Some Stability Properties of Goodwin's Growth Cycle Model

Abstract

This chapter generalizes Goodwin’s (1972) growth cycle model as reconsidered in :def :def Velupillai (1979) and it also extends the proofs of some assertions made by the latter author. This extended version which we shall introduce in Sect. 17.2 depends on a money-illusion parameter η in such a way that the Goodwin case becomes a bifurcation point between those parameter values (η > 0) where the extended model is globally asymptotically stable and those where it is totally unstable (η < 0). A by-product of this result is that Goodwin’s dynamical system obviously cannot be structurally stable. This method of demonstration replaces Velupillai’s formal proof by economic reasoning. Section 17.3 then shows why Velupillai’s demonstration of the closed-orbit structure of Goodwin’s model is not yet complete and it briefly indicates how to fill the existing gaps. Since this chapter is supplementary to :def :def Velupillai’s (1979) article, the reader should consult his paper for further explanations of the model and the symbols used.