Richard Murphey Goodwin (1913–1996)



Richard Goodwin was the pioneering endogenous, non-linear theorist of macrodynamic fluctuations, once referred to as trade cycle theory but now known as business cycle theory. His theoretical and policy frameworks spanned optimal growth planning, stabilization policy, iterative dynamics, coupled dynamics, capital theory, and, above all, innovative teaching. He worked on synthesizing the imaginative insights of Schumpeter on innovations, Keynes on the multiplier, Harrod on the accelerator, Leontief on an applicable model of Walrasian interdependence, and Sraffa on capital theory. His non-linear mathematics owed a great deal to Philip Le Corbeiller’s personal teaching and the development of classical theory of non-linear differential equations. His important discovery of a one-sided oscillator which does not depend on the cubic characteristic was made in the context of reviewing Hicks’s theory of the trade cycle. In this chapter, these elements are made to tell the story of Goodwin’s wonderful contributions to economics.


Non-linear dynamics Endogenous macrodynamics One-sided oscillator Optimal planning Stabilization policy Iterative dynamics Coupled dynamics 


Cited Works by Richard Goodwin

  1. Goodwin, R.M. (1943). ‘Keynesian and Other Interest Theories’. Review of Economics and Statistics, 25(1): 6–12.Google Scholar
  2. Goodwin, R.M. (1946). ‘Innovations and the Irregularity of Economic Cycles’. Review of Economics and Statistics, 28(2): 95–104.Google Scholar
  3. Goodwin, R.M. (1947). ‘Dynamical Coupling with Especial Reference to Markets Having Production Lags’. Econometrica, 15(3): 181–204.Google Scholar
  4. Goodwin, R.M. (1949a). ‘The Multiplier as Matrix’. Economic Journal, 59(236): 537–555.Google Scholar
  5. Goodwin, R.M. (1949b). ‘The Business Cycle as a Self-Sustaining Oscillation’. Econometrica, 17(2): 184–185.Google Scholar
  6. Goodwin, R.M. (1950). ‘A Non-Linear Theory of the Cycle’. Review of Economics and Statistics, 32(4): 316–320.Google Scholar
  7. Goodwin, R.M. (1951a). ‘The Nonlinear Accelerator and the Persistence of Business Cycles’. Econometrica, 19(1): 1–17.Google Scholar
  8. Goodwin, R.M. (1951b). ‘Iteration, Automatic Computers, and Economic Dynamics’. Metroeconomica, 3(1): 1–7.Google Scholar
  9. Goodwin, R.M. (1953). ‘Static and Dynamic Linear General Equilibrium Models’. In The Netherlands Economic Institute (ed.) Input-Output Relations. Proceedings of a Conference on Inter-Industrial Relations Held at Driebergen, Holland. Leiden: H.E. Stenfert Kroese NV: 54–87.Google Scholar
  10. Goodwin, R.M. (1961). ‘The Optimal Growth Path for an Underdeveloped Economy’. Economic Journal, 71(284): 756–774.Google Scholar
  11. Goodwin, R.M. (1967). ‘A Growth Cycle’. In part I of C. Feinstein (ed.) Socialism, Capitalism and Economic Growth: Essays Presented to Maurice Dobb. Cambridge: Cambridge University Press: 54–58.Google Scholar
  12. Goodwin, R.M. (1970). Elementary Economics from the Higher Standpoint. Cambridge: Cambridge University Press.Google Scholar
  13. Goodwin, R.M. (1974). ‘The Use of Normalized General Coordinates in Economic Planning’. Chapter 3 in A. Mitra (ed.) Economic Theory and Planning: Essays in Honour of A.K. Das Gupta. Calcutta: Oxford University Press: 26–38.Google Scholar
  14. Goodwin, R.M. (1977). Capital Theory in Orthogonalised General Co-ordinates. Presented at the Wicksell Symposium, held in Frostavallen, Sweden. Republished as Chapter 8 in Essays in Economic Dynamics (1982) by R.M. Goodwin. London: Macmillan: 153–172.Google Scholar
  15. Goodwin, R.M. (1982). Essays in Economic Dynamics. London: Macmillan.Google Scholar
  16. Goodwin, R.M. (1988). ‘The Multiplier-Accelerator Discretely Revisited’. In part I of R. Gianni and K. Velupillai (ed.) Growth Cycles and Multisectoral Economics: The Goodwin Tradition. Lecture Notes in Economics and Mathematical Systems. Number 309. Heidelberg: Springer-Verlag: 19–29.Google Scholar
  17. Goodwin, R.M. (1990). Chaotic Economic Dynamics. Oxford: Clarendon Press.Google Scholar
  18. Goodwin, R.M. (1991). ‘Letter to Nick Stern’. 16 August. Copy in the possession of the author.Google Scholar
  19. Goodwin, R.M. (1994). ‘A Reformulation and Extension of Hicksian Dynamics’. Chapter 6 in H. Hagemann and O.F. Hamouda (eds) The Legacy of Hicks: His Contributions to Economic Analysis. London: Routledge: 75–86.Google Scholar
  20. Goodwin, R.M. (2000). ‘A Superb Explanatory Device’. Chapter 13 in R. Leeson (ed.) A.W.H. Phillips: Collected Works in Contemporary Perspective. Cambridge: Cambridge University Press: 118–119.Google Scholar

Other Cited Works

  1. Andronov, A.A. and L. Pontryagin (1937). Systèmes Grossiers. Dokl. Akad. Nauk. SSSR. 14:247–251.Google Scholar
  2. Desai, M. and P. Ormerod (1998). ‘Richard Goodwin: A Short Appreciation’. Economic Journal, 108(450): 1,431–1,435.Google Scholar
  3. Ellsberg, D. (1951). Faculty Profile: Mathematical Economist. The Harvard Crimson, 24 May. Available at:
  4. Fermi, E., J. Pasta and S. Ulam (1955). Studies in Non-Linear Problems. Los Alamos Preprint: LA-1940.Google Scholar
  5. Frazer, R.A., W.J. Duncan and A.R. Collar (1938). Elementary Matrices and Some Applications to Dynamics and Differential Equations. Cambridge: Cambridge University Press.Google Scholar
  6. Gandolfo, G. (1981). Economic Dynamics: Methods and Models. Revised edition. Amsterdam: North-Holland.Google Scholar
  7. Gandy, R. (1954) [2001]. ‘Letter to M.H.A. Newman’. June. Reprinted in R.O. Gandy and C.E.M. Yates (eds) Collected Works of A.M. Turing – Volume 4: Mathematical Logic. Amsterdam: North-Holland: 265–267.Google Scholar
  8. Harcourt, G.C. (1985). ‘A Twentieth-Century Eclectic: Richard Goodwin’. Journal of Post Keynesian Economics, 7(3): 410–421.Google Scholar
  9. Harrod, R.F. (1936). The Trade Cycle: An Essay. Oxford: Clarendon Press.Google Scholar
  10. Harrod, R.F. (1951). ‘Induction and Probability’. Philosophy, 26(96): 37–52.Google Scholar
  11. Hicks, J.R. (1950). A Contribution to the Theory of the Trade Cycle. Oxford: Clarendon Press.Google Scholar
  12. Ichimura, S. (1955). ‘Toward a General Nonlinear Macrodynamic Theory of Economic Fluctuation’. Chapter 8 in K.K. Kurihara (ed.) Post-Keynesian Economics. London: George Allen & Unwin: 192–226.Google Scholar
  13. Jaffé, W. (1967). ‘Walras’ Theory of Tâtonnement: A Critique of Recent Interpretations’. Journal of Political Economy, 75(1): 1–19.Google Scholar
  14. Jaffé, W. (1980). ‘Walras’ Economics as Others See It’. Journal of Economic Literature, 18(2): 528–549.Google Scholar
  15. Jaffé, W. (1981). ‘Another Look at Léon Walras’ Theory of Tâtonnement’. History of Political Economy, 13(2): 313–336.Google Scholar
  16. Kaldor, N. (1957). ‘A Model of Economic Growth’. Economic Journal, 67(268): 591–624.Google Scholar
  17. Keynes, J.M. (1936) [1973]. The General Theory of Employment, Interest and Money. Volume VII of The Collected Writings of John Maynard Keynes. London: Macmillan.Google Scholar
  18. Kolmogorov, A.N. (1936). ‘Sulla Teoria di Volterra della Lotta per l’esistenza’. Giornale dell’ Istituto Italiano degli Attuari, 7: 74–80.Google Scholar
  19. Kuczynski, M. (2011). ‘Goodwin’s Lectures on the Phillips Machine in 1963’. Economia Politica, Special Issue, 28(1): 97–102.Google Scholar
  20. Le Corbeiller, Ph. (1931). Les Systémes Autoentretenus et les Oscillations de Relaxation. Paris: Librairie Scientifique Hermann et Cie.Google Scholar
  21. Le Corbeiller, Ph. (1933). ‘Les Systémes Autoentretenus et les Oscillations de Relaxation’. Econometrica, 1(3): 328–332.Google Scholar
  22. Le Corbeiller, Ph. (1936). ‘The Non-Linear Theory of the Maintenance of Oscillations’. Journal of the Institute of Electrical Engineers, 79(477): 292–300.Google Scholar
  23. Palis, J., Jr. and W. de Melo (1982). Geometric Theory of Dynamical Systems: An Introduction. Heidelberg: Springer-Verlag.Google Scholar
  24. Schumpeter, J.A. (1954). History of Economic Analysis. London: Allen & Unwin.Google Scholar
  25. Sedaghat, H. (1997). ‘The Impossibility of Unstable, Globally Attracting Fixed Points for Continuous Mappings of the Line’. The American Mathematical Monthly, 104(4): 356–358.Google Scholar
  26. Simon, H.A. (1952). ‘Causal Ordering and Identifiability’. Chapter III in W.C. Hood and T.C. Koopmans (eds) Studies in Econometric Method. New York: John Wiley & Sons: 49–74.Google Scholar
  27. Solow, R.M. (1990). ‘Goodwin’s Growth Cycle: Reminiscence and Rumination’. Chapter 4 in K. Velupillai (ed.) Nonlinear and Multisectoral Macrodynamics: Essays in Honour of Richard Goodwin. New York: New York University Press: 31–41.Google Scholar
  28. Tinbergen, J. (1937). ‘Review of The Trade Cycle, by Roy Harrod’. Weltwirtschaftliches Archiv, 45(3): 89–91.Google Scholar
  29. Velupillai, K.V. (1996). ‘Obituary: Professor Richard Goodwin’. The Independent, 9 August. Available at:
  30. Velupillai, K.V. (1998). ‘Richard M. Goodwin 1913–1996’. Economic Journal, 108(450): 1,436–1,449.Google Scholar
  31. Velupillai, K.V. (2015). ‘Richard Goodwin: The Indian Connection’. Economic & Political Weekly, 50(15): 80–84.Google Scholar
  32. Walker, D.A. (1987). ‘Walras’s Theories of Tatonnement’. Journal of Political Economy, 95(4): 758–774.Google Scholar
  33. Walker, D.A. (1988). ‘Iteration in Walras’s Theory of Tatonnement’. De Economist, 136(3): 299–231.Google Scholar
  34. Zambelli, S. (2010). ‘Flexible Accelerator Economic Systems as Coupled Oscillators’. Journal of Economic Surveys, 25(3): 608–633.Google Scholar
  35. Zambelli, S. (2011). ‘Coupled Dynamics in a Phillips Model of the Macroeconomy’. Economia Politica, Special Issue, 28(1): 171–188.Google Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Formerly Professore di Chiara FamaUniversity of TrentoTrentoItaly
  2. 2.Formerly Professor of EconomicsNew School for Social ResearchNew YorkUSA

Personalised recommendations