IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2102.07237.html
   My bibliography  Save this paper

An Axiom for Concavifiable Preferences in View of Alt's Theory

Author

Listed:
  • Yuhki Hosoya

Abstract

We present a necessary and sufficient condition for Alt's system to be represented by a continuous utility function. Moreover, we present a necessary and sufficient condition for this utility function to be concave. The latter condition can be seen as an extension of Gossen's first law, and thus has an economic interpretation. Together with the above results, we provide a necessary and sufficient condition for Alt's utility to be continuously differentiable.

Suggested Citation

  • Yuhki Hosoya, 2021. "An Axiom for Concavifiable Preferences in View of Alt's Theory," Papers 2102.07237, arXiv.org, revised Nov 2021.
    • Handle: RePEc:arx:papers:2102.07237
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2102.07237
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mas-Colell, Andreu, 1977. "The Recoverability of Consumers' Preferences from Market Demand Behavior," Econometrica, Econometric Society, vol. 45(6), pages 1409-1430, September.
    2. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    3. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
    4. Kannai, Yakar, 1980. "The ALEP definition of complementarity and least concave utility functions," Journal of Economic Theory, Elsevier, vol. 22(1), pages 115-117, February.
    5. Debreu, Gerard, 1976. "Least concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 121-129, July.
    6. Miyake, Mitsunobu, 2016. "Logarithmically homogeneous preferences," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 1-9.
    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. Hosoya, Yuhki, 2022. "An axiom for concavifiable preferences in view of Alt’s theory," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    2. Ali Khan, M. & Schlee, Edward E., 2017. "The nonconcavity of money-metric utility: A new formulation and proof," Economics Letters, Elsevier, vol. 154(C), pages 10-12.
    3. Edward E. Schlee & M. Ali Khan, 2022. "Money Metrics In Applied Welfare Analysis: A Saddlepoint Rehabilitation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 189-210, February.
    4. Apartsin, Yevgenia & Kannai, Yakar, 2006. "Demand properties of concavifiable preferences," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 36-55, December.
    5. Hosoya, Yuhki, 2011. "An existence result and a characterization of the least concave utility of quasi-linear preferences," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 251-252, March.
    6. Paolo Giovanni Piacquadio, 2017. "A Fairness Justification of Utilitarianism," Econometrica, Econometric Society, vol. 85, pages 1261-1276, July.
    7. John K.-H. Quah, 2000. "The Monotonicity of Individual and Market Demand," Econometrica, Econometric Society, vol. 68(4), pages 911-930, July.
    8. Bilancini, Ennio & Boncinelli, Leonardo, 2010. "Single-valuedness of the demand correspondence and strict convexity of preferences: An equivalence result," Economics Letters, Elsevier, vol. 108(3), pages 299-302, September.
    9. Yakar Kannai & Larry Selden, 2014. "Violation of the Law of Demand," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(1), pages 1-28, January.
    10. John Chipman, 2006. "Pareto and contemporary economic theory," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 53(4), pages 451-475, December.
    11. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
    12. Hayashi, Takashi, 2008. "A note on small income effects," Journal of Economic Theory, Elsevier, vol. 139(1), pages 360-379, March.
    13. Christopher Connell & Eric Rasmusen, 2012. "Concavifying the Quasiconcave," Working Papers 2012-10, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy.
    14. Yuhki Hosoya, 2022. "Non-Smooth Integrability Theory," Papers 2203.04770, arXiv.org, revised Mar 2024.
    15. Hosoya, Yuhki, 2013. "Measuring utility from demand," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 82-96.
    16. Cherchye, Laurens & De Rock, Bram & Vermeulen, Frederic, 2010. "An Afriat Theorem for the collective model of household consumption," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1142-1163, May.
    17. Hosoya, Yuhki, 2020. "Recoverability revisited," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 31-41.
    18. Charles-Cadogan, G., 2018. "Losses loom larger than gains and reference dependent preferences in Bernoulli’s utility function," Journal of Economic Behavior & Organization, Elsevier, vol. 154(C), pages 220-237.
    19. Bosmans, Kristof & Decancq, Koen & Ooghe, Erwin, 2015. "What do normative indices of multidimensional inequality really measure?," Journal of Public Economics, Elsevier, vol. 130(C), pages 94-104.
    20. Kannai, Yakar & Selden, Larry & Kang, Minwook & Wei, Xiao, 2016. "Risk neutrality regions," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 75-89.

    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:2102.07237. 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.