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Existence, continuity and utility representation of strictly monotonic preferences on continuum of goods commodity spaces

Author

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  • Hervés-Beloso, Carlos
  • Monteiro, Paulo Klinger

Abstract

It is an easy task for most commodity spaces, to find examples of strictly monotonic preference relations. For example, in the space of bounded sequences of real numbers.. However, it is not easy for spaces like the space of bounded functions defined in the real interval [0, 1]. In this note we investigate the roots of this difficulty. We show that strictly monotonic preferences on the space of bounded function on any set K always exist. However, if K is uncountable no such preference is continuous and none of them have a utility representation.

Suggested Citation

  • Hervés-Beloso, Carlos & Monteiro, Paulo Klinger, 2009. "Existence, continuity and utility representation of strictly monotonic preferences on continuum of goods commodity spaces," MPRA Paper 15157, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:15157
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    File URL: https://mpra.ub.uni-muenchen.de/15157/1/MPRA_paper_15157.pdf
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    References listed on IDEAS

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    1. Toranzo, Margarita Estevez & Beloso, Carlos Herves, 1995. "On the existence of continuous preference orderings without utility representations," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 305-309.
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    Cited by:

    1. Covarrubias, Enrique, 2013. "The number of equilibria of smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 263-265.
    2. Covarrubias, Enrique, 2011. "The equilibrium set of economies with a continuous consumption space," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 137-142, March.
    3. Covarrubias Enrique, 2010. "Regular Infinite Economies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-21, July.

    More about this item

    Keywords

    utility representation/ strictly monotonic preferences;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • B50 - Schools of Economic Thought and Methodology - - Current Heterodox Approaches - - - General

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