No. 2001-34 EQUILIBRIA WITHOUT THE SURVIVAL ASSUMPTION: A NON-STANDARD ANALYSIS APPROACH

It is well known that an equilibrium in the Arrow-Debreu model may fail to exist if a very restrictive condition called the survival assumption is not satis ed. We study two approaches that allow for the relaxation of this condition. Danilov and Sotskov (1980), and Florig (1998a) developed a concept of a generalized equilibrium based on a notion of hierarchic prices. Marakulin (1988, 1990) proposed a concept of an equilibrium with non-standard prices. In this paper, we establish the equivalence between non-standard and hierarchic equilibria. Furthermore, we show that the set of non-standard equilibria coincides with the fuzzy rejective core of an economy and is generically nite for any speci ed system of dividends.