Answer to Question #98725 in Microeconomics for Stijn Op Den Kelder

Question

5. You are the manager of a monopoly and your demand and cost functions are given by
P = 225 - 2Q
and
c(Q) = 1,100 + 3Q2
a. What price-quantity combination maximizes your firm’s profits?

Answer 1

$P = 225 - 2Q$

$c(Q) = 1100 + 3Q^2$

$TR=P*Q$

$TR=Q(225-2Q)$

$TR=225Q-2Q^2$

$MR=\Delta TR/\Delta Q$

$MR=\Delta 225Q-2Q^2/\Delta Q$

$MR=225-4Q$

$MC=\Delta TC/\Delta Q$

$MC=\Delta 1100 + 3Q^2/\Delta Q$

$MC=6Q$

 Monopoly firm profit maximize is, 

$$MR=MC$$

$225-4Q=6Q$

$Q=22.5$

$P = 225 - 2Q$

$P = 225 - 2*22.5$

$P=180$

Firm profit maximize price $\boxed{180}$ and quantity $\boxed{22.5}$