Existence of equilibria with infinitely many consumers and infinitely many commodities. A theorem based on models of commodity differentiation

This paper presents a general result on the existence of competitive equilibria in exchange economies in which consumers and commodities are both infinite in number. The result shows that - in this framework at least - the added assumptions necessary to handle models with infinitely many agents are remarkably similar to the additional restrictions needed when only finitely many commodities are available for trade. It is shown that the results apply, in a straightforward manner, to two of the common models of consumer choice when commodity differentiation is an important consideration.