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

Author

Listed:
  • 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)

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.

Suggested Citation

  • J. C. R. Alcantud & G. Bosi & C. Rodríguez-Palmero & M. Zuanon, 2003. "The relationship between Mathematical Utility Theory and the Integrability Problem: some arguments in favour," Microeconomics 0308002, EconWPA.
  • 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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    References listed on IDEAS

    as
    1. Dow, James & da Costa Werlang, Sergio Ribeiro, 1992. "Homothetic preferences," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 389-394.
    2. Stephen A. Clark, 1988. "An extension theorem for rational choice functions," Review of Economic Studies, Oxford University Press, vol. 55(3), pages 485-492.
    3. Shafer, Wayne J, 1977. "Revealed Preference and Aggregation," Econometrica, Econometric Society, vol. 45(5), pages 1173-1182, July.
    4. Liu, Pak-Wai & Wong, Kam-Chau, 2000. "Revealed homothetic preference and technology," Journal of Mathematical Economics, Elsevier, vol. 34(3), pages 287-314, November.
    5. 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.
    6. 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.
    7. Fabio Maccheroni, 2001. "Homothetic preferences on star-shaped sets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 24(1), pages 41-47, May.
    8. Knoblauch, Vicki, 1993. "Recovering homothetic preferences," Economics Letters, Elsevier, vol. 43(1), pages 41-45.
    9. 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.
    10. Andreu Mas-Colell, 1978. "On Revealed Preference Analysis," Review of Economic Studies, Oxford University Press, vol. 45(1), pages 121-131.
    11. J.C.R. Alcantud, 1999. "Weak utilities from acyclicity," Theory and Decision, Springer, vol. 47(2), pages 185-196, October.
    12. Castagnoli, Erio & Maccheroni, Fabio, 2000. "Restricting independence to convex cones," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 215-223, October.
    13. Candeal, J. C. & Indurain, E., 1995. "Homothetic and weakly homothetic preferences," Journal of Mathematical Economics, Elsevier, vol. 24(2), pages 147-158.
    14. Sondermann, Dieter, 1982. "Revealed Preference: An Elementary Treatment," Econometrica, Econometric Society, vol. 50(3), pages 777-779, May.
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    More about this item

    Keywords

    Strong Axiom of Homothetic Revelation; revealed preference; continuous homogeneous of degree one utility; integrability of demand.;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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