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Revealed smooth nontransitive preferences

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  • Hans Keiding

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  • Mich Tvede

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Abstract

In the present paper, we are concerned with the behavioural consequences of consumers having nontransitive preference relations. Data sets consist of finitely many observations of price vectors and consumption bundles. A preference relation rationalizes a data set provided that for every observed consumption bundle, all strictly preferred bundles are more expensive than the observed bundle. Our main result is that data sets can be rationalized by a smooth nontransitive preference relation if and only if prices can normalized such that the law of demand is satisfied. Market data sets consist of finitely many observations of price vectors, lists of individual incomes and aggregate demands. We apply our main result to characterize market data sets consistent with equilibrium behaviour of pure-exchange economies with smooth nontransitive consumers. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Hans Keiding & Mich Tvede, 2013. "Revealed smooth nontransitive preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 463-484, November.
  • Handle: RePEc:spr:joecth:v:54:y:2013:i:3:p:463-484 DOI: 10.1007/s00199-013-0765-z
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    References listed on IDEAS

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    1. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    2. Yves Balasko & Mich Tvede, 2010. "Individual preference rankings compatible with prices, income distributions and total resources," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 497-513.
    3. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, pages 135-145.
    4. Chiappori, Pierre-Andre & Rochet, Jean-Charles, 1987. "Revealed Preferences and Differentiable Demand: Notes and Comments," Econometrica, Econometric Society, vol. 55(3), pages 687-691, May.
    5. John Quah, 2006. "Weak axiomatic demand theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 677-699.
    6. Vadim Cherepanov & Tim Feddersen & Alvaro Sandroni, 2013. "Revealed preferences and aspirations in warm glow theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 501-535.
    7. Brown, Donald J & Matzkin, Rosa L, 1996. "Testable Restrictions on the Equilibrium Manifold," Econometrica, Econometric Society, pages 1249-1262.
    8. Yves Balasko & Mich Tvede, 2010. "General equilibrium without utility functions: how far to go?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 201-225.
    9. John Quah, 2006. "Weak axiomatic demand theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 677-699.
    10. Yves Balasko & Mich Tvede, 2010. "General equilibrium without utility functions: how far to go?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 201-225.
    11. 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 971-978, September.
    12. Shafer, Wayne J, 1974. "The Nontransitive Consumer," Econometrica, Econometric Society, vol. 42(5), pages 913-919, September.
    13. Françoise Forges & Vincent Iehlé, 2013. "Essential data, budget sets and rationalization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 449-461.
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    Cited by:

    1. Alfred Galichon & John Quah, 2013. "Symposium on revealed preference analysis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 419-423, November.

    More about this item

    Keywords

    Law of demand; Revealed preferences; GARP; SARP; SSARP; WARP; D1; D5;

    JEL classification:

    • D1 - Microeconomics - - Household Behavior
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium

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