There are three plants located in the city of Los Airless (LA) that emit SO 2 as

Question

There are three plants located in the city of Los Airless (LA) that emit SO2 as part of their production process. Currently, plant A emits 100 units of SO2, plant B emits 200 units of SO2, and plant C emits 500 units of SO2. The cost of cleanup is CA(yA)=2y2A at plant A, CB(yB)=y2B at plant B, and CC(yC)=2y2C at plant C, where yA is the amount cleaned up at plant A, yB is the amount cleaned up at plant B, and yC is the amount cleaned up at plant C. The total benefits of cleanup in LA are B(y)=1200y-y2, where y is the total amount cleaned up (yA +yB +yC).

a. Marginal cost of cleanup is _____ at plant A, _____at plant B, ____ at plant C.

b. If the firms abatement levels equate marginal costs, the marginal cost curve for cleanup for the entire LA area is ____.

c. The optimal level of cleanup of SO2 for LA is ______.

d. The effluent charge that achieves the efficient level of cleanup Is _____.

e. At this tax, plant A would clean up _____ units, plant B would clean up _____ units, and plant C would clean up ____ units. _____ percent of the initial amount of SO2 is cleaned up.

F. Suppose the government auctioned pollution permits that gave firms a right to pollute 1 unit of SO2 . What is the efficient number of permits to sell? What would be the equilibrium price of a permit if the efficient number of permits were sold? How would your analysis chage if the government decided to give the permits to the firms instead of selling them?

Explanation / Answer

a).

Consider the given problem, here the “Cost of cleanup of the 3 unit is given by, “Ca=2*Ya^2”, “Cb=Yb^2” and “Cc=2*Yc^2”.

So, the MC of plantA is given by “MCa=4*Ya”, in “plantB” “MCb=2*Yb” and in “planC” “MCc=4*Yc”.

b).

we can write “MCa=4*Ya” as “Ya=MCa/4” and “MCb=2*Yb” as “Yb=MCb/2” and “MCc=4*Yc” as “Yc=MCc/4”.

So, MC for the entire LA area is, Ya+Yb+Yc=MCa/4 + MCb/2 + MCc/4,

=> Y= (1/4)*(MCa + 2*MCb + MCc) = (1/4)*4MC = MC.

=> MC = Y.

c).

Now, at the equilibrium, MC=MB,

Where “B = 1200*Y – Y^2, be the Total Benefit, MB=1200 – 2*Y. So, MB=MC, =>

=> 1200 – 2*Y = Y, => 3*Y=1200, => Y=1200/3=400.

So, at the optimum, Y=400.

d)

So, at Y=400, MB=MC=400, so the effluent charge that achieves the efficient level of cleanup is “Y=400”.

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