Quasi-variational approach of a competitive economic equilibrium problem with utility function: Existence of equilibrium

A Walrasian pure exchange economy with utility functions, a particular case of a general economic equilibrium problem, is considered in this paper. We assume that each agent is endowed with goods and maximizes his utility function, under his budget constraints. We are able to characterize the Walrasian equilibria as solution of an associated quasivariational inequality. This approach allows us to obtain an existence result of equilibrium solutions. As an application, we provide the explicit equilibrium in the case of two agents and two goods.