On the Existence of Price Equilibrium in Economies with Excess Demand Functions

This paper provides a price equilibrium existence theorem in economies where commodities may be indivisible and aggregate excess demand functions may be discontinuous. We introduce a very weak notion of continuity, called recursive transfer lower semi-continuity, which is weaker than transfer lower semi-continuity and in turn weaker than lower semicontinuity. It is shown that the condition, together with Walras’s law, guarantees the existence of price equilibrium in economies with excess demand functions. The condition is also necessary, and thus our results generalize all the existing results on the existence of price equilibrium in economies where excess demand is a function.