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A note on economic equilibrium with nonsatiated utility functions

100%
Nockowska-Rosiak M.
Applicationes Mathematicae
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2013
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tom 40
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nr 1
117-126
EN
The purpose of this paper is to prove the existence of a Walrasian equilibrium for the Arrow-Debreu and Arrow-Debreu-McKenzie models with positive price vector with nonsatiated utility functions of consumers by using variational inequalities. Moreover, the same technique is used to give an alternative proof of the existence of a Walrasian equilibrium for the Arrow-Debreu and Arrow-Debreu-McKenzie models with nonnegative, nonzero price vector with nonsatiated utility functions.
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A note on variational-type inequalities for (η,θ,δ)-pseudomonotone-type set-valued mappings in nonreflexive Banach spaces

100%
Nockowska-Rosiak M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2013
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tom 33
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nr 1
41-45
EN
In this paper the existence of solutions to variational-type inequalities problems for (η,θ,δ)- pseudomonotone-type set-valued mappings in nonreflexive Banach spaces introduced in [4] is considered. Presented theorem does not require a compact set-valued mapping, but requires a weaker condition 'locally bounded' for the mapping.
3
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Economic equilibrium through variational inequalities

100%
Nockowska-Rosiak M.
Applicationes Mathematicae
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2009
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tom 36
|
nr 1
43-58
EN
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.
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