The investment gestation period in the so called Kaldor-Kalecki model. A new approach

This paper deals with the so-called Kaldor-Kalecki model. This is a class of models merging Kalecki’s idea on the existence of a time lag in the investment process with the well-known Kaldor’s business cycle model. A common approach in these models is to introduce the Kalecki investment gestation period by simply adding a finite time lag to the Kaldorian investment function. This method bypasses the complexities inherent in modeling the three stages of all investment decisions. Unlike this widespread custom, here we inverted the Kaldor-Kalecki binomial using Kaldor’s 1940 model to extend and complete Kalecki’s 1935 delayed differential equation defining his model. Considering the investment gestation period explicitly, our model yields a delay integro-differential system with delay-dependent coefficients. Keeping the Kaldorian assumption of a sigmoidal investment function, the system can have one or three equilibria. After a thorough analytical study, the numerical simulations of the model show that emerging Hopf bifurcations give rise to limit cycles. But, in addition to this typical result of Kaldorian models, we obtain a particular complex dynamic behavior, which is not only a novelty in the field of continuous time Kaldor-Kalecki models, but also a result perfectly consistent with Kaldor’s thought on the economic cycle.