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Answer on Microeconomics Question for gabby

Question #42328
A. Assume that the external cost of a certain type of air pollution is given by: EC = 730Q −6.5Q2 and the cost of abatement of the same pollution is
CA = 11Q2 +1020Q, where Q is the quantity of the air pollutant emitted. (Hint: MEC and MCA)

i. What is the optimal amount of emission fee per unit of pollutant that must be imposed to ensure an efficient level of air pollution?

ii. Find the value of total emission fee that the firm will pay and the total abatement costs that the firm will incur if it produces the optimum amount of air pollutant.
Expert's answer
A. EC = 730Q −6.5Q2 and the cost of abatement of the same pollution is 
CA = 11Q2 +1020Q, where Q is the quantity of the air pollutant emitted. (Hint: MEC and MCA).

i. The optimal amount of emission fee per unit of pollutant that is in the point, where MEC = MCA.
MEC = EC' = 730 - 13Q
MCA = CA' = 22Q + 1020
730 - 13Q = 22Q + 1020
9Q = -290
Q = -32.2 units must be imposed to ensure an efficient level of air pollution.

ii. The values of total emission fee that the firm will pay and the total
abatement costs that the firm will incur if it produces the optimum
amount of air pollutant are:
EC = 730*32.2 - 6.5*32.2^2 =  $16,755.5
CA = 11*32.2^2 + 1020*32.2 = $44,249.2.

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