There are three plants located in the city of Lost Airless (LA) that emit SO2 as

Question

There are three plants located in the city of Lost 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) = 2 y2A, at plant A, CB(yb)= y2B; at plant B, and CC(yC) = 2 y2C 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) = l200y — y2, where y is the total amount cleaned up (yA + yB + yC).

A) Marginal cost of cleanup_____at plant A, ____at plant B, and ____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) Total abatement costs associated with the optimal effluent tax are_____ . If standards are imposed that require each firm to reduce pollution by the same percentage, total abatement costs are______

G) 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 change if the government decided to give the permits to firms instead of selling them?

Explanation / Answer

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”.

e).

As we know that “MCa=4*Ya” as “Ya=MCa/4=400/4=100” and “MCb=2*Yb” as “Yb=MCb/2=400/2=200” and “MCc=4*Yc” as “Yc=MCc/4=400/4=100”.

So, at this tax plant A will clean up “100”units, plant B will clean up “200”units, plant C will clean up “100”units.

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