The Hopf bifurcation in the Kaldor-Kalecki model

By using the theory of dynamical systems and especially the theory of Hopf bifurcations the existence of limit cycles in the Kaldor-Kalecki model is discussed. This model is a modified version of the 1940 Kaldor model of business cycle with introduced the time-to-build parameter in investment function in the Kalecki way. In this paper the model is investigated in an approximation of a small lag. It is shown that such a model can be reduced to the Lienard equation which has a bifurcation value of lag parameter. From the Hopf theorem the sufficient conditions for generation of the limit cycle on the phase space are obtained. It is demonstrated how the amplitude of oscillation depends on the value of a lag parameter. Copyright (C) 1998 IFAC.