IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2301.13827.html
   My bibliography  Save this paper

The Optimality of Constant Mark-Up Pricing

Author

Listed:
  • Dirk Bergemann
  • Tibor Heumann
  • Stephen Morris

Abstract

We consider a nonlinear pricing environment with private information. We provide profit guarantees (and associated mechanisms) that the seller can achieve across all possible distributions of willingness to pay of the buyers. With a constant elasticity cost function, constant markup pricing provides the optimal revenue guarantee across all possible distributions of willingness to pay and the lower bound is attained under a Pareto distribution. We characterize how profits and consumer surplus vary with the distribution of values and show that Pareto distributions are extremal. We also provide a revenue guarantee for general cost functions. We establish equivalent results for optimal procurement policies that support maximal surplus guarantees for the buyer given all possible cost distributions of the sellers.

Suggested Citation

  • Dirk Bergemann & Tibor Heumann & Stephen Morris, 2023. "The Optimality of Constant Mark-Up Pricing," Papers 2301.13827, arXiv.org.
    • Handle: RePEc:arx:papers:2301.13827
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2301.13827
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Andreas Kleiner & Benny Moldovanu & Philipp Strack, 2021. "Extreme Points and Majorization: Economic Applications," Econometrica, Econometric Society, vol. 89(4), pages 1557-1593, July.
    2. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    3. Anne-Katrin Roesler & Balázs Szentes, 2017. "Buyer-Optimal Learning and Monopoly Pricing," American Economic Review, American Economic Association, vol. 107(7), pages 2072-2080, July.
    4. Toikka, Juuso, 2011. "Ironing without control," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2510-2526.
    5. Gabriel Carroll, 2017. "Robustness and Separation in Multidimensional Screening," Econometrica, Econometric Society, vol. 85, pages 453-488, March.
    6. Eric Maskin & John Riley, 1984. "Monopoly with Incomplete Information," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 171-196, Summer.
    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. Dirk Bergemann & Tibor Heumann & Stephen Morris, 2022. "Screening with Persuasion," Cowles Foundation Discussion Papers 2338, Cowles Foundation for Research in Economics, Yale University.
    2. Soheil Ghili & Russ Yoon, 2023. "An Empirical Analysis of Optimal Nonlinear Pricing," Papers 2302.11643, arXiv.org, revised Oct 2023.
    3. Han, Jun & Weber, Thomas A., 2023. "Price discrimination with robust beliefs," European Journal of Operational Research, Elsevier, vol. 306(2), pages 795-809.
    4. Dirk Bergemann & Alessandro Bonatti & Alex Smolin, 2018. "The Design and Price of Information," American Economic Review, American Economic Association, vol. 108(1), pages 1-48, January.
    5. Yang, Kai Hao, 2021. "Efficient demands in a multi-product monopoly," Journal of Economic Theory, Elsevier, vol. 197(C).
    6. Dirk Bergemann & Tibor Heumann & Stephen Morris, 2023. "Cost Based Nonlinear Pricing," Cowles Foundation Discussion Papers 2368, Cowles Foundation for Research in Economics, Yale University.
    7. Julie Holland Mortimer, 2007. "Price Discrimination, Copyright Law, and Technological Innovation: Evidence from the Introduction of DVDs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(3), pages 1307-1350.
    8. Bonatti, Alessandro & Bergemann, Dirk, 2022. "Data, Competition, and Digital Platforms," CEPR Discussion Papers 17544, C.E.P.R. Discussion Papers.
    9. Renato Gomes & Alessandro Pavan, 2013. "Cross-Subsidization and Matching Design," Discussion Papers 1559, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Roesler, Anne-Katrin & Deb, Rahul, 2021. "Multi-Dimensional Screening: Buyer-Optimal Learning and Informational Robustness," CEPR Discussion Papers 16206, C.E.P.R. Discussion Papers.
    11. Smolin, Alex & Ichihashi, Shota, 2022. "Data Collection by an Informed Seller," TSE Working Papers 22-1330, Toulouse School of Economics (TSE).
    12. Dennis L. Gärtner, 2010. "Monopolistic screening under learning by doing," RAND Journal of Economics, RAND Corporation, vol. 41(3), pages 574-597, September.
    13. Attila Ambrus & Emilio Calvano & Markus Reisinger, 2016. "Either or Both Competition: A "Two-Sided" Theory of Advertising with Overlapping Viewerships," American Economic Journal: Microeconomics, American Economic Association, vol. 8(3), pages 189-222, August.
    14. Tian Xia & Richard Sexton, 2010. "Brand or Variety Choices and Periodic Sales as Substitute Instruments for Monopoly Price Discrimination," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 36(4), pages 333-349, June.
    15. Laurence Jacquet & Etienne lehmann & Bruno Van Der Linden, 2012. "Signing distortions in optimal tax or other adverse selection models with random participation," THEMA Working Papers 2012-27, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    16. Ostrizek, Franz & Sartori, Elia, 2023. "Screening while controlling an externality," Games and Economic Behavior, Elsevier, vol. 139(C), pages 26-55.
    17. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2015. "The Limits of Price Discrimination," American Economic Review, American Economic Association, vol. 105(3), pages 921-957, March.
    18. Yao Luo & Isabelle Perrigne & Quang Vuong, 2018. "Structural Analysis of Nonlinear Pricing," Journal of Political Economy, University of Chicago Press, vol. 126(6), pages 2523-2568.
    19. Steven Berry & Alon Eizenberg & Joel Waldfogel, 2016. "Optimal product variety in radio markets," RAND Journal of Economics, RAND Corporation, vol. 47(3), pages 463-497, August.
    20. Stole, Lars A., 2007. "Price Discrimination and Competition," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 34, pages 2221-2299, Elsevier.

    More about this item

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2301.13827. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.