Question

Assume that there are two firms, each emitting 20 units of pollutants into the environment, for a total of 40 units in their region. The government sets an aggregate abatement standard (AST) of 20 units. The polluters' cost functions are as follows, where the dollar values are in thousands:

Polluter 1:       TAC₁= 10 + 0.75(A₁)²,                      Polluter 2:       TAC₂= 5 + 0.5(A₂)²,                          MAC₁= 1.5A₁,                                                           MAC₂= A_2.

a) Suppose that the government allocates the abatement responsibility uniformly, requiring each polluter to abate 10 units of pollution. Quantitatively assess the cost implications.

b) What is the cost effective abatement to polluter 1 and polluter 2?

Answer 1

(a).TAC1 = 10 + 0.75A1^2 , MAC1 = 1.5A1

TAC2 = 5 + 0.5A2^2 , MAC2 = A2.

If the two polluter uniformly distribute 10 units of pollution then

MAC1 at A1= 10 is = 1.5A1 = 1.5*10 = 15

TAC1 = 10 + 0.75A1^2 = 10 + 0.75*10^2 = 10 + 0.75*100 = 10 + 75 = 85.

MAC2 at A2 = 10 is = A2 = 10.

TAC2 = 5 + 0.5A2^2 = 5 + 0.5*10^2 = 5 + 0.5*100 = 5 + 50 = 55

So, if they uniformly reduce the emission by 10 units then TAC of firm1 is TAC1 = 85, and MAC of firm1 is 15.

TAC of firm2 is TAC2 = 55, and MAC of firm 2 is 10.

So, if they reduce the emission uniformly then the cost of emission is higher for polluter1 and cost of emission is lower for polluter2.

(b). Cost effective abatement to polluter 1 and polluter 2 will be reached when their marginal abatement cost are same such that total abatement is also 20.

It means for cost effective reduction MAC1 = MAC2 , such that A1 + A2 = 20.

MAC1 = 1.5A1 , if A1 = 8 units , then MAC1 = 1.5*8 = $12

MAC1 = A2, if A2 = 12 units, then MAC2 = A2 = $12.

So, for A1 = 8 units and A2 = 12 units, MAC1 = MAC2, such that A1 + A2 = 8 + 12 = 20 units.

So, Cost effective abatement is 8 units for polluter 1 and 12 units for polluter 2.