Question

Two plants are emitting a uniformly mixed pollutant called gunk into the beautiful sky over Tourist-Town. Suppose the aggregate marginal reduction costs is MB = 400/3 - (2/3)x. Plant G has marginal reduction costs of MB1 = 200-2(x1), while Plant K has marginal reduction costs of MB2 = 100 - (x2), where x1 and x2 are the emissions level for each firm, and x = x1 + x2.

1) How much will each plant pollute if there is no environmental regulations?

2) The city government decides that it can tolerate total emissions of no more than 110 kgs of gunk per day. What is the cost effective pollution level for each plant if total pollution must equal 110?

Answer 1

1).

Consider the given problem here there are two plant and there marginal reduction cost are given below.

=> MC1 = 200 – 2*X1, marginal reduction cost of plant G.

=> MC2 = 200 – X2, marginal reduction cost of plant K.

Now, without nay regulation each firm will pollute until marginal reduction cost is zero.

=> MC1 = 0, => 200 – 2*X1 = 0, => X1 = 200/2 = 100, => X1 = 100, for plant G.

=> MC2 = 0, => 100 – X2 = 0, => X2 = 100, for plant K. So, without any regulation both the plant will pollute 100 units, => total pollution by both the plants is “200 units”.

2).

Now, let’s assume the government have decided the total pollution will not exceed 110 units, => X1+X2=110 per day. The pollution allocation will be cost effective if the marginal reduction cost for both the plants are equal.

=> MC1 = MC2, => 200 – 2*X1 = 100 – X2, where “X1+X2 = 110”.

=> 200 – 2*X1 = 100 – (110-X1), => 200 – 2*X1 = X1 – 10, => 3*X1 = 210, => X1 = 70.

=> X2 = 110 – 70 = 40, => X2 = 40.

So, here “plant G” will pollute 70 units of pollution and “plant K” will pollute 40 units of pollution, => total pollution by both the firms is “110 units”.