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Cournot equilibrium revisited

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  • Corchón, Luis C.
  • Torregrosa, Ramón J.

Abstract

We provide necessary and sufficient conditions for the existence of Cournot equilibrium for a class of demand functions when firms are identical and produce under constant returns to scale. We focus on inelastic and convex demand yielding non-concave profit functions. We show that equilibrium is unique, stable and yields well-behaved comparative statics. The model can yield huge welfare losses, non-downward sloping Laffer curves and tax reforms that are never Pareto improving. In the Appendix we generalize our results on existence and uniqueness to more general inverse demand functions and non-identical firms.

Suggested Citation

  • Corchón, Luis C. & Torregrosa, Ramón J., 2020. "Cournot equilibrium revisited," Mathematical Social Sciences, Elsevier, vol. 106(C), pages 1-10.
    • Handle: RePEc:eee:matsoc:v:106:y:2020:i:c:p:1-10
    DOI: 10.1016/j.mathsocsci.2020.01.012
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    1. Delipalla, Sofia & Keen, Michael, 1992. "The comparison between ad valorem and specific taxation under imperfect competition," Journal of Public Economics, Elsevier, vol. 49(3), pages 351-367, December.
    2. Corchón, Luis C. & Zudenkova, Galina, 2009. "Computing welfare losses from data under imperfect competition with heterogeneous goods," International Journal of Industrial Organization, Elsevier, vol. 27(6), pages 646-654, November.
    3. Anderson, Simon P. & de Palma, Andre & Kreider, Brent, 2001. "The efficiency of indirect taxes under imperfect competition," Journal of Public Economics, Elsevier, vol. 81(2), pages 231-251, August.
    4. al-Nowaihi, A. & Levine, P. L., 1985. "The stability of the cournot oligopoly model: A reassessment," Journal of Economic Theory, Elsevier, vol. 35(2), pages 307-321, August.
    5. William Novshek, 1985. "On the Existence of Cournot Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(1), pages 85-98.
    6. Robert A. Ritz, 2018. "Oligopolistic competition and welfare," Chapters, in: Luis C. Corchón & Marco A. Marini (ed.), Handbook of Game Theory and Industrial Organization, Volume I, chapter 7, pages 181-200, Edward Elgar Publishing.
    7. David Hennessy, 2000. "Cournot Oligopoly Conditions under which Any Horizontal Merger Is Profitable," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 17(3), pages 277-284, November.
    8. Robert A. Ritz, 2014. "On Welfare Losses Due to Imperfect Competition," Journal of Industrial Economics, Wiley Blackwell, vol. 62(1), pages 167-190, March.
    9. Malcomson, James M., 1986. "Some analytics of the laffer curve," Journal of Public Economics, Elsevier, vol. 29(3), pages 263-279, April.
    10. Anderson, Simon P. & Renault, Regis, 2003. "Efficiency and surplus bounds in Cournot competition," Journal of Economic Theory, Elsevier, vol. 113(2), pages 253-264, December.
    11. Seade, Jesus K, 1980. "On the Effects of Entry," Econometrica, Econometric Society, vol. 48(2), pages 479-489, March.
    12. Roberts, John & Sonnenschein, Hugo, 1976. "On the existence of Cournot equilbrium without concave profit functions," Journal of Economic Theory, Elsevier, vol. 13(1), pages 112-117, August.
    13. Brons, Martijn & Nijkamp, Peter & Pels, Eric & Rietveld, Piet, 2008. "A meta-analysis of the price elasticity of gasoline demand. A SUR approach," Energy Economics, Elsevier, vol. 30(5), pages 2105-2122, September.
    14. Ewerhart, Christian, 2014. "Cournot games with biconcave demand," Games and Economic Behavior, Elsevier, vol. 85(C), pages 37-47.
    15. Ellis, Randall P. & Martins, Bruno & Zhu, Wenjia, 2017. "Health care demand elasticities by type of service," Journal of Health Economics, Elsevier, vol. 55(C), pages 232-243.
    16. Gahvari, Firouz, 1989. "The nature of government expenditures and the shape of the laffer curve," Journal of Public Economics, Elsevier, vol. 40(2), pages 251-260, November.
    17. Sofia Delipalla & Michael Keen, 2006. "Product Quality and the Optimal Structure of Commodity Taxes," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 8(4), pages 547-554, October.
    18. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    19. Amir, R., 1996. "Cournot oligopoly and theory of supermodular games," LIDAM Reprints CORE 1228, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    20. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
    21. Gahvari, Firouz, 1988. "Does the Laffer Curve Ever Slope Down?," National Tax Journal, National Tax Association;National Tax Journal, vol. 41(2), pages 267-269, June.
    22. Gahvari, Firouz, 1988. "Does the Laffer Curve Ever Slope Down?," National Tax Journal, National Tax Association, vol. 41(2), pages 267-69, June.
    23. F. H. Hahn, 1962. "The Stability of the Cournot Oligopoly Solution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 29(4), pages 329-331.
    24. Vincenzo Denicolo & Massimo Matteuzzi, 2000. "Specific and Ad Valorem Taxation in Asymmetric Cournot Oligopolies," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 7(3), pages 335-342, May.
    25. Dixit, Avinash K, 1986. "Comparative Statics for Oligopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 107-122, February.
    26. Pedro Ferreira, 2017. "Welfare Changes in the Cournot Setting with an Empirical Application to the Telecommunications Industry," Journal of Industrial Economics, Wiley Blackwell, vol. 65(1), pages 194-213, March.
    27. Judy Hsu & X. Wang, 2005. "On Welfare under Cournot and Bertrand Competition in Differentiated Oligopolies," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 27(2), pages 185-191, September.
    28. Dastidar, Krishnendu Ghosh, 2000. "Is a Unique Cournot Equilibrium Locally Stable?," Games and Economic Behavior, Elsevier, vol. 32(2), pages 206-218, August.
    29. Skeath, Susan E. & Trandel, Gregory A., 1994. "A Pareto comparison of ad valorem and unit taxes in noncompetitive environments," Journal of Public Economics, Elsevier, vol. 53(1), pages 53-71, January.
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    4. von Mouche, Pierre & Szidarovszky, Ferenc, 2024. "Aggregative games with discontinuous payoffs at the origin," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 77-84.

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