Question

Given that TC = 20,000 + 4 Q + 0.5 Q2

, determine the equations for TFC, TVC, AFC, AVC, AC, 

MC. Confirm that MC = AVC at the minimum point of the AVC curve.

Answer 1

Given that TC = 20,000 + 4 Q + 0.5 Q2

Equations for:

TFC=20,000; These are costs that do not vary with unit changes.

TVC=4Q+0.5Q²; These costs vary with changes in units of capital.

$AFC=\frac{20000}{Q}$

$AVC=\frac{4Q+0.5Q ^2}{Q}=4+0.5Q$

AC=$\frac{20000+4Q+0.5Q ^2}{Q}=\frac{20000}{Q}+4+0.5Q$

MC=4+Q; differentiate total cost function.

Confirm that MC = AVC at the minimum point of the AVC curve.

MC = AVC; 4+Q=4+Q; so, MC=AVC