ABSTRACT
The principal model in economic theory is the Walrasian model of general economic equilibrium. This chapter explains several simple, highly stylized versions of the Walrasian equilibrium model. It discusses the problems involved in proving the existence of equilibria and of computing equilibria. The chapter provides the possibility of multiplicity of equilibria. An equilibrium of this model is a vector of prices, one for each good, which the agents all take as given in solving their maximization problems, such that demand is equal to supply for every good. Although Wald A. had proved the existence of equilibria for two special models earlier, Arrow K. J. and G. Debreu and McKenzie L. realized that the existence of equilibria in more general models could be demonstrated using Brouwer's fixed-point theorem or some variant. The relationship between the existence theorem and Brouwer's theorem is very close: the existence of equilibrium follows quickly from Brouwer's theorem.
