# Homework 5 Answer Key - Economics 1480 Answer key#5 1 Rosen...

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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 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.

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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. Another possibility is that the utility-maximizing point for a cash subsidy differs
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