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Systems of variational inequalities related to economic equilibrium

Naniewicz Z., Nockowska M.

Control and Cybernetics

2007

Vol. 36, no 4

889-909

In the paper a new approach to the Walrasian general equilibrium model of economy is presented. The classical market clearing condition is replaced by suitably formulated variational inequality. It states that the market clears for a commodity if its equilibrium price is positive; otherwise, there may be an excess supply of the commodity in equilibrium and then its price is zero. Such approach enables establishing new existence results without assumptions which were fundamental for the currently used methods: (i) Dis-utility functions are not required to be strictly convex and they may attain their minima in the consumption sets (the local nonsatiation of preferences is not required). (ii) The boundary of the positive orthant is allowed for the price vector in equilibrium. It allows for investigation of certain new problems, e.g. bankruptcy conditions.