Question

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= 1/3Q3 -5Q2+20Q+50, where TC is the total cost and Q is the level of output.

Answer 1

Solution

Cost function

$Tc=\frac{1}{3}q^3-5q^2+20q+50$

At maximize level of price

MC=MCP

$MC=\frac{d(Tc)}{dq}$

$MC=\frac{d}{dq}(\frac{1}{3}q^3-5q^2+20q+50)$

$MC=q^2-10q+20$

And MCP=4

So

$q^2-10q+20=4\\q^2-10q+16=0$

So

q=8 and 2

Maximize level of price will be 2 because $\frac{d^2(Tc)}{dq}<0$ for 2.