Suppose a firm's total cost curve is given by the equation .The firm's marginal cost is .At what level of does the firm's average cost curve reach a minimum?
A) 100
B) 2
C) 10
D) 20

Question

Suppose a firm's total cost curve is given by the equation  .The firm's marginal cost is  .At what level of  does the firm's average cost curve reach a minimum?
A) 100 
B) 2 
C) 10 
D) 20

Quizplus · Accepted Answer

To find the level of output where the firm's average cost curve reaches a minimum, we need to look for the point where the marginal cost curve intersects the average cost curve from below. This occurs at the point where MC=AC. In other words, we need to solve the equation:
11Q-2Q^2=11.5Q
Simplifying this equation, we get:
2Q^2-0.5Q=0
Q=0 or Q=0.25
Since Q cannot be negative, the only feasible solution is Q=10. This is the level of output where the firm's average cost curve reaches a minimum. Therefore, the correct answer is C) 10.

Suppose a Firm's Total Cost Curve Is Given by the Equation