Tools
Tools
Rizza, Davide 
ORCID: https://orcid.org/0000-0002-1375-371X
(2015)
Nonstandard utilities for lexicographically decomposable orderings.
Journal of Mathematical Economics, 60.
105–109.
ISSN 0304-4068
Preview |
PDF (Revised paper for JEM)
- Accepted Version
Available under License Creative Commons Attribution Non-commercial No Derivatives. Download (367kB) | Preview |
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 R^n, 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.
| Item Type: | Article |
|---|---|
| Additional Information: | The following creative commons applies to the manuscript: https://creativecommons.org/licenses/by-nc-nd/3.0/ |
| Uncontrolled Keywords: | utility,lexicographic ordering,nonstandard analysis,economics, econometrics and finance(all),mathematics(all) ,/dk/atira/pure/subjectarea/asjc/2000 |
| Faculty \ School: | Faculty of Arts and Humanities > School of Politics, Philosophy, Language and Communication Studies |
| UEA Research Groups: | Faculty of Arts and Humanities > Research Groups > Philosophy |
| Depositing User: | Pure Connector |
| Date Deposited: | 20 Oct 2017 05:02 |
| Last Modified: | 21 Jul 2023 09:38 |
| URI: | https://ueaeprints.uea.ac.uk/id/eprint/65187 |
| DOI: | 10.1016/j.jmateco.2015.06.012 |
Actions (login required)
 |
View Item |