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Does less inequality among households mean less inequality among individuals ?

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  • Eugenio Peluso
  • Alain Trannoy

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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Paper provided by THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise in its series THEMA Working Papers with number 2004-11.

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Date of creation: 2004
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Handle: RePEc:ema:worpap:2004-11

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  1. Haddad, L. & Kanbur, R., 1989. "How Serious Is The Neglectof Intra-Household Inequality?," Papers, Stockholm - International Economic Studies 450, Stockholm - International Economic Studies.
  2. Kanbur, Ravi & Haddad, Lawrence, 1994. "Are Better Off Households More Unequal or Less Unequal?," Oxford Economic Papers, Oxford University Press, vol. 46(3), pages 445-58, July.
  3. Udo Ebert, 1999. "Using equivalent income of equivalent adults to rank income distributions," Social Choice and Welfare, Springer, Springer, vol. 16(2), pages 233-258.
  4. Sudhir Anand and Amartya Sen, 1995. "Gender Inequality in Human Development: Theories and Measurement," Human Development Occasional Papers (1992-2007), Human Development Report Office (HDRO), United Nations Development Programme (UNDP) HDOCPA-1995-01, Human Development Report Office (HDRO), United Nations Development Programme (UNDP).
  5. Yaari, Menahem E, 1977. "A Note on Separability and Quasiconcavity," Econometrica, Econometric Society, Econometric Society, vol. 45(5), pages 1183-86, July.
  6. Moyes, Patrick, 1987. "A new concept of Lorenz domination," Economics Letters, Elsevier, Elsevier, vol. 23(2), pages 203-207.
  7. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
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Cited by:
  1. Olivier Bargain, 2008. "Normative evaluation of tax policies: from households to individuals," Journal of Population Economics, Springer, Springer, vol. 21(2), pages 339-371, April.
  2. Mangiavacchi, Lucia & Piccoli, Luca, 2011. "Improving the measurement of child welfare in the context of intra-household inequality," Children and Youth Services Review, Elsevier, Elsevier, vol. 33(2), pages 226-232, February.
  3. Alessandra Michelangeli & Eugenio Peluso & Alain Trannoy, 2011. "Detecting a change in wealth concentration without the knowledge of the wealth distribution," Journal of Economic Inequality, Springer, Springer, vol. 9(3), pages 373-391, September.
  4. Lucia Mangiavacchi & Luca Piccoli, 2009. "Child welfare and intra-household inequality in Albania," Working Papers 149, ECINEQ, Society for the Study of Economic Inequality.
  5. Martina Menon & Elisa Pagani & Federico Perali, 2012. "A Characterization of Collective Individual Expenditure Functions," Working Papers, University of Verona, Department of Economics 20/2012, University of Verona, Department of Economics.
  6. Couprie Helene, Peluso Eugenio and Trannoy Alain, 2009. "Is power more evenly balanced in poor households?," THEMA Working Papers 2009-11, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  7. Alain Trannoy & Eugenio Peluso, 2009. "Preserving Dominance Relations Through Disaggregation: The Evil and the Saint," Working Papers, University of Verona, Department of Economics 60/2009, University of Verona, Department of Economics.
  8. Eugenio Peluso & Alain Trannoy, 2005. "Do redistributive schemes reduce inequality between individuals?," Working Papers, University of Verona, Department of Economics 26, University of Verona, Department of Economics.
  9. Helene Couprie & Eugenio Peluso & Alain Trannoy, 2007. "From Household to Individual Welfare Comparisons: A Double Concavity Test," IDEP Working Papers, Institut d'economie publique (IDEP), Marseille, France 0701, Institut d'economie publique (IDEP), Marseille, France, revised 01 2007.
  10. Eugenio Peluso & Alain Trannoy, 2012. "The Cake-eating problem: Non-linear sharing rules," Working Papers, University of Verona, Department of Economics 26/2012, University of Verona, Department of Economics.

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