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 excess demand functions may not be continuous. We introduce a weak notion of continuity, called recursive transfer lower semi-continuity, which, together with Walras’ 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.