Question

Consider a pure monopolist who faces demand Q= 205 - 2P and has a cost function C(Q) = 2Q.

Solve for the information below, assuming that the monopolist is maximizing profits.

The monopolist is able to produce at a constant marginal cost of _________

The monopolist's profit-maximizing level of output is Q* = ______

The monopolist's profit-maximizing price is P* = _________

Answer 1

The demand function faced by the monopolist is

Q= 205- 2P

The cost function is

C= 2Q

The marginal cost at which the profit of the monopolist would be maximized can be obtained by differentiating the cost funtion.

The profit maximizing marginal cost of the monopolist is

MC= 2

The profit of the monopolist is maximized where the marginal revenue = marginal cost.

The inverse demand function of the monopolist is

P= 102.5- Q/2

The total revenue of the monoplist

TR= PQ= 102.5Q -Q²/2

The marginal revenue becomes

MR= 102.5 -Q

Equatig, MR= MC

102.5 -Q= 2

Q= 100.5

The profit maximizing quantity of the monopolist is 100.5

The corresponding price can be obtained by the inverse demand fucntion

P= 102.5- 100.5/2= 52.25.