Question

Suppose there are two paper mills on an island. Both mills produce air pollution that is non-rival and non-excludable. All of the island’s citizens are negatively affected by the air pollution, but Children and Adults are affected differently. Specifically, the marginal benefits of pollution abatement (A) to the Child population is given by MBChild = 162 − 3A and the marginal benefits of pollution abatement to the Adult population is given by MBAdult = 108−2A. Not surprisingly, pollution abatement is costly for both paper mills. For Mill 1, marginal abatement costs are given by MAC1 = 12A and for Mill 2, MAC2 = 6A. Suppose there are no enforcement costs associated with ensuring that polluters comply with any abatement regulations. Using this information, answer the following questions.

Part (a) Aggregating benefits for Children and Adults, what is the marginal social benefit(MSB) function for pollution abatement? Graphically illustrate marginal benefits for Children (labeling it MBC), Adults (labeling it MBA), and the two combined (labeling it MSB). Make sure to also label all intercepts.

Part (b) Aggregating costs for Mill 1 and Mill 2, what is the marginal social cost (MSC) function for pollution abatement? Graphically illustrate marginal costs for Mill 1 (labeling it MAC1), Mill 2 (labeling it MAC2), and the two combined (labeling it MSC). Make sure to also label all intercepts.

Part (c) In the absence of regulation and bargaining, how much pollution will each Mill choose to abate?

Part (d) What is the socially optimal level of pollution abatement? Show this graphically, making sure to label the MSB and MSC curves as well as all intercepts and the equilibrium.

Part (e) Suppose the government chooses to achieve the abatement goal you found in Part (d) using a flat-rate emissions tax. What emissions tax would induce an overall abatement level that would achieve this goal? Under this tax, how many units of pollution would Mill 1 choose to abate? How many units of pollution would Mill 2 choose to abate?

Part (f) Suppose instead that the government chooses to achieve the abatement goal you found in Part (d) using a flat-rate emissions subsidy. What emissions subsidy would induce an overall abatement level that would achieve this goal? Under this subsidy, how many units of pollution would Mill 1 choose to abate? How many units of pollution would Mill 2 choose to abate?

Part (g) Without doing the calculation, can you tell whether total market abatement costs under the tax will be lower than, equal to, or greater than total market abatement costs under the subsidy? Briefly explain your answer

Part (h) Suppose it is discovered that pollution abatement is actually much more beneficial to children than we originally thought above. Suppose also that there are actually positive and sizable costs to enforcing pollution abatement regulations. Applying this new information, what can you say about the new socially optimal level of pollution relative to the level you found in Part(d)?

Answer 1

It may be seen that the socially optimum level of pollution is lesser than the abatement in pollution achieved by Mill 1 and Milll 2 both. The reason is that when Marginal Social Cost of pollution abatement is considered, which is higher than the Marginal Cost of pollution abatement incurred by Mill 1 and Mill 2 separately, the incentive to reduce pollution is more, hence, the socially optimum pollution is lower.

P.S. In part B, Marginal Cost of Mill 1 and Mill 2 have been labelled interchangeably. OB is MC for Mill 2, and OC is Marginal Cost for Mill 1.