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On the Arrow-Hahn utility representation method

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  • Gori, Michele
  • Pianigiani, Giulio

Abstract

In this paper we characterize metric spaces used in Beardon's generalization of Arrow-Hahn utility representation method as generalized Peano continua. For continuous preference relations defined on such metric spaces, we further construct an upper semi-continuous utility function which explicitly depends on the distance.

Suggested Citation

  • Gori, Michele & Pianigiani, Giulio, 2010. "On the Arrow-Hahn utility representation method," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 282-287, May.
    • Handle: RePEc:eee:matsoc:v:59:y:2010:i:3:p:282-287
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    References listed on IDEAS

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    1. Jose C. R. Alcantud & Ghanshyam B. Mehta, 2005. "Constructive Utility Functions on Banach spaces," Microeconomics 0502003, University Library of Munich, Germany.
    2. Candeal, Juan C. & Indurain, Esteban & Mehta, Ghanshyam B., 2004. "Utility functions on locally connected spaces," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 701-711, September.
    3. Monteiro, Paulo Klinger, 1987. "Some results on the existence of utility functions on path connected spaces," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 147-156, April.
    4. A. F. Beardon, 1997. "Utility representation of continuous preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 369-372.
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    More about this item

    Keywords

    Preference relation Utility function Convex metric space Generalized Peano continuum;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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