EXCESS-DEMAND FUNCTIONS, EQUILIBRIUM PRICES, AND EXISTENCE OF EQUILIBRIUM

For continuous aggregate excess demand functions of economies, the exi sting literature (e.g. Sonnenschein (1972, 1973), Mantel (1974), Debre u (1974), Mas-Colell (1977), etc.) achieves a complete characterizatio n only when the functions are defined on special subsets of positive p rices. In this paper, we allow the functions to be defined on a larger class of price sets, (allowing, for example the closed unit simplex, including its boundary). Besides characterizing excess demands for a l arger class of economies, our extension provides a useful tool for pro ving other results. It allows us to characterize the equilibrium price set for a larger class of economies. It also permits extending Uzawa' s observation (1962), by showing that Brouwer's Fixed-Point Theorem is implied by the Arrow-Debreu Equilibrium Existence Theorem (1954, Theo rem I).