Nonstandard utilities for lexicographically decomposable orderings

Davide Rizza

Journal of Mathematical Economics, 2015, vol. 60, issue C, 105-109

Abstract: Using a basic theorem from mathematical logic, I show that there are field-extensions of R on which a class of orderings that do not admit any real-valued utility functions can be represented by uncountably large families of utility functions. These are the lexicographically decomposable orderings studied in Beardon et al. (2002a). A corollary to this result yields an uncountably large family of very simple utility functions for the lexicographic ordering of the real Cartesian plane. I generalise these results to the lexicographic ordering of Rn, for every n>2, and to lexicographic products of lexicographically decomposable chains. I conclude by showing how almost all of these results may be obtained without any appeal to the Axiom of Choice.

Keywords: Utility; Lexicographic ordering; Nonstandard analysis (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:60:y:2015:i:c:p:105-109

DOI: 10.1016/j.jmateco.2015.06.012

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