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Existence and uniqueness of price equilibria in location-based models of differentiation with full coverage

Author

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  • Janko Hernández Cortés

    (Departament of Business Administration. ITAM.)

  • Paolo Morganti

    (Universidad Panamericana Facultad de Ciencias Económicas y Empresariales.)

Abstract

In location-based models of price competition, traditional sufficient conditions for existence and uniqueness of an equilibrium (Caplin and Nalebuff in Econometrica 59(1):25–59) are not robust for the firm that serves the right-tail of the consumers’ distribution. Interestingly, as we relax these conditions, we observe only two new alternative cases. Moreover, we identify a novel, easily testable condition for uniqueness that is weaker than log-concavity and that can also apply to Mechanism Design. Thanks to this general framework, we can solve the equilibrium of general vertical differentiation models numerically and show that inequality has a U-shaped effect on profits and prices of a high-quality firm. Moreover, we prove that extreme levels of concentration can dissolve natural monopolies and restore competition, contrary to the Uniform case.

Suggested Citation

  • Janko Hernández Cortés & Paolo Morganti, 2022. "Existence and uniqueness of price equilibria in location-based models of differentiation with full coverage," Journal of Economics, Springer, vol. 136(2), pages 115-148, July.
    • Handle: RePEc:kap:jeczfn:v:136:y:2022:i:2:d:10.1007_s00712-021-00770-8
    DOI: 10.1007/s00712-021-00770-8
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    References listed on IDEAS

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