Suppose a firm has the following total cost function: TC = 100 + 4q2.

Suppose a firm has the following total cost function: TC = 100 + 4q2. What is the minimum price necessary for the firm to earn profit? Below what price will the firm shut down in the short run?

What will be an ideal response?

ANSWER

AC = 100/q + 4q. This is minimized when dAC/dq = 0, or -100/q2 + 4 = 0. Solving yields q = 5 and AC = 40. Thus, a price greater than $40 is required for the firm to earn a profit. AVC = 4q and MC = 8q. Since AVC is below MC for all levels of output, AVC will be less than price for all levels of output. The firm will not shut down in the short run.