Question

Suppose a firm has a short run total cost curve given by Tc=100+20Q+Q³. The corresponding short run marginal cost curve is MC=20+2Q. What is the equation for average variable cost? And What is the minimum level of average variable cost?

Answer 1

TC = Q³ + 20Q + 100

TVC = Q³ + 20Q

TFC = 100

The equation for the average variable cost (AVC):

$AVC = \frac{TVC}{Q} \\ AVC = \frac{Q^3+20Q}{Q} = Q^2 + 20$

AVC reach its minimum if:

$AVC = MC \\ Q^2+20=20+2Q \\ Q = 2$

The minimum level of average variable cost Q = 2