Question

1. Two firms can reduce pollution at the following marginal abatement costs: MC1 = 12Q1 MC2 = 4Q2 where Qi is the abatement (pollution control) of firm i = 1, 2. In the absence of regulation, each firm would emit 40 units of emissions. Assume that each firm’s objective is to minimize its compliance costs

(c) The aggregate marginal cost function for this two-firm industry is: MC = 3Q Suppose the marginal benefit of pollution control is given by: MB = 35 − 0.5Q What is the efficient level of abatement?

Answer 1

Answer :

(c) :- MC1 = 12Q1

Q1 = MC1 / 12

MC2 = 4Q2

Q2 = MC2 / 4

Aggregate quantity, Q = Q1 + Q2 = (MC1 / 12) + (MC2 / 4) = (MC / 12) + (MC / 4) [MC: Aggregate MC]

Q = (1/12) x (MC + 3MC) = (1/12) x 4MC

Q = MC / 3

MC = 3Q

MC1 and MC2 are individual marginal cost curves and MC is the aggregative marginal cost curve.

Graphically as shown in the below :

(d) :- MB = 35 - 0.5Q = 35 - 0.5(Q1 + Q2) [Since Q = Q1 + Q2]

MB = 35 - 0.5Q1 - 0.5Q2

For firm 1, efficiency is achieved when MB = MC1

35 - 0.5Q1 - 0.5Q2 = 12Q1

12.5Q1 + 0.5Q2 = 35

25Q1 + Q2 = 70 [multiplying by 2] .......(1)

For firm 2, efficiency is achieved when MB = MC2

35 - 0.5Q1 - 0.5Q2 = 4Q2

0.5Q1 + 4.5Q2 = 35

Q1 + 9Q2 = 70 [multiplying by 2] .......(2)

Equilibrium is obtaine by solving (1) and (2).

Multiplying (2) by 25,

25Q1 + 225Q2 = 1,750 ........(3)

25Q1 + Q2 = 70 .............(1)

(3) - (1) results:

224Q2 = 1,680

Q2 = 7.5

Q1 = 70 - 9Q2 [from (2)] = 70 - (9 x 7.5) = 70 - 67.5 = 2.5