In a market, demand is given by P = 100 - Q and the (private) marginal cost of production for the aggregation of all firms (the industry supply curve) is given by MC = Q. Pollution by the industry creates external damages given by the (constant) marginal external cost curve MEC = 30.

(a) Calculate the output and price of if the industry operates under com petitive conditions without regulation.

(b) Calculate the socially efficient price and output of the industry.

(c) Calculate the deadweight loss due to operating at the competitive level of output rather than the socially efficient level of output.

Market price, quantity = 50, 50

Social price, quantity = 65, 35

Deadweight Loss = 112.5

Explanation:

In perfectly competitive markets, optimal equilibrium is where:

[Marginal Revenue = Price] = [Marginal Cost]

[ MR = 100 - Q] = [MC = Q]

100 - Q = Q

Q + Q = 100

2Q = 100 → Q = 100/2

Market Q = 50

P = 100 - Q → P = 100 - 50

Market P = 50

Socially efficient markets are where : additional (external) cost or additional benefit is also used to determine socially optimum quantity

[ MR = 100 - Q] = [TC = MC + EC]

100 - Q = Q + 30

100 - 30 = Q + Q

2Q = 70 → Q = 70 / 2

Social Q = 35

P = 100 - Q → P = 100 - 35

Social P = 65

Deadweight Loss

1/2 [ (P2 - P1) (Q1 - Q2) ]

1/2 [ (50 - 35) (65 - 50) ]

1/2 (15x15) ] → 1/2 (225)

Deadweight Loss = 112.5