Question

MC = 6 + 4Q P = 102 - 2Q

For the monopolist facing this demand curve with these costs, the profit-maximizing level of output is ___ units and price is ____ .
A. 13.5, $75
B. 12, $64
C. 16, $70
D. 12, $78
E. 18, $66

Answer 1

The profit-maximizing level of output for a monopolist facing this demand curve can be found by equating marginal revenue (MR) and marginal cost (MC). By solving the equation, we find that the profit-maximizing level of output is 12 units and the corresponding price is $78.

Step-by-step explanation:

The profit-maximizing level of output for a monopolist facing the given demand curve with these costs can be determined by finding the quantity where marginal revenue (MR) equals marginal cost (MC). In this case, we have the demand curve equation: MC = 6 + 4Q and P = 102 - 2Q. To find the profit-maximizing quantity, we need to solve the equation MR = MC.

First, we calculate the marginal revenue (MR) by taking the derivative of the demand curve equation P with respect to quantity (Q). Deriving P = 102 - 2Q with respect to Q gives us MR = 102 - 4Q.

Setting MR equal to MC, we have 102 - 4Q = 6 + 4Q. Simplifying, we get 8Q = 96, which means Q = 12. Therefore, the profit-maximizing level of output is 12 units. To find the corresponding price, we substitute this value of Q into the demand curve equation: P = 102 - 2Q. Substituting Q = 12, we find P = $78. Hence, the correct answer is D. 12 units and $78.