A utility company wants to build a coal-fired power plant. The would normally build a conventional plant, but is considering building a combined heat and power plant. The CHP plant costs $500 more to install but makes it cheaper to reduce CO2 emissions. The abatement cost curves for the two types of plants are:
Conventional: MACs = 400 - 4E
CHP: MACc = 100 - E
a) Suppose the government sets a tax of T=80. What will be the optimal level of CO2 emissions abatement for the firm operating the conventional plant? What will this firm's tax bill be? What will this firms total abatement costs be?
b) What would be the optimal level of CO2 emissions abatement for the firm if it decided to operate the CHP plant? What will the tax bill be for the firm operating a CHP plant? What will be the total abatement costs?
c) Which type of plant will the firm build and why? Use calculations in your answer
A. Assuming the government's tax is on a per emission level. That means the firm $80 per emission. At this level, the firm will be reduce (abate) the CO2 emissions till such time as its MAC is equal to tax paid per emission. So we get
80=400-4E
4E=320
E=80.
This will be optimal level of CO2 emissions for the firm.
The current total emission is E=80. The firm will pay=80*80=6400 tax.
Total abatement cost is given by .5*MAC*emission abated
Putting values for our case=
.5*80*20=800.
b. We will calculate same way as before.
Optimal abatement would be where tax=MAC. So,
80=100-E
E=20.
Tax will be 20*80=1600
Total abatement cost=.5*80*80=3200.
C. The firm should build a plant which has lesser Total Abatement cost+ Total Abatement tax as that is the amount the firm has to pay.
For plant B, total costs=1600+3200=4800.
For plant A, total costs=6400+800=7200.
Hence, the firm should build plant B.
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