Question

Consider an industry with a linear inverse demand, p = 300 – 2Q, and MC = AC = $60. Solve for industry output (Q), price (p), and profits if the industry is:

1. Perfectly competitive

2. Monopolistic

3. Show graphically (on the next page) the deadweight loss associated with monopoly when costs are constant as in this case. Point out differences in consumer surplus and producer surplus (if any) between the perfectly competitive and monopoly outcomes.

Answer 1

1) In perfectly competitive market, equilibrium occurs when demand equals MC which is occuring when price equals MC.

300 - 2Q = 60

Q = 120

Put value of Q = 120 in demand equation:

p = 60

2) In monopoly, equilibrium occurs when MC = MR.

Total revenue = Price * Quantity = 300Q - 2Q2

Marginal Revenue = Derivative of total revenue with respect to Q = 300 - 2Q

300 - 4Q = 60

Q = 60

Put value of Q in demand equation which makes p = 180

3) In perfectly competitive market, equilibrium occurs when demand equals MC which is occuring when price is $60 and quantity traded is 120 units.

Consumer surplus is area of portion A + B + C + D + E

In monopoly, equilibrium occurs when MC = MR. Quantity traded at this level is 75 units at price 150.

Consumer surplus under monopoly is sum of portion of A + B.

Producer surplus is sum of portion C + D

Deadweight loss is of portion E.