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9. Combining the results for dIG and dÎ we get: dÎ dIG = 1 y yk > 0 Proof. dÎ dI > 0 for the Atkinson Index. By the principle of transfers of inequality measures, a transfer from a poor to a richer household must increase inequality (cf. Cowell, 2000). Thus, we have that dIA > 0 when the transfer Î is applied.20 For instance, using the same deïnition of the transfer Î as above and equation (9), we obtain: âIA âÎ = â1 1 â Î n h yh y 1âÎ Î 1âÎ 1 â Î ny1âÎ yh + Î âÎ â yh+Î â Î âÎ
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