By Sykuta M.E., Cook M.L.

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IFS coincides with the generalized entropy family when υ¯ = 1, and the limiting indices ITML and ITE are obtained, respectively, when c¯ = 0, υ¯ = 1 and c¯ = 1, υ¯ = 1. ¯ The path independent indices arise, respectively, if c¯ = 0, υ¯ = 0 and c¯ = 0, υ¯ = c. Foster and Ok (1999) presented a picture of the potential conflict between the variance of logarithms and the Lorenz criterion. 64) is the Theil mean logarithmic deviation index. Blackorby et al. (1981) argued that between-group inequality can alternatively be defined as the inequality that results if each person receives his subj group’s Atkinson-Kolm-Sen representative income.

XJf 1nJ ), (iii) (x f 1n ). The overall income vector is given by (i), (ii) eliminates within-group inequality by social indifference and (iii) eliminates between-group inequality with social indifference. It may be worthwhile to mention here the Population Substitution Principle which requires j replacement of income of each member of a subgroup j by x f with a matter of 40 1 The Measurement of Income Inequality independence(Blackorby and Donaldson, 1984a). Given the basic assumptions about the social welfare function, we have x fj = (ξˆ )−1 (∑i∈SG j ξˆ (xi )/n j ), where SG j is the set of persons in subgroup j and the real valued function ξˆ defined on the set of positive real numbers is continuous, increasing and strictly concave.

This means that a unit consistent index is appropriate for comparison of inequality across countries that have different currency units. Thus, if the income distribution in country I is more unequal than that in country II when incomes are expressed in currency of country I, then a reversal of inequality ranking when incomes are expressed in currency of country II is regarded as a violation of unit consistency. An inequality index I : Γ+ → R1 is called unit consistent if for all x, y ∈ Γ+ , I(x) < I(y) implies I(cx) < I(cy), where c > 0 is any scalar.

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