Table Of ContentNONLINEAR AND MULTISECTORAL
MACRODYNAMICS
Nonlinear and
Multisectoral
Macrodynamics
Essays in Honour of Richard Goodwin
Edited by
Kumaraswamy Velupillai
Professor of Economics
University of Aalborg, Denmark
M
MACMILLAN
© Kumaraswamy Velupillai 1990
Softcover reprint of the hardcover 1st edition 1990
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First published 1990
Published by
THE MACMILLAN PRESS LTD
Houndmills, Basingstoke, Hampshire RG21 2XS
and London
Companies and representatives
throughout the world
British Library Cataloguing in Publication Data
Nonlinear and multi sectoral macrodynamics:
essays in honour of Richard Goodwin.
I. Economics
I. Velupillai, Kumaraswamy II. Goodwin,
R.M., 1913-
330
ISBN 978-1-349-10614-1 ISBN 978-1-349-10612-7 (eBook)
DOI 10.1007/978-1-349-10612-7
Contents
Notes on the Contributors VB
PART I: BIOGRAPHICAL NOTES
Introduction
Kumaraswamy Velupillai 3
2 Richard Goodwin Retrospective
J. K. Galbraith 6
3 The (Nonlinear) Life and (Economic) Times of Richard
M. Goodwin
Kumaraswamy Velupillai 7
PART II: NONLINEAR MACRODYNAMICS
4 Goodwin's Growth Cycle: Reminiscence and
Rumination
Robert M. Solow 31
5 Deterministic Chaos in Economics: An Occurrence in
Axiomatic Utility Theory
Paul A. Samuelson 42
6 A Model of Cyclical Growth
Richard Stone 64
7 Observations Concerning the Growth Cycle
Andrew Brody 90
8 A Reconsideration of Frisch's Original Cycle Model
BjOrn Thalberg 96
9 Social Rigidities, Growth Cycles and Development
Planning
Amiya Kumar Bagchi 118
v
vi Contents
PART III: MULTISECTORAL MACRODYNAMICS
10 Normalised General Coordinates and Vertically
Integrated Sectors in a Simple Case
Luigi L. Pasinetti 151
11 A Comparison Between Goodwin's Normalised General
Coordinates and Pasinetti's Vertical Integration
Methods
Terenzio Cozzi 165
12 Generalised Diagonal Coordinates in Dynamical
Analysis and Capital and Distribution Theory
Lionello F. Punzo 173
PART IV: EXOTICA
13 The Specification of Error Terms
Jan Tinbergen 201
14 Rationality in Disequilibrium
Siro Lombardini 207
15 Probabilistic Causality and Economic Models: Suppes,
Keynes and Granger
Alessandro Vercelli 224
Index of names 247
Index of subjects 251
Notes on the contributors
Professor Amiya Kumar Bagchi
Centre for Studies in Social Sciences
Calcutta
Professor Andrew Brody
Institute of Economics
Hungarian Academy of Sciences
Budapest
Professor Terenzio Cozzi
President of the Scientific Committee
Luigi Einaudi Foundation
and
University of Turin
Turin
Professor John Kenneth Galbraith
Harvard University
Cambridge MA
Professor Siro Lombardini
University of Turin
Turin
Professor Luigi L. Pasinetti
Universita Cattolica del Sacro Cuore
Milan
Professor Lionello F. Punzo
University of Pisa
Pisa
Professor Paul A. Samuelson
Nobel Laureate
Institute Professor
M.I.T.
Cambridge MA
vii
viii Notes on Contributors
Professor Robert M. Solow
Nobel Laureate
Institute Professor
M.LT.
Cambridge MA
Professor Sir Richard Stone
Nobel Laureate
Cambridge University
Cambridge
Professor Bjorn Thalberg
University of Lund
Lund
Professor Jan Tinbergen
Nobel Laureate
The Hague
Professor Kumaraswamy Velupillai
Aalborg University
Aalborg
Professor Alessandro Vercelli
University of Siena
Siena
PART I
Biographical Notes
1 Introduction
Kumaraswamy Velupillai
I first met Richard Goodwin 15 years ago: I was 25 and he was 60
years old. The years rolled along. He left Cambridge and took up a
Professorship in the University of Siena. A little later I joined him by
accepting an appointment in Fiesole. We celebrated his 70th birthday
in February 1983 in our house - minus our respective wives - which
was set amongst the gentle hills beyond Fiesole. The ratio of our ages
reached 1/2, having been less than that in the previous years! Now,
this year, he has reached the venerable age of 75 and I am 15 years
older than in 1973 and the ratio of our ages is greater than 1/2. In fact
it is about 0.5333 and then any number of 3s as you like. He has, in the
intervening years, been growing at the rate of 1.25 and I at 1.6. At this
rate, it is easy to see, I could even become older than Richard
Goodwin. This is the sort of linear nonsense Richard Goodwin has
been trying to expose for over 40 years.
The idea of a Festschrift for Richard Goodwin came up during a
splendid dinner in Bjorn Tha1berg's house in Lund when Professor
Amartya Sen was visiting the University - now more than ten years
ago. That is a measure of the length of time this book has been
maturing. The hope is that the vintages have aged with splendour and
grace, almost as Goodwin has.
There is a particular sadness to report. The late Professor Leif
Johansen had enthusiastically agreed to contribute for this volume.
Had this book been published as early as it was conceived his
prospective contribution would have enriched its contents.
Another apology, and this time to Professor Amartya Sen. He it
was who first encouraged and supported me to go ahead with the idea.
The various complications and difficulties in his own personal life, at
a crucial juncture, made it impossible for him to contribute to this
particular collection of essays.
To Professors Brody, Stone, Thalberg and Tinbergen I have a
different kind of apology. Their enthusiastic participation was mani
fested in almost immediate response to my initial requests. They and
almost all the others have had to wait several years to see this volume
3
