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
    File URL: https://libkey.io/10.1016/j.econlet.2017.02.007?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. Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July.
    2. 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.
    3. Lionel McKenzie, 1957. "Demand Theory Without a Utility Index," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 24(3), pages 185-189.
    4. David Gale, 1967. "On Optimal Development in a Multi-Sector Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(1), pages 1-18.
    5. Blackorby, Charles & Donaldson, David, 1988. "Money metric utility: A harmless normalization?," Journal of Economic Theory, Elsevier, vol. 46(1), pages 120-129, October.
    6. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
    7. 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.
    8. 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.
    9. 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.
    10. Debreu, Gerard, 1976. "Least concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 121-129, July.
    11. 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.
    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. Piera Mazzoleni & Elisa Pagani & Federico Perali, 2019. "The curvature properties of social welfare functions," Working Papers 493, ECINEQ, Society for the Study of Economic Inequality.
    2. Piera Mazzoleni & Elisa Pagani & Federico Perali, 2023. "On the Curvature Properties of “Long” Social Welfare Functions," Mathematics, MDPI, vol. 11(7), pages 1-14, March.

    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. 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.
    2. Paolo Giovanni Piacquadio, 2017. "A Fairness Justification of Utilitarianism," Econometrica, Econometric Society, vol. 85, pages 1261-1276, July.
    3. Hosoya, Yuhki, 2022. "An axiom for concavifiable preferences in view of Alt’s theory," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    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. 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.
    6. Abuelhaj, Tareq & Gassmann, Franziska & O'Donoghue, Cathal, 2018. "Price opinion data in subsidized economies: Empirical evidence from Iraq," MERIT Working Papers 2018-033, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    7. 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.
    8. Bosmans, Kristof & Decancq, Koen & Ooghe, Erwin, 2018. "Who's afraid of aggregating money metrics?," Theoretical Economics, Econometric Society, vol. 13(2), May.
    9. Pourya Valizadeh & Travis A Smith, 2020. "How Did The American Recovery and Reinvestment Act Affect the Material Well‐Being of SNAP Participants? A Distributional Approach," Applied Economic Perspectives and Policy, John Wiley & Sons, vol. 42(3), pages 455-476, September.
    10. Alcantud, J. C. R. & Manrique, A., 2001. "Continuous representation by a money-metric function," Mathematical Social Sciences, Elsevier, vol. 41(3), pages 365-373, May.
    11. 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.
    12. Donaldson, David, 1992. "On The Aggregation Of Money Measures Of Well-Being In Applied Welfare Economics," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 17(1), pages 1-12, July.
    13. Christopher Chambers & Takashi Hayashi, 2012. "Money-metric utilitarianism," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 809-831, October.
    14. Yuhki Hosoya, 2021. "An Axiom for Concavifiable Preferences in View of Alt's Theory," Papers 2102.07237, arXiv.org, revised Nov 2021.
    15. Mehta, Ghanshyam B., 1995. "Metric utility functions," Journal of Economic Behavior & Organization, Elsevier, vol. 26(2), pages 289-298, March.
    16. Yulei Luo & William T. Smith & Heng-fu Zou, 2009. "The Spirit of Capitalism and Excess Smoothness," Annals of Economics and Finance, Society for AEF, vol. 10(2), pages 281-301, November.
    17. Kihlstrom, Richard, 2009. "Risk aversion and the elasticity of substitution in general dynamic portfolio theory: Consistent planning by forward looking, expected utility maximizing investors," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 634-663, September.
    18. DECANCQ, Koen & FLEURBAEY, Marc & SCHOKKAERT, Erik, 2014. "Inequality, income, and well-being," LIDAM Discussion Papers CORE 2014018, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    19. Diego Nocetti & William T. Smith, 2011. "Precautionary Saving and Endogenous Labor Supply with and without Intertemporal Expected Utility," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43(7), pages 1475-1504, October.
    20. Blackorby, Charles & Laisney, Francois & Schmachtenberg, Rolf, 1993. "Reference-price-independent welfare prescriptions," Journal of Public Economics, Elsevier, vol. 50(1), pages 63-76, January.

    More about this item

    Keywords

    Money metric; Expenditure function; Least-concave representation;
    All these keywords.

    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.

    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/ecolet .

    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.