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The relationship between Mathematical Utility Theory and the Integrability Problem: some arguments in favour

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Author Info
J. C. R. Alcantud (Universidad de Salamanca)
G. Bosi (Università di Trieste)
C. Rodríguez-Palmero (Universidad de Valladolid)
M. Zuanon (Università Cattolica del Sacro Cuore)

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Abstract

The resort to utility-theoretical issues will permit us to propose a constructive procedure for deriving a homogeneous of degree one, continuous function that gives raise to a primitive demand function under suitably mild conditions. This constitutes the first elementary proof of a necessary and sufficient condition for an integrability problem to have a solution by continuous (subjective utility) functions. Such achievement reinforces the relevance of a technique that was succesfully formalized in Alcantud and Rodríguez-Palmero (2001). The analysis of these two works exposes deep relationships between two apparently separate fields: mathematical utility theory and the revealed preference approach to the integrability problem.

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Publisher Info
Paper provided by EconWPA in its series Microeconomics with number 0308002.

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Length: 25 pages
Date of creation: 28 Aug 2003
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Handle: RePEc:wpa:wuwpmi:0308002

Note: Type of Document - Tex; prepared on PC; to print on HP; pages: 25 ; figures: none
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Related research
Keywords: Strong Axiom of Homothetic Revelation; revealed preference; continuous homogeneous of degree one utility; integrability of demand.;

Find related papers by JEL classification:
D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

This paper has been announced in the following NEP Reports:

References listed on IDEAS
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.:
  1. Knoblauch, Vicki, 1993. "Recovering homothetic preferences," Economics Letters, Elsevier, vol. 43(1), pages 41-45. [Downloadable!] (restricted)
  2. Mas-Colell, Andreu, 1978. "On Revealed Preference Analysis," Review of Economic Studies, Blackwell Publishing, vol. 45(1), pages 121-31, February. [Downloadable!] (restricted)
  3. Bosi, Gianni & Candeal, Juan Carlos & Indurain, Esteban, 2000. "Continuous representability of homothetic preferences by means of homogeneous utility functions," Journal of Mathematical Economics, Elsevier, vol. 33(3), pages 291-298, April. [Downloadable!] (restricted)
  4. Shafer, Wayne J, 1977. "Revealed Preference and Aggregation," Econometrica, Econometric Society, vol. 45(5), pages 1173-82, July. [Downloadable!] (restricted)
  5. Liu, Pak-Wai & Wong, Kam-Chau, 2000. "Revealed homothetic preference and technology," Journal of Mathematical Economics, Elsevier, vol. 34(3), pages 287-314, November. [Downloadable!] (restricted)
  6. Fabio Maccheroni, 2001. "Homothetic preferences on star-shaped sets," Decisions in Economics and Finance, Springer, vol. 24(1), pages 41-47. [Downloadable!] (restricted)
  7. Dow, James & da Costa Werlang, Sergio Ribeiro, 1992. "Homothetic preferences," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 389-394. [Downloadable!] (restricted)
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  8. Castagnoli, Erio & Maccheroni, Fabio, 2000. "Restricting independence to convex cones," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 215-223, October. [Downloadable!] (restricted)
  9. Candeal, J. C. & Indurain, E., 1995. "Homothetic and weakly homothetic preferences," Journal of Mathematical Economics, Elsevier, vol. 24(2), pages 147-158. [Downloadable!] (restricted)
  10. Alcantud, J. C. R. & Rodriguez-Palmero, C., 1999. "Characterization of the existence of semicontinuous weak utilities," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 503-509, December. [Downloadable!] (restricted)
  11. Clark, Stephen A, 1988. "An Extension Theorem for Rational Choice Functions," Review of Economic Studies, Blackwell Publishing, vol. 55(3), pages 485-92, July. [Downloadable!] (restricted)
  12. Gianni Bosi, 2002. "Semicontinuous Representability of Homothetic Interval Orders by Means of Two Homogeneous Functionals," Theory and Decision, Springer, vol. 52(4), pages 303-312, June. [Downloadable!] (restricted)
  13. Sondermann, Dieter, 1982. "Revealed Preference: An Elementary Treatment," Econometrica, Econometric Society, vol. 50(3), pages 777-79, May. [Downloadable!] (restricted)
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