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Strictly monotonic preferences on continuum of goods commodity spaces

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Author Info

  • Hervés-Beloso, C.
  • Monteiro, P.K.

Abstract

We consider a set K of differentiated commodities. A preference relation on the set of consumption plans is strictly monotonic whenever to consume more of at least one commodity is more preferred. It is an easy task to find examples of strictly monotonic preference relations when K is finite or countable. However, it is not easy for spaces like l[infinity]([0,1]), the space of bounded functions on the unit interval. In this note we investigate the roots of this difficulty. We show that strictly monotonic preferences always exist. However, if K is uncountable no such preference on l[infinity](K) is continuous and none of them have a utility representation.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 46 (2010)
Issue (Month): 5 (September)
Pages: 725-727

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Handle: RePEc:eee:mateco:v:46:y:2010:i:5:p:725-727

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Utility representation Strictly monotonic preferences;

References

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  1. 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.
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Cited by:
  1. Enrique Covarrubias, 2011. "The Number of Equilibria of Smooth Infinite Economies," Working Papers 2011-02, Banco de México.
  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.

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