On the Study of an Economic Equilibrium with Variational Inequality Arguments

The main purpose of this paper is to investigate on the existence of a competitive equilibrium for a market with consumption and exchange. A variational representation is used to study this problem. More precisely, we consider an economy where utility functions are assumed concave and non-differentiable, and we characterize the equilibrium by means of a variational problem involving the subdifferential multimap. Thanks to this approach, by introducing suitable perturbed utility functions, we achieve an existence result when the operator is not coercive and the convex set might be unbounded.