Question

Let us assume the following regarding 2 firms:

	Firm A				Firm B
Emissions	Total abatement costs	Marginal abatement costs		Emissions	Total abatement costs	Marginal abatement costs
4	0	0		4	0	0
3		1		3		2
2		2		2		4
1		3		1		6
0		4		0		8

1 Please calculate the total abatement costs for both firms (see empty boxes in the table above, what are the corresponding values?)

2 What are the total abatement costs for the firms and economy to reduce 50% of the emissions with command and control policies?

3 How will cap and trade improve the situation, if each firm will get 2 permits?

4 What is the range of the price per permit so that trade will take place?

Answer 1

1) First see the completed table, which is taken by adding the marginal costs to arrive at total cost

Firm A	Firm B
Emissions	Total abatement cost	Marginal abatement cost	Emissions	Total abatement cost	Marginal abatement cost
4	0	0	4	0	0
3	1	1	3	2	2
2	3	2	2	6	4
1	6	3	1	12	6
0	10	4	0	20	8

2) Each firm's emissions are equal to 4 units today. A command and control policy to reduce 50% will require each firm to be at half of its current emission, i.e., at 2 units each

Firm A's total abatement cost would be $3 (the number in front of 2 units of emission)

Firm B's total abatement cost would be $6

Hence the total would be $3+$6 = $9

3) If each firm is given a permit for 2 units of emissions and they are able to trade the permits with each other, we can see that firm A will sell some of its permit to firm B. This means that firm A will end up with less emissions than 2 units and firm B with more than 2 units, since it is more expensive for firm B to  reduce pollution

Firm A's total pollution after trade of 1 unit worth of permits will be 1 unit and its cost of abatement will be $6 (being at 0 units of emission doesn't make sense since the cost is $10 which is higher than the $9 we got in previous answer)

Firm B's total pollution after trade of 1 unit worth of permits will be 3 units and its cost of abatement will be $2

Hence the total cost will be $6+$2 =$8, which is $1 less than if they were to reduce 2 units of emissions each

4) We see that firm A has had to incur an additional $3 (marginal cost of 3rd unit of abatement) and firm B has saved $4 by trading this permit. Hence the range of price that firm B needs to pay firm A for this permit is $3 to $4