Question

a. Assume that a society is composed of two polluters, with the marginal abatement costs of polluters 1 and 2, respectively, equal to:

MAC1 = 18 – E1

MAC2 = 12 – 2E2

Where MAC1 refers to the marginal abatement costs of polluter 1, and E1 refers to the level of emissions of polluter 1. What is the unregulated level of pollution for each polluter? Find the total level of emissions that would be generated if a per-unit pollution tax of four dollars were imposed. Perform the same exercise for taxes of six dollars and eight dollars.

b. Given the same two marginal abatement cost function in part (a), find the market price of a marketable pollution permit if pollution was limited to eighteen units through the issuance of marketable pollution permits. Assume initially that each polluter is given nine permits (that allow 1 unit of pollution each).

c. Given a societal marginal abatement cost function of:

MAC = 100 – 3E

and a societal marginal damage function of:

MD = 2E,

find the optimal level of pollution and the per-unit pollution tax that would achieve it.

d. MAC1 and MAC2 are two different societal marginal abatement cost functions. Which one is more likely to be associated with an optimal level of pollution that is at or near zero? Why?

MAC1 = 10 – 0.2E

MAC2 = 1/E

Answer 1

Answer A:-

MAC1 = 18 – E1

MAC2 = 12 – 2E2

For unregulated level of pollution

18 – E1 = 0 E1 = 18 (18 units of emission by polluter 1)

12 – 2E2 = 0 -2E2 = -12 E2 = 6 (6 units of emission by polluter 2)

When Tax is imposed:-

Tax = $4 :-

18 – E1 = 4

E1 = 14 (14 units of emission by polluter 1)

12 – 2E2 = 4

-2E2 = -8

E2 = 4 (4 units of emission by polluter 2)

Tax = $6:-

18 – E1 = 6

E1 = 12 (12 units of emission by polluter 1)

12 – 2E2 = 6

-2E2 = -6

E2 = 3 (3 units of emission by polluter 2)

Tax = $8:-

18 – E1 = 8

E1 = 10 (10 units of emission by polluter 1)

12 – 2E2 = 8

-2E2 = -4

E2 = 2 (2 units of emission by polluter 2)

Answer B:-

18 – E1 = 12 – 2(18 – E1)

18 – E1 = 12 – 36 + 2E1

18 = 3E1 – 24

3E1 = 42

E1 = 14

E2 = 18 – 14

E2 = 4

Price = 18 – E1           Price = 12 – 2E2

Price = 18 – 14          Price = 12 – 2(4)

Price = 4                      Price = 4

Market price will be $4.

Answer C:-

MAC = MD

100 – 3E = 2E

5E = 100

E = 20 (optimal emission level is 20 units)

tax = MAC at 20               units tax = MD at 20 units

tax = 100 – 3(20)             tax = 2(20)

tax = 40 tax = 40

Answer D:-

Over the different range of emission, there will be a decline in the value of MAC1. But the rate of decrease will be more in case of MAC2. After the emission level of 1, the value of MAC1 will be less than 1.

When the level of emission will reach the value of zero, the value of MAC2 will reach to infinity.

This will depict that for the various values of emission beyond 1, the selection of a marginal abatement cost function is 2.

If the level of emission is less than 1 and reaching the value of 1, we will select marginal abatement cost function 1.

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