Answer to Question #279627 in Microeconomics for Geoffroy

Question

Firm’s total cost function is given as 4Q3 – 40Q2 + 10Q. This firm operates in a perfectly competitive market. What is its profit maximizing level of output?

Answer 1

$TC=4Q^3-40Q^2+10Q$

$MC=12Q^2-80Q+10$

$MR=0$

Profit maximizing level of output is found when:

$MC= MR$

$12Q^2-80Q+10=0$

Solving the equation above using quadratic formula, we get:

$Q=\frac{80+\sqrt {6400-480}}{24}=6.54$

Profit maximizing level of output is 6.54.