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On the Arrow-Hahn utility representation method

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  • Michele Gori

    ()
    (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze)

  • Giulio Pianigiani

    ()
    (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze)

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.

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Bibliographic Info

Paper provided by Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa in its series Working Papers - Mathematical Economics with number 2009-03.

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Length: 8 pages
Date of creation: Sep 2009
Date of revision:
Handle: RePEc:flo:wpaper:2009-03

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Keywords: preference relation; utility function; convex metric space; generalized Peano continuum;

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  1. 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.
  2. 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.
  3. Jose C. R. Alcantud & Ghanshyam B. Mehta, 2005. "Constructive Utility Functions on Banach spaces," Microeconomics 0502003, EconWPA.
  4. A. F. Beardon, 1997. "Utility representation of continuous preferences," Economic Theory, Springer, vol. 10(2), pages 369-372.
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