Journal of Economic Dynamics and Control 16 (1992) 389-390. North-Holland

Chaotic economic dynamics by Richard M. Goodwin*

A book review

Richard H. Day University of Southern California, Los Angeles, CA 90089, USA

In ano the r p lace R icha rd Goodwin descr ibes the origin of this l i t t le book of essays as a kind of re l ig ious convers ion tha t took p lace af ter my lec ture on chaos in S iena in the Spr ing of 1985. As a resul t of that exper ience , he tells us tha t he began a r enewed a t t ack on the centra l p rob l e m of his scientific life, tha t of expla in ing growth and cycles on the basis of a unif icat ion of the cent ra l insights of Marx, Schumpe te r , and K e y n e s ) W h a t fol lowed has to be one of the most r e m a r k a b l e burs ts of creat ivi ty in all of economic science: r e m a r k a b l e both for its in te l lec tua l ach ievement and for the fact that it was ca r r i ed o u t when its au thor was a l r eady more than seventy years old!

Those who know Goodwin will not be surpr ised. He has ma in t a ine d an active in te l lec tua l and ar t is t ic life while at the same t ime in tensely enjoying ' t he life ' , as our I ta l ian f r iends say. 2 Indeed , the aes the t ic sense that has borne up every aspect of his be ing is ev ident in this volume; it a t ta ins a max imum of mean ing f rom engaging prose; it embraces ma thema t i ca l parsi- mony beaut i fu l i n t eg ra t ed with br ie f ref lect ions on the classical flow of ideas within which his own ref lect ions have emerged .

*Clarendon Press, Oxford, 1990. tRichard M. Goodwin, 'My Erratic Progress Toward Economic Dynamics', Chapter 19

in: R. Day, P. Chen, and I. Prigogine, eds., Nonlinear Dynamics and Evolutionary Economics, Proceedings for a conference in Austin, Texas, April 1989 (in preparation).

eSee his 'A Personal Perspective on Mathematical Economics', Banca Nazionale del Lavoro Quarterly Review 152 (March 1985) pp. 3-13; G.C. Harcourt, 'A Twentieth Century Eclectic: Richard Goodwin's Vision'; and Kumaraswamy Velupillai, 'The (Nonlinear) Life and (Eco- nomic) Times of Richard M. Goodwin', Chapter 3 in: K. Velupillai, ed., Nonlinear and Multisectoral Macrodynamics (Macmillan, New York, 1990).

0165-1889/92/$05.00 © 1992--Elsevier Science Publishers B.V. All rights reserved

390 R.H. Day, A book ret,iew

The book's introductory essay sketches a gradient price adjustment pro- cess. It then introduces a logistic adoption function of new (exogenously introduced) innovations, and uses this as a vehicle for discussing chaos in terms described in the classic papers of Lorenz and R6ssler. In Chapter 2 he replaces fixed land with a labor supply constraint in the classical growth story to derive a nonlinear chaos model. By exploiting a similar constraint in Chapter 3, he obtains a nonlinear version of the von Neuman model that gives fluctuating (rather than unbounded) growth and whose variables con- verge to a 'strange attractor'. The remaining seven essays produce variations on the themes introduced in these first three chapters: the integration of Schumpeterian and Keynesian ideas using Leont ief-von Neuman incarna- tions of Classical growth theory with ingeniously simple mathematical as- sumptions, to arrive at chaotically fluctuating growth. It is refreshing indeed to see this exposition of business cycle theory from the Keynesian- Schumpeter-Goodwin perspective instead of the contemporary fashion of optimal growth. These essays show that much is still to be gained by macroeconomic analysis unencumbered by an unrealistic and excessively stylized micro foundation.

I find his references to Marx gratuitous. How could a scholar noted for his genius at capturing complex theoretical concepts in simple models expressed in trenchant prose be such an admirer of one who complexified simple classical insights in such prolix and turgid tomes?

And readers will quickly discover that Goodwin's exposition suffers from his characteristic impatience with detailed notational exposition. As a result, they will have to do a lot of thinking on their own, possibly cross-referencing with some of the author's earlier works on which he occasionally draws implicitly. This will have the benefit of motivating a new generation to study them. 3 Besides, books don't have to be all things to all people. This one is a set of idea pieces, not well enough developed to serve as a comprehensive text, but brilliantly conceived to stimulate the dedicated student and to provoke a new generation of scholars to carry on the implied program of research. In the meantime, Professor Goodwin may have another religious conversion, and while others are struggling to master these 'old' ideas, he will have forged far ahead again with equally bold and imaginative intellectual strokes!

3In particular, see Richard M. Goodwin, Essays in Economic Dynamics and Essays in Linear Economic Structure (Macmillan Press, New York, 1982 and 1983)