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Does less inequality among households mean less inequality among individuals?

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  • Peluso, Eugenio
  • Trannoy, Alain

Abstract

Consider an income distribution among households of the same size in which individuals, equally needy from the point of view of an ethical observer, are treated unfairly. Individuals are split into two types, the dominant and the dominated. We look for conditions under which welfare and inequality quasi-orders established at the household level still hold at the individual one. A necessary and sufficient condition for the Generalized Lorenz test is that the income of dominated individuals is a concave function of the household income: individuals of poor households have to stand more together than individuals of rich households. This property also proves to be crucial for the preservation of the Relative and Absolute Lorenz criteria, when the more egalitarian distribution is the poorest. Extensions to individuals heterogeneous in needs and more than two types are also provided.
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  • Peluso, Eugenio & Trannoy, Alain, 2007. "Does less inequality among households mean less inequality among individuals?," Journal of Economic Theory, Elsevier, vol. 133(1), pages 568-578, March.
    • Handle: RePEc:eee:jetheo:v:133:y:2007:i:1:p:568-578
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    References listed on IDEAS

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    1. Couprie, Hélène & Peluso, Eugenio & Trannoy, Alain, 2010. "Is power more evenly balanced in poor households?," Journal of Public Economics, Elsevier, vol. 94(7-8), pages 493-507, August.
    2. Donni, Olivier & Molina, José Alberto, 2018. "Household Collective Models: Three Decades of Theoretical Contributions and Empirical Evidence," IZA Discussion Papers 11915, Institute of Labor Economics (IZA).
    3. Eugenio Peluso & Alain Trannoy, 2012. "The Cake-eating problem: Non-linear sharing rules," Working Papers 26/2012, University of Verona, Department of Economics.
    4. Olivier Bargain, 2008. "Normative evaluation of tax policies: from households to individuals," Journal of Population Economics, Springer;European Society for Population Economics, vol. 21(2), pages 339-371, April.
    5. M Denuit & L Eeckhoudt & O Jokung, 2013. "Non-differentiable transformations preserving stochastic dominance," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(9), pages 1441-1446, September.
    6. Helene Couprie & Eugenio Peluso & Alain Trannoy, 2007. "From Household to Individual Welfare Comparisons: A Double Concavity Test," IDEP Working Papers 0701, Institut d'economie publique (IDEP), Marseille, France, revised 01 2007.
    7. Eugenio Peluso & Alain Trannoy, 2012. "Preserving dominance relations through disaggregation: the evil and the saint," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 633-647, July.
    8. Elena Bárcena-Martín & Maite Blázquez & Santiago Budría & Ana I. Moro-Egido, 2017. "Child and Household Deprivation: A Relationship Beyond Household Socio-demographic Characteristics," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 132(3), pages 1079-1098, July.
    9. Mangiavacchi, Lucia & Piccoli, Luca, 2011. "Improving the measurement of child welfare in the context of intra-household inequality," Children and Youth Services Review, Elsevier, vol. 33(2), pages 226-232, February.
    10. Lucia Mangiavacchi & Luca Piccoli, 2009. "Child welfare and intra-household inequality in Albania," Working Papers 149, ECINEQ, Society for the Study of Economic Inequality.
    11. Martina Menon & Elisa Pagani & Federico Perali, 2016. "A class of individual expenditure functions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 291-305, October.
    12. Gao, Jianwei & Zhao, Feng, 2017. "Sufficient conditions of stochastic dominance for general transformations and its application in option strategy," Economics Discussion Papers 2017-40, Kiel Institute for the World Economy (IfW Kiel).
    13. Alessandra Michelangeli & Eugenio Peluso & Alain Trannoy, 2011. "Detecting a change in wealth concentration without the knowledge of the wealth distribution," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(3), pages 373-391, September.
    14. Martina Menon & Elisa Pagani & Federico Perali, 2012. "A Characterization of Collective Individual Expenditure Functions," Working Papers 20/2012, University of Verona, Department of Economics.

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    More about this item

    JEL classification:

    • D13 - Microeconomics - - Household Behavior - - - Household Production and Intrahouse Allocation
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

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