JAPANESE CONTRIBUTIONS TO NONLINEAR CYCLE THEORY IN THE 1950s*

Abstract

In the early 1950s pioneering contributions were made to the nonlinear theory of Keynesian macrodynamics by Shinichi Ichimura, Michio Morishima and Takuma Yasui. They were the first to formally investigate the existence, stability and uniqueness of limit cycles in macrodynamics. An attempt is made to place the contributions of this Japanese school of nonlinear trade cycle theorists within the context and development of mathematical economics in early post-war Japan. As an additional, although minor, exercise, Morishima's model of the cycle is simplified and generalized to show, using the AndronovHopf bifurcation theorem, the existence of a periodic orbit. JEL Classification Numbers: B31, C61, E32.

A note on the “unique” business cycle in the Keynesian theory

“…In Section 3, we analyze our Keynesian model by reducing it to a generalized Liénard system (cf. , 2008. By so doing, we establish the existence of a periodic orbit and verify the uniqueness of it for the case in which the speed of quantity adjustment is fast enough.…”

A Non‐linear Model of the Trade Cycle: Mathematical Reflections on Hugh Hudson's Classic

“…2 Goodwin's formalisation, under the influence of Harrod (1936) and Phillip Le Corbeiller's mathematical guidance, aimed at 'reducing' Harrod's Keynesian Dynamics to a second-order nonlinear differential equation; Hicks, although also explicitly acknowledging Harrod's influence, was more directly inspired also by the Swedes and Robertson, so that his formalization was in terms of piecewise (linear) difference equations. It was the outstanding Japanese trio of Yasui, Ichimura and Morishima who began the identification of the economics of Kaldor (1940), Hicks (1950) and Goodwin (1951) via the mathematics of nonlinear planar dynamical systems (see Velupillai, 2008, Ragupathy & Velupillai, 2012a Competition and Goodwin, who made the geometry of dynamics an expository device of supreme fertility and elegance (to which we return in the final section).…”