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

$ATC=\frac{TC}{q}$

$TC=1000+2Q+0.1Q^2$

$MC=\frac{\delta TC}{\delta q}=2+0.2Q$

$ATC=\frac{1000+2Q+0.1Q^2}{Q}$

$ATC=\frac{1000}{Q}+2Q+0.1Q^2$

Set MC=ATC

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

$0.2Q-0.1Q=\frac{1000}{Q}+2-2$

$0.1Q=\frac{1000}{Q}$

$0.1Q^2=1000\\Q^2=\frac{1000}{0.1}\\Q^2=10,000\\Q=100$

Price=MR=MC

$MC = 2 + 0.2Q$

substituting Q=100,

$MC = 2 + 0.2 (100) = 2 + 20 = 22$

The lowest price at which the firm can break even is 22