Cone conditions in general equilibrium theory

The modern convex-analytic rendition of the classical welfare theorems char acterizes optimal allocations in terms of supporting properties of preferen ces by nonzero prices. While supporting convex sets in economies with finit e 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 characterizatio ns 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 wit h many examples. Journal of Economic Literature Classification Numbers: D46 , D51. (C) 2000 Academic Press.