A monopolist faces inverse demand $P = 300 - 6 Q$ and has total cost TC = 120Q + 6Q² and marginal cost $M C = 120 + 6 Q$ . What is the maximum profit the monopolist can earn in this market?

Question

Quizplus · Accepted Answer

To determine the maximum profit, we need to find the monopolist's profit-maximizing level of output and price. 
First, we find the monopolist's profit-maximizing level of output by setting marginal cost equal to marginal revenue: 
MC = MR 
120 + 6Q = 300 - 12Q 
18Q = 180 
Q = 10 
Next, we can find the monopolist's profit-maximizing price by plugging the output level back into the inverse demand function: 
P = 300 - 6Q 
P = 300 - 6(10) 
P = 240 
Now we can calculate the monopoly's maximum profit: 
Profit = (P - MC) * Q 
Profit = (240 - (120 + 6(10))) * 10 
Profit = 600 
Therefore, the maximum profit the monopolist can earn in this market is $600.

A Monopolist Faces Inverse Demand P=300−6QP = 300 - 6 QP=300−6Q

A Monopolist Faces Inverse Demand $P = 300 - 6 Q$