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. MPC MB Q*=0 Qc Quantity (Q) 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? Justify your position with a diagram. D est. D true Assumption: Demand for gasoline is inelastic Outcome: Taxes perform better, because, if demand conditions are estimated as D est. And true demand is D true, DWL is lower under the tax (red triangle) than DWL under the standard (grey triangle). Q s Q * Q t

2 Question 5. (50 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 MPC=5 MPB=50-Q MPB=MPC 50-Q=5 Qc=45 Pc=MPB (Qc)=50-45) Pc=5 B. What is the socially-optimal (i.e., welfare maximizing) level, Q*, and what is the socially-optimal price, P*? MPB=50-Q MPC=5 MEC=5+ Q =MPC+MEC =10+Q MPB= 50-Q=10+Q 2Q=40 Q*=20 P*=MPB(Q*)= P*=30 C. Draw a graph that shows the private and social equilibrium points and the deadweight loss (DWL) at the private market equilibrium. MPB DWL Tax revenue P* MPC + t* t* Pc MPC Q* Qc Quantity (Q)

3 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 graph that corresponds to tax revenue. t*=mec(q*) t*=5+q* = t*= $25 MPB = MPC + t* 50- Q= = Q* 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 graph that shows market demand, MC, and the social equilibrium. MBi = X MC = 1, X Market Demand: For a public good, add vertically => MB = 100[ X] = 1,500 5X Optimal number of ramps is where MB = MC: 1,500 5X = 1, X => 25X = 250 => X* = 10 DWL MC P* MB X* = 10 Skate Ramps (X)

4 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? Lindahl Tax = MBi evaluated at X* Skaters: T s * = MBi(X*) = (10) = $14.50 Non-Skaters: T n * = 0 Total Revenue: 100*[($14.50/ramp)*(10 ramps)] = $14,500 Lindahl taxes would be difficult to implement, because skaters have an incentive to free-ride. 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 for the 18,000 Cal Poly students to exactly recover total cost? Total Cost: TC(X*) = 1,250(10) +10(10) 2 = $13,500 Equal-share tax (student fee for all 10 ramps): 13,500 / 18,000 = $0.75 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? Under an entry fee, only the 100 skaters would be willing to pay the entry fee to use the ramps: TC(X*) = $13,500 Entry Fee = 13,500 / 100 = $135.00

5 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. A. Find pollution demand for each firm and aggregate demand for pollution. Draw each of the three curves in a single graph. To find the aggregate marginal benefit curve, solve each of the individual marginal benefit curves for qi and then add them together. Writing MB as P we have: q1 = 50 - P for firm 1 and q2 = P for firm 2. Adding these together, we get aggregate demand: Q = q1 + q2 = 200 2P; or P = 100 ½Q DWL t*=80 MB T MB 1 MB 2 q 1 *=10 q 2 *=30 Q*=40 Pollution (Q) ½Q* = 20 B. Which firm is more efficient in reducing pollution? Explain. Firm 1 is more efficient at reducing pollution, and the reason is that MAC for a unit of pollution is lower for firm 1 than for firm 2. For any level of emissions, firm 1 derives less additional benefit from an increase in pollution than firm 2, which is to say its opportunity costs of abating a unit of pollution are lower. For example, if the two firms were emitting 30 units of pollution, firm 1 has a marginal abatement cost of 40 while firm 2 has a marginal abatement cost of 80. Notice that what matters for efficiency in this context is not so much the slope of the curves, but their relative heights. C. If the marginal social cost curve is given by = 40 + Q, what is the optimal level of emissions (Q*) to be produced? Show both the curve and Q* on the same graph. Q*: MB = => 100 ½Q = 40 + Q => 60 = 3/2Q => Q* = 40

6 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 the same graph. The optimal tax, t* = MEC(Q*) = (Q*) induces firms to choose to emit the optimal amount of pollution. Firms will choose to reduce their pollution if the cost of abating one more unit is cheaper than the cost of paying the tax on one more unit. Thus, firms will abate up to the point where MB = t. MB(Q*) = 100 ½(40) = $80 => The optimal level of the tax is T* = 80. Firm 1 will pollute up to the point where MB1 = 100-2q1 = 80, implying q1* = 10. Firm 2 will pollute up to the point where MB2 = (2/3)q2 = 80, implying q2* = 30. Notice that q1* + q2* = = 40 = Q*. 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. A tax and a uniform standard are equally efficient only if all firms have identical MB curves. G. Which scheme (tax or standard), do you think, provides a larger incentive for investing in cleaner technologies? Explain. Taxes provide a greater incentive. To see this, suppose the two marginal benefit curves above give the marginal abatement costs associated with two technologies instead of two firms. Firm 2 here, represents the dirtier technology. The initial outcome under the dirty technology is the same under a tax of $80 or a standard of 30 units. When a firm adopts a cleaner technology under the tax, it reduces its output in response to the tax to 10 units, which lowers the costs of abiding by the environmental policy. Under a standard, the firm continues to produce q = 30 units, but the marginal value of the last unit is less than $80, so taxes provide a larger incentive to invest in cleaner technologies. Not only will its costs of reducing pollution be lower, it will be producing less pollution under a tax. Hence, the cleaner technology allows the firm to reduce its tax payment as well. Formally, if we calculate the areas under the curves, the firm with the dirtier technology would incur a total abatement cost of = $7200 when there is a tax, while a firm with the cleaner technology would incur a total abatement cost of = $1700 when there is a tax. Thus, under a tax, adopting the cleaner technology saves = $5500. For a standard set at q = 30, the firm would incur abatement cost of $4800 to comply under the dirty technology (note that the difference is no tax payment is made), but the abatement cost falls to 0.5 (50-30) 40 = $400 under the cleaner technology. Hence, under a standard adopting the cleaner technology saves only $ = $4400. Since the savings from adopting cleaner technology are larger under the tax, a firm is more likely to adopt under a tax scheme than under a standards scheme, for instance if the cost of the technology is $5000, then a firm will want to adopt it only under a tax policy.