Suppose that two chemical firms each dump 100 kilograms of pollution into the local river during their regular production activities.

Firm A could reduce its pollution at a cost of 20 euros per kilogram.
Firm B could reduce its pollution at a cost of 50 euros per kilogram.
Scientists advise the government that there is an urgent need to reduce overall pollution from 200 kilograms to 80 kilograms.

a. What would be the lowest-cost way to reach this goal? That is, how much pollution reduction would each firm do?
What would be the cost of pollution reduction to firm A, the cost to firm B, and the cost for the two firms together? (As always, show your work. Note that the total amount of pollution reduction for the two firms together must be 120 kilograms.)

b. Typically, the government would not know the lowest-cost way to reach its goal, so it might simply ask each firm to reduce its pollution to 40 kilograms (so that total pollution emissions would be 80 kilograms). If the government did this, what would be the cost to firm A, the cost to firm B, and the total cost? (Again, show your work. Note that each firm does 60 kilograms of pollution reduction.)

c. Compare the total cost of pollution reduction in part (a) to the total cost in part (b).

d. Is there some policy that the government could use to reach its goal for pollution reduction at the lowest overall cost, even though it does not know the costs of each firm? Explain how the policy might work.

e. For bonus points, use numbers to show how both firms would be better off with the policy in part (d) rather than the policy in part (b).