A firm has the short-run total cost function c(y) = 4y2 +100. At what quantity of output is short-run average cost minimized?
A) 5
B) 2
C) 25
D) 0.40
E) None of the above.

Question

Quizplus · Accepted Answer

Short-run average cost is minimized when marginal cost equals average cost. Marginal cost is the derivative of total cost with respect to output, which is 8y. Average cost is total cost divided by output, which is (4y2 + 100)/y = 4y + 100/y. Setting marginal cost equal to average cost, we get 8y = 4y + 100/y, which simplifies to 4y2 = 100. Solving for y, we get y = 5.

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