Environmental Economics Homework 3

1. Suppose there are only two firms in a region emitting a particular pollutant, E. The firms have the following marginal abatement cost curves;

MAC₁ = 60 - 3E₁

MAC₂ = 50 - 2E₂

where E₁ and E₂ are emissions from firm 1 and firm 2 respectively. Suppose the policy maker does not want emissions to exceed 30 units of E.

Important note: This question is not just a pile of algebra. It emphasizes four results presented in lecture:

• Least cost emissions reductions require MAC to be equal across firms;
• The efficient level of emission reduction requires the aggregate MAC to be equal to MPD;
• If aggregate MAC equals MPD, then the MAC for each firm must be equal to MPD, because graphically, the aggregate MAC is the horizontal summation of the firm MACs;
• Since the MAC of each firm is equal to MPD at the efficient solution, it follows that maximization of social net benefits implies a least cost reduction of emissions. This last point is intuitive: to maximize social net benefits with respect to pollution control it must be the case that the cost of pollution control is minimized. That is, you can't say you are making society as well off as possible if it is possible to obtain the pollution reduction more cheaply.

a. What is the total abatement required from the two firms if emissions are limited to 30 units of E? Show your work, and highlight your answer.

b. How much will firm 1 emit, and how much will firm 2 emit, if abatement is achieved in a cost-effective manner and the total emissions of the two firms sums to 30? Show your work.

c. Suppose the marginal pollution damage curve for this pollutant is

MPD =2E-5 if E ≥ 0

Is 30 units of emissions the efficient level of emissions? Show your reasoning. If you say "no", indicate whether 30 units of emissions is too little or too much relative to the efficient level.

Q2. Suppose two firms are the only sources of sulfur dioxide (SO₂) in a certain region. The MAC curves for the two firms are the following:

MAC₁ = 60 - 3E₁

MAC₂ = 40 - E₂

where E1 and E2 are the emissions of firms 1 and 2, respectively.

Suppose the regulator decides to impose a particular type of command-and-control (CAC) regulation: proportional reduction. Under this scheme, each firm must reduce its emissions by 40%.

a. Determine the total level of abatement. Show your work.

b. Find the marginal abatement cost of each firm. Show your work.

c. Find the total abatement cost (TAC) of each firm (you can either integrate the MAC functions of each firm, or if you don't know how to integrate a function, then draw the graph of the MAC curves and use geometry to find the TAC of each firm). Show your work.

d. From an economic efficiency perspective, which of the two firms is abating too much?

e. Now assume that the regulator sees that this CAC regime costs more than necessary. That is, the regulator can get the same emissions reduction at a lower cost. To do this, the regulator imposes a tax on emissions.

What would be the appropriate tax to obtain the same level of emissions reduction?

Q3. Suppose a reduction in emissions results in total abatement cost to Firm A greater than total abatement cost to Firm B. Can one draw the following conclusions from this result?

a. The marginal abatement cost for Firm A is greater than the marginal abatement cost for Firm B.

Yes/No

b. The allocation of emissions across the two firms is not cost effective.

Yes/No

c. The efficient level of emissions is not obtained.

Yes/No