Question

The demand curve facing a monopoly is P= 100 +5Q. The firm cost is c(Q)=10+5Q. What is profit maximising output?

Answer 1

Given;

$P= 100 +5Q.$

$c(Q)=10+5Q.$

$TR=P\times Q\\=(100+5Q)Q\\=100Q+5Q^2\\MR=100+10Q$

$c(Q)=10+5Q\\MC=5$

The profit is maximized by producing at a point where MC=MR

$5=100+10Q\\-95=10Q\\Q=-9.5$