Quantify the cost savings associated with a cost-effective abatement allocation achieved through trading.

Question

Suppose two point sources are discharging phosphorus into Wisconsin’sFox River and face the following abatement costs for this pollutant:
Point Source 1: TAC1 = 500 + 0.35(A1)2
MAC1 = 0.7A1

Point Source 2: TAC2 = 750 + 1.05(A2)2
MAC2 = 2.1A2,

where A1 and A2 represent the abatement of phosphorus effluents in pounds by Source 1 and Source 2, respectively, and TAC and MAC are measured in hundreds of dollars.
Assume that the state environmental authority has set the total maximum daily load (TMDL) for the Fox River. To achieve this limit, 40 pounds of phosphorus must be abated across the two point sources. Use this information to answer the following questions.

Answer 1

The cost-effective solution is calculated as follows:
Cost-effectiveness requires: MAC1 = MAC2, or 0.7A1 = 2.1A2
Abatement standard requires: A1 + A2 = 40
Solving simultaneously: 0.7(40 – A2) = 2.1A2
Therefore: A2 = 10
A1 = 40 – 10 = 30
To check the solution, make sure that the MACsfor each firm are equal.
MAC1 = 0.7 (30) = $2,100 MAC2 = 2.1 (10) = $2,100
Each firm’s TACsat the cost-effective abatement allocation are calculated as:
TAC1 = 500 + 0.35 (30)2 = $81,500 TAC2 = 750 + 1.05(10)2 = $85,500
Therefore, the cost savings associated with the cost-effective solution are:
Combined TACs under a uniform standard = $64,000 + $117,000 = $181,000
Combined TACs under the cost-effective solution = $81,500 + $85,500 = $167,000
?Cost savings = $181,000 – $167,000 = $14,000.