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* = _________
The demand function faced by the monopolist is
Q= 205- 2P
The cost function is
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
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
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.
Get Answers For Free
Most questions answered within 1 hours.