Question

4. A firm operates in a perfectly competitive market. The market price of its product is 4 birr and the total cost function is given by 𝑇𝐶=13𝑄3−5𝑄2+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 its 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

$TC'=39Q^2-10Q+20,$

$TC'=0,$

$Q=0.13,$

$TC=19.4.$