Cone conditions in general equilibrium theory

The modern convex-analytic rendition of the classical welfare theorems characterizes optimal allocations in terms of supporting properties of preferences by nonzero prices. While supporting convex sets in economies with finite dimensional commodity spaces is usually a straightforward application of the separation theorem, it is not that automatic in economies with infinite dimensional commodity spaces. In the last 30 years several characterizations of the supporting properties of convex sets by non-zero prices have been obtained by means of cone conditions. In this paper. we present a variety of cone conditions, study their interrelationships, and illustrate them with many examples. Journal of Economic Literature Classification Numbers: D46, D51. (C) 2000 Academic Press.