Exchange price equilibria and variational inequalities
The Walrasian equilibria of a pure exchange economy are characterized as the solutions of a variational inequality. The theory of variational inequalities is then used to provide a simple proof of the existence of such equilibria under weak assumptions on the aggregate excess demand functions. The largest part of the paper is devoted to the further characterization of Walrasian equilibria under various monotonicity assumptions on the excess demand functions (i.e. weak, strict, and strong monotonicity). Under weak monotonicity, the set of equilibria is convex; under strict monotonicity, equilibrium is unique; under strong monotonicity, an equilibrium price vector depends continuously on the aggregate excess demand function. Finally, the connection between Walrasian equilibria and the solution of a convex programming problem is investigated.
scientific article; zbMATH DE number 4167791
scientific article