Question

Consider a monopolist with the following demand curve: P = 390-29. The monopolist faces MCM = ACM = 30 a) Solve the profit maximizing level of monopoly output, price, and profits. b) Suppose a potential entrant is considering entering, but the monopolist has a cost advantage. The potential entrant faces costs MCPE = ACPE = 40. Assuming the monopolist continues to profit-maximize, solve for the residual demand curve for the entrant. Assume the potential entrant follows the Cournot assumption about the monopolist's output. Solve for the entrant's output, price, and profits in this scenario. What are the new monopoly profits? Is there a price the monopolist could charge to deter entry? Solve for the limit price and output that will completely deter entry. What is the monopoly profit at this point?

Answer 1

as p : 390 - 20 - MCM = AM = 30 If MR=me, there will be may profit TR = PxQ = (390-20) Q dre - 390-2Q = MR :390 - 2Q 230 ; 20 - 360 :: Q = 180 Pe 390 - 2 (180) = 30 MC=30 TC 2 30Q = 30 (180) = 5400 1. Profit 2 TR-TC 30 K 180 -5900 da

  

b)

Market demand curve: P = 390-2(Q1+Q2)

MC2 = 40

MR2 = dPQ2/dQ2 = 390-2Q1-4Q2

Equate MR1 = MC2

390-2Q1-4Q2 = 40

Q2 = 87.5-0.5Q1

This is the residual demand curve of entrant (Firm 2)

c)

Residual demand curve of 2: Q2 = 87.5-0.5Q1

Similarly, residual demand curve of Firm 1: Q1 = 90-0.5Q2

Substitute these residual demand curves into each other. This gives the final values as:

Q1 = 61.67 units; Q2 = 56.67 units; P = $153.33

d)

Price which the monopolist can charge to deter entry = Any price lower than the entrant AC

That is, 40<P<30

Suppose P* = $35

Since this price will lie below its AC curve, the entrant would find it profitable to not enter the market.

Monopoly profit = (P-AC)Q = (35-30)177.5 = $887.50