Question

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

Answer 1

solution

cost function

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

MCP=6

for maximum profit will be at the point where

P=MCP=MC

and

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

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

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

and MPC=6

so

$q^2-10q+3=6$

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

by solving it

$q=-0.29\space\space ,\space10.29$

by ignoring negative value , the profit maximising level of output will be q=10.29.