The Kaldor-Kalecki model of business cycle as a two-dimensional dynamical system

In the paper we analyze the Kaldor-Kalecki model of business cycle. The time delay is introduced to the capital accumulation equation according to Kalecki's idea of delay in investment processes. The dynamics of this model is represented in terms of time delay differential equation system. In the special case of small time-to-build parameter the general dynamics is reduced to two-dimensional autonomous dynamical system, This system is examined in details by methods of qualitative analysis of differential equations. It is shown that there is a Hopf bifurcation leading to a limit cycle. Additionally stability of this solution is discussed.