A general equilibrium model of markets for commodities and assets is considered. The author develops the notion of a price system that admits no arbitrage opportunity and demonstrates the fundamenta l role of this concept for the theory of the existence of a competiti ve equilibrium. A price system admits no arbitrage opportunity for a consumer if every bundle of desired commodities has a positive market value. The author proves that the existence of a price system that a dmits no arbitrage opportunity for all consumers is sufficient for th e existence of an equilibrium. Copyright 1987 by The Econometric Society.

This paper develops a framework for a general equilibrium analysis of asset markets when the number of assets is infinite. Such markets have been studied in the context of asset pricing theories. Our main results concern the existence of an equilibrium. We show that an equilibrium exists if there is a price system under which no investor has an arbitrage opportunity. A similar result has been previously known to hold in finite asset markets. Our extension to infinite assets involves a concept of an arbitrage opportunity which is different from the one used in finite markets. An arbitrage opportunity in finite asset markets is a portfolio that guarantees non-negative payoff in every event, positive payoff in some event, and has zero price. For the case of infinite asset markets, we introduce a concept of sequential arbitrage opportunity which is a sequence of portfolios which increases an investor's utility indefinitely and has zero price in the limit. We show that a sequential arbitrage opportunity and an arbitrage portfolio are equivalent concepts in finite markets but not in their infinite counterpart.