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Complete solution of the integrability problem for homothetic demand functions

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  • José C. R. Alcantud
  • Carlos R. Palmero

Abstract

For any Walrasian demand function, the Strong Axiom implies (and is implied by) rationalizability by a complete preorder. However, these equivalent conditions do not ensure the existence of a continuous utility function or complete preorder giving raise to the primitive demand. We here propose a self‐contained proof of a related fact: if the demand is homothetic and continuous, the Strong Axiom characterizes the existence of a continuous and homogeneous of degree one subjective utility function (or a continuous and homothetic complete preorder) representing the demand. Our contruction depends upon standard tools and overturns the need for ad‐hoc axioms that were used in prior published literature on the topic.

Suggested Citation

  • José C. R. Alcantud & Carlos R. Palmero, 2010. "Complete solution of the integrability problem for homothetic demand functions," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(2), pages 263-271, June.
    • Handle: RePEc:bla:ijethy:v:6:y:2010:i:2:p:263-271
    DOI: 10.1111/j.1742-7363.2010.00134.x
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    References listed on IDEAS

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    1. José Alcantud & Gianni Bosi & Carlos Palmero & Magalì Zuanon, 2006. "Mathematical utility theory and the representability of demand by continuous homogeneous functions," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 5(3), pages 195-205, December.
    2. Liu, Pak-Wai & Wong, Kam-Chau, 2000. "Revealed homothetic preference and technology," Journal of Mathematical Economics, Elsevier, vol. 34(3), pages 287-314, November.
    3. Chipman, John S., 1974. "Homothetic preferences and aggregation," Journal of Economic Theory, Elsevier, vol. 8(1), pages 26-38, May.
    4. C. Rodríguez-Palmero & J.C. R.Alcantud, 2002. "A note on representability of consumer's behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 207-216.
    5. Sondermann, Dieter, 1982. "Revealed Preference: An Elementary Treatment," Econometrica, Econometric Society, vol. 50(3), pages 777-779, May.
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