Question

Given the following cost function, determine (a) the level of (nonzero) output at which the average cost function in minimized, and (b) the average cost at that level.

AC = 1000 -175Q + 12.5Q²

• An Average Cost is at a minimum when its derivative function (measuring its change) is zero.

Answer 1

a) AC = 1000 - 175Q + 12.5Q²

The first order derivative of AC function is: -175 + 25Q

The average cost function in minimized, when first order derivative of AC function is 0.

-175 + 25Q = 0

25Q = 175

Q = 175 / 25 = 7

Thus, the level of (nonzero) output at which the average cost function in minimized is 7.

b) AC = 1000 - 175(7) + 12.5(7)²

          = 1000 - 1225 + 612.5

          = $387.5

Thus, the average cost at that level of output is $387.5.