Suppose that there are n people in society, arranged (without loss of generality) in increasing order of income earned. Let x = (x₁, . . . , x_n) and y = (y₁, . . . , y_n) be two income distributions (with total incomes the same in the two cases).

(a) Show that the Lorenz curve for x must lie inside the Lorenz curve for y if (and only if)

for all k, with strict inequality for some k.

(b) (Extra credit.) Now suppose that the condition in part (a) does hold. Show that y can be attained from x by a sequence of regressive transfers. For details, see Fields and Fei [1978].

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k k Σ* Συ i=1 i=1