7. The newly elected president of an island nation has pledged to reduce air pol
ID: 2786394 • Letter: 7
Question
7. The newly elected president of an island nation has pledged to reduce air pollution. The nation has no close neighbors-the only source of air pollution are the two domestic chemical plants run by firm A and firm B. Firm A has been in operation for 50 years and has a pollution abatement (i.e. reduction) cost of x3, where x is a unit of pollution. Firm B, which operates a 6-month old plant has a pollution abatement cost of x2. Assume that neither firm is initially engaging in pollution abatement. The per unit benefit to a unit of pollution abatement experienced by the island's citizens is constant at $300. a. What is the socially optimal level of pollution abatement? How is the socially optimal level of abatement split between the two firms? b. The president considers engaging in command and control style quantity regulation and declares that each firm must engage in 80 units of pollution abatement. Is this socially optimal? Why or why not? c. Alternatively, the president considers providing a subsidy of $300 per unit of pollution abatement. What is the per firm and total level of pollution abatement? Is this socially optimal?Explanation / Answer
a.
The marginal cost of pollution for Frim A= X3 while for Firm B it is X2
The socially optimal level of pollution abatement is the point where Marginal cost= Marginal benefit.
Hence the optimal level for Firm A is the point where X3 = 300. Hence X= 100 units
The optimal level for firm B is the point where X2= 300, Hence X= 150 units
The total optimal level = 250 units
b.
The total abatement should be 80+80 = 160 units
The marginal cost of abatement should be equal for both firms which means that 3X= 2X
The 2 equations are
Xa+Xb= 160 and
3Xa= 2Xb
Solving for Xa
3Xa = 2*(160-Xa)
3Xa= 320-2Xa
5Xa= 320
Xa= 320/5 = 64
And
Xb= 160-64 = 96
The market clearing price will equal the marginal cost = 2*96 = 192
Hence this is not the optimal abatement
c.
The subsidy that will result in socially optimal outcome is the social marginal benefit which is equal to $300. This will result in socially optimal level.
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