Two steel factories are currently emitting 8,000 tons of pollution each (for a total of 16,000 tons). Pollution reduction (abatement) costs for Plant 1 are given by MCR1= 0.02Q and for Plant 2 by MCR2 = 0.03Q, where Q represents tons of abatement, and MCR the marginal cost of pollution reduction.
A. Suppose a tradable permit system is instituted in which permits for emissions of 6,000 tons of pollution are freely issued, 3,000 permits to each plant. What are the pollution reduction costs to each firm without trading? Use a graph to support your answer, showing 10,000 tons of total pollution reduction.
B. Using the same diagram you drew in Part A, explain which firm will sell permits (and how many), and which firm will buy permits. Assuming all permits sell for the same price, how much will each permit cost? Calculate each firm’s net costs after trading, considering their pollution reduction costs and the costs (or revenues) from the permit sale.
A). Without trading each firm have reduce 5000 tons of pollution,
So marginal cost of firm 1 of abatement=0.02Q
Total coat of firm 1 of abatement=0.01*Q^2
So cost of 5000 abatement=0.01*5000*5000=250,000
Same for firm 2
Q1=MCR/0.02. Q2= mcr/0.03
So firm 2 will sell permit of 1000 tons .and firm 1 will buy it.
The permit price=abatement cost of those 1000 tons to firm 1
Permit price =0.01*6000*6000-0.01*5000*5000=110,000
Firm 1 net cost =0.01*6000*6000+110,000=347,000
Firm 2 net cost =0.015*4000*4000-110,000=130,000
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