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An ordinal theorem of the maximum

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  • Marek Weretka

    (University of Wisconsin-Madison)

Abstract

This paper extends the notion of equivalent variation, Hicks (Value and capital, 1939) to an abstract decision problem. It also provides a modern, ordinal variant of the maximum theorem, Berge (Topological spaces: including a treatment of multi-valued functions, vector spaces, and convexity, Courier Corporation, Chelmsford, 1963) that formulates the assumptions in terms of underlying preferences and demonstrates the continuity of the classic preference-based welfare indices (i.e., the equivalent and compensating variations) as well as the upper hemicontinuity of the choice correspondence. We apply the theorem to relevant economic problems.

Suggested Citation

  • Marek Weretka, 2023. "An ordinal theorem of the maximum," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 353-373, July.
    • Handle: RePEc:spr:joecth:v:76:y:2023:i:1:d:10.1007_s00199-022-01458-w
    DOI: 10.1007/s00199-022-01458-w
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    References listed on IDEAS

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    1. Ausubel, Lawrence M & Deneckere, Raymond J, 1993. "A Generalized Theorem of the Maximum," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 99-107, January.
    2. Walker, Mark, 1979. "A Generalization of the Maximum Theorem," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(1), pages 267-272, February.
    3. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters, in: Real Analysis with Economic Applications, Princeton University Press.
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