Revealed Preference and the Number of Commodities
This work consists of two parts: First, it is shown that for a two-dimensional commodity space any homothetic utility function that rationalizes each pair of observations in a set of consumption data also rationalizes the entire set of observations. The result is stated as a pairwise version of Varian’s Homothetic Axiom of Revealed Preference and is used to provide a simplified nonparametric test of homotheticity. In the second part a unifying proof technique is presented to show that the Weak Axiom of Revealed Preference (WARP) implies the Strong Axiom of Revealed Preference (SARP) for two commodities yet not for more commodities. It also shows that preference cycles can be of arbitrary length.While these results are already known, the proof here generalizes and unifies the existing ones insofar as it gives necessary and sufficient conditions for preference cycles to exist. It is then shown that in two dimensions the necessary condition cannot be fulfilled, whereas in more than two dimensions the sufficient conditions can always be met. The proof admits an intuitive understanding of the reason by giving a geometric interpretion of preference cycles as paths on indifference surfaces.
|Date of creation:||Dec 2007|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://www.rwi-essen.de/
More information through EDIRC
|Order Information:||Web: http://www.rwi-essen.de/publikationen/|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Peters Hans & Wakker Peter, 1994. "WARP Does Not Imply SARP for More Than Two Commodities," Journal of Economic Theory, Elsevier, vol. 62(1), pages 152-160, February.
- John, Reinhard, 1997. "A Simple Cycle Preserving Extension of a Demand Function," Journal of Economic Theory, Elsevier, vol. 72(2), pages 442-445, February.
- Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
- Samiran Banerjee & James Murphy, 2006. "A simplified test for preference rationality of two-commodity choice," Experimental Economics, Springer, vol. 9(1), pages 67-75, April.
- Kihlstrom, Richard E & Mas-Colell, Andreu & Sonnenschein, Hugo, 1976. "The Demand Theory of the Weak Axiom of Revealed Preference," Econometrica, Econometric Society, vol. 44(5), pages 971-78, September.
- Knoblauch, Vicki, 1992. "A Tight Upper Bound on the Money Metric Utility Function," American Economic Review, American Economic Association, vol. 82(3), pages 660-63, June.
- Shafer, Wayne J., 1977. "Revealed preference cycles and the slutsky matrix," Journal of Economic Theory, Elsevier, vol. 16(2), pages 293-309, December.
- Liu, Pak-Wai & Wong, Kam-Chau, 2000. "Revealed homothetic preference and technology," Journal of Mathematical Economics, Elsevier, vol. 34(3), pages 287-314, November.
When requesting a correction, please mention this item's handle: RePEc:rwi:repape:0036. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sabine Weiler)
If references are entirely missing, you can add them using this form.