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On the Study of an Economic Equilibrium with Variational Inequality Arguments

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  • Maria Bernadette Donato

    (University of Messina)

  • Monica Milasi

    (University of Messina)

  • Carmela Vitanza

    (University of Messina)

Abstract

The main purpose of this paper is to investigate on the existence of a competitive equilibrium for a market with consumption and exchange. A variational representation is used to study this problem. More precisely, we consider an economy where utility functions are assumed concave and non-differentiable, and we characterize the equilibrium by means of a variational problem involving the subdifferential multimap. Thanks to this approach, by introducing suitable perturbed utility functions, we achieve an existence result when the operator is not coercive and the convex set might be unbounded.

Suggested Citation

  • Maria Bernadette Donato & Monica Milasi & Carmela Vitanza, 2016. "On the Study of an Economic Equilibrium with Variational Inequality Arguments," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 646-660, February.
    • Handle: RePEc:spr:joptap:v:168:y:2016:i:2:d:10.1007_s10957-014-0697-1
    DOI: 10.1007/s10957-014-0697-1
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    References listed on IDEAS

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    1. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(4), pages 1007-1017, August.
    2. G. Anello & M. Donato & M. Milasi, 2010. "A quasi-variational approach to a competitive economic equilibrium problem without strong monotonicity assumption," Journal of Global Optimization, Springer, vol. 48(2), pages 279-287, October.
    3. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1461-1465, December.
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    6. Alejandro Jofré & R. Terry Rockafellar & Roger J-B. Wets, 2007. "Variational Inequalities and Economic Equilibrium," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 32-50, February.
    7. D. Chan & J. S. Pang, 1982. "The Generalized Quasi-Variational Inequality Problem," Mathematics of Operations Research, INFORMS, vol. 7(2), pages 211-222, May.
    8. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(3), pages 819-821, June.
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    10. G. Idone & A. Maugeri & C. Vitanza, 2003. "Variational Inequalities and the Elastic-Plastic Torsion Problem," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 489-501, June.
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    Cited by:

    1. Maria Bernadette Donato & Monica Milasi & Antonio Villanacci, 2022. "Restricted Participation on Financial Markets: A General Equilibrium Approach Using Variational Inequality Methods," Networks and Spatial Economics, Springer, vol. 22(2), pages 327-359, June.

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