Chapter 2: Income Standards, Inequality, and Poverty
poverty line, or between two moderately poor people, who are much closer to the poverty line. Should the effect of transfer, no matter where it takes place, have the same effect on the poverty level? We elaborate this situation with an example. Consider the five-person income vector x = ($80, $100, $800, $50, 000, $70,000). Let the poverty line be set at $1,050. Then the first four people are identified as poor because their incomes are below the poverty line. First, suppose $10 is transferred from the second person to the first person. Then the post-transfer income vector is x' = ($90, $90, $800, $1,000, $50,000, $70,000). Transferring 10 percent of the second person’s income has increased the first person’s income by 12.5 percent. Suppose, instead, that the same $10 transfer takes place between the third and the fourth persons, who are also poor. The post-transfer income vector is x'' = ($80, $100, $810, $990, $50,000, $70,000), where transferring 1 percent of the fourth person’s income increases the third person’s income by 1.25 percent. This transfer makes hardly any difference in the large pool of income of the two richer poor people. Therefore, one might feel that a transfer of the same amount between two extreme poor and two richer poor should not have the same effect on the society’s overall poverty. The third dominance property, transfer sensitivity, requires a poverty measure to be more sensitive to a transfer between poor people at the lower end of the income distribution of the poor. In other words, this property requires that a poverty measure should change more when a transfer takes place between two extremely poor people than between two richer poor people. In terms of the example above, the level of deprivation should be lower in x' than in x''. Suppose the initial income distribution is x and distribution x" is obtained from distribution x by a progressive (or regressive) transfer between two extremely poor people. Suppose further that distribution x" is obtained from distribution x by a progressive (or regressive) transfer of the same amount between two richer poor people. The following is the transfer sensitivity property:
Transfer Sensitivity: A poverty measure that satisfies transfer sensitivity places greater emphasis on progressive (or regressive) transfers at the lower end of the distribution of the poor than at the upper end of the distribution of the poor; so P(x'; z) < (>) P(x"; z).
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