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A general model of price competition with soft capacity constraints

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  • Marie-Laure Cabon-Dhersin

    (Université de Rouen Normandie, CREAM)

  • Nicolas Drouhin

    (Université Paris-Saclay)

Abstract

We propose a general model of oligopoly with firms relying on a two factor production function. In a first stage, firms choose a certain fixed factor level. In the second stage, firms compete on price and adjust the variable factor to satisfy all the demand. When the factors are substitutable, the capacity constraint is “soft,” implying a convex cost function in the second stage. We show that there exists a continuum of subgame perfect equilibria in pure strategies, whatever the returns to scale. Among them, a payoff dominant one can always be selected. The equilibrium price may increase with the number of firms.

Suggested Citation

  • Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2020. "A general model of price competition with soft capacity constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(1), pages 95-120, July.
    • Handle: RePEc:spr:joecth:v:70:y:2020:i:1:d:10.1007_s00199-019-01203-w
    DOI: 10.1007/s00199-019-01203-w
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    Cited by:

    1. Elpiniki Bakaouka & Marc Escrihuela-Villar & Walter Ferrarese, 2022. "Endogenous Horizontal Mergers in Homogeneous Goods Industries with Bertrand Competition," DEA Working Papers 96, Universitat de les Illes Balears, Departament d'Economía Aplicada.
    2. Somogyi, Robert, 2020. "Bertrand–Edgeworth competition with substantial horizontal product differentiation," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 27-37.
    3. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2021. "Chamberlin without differentiation: Soft-capacity constrained price competition with free entry," Working Papers halshs-03378500, HAL.
    4. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2022. "Chamberlin without differentiation: Soft-capacity constrained price competition with free entry," Post-Print halshs-03378500, HAL.
    5. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2020. "Soft-Capacity constrained price competition with entry and a minimum firm size: Chamberlin without differentiation," Working Papers hal-02909801, HAL.
    6. Arijit Mukherjee, 2023. "Losses from cross-holdings in a duopoly with convex cost and strategic input price determination," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 81-91, April.
    7. Marie‐Laure Cabon‐Dhersin & Nicolas Drouhin, 2023. "Chamberlin without differentiation: Soft capacity constrained price competition with free entry," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(1), pages 118-126, March.
    8. Rui Ota & Hiroshi Fujiu, 2021. "Price Competition and Setup Cost," Mathematics, MDPI, vol. 9(3), pages 1-15, February.

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    More about this item

    Keywords

    Price competition; Tacit collusion; Convex cost; Capacity constraint; Limit pricing strategy; Returns to scale;
    All these keywords.

    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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