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Afriat and arbitrage

Author

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  • Alan Beggs

    (Oxford University)

Abstract

This paper presents a proof of Afriat’s (Int Econ Rev 8:67–77) theorem on revealed preference by using the idea that a rational consumer should not be vulnerable to arbitrage. The main mathematical tool is the separating hyperplane theorem.

Suggested Citation

  • Alan Beggs, 2021. "Afriat and arbitrage," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 167-176, October.
    • Handle: RePEc:spr:etbull:v:9:y:2021:i:2:d:10.1007_s40505-021-00208-w
    DOI: 10.1007/s40505-021-00208-w
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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. 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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    5. Federico Echenique & Sangmok Lee & Matthew Shum, 2011. "The Money Pump as a Measure of Revealed Preference Violations," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1201-1223.
    6. John Geanakoplos, 2013. "Afriat from MaxMin," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 443-448, November.
    7. 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-Rev.2, Osaka University, Graduate School of Economics, revised Aug 2016.
    8. 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.
    9. Francoise Forges & Enrico Minelli, 2009. "Afriat's theorem for generalized budget sets," Post-Print hal-00360726, HAL.
    10. 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.
    11. LeRoy,Stephen F. & Werner,Jan, 2014. "Principles of Financial Economics," Cambridge Books, Cambridge University Press, number 9781107024120.
    12. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
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    20. Krasa, Stefan & Yannelis, Nicholas C, 1994. "An Elementary Proof of the Knaster-Kuratowski-Mazurkiewicz-Shapley Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 467-471, May.
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    Cited by:

    1. Leandro Nascimento, 2022. "Bounded arbitrage and nearly rational behavior," Papers 2212.02680, arXiv.org, revised Jul 2023.

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    More about this item

    Keywords

    Afriat’s theorem; Revealed preference; Arbitrage; Separating hyperplane theorem;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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