Consider a society with two people, Ebenezer and Bob. Social welfare is given by: w = HE + U3, where 1],; is Ebenezer's utility and UH is Bob's utility. They have identical utility functions, where the marginal of utility of income diminishes with income: MUE : 3460 7 0.0215 and M113 : 3460 7 0.0213, where [E is Ebenezer's income and IE is Bob's income. Finally. Ebenezer is endowed with $100.000 of wealth, whereas Bob has $0. Under the four assumptions listed above, half of Ebenezer's wealth should be taxed and transfen'ed to Bob so that each has $50,000 of income. a. [2 points] Suppose that social welfare is not strictly utilitarian. Ebenezer is kind of a jerk, so society places twice as much weight on Bob's utility: W : HE + 2 - UH. When you take a dollar from Ebenezer, social welfare decreases by M U 5. But when you give that dollar to Bob, social welfare increases by 2 ' MUE. What is the optimal distribution of income now? (Hint: The social welfarefunctian has changedfrum what we considered in Class. But there's still only $100, 000 m go around; therefore, it is still the case that 1,; + IE : 100.000.) [2 points] Go back to assuming that social welfare is stn'ctly utilitarian. However, Ebenezer likes money more than Bob. Ebenezer's marginal utility of income is still M US : 3460 7 0.021}, but Bob's is lower and given by MUB = 2860 7 0.0213. What is the optimal distn'bution of income now? (Hint: Unlike the example in class, the two people have rlinerent marginal utiliryirlcans. But there '5 still only $100,000 to go around; therefore, it is still the case that IE + [B : 100.000.) [2 points] Go back to assuming that Ebenezer and Bob have the same utility functions. However, both have a constant mar _ina.l utili of income ' _. = 34-60. What is the ontinJal [2 points] Go back to assuming that Ebenezer and Bob have the same utility functions. However, both have a constant marginal utility of income given by M UE : M U3 : 3460. What is the optimal distribution of income now? (Him: The two people have a constant marginal utility of income, whereas we considered a diminishing marginal utility ofincome in class. But there's still only $100,000 to go around; therefore, it is still the case that IE + 13 = 100,000.) [2 points] Go back to assuming that Ebenezer and Bob have the same diminishing marginal utility function. (That is. MUE : 3460 7 0.02IE and MUB : 3460 7 0.0213.) However. the total amount of income is no longer fixed. Every $1.00 transfen'ed to Bob costs Ebenezer $1.20. Where the additional $0.20 of cost comes in the form of excess burden and administrative costs. When you give a dollar to Bob. social welfare increases by M UR. But in order to get that dollar, $1.20 is taken from Ebenezer. which implies that social welfare decreases by 1.2 - M U5. What is the optimal distribution of income now? Page 3 of4 (Hint: There is only a fatal af$100, 000 to go around Ifu'e lefEbenezer keep everything. For every $1.00 that we transfer to Bob, the total amount of wealth available decreases by $0. 20; therefore, IE + 13 : 100,000 7 0.2 '15.)
