Content:
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, that 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 non-monotone variational inequalities over bounded domains. Truncation arguments with specific estimates, based on the data in the economic model, are devised to transform the unbounded variational inequality that naturally comes up into a bounded one having the same solutions.
February 2005