# Chap007 - Part 2 Analysis of Public Expenditure Chapter 7...

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Part 2 – Analysis of Public Expenditure Chapter 7 – Income Redistribution: Conceptual Issues 1. Utilitarianism suggests that social welfare is a function of individuals’ utilities. Whether the rich are vulgar is irrelevant, so this part of the statement is inconsistent with utilitarianism. On the other hand, Stein’s assertion that inequality per se is unimportant is inconsistent with utilitarianism. 2. a. To maximize W, set marginal utilities equal; the constraint is I s + I c = 100. So, 400 - 2I s = 400 - 6I c. substituting I c = 100 - I s gives us 2I s = 6 (100 - I s ). Therefore, I s = 75, I c = 25. b. If only Charity matters, then give money to Charity until MU c = 0 (unless all the money in the economy is exhausted first). So, 400-6 I c = 0; hence, I c = 66.67. Giving any more money to Charity causes her marginal utility to become negative, which is not optimal. Note that we don’t care if the remaining money (\$33.33) is given to Simon or not. If only Simon matters, then, proceeding as above, MU s. 0 if I s = 100; hence, giving all the money to Simon is optimal. (In fact, we would like to give him up to \$200.) c. MU s = MU c for all levels of income. Hence, society is indifferent among all distributions of income. 3. The main conceptual problem with the poverty gap is that it doesn’t account for the income effect on labor force participation rates. The poverty gap is calculated assuming there are no behavioral responses; e.g., that labor income would remain unchanged even after the income was transferred to the poor population, but economic theory predicts that this will not be so. In fact, if the poor household were given enough income to bring it out of poverty, we would believe that the household would work less as a result of receiving this transfer. This complicates the analysis, of course, because once the household works less, then it will generate less labor income, thus lowering its overall

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Chap007 - Part 2 Analysis of Public Expenditure Chapter 7...

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