Question

Two firms are ordered by the federal government to reduce their pollution levels. Firm A’s marginal costs associated with pollution reduction is MC=150+3Q. Firm B’s marginal costs associated with pollution reduction is MC=10+9Q. The marginal benefit of pollution reduction is MB=250−4Q. a. What is the socially optimal level of each firm’s pollution reduction?
Compare the social efficiency of three possible outcomes: (1) require all firms to reduce pollution by the same amount; (2) charge a common tax per unit of pollution; or (3) require all firms to reduce pollution by the same amount, but allow pollution permits to be bought and sold.

Answer 1

Answer:

Given marginal costs and benefit

for firm A: MC=150+3Q

for firm B: MC=10+9Q

Marginal Benefit: MB=250-4Q

Socially optimal level of each firms pollution reduction

MC=MB

150+3Q=250-4Q

7Q=100

Q=14.3

for firm B

10+9Q = 250-4Q

13Q=240

Q=18.5

HERE THE THREE SCENARIOS

1) iF BOTH FIRMS ARE REQUIRED TO REDUCE POLLUTION BY THE SAME AMOUNT THEN

Total surplus is equal to total benefit minus total cost. The total benefit is equal to the area under the marginal benefit curve

The same total reduction could be achieved by requiring each firm to reduce pollution by 25.6 units. This would be less efficient than the social optimum since it would be less costly for firm B to reduce pollution by more and for firm A to reduce pollution by less

2)A common tax could be used to achieve the social optimum. Setting a tax of 250-4Q would lead firm A (respectively, B) to reduce pollution to the point where MC A = 250-4Q (respectively MC B = 250-4Q). Solving gives Q A = 14.3 and Q B = 18.5

3)POLLUTION PERMITS LEADS TO PROBLEM OF INTERNALIZATION

Requiring both firms to reduce pollution by 25.6 units but allowing them to trade pollution permits can also be used to achieve the social optimum.