Salant, Stephen W. and Shaffer, Greg (2002): Using Lorenz curves to represent firm heterogeneity in Cournot games.

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Abstract
We derive several comparativestatic results for Cournot games when firms have nonconstant marginalcost 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 decisionmaking under uncertainty to compare the riskiness of certain probability distributions with the same mean.
Item Type:  MPRA Paper 

Original Title:  Using Lorenz curves to represent firm heterogeneity in Cournot games 
Language:  English 
Keywords:  Lorenz curves, Herfindahl index, Cournot games 
Subjects:  D  Microeconomics > D6  Welfare Economics > D63  Equity, Justice, Inequality, and Other Normative Criteria and Measurement L  Industrial Organization > L1  Market Structure, Firm Strategy, and Market Performance > L13  Oligopoly and Other Imperfect Markets D  Microeconomics > D4  Market Structure, Pricing, and Design > D43  Oligopoly and Other Forms of Market Imperfection 
Item ID:  21876 
Depositing User:  Stephen W. Salant 
Date Deposited:  07 Apr 2010 09:47 
Last Modified:  27 Sep 2019 13:27 
References:  Allen, R. G. D. and J. R. Hicks, 1934 “A Reconsideration of the Theory of Value,”, Economica, 1, 5276 and 196219. Atkinson, A. B., 1970, On the Measurement of Inequality, Journal of Economic Theory, 2, 24463. Berge, C., 1963, Topological Spaces, New York: The Macmillan Company. Bergstrom, T. and H. Varian, 1985a, When are Nash Equilibria Independent of the Distribution of Agents’ Characteristics, Review of Economic Studies, 52, 715718. —— and ——, 1985b, Two Remarks on Cournot Equilibria, Economics Letters, 19, 58. Dalton, H., 1920, The Measurement of the Inequality of Incomes, Economic Journal, 30, 348361. Dasgupta, P., Sen, A., and D. Starrett, 1973, Notes on the Measurement of Inequality, Journal of Economic Theory, 6, 180187. Encaoua, D. and A. Jacquemin, 1980, Degree of Monopoly, Indices of Concentration and Threat of Entry, International Economic Review, 21, 87105. Fields, G., and J. Fei, 1978, On Inequality Comparisons, Econometrica, 46, 303316. Foster, J., 1985, Inequality Measurement, Proceedings of Symposia in Applied Mathematics, 33, 3168. FTC v. Bass Bros. Enters. Chicago: Commerce Clearing House, 1994. Gaudet, G. and S. Salant, 1991, Uniqueness of Cournot Equilibrium: New Results from Old Methods, Review of Economic Studies, 58, 399404. Hardy, G.H., Littlewood, J.E., and G. P´olya, 1934, 1952, Inequalities, London: Cambridge University Press. Lorenz, M.O., 1905, Methods of Measuring Concentration in Wealth, Journal of American Statistical Association, 9: 209219. Marshall, A.W., and I. Olkin, 1979, Inequalities: Theory of Majorization and its Applications, New York, NY: Academic Press, Inc. Muirhead, R., 1903, Some Methods Applicable to Identities and Inequalities of Symmetric Algebraic Functions of N Letters, Proceedings of Edinburgh Mathematical Society, 21, 14457. Rothschild, M. and J.E. Stiglitz, 1970, Increasing Risk I: A Definition, Journal of Economic Theory, 2, 225243. —— and ——, 1971, Increasing Risk II: Its Economic Consequences, Journal of Economic Theory, 3, 6684. —— and ——, 1973, Some Further Results in the Measurement of Inequality, Journal of Economic Theory, 6, 188204. Salant, S. and G. Shaffer, 1998, Optimal Asymmetric Strategies in Research Joint Ventures, International Journal of Industrial Organization, 16, 195208. Salant, S. and G. Shaffer, 1999, Unequal Treatment of Identical Agents in Cournot Equilibrium, American Economic Review, 89, 585604. Schur, I., 1923, Uber eine Klasse von Mittelbildungen mit Anwendungen auf die Determinantentheorie, Sitzungsber. Berl. Math. Ges., 22, 920. Tirole, J., 1988, The Theory of Industrial Organization, Cambridge, Massachusetts: MIT Press U.S. Department of Justice, Merger Guidelines. Chicago: Commerce Clearing House, 1992. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/21876 