A competitive firm has the short-run cost function c(y) = 2y3 - 16y2 + 128y + 10. The firm will produce a positive amount in the short run if and only if the price is greater than
A) $192.
B) $48.
C) $99.
D) $96.
E) $95.

Question

Quizplus · Accepted Answer

To produce a positive amount, the firm must have positive profits or, equivalently, price greater than average variable cost (AVC) since fixed costs are sunk in the short run. AVC = c(y)/y = 2y2 - 16y + 128 + 10/y. Taking the derivative of AVC with respect to y yields: AVC’ = 4y - 16 + 10/y2. Setting AVC’ = 0 to find the minimum AVC gives y = 5/2. Plugging y = 5/2 into AVC yields AVC = $96. Therefore, the firm will produce a positive amount if and only if the price is greater than $96. The correct answer is (D).

A Competitive Firm Has the Short-Run Cost Function C(y) =