Two Dynamic Models of Distributive and Financial Endogenous Cycles

This paper proposes two theoretical dynamic models (Models A and B) to analyze the interaction between distributive and financial cycles in capitalist economies. Model A assumes investment equals savings at the aggregate level but assumes a delay between capitalists saving their income and distributing it to firms for reinvestment, leading to credit demand from a rentier class. Model B extends and modifies Model A by representing capitalist incentives to invest through an investment function and accounting for the dynamic effect of non-zero excess demand. Analytical proofs for the existence of limit cycles in both models are provided using Hopf bifurcation theorems for four-dimensional and five-dimensional dynamical systems, and numerical simulations identify stable and limit cycles, unstable cycles, damped oscillations, and multiple relevant patterns. The results suggest that the stability of cycles is significantly influenced by the distribution of bargaining power between workers and capitalists, as well as the behavior of the central bank and the rentier class. Furthermore, the paper suggests two methods to identify financing regimes within capitalist cycles and concludes by providing insights for future analytical and empirical research.