Econometrica: Sep 1987, Volume 55, Issue 5
Competitive Equilibria in Production Economies with an Infinite-Dimensional Commodity Space
William R. ZameThis paper establishes the existence of competitive equilibria for economies with production and infinite-dimensional space of commodities. The commodity spaces treated are normed lattices, but no interiority assumptions are made on the positive cone; such infinite-dimensional spaces include most of those which have been found useful in economic analysis. The crucial assumptions are on compactness of the set of feasible allocations, continuity of preferences, boundedness of the marginal rates of substitution in consumption, and boundedness of the marginal efficiency of production. Examples are presented which show that without such assumptions, competitive equilibria may fail to exist.
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