
Journal of Convex Analysis 25 (2018), No. 2, 515527 Copyright Heldermann Verlag 2018 Generalized Variational Inequality and General Equilibrium Problem Maria B. Donato Dept. of Mathematics and Computer Science, University of Messina, Via F. Stagno D'Alcontres 31, 98166 Messina, Italy mbdonato@unime.it Monica Milasi Dept. of Mathematics and Computer Science, University of Messina, Via F. Stagno D'Alcontres 31, 98166 Messina, Italy mmilasi@unime.it Carmela Vitanza Dept. of Mathematics and Computer Science, University of Messina, Via F. Stagno D'Alcontres 31, 98166 Messina, Italy vitanzac@unime.it We present a study of the general economic equilibrium problem in the framework of the variational inequality approach. We describe the main aspects characterizing the model and the equilibrium definition. The utility functions, which represent the consumers' preferences over goods, are taken to be generalized concave and nondifferentiable. Our aim is to study the equilibrium by means of a suitable quasivariational inequality. As is wellknown, the difficulty to study a quasivariational inequality lies in the dependence of the convex constraint set on the solution. A crucial issue of our study is proving the equivalence between our quasivariational inequality and suitable variational inequalities. More precisely, we introduce a new and useful methodology, which allows us to solve associated variational inequalities (where the convex sets do not depend on solution) instead of a quasivariational inequality. Finally, our main result is achieved by using arguments of setvalued analysis. Keywords: Generalized quasivariational inequalities, generalized concavity, competitive equilibrium, production economy. [ Fulltextpdf (114 KB)] for subscribers only. 