Consider the following cost function: C = 0

• C = 0.2q(cubed) - 3q(squared) + 75q + 150

a. When output is 19 units, average cost is $_.

b. When output is 19 units, marginal cost is $_.

c. The output level where average variable cost equals marginal cost is _ units.

a. The average cost (AC) equals:

AC=C/q=0.2q2−3q+75+150/qAC=C/q=0.2q2−3q+75+150/q

At q = 19, AC=0.2(19)2−3(19)+75+150/19=98.09AC=0.2(19)2−3(19)+75+150/19=98.09

b. The marginal cost (MC) equals:

MC=0.6q2−6q+75MC=0.6q2−6q+75

At q = 19, MC=0.6(19)2−6(19)+75=177.6MC=0.6(19)2−6(19)+75=177.6

c. The average variable cost (AVC) equals MC at the minimum of the AVC. We have,

AVC=0.2q2−3q+75AVC=0.2q2−3q+75

To get the q, where AVC is at its minimum, take the derivative of AVC with respect to q and set it equals to zero:

AVC′=0.4q−3=0→q=7.5AVC′=0.4q−3=0→q=7.5

Note: The other approach is setting AVC = MC and solving for q.