Question

MC = 5 + Q P = 95 - 2Q

For the monopolist facing this demand curve with these costs, the profit-maximizing level of output is ___ units and price is ____ .
A. 18; $23
B. 20; $55
C. 18; $59
D. 30; $35 E. 22.5; $50

Answer 1

The profit-maximizing level of output for a monopolist is 18 units and the price is $59.

Step-by-step explanation:

The profit-maximizing level of output for a monopolist is found by setting marginal revenue (MR) equal to marginal cost (MC). Given the cost function MC = 5 + Q and the demand curve P = 95 - 2Q, we first need to find the MR function. Since MR is derived from the total revenue function, which is P x Q, we start by multiplying the demand equation by Q to get total revenue, TR = 95Q - 2Q^2. The marginal revenue function, MR, is the derivative of TR with respect to Q, which gives us MR = 95 - 4Q. We set MR equal to MC to find the profit-maximizing quantity: 95 - 4Q = 5 + Q. Solving for Q gives us Q = 18. We then plug this quantity back into the demand curve to find the price, which yields P = 95 - 2(18) = 59. Hence, the profit-maximizing level of output is 18 units, and the price is $59.