IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2404.10931.html
   My bibliography  Save this paper

The Relationship between Consumer Theories with and without Utility Maximization

Author

Listed:
  • Yuhki Hosoya

Abstract

To study the assumption that the utility maximization hypothesis implicitly adds to consumer theory, we consider a mathematical representation of pre-marginal revolution consumer theory based on subjective exchange ratios. We introduce two axioms on subjective exchange ratio, and show that both axioms hold if and only if consumer behavior is consistent with the utility maximization hypothesis. Moreover, we express the process for a consumer to find the transaction stopping point in terms of differential equations, and prove that the conditions for its stability are equal to the two axioms introduced in the above argument. Therefore, the consumer can find his/her transaction stopping point if and only if his/her behavior is consistent with the utility maximization hypothesis. In addition to these results, we discuss equivalence conditions for axioms to evaluate their mathematical strength, and methods for expressing the theory of subjective exchange ratios in terms of binary relations.

Suggested Citation

  • Yuhki Hosoya, 2024. "The Relationship between Consumer Theories with and without Utility Maximization," Papers 2404.10931, arXiv.org.
    • Handle: RePEc:arx:papers:2404.10931
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2404.10931
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Otani, Kiyoshi, 1983. "A characterization of quasi-concave functions," Journal of Economic Theory, Elsevier, vol. 31(1), pages 194-196, October.
    2. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    3. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    4. Hurwicz, Leonid & Richter, Marcel K., 1979. "An integrability condition with applications to utility theory and thermodynamics," Journal of Mathematical Economics, Elsevier, vol. 6(1), pages 7-14, March.
    5. Mas-Colell, Andreu, 1977. "The Recoverability of Consumers' Preferences from Market Demand Behavior," Econometrica, Econometric Society, vol. 45(6), pages 1409-1430, September.
    6. 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.
    7. Hosoya, Yuhki, 2013. "Measuring utility from demand," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 82-96.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Yuhki Hosoya, 2022. "Non-Smooth Integrability Theory," Papers 2203.04770, arXiv.org, revised Mar 2024.
    3. Hosoya, Yuhki, 2017. "The relationship between revealed preference and the Slutsky matrix," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 127-146.
    4. Hosoya, Yuhki, 2013. "Measuring utility from demand," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 82-96.
    5. Gerasímou, Georgios, 2010. "Consumer theory with bounded rational preferences," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 708-714, September.
    6. Biheng, Noé & Bonnisseau, Jean-Marc, 2015. "Regular economies with ambiguity aversion," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 24-36.
    7. 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.
    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. Paul Oslington, 2012. "General Equilibrium: Theory and Evidence," The Economic Record, The Economic Society of Australia, vol. 88(282), pages 446-448, September.
    10. Tallon, Jean-Marc, 1998. "Do sunspots matter when agents are Choquet-expected-utility maximizers?," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 357-368, March.
    11. repec:hal:pseose:halshs-01185486 is not listed on IDEAS
    12. W D A Bryant, 2009. "General Equilibrium:Theory and Evidence," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6875, December.
    13. 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.
    14. Tallon, Jean-Marc, 1998. "Do sunspots matter when agents are Choquet-expected-utility maximizers?," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 357-368, March.
    15. Rigotti, Luca & Shannon, Chris, 2012. "Sharing risk and ambiguity," Journal of Economic Theory, Elsevier, vol. 147(5), pages 2028-2039.
    16. Ralph W. Bailey & Jürgen Eichberger & David Kelsey, 2005. "Ambiguity and Public Good Provision in Large Societies," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 7(5), pages 741-759, December.
    17. Jürgen Eichberger & Simon Grant & David Kelsey, 2012. "When is ambiguity–attitude constant?," Journal of Risk and Uncertainty, Springer, vol. 45(3), pages 239-263, December.
    18. Shi, Yun & Cui, Xiangyu & Zhou, Xunyu, 2020. "Beta and Coskewness Pricing: Perspective from Probability Weighting," SocArXiv 5rqhv, Center for Open Science.
    19. Itzhak Gilboa & Andrew Postlewaite & Larry Samuelson & David Schmeidler, 2019. "What are axiomatizations good for?," Theory and Decision, Springer, vol. 86(3), pages 339-359, May.
    20. R. M. Harstad & R. Selten, 2014. "Bounded-rationality models:tasks to become intellectually competitive," Voprosy Ekonomiki, NP Voprosy Ekonomiki, issue 5.
    21. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2404.10931. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.