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Inequality and Welfare

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Lectures on Inequality, Poverty and Welfare

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 685))

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Abstract

This chapter provides an integrated way of approaching inequality measurement from a normative viewpoint, by using the notion of social evaluation function, instead of that of social welfare function. A social evaluation function is a mapping that is defined directly on the space of income distributions, without going through the intermediate step of individual utilities. This notion permits extending the standard normative approach to inequality and provides a general framework in which all the inequality indices can be confronted in terms of the properties that imply on this social evaluation function. Besides, we introduce here the notion on multidimensional inequality and welfare, that applies when more than one relevant dimension is involved. We illustrate this venue by means of the Human Development Index.

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Notes

  1. 1.

    He also assumes monotonicity (i.e., higher aggregate income implies higher social welfare), but this is a property we may be willing to drop to give more weight to equity considerations.

  2. 2.

    We assume implicitly that all incomes are different to avoid problems with differentiability in the SEF.

  3. 3.

    Let us mention the United Nations 1954 report on the standards of living, the “basic needs approach” fostered by the International Labour Organization in 1974, the Physical Quality of Life Index (PQLI), due to Morris (1979) [reformulated by Ram (1982)] or that proposed by the Daj Hammarskjöld Foundation. For more recent critiques, see Boarini, Johansson, and Mira d’Ercole, (2006), Stiglitz, Sen, and Fitoussi (2009) or Fleurbaey (2009).

  4. 4.

    There is still the possibility of not aggregating the different dimensions, either by using a dashboard of variables or applying dominance criteria to get partial orderings (e.g., Kolm (1977),

    1. (a)

      How should we treat the cross effects among dimensions on individuals and society?

    2. (b)

      How should we weight the different dimensions?

    3. (c)

      How should we choose the right units of measurement?

    Atkinson and Bourguignon (1982); see Savaglio (2006) for a discussion).

  5. 5.

    Some key contributions include Maasoumi (1986, 1989), Bourguignon and Chakravarty (1999), Tsui (1995, 1999), Weymark (2004), Gajdos and Weymark (2005).

  6. 6.

    For a discussion on different techniques for setting weights for multidimensional indices, see Decancq and Lugo (2013).

  7. 7.

    See Osberg (1985), Anand and Sen (1994a, 1994b), Hicks (1997), Phillipson and Soares (2001), Osberg and Sharpe (2002), Chakravarty (2003), Becker, Philipson, and Soares (2005), Foster et al. (2005), Herrero et al. (2010a, 2010b) for a critical appraisal and some alternative formulations.

  8. 8.

    The only reasonable argument that I know to treat income differently is due to Zambrano (2014), who interprets that health and education are direct capabilities whereas income is only an indirect one that refers to the command over resources.

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Authors and Affiliations

  1. Department of Economics, Universidad Pablo de Olavide, Seville, Spain

    Antonio Villar

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  1. Antonio Villar
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Villar, A. (2017). Inequality and Welfare. In: Lectures on Inequality, Poverty and Welfare. Lecture Notes in Economics and Mathematical Systems, vol 685. Springer, Cham. https://doi.org/10.1007/978-3-319-45562-4_6

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