Question

There are two firms, firm A and firm B. Their marginal abatement costs are MCA = 4AA and MCB = AB, where AA and AB are the tons of emissions abated by firm A and B, respectively.

a. Calculate the total cost if each firm is required to abate 50 tons of emissions.

b. Would this policy be cost effective and why?

c. What if the government set the total abatement to be 100 tons with tradable allowances, what is the total cost of this policy?

d. The policy maker knows that abatement is very costly for firm A and that they will need a large amount of allowances to cover their emissions. However, the policy maker really wants to appear fair by allocating half of the allowances to each firm at the start of the program. At the same time the policy maker doesn’t want to erode the cost effectiveness of the program given that firm A will need most of the allowances. How would you advise the policy maker and why?

e. Would a policy with a tradable emissions cap of 100 tons be socially optimal and why?

Answer 1

A) TACa=2Aa^2=2*50*50=5000

TACb=0.5Ab^2=0.5*50*50=1250

Total abatement cost=5000+1250=6250

B)No,this policy won't be cost efficent.because firm B has lower ABATEMENT cost so it should abate relatively more than firm B to be vost efficent.

C)So each will get 50 permit and allow to trade it.

Because firm B has lower ABATEMENT cost than firm A ,so firm A will buy permit from firm B.

MACa=4Aa,. Aa=0.25MACa

MACb=Ab. ,AB= MACb

Aggregate MAC:A=1.25MAC

MAC=0.8A

A=100

MAC=0.8*100=80

Aa=0.25*80=20( cost efficent allocation of ABATEMENT to firm A)

Ab=MACb=80( cost efficent allocation of abatement to firm b)

TACa=2*20*20=800

TACb=0.5*80*80=3200

Total abatement cost=800+3200=4000

D)The government need to allocate each firm half permits at first and make a rule that firm can buy and sell permit at price Equal to 80.

E)Yes , it is social efficent. because it allow firm who have higher abatement cost to buy permit from firms who has lower abatement cost. ,Which results in lower total abatement cost.