Convergence to equilibrium for a class of exchange economies

Abstract

For a class of stochastic dynamical models of exchange economies that we call ``fully connected Cobb-Douglas'', the paper proves convergence of the probability distribution to an equilibrium, in total variation metric as time goes to infinity. The convergence is exponential and the equilibrium is determined uniquely by the number of agents, their ``exponents'', and the initial amounts of money and goods in the economy.