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Using Lorenz curves to represent firm heterogeneity in Cournot games

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  • Salant, Stephen W.
  • Shaffer, Greg

Abstract

We derive several comparative-static results for Cournot games when firms have nonconstant marginal-cost curves which shift exogenously. The results permit us to rank certain vectors of equilibrium marginal costs with the same component sum according to their associated social surplus or industry profit. We arrange the components of each vector in ascending order and then construct from the resulting ordered vector its associated Lorenz curve. We show that if two Lorenz curves do not cross, the one reflecting greater inequality is associated with higher social surplus and industry profit. A duality result permits a corresponding ranking of equilibrium output vectors. The same partial ordering is used in the literature on income inequality to rank certain distributions of income and in the literature on decision-making under uncertainty to compare the riskiness of certain probability distributions with the same mean.

Suggested Citation

  • Salant, Stephen W. & Shaffer, Greg, 2002. "Using Lorenz curves to represent firm heterogeneity in Cournot games," MPRA Paper 21876, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:21876
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    References listed on IDEAS

    as
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    3. Gérard Gaudet & Stephen W. Salant, 1991. "Uniqueness of Cournot Equilibrium: New Results From Old Methods," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(2), pages 399-404.
    4. Encaoua, David & Jacquemin, Alexis, 1980. "Degree of Monopoly, Indices of Concentration and Threat of Entry," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 87-105, February.
    5. Dasgupta, Partha & Sen, Amartya & Starrett, David, 1973. "Notes on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 180-187, April.
    6. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    7. Greg Shaffer & Stephen W. Salant, 1999. "Unequal Treatment of Identical Agents in Cournot Equilibrium," American Economic Review, American Economic Association, vol. 89(3), pages 585-604, June.
    8. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
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    More about this item

    Keywords

    Lorenz curves; Herfindahl index; Cournot games;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • 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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