Question

A firm in a monopoly market is facing a demand curve P=100-2x , total revenue curve TR=10x2x2 and has total cost C=10+2x.
a) Find the profit maximizing output and price?
b) Is this firm making a profit? Calculate the profit.
c) Show this on a graph.

Answer 1

a)For a monopoly profit maximization

$MR=MC$

$P=100-2x$

$TR=P*Q$

$=(100-2x)x$

$=100x-2x^2$

$MR=$ $dTR \over dQ$ $=100-4x$

$TC=10+2x$

$MC=$ $dTC \over dQ$ $=2$

$MR=MC$

$100-4x=2$

$4x=98$

$x=24.5(output)$

Price

$P=100-2x$

$100-2(24.5)=51$

b) Yes

Profit $=TR-TC$

$TR=100(24.5)-2(24.5)^2$

$=1249.50$

$TC=10+2x$

$10+2(24.5)=59$

$1249.50-59=1190.5$