The Effect of the Mathematics of Finance on the Dynamics of a Credit Economy

Abstract

The general equilibrium theory of J.M. Keynes was developed in the 1930's to help explain the great depression and prevent future economic downturns. Out of this came the IS-LM (investment saving/liquid money) model, introduced by J.R. Hicks in 1936. There is controversy about the success of Hicks's approach, not the least of which is the lack of dynamical aspects in the theory. The thesis considers three interest groups identified as bankers, capitalists and workers. A coupled system of differential equations describes the flow of money, capital and credit over time. A mathematical analysis of the high dimensional system reveals the existence of equilibrium points. Their stability properties are determined. By modifying the equations, cycles appear corresponding to periods of boom and bust. Thus, shocks to the system, which are theorized by neoclassical economists to be due to external events, are shown to be possible using dynamical endogenous equations.