On the banks of the Great Fish River sit an oil refinery and a paper mill. Both generate a water pollutant called gunk that kills fish, reducing the profits of local fishing boats. But it is costly for the mill and the refinery to clean-up. The Environment Ministry needs to step in with a solution. (One way to solve this problem is to break up into three teams of two or three, with one team representing the mill, one the refinery and one the fishing folks.) The tables below show the marginal and total costs to the polluters for clean-up, and also show the marginal and total benefits of clean-up to the fishing community.
GUNK PAPER MILL OIL REFINERY FISHERS
Emitted Costs of Reduction Costs of Reduction Profit from Reduction
(tons/day) Total Marginal Total Marginal Total Marginal
0 $66.70 $16.70 $40.00 $26.70 $197.00 $0.70
1 $50.00 $10.00 $13.30 $5.30 $196.30 $0.90
2 $40.00 $6.70 $8.00 $2.30 $195.30 $1.10
3 $33.30 $4.80 $5.70 $1.30 $194.20 $1.40
4 $28.60 $3.60 $4.40 $0.80 $192.80 $1.80
5 $25.00 $2.80 $3.60 $0.60 $191.00 $2.20
6 $22.20 $2.20 $3.10 $0.40 $188.80 $2.80
7 $20.00 $1.80 $2.70 $0.30 $186.00 $3.40
8 $18.20 $1.50 $2.40 $0.20 $182.60 $4.30
9 $16.70 $1.30 $2.10 $0.20 $178.30 $5.30
10 $15.40 $1.90 $172.90 $6.70
There is one trick to reading this table. Recognize that the fishers’ profits are a function of the total pollution in the system (gunk produced by both the mill and the refinery), while the table shows the clean-up costs to each polluter as a function only of their own waste.
(a) What is the marginal cost to the refinery of cleaning up from 5 to 4? For the mill of cleaning up from 5 to 4? If both the refinery and the mill are at 5, then what is the benefit to the fishers of the refinery cleaning up to 4?
(b) Suppose that the Ministry puts in place a pollution tax of $3 per ton of gunk. How much pollution will the mill generate the refinery?
(c) Suppose instead that the Ministry decides on a cap-and-trade system, limiting total pollution to seven units. And to compensate fishers for damages, the Ministry gives the fishers all seven permits, allowing them to either hold them or sell them. Thus, no pollution is allowed initially. With the refinery starting out holding zero permits, how much would the refinery be willing to pay to get one permit from the fishers? Similarly, the mill starts out with zero permits. How much would the mill be willing to pay the fishers to get one permit? Finally, how much would the fishers need to be paid to sell one permit to the refinery? To sell a second permit to the mill?
(d) Follow the logic in part c. to its conclusion, and determine if the fishers would be willing to sell a 3rd, and 4th, and 5th and etc… permit for less than the refinery or mill would be willing to pay for these additional permits. What will be the final distribution of permits between the mill, the refinery and the fishers? At approximately what price will the final permit that changes hands sell for?