A firm has the short-run total cost function c(y)= 9y2 + 144.At what quantity of output is short-run average cost minimized?
A)4
B)16
C)0.75
D)3
E)None of the above.

Question

Quizplus · Accepted Answer

To minimize the short-run average cost (SAC), we first need to find the SAC function by dividing the total cost function by the quantity of output (y). The given total cost function is $c(y) = 9y^2 + 144$. The SAC is then $SAC = \frac{9y^2 + 144}{y}$.To find the minimum, we take the derivative of the SAC with respect to y and set it to zero. The derivative of SAC with respect to y is $SAC' = \frac{d}{dy}(\frac{9y^2 + 144}{y}) = 18y - 144/y^2$.Setting $SAC' = 0$ gives $18y - 144/y^2 = 0$. Solving for y, we find $y = 4$, which is when the short-run average cost is minimized.

A Firm Has the Short-Run Total Cost Function C(y)= 9y2