On the existence and stability of business cycles in a dynamic model of a closed economy

In this paper we analyze a macroeconomic model derived from Schinasi’s model of a closed economy. Rigorous analysis of the existence and stability of the equilibrium is carried out. We present a formula for the calculation of the focus constant in the bifurcation equation of the model. Thereafter we prove the existence and stability of business cycles by application of the Hopf bifurcation theorem. Finally, we give an example of a model with a stable business cycle and its graphical illustrations.