Table Of ContentZeitschrift fiir NationalOkonomie
Journal of Economics
Supplementum 1
Contributions to the
Von Neumann Growth Model
Proceedings of a Conference
Organized by the Institute for Advanced Studies
Vienna, Austria, July 6 and 7, 1970
Edited by
G. Bruckmann and W. Weber
Springer-Verlag Wien GmbH 1971
Dr. Gerhart Bruckmann
Professor at the University of Vienna
Director of the Institute for Advanced Studies
Dr. Wilhelm Weber
Professor at the University of Vienna
With 16 Figures
All rights reserved
No part of this book may be translated or reproduced
in any form without written permission from Springer-Verlag Wien GmbH
© 1971 by Springer-Verlag Wien
Ursprünglich erschienen bei Springer-Verlag Wien New York 1971
Library of Congress Catalog Card Number 71-155280
ISBN 978-3-662-22738-1 ISBN 978-3-662-24667-2 (eBook)
DOI 10.1007/978-3-662-24667-2
Preface
The short paper of John von Neumann, "0ber ein okonomisches
Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunkt
satzes", published 1937 in Vienna in German and translated into English
and subsequently published in the "Review of Economic Studies" (1945-
1946) as "A Model of General Economic Equilibrium" is one of the most
important contributions to modern mathematical economics, if the rele
vance of a paper is judged by the number of contributions which it ini
tiates. After the publication of the paper there was a time lag of several
years until Economic Theory payed attention to von Neumann's con
tribution. One reason was that the new mathematical methods - including
the modern theory of mathematical programming which was not developed
at that time - made it very difficult to understand the model. An im
portant step towards a better understanding of von Neumann's model
was the generalization by J. G. Kemeny, 0. Morgenstern and G. L.
Thompson, "A Generalization of the Von Neumann Model of an Ex
panding Economy" (1956) which also put emphasis on the economic inter
pretation. Since its publication the occupation with the von Neumann
growth model has become one of the mainstays of the theory of economic
growth and the theory of general economic equilibrium. The development
was along three lines:
l. The theory of multisectoral balanced growth (mainly the conditions
of equilibrium growth).
2. The theory of optimal growth, where the most wellknown problem
is the so-called "Turnpike theorem".
3. The problem of computation of the optimal price and intensity
vectors of a von Neumann economy.
To assist in the development of new contributions to the von Neu
mann growth theory an international conference was held at the Institute
for Advanced Studies in Vienna on July 6-7, 197 0, following a suggestion
by Prof. Oskar Morgenstern of New York City University who presided
over the conference. The papers published in this volume were presented
to the conference and they deal with the von Neumann growth model in
four contexts:
l. Equilibrium growth, 2. optimal growth, 3. computation problems
and 4. topics related to the von Neumann model.
VI Preface
The papers of M. J. Beckmann, T. C. Koopmans, 0. Morgen
stern and G. L. Thompson, M. Morishima, R. Radner and M.Tru
chon deal with the first topic.
The following five papers of C. J. Bliss, W. A. Brock, E. B. Keeler,
J. tos, L. W. McKenzie and D. A. Starrett belong to the second topic.
The papers of S. P. Burley, and G. L. Thompson and R. L. Weil
were dedicated to computation problems.
The last group consists of a number of contributions which cannot be
classified under the first three topics. A. K. Dixit is dealing with un
certainty and growth, whereas E. Drandakis and E. Mighas apply
control theory to the problem of optimal growth. The papers of T. S chat
tales and A. Zauberman are concerned with the relation between the
von Neumann model and the socialist planning.
The papers had the benefit of criticism and based on numerous sug
gestions made by the participants of the Vienna conference, nearly all
were re-drafted before final publication. The objective of the conference
was to stimulate new developments in the theory of economic growth and
general equilibrium analysis in the context with the von Neumann model
of an expanding economy. The papers presented in this volume demon
strate that the purpose of the conference was accomplished.
Linz, April 1971
Helmut Frisch
Chairman of the
Program Committee
Table of Contents
Part 1
Equilibrium Models Whim Have Their Origin in Von Neumann's Model
Bedunann, M.: The Period of Production in a Von Neumann World . . . . 3
Koopmans, T. C.: A Model of a Continuing State with Scarce Capital . . . 11
Morgenstern, 0., and G. L. Thompson: Further Consideration of "An Open
Expanding Economy Model" . . . . . . . . . . . . . . . . . . . . . . . 23
Morishima, M.: Consumption-investment Frontier, Wage-profit Frontier and
the Von Neumann Growth Equilibrium . . . . . . . . . . . . . . . . . 31
Radner, R.: Balanced Stochastic Growth at the Maximum Rate ........ 39
Trumon, M.: On the Importance of Lags in Growth Models . . . . . . . . . 53
Part 2
Optimization Models Based on Von Neumann's Model
Bliss, C. J.: Economic Efficiency in an Infinite Horizon Model . . . 65
Brock, W. A.: Sensitivity of Optimal Growth Paths with Respect to
a Change in Target Stocks . . . . . . . . . . . . . . . . . . . . . . . . 73
Keeler, E. 8.: A Twisted Turnpike Theorem ..... . 91
Los, J.: The Approximative Horizon in Von Neumann Models of Optimal
Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
McKenzie, L. W.: Capital Accumulation Optimal in the Final State ..... 107
Starrett, D. A.: Von Neumann Rays and Golden Rules: An Integrated View
of Intertemporal Production Models . . . . . . . . . . . . . . . . . . . 121
Part 3
Methods of Computation of Optimal Prices and Intensities
in a Von Neumann Model
Burley, S. P.: Calculating Von Neumann Trajectories by Simulated Market
Adjustments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Thompson, G. L., and R. L. Weil: Von Neumann Model Solutions Are
Generalized Eigensystems . . . . . . . . . . . . . . . . . . . . . . . . 13 9
VIII Table of Contents
Part 4
Toplca Related to &he Von Neamann Model
Dixit, A. K.: Maximal Growth when Food Output Is Uncertain .. 157
Drandalds, E., and E. Mlghas: Public Investment in Infrastructure and
Optimal Economic Growth .......•................ 167
SdlaUeles, T.: The Von Neumann Growth Model and Socialist Planning .. 185
Zauberman, A. (assisted by G. Monon): Soviet Work Related to the
Von Neumann Model and Turnpike Theories and Some Ramifications.
A Critical Review . . . . . . . . . . . . . . . . . . . . . . . . . . • . 191
Program of the Conference
Monday, July 6, 1970
8.45-9.00 Introduction by Prof. Oskar Morgenstern (U.S.A.)
9.00- 9.20 Economic Efficiency B 1 is s, Christopher J.
in an Infinite Horizon Model (U.K.)
9.20- 9.45 Discussion Discussant:
S t rei s sler, Erich
(Austria)
9.45-10.05 Calculating Von Neumann's Tra Burley, Simon Peter
jectories by Simulated Market (Australia)
Adjustments
10.05-10.30 Discussion Discussant:
Godfrey, Michael D.
(U.K.)
11.00-11.20 Further Remarks to "An Open Morgenstern, Oskar
Expanding Economy Model" (U.S. A.)
Thompson, Gerald L.
(U.S.A.)
11.20-11.45 Discussion Discussant:
Schwodiauer, Gerhard
(Austria)
11.45-12.05 Capital and Interest Beckmann, Martin J.
in a Von Neumann World (Germany)
12.05-12.30 Discussion Discussant:
Henn, Rudolf
(Germany)
14.30-14.50 Consumption-investment Frontier, Morishima, Mimio
Wage-profit Frontier and the Von (U.K.)
Neumann Growth Equilibrium
14.50-15.15 Discussion Discussant:
Morton, George
(U.K.)
15.15-15.35 On Some Efficiency Characteristics Starrett, David A.
of a General Production Model (U.S.A.)
X Program of the Conference
15.35-16.00 Discussion Discussant:
Keeler, Emmett B.
(U.S.A.)
16.00-16.20 The Generalized Von Neumann Frisch, Helmut
Model and Some Results of the (Austria)
Theory of Growth
16.20-16.45 Discussion Discussant:
Dixit, Avinash K.
(U.K.)
16.45-17.05 Soviet Work Related to the Von Zauberman, Alfred
Neumann and Turnpike Theories (U.K.)
Morton, George
(U.K.)
17.05-17.30 Discussion Discussant:
Radner, Roy
(U.S.A.)
Tuesday, July 7, 1970
9.00- 9.20 A Von Neumann Type Model with Koopmans, Tjalling C.
Timing Preference for Consump (U.S.A.)
tion
9.20- 9.45 Discussion Discussant:
Frisch, Helmut
(Austria)
9.45-10.05 Public Investment in Infrastructure Drandakis, Emmanuel
and Optimal Economic Growth (U.S. A.)
Mighas, Elias
(Greece)
10.05-10.30 Discussion Discussant:
Zauberman, Alfred
(U.K.)
11.00-11.20 Sensitivity of Optimal Growth Brock, William A.
Paths with Respect to a Change (U.S.A.)
in Target Sto<Xs
11.20-11.45 Discussion Discussant:
Starrett, David A.
(U.S. A.)
11.45-12.05 A Twisted Turnpike Theorem Keeler, Emmett B.
(U.S.A.)
12.05-12.30 Discussion Discussant:
McKenzie, Lionel W.
(U.S.A.)
