Optimal stationary consumption with stochastic production and resources

Abstract

Uncertainty about technology and resources is represented in terms of uncertainty about an (exogenous) environment whose successive states form a stationary stochastic process, with probabilities that are unaffected by economic decisions. The successive states of the economy depend both on the environment and on the decisions taken with regard to production and consumption. It is shown that, under conditions that are natural extensions of “neoclassical” conditions in the case of certainty, (1) Capital saturation is possible, i.e., an optimal stationary stochastic program exists, and (2) An optimal program can be sustained by a price system that takes the form of a stationary stochastic process of price vectors. In other words, an optimal stationary program can be sustained by a stochastic “equilibrium,” in which at each date the optimal production decisions maximize expected intertemporal profit, and the optimal aggregate consumption vector has minimum cost among all aggregate consumption vectors yielding no less (social) utility.