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Beyond the Uniform Distribution: Equilibrium Prices and Qualities in a Vertically Differentiated Duopoly

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  • C. Benassi
  • A. Chirco
  • C. Colombo

Abstract

The paper proves the existence of a subgame perfect Nash equilibrium in a vertically differentiated duopoly with uncovered market, for a large set of symmetric and asymmetric distributions of consumers, including, among others, all logconcave distributions. The proof relies on the ’income share elasticity’ representation of the consumers’ density function, which ensures the analytical tractability of the firms’ optimality conditions at a high level of generality. Some illustrative examples of the solution are offered, in order to assess the impact of distributive shocks on the equilibrium market configuration.

Suggested Citation

  • C. Benassi & A. Chirco & C. Colombo, 2015. "Beyond the Uniform Distribution: Equilibrium Prices and Qualities in a Vertically Differentiated Duopoly," Working Papers wp1044, Dipartimento Scienze Economiche, Universita' di Bologna.
  • Handle: RePEc:bol:bodewp:wp1044
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    References listed on IDEAS

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    1. Jean‐Marc Bonnisseau & Rim Lahmandi‐Ayed, 2007. "Vertical differentiation with non‐uniform consumers' distribution," International Journal of Economic Theory, The International Society for Economic Theory, vol. 3(3), pages 179-190, September.
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    5. Yurko, Anna V., 2011. "How does income inequality affect market outcomes in vertically differentiated markets?," International Journal of Industrial Organization, Elsevier, vol. 29(4), pages 493-503, July.
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    7. Corrado Benassi & Alessandra Chirco & Caterina Colombo, 2005. "A Model Of Monopolistic Competition With Personal Income Dispersion," Metroeconomica, Wiley Blackwell, vol. 56(3), pages 305-317, July.
    8. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
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    Cited by:

    1. Barigozzi, Francesca & Ma, Ching-to Albert, 2018. "Product differentiation with multiple qualities," International Journal of Industrial Organization, Elsevier, vol. 61(C), pages 380-412.

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    More about this item

    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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