GQVIs for studying competitive equilibrium problem when utilities are locally Lipschitz and quasi-concave

Abstract

We establish an existence result on competitive equilibrium problem for an exchange economy when the consumers' utilities are represented by a locally Lipschitz continuous and quasi-concave functions. The consumer's demand is found to be actually a multi-valued map. Furthermore, any competitive equilibrium satisfies Walras' law, too. To achieve this goal, the theory of Nonsmooth Analysis combined with the Generalized Quasi-Variational Inequalities (GQVIs) is used.