Question

A firm in a perfectly competitive market has the following cost function:

C = 1/3q3 – 5q2

+ 30q +10

If the market-clearing price is 6, obtain the profit maximising level of output

Answer 1

solution

cost function

c(q)=$\frac{1}{3}q^3-5q^2+30q+10$

MCP=6

for maximum profit will be at the point where

P=MCP=MC

and

MC=$\frac{dC(q)}{dq}$

$MC=\frac{d}{dq}(\frac{1}{3}q^3-5q^2+30q+10)$

MC=$q^2-10q+30$

and MPC=6

so

$q^2-10q+30=6$

$q^2-10q+24=0$

by solving it

$q=4\space\space ,\space 6$

the profit maximizing level of output will be q=6