Homework Answer 5

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Economics 1480 Answer key #5 1) Rosen Chapter 12: problem 2 a. To maximize W, set marginal utilities equal; the constraint is Is + Ic = 100. So, 400 - 2Is = 400 - 6Ic. substituting Ic = 100 - Is gives us 2Is = 6 (100 - Is ). Therefore, Is = 75, Ic = 25. b. If only Charity matters, then give money to Charity until MUc = 0 (unless all the money in the economy is exhausted first). So, 400-6 Ic = 0; hence, Ic = 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, MUs. 0 if Is = 100; hence, giving all the money to Simon is optimal. (In fact, we would like to give him up to $200.) c. MUs = MUc for all levels of income. Hence, society is indifferent among all distributions of income. 2) Rosen Chapter 12: problem 3 Suppose the government is initially providing an in-kind benefit of 10 units of free public transportation, worth $2 each, so the cost of the subsidy is $20. Without the subsidy, income is $40. With no subsidy, the consumer maximizes utility at point A, and with an in-kind benefit of 10 units of free public transportation, the consumer maximizes utility at point B. A cash subsidy equal to $20 would allow the consumer to reach point B as well, so the government could convert an in-kind subsidy valued at $20 to a cash subsidy of $20 and leave people equally well off. Other goods B A 10 20 30 Public Another possibility is that the utility-maximizing point for a cash subsidy differs from the utility-maximizing point for an in-kind subsidy, as illustrated in the next graph. In this case, an in-kind subsidy, costing $20, would allow the consumer to move from point A’ to point C’, while a cash subsidy of $20 would

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