IDEAS home Printed from https://ideas.repec.org/p/tin/wpaper/20120113.html
   My bibliography  Save this paper

Capacity Choice under Uncertainty with Product Differentiation

Author

Listed:
  • Christiaan Behrens

    (VU University Amsterdam)

  • Mark Lijesen

    (VU University Amsterdam)

Abstract

We explore the characteristics of a capacity-then-price game for a duopoly market with product differentiation and stochastic demand. The analysis shows that a minimum threshold value for the level of vertical product differentiation exists, relative to horizontal product differentiation, for which existence of a Nash equilibrium in pure strategies is guaranteed. We find that when the quality and cost differences between the firms exactly offset each other, demand uncertainty causes equilibrium outcomes in capacities to become asymmetric. Without demand uncertainty, only a symmetric equilibrium can be established. This difference between stochastic and deterministic demand is the main driver behind our finding that if the regulator ignores the stochastic nature of demand, regulation lowers welfare for a large range of parameters, that is for approximately 10 per cent of the plausible parameter space.

Suggested Citation

  • Christiaan Behrens & Mark Lijesen, 2012. "Capacity Choice under Uncertainty with Product Differentiation," Tinbergen Institute Discussion Papers 12-113/VIII, Tinbergen Institute, revised 20 Feb 2014.
    • Handle: RePEc:tin:wpaper:20120113
    as

    Download full text from publisher

    File URL: https://papers.tinbergen.nl/12113.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Reynolds, Stanley S. & Wilson, Bart J., 2000. "Bertrand-Edgeworth Competition, Demand Uncertainty, and Asymmetric Outcomes," Journal of Economic Theory, Elsevier, vol. 92(1), pages 122-141, May.
    2. Stephen Martin, 1999. "Kreps And Scheinkman With Product Differentiation: An Expository Note," CIE Discussion Papers 1999-11, University of Copenhagen. Department of Economics. Centre for Industrial Economics.
    3. Yin, Xiangkang & Ng, Yew-Kwang, 1997. "Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes: A Case with Product Differentiation," Australian Economic Papers, Wiley Blackwell, vol. 36(68), pages 14-22, June.
    4. Jean J. Gabszewicz & Sougata Poddar, 1997. "Demand fluctuations and capacity utilization under duopoly," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 131-146.
    5. Lepore, Jason J., 2012. "Cournot outcomes under Bertrand–Edgeworth competition with demand uncertainty," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 177-186.
    6. de Frutos, María-Ángeles & Fabra, Natalia, 2011. "Endogenous capacities and price competition: The role of demand uncertainty," International Journal of Industrial Organization, Elsevier, vol. 29(4), pages 399-411, July.
    7. Osborne, Martin J. & Pitchik, Carolyn, 1986. "Price competition in a capacity-constrained duopoly," Journal of Economic Theory, Elsevier, vol. 38(2), pages 238-260, April.
    8. Jean-Pascal Benassy, 1989. "Market Size and Substitutability in Imperfect Competition: A Bertrand-Edgeworth-Chamberlin Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(2), pages 217-234.
    9. Gal-Or, Esther, 1984. "Price Dispersion with Uncertain Demand," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(2), pages 441-457, June.
    10. Hviid, Morten, 1991. "Capacity constrained duopolies, uncertain demand and non-existence of pure strategy equilibria," European Journal of Political Economy, Elsevier, vol. 7(2), pages 183-190, July.
    11. Acemoglu, Daron & Bimpikis, Kostas & Ozdaglar, Asuman, 2009. "Price and capacity competition," Games and Economic Behavior, Elsevier, vol. 66(1), pages 1-26, May.
    12. Young David, 2010. "Endogenous Investment and Pricing under Uncertainty," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-29, January.
    13. Schulz, Norbert, 1999. "Capacity constrained price competition and entry deterrence in heterogeneous product markets," W.E.P. - Würzburg Economic Papers 7, University of Würzburg, Department of Economics.
    14. 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. de Frutos, María-Ángeles & Fabra, Natalia, 2011. "Endogenous capacities and price competition: The role of demand uncertainty," International Journal of Industrial Organization, Elsevier, vol. 29(4), pages 399-411, July.
    2. Attila Tasnádi, 2016. "Endogenous timing of moves in Bertrand–Edgeworth triopolies," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(4), pages 317-334, December.
    3. James D. Dana Jr. & Kevin R. Williams, 2018. "This paper develops an oligopoly model in which firms first choose capacity and then compete in prices in a series of advance-purchase markets. We show the existence of multiple sales opportunities cr," Cowles Foundation Discussion Papers 2136R4, Cowles Foundation for Research in Economics, Yale University, revised Nov 2021.
    4. A. Bërdëllima, 2021. "Duopoly price competition with limited capacity," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 143-154, April.
    5. Vettas, Nikolaos & Kotseva, Rossitsa & Christou, Charalambos, 2007. "Pricing, Investments and Mergers with Intertemporal Capacity Constraints," CEPR Discussion Papers 6433, C.E.P.R. Discussion Papers.
    6. Lenhard, Severin, 2022. "Imperfect competition with costly disposal," International Journal of Industrial Organization, Elsevier, vol. 82(C).
    7. Alexander Maslov, 2023. "Bertrand Duopoly in Online Consumer-to-Consumer Markets," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 63(1), pages 97-109, August.
    8. Kalyan Talluri & Víctor Martínez de Albéniz, 2010. "Dynamic price competition with fixed capacities," Economics Working Papers 1205, Department of Economics and Business, Universitat Pompeu Fabra.
    9. James D. Dana & Kevin R. Williams, 2022. "Intertemporal Price Discrimination in Sequential Quantity-Price Games," Marketing Science, INFORMS, vol. 41(5), pages 966-981, September.
    10. James D. Dana Jr. & Kevin R. Williams, 2018. "Intertemporal Price Discrimination in Sequential Quantity-Price Games," Cowles Foundation Discussion Papers 2136R2, Cowles Foundation for Research in Economics, Yale University, revised Mar 2019.
    11. Kalyan Talluri & Victor Martínez-de-Albéniz, 2010. "Dynamic Price Competition with Fixed Capacities," Working Papers 425, Barcelona School of Economics.
    12. Somogyi, Robert, 2020. "Bertrand–Edgeworth competition with substantial horizontal product differentiation," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 27-37.
    13. James D. Dana Jr. & Kevin R. Williams, 2020. "Intertemporal Price Discrimination in Sequential Quantity-Price Games," NBER Working Papers 26794, National Bureau of Economic Research, Inc.
    14. Jason J. Lepore & Aric P. Shafran, 2013. "Consumer Rationing and Cournot Outcomes: Experimental Evidence," Southern Economic Journal, John Wiley & Sons, vol. 79(3), pages 727-746, January.
    15. James D. Dana Jr. & Kevin R. Williams, 2018. "Intertemporal Price Discrimination in Sequential Quantity-Price Games," Cowles Foundation Discussion Papers 2136R3, Cowles Foundation for Research in Economics, Yale University, revised Feb 2020.
    16. Vettas, Nikolaos & Biglaiser, Gary, 2004. "Dynamic Price Competition with Capacity Constraints and Strategic Buyers," CEPR Discussion Papers 4315, C.E.P.R. Discussion Papers.
    17. Tasnádi, Attila, 2001. "A Bertrand-Edgeworth-oligopóliumok. Irodalmi áttekintés [Bertrand-Edgeworth oligopolies - a survey of the literature]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(12), pages 1081-1092.
    18. Gregor Zöttl, 2010. "A Framework of Peak Load Pricing with Strategic Firms," Operations Research, INFORMS, vol. 58(6), pages 1637-1649, December.
    19. Veronika Grimm & Gregor Zoettl, 2006. "Capacity Choice under Uncertainty: The Impact of Market Structure," Working Paper Series in Economics 23, University of Cologne, Department of Economics.
    20. Lepore, Jason J., 2012. "Cournot outcomes under Bertrand–Edgeworth competition with demand uncertainty," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 177-186.

    More about this item

    Keywords

    Price competition; Capacity choice; Demand uncertainty; Product differentiation; Price dispersion;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

    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:tin:wpaper:20120113. 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: Tinbergen Office +31 (0)10-4088900 (email available below). General contact details of provider: https://edirc.repec.org/data/tinbenl.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.