Suppose a firm's total cost curve is given by the equation $T C = Q ^ { 2 } + 2 Q + 100$ . The firm's marginal cost is $M C = 2 Q + 2$ . At what level of $Q$
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 $T C = Q ^ { 2 } + 2 Q + 100$ . The firm's marginal cost is $M C = 2 Q + 2$ . At what level of $Q$
 does the firm's average cost curve reach a minimum?
A) 100
B) 2
C) 10
D) 20

Quizplus · Accepted Answer

The average cost (AC) curve is given by:
AC = TC/Q
Substituting the equation for TC in terms of Q, we get:
AC = Q + 2 + 100/Q
To find the minimum point on this curve, we need to take the first derivative of AC with respect to Q and set it equal to zero.
d(AC)/dQ = 1 - 100/Q^2
Setting this equal to zero and solving for Q, we get Q = 10.
Therefore, the firm's average cost curve reaches a minimum at Q = 10.

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