Question

Consider two firms (i.e., firms 1 & 2) with heterogeneous marginal abatement cost functions:

MAC1 =12−2E1MAC2 =10−E2.

Assume the marginal external damages from emissions are: M E D = 12 E A .

where EA is the sum of the two firms’ emissions.

1. What quantity of emissions do firms produce in the absence of government intervention? What are the total external damages? What are the total abatement costs?

2. Derive the aggregate marginal abatement cost function (Hint: This will be a kinked function. From the MAC functions you should be able to determine the kink point. Then invert the MAC functions to solve for the emissions functions. Finally, sum up emissions conditional on different MAC levels).

3. What is the socially efficient level of emissions? How much does each firm emit at the socially efficient level? How much does each firm abate relative to the market equilibrium?

4. Assume the government uses a tradable permits program to achieve the social optimum. What quantity of emissions permits should the government allocate? If the government auctions permits off initially to the highest bidder, how many permits will each firm buy? How much will each firm pay in total for these permits?

5. Assume the government uses an emissions tax to achieve the social optimum. At what level should this tax be set? How much revenue will the tax generate?

6. Assume the government implements a command and control policy where each firm must cut its emissions in half relative to the situation where there is no government intervention. What would be the total abatement costs and total external damages from this policy? Would the policy be efficient? Why or why not?

Answer 1

Marginal Abatement Cost Function 1- MAC1 =12−2E1

Marginal Abatement Cost Function 2- MAC2 =10−E2

Marginal External Damages from Emissions M E D = 12 E A

Where, EA= E1 + E2

Emissions produced by firm 1- E1= 12-1/2 MAC

Emissions produced by firm 2- E2= 10-MAC

Total External Damages- E= E1+E2 = 22- 3/2MAC

Total Abatement Costs

Aggregate Marginal Abatement Cost Function

MAC=44/3-2/3E

socially efficient level of emissions= 44/3-2/3E = 12E

18E=44/3

E= 14.73

MED= 12 E A=176.76