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Price versus quantity in a mixed duopoly: The case of relative profit maximization

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  • Nakamura, Yasuhiko

Abstract

This paper examines the endogenous choice problem of each firm's price or quantity contract in a mixed duopoly composed of one social welfare maximizing public firm and one relative profit-maximizing private firm. In this paper, we show that unless the degree of product differentiation and the degree of importance of the private firm's relative performance are low, the quantity competition can analytically become the unique equilibrium market structure on the basis of the dominant strategies of the public firm and the private firm when the degree of importance of firm 1's relative performance is sufficiently high. This result contrasts strikingly with that obtained in a standard mixed duopoly composed of one social welfare-maximizing public firm and one absolute profit maximizing private firm. In addition, even in the area wherein both the degree of product differentiation and the degree of the private firm's relative performance are sufficiently low, through numerical simulations, the quantity competition tends to become the unique equilibrium market structure when the degree of importance of the private firm's relative performance is sufficiently high, whereas the price competition tends to become the unique equilibrium market structure when the degree of importance of the private firm's relative performance is sufficiently low.

Suggested Citation

  • Nakamura, Yasuhiko, 2015. "Price versus quantity in a mixed duopoly: The case of relative profit maximization," Economic Modelling, Elsevier, vol. 44(C), pages 37-43.
    • Handle: RePEc:eee:ecmode:v:44:y:2015:i:c:p:37-43
    DOI: 10.1016/j.econmod.2014.09.019
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Yasuhiko Nakamura, 2019. "Combining the Endogenous Choice of the Timing of Setting the Levels of Strategic Contracts and Their Contents in a Managerial Mixed Duopoly," Journal of Industry, Competition and Trade, Springer, vol. 19(2), pages 235-261, June.
    2. Xu, Lili & Chen, Yuyan & Lee, Sang-Ho, 2022. "Emission tax and strategic environmental corporate social responsibility in a Cournot–Bertrand comparison," Energy Economics, Elsevier, vol. 107(C).
    3. Xu, Lili & Cho, Sumi & Lee, Sang-Ho, 2016. "Emission tax and optimal privatization in Cournot–Bertrand comparison," Economic Modelling, Elsevier, vol. 55(C), pages 73-82.
    4. Nguyen, Xuan, 2015. "On the efficiency of private and state-owned enterprises in mixed markets," Economic Modelling, Elsevier, vol. 50(C), pages 130-137.
    5. Chang Ray-Yun & Hu Jin-Li & Lin Yan-Shu, 2018. "The Choice of Prices versus Quantities under Outsourcing," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 18(2), pages 1-20, July.
    6. Moghadam, Hamed Markazi, 2021. "A nonparametric approach to evolutionary oligopoly games: An application to the crude oil industry," Economic Modelling, Elsevier, vol. 101(C).
    7. Amarjyoti Mahanta, 2019. "Endogenous strategic variable in a mixed duopoly," Journal of Economics, Springer, vol. 128(1), pages 47-65, September.
    8. José Méndez‐Naya & José A. Novo‐Peteiro, 2023. "Partial privatization with endogenous choice of strategic variable," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 44(2), pages 1215-1227, March.
    9. Wang, Chia-Chi & Chiou, Jiunn-Rong, 2018. "Optimal privatization policy with Bertrand competition," International Review of Economics & Finance, Elsevier, vol. 56(C), pages 538-546.
    10. Xu, Lili & Matsumura, Toshihiro, 2022. "Welfare-reducing price competition under relative performance delegation with convex costs," Economic Modelling, Elsevier, vol. 112(C).

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