Competitive prices for a stochastic input–output model with infinite time horizon

Consider a one-sector stochastic input–output model with infinite time horizon. The technology in each time period exhibits constant returns to scale on positive linear combinations of a finite number of basic input–output pairs. Furthermore, perfect information is available as a filtration generated by finite partitions of the state space. By definition, competitive prices require expected profit maximization in every time period. The Riesz representation of a sequence of competitive price functionals yields a state-price deflator with a supermartingale property. We show that there exists a competitive price system for some feasible program if and only if there is No Free Production (NFP). Furthermore, there exists a competitive price system for a particular program if and only if if NFP holds and the program is short-run efficient. This model includes a securities market model with or without convex cone trading constraints as a special case. Under these circumstances, NFP reduces to No Arbitrage and we recover a version of the fundamental theorem of asset pricing. The author expresses gratitude for the advice of two anonymous referees, one who pointed out the simple way to prove the key lemma and the other who helped integrate the conclusions into the existent literature.