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Two polluting firms can control emissions of a pollutant by incurring the following marginal abatement costs:...

Two polluting firms can control emissions of a pollutant by incurring the following marginal abatement costs: MAC1 = $300?1, and MAC2 = $100?2 where ?1, and ?2 are the amount of emissions abated (i.e., pollution controlled) by firm 1 and firm 2 respectively. Assume that with no abatement of emissions at all, firm 1 would release 15 units of pollution and firm 2 would release 10 units, for a total of 25 units. Assume the target level of abatement is 12 units. We do not know if this is the socially efficient level or not. Compute the level of emissions per firm that is cost effective for society?

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Answer #1

Given that

MAC1 = $300?1

MAC2 = $100?2

The target level of abatement is 12 units. This indicates that the total amount of emissions abated (i.e., pollution controlled) by firm 1 and firm 2 should be 12 units.

A1+A2= 12

A1= 12-A2 ... (1)

For cost-effectiveness, both the firms should have the same marginal abatement costs. MAC1=MAC2

300A1 = 100A2

300 (12-A2) = 100A2

3600 = 400A2

A2=9 units

A1 = 12-9 =3 units

Therefore, firm 1 should abate 3 units of pollution whereas firm 2 should abate 9 units of pollution.

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