Fall 2007 Economics 431 Final Exam Prof. Hamilton

Transcription

1 Fall 2007 Economics 431 Final Exam Prof. Hamilton Name: Question 1. (25 points) On January 1, 1998, the State of California introduced a ban on smoking in public bars because of health risks to employees and non-smoking patrons. Can the optimal level of emissions for a pollutant ever be equal to zero? Briefly explain with aid of a diagram. Question 2. (25 points). Uncertainty and the Choice of Standards or Taxes Motor vehicles release nitrogen oxide ( NO X ) and volatile organic compounds ( VOCs ) that react with sunlight to produce ground-level ozone. Ground-level ozone is the primary ingredient in smog and can have harmful effects on human health and the environment. The state of California is considering a policy to control ground-level ozone pollution with one of two environmental policies: (1) a tax on gasoline; or (2) a standard on the quantity of gasoline service stations can sell. Suppose the marginal social cost per gallon of gasoline is known, but the government has only a rough estimate of consumer demand for gasoline. If the policy is to be determined based on the intersection between estimated demand for gasoline and marginal social cost, which of the two policies would you recommend? State your assumption(s) and justify your position with a diagram.

2 Question 3. (40 points). Suppose you are hired to set wastewater policy for the city of Los Osos. Consumers in Los Osos derive total private benefit of TPB = 50Q - 0.5Q 2, where Q is the quantity of wastewater. The total private cost of wastewater disposal is TPC = 5Q. Wastewater from residential septic tanks in Los Osos percolates into Morro Bay and harms birds, fish, and wildlife and damages increase in the amount of wastewater. The total external cost of wastewater is TEC = 5Q + 0.5Q 2 A. Find the competitive output level, Qc, and output price, Pc, in an unregulated market B. What is the socially-optimal (i.e., welfare maximizing) level, Q*, and what is the socially-optimal price, P*? C. Draw a diagram that shows the private and social equilibrium points and the deadweight loss (DWL) at the private market equilibrium. D. Calculate the level of the tax on wastewater disposal, t*, that corrects the market failure. For full credit, demonstrate that this tax rate achieves Q* in the regulated market by formally deriving the private market equilibrium under the tax. Shade the area on your diagram that corresponds to tax revenue.

3 Question 4. (40 points). Public Goods and Cal Poly Skate Park. Suppose you are asked to look into building a skate park on Cal Poly campus. Out of 18,000 students on campus, 100 students are interested in skating ramps and the other 17,100 students derive zero benefit from skate ramps. For each of the 100 skaters, the total benefit of skate ramps is TBi = 15X X 2 per year, where X is the number of ramps. The total cost each year to provide and maintain the skate ramps on campus is TC = 1,250X + 10X 2. A. How many skate ramps would maximize student welfare, X*? Draw a diagram that shows market demand, MC, and the social equilibrium. B. What is the value of the Lindahl tax for skaters and non-skaters that would finance the socially optimal number of skate ramps, X*? What is total amount of taxes collected? If each student was assessed her Lindahl tax rate each year as a student fee, do you think this tax would be easy to implement? Why or why not?

4 C. Suppose you instead decide to finance the skate park with an equal-share tax for all students that exactly recovers the total cost of providing X* ramps. What student fee could be charged each year to the 18,000 Cal Poly students to exactly recover total cost of X* skate ramps? D. If you decide to limit access to the skate park and change season passes to skaters for entry to the skate park. Assuming there are no additional costs of limiting access, what entry fee would be charged for a season pass for the use of X* skate ramps to exactly recover total cost? EXTRA CREDIT: Is skating a crime? Question 5. (70 points) Two polluting firms are located on a river and receive the marginal benefits from pollution given by: MB 1 = 100 2q 1 for firm 1, and MB 2 = 100 (2/3)q 2 for firm 2, where q 1 and q 1 represent the amount of emissions produced by each firm. Total pollution for the two firms combined is Q = q 1 + q 2.

5 A. Find pollution demand for each firm and aggregate demand for pollution. Draw each of the three curves in a single (large) diagram. B. Which firm is more efficient in reducing pollution? Explain. C. If the marginal social cost curve is given by MSC = 40 + Q, what is the optimal level of emissions (Q*) to be produced? Show both the MSC curve and Q* on your diagram. D. What is the optimal tax to be levied to achieve Q*? Given this tax, find the amount of emissions produced by each firm, q 1 * and q 2 *. Show these levels on your diagram.

6 E. Suppose that instead of a tax, the government decides to adopt a uniform standard equal to ½Q* for each firm. Show this allocation on your diagram and demonstrate that it is inefficient by identifying the gains from exchange on your diagram if pollution trading is allowed. F. Under what conditions would a tax or a uniform standard be equally efficient in reaching the optimal pollution level? Explain. G. Which scheme (tax or standard), do you think provides a larger incentive for investing in cleaner technologies? Explain.