Kaldor–Kalecki New Model on Business Cycles

R.G. Goodwin mentioned that “economists will be led, as natural scientists have been led, to seek in nonlinearities an explanation of the maintenance of oscillation” (Goodwin, Econometrica 19(1), 1951); following this reasoning, we studied business cycles as if they were generated by nonlinear differential equations which prove that the proposed model exhibits chaotic behavior. The main goal of this chapter is to study chaotic behaviour within Kaldor’s framework described in Chap. 12 . In the following, we suggest an alternative to the usual models in the literature. Our approach is consistent with chaotic dynamics and adheres to the Kaldorian specifications. This is obtained by declaring that investment and saving functions, I and S respectively are: nonlinear, regular, increasing (or at least not decreasing) whilst capital and income are growing. This is achieved by a new functional specification of the investment and consumption as variants of the hyperbolic tangent rather than the usual arctangent available in literature. Apart from a full set of parameters useful for calibrations, an additional feature of this model is the ability to embed randomness. The latter opens the way to a mixture of stochastic and deterministic chaos.