Question

Given the following cost function, determine (a) the level of (nonzero) output at which the average...

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.
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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.

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