Question

Suppose that there are three firms in a region that are producing a common emission. The marginal abatement cost (MAC) for each firm is given by:

MAC1 = 240 – 2E1

MAC2 = 192 – 1.6E2

MAC3 = 320 – 2.67E3

The marginal damage function for the region is given as MD = (4/3)ET {where ET = E1 + E2 +E3}

a) Find the aggregate MAC for the region.

b) Find the socially optimal level of Emissions for the region

c) Suppose that the government imposes a Uniform Standard on the three firms that achieves the socially optimal level. What will be each firm’s MAC and TAC?

d) Now, instead of a standard, the government uses an Emission Tax. Find the tax rate that achieves the socially optimal level of emissions. Determine each firms emissions, TAC, and Tax Bill. Compare the total cost to each firm from a tax policy to your answer in (c).

e) Suppose the government decides to use a Marketable Permit program. If permits are initially given to each firm in the amount equal to the uniform standard, then:

e1). Determine the final allocation of permits (after trading)

e2). What is the net cost to each firm (TAC plus/minus permit revenues/costs)

e3). Compare each firm’s total cost under permit system to that of the uniform standard and the emission tax.

Answer 1

Part (A)

Aggregate marginal abatement cost for the region

Part (B)

socially optimal level of emissions for the region where marginal damage equals aggregate marginal abatement costs

Part (C)

government imposes a Uniform Standard on the three firms that achieves the socially optimal level

Now all 3 firms will have equal amount of emissions

Part (D)

the government uses an Emission Tax, that achieves the socially optimal level of emissions.

tax rate will be equal to MACs of the firm at socially efficient outcome of the emission

tax rate is 159.32

total abatement cost for firm 1 and 3 is higher in case of standard compared to that for tax

whereas total abatement cost for firm 2 is higher in case of tax compared to that for standard

Where