IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v154y2017icp10-12.html
   My bibliography  Save this article

The nonconcavity of money-metric utility: A new formulation and proof

Author

Listed:
  • Ali Khan, M.
  • Schlee, Edward E.

Abstract

We offer a new, succinct proof of the fact that the money metric utility is concave for any preference relation representable by a concave function if and only if the indirect utility is affine in wealth. Our proof exploits the existence of a least concave representation established in Debreu (1976), and brings into salience the observation that the money-metric utility to be itself a least-concave representation of the preferences if it is concave. This observation is apparently new.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ecolet:v:154:y:2017:i:c:p:10-12
    DOI: 10.1016/j.econlet.2017.02.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165176517300526
    Download Restriction: Full text for ScienceDirect subscribers only

    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. David Gale, 1967. "On Optimal Development in a Multi-Sector Economy," Review of Economic Studies, Oxford University Press, vol. 34(1), pages 1-18.
    2. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
    3. Ali Khan, M. & Piazza, Adriana, 2012. "On the Mitra–Wan forestry model: A unified analysis," Journal of Economic Theory, Elsevier, vol. 147(1), pages 230-260.
    4. M. Ali Khan & Edward E. Schlee, 2016. "On Lionel McKenzie's 1957 intrusion into 20th-century demand theory," Canadian Journal of Economics, Canadian Economics Association, vol. 49(2), pages 589-636, May.
    5. 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.
    6. Debreu, Gerard, 1976. "Least concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 121-129, July.
    7. 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.
    8. Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July.
    9. Lionel McKenzie, 1957. "Demand Theory Without a Utility Index," Review of Economic Studies, Oxford University Press, vol. 24(3), pages 185-189.
    10. Blackorby, Charles & Donaldson, David, 1988. "Money metric utility: A harmless normalization?," Journal of Economic Theory, Elsevier, vol. 46(1), pages 120-129, October.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Money metric; Expenditure function; Least-concave representation;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

    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:eee:ecolet:v:154:y:2017:i:c:p:10-12. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/ecolet .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.