Question

Suppose that the total cost equation (TC) for a monopolist is given by
TC = 500 + 20Q2
Let the demand equation be given by
P = 400 20Q
What are the profit-maximizing price and quantity?

Answer 1

The profit-maximizing quantity can be found at MR = MC:

$MR = TR'(Q) = 400 - 40Q,$

$MC = TC'(Q) = 40Q,$

$400 - 40Q = 40Q,$

Q = 5 units,

P = 400 - 20×5 = 300.