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Cost of Inequality, the Uniform Rule and Cooperative Games

Author

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  • Arsen Palestini

    () (MEMOTEF, Sapienza University of Rome, Via del Castro Laurenziano 9, 00161 Rome, Italy.)

  • Giuseppe Pignataro

    () (Department of Economics, University of Bologna, Strada Maggiore 45, 40125 Bologna, Italy.)

Abstract

The assessment of income inequality can be investigated looking at the solution concepts of the cooperative game theory. We propose a multi-factorial decomposition of the Atkinson index by income sources and evaluate it as a cooperative game of the social cost of inequality. This framework extends the distributive and efficient properties of the uniform rule (Sprumont [35]) in a setup with heterogeneous income sources and single-peaked preferences. We provide an axiomatic foundation of this preference-based allocation rule, called weakly uniform rule, with a further comparison with the solution concept of nucleolus. Sufficient conditions for their coincidence are therefore defined. Finally we characterize a welfare loss game expressed as the difference between the sum of inequalities generated by each source and the cost of the entire distribution. We show that income factors' contributions may increase or decrease the income inequality in the society ensuring different perspectives in terms of public policies.

Suggested Citation

  • Arsen Palestini & Giuseppe Pignataro, 2014. "Cost of Inequality, the Uniform Rule and Cooperative Games," Working Papers 322, ECINEQ, Society for the Study of Economic Inequality.
  • Handle: RePEc:inq:inqwps:ecineq2014-322
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    File URL: http://www.ecineq.org/milano/WP/ECINEQ2014-322.pdf
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    References listed on IDEAS

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    1. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    2. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    3. Charles Blackorby & David Donaldson & Maria Auersperg, 1981. "A New Procedure for the Measurement of Inequality within and among Population Subgroups," Canadian Journal of Economics, Canadian Economics Association, vol. 14(4), pages 665-685, November.
    4. Frank A. Cowell, 1980. "On the Structure of Additive Inequality Measures," Review of Economic Studies, Oxford University Press, vol. 47(3), pages 521-531.
    5. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    6. Lidia Ceriani & Paolo Verme, 2012. "The origins of the Gini index: extracts from Variabilità e Mutabilità (1912) by Corrado Gini," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, pages 421-443.
    7. Frank Cowell & Udo Ebert, 2004. "Complaints and inequality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(1), pages 71-89, August.
    8. Anthony Shorrocks, 2013. "Decomposition procedures for distributional analysis: a unified framework based on the Shapley value," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, pages 99-126.
    9. Silber, Jacques, 1989. "Factor Components, Population Subgroups and the Computation of the Gini Index of Inequality," The Review of Economics and Statistics, MIT Press, pages 107-115.
    10. Shlomo Yitzhaki, 1979. "Relative Deprivation and the Gini Coefficient," The Quarterly Journal of Economics, Oxford University Press, vol. 93(2), pages 321-324.
    11. Pyatt, Graham, 1976. "On the Interpretation and Disaggregation of Gini Coefficients," Economic Journal, Royal Economic Society, vol. 86(342), pages 243-255, June.
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    More about this item

    Keywords

    Atkinson index; cost game; uniform rule; income sources; single-peaked preferences.;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D33 - Microeconomics - - Distribution - - - Factor Income Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty

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