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Social Welfare Functions and Income Distributions

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Efficiency and Equity in Welfare Economics

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 661))

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Abstract

Old welfare economics, Pigou (1920), considered social welfare as a cardinal notion, while new welfare economics,Little(1950) and Graaff (1957), consider social welfare as an ordinal notion.

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Notes

  1. 1.

    At the end of nineteenth century, Pareto was the first scholar to consider utility (he called it “ophelimity”) as an ordinal notion, then Robbins (1932, 1935) cogently argued the ordinal character of utility. Robbins expressly wrote: There is no means of testing the magnitude of A’s satisfaction as compared with B’s. (1935, pp. 139–140).

  2. 2.

    See, for instance, Arrow et al. (1960).

  3. 3.

    It is a well known fact that there are an infinite number of ways to generate a social welfare function from a given social preference relation.

  4. 4.

    Working directly with individual incomes bypasses a number of serious problems that occur when considering production. For instance the indivisibility of some goods, increasing returns to scale in production, externalities, non-convexities, … . It is obvious that general welfare economics must be concerned with such issues.

  5. 5.

    On social welfare functions and the axioms which they are required to satisfy, see D’Aspremont and Gevers (2002). Also remember that there are some economists who try to show the impossibility of criteria for aggregating preferences; see Gul and Pesendorfer (2007).

  6. 6.

    As usual in many branches of economic theory, the problem exists of the invulnerability to manipulation of an economic agent or coalition of agents when a social welfare function generates a social choice rule. On this see Campbell and Kelly (2006).

  7. 7.

    See, for instance, Nash (1950).

  8. 8.

    We can also qualify (2.1) as being neutral, but this adjective is too reductive.

  9. 9.

    In some sense, this undermines the ordinal character of W.

  10. 10.

    See Pollak (1971).

  11. 11.

    For instance, a government democratically elected by all citizens.

  12. 12.

    On problems of progressive income taxation and their redistributional effects see Lambert (1993, Chap. 6) and Lambert (1999). An early paper on the mathematical theory of optimum income taxation is Mirrlees (1971), who proposes decreasing marginal tax rates. A different viewpoint in favour of increasing marginal tax rates is presented by Diamond (1998).

  13. 13.

    The same result is obtained also for social welfare functions expressed by the Atkinson formulae (2.4) and by (2.5).

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Authors and Affiliations

  1. Dipto. Matematica, Università di Milano, Milano, Italy

    Prof. PierCarlo Nicola

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  1. Prof. PierCarlo Nicola
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Nicola, P. (2013). Social Welfare Functions and Income Distributions. In: Efficiency and Equity in Welfare Economics. Lecture Notes in Economics and Mathematical Systems, vol 661. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30071-4_2

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  • DOI: https://doi.org/10.1007/978-3-642-30071-4_2

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