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

$TC = 1000+2Q+0.1Q^2 \\ MC = 2 + 0.2Q \\ AC = \frac{1000}{Q} + 2 + 0.1Q$

Set MC=AC for minimum AC

$2 + 0.2Q = \frac{1000}{Q} + 2 + 0.1Q \\ 0.1Q = \frac{1000}{Q} \\ 0.1Q^2 = 1000 \\ Q^2 = 10000 \\ Q = 100 \\ AC = \frac{1000}{100}+2+0.1 \times 100 \\$

= 10 + 2 +10 = $22

This is the lowest price at which the firm can break even.