IDEAS home Printed from https://ideas.repec.org/p/bol/bodewp/372.html
   My bibliography  Save this paper

Non-Linear Market Demand and Capital Accumulation in A Differential Oligopoly Game

Author

Listed:
  • R. Cellini
  • L. Lambertini

Abstract

We investigate a differential oligopoly game where firms compete in account Market whose demand function is always downward sloping but can take any degree of curvature. There exist two economically meaningful saddle points, one dictated by demand conditions, the other by the Ramsey rule. In steady state, optimal capital is non-decreasing in market size. Then we show that the socially efficient output is independent of the curvature of market demand. This entails that the welfare loss associated to the Cournot equilibrium decreases as market size increases.

Suggested Citation

  • R. Cellini & L. Lambertini, 2000. "Non-Linear Market Demand and Capital Accumulation in A Differential Oligopoly Game," Working Papers 372, Dipartimento Scienze Economiche, Universita' di Bologna.
    • Handle: RePEc:bol:bodewp:372
    as

    Download full text from publisher

    File URL: http://amsacta.unibo.it/4937/1/372.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, April.
    2. Lambertini, Luca, 1996. "Cartel Stability and the Curvature of Market Demand," Bulletin of Economic Research, Wiley Blackwell, vol. 48(4), pages 329-334, October.
    3. Carl Davidson & Raymond Deneckere, 1986. "Long-Run Competition in Capacity, Short-Run Competition in Price, and the Cournot Model," RAND Journal of Economics, The RAND Corporation, vol. 17(3), pages 404-415, Autumn.
    4. Anderson, Simon P. & Engers, Maxim, 1992. "Stackelberg versus Cournot oligopoly equilibrium," International Journal of Industrial Organization, Elsevier, vol. 10(1), pages 127-135, March.
    5. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, April.
    6. Jean-Pierre Benoit & Vijay Krishna, 1987. "Dynamic Duopoly: Prices and Quantities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(1), pages 23-35.
    7. Davidson, Carl & Deneckere, Raymond J, 1990. "Excess Capacity and Collusion," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(3), pages 521-541, August.
    8. Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-1164, September.
    9. Anderson, Simon P & Engers, Maxim, 1994. "Strategic Investment and Timing of Entry," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(4), pages 833-853, November.
    10. William Novshek, 1980. "Cournot Equilibrium with Free Entry," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(3), pages 473-486.
    11. Levitan, Richard & Shubik, Martin, 1972. "Price Duopoly and Capacity Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(1), pages 111-122, February.
    12. William A. Brock & José A. Scheinkman, 1985. "Price Setting Supergames with Capacity Constraints," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(3), pages 371-382.
    13. Fershtman, Chaim & Muller, Eitan, 1984. "Capital accumulation games of infinite duration," Journal of Economic Theory, Elsevier, vol. 33(2), pages 322-339, August.
    14. 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.
    15. Kydland, Finn, 1977. "Equilibrium solutions in dynamic dominant-player models," Journal of Economic Theory, Elsevier, vol. 15(2), pages 307-324, August.
    16. Cellini, Roberto & Lambertini, Luca, 1998. "A Dynamic Model of Differentiated Oligopoly with Capital Accumulation," Journal of Economic Theory, Elsevier, vol. 83(1), pages 145-155, November.
    17. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Baldini, Massimo & Lambertini, Luca, 2011. "Profit taxation and capital accumulation in a dynamic oligopoly model," Japan and the World Economy, Elsevier, vol. 23(1), pages 13-18, January.
    2. R. Cellini & L. Lambertini, 2003. "Capital Accumulation and Horizontal Mergers in Differential Oligopoly Games," Working Papers 477, Dipartimento Scienze Economiche, Universita' di Bologna.
    3. Calzolari, Giacomo & Lambertini, Luca, 2007. "Export restraints in a model of trade with capital accumulation," Journal of Economic Dynamics and Control, Elsevier, vol. 31(12), pages 3822-3842, December.
    4. R. Cellini & L. Lambertini, 2008. "Weak and Strong Time Consistency in a Differential Oligopoly Game with Capital Accumulation," Journal of Optimization Theory and Applications, Springer, vol. 138(1), pages 17-26, July.
    5. Giacomo Calzolari & Luca Lambertini, 2006. "Tariffs vs Quotas in a Model of Trade with Capital Accumulation," Review of International Economics, Wiley Blackwell, vol. 14(4), pages 632-644, September.
    6. R. Cellini & L. Lambertini, 2001. "Differential Oligopoly Games where the Closed-Loop Memoryless and Open-Loop Equilibria Coincide," Working Papers 402, Dipartimento Scienze Economiche, Universita' di Bologna.
    7. R. Cellini & L. Lambertini, 2002. "Advertising with Spillover Effects in a Differential Oligopoly Game With Differentiated Goods," Working Papers 430, Dipartimento Scienze Economiche, Universita' di Bologna.

    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. R. Cellini & L. Lambertini, 2000. "Differential Games and Oligopoly Theory: An Overview," Working Papers 369, Dipartimento Scienze Economiche, Universita' di Bologna.
    2. Bergman, Mats A., 1998. "Endogenous Timing of Investments Yields Modified Stackelberg Outcomes," SSE/EFI Working Paper Series in Economics and Finance 272, Stockholm School of Economics.
    3. Knittel, Christopher R. & Lepore, Jason J., 2010. "Tacit collusion in the presence of cyclical demand and endogenous capacity levels," International Journal of Industrial Organization, Elsevier, vol. 28(2), pages 131-144, March.
    4. Knittel, Christopher R. & Lepore, Jason J., 2010. "Tacit collusion in the presence of cyclical demand and endogenous capacity levels," International Journal of Industrial Organization, Elsevier, vol. 28(2), pages 131-144, March.
    5. 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.
    6. Vettas, Nikolaos & Biglaiser, Gary, 2004. "Dynamic Price Competition with Capacity Constraints and Strategic Buyers," CEPR Discussion Papers 4315, C.E.P.R. Discussion Papers.
    7. 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.
    8. Cellini, Roberto & Lambertini, Luca, 1998. "A Dynamic Model of Differentiated Oligopoly with Capital Accumulation," Journal of Economic Theory, Elsevier, vol. 83(1), pages 145-155, November.
    9. 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.
    10. Baik, Kyung Hwan, 1995. "Horizontal mergers of price-setting firms with sunk capacity costs," The Quarterly Review of Economics and Finance, Elsevier, vol. 35(3), pages 245-256.
    11. Raymond J. Deneckere & Dan Kovenock, 1992. "Price Leadership," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(1), pages 143-162.
      • Raymond Deneckere & Dan Kovenock, 1988. "Price Leadership," Discussion Papers 773, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. Attila Tasnádi, 2010. "Quantity-setting games with a dominant firm," Journal of Economics, Springer, vol. 99(3), pages 251-266, April.
    13. Vives, Xavier & Jun, Byoung, 2001. "Incentives in Dynamic Duopoly," CEPR Discussion Papers 2899, C.E.P.R. Discussion Papers.
    14. Prabal Roy Chowdhury, 2004. "Bertrand-Edgeworth equilibrium: Manipulable residual demand," Discussion Papers 04-15, Indian Statistical Institute, Delhi.
    15. Tasnadi, Attila, 2004. "Production in advance versus production to order," Journal of Economic Behavior & Organization, Elsevier, vol. 54(2), pages 191-204, June.
    16. Farm, Ante, 2009. "Market Sharing and Price Leadership," Working Paper Series 3/2009, Stockholm University, Swedish Institute for Social Research.
    17. Sherif Nasser & Danko Turcic, 2016. "To Commit or Not to Commit: Revisiting Quantity vs. Price Competition in a Differentiated Industry," Management Science, INFORMS, vol. 62(6), pages 1719-1733, June.
    18. R. Cellini & L. Lambertini, 2002. "Price vs Quantity in a Dynamic Duopoly Game with Capacity Accumulation," Working Papers 449, Dipartimento Scienze Economiche, Universita' di Bologna.
    19. R. Cellini & L. Lambertini, 2003. "Capacity Accumulation and Utilization in a Differential Duopoly Game," Working Papers 465, Dipartimento Scienze Economiche, Universita' di Bologna.
    20. Jean J. Gabszewicz & Jacques-François Thisse, 2000. "Microeconomic theories of imperfect competition," Cahiers d'Économie Politique, Programme National Persée, vol. 37(1), pages 47-99.

    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:bol:bodewp:372. 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: Dipartimento Scienze Economiche, Universita' di Bologna (email available below). General contact details of provider: https://edirc.repec.org/data/sebolit.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.