1.
A paper mill and an oil refinery both operation on the bank of the Great Fish River. Both generate a water pollutant called gunk that kills fish, thus reducing the profits of the local fishery. The Environmental Ministry is analyzing alternative regulations to address this pollution problem, including implementing a pollution tax or a cap-and-trade system.
The following table shows the marginal and total costs of to the polluters (mill and refinery) for cleaning up gunk, as well as the marginal and total benefits of cleanup to the fishery (measured as change in profit). Assume there is only one fishery affected.
GUNK REDUCED PAPER MILL OIL REFINERY
Cost of Reduction ($) Cost of Reduction ($)
(tons/day) Total Marginal Total Marginal
0 0 0 0 0
1 1.30 1.30 0.20 0.20
2 2.80 1.50 0.50 0.30
3 4.60 1.80 0.80 0.30
4 6.80 2.20 1.20 0.40
5 9.60 2.80 1.70 0.50
6 13.20 3.60 2.50 0.80
7 17.90 4.70 3.80 1.30
8 24.60 6.70 6.10 2.30
9 34.60 10.00 11.40 5.30
10 51.30 16.70 38.10 26.70
GUNK REDUCED FISHERY GUNK REDUCED FISHERY
Profit from Reduction ($) Profit from Reduction ($)
(tons/day) Total Marginal (tons/day) Total Marginal
0 54.10 0 11 178.30 5.40
1 70.90 16.80 12 182.60 4.30
2 86.60 15.70 13 186.00 3.40
3 101.20 14.60 14 188.80 2.80
4 114.80 13.60 15 191.00 2.20
5 127.40 12.60 16 192.80 1.80
6 139.30 11.90 17 194.20 1.40
7 149.70 10.40 18 195.30 1.10
8 158.70 9.00 19 196.30 1.00
9 166.40 7.70 20 197.00 0.70
10 172.90 6.50
Note that the fishery’s profits are a function of the TOTAL pollution in the system, that is, the sum of the gunk produced by both the mill and the refinery, while the cleanup costs for each polluter is a function only of its own waste.
a. Understanding the table:
• What is the marginal cost to the mill of cleaning up one additional ton of gunk if it has already cleaned up 3 tons/day?
• What is the marginal cost to the refinery of cleaning up one additional ton of gunk per day if it is currently cleaning up 3 tons/day?
• If both the mill and the refinery are cleaning up 3 tons/day, what is the marginal benefit to the fishery of the refinery cleaning up one more ton per day?
b. Suppose that the Ministry imposes a pollution tax of $3 per ton of gunk and that both the mill and the refinery would emit 10 tons of gunk in the absence of any regulation.
• How much gunk would the mill reduce if faced with this tax?
• How much gunk would the refinery reduce?
• What would total gunk emissions be? Remember that your answers to the first two bullet points on this part are gunk reduction from a level of 10 tons/day for each.
• What is the fishery’s profit at this level of gunk reduction?
c. Suppose that instead of a tax, the Ministry decides on a cap-and-trade system, limiting total pollution to 7 tons/day. To compensate the fishers for damages, the Ministry gives the fishery all seven permits, allowing it to either hold them or sell them. Thus no pollution is allowed initially.
• How much would the mill be willing to pay for one gunk permit? Keep in mind it is not allowed to pollute at all without a permit.
• How much would the refinery be willing to pay for one permit, given that it has zero initially now?
• How much would the fishery need to be paid to induce it to sell one gunk permit?
d. Follow the logic in part c to determine if the fishery would be willing to sell the second, third, fourth and so on permit for less than the mill or refinery would be willing to pay for additional permits.
• What will be the final distribution of the seven pollution permits? Be clear as to how many each party (mill, refinery, fishery) holds after trading.
• If the fishery sells just one permit at a time to the highest bidder, at approximately what price (or what price range) will the final permit that changes hands sell for?
e. How does the emissions reduction distribution in part d compare to that in part b?
2.
In July 1997, the EPA announced new air quality standards for small particulate matter (2.5 micrometers in diameter) referred to as PM2.5. Previously particulate matter less than 10 microns in diameter were regulated. Steel mills are a major source of these smaller particles and therefore had to find ways to abate. Consider the following hypothetical model of two steel plants, one owned by Bethlehem Steel (B) and one owned by National Steel (N), both located in Pittsburgh, Pennsylvania:
Bethlehem: (Marginal Cost) MCB = 1.1AB
(Total Cost) TCB =0.55(AB)2
National: (Marginal Cost) MCN = 0.4AN
(Total Cost) TCN = 0.2(AN)2
Assume that each plant emits 40 units of PM2.5 for a total of 80 units. In order for the Pittsburgh area to meet the new standard, the EPA determines that the combined abatement for both plants must total 30 units.
a. Assuming the new abatement standard is implemented uniformly between the two firms, find the total cost of abatement for each firm and the overall total cost of abatement. Show your work.
b. Mathematically or graphically demonstrate that your answer to (a) is NOT cost effective.
c. Find the cost effective solution for 30 total units of abatement. Show your work and clearly indicate both AB and AN. Note that this is similar to the “Puzzle” on page 317 but with MC as a function of abatement levels (level of pollution reduced) rather than as a function of pollution. But see the solution to that puzzle if you need help solving this problem.
d. Verify that your solution in (c) is cost effective by showing that the marginal cost of abatement is the same for both firms.
e. Under the cost effective solution, which firm experiences increased total costs relative to the uniform abatement policy? Why? What happens to the total costs for the other firm? Why?
f. Calculate the total cost savings associated with the cost effective solution relative to the uniform abatement standard. Show your work.