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Variational Inequalities and Economic Equilibrium

Center for Mathematical Modelling and Department of Mathematical Engineering, University of Chile, Casilla 170/3, Correo 3, Santiago, Chile
Department of Mathematics, University of Washington, Seattle, Washington 98195-4350
Department of Mathematics, University of California, Davis, California 95616
ajofre{at}dim.uchile.cl
rtr{at}math.washington.edu
rjbwets{at}ucdavis.edu

Variational inequality representations are set up for a general Walrasian model of consumption and production with trading in a market. The variational inequalities are of functional rather than geometric type and therefore are able to accommodate a wider range of utility functions than has been covered satisfactorily in the past. They incorporate Lagrange multipliers for budget constraints, which are shown to lead to an enhanced equilibrium framework with features of collective optimization. Existence of such an enhanced equilibrium is confirmed through a new result about solutions to nonmonotone variational inequalities over bounded domains. Truncation arguments with specific estimates, based on the data in one economic model, are devised to transform the unbounded variational inequality that naturally comes up into a bounded one having the same solutions.

Key Words: Walrasian economic equilibrium; functional variational inequalities; equilibrium computations; equilibrium constraints; complementarity problems
History: Received: November 30, 2005; revision received: May 11, 2006;