Richard Murphey Goodwin (1913-1996

K. Vela Velupillai

Introduction

Those who had the privilege to attend Richard Goodwin’s lectures, at Harvard, Cambridge, or Siena, regularly over a period of half a century, know the wonderful ways in which he used his considerable artistic skills to illustrate (sic!) the geometry of global economic dynamics and multisectoral interdependence. The triptych of ‘global behavior, interaction of the parts, dynamics’, tamed by ingenious geometry remained the guiding principle of Goodwin’s writings, teaching, and thinking.

It was, after all, the geometric way of understanding global dynamics (cf. Palis and de Melo 1982) that enabled him to devise the famous one-sided oscillator, motivated by the economic intuition that the Hicksian ‘floor’ was

Much of the pure facts of Richard Goodwin’s life are taken from one or another of my own earlier writings on Goodwin (particularly, Velupillai 1996, 1998). Goodwin never failed to remind me that his middle name was ‘Murphey with an “e”’! My indebtedness to the written contributions, and personal friendship, of Ralph Abraham, Richard Day, Geoff Harcourt, Ragu Ragupathy, Otto Rossler, and Stefano Zambelli are too obvious to require explicit acknowledgement. They are, alas, not responsible for the remaining infelicities.

K.V. Velupillai (H)

Formerly Professore di Chiara Fama, University of Trento, Italy

Formerly Professor of Economics, New School for Social Research, USA e-mail: This email address is being protected from spam bots, you need Javascript enabled to view it

© The Editor(s) (if applicable) and The Author(s) 2017 815

R.A. Cord (ed.), The Palgrave Companion to Cambridge Economics,

DOI 10.1057/978-1-137-41233-1_36

not a necessary condition for the maintenance of oscillation as a limit cycle.¹ Then there was the geometry of vector-matrix analysis and spectral theory, both linking interaction of the parts with dynamics, to his innovative ways of building global behaviour on the basis of independent local analysis (without the tiresome appeal or non-appeal to analytically arid issues of aggregation).

Others, even without the pleasure and privilege of attending his normal series of lectures, who struggled through to eventual enlightenment by reading, and working through, the classics on non-linear and multisectoral macrodynamics that emanated from his exquisite pen, quite apart from being impressed by the ingenious geometry, were also struck by Goodwin’s systematic use of simulations.^{[1] [2]} He struggled to convince himself and his readers that plausible empirically sensible numbers for key parameters, in the relevant range for crucial variables, made economic sense. Indeed, this was manifested in all his classics, between ‘Keynesian and Other Interest Theories’ (Goodwin 1943) and ‘A Growth Cycle’ (Goodwin 1967), including the remarkably original Elementary Economics from the Higher Standpoint (Goodwin 1970)—and those that emanated from his pen (and fertile mind), all the way to ‘the end’.

Goodwin was also the pioneer, in economics, of using the Perron-Frobenius (cf. Goodwin 1953) results for non-negative square matrices, in conjunction with what he called normalized general coordinates, a method by which interdependence was simplified by a coordinate transformation (cf. Goodwin 1949a; Frazer et al. 1938), which allowed consideration of independent artificial sectors at an analytic stage. This enabled Goodwin to enunciate what I refer to as his precept: aggregate dynamics must be non-linear; multisectoral dynamics must be linear.^[3] The coordinate transformation allowed the interdependent multisectoral dynamics to be ‘reduced’ to independent sectoral analysis, using non-linear methods.

Goodwin was born in Newcastle, Indiana, and attended local schools before going to Harvard College in 1930, to major in political science, to prepare, eventually, to study law, on the advice of his grandfather, a lawyer turned banker. The Depression led to the downfall of his grandfather’s bank and, independently, his father became bankrupt. The political science that

Goodwin continued to study was now given a Marxian twist and a lifelong adherence to left-wing politics.

He spent three years from 1934 as a Rhodes Scholar at St John’s College, Oxford—where his Tutor had the foresight to send him to Roy Harrod at Christ Church, with whom he read The General Theory in its proof version (cf. Harcourt 1985: 414)—and returned to Harvard where, from 1938 to 1950, he was a member of the economics department, but also taught physics (during the Second World War). It was during this brief period that he met, and befriended, Philippe Le Corbeiller, who taught him the theoretical technology of planar non-linear dynamics.^[4] Fleeing Harvard from the increasing difficulties of the ‘McCarthy era’, and with the help of Richard Stone, then Director of the Department of Applied Economics, he found refuge at Cambridge, England, in 1952.

He spent the next three decades at Cambridge, as a Fellow,^[5] Director of Studies in Economics (and Wine Steward) of Peterhouse, Girdlers’ Lecturer,^[6] and, finally, as Reader in Economic Theory in the Faculty of Economics and Politics.^[7] On retirement in 1980, he took up a Professorship in the Faculty of Economics at the ancient University of Siena, which enabled him to return in a formal way to his beloved Italy. That faculty of economics is now renamed in his honour as the Dipartimento di Economia ‘R. Goodwin’.

Although formal retirement in Siena came at the age of 75, he continued to teach there almost till death intervened, in his 83rd year. Goodwin was an active and interested participant of graduate seminars at the University of Siena,^[8] which were, appropriately, held in the Sala Goodwin, which was tastefully adorned with some of his own paintings.

The rest of this essay is structured as follows. In the next section, Goodwin’s pioneering contribution to non-linear macrodynamics is discussed, with some geometric hilfenkonstruktions. The topic in Section 3 is his extraordinarily imaginative and fertile contributions to varieties of ways to study linear, multisectoral, interdependent economics. In Section 4, an attempt is made to summarize his intellectual legacy.

• [1] Le Corbeiller’s letter to Goodwin, dated 29 March 1958 (the original, handwritten version of which wasgiven to me by Goodwin, at the time of his formal retirement at Cambridge, in 1980), illustrates the wayhe came to the conclusion that a characteristic with only one bend—‘one nonlinearity’, as he called it—was sufficient to generate a limit cycle on the plane. See also Goodwin (1950, 1990) and Velupillai (1998).
• [2] However, it is not the kind of ‘mindless simulation’ that is currently fashionable in many frontiers ofso-called computational economics, agent-based economics, and even stock-flow consistent modelling ofdisaggregated economies. Goodwin’s simulations were in the mode of what I have come to call the Fermi—Pasta—Ulam method of analysis (Fermi et al. 1955), and its perfect execution was in Goodwin (1947). Ihave always maintained that this is the authentic, and proper, way to do ‘agent-based economics’.
• [3] It is useful to contrast this with what I call Turing’s Precept: ‘Description must be non-linear; predictionmust be linear (quoted in Gandy 1954 [2001]: 266; italics added).
• [4] As Goodwin told me during a personal conversation in September 1977 at my home in Svanshall,Sweden: ‘I was walking down the corridor of the Physics Department when I saw the name “Ph. LeCorbeiller” on one of the doors. I knocked, the door was opened by a distinguished looking, elegantlydressed, gentleman. I asked him whether he was the Le Corbeiller who had written on the desirability ofusing van der Pol’s theory of relaxation oscillations in the first volume of Econometrica (Le Corbeiller1933). He answered yes. I asked him whether he would teach me the theory of nonlinear dynamics. He,then, literally took me “by the hand” and taught me nonlinear dynamics’. Goodwin had not only read LeCorbeiller’s 1933 piece, but also Le Corbeiller (1931) and, later, mastered the geometry of relaxationoscillations that was a pedagogical masterpiece in Le Corbeiller (1936). This latter method remained hislifelong way of devising, drawing, and explaining the geometry of non-linear macrodynamics. It was thismethod that enabled him to discover the one-sided oscillator, mentioned above. It is a method that seemsto have been ‘hollowed out’ in this modern age of blind computer simulations. I am, now, the proudowner of Goodwin’s copies of Le Corbeiller (1931, 1936).
• [5] He told me, in a personal conversation in the mid-1970s, that Dennis Robertson was sent Goodwin’spapers for evaluation by the Governing Body of Peterhouse and that the great successor to Pigou andMarshall responded by writing in his official report: ‘I do not agree with anything Goodwin writes, but Iwould not miss them for the world!’ Later, it was Harry Johnson who was sent by Richard Kahn and JoanRobinson to ‘interview’ Goodwin, to ‘investigate his suitability to become a member of the CambridgeFaculty of Economics and Politics’.
• [6] Following, therefore, in the footsteps of H.O. Meredith, later a distinguished Professor of Economics atQueen’s University in Belfast (where, several generations later, this minor author ‘succeeded’ that legendary scholar), who was himself succeeded by Maynard Keynes. When Goodwin retired as Director ofStudies in Economics at Peterhouse, I had the pleasure and privilege of taking over that coveted post, notleast due to Goodwin’s efforts and influence.
• [7] The last time I visited the fourth floor of the Sidgwick site, a decade or so ago, where the Faculty of Economicsand Politics of the University of Cambridge is housed, the corridors were adorned by some of Goodwin’s paintings which, he told me, had been bought during Professor Aubrey Silbertson’s tenure as the Chairman.
• [8] During my own years at the European University Institute in Fiesole, 1981-1985, picturesquely locatedin the hills outside Florence, he was a frequent visitor to the graduate and staff seminars there.