Activity Analysis in the Theory of Growth and Planning: Proceedings of a Conference held by the International Economic Association

343 Pages·1967·28.929 MB·English

by  E. Malinvaud, M. O. L. Bacharach (eds.)

INTERNATIONAL ECONOMIC ASSOCIATION
CONFERENCE VOLUMES, Numbers 1-50
NUMBER 16
Activity Analysis in the Theory of
Growth and Planning
ACTIVITY ANALYSIS
IN THE THEORY OF
GROWTH AND PLANNING
Proceedings of a Conference held by
the International Economic Association
EDITED BY
E. MALINVAUD
AND
M. 0. L. BACHARACH
M
. .
S
TOCKTON
P R E S S
© International Economic Association 1967
Softcover reprint of the hardcover 1st edition 1967 978-0-333-40644-1
All rights reserved. No reproduction, copy or transmission
of this publication may be made without written permission.
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or transmitted save with written permission or in accordance
with the provisions of the Copyright Act 1956 (as amended).
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this publication may be liable to criminal prosecution and
civil claims for damages.
First published 1967
This 50-volume set reprinted 1986 jointly by
THE MACMILLAN PRESS LTD
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and London
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and
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Distributed exclusively in Japan
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Published in the United States and Canada by
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ISBN 978-1-349-08463-0 ISBN 978-1-349-08461-6 (eBook)
DOI 10.1007/978-1-349-08461-6
CONTENTS
PAGE
LIST OF PARTICIPANTS vi
ACKNOWLEDGEMENTS vii
INTRODUCTION. Edmond Malinvaud viii
PART I
STUDIES ON GROWTH THEORY
CHAP.
1. EcoNOMic GROWTH AT A MAXIMAL RATE. T. C. Koopmans 3
2. MAXIMAL PATHS IN THE VON NEUMANN MODEL.
L. W. McKenzie 43
3. SOME ANALYTICAL AND PRACTICAL ASPECTS ON THE THEORY
OF CAPITAL. M. Allais 64
PART II
PLANNING THEORY
4. DYNAMIC PROGRAMMING OF EcoNOMIC GROWTH. R. Radner 111
5. PROGRAMMING INVOLVING INFINITELY MANY VARIABLES
AND CONSTRAINTS. L. Hurwicz 142
6. ALTERNATIVE PREFERENCE FUNCTIONS IN PROBLEMS OF INVEST-
MENT PLANNING ON THE NATIONAL LEVEL. S. Chakravarty 150
7. DECENTRALIZED PROCEDURES FOR PLANNING. E. Malinvaud 170
PART III
PLANNING EXPERIENCES
8. MATHEMATICAL PROGRAMMING OF LONG-TERM PLANS IN
HuNGARY. J. Kornai 211
9. CoNSISTENT PROJECTIONS IN MuLTI-SEcToR MoDELS.
J. R.N. Stone 232
10. PROGRAMMING MODELS OF INTERREGIONAL EFFICIENCY AND
LAND UsE IN AGRICULTURE. E. 0. Heady, N. S. Randhawa,
and M.D. Skold 245
11. AN EXPERIMENTAL MODEL FOR INVESTMENT PLANNING.
S. Rafael 269
PART IV
REPORT ON THE PROCEEDINGS
SuMMARY RECORD OF THE DEBATE. M. 0. L. Bacharach 281
INDEX 331
v
LIST OF PARTICIPANTS
Professor M. Allais, Ecole des Mines, Paris, France.
Mr. M. 0. L. Bacharach, University of Cambridge, U.K.
Professor S. Chakravarty, Presidency College, Calcutta, India.
Professor R. Dorfman, Harvard University, Cambridge, Mass., U.S.A.
Mr. M. J. Farrell, University of Cambridge, U.K.
Professor L. Fauvel, Faculte de Droit, University of Paris, France.
Professor F. M. Fisher, Massachusetts Institute of Technology, Cam-
bridge, Mass., U.S.A.
Professor W. M. Gorman, University of Oxford, U.K.
Dr. F. H. Hahn, University of Cambridge, U.K.
Professor E. 0. Heady, Iowa State University, Ames, Iowa, U.S.A.
Professor L. Hurwicz, University of Minnesota, Minneapolis, Minn.,
U.S.A.
Professor T. C. Koopmans, Yale University, New Haven, Conn., U.S.A.
Dr. J. Kornai, Computing Centre of the Hungarian Academy of Sciences,
Budapest, Hungary.
Professor A. A. Lazaris, Athens, Greece.
Professor L. W. McKenzie, University of Rochester, N.Y., U.S.A.
Dr. M. McManus, University of Birmingham, U.K.
Professor E. Malinvaud, Institut National de la Statistique et des Etudes
Economiques, Paris, France.
Dr. G. Morton, London School of Economics, U.K.
Mr. Philippe Mouchez, Faculte de Droit, University of Clermont
Ferrand, France.
Dr. A. Nagy, Hungarian Chamber of Commerce, Budapest, Hungary.
Professor A. Nataf, Centre de Recherches Mathematiques pour la Plani-
fication, Arcueil, France.
Professor G. U. Papi, University of Rome, Italy.
Mr. M. Posner, University of Cambridge, U.K.
Professor R. Radner, University of California, Berkeley, Calif., U.S.A.
Dr. S. Rafael, Institute of National Planning, Cairo, U.A.R.
Professor E. A. G. Robinson, University of Cambridge, U.K.
Professor J. R.N. Stone, University of Cambridge, U.K.
vi
ACKNOWLEDGEMENTS
THE International Economic Association wishes to express its
gratitude to all those who have contributed to the success of the con
ference, held at Cambridge in July 1963, of which the papers and dis
cussions are recorded in this volume. The Association is particularly
indebted to Professor Malinvaud, who was largely responsible for its
planning, and to Mr. Michael Bacharach, who has discharged a much
more than usually onerous task in recording the discussions and in
preparing the papers for publication. It is to the authors of the
papers themselves, however, that thanks are principally due. The
readers of this volume can judge for themselves the importance of
the papers both to activity analysis proper and to the longer-term
development of economic theory along these new lines. Secondly
we would wish to thank both the Master and Fellows of Clare
College, Cambridge, for allowing the conference to enjoy the
amenities of their college, and the Faculty of Economics and Politics
of the University of Cambridge for making available a most comfort
able and convenient conference room. Finally we wish to express
the gratitude of the International Economic Association both to
UNESCO and to the Ford Foundation which have provided the
funds which have made possible the work of the Association generally
and the holding of this Conference in particular.
vii
INTRODUCTION
BY
E. MALINVAUD
lnstitut National de Ia Statistique et des Etudes Economiques, Paris
Chairman of Programme Committee
THE term 'activity analysis' was introduced ten years ago to designate
a new approach to many economic problems, both theoretical and
applied, an approach in which the technical constraints on produc
tion, transportation, and distribution receive a formalization that
differs from the one commonly used in the first half of the century.
According to the traditional model of production, any factor or
product is considered as substitutable for any other factor or product.
This implies the smoothness of the isoquant or cost curves, and
is formalized by the differentiability assumption for production
functions.
In activity analysis, the basic concept is the activity characterized
by fixed proportions between inputs and outputs called 'technical
coefficients'. An activity may be operated on a smaller or larger
scale; no other possibility exists within it. But various activities
may be operated simultaneously, each one at the most appropriate
level for the purpose to be served. The choice of the activities to be
used and of their levels of operation replaces the traditional choice
of the best combination of inputs and outputs. In the simplest cases
the problem takes the form of a linear programme and may be solved
by the techniques developed during the last twenty years. 1
Activity analysis was quickly adopted by economists who were
aware of the inadequacies of the marginal concepts in representing
the conditions of production now prevailing in industry. There
followed a re-examination of the branches of economic theory in
which the representation of technical constraints plays an essential
role: the theory of the firm, the theory of general economic equili
brium, the theory of the allocation of resources, etc. In all cases, it
was found that the main results of the traditional theory could be
maintained and generalized.2
1 Linear programming and activity analysis were introduced independently by
the. Russian mathematician L. V. Kantorovitch and by a group of American
economists and mathematicians (see notably Kantorovitch (1939) and Koopmans
(1951)). For details of all bibliographical references in this Introduction, seep. xv.
2 Among the many books and articles that popularized activity analysis, we may
quote the following: Dorfman (1951), Koopmans (1957), Dorfman, Samuelson,
and Solow (1958), Kantorovitch (1959).
viii
Introduction
Simultaneously, activity analysis revealed itself to be of great
power in solving many practical problems. Thus, within a very
short time, it succeeded in becoming one of the main tools of econo
mic sctence.
When the International Economic Association decided to organize
a Round Table on activity analysis, a question of principle had first
to be answered. Would the Round Table aim at improving com
munication between specialists in the field and economists working
with more traditional analytical tools? Or would it, on the other
hand, be devoted to bringing into contact research workers pursuing
significant projects using activity analysis? It was thought that the
first purpose could hardly be served by a small conference and that,
in any case, many successful efforts had already been made to ex
pound activity analysis to general economists.1
Like the other Round Tables sponsored by the International
Economic Association, the one reported here was intended to
stimulate research. The reader should therefore not be surprised
by the highly technical character of some of the papers. Activity
analysis was created within mathematical economics. It is only
natural that research in the field should rely on mathematics, and
that some contributions should be difficult to read even for well
trained mathematical economists. The authors have done their best
to present the motivations and implications of their analysis. The
discussions reported at the end of the book should help to clarify
any obscurity that could remain.
It was soon realized that the subject of the Round Table had to be
fairly narrowly defined. Since activity analysis is not a particular
branch of economic science, but simply a new approach, the various
speakers could have addressed themselves to quite different problems,
and the discussion would then have lacked a sufficient degree of unity.
The programme of the Round Table was therefore limited to three
closely related subjects on which important research is now being
carried on: the theory of growth, the theory of planning, and planning
experience.
In calling for contributions to the Round Table, emphasis was
placed as much on these three subject-matters as on the activity
analysis formulation. This explains why some of the papers
1 See the references given in footnote 1, above. See also, on a still less technical
level, Baumol (1961).
ix
Introduction
published here do not make much use of activity analysis stricto sensu:
either the authors consider problems for which the exact form taken
by the representation of technological constraints does not matter, or
they even prefer formulations which depend on the classical produc
tion functions as much as on the definition of 'activities'.
* * *
Even though such a division is partly artificial, the papers have
been grouped under three main headings: growth theory, planning
theory, and planning experience.
The first three papers study the qualitative features of growth
patterns in models containing many commodities. By a formal
study of some characteristics of growth paths, they aim at improving
our understanding of the problems connected with the physical
limitations on growth and with the simultaneous development of the
various industries.
T. C. Koopmans opens the book with an exposition of what is now
called 'turnpike theory', namely the theory built around the following
central assertion which is valid under well-specified conditions: in
any given technology, there exists a particular combination of activi
ties that permits growth at the highest possible speed; moreover, any
path that is optimal with respect only to its terminal state, i.e. any
'maximal path', uses for most of the time this particular combination
or a combination close to it. The question is more complex than
was first thought: it is not necessarily true that the maximizing
combination of activities is unique; even if it is, growth at maximal
speed may, in some cases, be achieved by a continuous switching
from one combination to another within a set of equally profitable
combinations. Thus, a complete characterization of all maximal
paths may become difficult. In connection with this theory, to
which he has already contributed on other occasions, L. McKenzie
presents a systematic study of maximal paths in the general model
first introduced by J. von Neumann. 1
M. Allais considers the asymptotic behaviour of growth paths that
fulfil certain general conditions. He shows that the properties of
any such path can be derived from those of another 'homologous'
1 During the meeting, R. Dorfman presented a duality theorem for von Neu
mann's model. This theorem permits a new derivation and an extension of the
result concerning the existence of a growth-maximizing combination of activities.
(See the Summary Record of the Debate, p.p. 290-4.)
X