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.

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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