Proper preferences and quasi-concave utility functions

  • Richard S
  • Zame W
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It is shown that preferences which are continuous, convex and uniformly proper [Mas-Colell (1983)] on the positive cone of a Banach lattice can be represented by a quasi-concave utility function which is defined on a larger domain with non-empty interior. This utility function may be chosen to be either upper or lower semi-continuous on its domain, and continuous at each point of the positive cone. Conversely, any preference relation on the positive cone which is monotone and arises from such a utility function is shown to satisfy a condition which is slightly weaker than uniform properness but which (in the presence of appropriate compactness assumptions) is sufficient to establish the existence of quasi-equilibria. An example is presented to illuminate the role played by the uniformity requirement. © 1986.

Author-supplied keywords

  • Banach lattices
  • competitive equilibrium
  • uniformly proper preferences
  • utility functions

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  • Scott F. Richard

  • William R. Zame

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