Question

A monopolist can produce at a constant average (and marginal) cost of AC = MC = $5.
It faces a market demand curve given by Q = 53 – P.
a. Calculate the profit-maximizing price and quantity for this monopolist. Also
calculate its profits.

Answer 1

Since Q = 53 - P,

P = 53 - Q

Profit is maximized when MR = MC.

Total revenue (TR) = P1$\times$ $Q_{1}$ = 53Q - Q²

P1​= 53Q - Q²

MR = $\frac{dtr}{dq}$=53 - 2Q

53 - 2Q = 5

2Q = 48

Q = 24

P = 53 - 24 = 29

Profit = Q$\times$(P - AC) = 24$\times$(29 - 5) = 576