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 Poincaré–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 = Tbif. The dependence of T = Tbif 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 Liénard equation.