IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v59y2015i1p169-200.html
   My bibliography  Save this article

Revealed preference theory for finite choice sets

Author

Listed:
  • Sam Cosaert
  • Thomas Demuynck

Abstract

The theory of revealed preferences offers an elegant way to test the neoclassical model of utility maximization subject to a linear budget constraint. In many settings, however, the set of available consumption bundles does not take the form of a linear budget set. In this paper, we adjust the theory of revealed preferences to handle situations where the set of feasible bundles is finite. Such situations occur frequently in many real life and experimental settings. We derive the revealed preference conditions for consistency with utility maximization in this finite choice set setting. Interestingly, we find that it is necessary to make a distinction between the cases where the underlying utility function is weakly monotone, strongly monotone and/or concave. Next, we provide conditions on the structure of the finite choice sets for which the usual revealed preference condition (i.e. GARP) is still valid. We illustrate the relevance of our results by means of an illustration based on two experimental data sets that contain choice behaviour from children and young adults. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Sam Cosaert & Thomas Demuynck, 2015. "Revealed preference theory for finite choice sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 169-200, May.
    • Handle: RePEc:spr:joecth:v:59:y:2015:i:1:p:169-200
    DOI: 10.1007/s00199-014-0813-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00199-014-0813-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00199-014-0813-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. List John A. & Millimet Daniel L, 2008. "The Market: Catalyst for Rationality and Filter of Irrationality," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 8(1), pages 1-55, November.
    2. Syngjoo Choi & Shachar Kariv & Wieland M?ller & Dan Silverman, 2014. "Who Is (More) Rational?," American Economic Review, American Economic Association, vol. 104(6), pages 1518-1550, June.
    3. Laura Blow & Martin Browning & Ian Crawford, 2008. "Revealed Preference Analysis of Characteristics Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(2), pages 371-389.
    4. Sam Cosaert & Thomas Demuynck, 2015. "Revealed preference theory for finite choice sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 169-200, May.
    5. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    6. 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.
    7. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2011. "Testable implications of general equilibrium models: An integer programming approach," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 564-575.
    8. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
    9. Fisman, Raymond J & Kariv, Shachar & Markovits, Daniel, 2005. "Individual Preferences for Giving," Department of Economics, Working Paper Series qt3h7672sq, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    10. Philippe Février & Michael Visser, 2004. "A Study of Consumer Behavior Using Laboratory Data," Experimental Economics, Springer;Economic Science Association, vol. 7(1), pages 93-114, February.
    11. Douglas M. Gale & Shachar Kariv & Syngjoo Choi & Raymond Fisman, 2007. "Revealing Preferences Graphically: An Old Method Gets a New Tool Kit," American Economic Review, American Economic Association, vol. 97(2), pages 153-158, May.
    12. Laurens Cherchye & Thomas Demuynck & Bram De Rock, 2013. "Nash‐Bargained Consumption Decisions: A Revealed Preference Analysis," Economic Journal, Royal Economic Society, vol. 123, pages 195-235, March.
    13. Hoderlein, Stefan, 2011. "How many consumers are rational?," Journal of Econometrics, Elsevier, vol. 164(2), pages 294-309, October.
    14. Sabrina Bruyneel & Laurens Cherchye & Sam Cosaert & Bram De Rock & Siegfried Dewitte, 2012. "Are the Smart Kids More Rational ?," Working Papers ECARES ECARES 2012-050, ULB -- Universite Libre de Bruxelles.
    15. Varian, Hal R., 1990. "Goodness-of-fit in optimizing models," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 125-140.
    16. Richard Blundell & Joel L. Horowitz & Matthias Parey, 2013. "Nonparametric estimation of a heterogeneous demand function under the Slutsky inequality restriction," CeMMAP working papers CWP54/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    17. Laurens Cherchye & Bram De Rock & Vincenzo Platino, 2013. "Private versus public consumption within groups: testing the nature of goods from aggregate data," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 485-500, November.
    18. Raymond Fisman & Shachar Kariv & Daniel Markovits, 2007. "Individual Preferences for Giving," American Economic Review, American Economic Association, vol. 97(5), pages 1858-1876, December.
    19. Yatchew, Adonis John, 1985. "A note on non-parametric tests of consumer behaviour," Economics Letters, Elsevier, vol. 18(1), pages 45-48.
    20. Daniel Burghart & Paul Glimcher & Stephanie Lazzaro, 2013. "An expected utility maximizer walks into a bar..," Journal of Risk and Uncertainty, Springer, vol. 46(3), pages 215-246, June.
    21. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2014. "Revealed preference analysis for convex rationalizations on nonlinear budget sets," Journal of Economic Theory, Elsevier, vol. 152(C), pages 224-236.
    22. Cox, James C, 1997. "On Testing the Utility Hypothesis," Economic Journal, Royal Economic Society, vol. 107(443), pages 1054-1078, July.
    23. 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.
    24. William T. Harbaugh & Kate Krause & Timothy R. Berry, 2001. "GARP for Kids: On the Development of Rational Choice Behavior," American Economic Review, American Economic Association, vol. 91(5), pages 1539-1545, December.
    25. Richard W. Blundell & Martin Browning & Ian A. Crawford, 2003. "Nonparametric Engel Curves and Revealed Preference," Econometrica, Econometric Society, vol. 71(1), pages 205-240, January.
    26. Mattei, Aurelio, 2000. "Full-scale real tests of consumer behavior using experimental data," Journal of Economic Behavior & Organization, Elsevier, vol. 43(4), pages 487-497, December.
    27. Syngjoo Choi & Shachar Kariv & Wieland M?ller & Dan Silverman, 2014. "Who Is (More) Rational?," American Economic Review, American Economic Association, vol. 104(6), pages 1518-1550, June.
    28. Blundell, Richard & Kristensen, Dennis & Matzkin, Rosa, 2014. "Bounding quantile demand functions using revealed preference inequalities," Journal of Econometrics, Elsevier, vol. 179(2), pages 112-127.
    29. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2011. "Testable implications of general equilibrium models: An integer programming approach," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 564-575.
    30. Echenique, Federico & Ivanov, Lozan, 2011. "Implications of Pareto efficiency for two-agent (household) choice," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 129-136, March.
    31. Francoise Forges & Enrico Minelli, 2009. "Afriat's theorem for generalized budget sets," Post-Print hal-00360726, HAL.
    32. Richard Blundell & Martin Browning & Ian Crawford, 2008. "Best Nonparametric Bounds on Demand Responses," Econometrica, Econometric Society, vol. 76(6), pages 1227-1262, November.
    33. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, September.
    34. Matthew Polisson & John K.-H. Quah, 2013. "Revealed Preference in a Discrete Consumption Space," American Economic Journal: Microeconomics, American Economic Association, vol. 5(1), pages 28-34, February.
    35. 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.
    36. Stefan Hoderlein & Jörg Stoye, 2014. "Revealed Preferences in a Heterogeneous Population," The Review of Economics and Statistics, MIT Press, vol. 96(2), pages 197-213, May.
    37. repec:feb:framed:0070 is not listed on IDEAS
    38. Selten, Reinhard, 1991. "Properties of a measure of predictive success," Mathematical Social Sciences, Elsevier, vol. 21(2), pages 153-167, April.
    39. Timothy K. M. Beatty & Ian A. Crawford, 2011. "How Demanding Is the Revealed Preference Approach to Demand?," American Economic Review, American Economic Association, vol. 101(6), pages 2782-2795, October.
    40. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    41. Forges, Françoise & Iehlé, Vincent, 2014. "Afriat’s theorem for indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 1-6.
    42. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, vol. 59(6), pages 1779-1786, November.
    43. Françoise Forges & Vincent Iehlé, 2013. "Essential data, budget sets and rationalization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 449-461, November.
    44. repec:dau:papers:123456789/9256 is not listed on IDEAS
    45. repec:dau:papers:123456789/4099 is not listed on IDEAS
    46. James Andreoni & John Miller, 2002. "Giving According to GARP: An Experimental Test of the Consistency of Preferences for Altruism," Econometrica, Econometric Society, vol. 70(2), pages 737-753, March.
    47. Sabrina Bruyneel & Laurens Cherchye & Bram De Rock, 2012. "Collective consumption models with restricted bargaining weights: an empirical assessment based on experimental data," Review of Economics of the Household, Springer, vol. 10(3), pages 395-421, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Polisson, Matthew & Renou, Ludovic, 2016. "Afriat’s Theorem and Samuelson’s ‘Eternal Darkness’," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 36-40.
    2. Grégory Jolivet & Hélène Turon, 2019. "Consumer Search Costs and Preferences on the Internet," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(3), pages 1258-1300.
    3. Forges, Françoise & Iehlé, Vincent, 2014. "Afriat’s theorem for indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 1-6.
    4. Sabrina Bruyneel & Laurens Cherchye & Sam Cosaert & Bram De Rock & Siegfried Dewitte, 2020. "Verbal Aptitude Hurts Children’s Economic Decision Making Accuracy," Working Papers ECARES 2020-22, ULB -- Universite Libre de Bruxelles.
    5. Smeulders, Bart & Crama, Yves & Spieksma, Frits C.R., 2019. "Revealed preference theory: An algorithmic outlook," European Journal of Operational Research, Elsevier, vol. 272(3), pages 803-815.
    6. Anastasia Burkovskaya, 2022. "A model of state aggregation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(1), pages 121-149, February.
    7. Sam Cosaert & Thomas Demuynck, 2015. "Revealed preference theory for finite choice sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 169-200, May.
    8. Sam Cosaert & Veerle Hennebel, 2023. "Parental Childcare with Process Benefits," Economica, London School of Economics and Political Science, vol. 90(357), pages 339-371, January.
    9. Demuynck, Thomas & Hjertstrand, Per, 2019. "Samuelson's Approach to Revealed Preference Theory: Some Recent Advances," Working Paper Series 1274, Research Institute of Industrial Economics.
    10. repec:hal:wpaper:halshs-00870052 is not listed on IDEAS
    11. John Quah & Hiroki Nishimura & Efe A. Ok, 2013. "A Unified Approach to Revealed Preference Theory: The Case of Rational Choice," Economics Series Working Papers 686, University of Oxford, Department of Economics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ian Crawford & Bram De Rock, 2014. "Empirical Revealed Preference," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 503-524, August.
    2. Demuynck, Thomas & Hjertstrand, Per, 2019. "Samuelson's Approach to Revealed Preference Theory: Some Recent Advances," Working Paper Series 1274, Research Institute of Industrial Economics.
    3. Laurens Cherchye & Thomas Demuynck & Bram De Rock, 2013. "Nash‐Bargained Consumption Decisions: A Revealed Preference Analysis," Economic Journal, Royal Economic Society, vol. 123, pages 195-235, March.
    4. Yoram Halevy & Dotan Persitz & Lanny Zrill, 2018. "Parametric Recoverability of Preferences," Journal of Political Economy, University of Chicago Press, vol. 126(4), pages 1558-1593.
    5. Matej Opatrny, 2018. "Extent of Irrationality of the Consumer: Combining the Critical Cost Eciency and Houtman Maks Indices," Working Papers IES 2018/11, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Apr 2018.
    6. Pawe{l} Dziewulski & Joshua Lanier & John K. -H. Quah, 2024. "Revealed preference and revealed preference cycles: a survey," Papers 2405.08459, arXiv.org.
    7. Heufer, Jan, 2014. "Nonparametric comparative revealed risk aversion," Journal of Economic Theory, Elsevier, vol. 153(C), pages 569-616.
    8. Jim Engle-Warnick & Natalia Mishagina, 2014. "Insensitivity to Prices in a Dictator Game," CIRANO Working Papers 2014s-19, CIRANO.
    9. Brocas, Isabelle & Carrillo, Juan D. & Combs, T. Dalton & Kodaverdian, Niree, 2019. "Consistency in simple vs. complex choices by younger and older adults," Journal of Economic Behavior & Organization, Elsevier, vol. 157(C), pages 580-601.
    10. Dziewulski, Paweł, 2020. "Just-noticeable difference as a behavioural foundation of the critical cost-efficiency index," Journal of Economic Theory, Elsevier, vol. 188(C).
    11. Smeulders, Bart & Crama, Yves & Spieksma, Frits C.R., 2019. "Revealed preference theory: An algorithmic outlook," European Journal of Operational Research, Elsevier, vol. 272(3), pages 803-815.
    12. Pawel Dziewulski, 2018. "Just-noticeable difference as a behavioural foundation of the critical cost-efficiency," Economics Series Working Papers 848, University of Oxford, Department of Economics.
    13. Wang, Jian & Iversen, Tor & Hennig-Schmidt, Heike & Godager, Geir, 2020. "Are patient-regarding preferences stable? Evidence from a laboratory experiment with physicians and medical students from different countries," European Economic Review, Elsevier, vol. 125(C).
    14. Mark Dean & Daniel Martin, 2011. "Testing for Rationality with Consumption Data: Demographics and Heterogeneity," Working Papers 2011-11, Brown University, Department of Economics.
    15. Thomas Demuynck & John Rehbeck, 2023. "Computing revealed preference goodness-of-fit measures with integer programming," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(4), pages 1175-1195, November.
    16. van Bruggen, Paul & Heufer, Jan, 2017. "Afriat in the lab," Journal of Economic Theory, Elsevier, vol. 169(C), pages 546-550.
    17. Heufer, Jan & Hjertstrand, Per, 2019. "Homothetic preferences revealed," Journal of Economic Behavior & Organization, Elsevier, vol. 157(C), pages 602-614.
    18. Eileen Tipoe & Abi Adams & Ian Crawford, 2022. "Revealed preference analysis and bounded rationality [Consume now or later? Time inconsistency, collective choice and revealed preference]," Oxford Economic Papers, Oxford University Press, vol. 74(2), pages 313-332.
    19. 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.
    20. Aluma Dembo & Shachar Kariv & Matthew Polisson & John Quah, 2021. "Ever since Allais," IFS Working Papers W21/15, Institute for Fiscal Studies.

    More about this item

    Keywords

    Revealed preferences; Finite choice sets; Experimental economics; C18; C91; D11; D12;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:59:y:2015:i:1:p:169-200. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.