Question

The following table shows the MB of polluting to firm A and firm B (which represents the MC of abatement of pollution to the firms)

Emissions	MB firm A	MB firm B
20	0	0
19	4	2
18	8	4
17	12	6
16	16	8
15	20	10
14	24	12
13	28	14
12	32	16
11	36	18
10	40	20
9	44	22
8	48	24
7	52	26
6	56	28
5	60	30
4	64	32
3	68	34
2	72	36
1	76	38

A. Imagine an environmental standard where each firm is allowed to emit 11 units. 1. What is the total cost of this standard to firm A? Firm B? 2. What is the total cost to the industry made up of these two firms?

B. Now suppose that a tax of $24 per unit of emissions is imposed. 1. How many units of emissions will firm A choose to emit? Firm B? 2. What is the total cost to this industry for the reduction in emissions?

C. Now suppose each firm is issued 11 permits in a tradable emissions permits market. 1. Who will purchase permits? Who will sell? 2. Where will the price of permits sell?

Answer 1

A).

Consider the given problem here there are two firms “firm A” and “firm B” and their respective marginal abatement cost curve are also given in the question. Now, both of them are allowed to emit “11 units”, => each will emit “20-11 = 9 units”. So, the total cost of both firms are given below.

=> TCA = 0 + 4 + 8 + 12 + 16 + 20 + 24 + 28 + 32 = $144.

=> TCB = 0 + 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 = $72.

So, the total cost industry to the industry is “TCA + TCB = 144 + 72 = 216”.

B).

Let’s assume that a “$24 unit tax” is imposed. Now, for the emission reduction “6” “firm A’s” corresponding “MAC” is “24 = tax”, => “firm A” will reduce emission by 6 units. Similarly, for the emission reduction “12” “firm B’s” corresponding “MAC” is “24 = tax”, => “firm B” will reduce emission by 12 units.

So, total cost of the industry is give below.

=> TC = TCA + TCB.

=> TC = (4+8+12+16+20+24) + (2+4+6+8+10+12+14+16+18+20+22+24) = 84 + 156 = $240.

C).

Let’s assume that each firm is issued 11 permits in tradable emission permit market. Now, if “firm A” want to increase emission by “1 unit” then “firm A’s” cost will decrease by “$32”, => “firm A” will pay maximum of “32” and “firm B’s” cost will increase by “$20” , => “firm B” want minimum of “$20”. So, here trade is possible and “firm A” will buy pollution permit and “firm B” will sell the pollution permit.

Now if “A” want to buy 3 units pollution permit that is will pollute “11+3=14 units” implied the corresponding MAC is “$24” implied “firm A” want to pay maximum of “24” per permit. So, “firm B” will pollute “11-3=8 units” implied the corresponding MAC is “$24” implied “firm B” want to take minimum of “24” per permit. The price will between 24 per unit, where “A” will buy 3 units and “B” will sell 3 units.