On the existence of price equilibrium in economies with excess demand functions

Abstract

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.Journal of Economic Literature Classification Number: C62, C72, D44, D61, D82.

Existence and well-posedness for excess demand equilibrium problems

“…Quah [28] provided an equilibrium existence proof in which the excess demand function of an exchange economy obeys the weak axiom of revealed preference. Recently, Tian [30] has established the existence of price equilibrium in economies where commodities can be indivisible but excess demand functions can be discontinuous or do not have any other structural property beyond Walras' law.…”

“…Usually, to establish the existence of solutions to (EDEP), most of authors assume that the excess demand function holds the homogeneity property. Then, employing the auxiliary excess demand equilibrium problem with its constraint set defined by p ∈ A | l i=1 p i = 1 , sufficient conditions of the existence of (EDEP) are considered, for more details we refer the readers to [6,20,30,34] and the references therein. Herein, we apply Glicksberg's fixed point theorem to investigate the solvability of (EDEP) without assuming the homogeneity property of excess demand functions.…”