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UT ECO 321 - Problem Set 3 Solutions

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1. The hypothetical sport of Major League Calvinball uses what is known as a 5–3–1 system to vote for the league’s Most Valuable Player (MVP) in each league. In a 5–3–1 system, each voter gets to vote for three different players they consider worthy of the award. Their first-place candidate gets 5 points, their second-place candidate gets 3 points, and their third-place candidate gets 1 point. Points are then added up across all voters, and the player with the most total points wins the award. Suppose there are three voters—Neyer, Law, and Phillips—and five potential candidates for the award— Alex, David, Raffy, Manny, and Mario. The table below shows how each voter ranks the candidates. Raffy is embroiled in a substance abuse scandal. The “guilty” or “in-nocent” verdict will come out the day before voting, and a guilty verdict will ban him from being voted on as an MVP and all players ranked below him on a given voter’s ballot will be “bumped up” one spot on that ballot. a) Who will win the MVP if Raffy is found innocent? If Raffy is found innocent, David gets 10 points (5 from Neyer and 5 from Law). Alex gets 9 points (3 from each voter), Raffy gets 7 points, and Manny gets 1 point. David wins the MVP. b) Who will win the MVP if Raffy is found guilty? If Raffy is found guilty, David still gets 10 points. But Alex now gets 11 points: 5 from Phillips and 3 each from Neyer and Law. So Alex wins the MVP. c) What problem with consistent aggregation does this illustrate? This illustrates a violation of the independence of irrelevant alternatives. Raffy wasn’t going to win the competition either way, but the winner changes depending on whether he is in the competition or not 2. Carrboro has three equal-sized groups of people: (1) type A people consistently prefer more police protection to less; (2) type B people prefer high levels of police protec-tion to low levels and they prefer low levels to medium levels; (3) type C people prefer medium levels to low levels, which they in turn prefer by a modest amount to high levels. A. Which types of people have single-peaked preferences? Which have multipeaked preferences?Types A and C have single-peaked preferences, with peaks at “high” and “medium” respectively. Type B has multiple-peaked preferences, with peaks at “high” and “low” and a dip at “medium.” B. Will majority voting generate consistent outcomes in this case? Why or why not? Majority voting does not usually generate consistent outcomes when some voters have preferences that fail to be single peaked. But they do happen to generate consistent out-comes in this case. If “high” and “low” are the two options on the ballot, “high” will win, since types A and B will vote for it. Similarly “high” wins when “high” and “medium” are the two options on the ballot. When “low” and “medium” are on the ballot, “medium” wins, since types A and C will vote for it. Finally, when all three are on the ballot, types A and B will both vote for “high,” which will therefore win. Notice that there are no cycles, so the voting outcomes are, in fact, consistent. The decisions coincide with those that would be made by a society that prefers “high” to “medium” and “medium” to “low.” 3. The city of Minnegan is considering two alternative methods of funding local road construction, matching grants and block grants. In the case of the matching grant, Minnegan will spend $1 for every $1 spent by localities. a. What is the price of an additional dollar of local spending in each case? The “price” of spending $1 on road construction is reduced to 50¢ by the matching grant. The other 50¢ of the $1 spent comes from the matching grant. The block grant would not change the relative price of road construction. Since block grant money can be used to purchase anything, the price, or opportunity cost, of $1 worth of road construction is still $1. b. . Which of the two methods do you think would lead to higher levels of local spend-ing on roads? Explain your answer. Both grants will increase spending through the income effect: Minnegan is wealthier with either and is likely to spend more money on several projects, including roads. The matching grant reduces the relative cost of road construction, however, so in addition to the income effect, the substitution effect will induce more road building. The matching grant is more likely to lead to higher levels of spending on roads. 4. The state of Massachusetts recently ran an advertising campaign for the state lottery that claimed, “Even when you lose, you win.” The gist of the advertisement was that lottery revenue was used for particularly good ends like education. Suppose that lot-tery revenues are indeed earmarked for education. How would traditional economic theory evaluate the claim behind the ad campaign? How would an economist who be-lieved in the flypaper effect evaluate it? Traditional theory would suggest that the earmarking of lottery revenues for education is largely irrelevant. Simply saying that this revenue is used for that purpose does not mean that spending on education would be any different if the revenue was instead raised by an-other source such as taxation. That is, lottery revenue spending on education may simply crowd out othereducation spending, leading to no increase in total spending on education. If the flypaper effect is true, however, earmarks matter; according to the flypaper effect, money “sticks” where it is sent, so earmarking particular funds for education will have a much smaller crowding-out effect on other sources of education spending. 5. The state of Delaland has two types of town. Type A towns are well-to-do, and type B towns are much poorer. Being wealthier, type A towns have more resources to spend on education; their demand curve for education is Q = 100 – 2P, where P is the price of a unit of education. Type B towns have a demand curve for education that is given by Q = 100 – 5P. a. If the cost of a unit of education is $15 per unit, how many units of education will the two types of town demand? Type A towns will demand Q = 100 – 2(15) = 70 units of education, while type B towns will demand Q = 100 – 5(15) = 25 units of education. b. In light of the large discrepancies in educational quality across their two types of town, Delaland decides to redistribute from type A towns to


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