Question

Suppose that a dominant firm faces fringe competition with capacity K=12 units, and market demand Q=2096-4P.

Suppose further that the dominant firm and fringe competition are able to produce with total costs given by C(Q)=20Q.

Assume that the dominant firm and fringe competition are profit maximizers.

a. The marginal cost of a unit of output for the dominant firm is __________

b. The output of the fringe competition is ___________ units.

c. The profit-maximizing level of output for the dominant firm is Q* = __________

d. The profit-maximizing price for the dominant firm is P*= __________

Answer 1

a) The cost function of the dominant firm is given as

C= 20Q

The marginal cost would be

MC= 20

c) The profit of the dominant firm would be obtained at a point where the marginal revenue is equal to the marginal cost of the dominant firm.

The market demand function is

Q= 2096- 4P

The inverse demand function is

P= 524- Q/4

The total revenue function

PQ= 524Q- Q²/4

The marginal revenue function becomes

MR= 524- Q/2

The profit maximizing quantity can be obtained at a pont where MR= MC

524- Q/2 =20

Q= 1008

Th profit maximizing quantity of the doinant firm is Q= 1008

d) The corresponding profit maximizing price of the dominant firm can be obtained from the inverse demand function.

P= 524- 1008/4 = 272