Question

In: Economics

You work for the state environmental office and have been told that you are now in charge of determining the optimal amount of pollution allowed from powerplants in the area.


You work for the state environmental office and have been told that you are now in charge of determining the optimal amount of pollution allowed from powerplants in the area. You recognize that emissions from this powerplant causes damage to the environment, but that it is also costly to reduce the number of emissions due to reduced production of the plant. After doing some research you find that the Marginal Damage Cost (MDC) and Marginal Abatement Cost (MAC) can be represented by the following equations: MDC = 3e and MAC = 100 – 2e

a. Solve for the optimal level of emissions (e*)

b. Using the information from 1A, What are the marginal costs at the optimal level of emissions

c. Using the information from Question 1A, Calculate the Total Damage Cost at the optimal level of emissions (hint: drawing a graph may help you answer this question)

d. Using the information from Question 1A, Calculate the Total Abatement Cost at the optimal level of emissions (hint: drawing a graph may help you answer this question)

e. Using the information from Question 1A, calculate the total pollution costs at the optimal level of emissions


Solutions

Expert Solution

Note that you might already know from part a, that the optimal level of emissions is 20.

c. The total damage will be the inverse derivative or the integration of the marginal damage given in the question,

Hence the total damage cost will be (3/2)e^2

Thus, the total damage cost at optimal emission of 20 is (3/2)*20*20=600

d. Similarly, the total abatement cost will be the inverse derivative or the integration of the marginal abatement cost given in the question,

Hence the total abatement cost will be 100e-e^2

Thus, the total abatement cost at optimal emission of 20 is 100*20-20*20=1600

e. Now note that out of the total pollution cost, there are abatement costs which is private to the firms and also there are environmental costs which is caused by the firm which is an external cost. The total cost of pollution includes the total abatement cost or private costs and the total external costs or social costs.

Hence total pollution cost= 600+1600=2200


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