Question

Two firms can reduce emissions of an air pollutant at the following marginal costs:

MAC1 = 500q1 MAC2 = 300q2 (1)

where q1 and q2 are, respectively, the amount of emissions reduced by the first and second firm. Total abatement cost functions for the two firms are, respectively:

TAC1 = 1000 + 250(q1)^2 TAC2 = 1000 + 150(q^2) (2)

Assume that with no control at all, each firm would be emitting 40 units of emissions (for aggregate emissions of 80 tons), and assume that there are no significant transaction costs.

a. What are the total industry costs of abatement (for both firms combined) if they employ a uniform emission standard to achieve an aggregate reduction (for both firms combined) of 48 tons of emissions?

b. What are the marginal abatement costs for firm 1 and for firm 2 at the outcome under the standard considered in part (a)? Does this outcome fulfill the equimarginal principle? Why or why not?

c. Compute the cost-effective allocation of control responsibility to meet the required total reduction of 48 tons of emissions (in other words, what’s the cheapest way for these two firms to abate 48 tons?). How many units of emissions will each firm abate under a cost-effective allocation instead of a uniform allocation? Briefly, compare this result with the one you derived in (a).

d. What are the total industry costs of abatement (for both firms combined) under this costeffective allocation? Compare this result with the one you derived in (a).

Answer 1