Abstract
An indicator of the income distribution of a country is the Gini coefficient.1 This coefficient can be computed with the help of the Lorenz curve.2 First we shall show how this curve is constructed. Suppose the following distribution of income:
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C. Gini, 1912. Variabilità e mutibilità . In: C. Gini, 1955. Memorie di metodologia statistica: Vol. 1: Variabilità e concentrazione. Libreria Eredi Virgilio Veschi, Rome.
M.O. Lorenz, 1905. Methods for measuring concentration of wealth. Journal of the American Statistical Association, 9, pp. 209–219. The Lorenz curve is also called Lorenz-Gini curve, because both authors developed the idea independently.
An important thing to notice here is that, in this case, the Gini coefficient has to measure the distribution of primary wages. One cannot maximize welfare by equalizing secondary wages (by taxing or otherwise). The important point to stress is that marginal products of different kinds of labour are equal in the optimum. A tool that may contribute to this end is education.
In the real world this can only be approached, for example, by adapting the education system such that students are guided toward the specialization with high marginal productivity. The market itself is a tool to that end. Higher wages in certain sectors attract more labour than sectors with relatively low wages. However, differences in wages will always exist. Certain types of labour remain scarce because they require relatively more skill and/or natural talents (football players, musicians etc.)
I derived before:. This is the same as g = 0. Proof: g = 0, so: and. So
Of course this proof can be extended to an unspecified number of branches and types of labour.
Of course it is possible to extend the analysis to more than two persons.
For the positive relation between income and environmental research and development, see: Komen R., S. Gerkin and H. Folmer, 1997. Income and environmental RD: some empirical evidence from OECD countries. Accepted for Environment and Development Economics.
If γ1 = βγ2, then. Now, if the number of the groupes is equal the gini coefficient is: (see the beginning of this chapter).
M. Blaug, 1985. Great Economists since Keynes. Wheatsheaf, Brighton.
The first order conditions for minimum diseconomies are the same as for maximum welfare in the previous section. Further it is assumed that all agents are identical. In that case, in terms of the previous section: γ2+ δ2α2 = γ1 + δ1α1. This means that in the optimum the gini coefficient g must be 0 and that D is an increasing function of g.
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© 1998 Springer Science+Business Media Dordrecht
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Heijman, W.J.M. (1998). Income Distribution. In: The Economic Metabolism. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5038-5_9
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DOI: https://doi.org/10.1007/978-94-011-5038-5_9
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