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continuation on page 385
Lecture Notes
in Economics and
Mathematical Systems
Managing Editors: M. Beckmann and W. Krelle
293
D. Batten J. Casti B. Johansson (Eds.)
Economic Evolution and
Structural Adjustment
Proceedings of Invited Sessions on
Economic Evolution and Structural Change
Held at the 5th International Conference
on Mathematical Modelling at the University
of California, Berkeley, California, USA
July 29-31, 1985
Springer-Verlag Berlin Heidelberg GmbH
Editorial Board
H. Albach M. Beckmann (Managing Editor) P. Dhrymes
G. Fandel G. Feichtinger J. Green W. Hildenbrand W. Krelle (Managing Editor)
H.P.Kunzi K.Ritter R.Sato U.Schittko P.Schonfeld R.Selten
Managing Editors
Prof. Dr. M. Beckmann
Brown University
Providence, Rl 02912, USA
Prof. Dr. W. Krelle
lnstitut fUr Gesellschafts-und Wirtschaftswissenschaften
der Universitat Bonn
Adenauerallee 24-42, D-5300 Bonn, FRG
Editors
Prof. Dr. David Batten
Department of Economics, University of UmeA
S-90 1 87 UmeA, Sweden
Prof. John L. Casti
Institute for Econometrics & Operations Research, Techn. Univ. of Vienna
ArgentinierstraBe 8, A-1 040 Vienna, Austria
Prof. Dr. Borje Johansson
CERUM (Centre for Regional Science Research)
and
Department of Economics, University of Umea
S-901 87 Umea, Sweden
ISBN 978-3-540-18183-5 ISBN 978-3-662-02522-2 (eBook)
DOI 10.1007/978-3-662-02522-2
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©Springer-Verlag Berlin Heidelberg 1987
Originally published by Springer-Verlag Berlin Heidelberg New York in 1987
Preface
Since the beginning of the fifties, the ruling paradigm in the discipline of economics
has been that of a competitive general equilibrium. Associated dynamic analyses
have therefore been preoccupied with the stability of this equilibrium state,
corresponding simply to studies of comparative statics. The need to permeate the
boundaries of this paradigm in order to open up new pathways for genuine dynamic
analysis is now pressing.
The contributions contained in this volume spring from this very ambition. A
growing circle of economists have recently been inspired by two distinct but
complementary sources: (i) the pathbreaking work of Joseph Schumpeter, and (ii)
recent contributions to physics, chemistry and theoretical biology. It turns out that
problems which are firmly rooted in the economic discipline, such as innovation,
technological change, business cycles and economic development, contain many
clear parallels with phenomena from the natural sciences such as the slaving
principle, adiabatic elimination and self-organization. In such dynamic worlds,
adjustment processes and adaptive behaviour are modelled with the aid of the
mathematical theory of nonlinear dynamical systems. The dynamics is defined for a
much wider set of conditions or states than simply a set of competitive equilibria. A
common objective is to study and classify ways in which the qualitative properties of
each system change as the parameters describing the system vary.
The origins of the present volume may be traced to comparative studies of spatial and
economic dynamics which were initiated at the International Institute for Applied
Systems Analysis (IIASA) in 1982. Among other tasks, the international reference
group for these studies provided insights into the theoretical development of models
and methods suited for the dynamic analyses of economic change processes. Many of
the contributions contained herein have come from members of this reference group
who have been undertaking basic research into dynamic processes such as competi
tion, economic development and spatial adjustments.
Most of the papers were presented during four special sessions held at the 5th
International Conference on Mathematical Modelling, on the campus of the
University of California in Berkeley, California from July 29-31, 1985. Three
additional chapters have been prepared by those authors who were invited to
IV
contribute to these sessions but could not attend. Thus the volume is as complete and
unified as possible.
The editorial work has been undertaken by the Centre for Regional Science Research
(CERUM) at the University of UmeA."' The work has been supported in other ways by
the Department of Economics at the same university as well as by IIASA and the
University of Karlstad. In particular, Jenny Wundersitz (CERUM) coordinated all
editorial tasks and Ingrid Lindqvist (University of Karlstad) prepared and revised the
manuscript. For their perseverence and perceptive attention to detail, the editors are
sincerely grateful.
UmeA, February 1987
David Batten
John Casti
B6rje Johansson
*
The work on this volume has been done within a project supported by Riksbankens
Jubileumsfond, grant 84/2.66: 1.
Table of Contents
Chapter 1
Economic Dynamics, Evolution and Structural Adjustment 1
B. Johansson, D. Batten, J. Casti
PART A: DYNAMIC COMPETITION AND ECONOMIC EVOLUTION 25
Chapter 2
Creativity and Economic Dynamics Modelling 27
A.E. Andersson
Chapter 3
The General Theory of Disequilibrium Economics and of Economic Evolution 46
R.H.Day
Chapter4
The Balanced Path of Economic Development: A Fable for Growth Merchants 64
D.E Batten
ChapterS
Competitive Growth of Firms in an Industry 86
E. Akin
Chapter 6
Technical Progress, Capital Accumulation, and Effective Demand:
A Self-Organization Model. 116
G. Silverberg
Chapter 7
Technological Vintages and Substitution Processes 145
B. Johansson
Chapter 8
Log-Linear Relative Dynamics: Unification of Theories 166
M. Sonis
PART B: PERIODIC CYCLES AND STRUC1URAL ADJUSTMENT 185
Chapter 9
The Schumpeter Clock 187
G. Haag, W. Weidlich and G. Mensch
Chapter 10
Complex Dynamics in Continuous Models of the Business Cycle 227
T.Puu
VI
Chapter 11
Generalizations of Goodwin's Growth Cycle Model 260
I. Glombowski and M. Kruger
Chapter 12
A Multisector Model of the Trade Cycle 291
A. Medio
Chapter 13
(M,R)-Systems as a Framework for Modeling Structural Change in a
Global Industry 313
J. Casti
PARTC: LOCATION ANDSPATIALDYNAMICS 335
Chapter 14
Continuous Models of Spatial Dynamics 337
M. J. Beckmann
Chapter 15
The Onset of Turbulence in Discrete Relative Multiple Spatial Dynamics 349
D.S. Dendrinos and M. Sonis
Chapter 16
Adoption and Diffusion of Innovations and Evolution of Spatial Systems 368
H. Blommestein and P. Nijkamp
List of Contributors 381
Chapter 1
Economic Dynamics, Evolution and Structural
Adjustment
B.JOHANSSON, D. BATTEN and J.CASTI
From perspectives represented in this volume, contemporary economics may be
regarded as a mature discipline. It has brought the state of the art close to the
boundaries of the predominant paradigm. Breaking through these boundaries implies
a search for alternatives or at least some alterations to this paradigm. Many of the
contributions contained herein spring from such ambitions. The different chapters
consist of various attempts to permeate the boundaries or to open up new pathways
within the existing paradigm, and in several cases to break with the established
tradition.
On occasions, economic theory and modelling has adopted concepts and research
strategies from the natural tv:iences, in particular from classical physics. A growing
circle of economic theorists have recently been inspired by some other developments
within the natural sciences. In this volume one can certainly identify influences of
this kind. Approaches and rc'ncepts introduced in the models are inspired by recent
contributions to physics, chemistry and theoretical biology. Moreover, techniques
for rendering the analysis of dynamical systems more tractable have been imported
and adapted from the natural and engineering sciences. However, the problems so
addressed are firmly rooted 1 the economic discipline with a special focus on
technological change, bus cycles, economic development and growth. The
pathbreaking work of Schum1•tao;:r is a mutual source of inspiration for many of the
authors. In this spirit the whole collection is concerned with the dynamic analysis of
market economies and competition in the marketplace.
2
1. MODELS OF ECONOMIC DYNAMICS
The two chapters on dynamics to be found in Samuelson's "Foundations of Economic
Analysis" ( 1946) reveal that the evolution of most theoretical ideas and principles
generally undergoes long incubation periods. Samuelson's explanations and
interpretations of comparative statics, stability of equilibria, cycles and parametriza
tion of dynamic processes contain many parallels with phenomena such as the
slaving principle, adiabatic elimination, and self-organization (Haken, 1978; 1983).
However, his discussion concentrates primarily on two aspects of economic dynamics,
namely the stability of equilibria and business cycles. As such, Samuelson's
contribution has little to say about economic growth, which has basically been a post
war field of interest.
Walrasian equilibrium models - in the guise of general competitive analysis - gained
some momentum in the beginning of the 1950s. In retrospect one may recall a
comprehensive research programme focussed on the existence of competitive
equilibria, safeguarded by equilibrium prices. The associated dynamic analysis was
therefore preoccupied with the stability of such equilibria. A great deal of theoretical
effort was spent on the study of "artificial" price adjustment processes using the
method of Lyapunov (see, e.g., Arrow and Hahn, 1971). The term "artificial" is
justified here by the fact that the studies were not principally concerned with
adjustment processes themselves, but rather with the stability of the essentially static
notion of a competitive equilibrium. Indeed, the extent of any dynamic analysis was
generally constrained by the equilibrium notion of the research programme. It may
also be characterized as an underpinning for the static equilibrium analysis. As
emphasized in the early work of Samuelson (1946), a static market equilibrium is of
general interest only if it is stable. One might add that a competitive equilibrium will
have little importance if it is not structurally stable or generic. Metaphorically
speaking, if we repeat the market experiment under approximately the same
conditions we would like to obtain approximately the same results (compare Hirsch
and Smale, 1974).
Growth theory comprises the process of capital accumulation intertwined with
increases in production and consumption. The reconstruction of the world economy
after the Second World War provided stimuli for analyzing growth problems. Von
Neumann's German version of the influential "A Model of General Economic
