Uniqueness in Planar Endogenous Business Cycle Theories

We examine some uniqueness theorems concerning the attractors (limit cycles) of dynamic planar models of non-linear, endogenous theories of business cycle. We confine our attention to the pioneering models of Goodwin, Kaldor, Hicks and their variations. For Goodwin’s non-linear multiplier-accelerator model with a single non- linearity, we provide sufficient conditions for establishing uniqueness of the limit cycle based on a theorem by de Figueiredo. We also discuss issues concerning the algorithmic decidability of the number of attractors for these models within the framework of computable analysis.