The new mayor has pledged to reduce air pollution, and the only source of air po

Question

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) What is the marginal abatement cost for plant A? What is the marginal abatement cost for plant B?

b) What is the socially optimal level of pollution abatement? How is the socially optimal level of abatement split between the two plants?

Explanation / Answer

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

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