Time Delays and Business Cycles: Hilferding's model revisited

This paper develops a Marxian model of the business cycle based on Hilferding's theory of disproportionality in capital accumulation in a two-sector economy. The disproportionality arises from the existence of time delays in production generated by the differential capital intensity in the two sectors. The time delays produce an asymmetric price structure that causes overproduction and crisis. The model is constructed using delay-differential equations. Numerical simulations show that the model produces an economy-wide business cycle phenomenon. The domain of the time delay parameter is investigated, and shows that the model produces a wide variety of dynamics from monotonic convergence to explosive oscillations. Moreover, the solution shows that intersectoral investment flows transmit the instability in capital accumulation and that longer time delays produce higher cycle amplitudes.