Given the average total cost function:

• AC=200−Q2AC=200−Q2

The average total cost will be minimized when the first-order derivative of the average cost function with respect to output is equal to zero.

• ΔACΔQ=−2QΔACΔQ=−2Q

Equating the derivative to zero and solving for Q:

• ΔACΔQ=−2Q=0ΔACΔQ=−2Q=0

• Q=0Q=0

Thus, Q = 0 is the quantity of output that minimizes the average total cost.

At the quantity that minimizes the average total cost, the minimum average total cost is equal to:

• AC=200−(02)=$200