IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v98y2022ics0304406821001464.html
   My bibliography  Save this article

An axiom for concavifiable preferences in view of Alt’s theory

Author

Listed:
  • Hosoya, Yuhki

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

  • Hosoya, Yuhki, 2022. "An axiom for concavifiable preferences in view of Alt’s theory," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    • Handle: RePEc:eee:mateco:v:98:y:2022:i:c:s0304406821001464
    DOI: 10.1016/j.jmateco.2021.102583
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406821001464
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2021.102583?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. Gerasimou, Georgios, 2021. "Simple preference intensity comparisons," Journal of Economic Theory, Elsevier, vol. 192(C).
    2. Mas-Colell, Andreu, 1977. "The Recoverability of Consumers' Preferences from Market Demand Behavior," Econometrica, Econometric Society, vol. 45(6), pages 1409-1430, September.
    3. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
    4. Debreu, Gerard, 1976. "Least concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 121-129, July.
    5. Samuelson, Paul A, 1974. "Complementarity-An Essay on the 40th Anniversary of the Hicks-Allen Revolution in Demand Theory," Journal of Economic Literature, American Economic Association, vol. 12(4), pages 1255-1289, December.
    6. Larry G. Epstein & Jiankang Zhang, 1999. "Least convex capacities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(2), pages 263-286.
    7. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    8. 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.
    9. 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)

    Citations

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


    Cited by:

    1. Yuhki Hosoya, 2023. "Utilitarian Theorems and Equivalence of Utility Theories," Papers 2304.09973, arXiv.org, revised Sep 2023.

    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, 2021. "An Axiom for Concavifiable Preferences in View of Alt's Theory," Papers 2102.07237, arXiv.org, revised Nov 2021.
    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. Susanne Fuchs-Seliger, 2016. "Axiomatic Models of Rational Behavior and Interpretations," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 33(4), pages 385-401, December.
    9. 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.
    10. Louis Eeckhoudt & Elisa Pagani & Eugenio Peluso, 2023. "Multidimensional risk aversion: the cardinal sin," Annals of Operations Research, Springer, vol. 320(1), pages 15-31, January.
    11. 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.
    12. Khorunzhina, Natalia, 2021. "Intratemporal nonseparability between housing and nondurable consumption: Evidence from reinvestment in housing stock," Journal of Monetary Economics, Elsevier, vol. 117(C), pages 658-670.
    13. 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.
    14. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
    15. M. Ali Khan & Edward E. Schlee, 2016. "On Lionel McKenzie's 1957 intrusion into 20th‐century demand theory," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 49(2), pages 589-636, May.
    16. Hayashi, Takashi, 2008. "A note on small income effects," Journal of Economic Theory, Elsevier, vol. 139(1), pages 360-379, March.
    17. 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.
    18. Gregory S. Amacher & Erkki Koskela & Markku Ollikainen, 2002. "Forest Rotations and Stand Interdependency: Ownership Structure and Timing of Decisions," CESifo Working Paper Series 673, CESifo.
    19. Heufer, Jan & Hjertstrand, Per, 2019. "Homothetic preferences revealed," Journal of Economic Behavior & Organization, Elsevier, vol. 157(C), pages 602-614.
    20. Yuhki Hosoya, 2022. "Non-Smooth Integrability Theory," Papers 2203.04770, arXiv.org, revised Mar 2024.

    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:98:y:2022:i:c:s0304406821001464. 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.