Question

Suppose a society has the following marginal abatement cost (MAC) and marginal damage (MD) functions MAC = 140 – 4E MD = 3E Where E denotes the level of pollution.

a) What is the unregulated level of pollution?

b) What is the optimal level of pollution? Sketch the MAC and MD functions and show the optimal level of pollution in the diagram.

c) Find the per-unit pollution tax that would achieve the optimal level of pollution. Show the level of tax along with the MAC curve in the diagram.

d) Explain and show in the diagram how the pollution level may be affected if the pollution tax leads the polluting firms to switch to a new cost-saving pollution control technology

Answer 1

MAC1/a1 = MAC2/a2 = - (ambient permit price)

Also, a1 e1 + a2 e2 = 12

ei = 20 – qi (i = 1,2)

Rewriting,

a1(20 - q1) + a2(20 - q2) =12 (i)

0.3q1/1.5 = p (ii)

0.5q2/1 = p (iii)

Three equations and three unknowns (p, q1, q2)

Rewrite (i) as 1.5(20 - q1) + 1(20 - q2) = 12

1.5q1 + q2 = 38

Rewrite (ii) and (iii) as

0.3q1 = 1.5p

0.5q2 = p

or 0.3q1 = 1.5(0.5q2)

q1 = 5q2/2 or q2 = 2q1/5

So, 1.5q1 + 0.4q1 = 38

q1* = 20 ; q2* = 8 ; p = $4 (per unit pollution or per ppm)

Pollution generated by firm 1 = 1.5e1 = 1.5(0) = 0

Pollution generated by firm 2 = 1.e2 = 1(12) = 12