IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v49y2013i6p506-508.html
   My bibliography  Save this article

A simple proof of the nonconcavifiability of functions with linear not-all-parallel contour sets

Author

Listed:
  • Reny, Philip J.

Abstract

Consider a real-valued function that, on a convex subset of a real vector space, is continuous on line segments and has convex contour sets. Inspired by a compelling intuitive argument due to Aumann (1975), we provide a simple proof that no strictly increasing transformation of such a function can be concave unless all contour sets are parallel, i.e., unless for every pair of contour sets, either their affine hulls are disjoint or one of their affine hulls contains the other.

Suggested Citation

  • Reny, Philip J., 2013. "A simple proof of the nonconcavifiability of functions with linear not-all-parallel contour sets," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 506-508.
    • Handle: RePEc:eee:mateco:v:49:y:2013:i:6:p:506-508
    DOI: 10.1016/j.jmateco.2013.10.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406813000980
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2013.10.006?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. Aumann, Robert J, 1975. "Values of Markets with a Continuum of Traders," Econometrica, Econometric Society, vol. 43(4), pages 611-646, July.
    2. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
    3. Monteiro, Paulo Klinger, 2010. "A Class of Convex Preferences Without Concave Representation," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 64(1), March.
    4. Simon Grant & Atsushi Kajii & Ben Polak, 2000. "Temporal Resolution of Uncertainty and Recursive Non-Expected Utility Models," Econometrica, Econometric Society, vol. 68(2), pages 425-434, March.
    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. Gonczarowski, Yannai A. & Kominers, Scott Duke & Shorrer, Ran I., 0. "To infinity and beyond: a general framework for scaling economic theories," Theoretical Economics, Econometric Society.

    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. Richter, Marcel K. & Wong, K.-C.Kam-Chau, 2004. "Concave utility on finite sets," Journal of Economic Theory, Elsevier, vol. 115(2), pages 341-357, April.
    2. 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.
    3. John S. Chipman, 2010. "The Utility-Possibility Frontier," Chapters, in: Mark Blaug & Peter Lloyd (ed.), Famous Figures and Diagrams in Economics, chapter 34, Edward Elgar Publishing.
    4. Paolo Giovanni Piacquadio, 2017. "A Fairness Justification of Utilitarianism," Econometrica, Econometric Society, vol. 85, pages 1261-1276, July.
    5. Omer Edhan, 2012. "Payoffs in Nondifferentiable Perfectly Competitive TU Economies," Discussion Paper Series dp629, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    6. de Castro, Luciano I. & Galvao, Antonio F. & Nunes, Daniel da Siva, 0. "Dynamic economics with quantile preferences," Theoretical Economics, Econometric Society.
    7. Athreya, Kartik B., 2014. "Big Ideas in Macroeconomics: A Nontechnical View," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262019736, December.
    8. 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.
    9. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    10. Faruk Gul & Paulo Natenzon & Wolfgang Pesendorfer, 2021. "Random Evolving Lotteries and Intrinsic Preference for Information," Econometrica, Econometric Society, vol. 89(5), pages 2225-2259, September.
    11. Gomez, Juan Camilo, 2006. "Achieving efficiency with manipulative bargainers," Games and Economic Behavior, Elsevier, vol. 57(2), pages 254-263, November.
    12. ,, 2010. "Rationalizable voting," Theoretical Economics, Econometric Society, vol. 5(1), January.
    13. Gabriel Desgranges & Sayantan Ghosal, 2021. "Heterogeneous beliefs and approximately self-fulfilling outcomes," Working Papers 2021_07, Business School - Economics, University of Glasgow.
    14. Louis Makowski & Joseph M. Ostroy, 1990. "The Existence of Perfectly Competitive Equilibrium a la Wicksteed," UCLA Economics Working Papers 606, UCLA Department of Economics.
    15. Fatma Lajeri-Chaherli, 2016. "On The Concavity And Quasiconcavity Properties Of ( Σ , Μ ) Utility Functions," Bulletin of Economic Research, Wiley Blackwell, vol. 68(3), pages 287-296, April.
    16. Jon Eguia, 2013. "On the spatial representation of preference profiles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 103-128, January.
    17. , & ,, 2015. "Hidden actions and preferences for timing of resolution of uncertainty," Theoretical Economics, Econometric Society, vol. 10(2), May.
    18. Ben-Shahar, Danny & Deng, Yongheng & Sulganik, Eyal, 2009. "Property appraisal in high-rises: A cooperative game theory approach," Journal of Housing Economics, Elsevier, vol. 18(1), pages 25-33, March.
    19. Rosenthal, Robert W., 1976. "Lindahl's solution and values for a public-goods example," Journal of Mathematical Economics, Elsevier, vol. 3(1), pages 37-41, March.
    20. Isabel Cairó & Jae W. Sim, 2020. "Market Power, Inequality, and Financial Instability," Finance and Economics Discussion Series 2020-057, Board of Governors of the Federal Reserve System (U.S.).

    More about this item

    Keywords

    Concavifiability;

    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:mateco:v:49:y:2013:i:6:p:506-508. 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.