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Does less inequality among households mean less inequality among individuals ?

  • Eugenio Peluso
  • Alain Trannoy

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. Sudhir Anand and Amartya Sen, 1995. "Gender Inequality in Human Development: Theories and Measurement," Human Development Occasional Papers (1992-2007) HDOCPA-1995-01, Human Development Report Office (HDRO), United Nations Development Programme (UNDP).
  2. Haddad, Lawrence & Kanbur, Ravi, 1989. "How serious is the neglect of intrahousehold inequality ?," Policy Research Working Paper Series 296, The World Bank.
  3. Moyes, Patrick, 1987. "A new concept of Lorenz domination," Economics Letters, Elsevier, vol. 23(2), pages 203-207.
  4. Yaari, Menahem E, 1977. "A Note on Separability and Quasiconcavity," Econometrica, Econometric Society, vol. 45(5), pages 1183-86, July.
  5. 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.
  6. Udo Ebert, 1999. "Using equivalent income of equivalent adults to rank income distributions," Social Choice and Welfare, Springer, vol. 16(2), pages 233-258.
  7. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
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