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Exact and Useful Optimization Methods for Microeconomics

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  • Balder, Erik

Abstract

This paper points out that the treatment of utility maximization in current textbooks on microeconomic theory is deficient in at least three respects: breadth of coverage, completeness-cum-coherence of solution methods and mathematical correctness. Improvements are suggested in the form of a Kuhn-Tucker type theorem that has been customized for microeconomics. To ensure uniqueness of the optimal solution (if applicable), an apparently new adaptation of the notion of strict quasiconcavity is introduced. The role of the domain of differentiability of the utility function is emphasized. This is not only to repair a widespread error in the microeconomic literature but also to point out that this domain can be chosen sensibly in order to include the maximization of certain nondifferentiable utility functions, such as Leontiev utility functions. To underscore the usefulness of the optimality conditions obtained here, five quite different instances of utility maximization are completely solved by a single coherent method.

Suggested Citation

  • Balder, Erik, 2008. "Exact and Useful Optimization Methods for Microeconomics," MPRA Paper 47080, University Library of Munich, Germany, revised 04 Mar 2011.
    • Handle: RePEc:pra:mprapa:47080
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    File URL: https://mpra.ub.uni-muenchen.de/47080/1/MPRA_paper_47080.pdf
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    References listed on IDEAS

    as
    1. J. P. Crouzeix, 1980. "Conditions for Convexity of Quasiconvex Functions," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 120-125, February.
    2. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    microeconomics; utility maximization; Kuhn-Tucker theorem;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D00 - Microeconomics - - General - - - General

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