Marginal Benefits of Abating Emissions

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Problem Set 10
Please provide detailed explanations. Show all your work.

Externalities 1
Assume that scientific studies provide you with the following information concerning the benefits and costs of sulfur dioxide emissions:
Marginal benefits of abating (reducing) emissions: MB = 400 - 10A
Marginal costs of abating emissions: MC = 100 + 20A
where A is the quantity abated in millions of tons and the benefits and costs are given in dollars per ton.
a) What is the socially efficient level of emissions abatement?
The socially efficient level is obtained where MB = MC
i.e., 400 - 10A = 100 + 20A
or 20A + 10A = 400 - 100
or 30A = 300
Therefore, A = 10
b) What are the marginal benefit and marginal cost of abatement at the socially efficient level of abatement?
At A = 10, MB = 400 - 10A = 400 - 10*10 = 300
At A = 10, MC = 100 + 20A = 100 + 20*10 = 300

b) What happens to net social benefits (benefits minus costs) if you abate one million more tons than the socially efficient level? One million fewer?
Net Marginal benefit = MB - MC = 400 - 10A - (100 + 20A) = 300 - 30A
If A = 1, MB = 300 - 30 = 270
If A = -1, MB = 300 - (-30) = 330

c) Why is it socially efficient to set marginal benefits equal to marginal costs rather than abating until total benefits equals total costs?
Marginal social benefits of abatement reflect the health, esthetic, and other environmental benefits as pollution is reduced. As the marginal social benefit equation shows, a little pollution reduction yields high benefits. As pollution abatement approaches 100%, the incremental benefit of reducing pollution falls as the benefits as less noticeable. If we can swim, fish, boat and picnic at the local river, we are not likely to notice the pollutants that remain in the sediment. Certainly, the cost of removing the entire ...