Question

Suppose two power plants within the Cedar Valley emit sulfur dioxide (SO_2) that exceeds the emission standard. To meet the standard, 200 units of SO_2 must be abated in total. The two firms have the following marginal abatement costs, where A_i is units of SO_2 abatement:  

MAC_1 = 0.05A_1

MAC_2 = 0.09A_2

a. Is a uniform policy of equal reduction (100 units of abatement per firm) cost-effective? Justify your answer.

b. How many units of SO_2 should be abated by each firm to meet the standard at the least cost?

c. What is the marginal cost of abatement for each firm under the cost-effective abatement plan you found in part (b)?

d. What is the welfare cost of using a uniform policy?

Answer 1

a)

At Cost effective solutions

MAC should be equalized across all firms,

So, In Uniform Standard, A₁ = A₂ = l00.

Now MAC₁ = .005 x l00 = 5

MAC₂ = 0.09 x l00 = 9

thus as

MAC₁ ≠ MAC₂ , So it is not Cost - effective

b)

At least Cost, MAC₁ = MAC₂

0.05 A₁ = 0.09 A₂ and A₁ + A₂ = 200

5A₁ = 9A₂

Put A₁ = 200 - A₂

=> 5 ( 200 - A₂ ) = 9A₂

=> 1000 = 14A₂

=> A₂* = 500 /7

=> A₁ = 200 - 500/7

=  900/7

c) MAC₁ = 0.05A₁*

= 0.05 x 900/7

= 45/7

MAC₂ = 0.09A₂*

= 0.09 x 500/7

= 45/7

d) Total cost

TAC = TAC₁ + TAC₂ =  ∫ MAC₁ +  ∫ MAC₂

= ( 0.05A₁)² / 2 + (0.09A₂)² / 2

= ( 0.05 x 100 )² / 2 + ( 0.09 x 100 )² / 2

= 700

Uniform Policy, TAC = 700

Cost effective solution, TAC = (0.05/2) x (900/7)² + (0.09/2) x (500/7)²

= 642.86

So, Welafare cost of uniform policy = 700 - 642.86

= $ 57.14