## Economic equilibrium through variational inequalities

### Volume 36 / 2009

Applicationes Mathematicae 36 (2009), 43-58
MSC: Primary 91B50; Secondary 65K10.
DOI: 10.4064/am36-1-4

#### Abstract

The purpose of this paper is to present an alternative proof of the existence of the Walrasian equilibrium for the Arrow–Debreu–McKenzie model by the variational inequality technique. Moreover, examples of the generalized Arrow–Debreu–McKenzie model are given in which the price vector can reach the boundary of the orthant allowing a commodity to be of price zero at equilibrium. In such a case its supply exceeds demand. It is worth mentioning that utility functions in this model are allowed not to be strictly concave and they can reach their maximum in the commodity space.