Table Of ContentDecentralization in
Infinite Horizon Economies
Decentralization in
Infinite Horizon Economies
EDITED BY
Mukul Majumdar
§l
Routledge
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~
Taylor & Francis Group
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First publishing 1992 by Westview Press, Inc.
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Library of Congress Cataloging-in-Publication Data
Decentralization in infinite horizon economies 1 edited by Mukul
Majumdar.
p. em.
ISBN 0-8133-8090-1
l. Decentralization in management. 2. Decision-making.
3. Resource allocation. 4. Mathematical optimization.
I. Majumdar, Mukul, 1944-
HDSO.D44 1992
339.4'2-dc20 91-45889
CIP
ISBN 13:978-0-367-01594-7 (hbk)
Contents
Foreword vii
Acknowledgments ix
1 Decentralization in lnfmite Horizon Economies:
An Introduction, Mukul Majumdar 1
2 Optimal Intertemporal Allocation Mechanisms and
Decentralization of Decisions, Leonid Hurwicz and
Mukul Majumdar 12
3 On Characterizing Optimal Competitive Programs
in Tenns of DeCentralizable Conditions,
William A. Brock and Mukul Majumdar 46
4 Characterization of Intertemporal Optimality
in Tenns of Decentralizable Conditions:
The Discounted Case, Swapan Dasgupta and Tapan Mitra 58
5 Intertemporal Optimality in a Closed Linear Model
of Production, Swapan Dasgupta and Tapan Mitra 72
6 On Characterizing Optimality of Stochastic
Competitive Processes, Yaw Nyarko 100
7 A Characterization of lnfmite Horizon Optimality
in Tenns of Finite Horizon Optimality and a
Critical Stock Condition, Tapan Mitra and Debraj Ray 114
8 A Necessary Condition for Decentralization and
an Application to Intertemporal Allocation,
Leonid Hurwicz and Hans F. Weinberger 119
v
vi
9 Decentralized Evolutionary Mechanisms for
Intertemporal Economies: A Possibility Result,
VenkateshBala, Mukul Majumdar, and Tapan Mitra 152
10 Complements and Details, Mulcul Majumdar 181
About the Book and Editor 191
List of Contributors 193
Foreword
How can Pareto efficiency be achieved by a decentralized price system which
operates through time with no definite tenninal date? After forty years of
research, the problems raised by this question are not exhausted. This
book presents a set of recent articles dealing with the issue and very
usefully contributes to our understanding of it, and I am glad to greet its
publication.
The challenging difficulties motivating these articles appear when the
full extent of decentralization of economic activities is recognized in an
infinite horizon framework. Since the early times when the problem was fJrSt
considered in mathematical economics, skepticism about its significance
was expressed: Could the shift from a fmite to an infmite horizon have
serious implications for the mathematical properties of resource allocation
theory or for their interpretation? Intuition gave a negative answer, so that
many people too easily claimed that the problems had been somehow solved; a
loose reference was then given to one paper or the other that really dealt only
with a related question but not with the hard ones. This still happens
occasionally.
It would, of course, be still less justified to claim that the virtues of the
price system stand or fall depending on whether one looks at a finite or an
infinite horizon. We must, however, agree with a more modest but stubborn
proposition, namely that we are facing one of those cases in which scientists
have to feel uncomfortable because the validity of some centtal propositions
in their discipline remains exposed to doubt with respect to some not
fully negligible circumstances. This lack of comfort is the true reason for
digging deeper into the pending issues, as is done by the various chapters in
this book.
Mukul Majumdar provides in the introductory chapter an excellent
presentation of the issues raised by the contributors and their results. He
is obviously much more qualified for such a task than I, as I have not
worked on the subject for so many years. I may, however, be pennitted to
signal to the reader one development that, among others, looks to me as
particularly worth pursuing. Chapters 8 and 9 explore the concept of an
evolutionary process, in which agents make rolling plans up to a finitely
distant horizon and periodically revise these plans before reaching their horizon;
the constraints at the tenninal date of a rolling plan are then somehow related
to infonnation available at its initial date. This framework appears the
vii
viii FOREWORD
most relevant one to study. Since these two chapters, respectively, give a
negative result and a positive one, there is ample room for further research,
aiming in particular at generalizing the positive result and at closing the gap
with the negative one.
Edmond Malinvaud
College de France, Paris
Acknowledgments
In 1968 I was a research assistant in a project directed by Daniel McFadden
and Roy Radner at the University of California-Berkeley. Both were generous
in sharing time with me to discuss outstanding theoretical issues in
intertemporal economics as was Avinash Dixit My attention was drawn to the
classic paper of Edmond Malinvaud and the role of his "transversality
condition" in signalling inefficiency due to capital overaccumulation in a
decentralized competitive economy. In 1975, when John Chipman invited me to
give a seminar at the University of Minnesota, Leonid Hurwicz speculated on a
more general question on the possibility of attaining intertemporal efficiency or
optimality by designing some decentralized-but not necessarily competitive-
resource allocation mechanism. Collaboration with Leonid Hurwicz started in
1977 and eventually led to the essays collected in this volume. It has been a
pleasure to interact with the contributors.
Over the last twenty years, I have had the good fortune of collaborating with
Tapan Mitra. His insights into the structure of dynamic models have been
exceptionally helpful in deriving definitive results that I could not have proved
on my own. In this project, too, he has played an exceptional role.
Edmond Malinvaud's influence on my research defies adequate
acknowledgment. I have also benefitted from the important studies on growth
and capital theory by David Cass, David Gale, Bezalel Peleg, and David Starrett
Some of the essays in this collection appeared in a symposium in The
Journal of Economic Theory (volume 45, number 2, August 1988) that I
organized. In that connection I am most grateful to Karl Shell for his help and
encouragement. For giving me permission to reprint, I would like to thank
Academic Press and Springer Verlag.
Financial support from the National Science Foundation, the Guggenheim
Foundation, and Cornell University has enabled me to take a long-run view of
research. Indeed, successive chairs of the Economics Department-T.C. Liu
(who took a chance on me), Erik Thorbecke, Kenneth Burdett, and David
Easley-contributed to the creation of an environment that enabled me to
pursue a single theme over a long period.
For preparation of this volume I owe much to Ann Stiles and to my research
assistant, Manjira Roychoudhury. The project would not have materialized
without the enthusiasm of Spencer Carr.
Mukul Majumdar
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