The marginal control cost curves for three air pollutant sources affecting a sin
ID: 1189048 • Letter: T
Question
The marginal control cost curves for three air pollutant sources affecting a single receptor are:
MC1 = 200(q1), MC2 = 100(q2), and MC3 = 1,200, where all costs are measured in dollars ($).
Their respective transfer coefficients are a1 = 2.0, a2 = 1.0, a3 = 1.2. In the absence of any
pollution controls, sources 1 and 2 each emit 20 units of pollution while source 3 emits 12 units.
The ambient standard is 36 ppm
.
(a) If an ambient permit system were established, how many permits would be issued, what price would eventually prevail, and if the ambient permits were auctioned off and NOT freely allocated, how much would each source spend on ambient permits?
(b) What are the total control costs for the three sources?
Explanation / Answer
a) Since ambient standard is 36ppm , 16 permits will be issued.
MAC1/a1=MAC2/a2=mac3/a3= -x ( ambient permit price)
a1e1+a2e2+a3e3 = 16
e(i)= 20- q(i) ( i = 1,2 )
a1(20-q1)+a2(20-q2) = 16 => 2(20-q1) + 1(20-q2) = 16
=> 40 - 2q1 + 20 - q2 = 16
=> 60 - 2q1 - q2 = 16
=> 44 = 2q1 + q2
200q1/2 = p
100q2/1= p
=> 200q1/2 = 100q2/1
three equations and three unknowns
q1=q2= 44/3 = 14.7
p = 100(44/3) =1470
e1=e2= 20 - 14.7 = 5.3
b) Pollution generated by firm 1 and firm 2 is equal = 2(5.3) = 10.6
Source 1 and source 2 demand for ambient permit is equal and will spend 10.6 X 1470 = 15582
Source 3 will spend = 1200 X 12 = 14400
Total cost = 29982 $
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.