For each of the following cost functions, if possible, find minimum AC

For each of the following cost functions, if possible, find minimum AC and minimum AVC.

a. TC = 40,000 + 20 Q
b. TC = 1000 + 2Q + 0.1 Q2

ANSWER

a. Set MC = AC.
20 = (40,000/Q) + 20
In this case, AC is decreasing everywhere, and thus there is no minimum average cost (although it will approach $20).
Set MC = AVC.
20 = 20
Q = 0, and at that point, AVC = $20.
b. Set MC = AC.
2 + 0.2Q = (1000/Q) + 2 + 0.1Q
Q = 100, and at that point, AC = $22.
Set MC = AVC.
2 + 0.2Q = 2 + 0.1Q
Q = 0, and at that point, AVC = $2.