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Inequality, welfare and monotonicity

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  • Amiel, Yoram
  • Cowell, Frank

Abstract

We stablish a general relationship between the standard form of the individualistic social-welfare function and the "reduced-form" version that is expressed in terms of inequality and mean income. This shows the relationship between the property of monotonicity and the slope of the equity-efficient trade-off. Particularly simple results are available for a large class of inequality measures that includes the Gini. These results do not require differentiability of the social-welfare function.

Suggested Citation

  • Amiel, Yoram & Cowell, Frank, 1997. "Inequality, welfare and monotonicity," LSE Research Online Documents on Economics 2222, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:2222
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    References listed on IDEAS

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    1. Chipman, John S., 1974. "The welfare ranking of Pareto distributions," Journal of Economic Theory, Elsevier, vol. 9(3), pages 275-282, November.
    2. Amiel, Yoram & Cowell, Frank, 1994. "Monotonicity, dominance and the Pareto principle," Economics Letters, Elsevier, vol. 45(4), pages 447-450, August.
    3. Dagum, Camilo, 1990. "On the relationship between income inequality measures and social welfare functions," Journal of Econometrics, Elsevier, vol. 43(1-2), pages 91-102.
    4. Porath Elchanan Ben & Gilboa Itzhak, 1994. "Linear Measures, the Gini Index, and The Income-Equality Trade-off," Journal of Economic Theory, Elsevier, vol. 64(2), pages 443-467, December.
    5. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    6. Donaldson, David & Weymark, John A., 1983. "Ethically flexible gini indices for income distributions in the continuum," Journal of Economic Theory, Elsevier, vol. 29(2), pages 353-358, April.
    7. Newbery, David, 1970. "A theorem on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 264-266, September.
    8. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    9. Creedy, John & Wilhelm, Mark, 2002. "Income Mobility, Inequality and Social Welfare," Australian Economic Papers, Wiley Blackwell, vol. 41(2), pages 140-150, June.
    10. Yaakov Kondor, 1975. "Value Judgements Implied By The Use Of Various Measures Of Income Inequality," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 21(3), pages 309-321, September.
    11. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
    12. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    13. Chakravarty, Satya R, 1988. "Extended Gini Indices of Inequality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(1), pages 147-156, February.
    14. Kondor, Yaakov, 1975. "Value Judgements Implied by the Use of Various Measures of Income Inequality," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 21(3), pages 309-321, September.
    15. Blackorby, Charles & Donaldson, David, 1980. "A Theoretical Treatment of Indices of Absolute Inequality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 107-136, February.
    16. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    17. Blackorby, Charles & Donaldson, David, 1978. "Measures of relative equality and their meaning in terms of social welfare," Journal of Economic Theory, Elsevier, vol. 18(1), pages 59-80, June.
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    More about this item

    Keywords

    Inequality; social welfare; monotonicity;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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