Existence and optimality of a general equilibrium with endogenous uncertainty

Abstract

Kenneth Arrow once said that uncertainty about prices may be the most important form of economic uncertainty. Yet tI1e treatment of uncertainty in Arrow-Debreu markets reflects only nature's moves. It therefore neglects price uncertainty, because prices depend on human behavior. This chapter attempts to close the gap. It defines a new concept of general equilibrium in markets where traders are uncertain about prices, and proves the existence of such an equilibrium. Traders do not know the possible equilibrium prices a priori. The state space which represents price uncertainty, and the financial instruments used to hedge this uncertainty, are all defined endogenously as part of a market equilibrium. To motivate the problem,I show in Proposition 1 that trying to hedge price uncertainty within an Arrow-Debreu framework leads to paradoxical outcomes, which are connected with Russell's paradox in logics. Thus a new framework is needed.