Question

A firm has a long-run total cost function of C(Q) = 180,000 +

30Q + 2Q2 for Q > 0 and C(0) = 0, with MC(Q) = 30 + 4Q. a. What
is the average total cost function? b. At what quantity is ATC
minimize

Answer 1

The average total cost can be calculated by dividing the total cost by the quantity. To find the minimum average total cost, take the derivative of the average total cost function and set it equal to zero.

Step-by-step explanation:

The average total cost (ATC) can be calculated by dividing the total cost (TC) by the quantity (Q). In this case, the total cost function is C(Q) = 180,000 + 30Q + 2Q^2. The average total cost function (ATC) is given by ATC(Q) = C(Q)/Q.

To find the minimum average total cost, we can take the derivative of the average total cost function with respect to quantity (Q) and set it equal to zero. Solving for Q will give us the quantity at which the average total cost is minimized.