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Revealed Preference Test and Shortest Path Problem; Graph Theoretic Structure of the Rationalizability Test

Author

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  • Kohei Shiozawa

    (Graduate School of Economics, Osaka University)

Abstract

This paper provides substantial relations between revealed preference tests of a data set and shortest path problems of a network (a directed graph with weighted edges) by using a simple and straight- forward graph theoretic argument. It clari es the interpretation of the revealed preference tests, re nes the Afriat inequality, and give us an uni ed perspective of several forms of rationalizability tests and the classical utility representation problem of preferences. Furthermore, I provide several graph theoretic procedures to check rationalizability condition (GARP) which are more effcient than the most frequently used procedure of Varian (1982).

Suggested Citation

  • Kohei Shiozawa, 2015. "Revealed Preference Test and Shortest Path Problem; Graph Theoretic Structure of the Rationalizability Test," Discussion Papers in Economics and Business 15-17, Osaka University, Graduate School of Economics.
    • Handle: RePEc:osk:wpaper:1517
    as

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    References listed on IDEAS

    as
    1. A. Fostel & H. Scarf & M. Todd, 2004. "Two new proofs of Afriat’s theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(1), pages 211-219, July.
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    4. Teo Chung Piaw & Rakesh V. Vohra, 2003. "Afrait's Theorem and Negative Cycles," Discussion Papers 1377, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Donald Brown & Caterina Calsamiglia, 2007. "The Nonparametric Approach to Applied Welfare Analysis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 183-188, April.
    6. Vohra,Rakesh V., 2011. "Mechanism Design," Cambridge Books, Cambridge University Press, number 9780521179461.
    7. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, vol. 59(6), pages 1779-1786, November.
    8. repec:dau:papers:123456789/4099 is not listed on IDEAS
    9. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    10. Vohra,Rakesh V., 2011. "Mechanism Design," Cambridge Books, Cambridge University Press, number 9781107004368.
    11. Kolesnikov, Alexander V. & Kudryavtseva, Olga V. & Nagapetyan, Tigran, 2013. "Remarks on Afriat’s theorem and the Monge–Kantorovich problem," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 501-505.
    12. Francoise Forges & Enrico Minelli, 2009. "Afriat's theorem for generalized budget sets," Post-Print hal-00360726, HAL.
    13. Hal R. Varian, 1983. "Non-parametric Tests of Consumer Behaviour," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 99-110.
    14. Varian, Hal R, 1984. "The Nonparametric Approach to Production Analysis," Econometrica, Econometric Society, vol. 52(3), pages 579-597, May.
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    Cited by:

    1. Kohei Shiozawa, 2015. "Note on goodness-of-fit measures for the revealed preference test: The computational complexity of the minimum cost index," Economics Bulletin, AccessEcon, vol. 35(4), pages 2455-2461.

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    More about this item

    Keywords

    Revealed Preference; Afriat Inequality; Cyclical Consistency; Generalized Axiom of Revealed Preference (GARP); Shortest Path Problem;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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