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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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    Cited by:

    1. 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.
    2. Y. Charles Li & Hong Yang, 2016. "A mathematical model of demand-supply dynamics with collectability and saturation factors," Papers 1606.06720, arXiv.org.
    3. 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.
    4. Condorelli, Daniele, 2022. "A lower-bound on monopoly profit for log-concave demand," Economics Letters, Elsevier, vol. 210(C).

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