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Variational Analysis for the Consumer Theory

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  • Jean-Paul Penot

    (Université Pierre et Marie Curie)

Abstract

We look for an interpretation of the demand correspondence in the consumer theory as a generalized derivative of the inverse utility function. We test the main concepts of nonsmooth analysis for such an objective. The proofs only use classical methods in optimization such as penalization and optimality conditions.

Suggested Citation

  • Jean-Paul Penot, 2013. "Variational Analysis for the Consumer Theory," Journal of Optimization Theory and Applications, Springer, vol. 159(3), pages 769-794, December.
    • Handle: RePEc:spr:joptap:v:159:y:2013:i:3:d:10.1007_s10957-013-0289-5
    DOI: 10.1007/s10957-013-0289-5
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    References listed on IDEAS

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    1. Jean-Paul Penot, 2005. "Unilateral Analysis and Duality," Springer Books, in: Charles Audet & Pierre Hansen & Gilles Savard (ed.), Essays and Surveys in Global Optimization, chapter 0, pages 1-37, Springer.
    2. Crouzeix, J. -P., 1983. "Duality between direct and indirect utility functions : Differentiability properties," Journal of Mathematical Economics, Elsevier, vol. 12(2), pages 149-165, October.
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    Cited by:

    1. María D. Fajardo & Margarita M. L. Rodríguez & José Vidal, 2016. "Lagrange Duality for Evenly Convex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 109-128, January.
    2. Vu Thi Huong & Jen-Chih Yao & Nguyen Dong Yen, 2017. "On the Stability and Solution Sensitivity of a Consumer Problem," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 567-589, November.

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