Suppose the demand for a monopoly firms product is Q 80 Pr

Suppose the demand for a monopoly firm’s product is Q = 80 – Price. If the firm’s marginal cost (MC) is constant at $10, profit- maximizing price is ________ and profit-maximizing output is _______.

Solution

Q = 80 - P

P = 80 - Q

Total Revenue = Price * Quantity

(80-Q) * Q

= 80Q-Q^2

Marginal Revenue =differentiating total revenue with respect to Quantity = 80 - 2Q

The monopolist produces at the point where marginal revenue of the firm is equal to marginal cost.

80 - 2Q = 10

70 = 2Q

Q = 35 units

P = 80 - 35 = $ 45

Thus, profit maximizing price = $45 and profit maximizing quantity = 35 units.