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Exchange price equilibria and variational inequalities. (English) Zbl 0709.90013
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.
Reviewer: P.J.Deschamps

91B50 General equilibrium theory
49J40 Variational inequalities
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C25 Convex programming
Full Text: DOI
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