A firm's total cost function is given as:
TC = q³( 10 + 5q²)
Where:
TC = total cost
q = quantity produced
To find the average cost function, we need to first find the total cost for a given quantity produced. The average cost (AC) is calculated by dividing the total cost by the quantity produced.
Average Cost (AC) = TC / q
Substitute the given total cost function TC = q³(10 + 5q²) into the formula:
AC = (q³(10 + 5q²)) / q
AC = 10q + 5q²
Therefore, the firm's average cost function is AC = 10q + 5q².