The Kaldor-Kalecki business cycle model

The question of the determination of investment decisions and their links with economic activity leads us to formulate a new business cycle model. It is based on the dynamic multiplier approach and the distinction between investment and implementation. The study of the nonlinear behaviour of the Kaldor-Kalecki model represented by the second-order delay differential equations is presented. It is shown that the dynamics depends crucially on the time-delay parameter T - the gestation time period of investment. We apply the Poincare-Andronov-Hopf bifurcation theorem generalized for functional differential equations. It allows us to predict the occurrence of a limit cycle bifurcation for the time-delay parameter T = T-bif. The dependence of T = T-bif on the parameters of our model is discussed. As T is increased, the system bifurcates to limit cycle behaviour, then to multiply periodic and aperiodic cycles, and eventually tends towards chaotic behaviour. Our analysis of the dynamics of the Kaldor-Kalecki model gives us that the limit cycle behaviour is independent of the assumption of nonlinearity of the investment function. The limit cycle is created only due to the time-delay parameter via the Hopf bifurcation mechanism. We also show that for a small time-delay parameter, the Kaldor-Kalecki model assumes the form of the Lienard equation.