IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2212.12623.html
   My bibliography  Save this paper

The Simple Economics of Optimal Bundling

Author

Listed:
  • Frank Yang

Abstract

We study optimal bundling when consumers differ in one dimension. We introduce a partial order on the set of bundles defined by (i) set inclusion and (ii) sales volumes (if sold alone and priced optimally). We show that if the undominated bundles with respect to this partial order are nested, then nested bundling (tiered pricing) is optimal. We characterize which nested menu is optimal: Selling a given menu of nested bundles is optimal if a smaller bundle in (out of) the menu sells more (less) than a bigger bundle in the menu. We present three applications of these insights: the first two connect optimal bundling and quality design to price elasticities and cost structures; the last one establishes a necessary and sufficient condition for costly screening to be optimal when a principal can use both price and nonprice screening instruments.

Suggested Citation

  • Frank Yang, 2022. "The Simple Economics of Optimal Bundling," Papers 2212.12623, arXiv.org, revised Apr 2023.
    • Handle: RePEc:arx:papers:2212.12623
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2212.12623
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Pavlov Gregory, 2011. "Optimal Mechanism for Selling Two Goods," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-35, February.
    2. Constantinos Daskalakis & Alan Deckelbaum & Christos Tzamos, 2017. "Strong Duality for a Multiple‐Good Monopolist," Econometrica, Econometric Society, vol. 85, pages 735-767, May.
    3. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
    4. Justin P. Johnson & David P. Myatt, 2003. "Multiproduct Quality Competition: Fighting Brands and Product Line Pruning," American Economic Review, American Economic Association, vol. 93(3), pages 748-774, June.
    5. Stephen W. Salant, 1989. "When is Inducing Self-Selection Suboptimal for a Monopolist?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 104(2), pages 391-397.
    6. Frank Yang, 2021. "Costly Multidimensional Screening," Papers 2109.00487, arXiv.org, revised Aug 2022.
    7. Manelli, Alejandro M. & Vincent, Daniel R., 2007. "Multidimensional mechanism design: Revenue maximization and the multiple-good monopoly," Journal of Economic Theory, Elsevier, vol. 137(1), pages 153-185, November.
    8. Gabriel Carroll, 2017. "Robustness and Separation in Multidimensional Screening," Econometrica, Econometric Society, vol. 85, pages 453-488, March.
    9. Eric T. Anderson & James D. Dana, Jr., 2009. "When Is Price Discrimination Profitable?," Management Science, INFORMS, vol. 55(6), pages 980-989, June.
    10. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    11. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    12. Nancy L. Stokey, 1979. "Intertemporal Price Discrimination," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 93(3), pages 355-371.
    13. Rochet, Jean-Charles, 1987. "A necessary and sufficient condition for rationalizability in a quasi-linear context," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 191-200, April.
    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. Mark Armstrong, 2016. "Nonlinear Pricing," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 583-614, October.
    2. Bikhchandani, Sushil & Mishra, Debasis, 2022. "Selling two identical objects," Journal of Economic Theory, Elsevier, vol. 200(C).
    3. Schäfers, Sebastian, 2022. "Product Lotteries and Loss Aversion," Working papers 2022/06, Faculty of Business and Economics - University of Basel.
    4. Kazumura, Tomoya & Mishra, Debasis & Serizawa, Shigehiro, 2020. "Strategy-proof multi-object mechanism design: Ex-post revenue maximization with non-quasilinear preferences," Journal of Economic Theory, Elsevier, vol. 188(C).
    5. Veiga, André, 2018. "A note on how to sell a network good," International Journal of Industrial Organization, Elsevier, vol. 59(C), pages 114-126.
    6. Alexey Kushnir & James Michelson, 2022. "Optimal Multi-Dimensional Auctions: Conjectures and Simulations," Papers 2207.01664, arXiv.org.
    7. Joan Calzada & Guillem Ordóñez, 2012. "Competition in the news industry: fighting aggregators with versions and links," Working Papers 12-22, NET Institute.
    8. Debasis Mishra & Kolagani Paramahamsa, 2022. "Selling to a principal and a budget-constrained agent," Discussion Papers 22-02, Indian Statistical Institute, Delhi.
    9. Hart, Sergiu & Nisan, Noam, 2019. "Selling multiple correlated goods: Revenue maximization and menu-size complexity," Journal of Economic Theory, Elsevier, vol. 183(C), pages 991-1029.
    10. Jean‐Charles Rochet & John Thanassoulis, 2019. "Intertemporal price discrimination with two products," RAND Journal of Economics, RAND Corporation, vol. 50(4), pages 951-973, December.
    11. Yeon-Koo Che & Weijie Zhong, 2021. "Robustly Optimal Mechanisms for Selling Multiple Goods," Papers 2105.02828, arXiv.org, revised Aug 2022.
    12. Tóbiás, Áron, 2018. "Non-linear pricing and optimal shipping policies," Games and Economic Behavior, Elsevier, vol. 112(C), pages 194-218.
    13. Sun, Ching-jen, 2007. "Dynamic Price Discrimination and Quality Provision Based on Purchase History," MPRA Paper 9855, University Library of Munich, Germany, revised Aug 2008.
    14. Seung Han Yoo, 2018. "Membership Mechanisms," Discussion Paper Series 1804, Institute of Economic Research, Korea University.
    15. Debasis Mishra & Kolagani Paramahamsa, 2022. "Selling to a principal and a budget-constrained agent," Papers 2202.10378, arXiv.org, revised Jul 2022.
    16. Robert J. McCann & Kelvin Shuangjian Zhang, 2023. "A duality and free boundary approach to adverse selection," Papers 2301.07660, arXiv.org, revised Nov 2023.
    17. Dirk Bergemann & Tibor Heumann & Stephen Morris, 2022. "Screening with Persuasion," Cowles Foundation Discussion Papers 2338, Cowles Foundation for Research in Economics, Yale University.
    18. X. Ruiz del Portal, 2012. "Conditions for incentive compatibility in models with multidimensional allocation functions and one-dimensional types," Review of Economic Design, Springer;Society for Economic Design, vol. 16(4), pages 311-321, December.
    19. Joan Calzada & Tommaso M. Valletti, 2012. "Intertemporal Movie Distribution: Versioning When Customers Can Buy Both Versions," Marketing Science, INFORMS, vol. 31(4), pages 649-667, July.
    20. Tommaso M. Valletti & Stefan Szymanski, 2006. "Parallel Trade, International Exhaustion And Intellectual Property Rights: A Welfare Analysis," Journal of Industrial Economics, Wiley Blackwell, vol. 54(4), pages 499-526, December.

    More about this item

    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:2212.12623. 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.