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A generalization of Rader's utility representation theorem

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  • Bosi, Gianni
  • Zuanon, Magalì

Abstract

Rader's utility representation theorem guarantees the existence of an upper semicontinuous utility function for any upper semicontinuous total preorder on a second countable topological space. In this paper we present a generalization of Rader's theorem to not necessarily total preorders that are weakly upper semicontinuous.

Suggested Citation

  • Bosi, Gianni & Zuanon, Magalì, 2010. "A generalization of Rader's utility representation theorem," MPRA Paper 24314, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:24314
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    File URL: https://mpra.ub.uni-muenchen.de/24314/1/MPRA_paper_24314.pdf
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    References listed on IDEAS

    as
    1. Trout Rader, 1963. "The Existence of a Utility Function to Represent Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 229-232.
    2. Bosi, G. & Mehta, G. B., 2002. "Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 311-328, November.
    3. Romano Isler, 1997. "Semicontinuous utility functions in topological spaces," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 20(1), pages 111-116, June.
    4. Ghanshyam B. Mehta, 1997. "A remark on a utility representation theorem of Rader (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 367-370.
    5. Richter, Marcel K, 1980. "Continuous and Semi-Continuous Utility," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(2), pages 293-299, June.
    6. Alcantud, J. C. R. & Rodriguez-Palmero, C., 1999. "Characterization of the existence of semicontinuous weak utilities," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 503-509, December.
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    More about this item

    Keywords

    Weakly upper semicontinuous preorder; utility function;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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