Chapter 2: Income Standards, Inequality, and Poverty
Transfer Principle: If distribution x' is obtained from distribution x by a regressive transfer, then W(x') < W(x). If distribution x" is obtained from distribution x by a progressive transfer, then W(x") > W(x). One justification of the transfer principle invokes a utilitarian form of welfare function that takes welfare to be the average level of (indirect) utility in society and assumes that all utility functions are identical and strictly increasing (see Atkinson 1970). In this context, the intuitive assumption of diminishing marginal utility yields the transfer principle. Diminishing marginal utility requires that the loss to the poorer giver is greater than the gain to the richer receiver because of a regressive transfer. Hence, overall welfare falls, or, equivalently, the gain to the poorer receiver is greater than the loss to the richer giver because of a progressive transfer—hence, welfare rises. The fifth property is normalization. This property requires that if incomes are the same across all people in a society, then the income standard should be represented by that commonly held income. This property is intuitive. For example, let the income vector of a three-person society be ($20k, $20k, $20k). Then the income standard should be $20k. Normalization: For the income distribution, x = (b, b, …, b), W(x) = b. The sixth property is linear homogeneity. This property requires that if an income distribution is obtained from another income distribution by changing the incomes by some proportion, then the income standard should also change by the same proportion. For example, if everyone’s income in a society doubles, then the society’s income standard doubles. If everyone’s income is halved, then the society’s income standard is halved. Linear Homogeneity: If distribution x' is obtained from distribution x such that x' = cx where c > 0, then W(x') = cW(x). Subgroup consistency is the final property presented here. In some empirical applications, there is a natural concern for certain identifiable population subgroups as well as for the overall population. We might be interested, for instance, in the performances of various states or subregions of a country to understand how the overall improvement in income standard is distributed across those regions.
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