The Kaldor‐Kalecki business cycle model

The question of the determination of investment decisions and their links with economicactivity leads us to formulate a new business cycle model. It is based on the dynamic multiplierapproach and the distinction between investment and implementation. The study of thenonlinear behaviour of the Kaldor‐Kalecki model represented by the second‐order delaydifferential equations is presented. It is shown that the dynamics depends crucially on thetime‐delay parameter T ‐ the gestation time period of investment. We apply the Poincaré‐Andronov‐Hopf bifurcation theorem generalized for functional differential equations. Itallows us to predict the occurrence of a limit cycle bifurcation for the time‐delay parameterT = 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 andaperiodic cycles, and eventually tends towards chaotic behaviour. Our analysis of the dynamicsof the Kaldor‐Kalecki model gives us that the limit cycle behaviour is independent of theassumption of nonlinearity of the investment function. The limit cycle is created only due tothe time‐delay parameter via the Hopf bifurcation mechanism. We also show that for a smalltime‐delay parameter, the Kaldor‐Kalecki model assumes the form of the Liénard equation.