Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/2394.html
   My bibliography  Save this paper

Dynamic Price Competition with Capacity Constraints

Author

Listed:
  • Jose M. Betancourt

    (Yale University)

  • Ali Horta su

    (University of Chicago)

  • Aniko …ry

    (Carnegie Mellon University)

  • Kevin R. Williams

    (Yale University)

Abstract

We study dynamic price competition between sellers offering differentiated products with limited capacity and a common sales deadline. In every period, firms simultaneously set prices, and a randomly arriving buyer decides whether to purchase a product or leave the market. Given remaining capacities, firms trade off selling today against shifting demand to competitors to obtain future market power. We provide conditions for the existence and uniqueness of pure-strategy Markov perfect equilibria. In the continuous-time limit, prices solve a system of ordinary differential equations. We derive properties of equilibrium dynamics and show that prices increase the most when the product with the lowest remaining capacity sells. Because firms do not fully internalize the social option value of future sales, equilibrium prices can be inefficiently low such that both firms and consumers would benefit if firms could commit to higher prices. We term this new welfare effect the Bertrand scarcity trap.

Suggested Citation

  • Jose M. Betancourt & Ali Horta su & Aniko …ry & Kevin R. Williams, 2024. "Dynamic Price Competition with Capacity Constraints," Cowles Foundation Discussion Papers 2394, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2394
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/2024-07/d2394.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Guillermo Gallego & Garrett van Ryzin, 1994. "Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons," Management Science, INFORMS, vol. 40(8), pages 999-1020, August.
    2. Kalyan Talluri & Garrett van Ryzin, 2004. "Revenue Management Under a General Discrete Choice Model of Consumer Behavior," Management Science, INFORMS, vol. 50(1), pages 15-33, January.
    3. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    4. Gale, Ian L & Holmes, Thomas J, 1993. "Advance-Purchase Discounts and Monopoly Allocation of Capacity," American Economic Review, American Economic Association, vol. 83(1), pages 135-146, March.
    5. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, vol. 56(3), pages 571-599, May.
    6. Kevin R. Williams, 2022. "The Welfare Effects of Dynamic Pricing: Evidence From Airline Markets," Econometrica, Econometric Society, vol. 90(2), pages 831-858, March.
    7. James D. Dana Jr., 1999. "Equilibrium Price Dispersion Under Demand Uncertainty: The Roles of Costly Capacity and Market Structure," RAND Journal of Economics, The RAND Corporation, vol. 30(4), pages 632-660, Winter.
    8. David M. Kreps & Jose A. Scheinkman, 1983. "Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 326-337, Autumn.
    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. Aniko …ry & Ali Horta su & Kevin Williams, 2022. "Dynamic Price Competition: Theory and Evidence from Airline Markets," Cowles Foundation Discussion Papers 2341R1, Cowles Foundation for Research in Economics, Yale University, revised Apr 2023.
    2. Alderighi, Marco & Gaggero, Alberto A. & Piga, Claudio A., 2022. "Hidden prices with fixed inventory: Evidence from the airline industry," Transportation Research Part B: Methodological, Elsevier, vol. 157(C), pages 42-61.
    3. Andrew Sweeting, 2008. "Equilibrium Price Dynamics in Perishable Goods Markets: The Case of Secondary Markets for Major League Baseball Tickets," NBER Working Papers 14505, National Bureau of Economic Research, Inc.
    4. Nicolas De Roos & Gordon Mills & Stephen Whelan, 2010. "Pricing Dynamics in the Australian Airline Market," The Economic Record, The Economic Society of Australia, vol. 86(275), pages 545-562, December.
    5. Kevin R. Williams, 2017. "Dynamic Airline Pricing and Seat Availability," Cowles Foundation Discussion Papers 2103, Cowles Foundation for Research in Economics, Yale University.
    6. Diego Escobari, 2012. "Dynamic Pricing, Advance Sales and Aggregate Demand Learning in Airlines," Journal of Industrial Economics, Wiley Blackwell, vol. 60(4), pages 697-724, December.
    7. Escobari, Diego, 2009. "Systematic peak-load pricing, congestion premia and demand diverting: Empirical evidence," Economics Letters, Elsevier, vol. 103(1), pages 59-61, April.
    8. Andrew Sweeting, 2012. "Dynamic Pricing Behavior in Perishable Goods Markets: Evidence from Secondary Markets for Major League Baseball Tickets," Journal of Political Economy, University of Chicago Press, vol. 120(6), pages 1133-1172.
    9. Li, Michael Z. F., 2001. "Pricing non-storable perishable goods by using a purchase restriction with an application to airline fare pricing," European Journal of Operational Research, Elsevier, vol. 134(3), pages 631-647, November.
    10. Yalç{i}n Akçay & Harihara Prasad Natarajan & Susan H. Xu, 2010. "Joint Dynamic Pricing of Multiple Perishable Products Under Consumer Choice," Management Science, INFORMS, vol. 56(8), pages 1345-1361, August.
    11. Ma, Wenliang & Wang, Qiang & Yang, Hangjun & Zhang, Guoquan & Zhang, Yahua, 2020. "Understanding airline price dispersion in the presence of high-speed rail," Transport Policy, Elsevier, vol. 95(C), pages 93-102.
    12. Belleflamme,Paul & Peitz,Martin, 2015. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9781107687899, January.
    13. Kevin R. Williams, 2017. "The Welfare Effects of Dynamic Pricing: Evidence from Airline Markets," Cowles Foundation Discussion Papers 2103R2, Cowles Foundation for Research in Economics, Yale University, revised Jun 2021.
    14. Yannis Kerkemezos & Bas Karreman, 2020. "On the Benefits of Being Alone: Scheduling Changes, Intensity of Competition and Dynamic Airline Pricing," Tinbergen Institute Discussion Papers 20-042/VII, Tinbergen Institute.
    15. Kevin R. Williams, 2022. "The Welfare Effects of Dynamic Pricing: Evidence From Airline Markets," Econometrica, Econometric Society, vol. 90(2), pages 831-858, March.
    16. Kevin R. Williams, 2017. "Dynamic Airline Pricing and Seat Availability," Cowles Foundation Discussion Papers 2103R, Cowles Foundation for Research in Economics, Yale University, revised May 2020.
    17. Sieg, Gernot & Wessel, Jan, 2022. "I would if I could: Passing through VAT reductions in the german rail industry," Economics of Transportation, Elsevier, vol. 32(C).
    18. Allen, Beth & Thisse, Jacques-Francois, 1992. "Price Equilibria in Pure Strategies for Homogeneous Oligopoly," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 1(1), pages 63-81, Spring.
    19. Roy Chowdhury, Prabal, 2008. "Bertrand-Edgeworth equilibrium with a large number of firms," International Journal of Industrial Organization, Elsevier, vol. 26(3), pages 746-761, May.
    20. Dasci, A. & Karakul, M., 2009. "Two-period dynamic versus fixed-ratio pricing in a capacity constrained duopoly," European Journal of Operational Research, Elsevier, vol. 197(3), pages 945-968, September.

    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:cwl:cwldpp:2394. 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: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    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.