Revealed preference in a discrete consumption space
We show that an agent maximizing some utility function on a discrete (as opposed to continuous) consumption space will obey the generalized axiom of revealed preference (GARP) so long as the agent obeys cost efficiency. Cost efficiency will hold if there is some good, outside the set of goods being studied by the modeler, that can be consumed by the agent in continuous quantities. An application of Afriat's Theorem then guarantees that there is a strictly increasing utility function on the discrete consumption space that rationalizes price and demand observations in that space.
|Date of creation:||07 Mar 2012|
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- Herbert E. Scarf & Ana Fostel & Michael J. Todd, 2004.
"Two New Proofs of Afriat's Theorem,"
Yale School of Management Working Papers
ysm377, Yale School of Management.
- Anna Fostel & Herbert E. Scarf & Michael J. Todd, 2003. "Two New Proofs of Afriat's Theorem," Cowles Foundation Discussion Papers 1415, Cowles Foundation for Research in Economics, Yale University.
- M.J. Todd & A. Fostel & H.E. Scarf, 2004. "Two New Proofs of Afriat's Theorem," Econometric Society 2004 North American Summer Meetings 632, Econometric Society.
- Francoise Forges & Enrico Minelli, 2006.
"Afriat’s Theorem for General Budget Sets,"
CESifo Working Paper Series
1703, CESifo Group Munich.
- Donald J. Brown & Caterina Calsamiglia, 2005.
"The Nonparametric Approach to Applied Welfare Analysis,"
Cowles Foundation Discussion Papers
1507, Cowles Foundation for Research in Economics, Yale University.
- Donald Brown & Caterina Calsamiglia, 2007. "The Nonparametric Approach to Applied Welfare Analysis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 183-188, April.
- W. E. Diewert, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Oxford University Press, vol. 40(3), pages 419-425.
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