Question

Two polluters, A and B, have marginal abatement cost functions given by MACA=28- 2EA and MACB= 32- 2EB. (a) If the goal is to reduce the combined/total emissions from the two firms to 20 units in a cost-effective manner, then how should emission standards be set? (b) Now imagine that the two polluters are participating in a TDP/TEP market( transferable emission permits market) along with many other polluters. If the price of a permit is $10/unit in the market and Polluter A is given 12 permits by the government regulator initially, then how many permits is it likely to buy or sell? What amount of net benefits can it expect from the trade? [ Parts (a) and (b) aren't related to each other]

Answer 1

a) If the goal is to reduce the emission level total 20 units from firm A and B. This will be determined by equimarginal principle. According to this principle two firm's pollution level will be that where MAC of A and B equalised so that total pollution level also achieved by two firms.

In the following table we calculate the MAC of A and B at each level of emission.

MAC A = 28 - 2EA . MAC B = 32 - 2EB.

Emission Level	MAC of A	MAC of B
1	26	30
2	24	28
3	22	26
4	20	24
5	18	22
6	16	20
7	14	18
8	12	16
9	10	14
10	8	12
11	6	10
12	4	8
13	2	6
14	0	4
15	--	2
16	--	0

From the above table we can take the emission level of 9 units for firm A and 11 units for firm B. At 9 units of emission by firm A, MAC is $10 and at 11 units of emission by firm B , MAC is $10.

So, there should be given the pollution permit to A is 9 units and pollution permit to B is 11 units. (Ans).

(b) Firm A is given pollution permit of 12 units and price of pollution for trading is $10.

Now, firm A will do the pollution upto that level where MAC of the firm equalised with price of permit.

We can see at the pollution level of 9 units MAC of A is $10. Pollution permit price is also $10.

So firm A will do the pollution upto 9 units. Then remaining 12 -9 = 3 units firm A will sell to firm B.

Firm A will sell 3 units of permit to firm B. (Ans).

Now by selling 3 units of permit to firm B , firm A gets 3*$10 = $30.

Now when E = 12 , MAC of A is 28 - 2*12 = $4

When E = 11, MAC of A is 28 -2*11 = $6

When E = 10, MAC of A is 28 - 2*10 = $8.

So total abatement cost of reducing emission by 3 units is $4+$6+$8 =$18.

So, net benefit firm A can expect is $30 - $18 = $12. (Ans)