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Does Less Inequality among Households Mean Less Inequality among Individuals?

  • Eugenio Peluso


    (THEMA, Université de Cergy-Pontoise)

  • 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 Institut d'economie publique (IDEP), Marseille, France in its series IDEP Working Papers with number 0407.

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Length: 35 pages
Date of creation: Apr 2004
Date of revision: Jun 2004
Handle: RePEc:iep:wpidep:0407
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  1. Haddad, Lawrence & Kanbur, Ravi, 1990. "How Serious Is the Neglect of Intra-Household Inequality?," Economic Journal, Royal Economic Society, vol. 100(402), pages 866-81, September.
  2. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
  3. 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).
  4. 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.
  5. Yaari, Menahem E, 1977. "A Note on Separability and Quasiconcavity," Econometrica, Econometric Society, vol. 45(5), pages 1183-86, 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. Moyes, Patrick, 1987. "A new concept of Lorenz domination," Economics Letters, Elsevier, vol. 23(2), pages 203-207.
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