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).

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).

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?

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

Answer: am answered with a-g only

A)

Aggregating benefits for children and adults, we obtain the marginal social benefit function for pollution abatement as:

MSB = MBChild + MBAdult

MSB =162 - 3A + 108 - 2A

MSB = 270 - 5A

B)

Aggregating costs for mill 1 and mill 2, we obtain the marginal social cost(MSC) function for pollution abatement as:

MAC1 = 12A

MAC2= 6A

MSC = MAC1 + MAC2

MSC = 12A+ 6A

MSC = 18A

C)

In the absence of regulation and bargaining, each mill will equate its marginal abatement cost to marginal social benefit:

For Mill1:

MSB = MAC1

i.e. 270 - 5A = 12A

=> 270 = 17A

=> A = 15.88 units

For Mill 2:

MSB = MAC2

i.e. 270 -5A = 6A

=> 270 = 11 A

=> A = 24.54 units

So, mill 1 will choose to abate 15.88 units and mill 2 will choose to abate 24.54 units.

D)

MAB( child)=162-3A

MAB(adult)=108-2A

Aggregate MAB=MAB(child)+MaB(adult)=270-5A

MAC1=12A1. A1=MAc1/12

MAC2=6A2. A2=MAc2/6

Aggregate MAC;A=A1+A2=3MAC/12=MAC/4

MAC=4A

Social efficient abatement is where Aggregate MB and Aggregate MAC si Equal,

270-5A=4A

270=9A

A=270/9=30

E)

aggregate MAC at optimal abatement=4*30=120

So emission tax =120 will lead to social optimal abatement.

Firm abate till Abatement cost is lower than emission tax because it will less costlier to abate than paying tax.

A1=120/12=10

A2=120/6=20

F)

The subsidy Equal to 120 will lead to social optimal abatement.

For each additional Abatement,firm will get 120 subsidy

The firm will keep abate till MAC is lower than subsidy, because firm will get additional Profit from subsidy .as soon as MAC rise 120 ,firm will get negitive cash flow from abatement.

G)

Because the Abatement amount is same in both taxes and subsidy scheme. So abatement cost to firm will be same for firms in both case,but eventually goverment is giving subsidy to firms ,so net cost to society of abatement is equal to difference of total subsidy and firm abatement cost ,which will be higher .

So subsidy scheme will be more costlier