Economics 321: Public Economics Prof. Marika Cabral TA: Katherine Keisler Fall 2017 UT Austin Problem Set 3 (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. 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? 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? b. Will majority voting generate consistent outcomes in this case? Why or why not? 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. b. Suppose that Boomtown chooses to purchase 150 units of park maintenance. Draw the town’s indifference curve for this choice. 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.5. [Ch 10] Think about two public goods—public schools and food assistance for needy families. Consider the implications of the Tiebout model. Which of the goods is more efficiently provided locally? Which is more efficiently provided centrally? Explain. 6. [Ch 10] 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 – 3P, 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 – 6P. a. If the cost of a unit of education is $10 per unit, how many units of education will the two types of town demand? 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 type B towns. In particular, type A towns by $5 for each unit of education they provide, and they give type B towns $5 for each unit of education they provide. What are the new tax prices of education in the two towns? How many units of education do the towns now purchase? c. Delaland wants to completely equalize the units of education across towns by taxing type A towns for each unit of education they provide and subsidizing type B towns for each unit of education they provide. It wants to do this in such a way that the taxes on type A towns are just enough to finance the subsidies on type B towns. If there are 4 type A towns for every 5 type B towns, how big a tax should Delaland levy on type A towns? How big a subsidy should they provide to type B towns? 7. [Ch 11] Suppose that a family with one child has $30,000 per year to spend on private goods and education, and further suppose that all education is privately provided. Draw this family’s budget constraint. Suppose now that an option of free public education with spending of $5,000 per pupil is introduced to this family. Draw three different indifference curves corresponding to the following three situations: (a) a free public education would increase the amount of money that is spent on the child’s education; (b) a free public education would decrease the amount of money that is spent on the child’s education; and (c) a free public education would not affect the amount of money spent on the child’s education. 8. [Ch 11] Suppose you want to evaluate the effectiveness of vouchers in improving educational attainment by offering a voucher to any student in a particular town who asks for one. What is wrong with simply comparing the educational performance of the students receiving vouchers with those who do not receive vouchers? What would be a better way to study the effectiveness of vouchers? 9. [Ch 11] Many state constitutions explicitly require that states provide an “adequate” level of school funding. How might raising this level of “adequacy” actually lead to reduced overall levels of educational spending?10. [Ch 12] Suppose that you have a job paying $100,000 per year. With a 10% probability, next year your wage will be reduced to $80,000 for the year. a. What is your expected income next year? b. Suppose that you could insure yourself against the risk of reduced consumption next year. What would the actuarially fair insurance premium be? 11. [Ch 12] Small companies typically find it more expensive, on a per employee basis, to buy health insurance for their workers, as compared with larger companies. Similarly, it is usually less expensive to obtain health insurance through an employer-provided plan than purchasing it directly from an insurance company—even if your employer requires you to pay the entire premium. Use the ideas from this chapter to explain these observations. 12. [Ch 12] Chimnesia has two equally sized groups of people: smokers and nonsmokers. Both types of people have utility U = ln(C), where C is the amount of consumption that people have in any period. So long as they are healthy, individuals will consume their entire income of $50,000. If they need medical attention (and have no insurance), they will have to spend $20,000 to get healthy again, leaving them with only $30,000 to consume. Smokers have a 15% chance of requiring major