Question

Consider a Monopoly. Suppose the Demand function for the industry is Q = 440 − 4P. The total cost (TC) function for the firm is TC = 2.25Q^2 + 1,600. The marginal revenue (MR) function is then MR = 110 – 0.5Q. If the marginal cost (MC) function for the firm is MC = 4.5Q, what is the price the Monopoly will charge?

Group of answer choices

$4.50

$104.5

$110

$440

Answer 1

In order to maximize profit a monopolist produces that quantity at which MR = MC where MR = Marginal Revenue and MC = Marginal Cost.

So, MR = MC => 110 - 0.5Q = 4.5Q => Q = 110/5 = 22

So Monopolsit will produce 22 units.

Now, From demand curve we have : Q = 440 - 4P and also Q = 22

=> 22 = 440 - 4P => P = 104.5

Thus When Quantity = 22, Consumers willingness to pay(P from demadn curve tells us willingness to pay) is 104.5 and thus monopolist will charge price = 104.5

So, profit maximizing price = 104.5.

Hence, the correct answer is (b) $104.5