Question

4. Consider an industry with three firms. Firm 1’s marginal cost of abatement (MCA)=20-2E1, where E is the tons of pollution emitted. Firm 2’s MCA=10-E2. Firm 3’s MCA=40-2E3. Please draw a diagram to support your answers to the following questions. If there is no policy to reduce pollution, how much pollution will be emitted by each firm? What will be total pollution? If the government imposes a tax of $10/ton, how much pollution will be emitted by each firm? What will be total pollution? What will be the total cost of abatement? If the government imposes a limit on pollution, where the limit is the total amount of pollution you found in part b, and each firm is allowed to pollute the same amount, what will be the total cost of abatement? Which policy is more efficient, the tax or the limit on pollution?

Answer 1

damage due to pollution = D(p) = p2 /2 2. p = 2eA + eM [eA = automobile emissions; eM = steel mill emissions] qA, qM = abatement (reduction) in auto/steel mill emissions from uncontrolled level 3. TC(qA) = (qA) 2 , therefore MAC(qA) = 2qA 4. TC(qM) = (qM) 2 , therefore MAC(qM) = 2qM 5. eA + qA = 10 or qA = 10 - eA 6. eM + qM = 10 or qM = 10 - eM