Question

A firm operates in aperfectly competitive market . The market price of it's product is 4 birr and the total cost function is given by TC=1/3Q^3-5Q^2+20Q+50,Where TC is the total cost and Q is the level of output

A. What level of output should the firm produce to maximize it's profit ?

B. Determine the level of profit at equilibrium ?

C. What minimum price is required by the firm to stay in the market ?

Answer 1

$TC=\frac 13Q^3-5Q^2+20Q+50,$

$TC'=Q^2-10Q+20,$

$TC''=2Q-10,$

$TC''=0,$

$Q=5,$

$TC'=-5.$