Assume that two power plants, Firm 1 and Firm 2, release arsenic in a small urba
ID: 1217240 • Letter: A
Question
Assume that two power plants, Firm 1 and Firm 2, release arsenic in a small urban community that exceeds the emissions standard. To meet the standard, 40 units of SO2 must be abated in total. The two firms face the following abatement costs:
MAC1 = 0.7A1
MAC2 = 3.3A2
where costs are measured in thousands of dollars.
a) In abating equally (Uniform Standards) which firm would have a larger marginal abatement cost, and point which company is less efficient (show this mathematically and show your work)
b) If both companies want to be cost effective (cost efficient criteria), in which MAC1 = MAC2, how are abatement levels be reallocated?, (Math Required, show your work )
c) Under cost effective criteria which company has to abate more, why, and what are the possible complications, explain?
d) Under cost effective criteria what are the total abatement cost for each plant? (Math Required)
Explanation / Answer
A) Abating equally means 20 units each
MAC1 = 0.7 * 20 = 14 thousand
MAC2 = 3.3 * 20 = 66 thousand
Firm 2 is less efficient in abating SO2 and it has high marginal cost compared to firm 1.
B) Putting MAC1 = MAC2
0.7*A1 = 3.3*A2
Now A1 + A2 = 40
0.7 * (40 - A2) = 3.3 * A2
28 - 0.7A2 = 3.3A2
28 = 4A2 so tha A2 = 7 and A1 = 33
C) Firm 1 has less marginal cost and it is more efficient in abatement in comparison with Firm 2. However, if such criteria has been choosen then it will be unfair to Firm 1 and it will further disincetivize Firm 2 to lower its cost by increasing its efficiency. Firm 1 could also see the point that there is no incentive to have efficient and it may raise its marginal cost for abatement.
D) From the solution B, wekanow that A1 = 33 and A2 = 7
So putting these values
MAC1 = 0.7 * 33 = 23.1 thousands
MAC2 = 3.3 * 7 = 23.1 thousands