NONLINEAR 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 All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No paragraph of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, 33-4 Alfred Place, London WCIE 7DP. Any person who does any unauthorised act in relation to this publication may be liable to criminal prosecution and civil claims for damages. 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