Question

The aggregate MAC function for some polluter is given by MAC=200-2E, where E is measured in millions of tons, and the MD function is given by MD = 2E.                       

Graph both functions and solve for the socially-efficient level of emissions.

What size emissions tax per ton is needed to achieve the socially-efficient level of emissions? Explain.

Compute the total tax bill and total abatement cost to polluters if they reduced their emissions to the socially-efficient level. What is the net gain to society from this tax policy?

Answer 1

a).

Consider the given problem here the “MAC” and “MD” are given in the question. So, at the optimum “MAC” must be equal to “MD”.

=> MAC=MD, => 200 - 2*E = 2E, => 4E = 200, => E=200/4 = 50, => E=50. So, the socially efficient level of emission is given by, => E* = 50 units.

b).

Now, at “E=50” the “MD” is given by, => MD=2E=2*50=100”, => MAC=MD=100”, => to get the socially efficient level of “E” the emission tax should be “t=MD=100” per unit of emission.

c).

Now, if the firm reduce its emission to the socially optimum level that is “E=50”, => the total tax bill is given by, => t*E = 100*50 = $5,000. Now, with zero emission tax the firm will emit such that the “MAC=0”, => the level of emission is “100”. Now, if the emission tax is imposed, => firm will reduce emission to “50”, => the total abatement cost is given by “EB1B2”, => the total abatement cost is given by.

=> EB1B2 = 0.5*t*(100-50) = 0.5*100*50 = $2,500, => Total Abatement Cost = EB1B2 = $2,500.

So, here the firm is polluting “50 units”, => the total damage is given by “OEB”, => the net gain is given by.

=> OA2E = 0.5*50*(200-0) = 0.5*50*200 = $5,000, => OA2E = $5,000. So, here the net gain is given by “OA2E = $5,000”.