Economics 321: Public Economics Prof. Marika Cabral TA: Katherine Keisler Fall 2017 UT Austin Problem Set 3 Solution (due Mon October 23) 1. [Ch 9] In a recent study, Americans stated that they were willing to pay $70 billion to protect all endangered species and also stated that they were willing to pay $15 billion to protect a single species. Which problem with Lindahl pricing does this demonstrate? Explain. This illustrates the preference knowledge problem. Lindahl pricing requires an accurate measure of each individual’s marginal willingness to pay, but people often do not have a good idea of their own marginal willingness to pay for things that are not ordinarily bought or sold in the market. Endangered species protection is an abstract concept, so it is unlikely that people had thought about their willingness to pay for it before being surveyed. At $15 billion per species, all endangered species could not be protected for $70 billion. It appears that the respondents either overstated their willingness to pay to preserve one species or understated their willingness to pay to preserve all endangered species. 2. [Ch 9] Alfie, Bill, and Coco each value police protection differently. Alfie’s demand for the public good is Q = 60 – 5P, Bill’s demand is Q = 80 – 4P, and Coco’s demand is Q =100– 10P. If the marginal cost of providing police protection is $12.5, what is the socially optimal level of police provision? Under Lindahl pricing, what share of the tax burden would each of the three people pay? To answer these questions, first rewrite each demand so that P is expressed as a function of Q: Alfie: PA = 12 – 0.2Q; Bill: PB = 20 – 0.25Q; Coco: PC = 10 – 0.1Q. Adding each person’s willingness to pay yields PA + PB + PC = 42 – 0.55Q. The left-hand side gives the marginal social benefit of providing the Qth unit of the good. Setting this marginal benefit equal to the marginal cost gives the socially optimum level of provision: 42 – 0.55Q = 12.5, or Q = 53.64 When Q = 53.64, Alfie’s marginal benefit is 12 – 0.2(53.64) = 1.272 . Similarly, Bill’s marginal benefit is 20 – 0.25(53.64) = 6.59, and Coco’s is 10 – 0.1(53.64) = 4.636. Hence, Alfie’s share of the tax burden under Lindahl pricing is 1.272/12.5 ≈ 10.18%, and Bill and Coco’s shares are approximately 52.72% and 37.09%, respectively. 3. [Ch 9] 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 protection 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 multi-peaked 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.” 4. [Ch 10] The (identical) citizens of Boomtown have $3 million to spend either on park maintenance or private goods. Each unit of park maintenance costs $10,000. a. Graph Boomtown’s budget constraint. Boomtown can afford up to $3 million of the private good or up to 300 units ($3 million/$10,000) of park maintenance, with a constant trade-off of 1 unit of the private good for every $10,000 of the public good. The budget constraint, depicted in the graph in part b, is the line segment connecting ($3 million, 0) and (0, 300 units). b. Suppose that Boomtown chooses to purchase 150 units of park maintenance. Draw the town’s indifference curve for this choice. Boomtown’s indifference curve must be tangent to the budget constraint at the point ($1.5 million, 150 units), as shown in the following figure. c. Now suppose that the state government decides to subsidize Boomtown’s purchase of park maintenance by providing the town with 1 unit of maintenance for every 2 units the town purchases. Draw the new budget constraint. Will Boomtown purchase more or fewer units of park maintenance? Will Boomtown purchase more or fewer units of the private good? Illustrate your answer, and explain. This policy does not change the quantity of private goods Boomtown can afford. But for every 2 units of park maintenance Boomtowners now purchase they acquire a total of 3 units. So if they spend all their money on park maintenance, they can get a total of 450 units of park maintenance. The budget constraint thus rotates around the point ($3 million, 0) and intersects the vertical axis at (0, 450 units), as shown in the figure on the next page. The subsidy has both an income and a substitution effect. The income effect occurs because Boomtown can now afford to buy more of each good than the original choice of ($1.5 million,150 units). Assuming both are normal goods, this will lead Boomtown to choose more private goods as well as more park maintenance. The substitution effect occurs because the subsidy makes park maintenance cheaper in terms of private goods. This will make Boomtown purchase more park maintenance and fewer private goods. We therefore know that Boomtown will purchase more park maintenance, but it is unclear whether the town will purchase more or fewer private goods. In the following illustration, they choose to purchase more private goods, but the graph could be drawn the other