Question

1.Skagit County is interested in reducing water pollution from fish processing plants. It is considering putting a tax on the level of effluents that plants discharge into the water. Suppose

there are 2 plants, each with the following marginal abatement costs per million gallons of water. Suppose also that without abatement, each firm would discharge 60 million gallons of polluted water:

Plant A: MAC = 40 + .5Q

Plant B: MAC = 20 + 2Q

a) If the county sets the effluent tax at $60 per million gallons, how many more clean gallons of water will be produced (i.e. how much will pollution be reduced.)

b) Instead of the effluent tax, the county is considering issuing tradeable permits to pollute. Suppose the county decided to issue permits that end up requiring a reduction of the total number of gallons that you found in part a. If it divides these permits so that the amount that needs to be reduced is evenly split between the two firms, what will happen? Will we reach a different answer from part a? Explain why or why not.

c) Yet another option the city is considering is to impose quotas on the amount of effluents. Suppose the county is considering requiring a quota on the amount of effluent each firm can release per million gallons of water. Is this likely to be more or less efficient than the outcome of part b?

Answer 1

Consider the given problem here there are 2 plant and their “MAC” is also given in the question.

a).

Let’s assume that the “effluent tax” is at, “$60” per million gallon. So here by setting “MAC=60” we will get the corresponding pollution reduction.

So, for “plant a”, MACa = 40 + 0.5*Qa, => 60 = 40 + 0.5*Qa, => 0.5*Qa = 20, => Qa = 20/0.5 = 40.

So, for “plant b”, MACb = 20 + 2*Qb, => 60 = 20 + 2*Qb, => 2*Qb = 40, => Qb = 40/2 = 20.

So, “Qa=40” and “Qb=20” implied that the “plant a” will reduce “40 units” and “plant b” will reduce “20 units” of pollution.

So, after the imposition of the “effluent tax”, “plant a” will pollute “60-40=20 units” and “plant b” will pollute “60-40=20” units. So, the total reduction of pollution is “40 + 20 =60 units”.

Consider the following fig.

b).

If it divides the permit, so that the amounts that needs to be reduced is evenly split between 2 firms.

So, total pollution reduction is “60 units”, => each firms are receiving pollution permit of “30units”.

Now we can see at “Qa=30”, “MACa=40+0.5*30=55” and at “Qb=30”, => “MACb=20+2*30=80”. So, we can see that “MACb > MACa”, => here “pollution permits” are tradable => “firm b” will purchase some pollution permits from “firm a”, => “firm b” will increase its “pollution”, => “Qb” will reduce from “30 units” and “firm a” will reduce “pollution” further, => “Qa” increase and “firm b” will pay to “firm a”.

So, here one important question is “how much firm b will purchase permits from firm a”. So, here “firm b” will purchase until the condition “MACa = MACb” will established. So, according to this condition “Qa=40” and “Qb=20” and “MACa=MACb=60”, => “firm b” will purchase “10 units” of permit from “firm a”. So, here the situation is differ but the ultimate result is same as “a”.

c).

Now, let’s assume that the country is imposing quota on the amount of effluent each firms can release per million gallons of water. Let’s assume that for each firm the quota is “30 units”, => each firms are permitted to pollute “30 units”. So, consider the above fig where under this situation the “total abatement cost are “OBD1Q1” and “OAC1Q1” for “firm a” and “firm b” respectively. Now in “part b” the “total abatement cost are “OBD2Q3” and “OAC2Q2” for “firm a” and “firm b” respectively. So, if we compare these 2 costs then we can see that for “firm a” the “cost” has increased by “D1D2Q3Q1” and for “firm b” it has decreased by “C2C1Q2Q1”. So, “D1D2Q3Q1” is less than “C2C1Q2Q1”, => the total cost has decreased, => the “tradable permit” is efficient compared to “quota”.