VARIATIONAL INEQUALITIES AND DYNAMIC MARKET EQUILIBRIUM PROBLEMS Patrizia DANIELE Dipartimento di Matematica e Informatica, Università di Catania Viale A. Doria, 6 – 95125 CATANIA (ITALIA)

                    e-mail: daniele@dmi.unict.it

Abstract. In the last years some papers have been devoted to the study of the “Spatial Price Equilibrium Problem” in the case of excess of the supplies and of the demands. The equilibrium conditions that describe this “disequilibrium” model, in the case of price formulation, are expressed in terms of a Variational Inequality.

This more general and realistic model, which generalizes the classical spatial price equilibrium problems formulated by A.A. Cournot, A.C. Pigou, S. Enke, P.A. Samuelson, T. Takamaya and G.G. Judge, adopts, unchanged, the concept of equilibrium, namely that:

“The demand price is equal to the supply price plus the cost of transportation, if there is trade between the pair of supply and demand markets”.

It is worth remarking that this classical equilibrium principle follows the user-optimized approach instead of the system-optimizing one and that these different approaches have been noted first by A.C. Pigou.

However, in order to obtain a model that takes into account the essential features of our socio–economic world, we cannot avoid to consider the time dependence of phenomena.

The aim of this paper is to further improve the time dependent economic equilibrium problem by considering the case in which the markets are at the same time demand and supply markets. This model is expressed in terms of an evolutionary Variational Inequality, for which we provide existence results and a computational procedure.