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

Author

Listed:
  • Caterina Colombo
  • Corrado Benassi

    ()

  • Alessandra Chirco

    ()

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

  • Caterina Colombo & Corrado Benassi & Alessandra Chirco, 2015. "Beyond the Uniform Distribution: Equilibrium Prices and Qualities in a Vertically Differentiated Duopoly," Working Papers 2015154, University of Ferrara, Department of Economics.
  • Handle: RePEc:udf:wpaper:2015154
    as

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    References listed on IDEAS

    as
    1. Osharin, Alexander & Thisse, Jacques-François & Ushchev, Philip & Verbus, Valery, 2014. "Monopolistic competition and income dispersion," Economics Letters, Elsevier, vol. 122(2), pages 348-352.
    2. 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.
    3. 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.
    4. 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.
    5. Avner Shaked & John Sutton, 1982. "Relaxing Price Competition Through Product Differentiation," Review of Economic Studies, Oxford University Press, vol. 49(1), pages 3-13.
    6. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    7. Anderson, Simon P. & Goeree, Jacob K. & Ramer, Roald, 1997. "Location, Location, Location," Journal of Economic Theory, Elsevier, vol. 77(1), pages 102-127, November.
    8. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, January.
    9. Jaskold Gabszewicz, J. & Thisse, J. -F., 1979. "Price competition, quality and income disparities," Journal of Economic Theory, Elsevier, vol. 20(3), pages 340-359, June.
    10. Corrado Benassi & Alessandra Chirco & Caterina Colombo, 2006. "Vertical Differentiation And The Distribution Of Income," Bulletin of Economic Research, Wiley Blackwell, vol. 58(4), pages 345-367, October.
    11. 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.
    12. Esteban, Joan M, 1986. "Income-Share Elasticity and the Size Distribution of Income," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(2), pages 439-444, June.
    13. Corrado Benassi & Alessandra Chirco & Marcella Scrimitore, 2002. "Income concentration and market demand," Oxford Economic Papers, Oxford University Press, vol. 54(4), pages 584-596, October.
    14. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
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    More about this item

    Keywords

    Vertical differentiation; duopoly; non-uniform distribution; subgame perfect equilibrium; income share elasticity;

    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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