IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v244y2024ics0165176524005214.html
   My bibliography  Save this article

Robust lower bounds on monopoly profit with α-concave demand

Author

Listed:
  • Le, Toan

Abstract

I extend Condorelli’s lower bound on monopoly profit from log-concave demand to a broader class of α-concave demand, with α=0 corresponding to log-concavity and α=1 to concavity. The monopoly profit is at least 1(1+α)1/α of the area under the demand curve. I further derive upper bounds for consumer surplus and deadweight loss relative to monopoly profit and show all three bounds are sharp.

Suggested Citation

  • Le, Toan, 2024. "Robust lower bounds on monopoly profit with α-concave demand," Economics Letters, Elsevier, vol. 244(C).
    • Handle: RePEc:eee:ecolet:v:244:y:2024:i:c:s0165176524005214
    DOI: 10.1016/j.econlet.2024.112037
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165176524005214
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2024.112037?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Bulow, Jeremy & Roberts, John, 1989. "The Simple Economics of Optimal Auctions," Journal of Political Economy, University of Chicago Press, vol. 97(5), pages 1060-1090, October.
    2. Condorelli, Daniele & Szentes, Balázs, 2022. "Surplus sharing in Cournot oligopoly," LSE Research Online Documents on Economics 111890, London School of Economics and Political Science, LSE Library.
    3. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Social Choice: A Mean Voter Theorem," Econometrica, Econometric Society, vol. 59(1), pages 1-23, January.
    4. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April.
    5. Condorelli, Daniele & Szentes, Balázs, 2022. "Surplus sharing in Cournot oligopoly," Theoretical Economics, Econometric Society, vol. 17(3), July.
    6. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    7. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    8. Condorelli, Daniele, 2022. "A lower-bound on monopoly profit for log-concave demand," Economics Letters, Elsevier, vol. 210(C).
    9. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    10. An, Mark Yuying, 1998. "Logconcavity versus Logconvexity: A Complete Characterization," Journal of Economic Theory, Elsevier, vol. 80(2), pages 350-369, June.
    11. Gui, Qingyun & Huang, Yi C., 2022. "On Condorelli inequality for log-concave demand," Economics Letters, Elsevier, vol. 215(C).
    Full references (including those not matched with items on IDEAS)

    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. Christian Ewerhart, 2013. "Regular type distributions in mechanism design and $$\rho $$ -concavity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(3), pages 591-603, August.
    2. Schweizer, Nikolaus & Szech, Nora, 2015. "A quantitative version of Myerson regularity," Working Paper Series in Economics 76, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    3. Madeleine Cule & Richard Samworth & Michael Stewart, 2010. "Maximum likelihood estimation of a multi‐dimensional log‐concave density," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 545-607, November.
    4. William P. Barnett & Daniel A. Levinthal, 2017. "Special Issue Introduction: Evolutionary Logics of Strategy and Organization," Strategy Science, INFORMS, vol. 2(1), pages 1-1, March.
    5. Schweizer, Nikolaus & Szech, Nora, 2015. "The quantitative view of Myerson regularity," Discussion Papers, Research Unit: Economics of Change SP II 2015-307, WZB Berlin Social Science Center.
    6. Simon Cowan, 2007. "The welfare effects of third-degree price discrimination with nonlinear demand functions," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 419-428, June.
    7. Simon Loertscher & Leslie M. Marx, 2022. "To sell public or private goods," Review of Economic Design, Springer;Society for Economic Design, vol. 26(3), pages 385-415, September.
    8. Luyi Yang & Laurens Debo & Varun Gupta, 2017. "Trading Time in a Congested Environment," Management Science, INFORMS, vol. 63(7), pages 2377-2395, July.
    9. Mares, Vlad & Swinkels, Jeroen M., 2014. "On the analysis of asymmetric first price auctions," Journal of Economic Theory, Elsevier, vol. 152(C), pages 1-40.
    10. Schmitz, Patrick W., 2002. "On Monopolistic Licensing Strategies under Asymmetric Information," Journal of Economic Theory, Elsevier, vol. 106(1), pages 177-189, September.
    11. Simon Loertscher & Andras Niedermayer, 2012. "Fee-Setting Mechanisms: On Optimal Pricing by Intermediaries and Indirect Taxation," Department of Economics - Working Papers Series 1162, The University of Melbourne.
    12. Kirkegaard, René & Overgaard, Per Baltzer, "undated". "Buy-Out Prices in Online Auctions: Multi-Unit Demand," Economics Working Papers 2003-4, Department of Economics and Business Economics, Aarhus University.
    13. Bulow, Jeremy & Klemperer, Paul, 1994. "Rational Frenzies and Crashes," Journal of Political Economy, University of Chicago Press, vol. 102(1), pages 1-23, February.
    14. Tetsuro Mizoguchi & Nguyen Van Quyen, 2009. "Amakudari: The Post-Retirement Employment of Elite Bureaucrats in Japan," Keio/Kyoto Joint Global COE Discussion Paper Series 2009-011, Keio/Kyoto Joint Global COE Program.
    15. Sjaak Hurkens & Doh-Shin Jeon & Domenico Menicucci, 2019. "Dominance and Competitive Bundling," American Economic Journal: Microeconomics, American Economic Association, vol. 11(3), pages 1-33, August.
    16. Sun, Wuqin & Wang, Dazhong & Zhang, Yue, 2018. "Optimal profit sharing mechanisms with type-dependent outside options," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 57-66.
    17. Nicolás Figueroa & Vasiliki Skreta, 2011. "Optimal allocation mechanisms with single-dimensional private information," Review of Economic Design, Springer;Society for Economic Design, vol. 15(3), pages 213-243, September.
    18. Mailath, George J. & Nöldeke, Georg, 2006. "Extreme Adverse Selection, Competitive Pricing, and Market Breakdown," Working papers 2006/09, Faculty of Business and Economics - University of Basel.
    19. Martimort, David, 2019. ""When Olson Meets Dahl": From Inefficient Groups Formation to Inefficient Policy-Making," CEPR Discussion Papers 13843, C.E.P.R. Discussion Papers.
    20. Mailath, George J. & Nöldeke, Georg, 2008. "Does competitive pricing cause market breakdown under extreme adverse selection?," Journal of Economic Theory, Elsevier, vol. 140(1), pages 97-125, May.

    More about this item

    Keywords

    ;
    ;

    JEL classification:

    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly

    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:244:y:2024:i:c:s0165176524005214. 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.