IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v67y2016icp1-9.html
   My bibliography  Save this article

Logarithmically homogeneous preferences

Author

Listed:
  • Miyake, Mitsunobu

Abstract

An extended-real-valued function on R+n is called logarithmically homogeneous if it is given by the logarithmic transformation of a homogeneous function on R+n. Specifying a consumer’s preference on the consumption set by a difference comparison relation, this paper provides some axioms on the relation under which the full class of utility functions representing the relation are logarithmically homogeneous. It is also shown that all the utility functions are strongly concave and all the indirect utility functions are logarithmically homogeneous. Moreover, the additively separable logarithmic utility functions are derived by strengthening one of the axioms.

Suggested Citation

  • Miyake, Mitsunobu, 2016. "Logarithmically homogeneous preferences," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 1-9.
    • Handle: RePEc:eee:mateco:v:67:y:2016:i:c:p:1-9
    DOI: 10.1016/j.jmateco.2016.08.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406816301021
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2016.08.005?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. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, January.
    2. Dow, James & da Costa Werlang, Sergio Ribeiro, 1992. "Homothetic preferences," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 389-394.
    3. M. Kaneko, 1984. "On interpersonal utility comparisons," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 1(3), pages 165-175, October.
    4. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    5. Trockel, Walter, 1989. "Classification of budget-invariant monotonic preferences," Economics Letters, Elsevier, vol. 30(1), pages 7-10.
    6. Mantel, Rolf R., 1976. "Homothetic preferences and community excess demand functions," Journal of Economic Theory, Elsevier, vol. 12(2), pages 197-201, April.
    7. Bosi, Gianni & Candeal, Juan Carlos & Indurain, Esteban, 2000. "Continuous representability of homothetic preferences by means of homogeneous utility functions," Journal of Mathematical Economics, Elsevier, vol. 33(3), pages 291-298, April.
    8. Qin, Cheng-Zhong & Shubik, Martin, 2015. "A note on uncertainty and perception concerning measurable utility," Economics Letters, Elsevier, vol. 130(C), pages 83-84.
    9. Weymark, John A, 1985. "Money-Metric Utility Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 219-232, February.
    10. Wakker, Peter P. & Zank, Horst, 1999. "A unified derivation of classical subjective expected utility models through cardinal utility," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 1-19, August.
    11. Friedman, James W, 1973. "Concavity of Production Functions and Non-Increasing Returns to Scale," Econometrica, Econometric Society, vol. 41(5), pages 981-984, September.
    12. Candeal, J. C. & Indurain, E., 1995. "Homothetic and weakly homothetic preferences," Journal of Mathematical Economics, Elsevier, vol. 24(2), pages 147-158.
    13. Rader, Trout, 1976. "Equivalence of consumer surplus, the divisia index of output, and Eisenberg's addilog social utility," Journal of Economic Theory, Elsevier, vol. 13(1), pages 58-66, August.
    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. Hosoya, Yuhki, 2022. "An axiom for concavifiable preferences in view of Alt’s theory," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    2. Chen, Yi-Hsuan & Vinogradov, Dmitri V., 2021. "Coins with benefits: On existence, pricing kernel and risk premium of cryptocurrencies," IRTG 1792 Discussion Papers 2021-006, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    3. Yuhki Hosoya, 2021. "An Axiom for Concavifiable Preferences in View of Alt's Theory," Papers 2102.07237, arXiv.org, revised Nov 2021.

    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. Marc Le Menestrel & Bertrand Lemaire, 2004. "Biased quantitative measurement of interval ordered homothetic preferences," Economics Working Papers 789, Department of Economics and Business, Universitat Pompeu Fabra.
    2. J. C. R. Alcantud & G. Bosi & C. Rodríguez-Palmero & M. Zuanon, 2003. "The relationship between Mathematical Utility Theory and the Integrability Problem: some arguments in favour," Microeconomics 0308002, University Library of Munich, Germany.
    3. Bosi, Gianni & Campion, Maria J. & Candeal, Juan C. & Indurain, Esteban & Zuanon, Magali E., 2007. "Isotonies on ordered cones through the concept of a decreasing scale," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 115-127, September.
    4. 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.
    5. Marcus Berliant & Yves Zenou, 2014. "Labor Differentiation and Agglomeration in General Equilibrium," International Regional Science Review, , vol. 37(1), pages 36-65, January.
    6. Heifetz, Aviad & Minelli, Enrico, 2002. "Informational smallness in rational expectations equilibria," Journal of Mathematical Economics, Elsevier, vol. 38(1-2), pages 197-218, September.
    7. Bosi, Gianni & Candeal, Juan Carlos & Indurain, Esteban, 2000. "Continuous representability of homothetic preferences by means of homogeneous utility functions," Journal of Mathematical Economics, Elsevier, vol. 33(3), pages 291-298, April.
    8. Guoqiang Tian, 2016. "On the existence of price equilibrium in economies with excess demand functions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(1), pages 5-16, April.
    9. Claudio Zoli, 2012. "Characterizing Inequality Equivalence Criteria," Working Papers 32/2012, University of Verona, Department of Economics.
    10. repec:dau:papers:123456789/5374 is not listed on IDEAS
    11. Elena L. Mercato & Vincenzo Platino, 2017. "On the regularity of smooth production economies with externalities: competitive equilibrium à la Nash," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 287-307, January.
    12. Gianni Bosi, 2002. "Semicontinuous Representability of Homothetic Interval Orders by Means of Two Homogeneous Functionals," Theory and Decision, Springer, vol. 52(4), pages 303-312, June.
    13. 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.
    14. Andrea Attar & Thomas Mariotti & François Salanié, 2019. "On a class of smooth preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 37-57, May.
    15. Elena L. Mercato & Vincenzo Platino, 2017. "Private ownership economies with externalities and existence of competitive equilibria: a differentiable approach," Journal of Economics, Springer, vol. 121(1), pages 75-98, May.
    16. W D A Bryant, 2009. "General Equilibrium:Theory and Evidence," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6875, August.
    17. Klaus Ritzberger & Frank Milne, 2002. "Strategic pricing of equity issues," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 271-294.
    18. David Perez-Castrillo & David Wettstein, 2004. "An Ordinal Shapley Value for Economic Environments (Revised Version)," UFAE and IAE Working Papers 634.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    19. Berliant, Marcus & Kung, Fan-chin, 2009. "Bifurcations in regional migration dynamics," Regional Science and Urban Economics, Elsevier, vol. 39(6), pages 714-720, November.
    20. Toda, Alexis Akira & Walsh, Kieran James, 2024. "Recent advances on uniqueness of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    21. Lehmann-Waffenschmidt, Marco, 1995. "On the equilibrium price set of a continuous perturbation of exchange economies," Journal of Mathematical Economics, Elsevier, vol. 24(5), pages 497-519.

    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:67:y:2016:i:c:p:1-9. 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.