Variational methods for equilibrium problems involving quasi-concave utility functions

This paper deals with the existence of competitive equilibrium points in a Walrasian pure exchange economy with utility function. An existence result involving quasi-concave utility functions is established. In particular, a previous result by the authors involving concave utility functions is improved. The approach is variational. Indeed, competitive equilibrium points will be found out as solutions of a quasivariational inequality in a finite dimensional space. In particular, an existence result for (generalized) quasi-variational inequalities established by Cubiotti is applied.