Question

Suppose a monopoly has constant marginal costs of $20 per unit. Demand for the monopolist’s product is Q = 100 - P. Please show the work to receive the full credit.

i.     What are the profit maximizing price and quantity for this monopoly?                    (4)

ii.    How many units of the product would the competitive market supply? What would the equilibrium price be?              

iii. Calculate how much consumer surplus would be lost if this market started off as perfectly competitive but then became monopolistic.                                                                                                                              (4)

iv. Calculate how much producer surplus would be gained if this market started off as perfectly competitive but then became monopolistic.

Answer 1

Demand : Q=100-P

MR= 100-2Q

MC=$20

i. Monopoly outcome is at MR=MC.

100-2Q=20

Equilibrium quantity Q*= 40

Equilibrium Price P*= 100-40=$60

ii. Competitive market equilibrium is at MC= P.

100-Q= 20

Q**=80

P**= $20

iii. Consumer surplus under perfect competition:

0.5*(100-20)(80)= $3200

Consumer surplus under Monopolistic competition:

0.5(100-60)(40)= $800

Fall in consumer surplus= $3200-$800= $2400

iv. Producer surplus under perfect competition=0 since MC is a straight line.

Producer surplus under Monopolistic competition:

0.5(60-20)(40)= $800

Gain in producer surplus= $800