The new mayor has pledged to reduce air pollution, and the only source of air pollution in the city are two cement plants, plant A and plant B. 25 years ago, when plant A was constructed, the cement production technology produced a lot more pollution; it therefore has a pollution abatement cost of 5c3, where c is a unit of pollution. Plant B was constructed 2 months ago; it has a pollution abatement cost of 10c2. Assume that neither plant is initially engaging in pollution abatement. The per unit benefit to a unit of pollution abatement is constant at $1500. Unless told otherwise, assume the plants are owned by different firms.

A)  marginal abatement cost for plant A is 15c^2  marginal abatement cost for plant B is 20c

B)  at social optimal level

15c^2 + 20c = 1500

3c^2 + 4c = 300

we get c=9.35

plant A contribution =1312

plant B contribution= 188

c) The mayor considers engaging in direct quantity regulation (also called "command- and-control") and declares that each firm must engage in 42.5 units of pollution abate- ment. (i) Is this socially optimal? Why or why not? (ii) If the plants are controlled by the same firm, would it be socially optimal of the mayor to state that the firm must engage in 85 units of pollution abatement? Why or why not?

d) Instead the mayor considers providing a subsidy of 1500 per unit of pollution abatement. What is the per plant and total level of pollution abatement? Is this socially optimal?

e) The mayor also considers issuing pollution permits and establishing a market for these permits. Plant A is given an initial endowment of permits such that it must engage in 60 units of pollution abatement (reduction). Plant B is given an initial endowment of permits such that it must engage in 25 units of pollution abatement (reduction). Assume the market for pollution permits is perfectly competitive. (i) What is the market clearing price for pollution permits? What level of pollution abatement (reduction) does each firm engage in? Is this socially optimal? How does the level of abatement compare here with part d?

f) [BONUS] Dropping the perfect competition assumption, what problems are likely to arise in practice in the permit market? How are the amount of trade and the permit price likely to change? Discuss

g) You are the economist responsible for advising the mayor on environmental issues. Which of the above policies would you recommend? Why?