Question

A competitive refining industry produces one unit of waste for each unit of refined product. The industry disposes of the waste by releasing it into the atmosphere. The marginal benefit for the refined product is given by MB = 24 - Q, where MB is the marginal benefit when quantity Q of the product is consumed. The inverse supply curve (also the marginal private cost curve) for refining is MPC = 2 + Q, where MPC is the marginal private cost when the industry produces Q units. The marginal external cost curve is MEC = 0.5Q, where MEC is the marginal external cost when the industry releases Q units of waste. a) Draw a well-labelled diagram showing MB, MPC, MEC, and MSC. b) What are the equilibrium price and quantity for the refined product when there is no correction for the externality? c) How much of the chemical should the market supply at the social optimum？ d) How large is the deadweight loss from the externality? e) Suppose the government imposes an emissions fee of $T per unit of emissions. How large should the emissions fee be if the market is to produce the economically efficient amount of the refined product

Answer 1

(a)

From MB function, When Q = 0, MB = 24 (Vertical intercept) & when MB = 0, Q = 24 (Horizontal intercept).

From MPC function, When Q = 0, MPC = 2 (Vertical intercept)

From MEC function, When Q = 0, MEC = 0 (Vertical intercept)

MSC = MPC + MEC = 2 + Q + 0.5Q = 2 + 1.5Q

From MSC function, When Q = 0, MSC = 2 (Vertical intercept)

The graphs are as follows.

(b)

In equilibrium, MB = MPC

24 - Q = 2 + Q

2Q = 22

Q = 11

Price = 2 + 11 = 13

(c)

In social optimal, MB = MSC

24 - Q = 2 + 1.5Q

2.5Q = 22

Q = 8.8

Price = 24 - 8.8 = 15.2

(d)

Deadweight loss = (1/2) x Difference in price x Difference in quantity = (1/2) x (15.2 - 13) x (11 - 8.8)

= (1/2) x 2.2 x 2.2

= 2.42

(e)

The emission fee, equivalent to a Pigouvian tax, is equals to MEC when Q is at socially optimal level.

Emission fee = 0.5Q = 0.5 x 8.8 = 4.4