Endogenous Cycles in the Sraffian Supermultiplier Model

In this paper, we examine the presence of limit cycles in the baseline and a non-linear Sraffian supermultiplier model (SSM). We use the propensity to invest as the bifurcation parameter and identify the conditions necessary for the emergence of cycles in the SSM. To accomplish this, we deliver a formal analysis of the dynamic stability of its equilibrium path and present the conditions required for a Hopf bifurcation to occur, resulting in persistent periodic fluctuations among its endogenous variables. Besides, we show that the non-linear model display dynamics similar to the baseline SSM, which reinforces our view that the robustness of cycles in the baseline model does not depend on any additional non-linearity assumption