Question

Consider a monopolist facing the following demand curve: Q = 390 – 0.5P. Further 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. Thepotential entrant faces costs MCPE = ACPE = 40. Assuming the monopolist continues to profit-maximize,solve the residual demand curve for the potential entrant

c. Assume the potential entrant follows the Cournot assumption about the monopolist’s output and solve thepotential entrant’s output, price, and profits in this scenario.

d. What is the Cournot-Nash equilibrium output in this industry? Compute the profits of the monopolist and the potential entrant, respectively.

e. Is there a price the monopolist could charge to deter entry? If yes, solve for the limit price and output that will completely deter entry and compute the monopoly profit at this point?

Answer 1

a) Given,

P = 390 - 0.5Q

TR (Total Revenue) = P * Q = (390 - 0.5Q) * Q

=> TR = 390Q - 0.5Q^2

MR (Marginal Revenue) = TR / Q

=> MR = 390 - Q

MC = 30

For monopolist the profit-maximizing condition is MR = MC. So,

390 - Q = 30

=> 390 - 30 = 4Q

=> 360 = Q

=> Q = 360

From demand function we get,

P = 390 - (0.5 * 360)

=> P = $210

Therefore, here for monopolist the profit-maximizing price is $210 and quantity is 360 units.

TR = P * Q = 210 * 360 = $75,600

TC = AC * Q = 30 * 360 = $10,800

Profit = TR - TC = 75,600 - 10,800

=> Profit = $64,800

Therefore, here for monopolist the profit is $64,800.

b)

Market demand curve: P = 390-0.5(Q1+Q2)

MC2 = 40

MR2 = dPQ2/dQ2 = 390-0.5Q1-Q2

Equate MR1 = MC2

390-0.5Q1-Q2 = 40

Q2 = 350-0.5Q1

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

c)

Residual demand curve of 2: Q2 = 350-0.5Q1

Similarly, residual demand curve of Firm 1: Q1 = 360-0.5Q2

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

Q1 = 246.67 units; Q2 = 226.67 units; P = $153.33

e)

Since MR = MC

390 - 0.5Q = 40

Q = 700

p = 390 - 0.5*700 = 40

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 = (40 - 30)700 = $7000