Assume that two power plants, Firm 1 and Firm 2, release arsenic in a small urba
ID: 1168394 • 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 = 18 + 0.7A1 MAC2 = 15 + 3.2A2,
where costs are measured in thousands of dollars.
a) Prove that a uniform standard will not meet the cost-effectiveness criterion.
b) Determine the abatements for company 1 and 2 under the cost effective criterion.
c) Determine Total abatement cost for both companies under cost effective criterion
d) Are there any cost savings on implementing the cost effective criterion with respect to uniform standards, if so please show the savings
Explanation / Answer
Ans:
A)
A uniform standard means that each firm must abate the same amount, which in this case would be 20 units of SO2 each. Using this value, we find each firm’s marginal abatement costs. The results are MAC1 = 18 + 0.7(20) = $32 thousand, and MAC2 = 15 + 3.2(20) = $79 thousand. Since the MACs are not equal, we know the cost-effectiveness criterion is not met.
B)
To achieve cost-effectiveness, the abatement requirements per firm must be reallocated so that the MACs are equal, subject to the sum of the two abatement levels, A1 + A2, equaling 40 units. This is found as follows:
Cost-effectiveness requires: MAC1 = MAC2
18 + 0.7A1 = 15 + 3.2A2
Abatement standard requires: A1 + A2 = 40
Solving simultaneously: 18 + 0.7(40 – A2) = 15 + 3.2A2
Therefore: 46 – 0.7A2 = 15 + 3.2A2, so 3.9A2 = 31, or A2 = 7.95, and
A1 = 40 – 7.95 = 32.05
Check your result by finding MAC1 and MAC2 evaluated at the abatement levels found, and make sure they are equal. In this case, MAC1 = 18 + 0.7(32.05) = $40.4 thousand approx, and MAC2 = 15 + 3.2(7.95) = $40.4 thousand approx.
NOTE: To solve c and d part we need TAC1 and TAC2 equations.