Question

A firm in a perfectly competitive market has the following cost function c= 1/3q^2-5q^2+3q+10 if the market clearing price is 6 obtain the profit maximizing level of output.

Answer 1

If the market clearing price is P = 6, then the profit maximizing level of output is produced at:

P = MC,

$MC = TC'(q) = (1/3q^3 - 5q^2 + 3q + 10)' = q^2 - 10q + 3 = 6,$

$q^2 - 10q - 3 = 0,$

q1 = (10 + 9.38)/2 = 9.69 units,

q2 = (10 - 9.38)/2 = 0.11 units (is not possible in our case).