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EEP101/ECON125 Environmental Economics Problem Set 2
发布时间：2023-02-21
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Environmental Economics, EEP101/ECON125
Problem Set 2
Spring 2023
1 Externalities and Pigouvian Taxes
Multiple Choice: You do not need to show your work, though you may find it helpful in answering these questons to sketch a graph. Recall that the Pigouvian prescription says to fix an externality by setting a tax rate equal to marginal damages (marginal external cost) at the optimal quantity. When marginal ex- ternal damages are constant, the “at the optimal quantity”part is redundant. But, when marginal external damages are changing with the quantity of the good, then you have to figure out the right quantity to determine the right tax rate.
Consider a market where total private benefits are equal to TB = 105Q − 
Q2 . Total private costs are TC = 5Q + 
Q2 . Total external damages (costs) are equal to TED = 
Q2 . Assume the externality is on the production side of the market and increases total social cost. (To determine marginal benefit, private marginal cost, and marginal damage, you will need to take the derivative of the corresponding functions. You may find it helpful to sketch a graph.)
1. (3 points) What is the socially optimal quantity of production in the mar- ket?
a) 100
b) 25
c) 200
d) 50
e) 55
2. (3 points) What is the efficient tax rate (the Pigouvian prescription)?
a) 25
b) 33
c) 50
d) 66
e) 20
3. (3 points) What is the magnitude of government revenues from the efficient corrective tax?
a) 1650
b) 2500
c) 0
d) 1250
e) 2000
4. (3 points) What is the magnitude of consumer surplus in the presence of the efficient tax?
a) 50
b) 1250
c) 2500
d) 1000
e) 25
5. (3 points) What most nearly represents the magnitude of the deadweight loss (in the absence of a corrective policy)?
a) 72
b) 67
c) 289
d) 38
e) 612
2 Market-based instruments and the equimarginal principle
Show your work: Suppose steel production by two firms, JFE Steel (JFE) and U.S. Steel (USS), causes air pollution damages of $90 per ton of pollution emis- sions (E). Further, suppose the two firms have private marginal costs of produc- tion (PMC) equal to 2Q, where Q denotes units of steel production. JFE emits one ton of pollution per ton of steel, i.e., EJ FE = QJ FE, whereas USS emits one-third ton of pollution per ton of steel, i.e., EU SS = 1/3QU SS . Hence, total pollution is equal to EJ FE + EU SS = QJ FE + 1/3QU SS . The companies sell steel into a market with perfectly elastic demand at price $180.
1. (6 points) How much steel does each firm produce if there is no pollution regulation? What are the profits for each firm? What is total production of steel and total profit in the industry (the sum of each firm’s profits)?
2. (2 points) What is the socially optimal quantity of steel production? What is the socially optimal quantity of pollution?
3. (7 points) Suppose the local government imposes a uniform standard on pollution such that total pollution is equal to the socially optimal quantity of pollution. How much steel does each firm produce? What are the profits for each firm? What are total production and total profits? Are any permits unused?
4. (5 points) Now suppose the local government allows the firms to trade the pollution quotas they were (freely) allocated in (c). Further, suppose the price of permits is equal to the competitive permit market price of $90. How much does each firm produce? What are profits for each firm and total profits?
5. (7 points) Suppose instead that the local government imposes a Pigouvian tax on pollution. What is the amount of the optimal tax? How much does each firm produce? What are profits to each firm? What is the amount of government revenue and what are total profits to the firms?
6. (5 points) What is total surplus (Government Revenues + Producer Sur- plus (Profits in this problem) – Total External Cost) in (3), (4), and (5). Compare and explain briefly. (Note that there is no consumer surplus because of the perfectly elastic demand and the upward sloping supply curve.)
7. Extra Credit (4 points) Do the firms prefer the tax or the tradable permits? (Hint: compare profits under each regime.) Would your answer change if the government auctioned the permits rather than allocating them freely and uniformly? If so, how? Explain using words or math.
3 Principle of Targeting
1. (4 points) Identify a targeted policy to address the pollution externality associated with electricity production from fossil fuel power plants.
2. (4 points) Identify two policies for addressing the externality that (a) do not abide by the principal of targeting, and (b) are implemented in some jurisdiction. For each, identify the jurisdiction.
3. (4 points) Explain briefly how each of the policies in (2) accomplishes the government objective of reducing power-sector emissions in a costlier way than does (1).
