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Homework answers / question archive / Assume that two power plants, Firm 1 and Firm 2, release sulfur dioxide (SO2)in a small urban community that exceeds the emissions standard
Assume that two power plants, Firm 1 and Firm 2, release sulfur dioxide (SO2)in a small urban community that exceeds the emissions standard. To meet the standard, 30 units of Soz must be abated in total. The two firms face the following abatement costs: MAC, = 16 + 0.5A, MAC2 = 10 + 2.5A2, (where costs are measured in thousands of dollars.) a. Prove that a uniform standard will not meet the cost-effectiveness criterion. (Meaning both firms must abate the same amount. Since the standard is 30, each firm must abate 15 units each. Think about the summer/winter homework question). b. Calculate how the abatement levels should be reallocated across the two firms to minimize costs, Paragraph B 1
Given that
MAC1= 16 + 0.5A1
MAC2 = 10 + 2.5A2
a.
According to the uniform standards, firm 1 and firm 2 should release same level of sulfur dioxide (SO2). Usually, the marginal abatement cost is considered while determining the standard level of emission.
If there is no uniformity in the marginal cost then a uniform standard will not meet the cost-effective criterion. The following is a calculation of marginal abatement costs.
Marginal Abatement cost1 = 16 + 0.5 (20)
= 16 + 10
= 26
Marginal Abatement cost 2 = 10 + 2.5 (20)
= 10 + 50
= 60
For firm 1, marginal abatement cost is 26 and for firm 2 it is 60. The difference in the marginal abatement costs shows that the cost effective criterion is not met. There should be uniformity in the marginal abatement costs for the both firms to meet the cost effective criterion.
b.
The abetment requirement per firm should be allocated equally to obtain cost effectiveness. The total of the abetment cost (firm 1 and firm 2) should be equal to 40 units. The following is a calculation of marginal abatement costs.
Criterion for cost effectiveness 
Marginal abatement cost 1 = Marginal abatement cost 2.
16 + 0.5A1 = 10 + 2.5A2
Solving equation,
16 + 0.5 (40 - A2) = 10 + 2.5A2
36 + 0.5A2 = 10 + 2.5A2
26 = 3A2
A2 = 26/3
A2 = 8.67
If A2 equals to 8.67 then A1 equals to 31.33(40-8.67) units. Thus, to obtain cost effectiveness firm 1 should be allocated 31.33 units and firm 2 should be allocated 8.67 units. The marginal abatement cost can be checked by using these units.
Marginal Abatement cost 1 = 16 + 0.5 (31.33)
= 16 + 15.67
= 31.67
Marginal Abatement cost 2 = 10 + 2.5 (8.67)
= 10 + 21.67
= 31.67
Now, the marginal abatement cost for firm 1 and firm 2 is equal. This uniform standard meets the cost-effectiveness criterion.
