IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v49y2013i1p82-96.html
   My bibliography  Save this article

Measuring utility from demand

Author

Listed:
  • Hosoya, Yuhki

Abstract

This study presents a new method to calculate a preference relation from a demand function. Our method works well under the weak axiom and can calculate a smooth utility function if the demand function obeys the strong axiom. Further, if the demand function is derived from a customary utility function, our method restores the original preference. Our method provides a complete and rigorous proof of Samuelson’s conjecture. In addition to these results, we guarantee the recoverability: i.e., the uniqueness of the preference relation corresponding to a demand function.

Suggested Citation

  • Hosoya, Yuhki, 2013. "Measuring utility from demand," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 82-96.
    • Handle: RePEc:eee:mateco:v:49:y:2013:i:1:p:82-96
    DOI: 10.1016/j.jmateco.2012.10.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406812000900
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2012.10.001?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Debreu, Gerard, 1976. "Smooth Preferences: A Corrigendum," Econometrica, Econometric Society, vol. 44(4), pages 831-832, July.
    2. John Quah, 2006. "Weak axiomatic demand theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(3), pages 677-699, November.
    3. Mas-Colell, Andreu, 1977. "The Recoverability of Consumers' Preferences from Market Demand Behavior," Econometrica, Econometric Society, vol. 45(6), pages 1409-1430, September.
    4. Otani, Kiyoshi, 1983. "A characterization of quasi-concave functions," Journal of Economic Theory, Elsevier, vol. 31(1), pages 194-196, October.
    5. Hugh Rose, 1958. "Consistency of Preference: The Two-Commodity Case," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 124-125.
    6. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-615, July.
    7. Richter, Marcel K., 1979. "Duality and rationality," Journal of Economic Theory, Elsevier, vol. 20(2), pages 131-181, April.
    8. 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.
    9. Kim, Taesung & Richter, Marcel K., 1986. "Nontransitive-nontotal consumer theory," Journal of Economic Theory, Elsevier, vol. 38(2), pages 324-363, April.
    10. Hurwicz, Leonid & Richter, Marcel K, 1979. "Ville Axioms and Consumer Theory," Econometrica, Econometric Society, vol. 47(3), pages 603-619, May.
    11. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, Decembrie.
    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. Yuhki Hosoya, 2021. "Consumer Optimization and a First-Order PDE with a Non-Smooth System," SN Operations Research Forum, Springer, vol. 2(4), pages 1-36, December.
    2. Yan Yang, 2019. "A New Solution to Market Definition: An Approach Based on Multi-dimensional Substitutability Statistics," Papers 1906.10030, arXiv.org.
    3. Yuhki Hosoya, 2022. "Non-Smooth Integrability Theory," Papers 2203.04770, arXiv.org, revised Mar 2024.
    4. Hosoya, Yuhki, 2017. "The relationship between revealed preference and the Slutsky matrix," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 127-146.
    5. Yuhki Hosoya, 2024. "Non-smooth integrability theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(2), pages 475-520, September.
    6. Yuhki Hosoya, 2024. "The Relationship between Consumer Theories with and without Utility Maximization," Papers 2404.10931, arXiv.org.

    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. Hosoya, Yuhki, 2017. "The relationship between revealed preference and the Slutsky matrix," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 127-146.
    2. Aguiar, Victor H. & Hjertstrand, Per & Serrano, Roberto, 2020. "A Rationalization of the Weak Axiom of Revealed Preference," Working Paper Series 1321, Research Institute of Industrial Economics.
    3. Victor H. Aguiar & Per Hjertstrand & Roberto Serrano, 2020. "Rationalizable Incentives: Interim Implementation of Sets in Rationalizable Strategies," Working Papers 2020-16, Brown University, Department of Economics.
    4. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2018. "Transitivity of preferences: when does it matter?," Theoretical Economics, Econometric Society, vol. 13(3), September.
    5. Andrea Mantovi, 2016. "Smooth preferences, symmetries and expansion vector fields," Journal of Economics, Springer, vol. 119(2), pages 147-169, October.
    6. Jerison, David & Jerison, Michael, 1993. "Approximately Rational Consumer Demand," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 217-241, April.
    7. Victor Aguiar & Roberto Serrano, 2015. "Slutsky Matrix Norms and Revealed Preference Tests of Consumer Behaviour," Working Papers 2015-1, Brown University, Department of Economics.
    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), vol. 45(1), pages 201-225, October.
    9. repec:dau:papers:123456789/5374 is not listed on IDEAS
    10. Freixas, Xavier & Mas-Colell, Andreu, 1987. "Engel Curves Leading to the Weak Axiom in the Aggregate," Econometrica, Econometric Society, vol. 55(3), pages 515-531, May.
    11. Jorge Marques, 2013. "Mathematical Modeling of Consumer's Preferences Using Partial Differential Equations," GEMF Working Papers 2013-15, GEMF, Faculty of Economics, University of Coimbra.
    12. Victor H. Aguiar & Roberto Serrano, 2018. "Cardinal Revealed Preference, Price-Dependent Utility, and Consistent Binary Choice," Working Papers 2018-3, Brown University, Department of Economics.
    13. Krebs, Tom, 2007. "Rational expectations equilibrium and the strategic choice of costly information," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 532-548, June.
    14. Victor H. Aguiar & Roberto Serrano, 2018. "Classifying bounded rationality in limited data sets: a Slutsky matrix approach," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 9(4), pages 389-421, November.
    15. Brighi, Luigi, 2004. "A stronger criterion for the Weak Weak Axiom," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 93-103, February.
    16. Gerasímou, Georgios, 2010. "Consumer theory with bounded rational preferences," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 708-714, September.
    17. Hayashi, Takashi, 2008. "A note on small income effects," Journal of Economic Theory, Elsevier, vol. 139(1), pages 360-379, March.
    18. Sakai, Toyotaka, 2009. "Walrasian social orderings in exchange economies," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 16-22, January.
    19. Perets, Hovav & Shitovitz, Benyamin & Spiegel, Menahem, 2012. "Trading equilibrium in a public good economy with smooth preferences and a mixed measure space of consumers," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 163-169.
    20. Kovács, Máté, 2009. "Kinyilvánított preferencia és racionalitás [Declared preference and rationality]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(6), pages 546-562.
    21. Yuhki Hosoya, 2021. "Consumer Optimization and a First-Order PDE with a Non-Smooth System," SN Operations Research Forum, Springer, vol. 2(4), pages 1-36, December.

    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:eee:mateco:v:49:y:2013:i:1:p:82-96. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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.