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Equality among Unequals

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  • Mathieu Faure

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Nicolas Gravel

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper establishes an equivalence between three incomplete rankings of distributions of income among agents that are vertically differentiated with respect to some other non-income characteristic (health, household size, etc.). The first ranking is that associated with the possibility of going from one distribution to the other by a finite sequence of income transfers from richer and more highly ranked agents to poorer and less highly ranked ones. The second ranking is the unanimity of all comparisons of two distributions made by a utilitarian planer who assumes that agents convert income into utility by the same function exhibiting a marginal utility of income that is decreasing with respect to both income and the source of vertical differentiation. The third ranking is the Bourguignon (1989) ordered poverty gap dominance criterion.

Suggested Citation

  • Mathieu Faure & Nicolas Gravel, 2017. "Equality among Unequals," Working Papers halshs-01430195, HAL.
    • Handle: RePEc:hal:wpaper:halshs-01430195
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01430195
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    References listed on IDEAS

    as
    1. Fields, Gary S & Fei, John C H, 1978. "On Inequality Comparisons," Econometrica, Econometric Society, vol. 46(2), pages 303-316, March.
    2. Ebert, Udo, 1997. "Social Welfare When Needs Differ: An Axiomatic Approach," Economica, London School of Economics and Political Science, vol. 64(254), pages 233-244, May.
    3. Gravel, Nicolas & Moyes, Patrick, 2012. "Ethically robust comparisons of bidimensional distributions with an ordinal attribute," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1384-1426.
    4. Stephen P. Jenkins & Peter J. Lambert, 1993. "Ranking Income Distributions When Needs Differ," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 39(4), pages 337-356, December.
    5. Nicolas Gravel & Patrick Moyes & Benoît Tarroux, 2009. "Robust International Comparisons of Distributions of Disposable Income and Regional Public Goods," Economica, London School of Economics and Political Science, vol. 76(303), pages 432-461, July.
    6. Decancq, Koen, 2012. "Elementary multivariate rearrangements and stochastic dominance on a Fréchet class," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1450-1459.
    7. N. Gravel & Patrick Moyes & B. Tarroux, 2008. "Robust international comparisons of distributions of disposable income and access to regional public goods," Post-Print hal-00157357, HAL.
    8. David Levhari & Jacob Paroush & Bezalel Peleg, 1975. "Efficiency Analysis for Multivariate Distributions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(1), pages 87-91.
    9. Fleurbaey, Marc & Hagnere, Cyrille & Trannoy, Alain, 2003. "Welfare comparisons with bounded equivalence scales," Journal of Economic Theory, Elsevier, vol. 110(2), pages 309-336, June.
    10. Bourguignon, Francois, 1989. "Family size and social utility : Income distribution dominance criteria," Journal of Econometrics, Elsevier, vol. 42(1), pages 67-80, September.
    11. André Decoster & Erwin Ooghe, 2006. "A Bounded Index Test To Make Robust Heterogeneous Welfare Comparisons," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 52(3), pages 361-376, September.
    12. Larry G. Epstein & Stephen M. Tanny, 1980. "Increasing Generalized Correlation: A Definition and Some Economic Consequences," Canadian Journal of Economics, Canadian Economics Association, vol. 13(1), pages 16-34, February.
    13. Jenkins, Stephen P & Lambert, Peter J, 1993. "Ranking Income Distributions When Needs Differ," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 39(4), pages 337-356, December.
    14. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
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    Cited by:

    1. Magdalou, Brice, 2021. "A model of social welfare improving transfers," Journal of Economic Theory, Elsevier, vol. 196(C).
    2. Francesco Andreoli & Claudio Zoli, 2020. "From unidimensional to multidimensional inequality: a review," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 5-42, April.

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    More about this item

    Keywords

    equalization; transfers; heterogenous agents; poverty gap; dominance; utilitarianism;
    All these keywords.

    JEL classification:

    • D30 - Microeconomics - - Distribution - - - General
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty

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