Uniqueness in Planar Endogenous Business Cycle Theories

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Venkatachalam, Ragupathy and Kao, Ying-Fang. 2021. Uniqueness in Planar Endogenous Business Cycle Theories. In: Kumaraswamy Velupillai, ed. Keynesian, Sraffian, Computable and Dynamic Economics: Theoretical and Simulational (Numerical) Approaches. Basingstoke: Palgrave Macmillan, pp. 273-310. ISBN 9783030581305 [Book Section]

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Official URL: https://www.palgrave.com/gp/book/9783030581305

Abstract or Description

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.

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