Question

Suppose two point sources are discharging phosphorus into Wisconsin’s Fox 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.

a. If a uniform abatement standard is used by the regulatory authority, what would be the dollar values of TAC and MAC for each source?

b. Based on your answer to part (a), is there an economic incentive for the sources to participate in the trading program? Explain briefly.

Answer 1

(A)

$A1 + A2 = 40$

by abatement

$F2 = A2$

under uniform policy, each abates

$A1= A2 = \frac{40}{2} = 20$ units

So $MAC 1 = 7A1 = \frac{7\times20}{10} = 14$

$MAC2 = 2.1A2 =\frac{ 2.1\times 20}{10} = 22$

$TAC 1 = 500 + 0.35\times(A)$ ²

= 500+0.35(14)² = 568.6

$TAC2 = 720+ 1.05\times(A2)$ ²

= 750 + 0.05(22)² = 1258.2.

TC of abatement is = 1826.8

(B) since at A1 =A2 = 20, MAC 1 ≠ MAC2, thus there is no cost effective achieved. This is because , marginal abatement costs must be equalized. So by trading program, they could equalize their MAC and hence achieve cost effective.