Question

A perfectly competitive firm has the cost function TC = 1000 +  2Q  + 0.1  Q2. What is the lowest price at which this firm can break even? 

Answer 1

$MC = 2 + 0.2Q$

$AC = \frac {1000} {Q} + 2 + 0.1Q$

Set MC = AC.

For minimum AC, or $2 + 0.2Q = \frac {1000} {Q} + 2 + 0.1Q, or Q = 100$ , and at that point, AC = $22.

This is the lower price that the firm can break even.