Catastrophe Theory and the Business Cycle

In this paper we examine a variation on Kaldor’s (1940) model of the business cycle using some of the methods of catastrophe theory. (Thom (1975), Zeeman (1977)). The development proceeds in several stages. Section I provides a brief outline of catastrophe theory, while Section II applies some of these techniques to a simple macroeconomic model. This model yields, as a special case, Kaldor’s business cycles. In an appendix to this paper, we provide a more rigorous treatment of the cyclic behavior of the model following the work of Chang and Smyth (1971). In Section III, we describe a generalization of Kaldor’s model that allows not only for cyclical recessions, but also allows for long term depressions. Section IV presents a brief review and summary. This paper is frankly speculative. It presents, in my opinion, some interesting models concerning important macroeconomic phenomena. However, the hypotheses of the models are neither derived from microeconomic models of maximizing behavior, nor are they subjected to serious empirical testing. The hypotheses are not without economic plausibility, but they are far from being established truths. Hence, this paper can only be said to present some interesting stories of macroeconomic instability. Whether these stories have any empirical basis is an important, and much more difficult, question.