On the equilibrium price set of a continuous perturbation of exchange economies

Abstract

The main result of the paper shows that a certain global structure property of the equilibrium set of a continuous perturbation of exchange economies which recently has been established by Mas-Colell and by the author in fact is the only one which generally holds. To achieve this we extend the well-known decomposition method for excess demand functions developed and advanced by Sonnenschein, Debreu, Mantel, and Mas-Colell to the one-parametrized case. Our proof moreover shows that the addressed decomposition method is continuous in that it assigns neighbouring exchange economies to neighbouring excess demand functions. Together with the global results by Balasko and the local results by Allen the present results contribute to a deepened understanding of the structure of the graph of the Walras correspondence.