IMPACT OF TAXES AND TRANSFERS

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Enami, Lustig, Aranda, No. 25, November 2016 It can be shown that (9) L X (p) = (1 + b) C X+B (p) − b C B (p) which implies that (10) L X (p) ≥ C X+B (p) C X+B (p) ≥ C B (p). If we assume no re-ranking, that is, (11) −1 ≤ b’(x) where b’(x) is the increase in benefits that occurs as pre-transfer income X rises, the ranking of people by pre-transfer and post-transfer income does not change. Thus, equation 10 can be rewritten as (10)’ L X (p) ≥ L X+B (p) L X+B (p) ≥ C B (p). Under no reranking, incomes are less unequal after transfers than before if and only if transfers are distributed more equally than the income to which they apply. If the average transfer rate b(x) decreases with income everywhere, then transfers are distributed more equally than pretransfer income. This scenario is shown in figure 4. 20
Enami, Lustig, Aranda, No. 25, November 2016 Figure 4. A Progressive Transfer: Lorenz Curve of Pre-Transfer Income, Concentration Curve of an Equalizing Transfer, and Lorenz Curve of Post-Transfer Income For instance, although cash transfers are very unlikely to be regressive, this is not the case with subsidies, contributory pensions, and spending on tertiary education, which are sometimes regressive in the real world. An everywhere regressive transfer will fulfill the following condition: (10)’’ L X (p) ≤ L X+B (p) L X+B (p) ≤ C B (p) When 10’’ occurs, benefits will be unequalizing. However, equalizing transfers may not be pro-poor. As long as the relative size of the transfer declines with income, a transfer will be equalizing. In order to be pro-poor, however, the absolute size of the transfer also needs to decline with income (although not so much that the marginal benefit is less than −1). That is, the share of a transfer going to the rich can be higher than the share going to the poor even if a transfer is equalizing (or progressive). Figure 5 shows the concentration curve for a transfer that is both equalizing and pro-poor. 21
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IMPACT OF TAXES AND TRANSFERS

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