Question

Two thermic power plants have the following marginal and total cost of abatement of nitrogen oxide (NOx) emissions. When faced with no restrictions each of them emits maximum 100 ppm (parts per million) of NOx.

Firm 1: MAC1=5 A1 TAC1=2.5 (A1)^2

Firm 2: MAC2 = 10 A2 TAC2= 5(A2)^2

1. (8 pts) The EPA finds the total NOx emissions of 200 ppm too much and seeks for improvement in air quality by specifying the reduction of 40% in total emissions from 200 ppm to 120 ppm. Calculate and graph the cost minimizing allocation of abatement activities for the two firms that will achieve the total desired abatement level A=80 ppm. (You can show both firms’ MAC cost curves and their cost minimizing allocation of abatement in the same graph).

2. (6 pts) Calculate and show on a graph, the change in total cost that would occur if the EPA required equal pollution reductions by both forms: A1=A2=40 ppm.

3. (6 pts) The EPA conducts a study of the health benefits from reducing nitrogen oxide emissions and finds that they are constant at $300/ppm. How should this information on the marginal social benefit of abatement be used? How should the EPA adjust its desired level of pollution abatement?

4. (10 pts) EPA has decided to implement a pollution permit market and issue tradable permits for 80 ppm of emissions. Under this proposal, considering the maximum abatement for each polluter is 80 ppm of emissions (A_MAX=80), derive each firm’s demand curve for permits; calculate the equilibrium price of a permit, and the level of pollution abatement for each firm. Is it cost minimizing?

Answer 1

A)MAC1=5A1. A1=MAC1/5

MAc2=10A2. A2=MAC2/10

Aggregate MAC; A=3MAC/10

MAC=10A/3

Required A=80

MAC=10*80/3=800/3

A1=MAC1/5=800/3)/5=800/15=160/3

A2=MAC2/10=800/3)/10=80/3

Cost minimization abatement distribution.

TAC1=2.5*160/3*160/3=64000/9

TAC2=5*80/3*80/3=32,000/9

TAC=96000/9=10,666.67

B) TAC1=2.5*40*40=4000

TAC2=5*40*40=8000

TAC=12000

Change in total abatement cost=12,000-10,666.67=1333.33

C)The EPA will choose that MAXIMIZE net social benefit.

So EPA will choose that abatement,where MAC=300

Aggregate MAC=10A/3

Social optimal abatement,

10A/3=300

A=300*3/10=90

D)

The inverse of MAC will be demand of permit,

P=500-5D1( firm 1 demand)

D1=100-0.2P

P=1000-10D2( firm 2 demand)

D2=100-0.1p

Market demand,D=200-0.3P

TOtal permit=80

Equilibrium price of permit,

80=200-0.3P

0.3p=120

P=120/0.3=400( per permit)

D1=100-0.2*400=20

D2=100-0.1*400=60

A1=100-20=80

A2=100-60=40

TAC1=2.5*80*80=16,000

TAC2=5*40*40=8000

TAC=24,000

Yes ,This is cost minimizing.

Note: In part D total abatement is 120 but in part a) Total abatement is 80, that is why total cost is different.