A general equilibrium model of markets for commodities and assets is considered. We develop the notion of a price system that admits no arbitrage opportunity, and we demonstrate the fundamental role of this concept for the theory of the existence of a competitive equilibrium. A price system admits no arbitrage opportunity for a consumer if every bundle of desired commodities has a positive market value. We prove that the existence of a price system that admits no arbitrage opportunity for all consumers is sufficient for the existence of an equilibrium.