Continuity and uniqueness of equilibria for linear exchange economies

The purpose of this paper is to study the continuity and uniqueness properties of equilibria for linear exchange economies. We characterise the sets of utility vectors and initial endowments for which the equilibrium price is unique and respectively the set for which the equilibrium allocation is unique. We show that the equilibrium allocation correspondence is continuous with respect to the initial endowments and we characterize the set of full measure where the equilibrium allocation correspondence with respect to the initial endowments and utility vectors is continuous.