations will be unanimously rejected by the full sequence of
consumers. Therefore, it is obvious that there is another way in
which the overlapping generations model departs from standard
Arrow-Oebreu economies. The well known result that the set of
competitive equilibria is a subset of the set of core allocations (and
as the economy is replicated it coincides with) will not apply either.
It is our purpose to provide a detailed examination of this point.
Since Samuelson's [50] contribution overlapping
generations models have been seen as the appropriate framework in
which the "social contrIvance of money" could be examined. The
introduction of fiat' money permits the implementation of Pareto
optimum allocations that could not have been reached in barter
economies. The question arises of whether the institution of fiat
money is a stable one, Le. will not be refused by some agents, In
Samuelson's [50] words «the use of money can itself be regarded as
a social compact» (p.482). But, as he points out, «in terms of
immediate self -interest the existing productive workers should
perhaps unilaterally repudiate the money upon which the aged hope to
live in retirement. So a continuing social compact is required» (ibid.
,p.482, footnote 22). Besides their relevance for the foundations of
monetary theory, these questions may shed some light on problems