IDEAS home Printed from https://ideas.repec.org/a/kap/jeczfn/v140y2023i2d10.1007_s00712-023-00830-1.html
   My bibliography  Save this article

Cournotian duopolistic firms may be Walrasian: a case in the Gabszewicz and Vial model

Author

Listed:
  • Francesca Busetto

    (Università degli Studi di Udine)

  • Giulio Codognato

    (Università degli Studi di Udine
    Economix, UPL, Univ Paris Nanterre, CNRS)

  • Giorgia Pavan

    (Università degli Studi di Udine)

  • Simone Tonin

    (Università degli Studi di Udine)

Abstract

In this paper, we present a refreshed version of the original model proposed by Gabszewicz and Vial (J Econ Theory 4:381–400, 1972) and we use their main example to review the main theoretical issues related to the notion of Cournot-Walras equilibrium. We compute, in the Gabszewicz and Vial main example, two different Cournot-Walras equilibria associated with different normalization rules. Moreover, in the same example, we compute a Utility-Cournot-Walras equilibrium as defined by Grodal (in: Allen (ed) Economics in a changing world, Macmillan, London, 1996) and we show that it coincides with the unique Walras equilibrium. Furthermore, using a proposition proved by Grodal (1996), we build a normalization rule with respect to which there is a Cournot-Walras equilibrium that coincides with the Utility-Cournot-Walras equilibrium and hence with the unique Walras equilibrium. To the best of our knowledge, this example provides the first case of Cournotian duopolistic firms being Walrasian in a production economy.

Suggested Citation

  • Francesca Busetto & Giulio Codognato & Giorgia Pavan & Simone Tonin, 2023. "Cournotian duopolistic firms may be Walrasian: a case in the Gabszewicz and Vial model," Journal of Economics, Springer, vol. 140(2), pages 121-140, October.
    • Handle: RePEc:kap:jeczfn:v:140:y:2023:i:2:d:10.1007_s00712-023-00830-1
    DOI: 10.1007/s00712-023-00830-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00712-023-00830-1
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1007/s00712-023-00830-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Jaskold Gabszewicz, Jean & Vial, Jean-Philippe, 1972. "Oligopoly "A la cournot" in a general equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 4(3), pages 381-400, June.
    2. Codognato, Giulio & Ghosal, Sayantan & Tonin, Simone, 2015. "Atomic Cournotian traders may be Walrasian," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 1-14.
    3. José Azar & Xavier Vives, 2021. "General Equilibrium Oligopoly and Ownership Structure," Econometrica, Econometric Society, vol. 89(3), pages 999-1048, May.
    4. DeAngelo, Harry, 1981. "Competition and Unanimity," American Economic Review, American Economic Association, vol. 71(1), pages 18-27, March.
    5. Busetto, Francesca & Codognato, Giulio & Julien, Ludovic, 2020. "Atomic Leontievian Cournotian traders are always Walrasian," Games and Economic Behavior, Elsevier, vol. 122(C), pages 318-327.
    6. Birgit Grodal & Egbert Dierker, 1999. "The price normalization problem in imperfect competition and the objective of the firm," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(2), pages 257-284.
    7. Bonanno, Giacomo, 1990. "General Equilibrium Theory with Imperfect Competition," Journal of Economic Surveys, Wiley Blackwell, vol. 4(4), pages 297-328.
    8. Stefano Demichelis & Klaus Ritzberger, 2011. "A general equilibrium analysis of corporate control and the stock market," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(2), pages 221-254, February.
    9. Busetto, Francesca & Codognato, Giulio & Julien, Ludovic, 2021. "Atomic Leontievian Walrasian traders are always Cournotian," Economics Letters, Elsevier, vol. 207(C).
    10. Egbert Dierker & Birgit Grodal, 1998. "Modelling Policy Issues in a World of Imperfect Competition," Scandinavian Journal of Economics, Wiley Blackwell, vol. 100(1), pages 153-179, March.
    11. Dierker, Egbert & Grodal, Birgit, 1998. " Modelling Policy Issues in a World of Imperfect Competition," Scandinavian Journal of Economics, Wiley Blackwell, vol. 100(1), pages 153-179, March.
    12. José Azar & Xavier Vives, 2021. "Reply to: Comments on “General Equilibrium Oligopoly and Ownership Structure”," Econometrica, Econometric Society, vol. 89(3), pages 1061-1063, May.
    13. Giulio Codognato & Francesca Busetto & Ludovic A. Julien, 2021. "Atomic Leontievian Walrasian traders are always Cournotian," Post-Print hal-03315766, HAL.
    14. Alex Dickson & Simone Tonin, 2021. "An introduction to perfect and imperfect competition via bilateral oligopoly," Journal of Economics, Springer, vol. 133(2), pages 103-128, July.
    15. GABSZEWICZ, Jean & MICHEL, Philippe, 1992. "Oligopoly equilibria in exchange economies," LIDAM Discussion Papers CORE 1992047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. Xavier Vives, 1987. "Small Income Effects: A Marshallian Theory of Consumer Surplus and Downward Sloping Demand," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(1), pages 87-103.
    17. Hayashi, Takashi, 2013. "Smallness of a commodity and partial equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 148(1), pages 279-305.
    18. Klaus Ritzberger, 2007. "Price normalization under imperfect competition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(2), pages 365-368, November.
    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. Ramón Torregrosa, 2008. "Macroeconomic effects of an indirect tax substitution," Journal of Economics, Springer, vol. 94(3), pages 199-221, September.
    2. Dirk Willenbockel, 2005. "The Price Normalisation Problem in General Equilibriun Models with Oligopoly Power: An Attempt at Perspective," GE, Growth, Math methods 0505002, University Library of Munich, Germany.
    3. Esteban-Bravo, Mercedes, 2000. "Existence and computation of a Cournot-Walras equilibrium," DES - Working Papers. Statistics and Econometrics. WS 9968, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Chang, Winston W. & Chen, Tai-Liang & Saito, Tetsuya, 2021. "Formation of symmetric free-trade blocs, optimal tariff structure, and world welfare," Journal of Asian Economics, Elsevier, vol. 77(C).
    5. WILLENBOCKEL Dirk, 2010. "The Numeraire Problem in General Equilibrium Models with Market Power: Much Ado About Nothing?," EcoMod2003 330700152, EcoMod.
    6. David R. Collie, 2019. "Taxation under oligopoly in a general equilibrium setting," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 21(4), pages 738-753, August.
    7. Jean-Marc Bonnisseau & Michael Florig, 2005. "Non-existence of Duopoly Equilibria: A Simple Numerical Example," Journal of Economics, Springer, vol. 85(1), pages 65-71, July.
    8. Suleyman Basak & Anna Pavlova, 2005. "Monopoly Power and the Firm’s Valuation: A Dynamic Analysis of Short versus Long-Term Policies," Studies in Economic Theory, in: Alessandro Citanna & John Donaldson & Herakles Polemarchakis & Paolo Siconolfi & Stephan E. Spear (ed.), Essays in Dynamic General Equilibrium Theory, pages 1-34, Springer.
    9. J. Peter Neary, 2016. "International Trade in General Oligopolistic Equilibrium," Review of International Economics, Wiley Blackwell, vol. 24(4), pages 669-698, September.
    10. Mercenier, Jean, 1995. "Can "1992" reduce unemployment in Europe? On welfare and employment effects of Europe's move to a single market," Journal of Policy Modeling, Elsevier, vol. 17(1), pages 1-37, February.
    11. Lahmandi-Ayed, Rim & Laussel, Didier, 2018. "When do imperfectly competitive firms maximize profits? The lessons from a simple general equilibrium model with shareholders’ voting," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 6-12.
    12. Busetto, Francesca & Codognato, Giulio & Julien, Ludovic, 2021. "Atomic Leontievian Walrasian traders are always Cournotian," Economics Letters, Elsevier, vol. 207(C).
    13. Basak, Suleyman & Pavlova, Anna, 2004. "Monopoly Power and the Firm€ٳ Valuation:," Working papers 4234-01, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    14. Paolo Bertoletti & Federico Etro, 2022. "Monopolistic competition, as you like it," Economic Inquiry, Western Economic Association International, vol. 60(1), pages 293-319, January.
    15. Rudy Colacicco, 2015. "Ten Years Of General Oligopolistic Equilibrium: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 29(5), pages 965-992, December.
    16. Ludovic A. Julien, 2021. "Noncooperative oligopoly equilibrium in markets with hierarchical competition," EconomiX Working Papers 2021-14, University of Paris Nanterre, EconomiX.
    17. Michael Zierhut, 2021. "Indeterminacy of Cournot–Walras equilibrium with incomplete markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 81-114, February.
    18. Klaus Ritzberger, 2007. "Price normalization under imperfect competition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(2), pages 365-368, November.
    19. , & ,, 2015. "Strategy-proofness and efficiency with non-quasi-linear preferences: a characterization of minimum price Walrasian rule," Theoretical Economics, Econometric Society, vol. 10(2), May.
    20. Ken-Ichi Shimomura & Jacques-François Thisse, 2012. "Competition among the big and the small," RAND Journal of Economics, RAND Corporation, vol. 43(2), pages 329-347, June.

    More about this item

    Keywords

    Cournot-Walras equilibrium; Walras equilibrium; Price normalization; Profit maximization;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

    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:kap:jeczfn:v:140:y:2023:i:2:d:10.1007_s00712-023-00830-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.