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Journal of Convex Analysis 25 (2018), No. 2, [final page numbers not yet available]
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 non-differentiable. Our aim is to study the equilibrium by means of a suitable quasi-variational inequality.
As is well-known, the difficulty to study a quasi-variational 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 quasi-variational 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 quasi-variational inequality. Finally, our main result is achieved by using arguments of set-valued analysis.

Keywords: Generalized quasi-variational inequalities, generalized con\-ca\-vi\-ty, competitive equilibrium, production economy.

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