Question

Imagine a perfectly competitive firm producing good A with cost function

TC=400+20Q-2Q²+2/3Q³, where Q is quantity produced

a. determine the firm’s short run supply curve

b. What is the profit maximizing level of output when price of A is birr 180?

Answer 1

a. the firm’s short run supply curve is MC

$MC=TC'=(400+20Q-2Q2+2/3Q3)'=20-4Q+2Q^2$

b.

MC=P

$20-4Q+2Q^2=180$

$20-4Q+2Q^2-180=0$

$2Q^2-4Q-160=0$

$Q^2-2Q-80=0$

Q=10

$profit=MR-MC=180\times10-(20-4\times10+2(10^2))=1800-20+40-200=1620$