Question

Suppose that the firm operates in a perfectly competitive market. The market price of his

product is$10. The firm estimates its cost of production with the following cost function:

TC=10q-4q2+q3

Answer 1

From the above information, we can determine the level of output that this firm should produce to maximize its profit.

Under perfect competition MR = P.

where P = MR = MC.

P = $10

MC = derivative of the Total Cost (TC) in relative to quantity

TC $=10q-4q^2+q^3$

MC $=$ $\frac{\partial TC} {\partial q} ​ = 10 – 8q + 3q2$

MC $=10-8q+3q^2$

to derive the level of output that maximizes the firm’s profit,

P = MC

$10=10-8q+3q^2$

$3q^2-8q=0$

$3q^2=8q$

$3q=8$

$q=8/3$

$=2.667$

The level of output that the firm should produce to maximize its profit: q = 2.667