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Efficiency loss in a Cournot oligopoly with convex market demand

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  • Tsitsiklis, John N.
  • Xu, Yunjian

Abstract

We consider a Cournot oligopoly model where multiple suppliers (oligopolists) compete by choosing quantities. We compare the social welfare achieved at a Cournot equilibrium to the maximum possible, for the case where the inverse market demand function is convex. We establish a lower bound on the efficiency of Cournot equilibria in terms of a scalar parameter derived from the inverse demand function, namely, the ratio of the slope of the inverse demand function at the Cournot equilibrium to the average slope of the inverse demand function between the Cournot equilibrium and a social optimum. Also, for the case of a single, monopolistic, profit maximizing supplier, or of multiple suppliers who collude to maximize their total profit, we establish a similar but tighter lower bound on the efficiency of the resulting output. Our results provide nontrivial quantitative bounds on the loss of social welfare for several convex inverse demand functions that appear in the economics literature.

Suggested Citation

  • Tsitsiklis, John N. & Xu, Yunjian, 2014. "Efficiency loss in a Cournot oligopoly with convex market demand," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 46-58.
    • Handle: RePEc:eee:mateco:v:53:y:2014:i:c:p:46-58
    DOI: 10.1016/j.jmateco.2014.06.001
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. Friedman, James, 1993. "Oligopoly theory," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 11, pages 491-534, Elsevier.
    5. Gérard Gaudet & Stephen W. Salant, 1991. "Uniqueness of Cournot Equilibrium: New Results From Old Methods," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(2), pages 399-404.
    6. repec:bla:econom:v:38:y:1971:i:150:p:199-203 is not listed on IDEAS
    7. William Novshek, 1980. "Cournot Equilibrium with Free Entry," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(3), pages 473-486.
    8. 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).
    9. Lahiri, Sajal & Ono, Yoshiyasu, 1988. "Helping Minor Firms Reduces Welfare," Economic Journal, Royal Economic Society, vol. 98(393), pages 1199-1202, December.
    10. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
    11. Jonathan Kluberg & Georgia Perakis, 2012. "Generalized Quantity Competition for Multiple Products and Loss of Efficiency," Operations Research, INFORMS, vol. 60(2), pages 335-350, April.
    12. Corchón, Luis C., 2008. "Welfare losses under Cournot competition," International Journal of Industrial Organization, Elsevier, vol. 26(5), pages 1120-1131, September.
    13. Novshek, William & Sonnenschein, Hugo, 1978. "Cournot and Walras equilibrium," Journal of Economic Theory, Elsevier, vol. 19(2), pages 223-266, December.
    14. repec:bla:econom:v:36:y:1969:i:143:p:304-09 is not listed on IDEAS
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    Cited by:

    1. Condorelli, Daniele & Szentes, Balazs, 2020. "Surplus Bounds in Cournot Monopoly and Competition," CRETA Online Discussion Paper Series 62, Centre for Research in Economic Theory and its Applications CRETA.
    2. Condorelli, Daniele, 2022. "A lower-bound on monopoly profit for log-concave demand," Economics Letters, Elsevier, vol. 210(C).
    3. Condorelli, Daniele & Szentes, Balazs, 2020. "Surplus Bounds in Cournot Monopoly and Competition," The Warwick Economics Research Paper Series (TWERPS) 1292, University of Warwick, Department of Economics.
    4. Y. Charles Li & Hong Yang, 2016. "A mathematical model of demand-supply dynamics with collectability and saturation factors," Papers 1606.06720, arXiv.org.

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