Answer to Question #285911 in Macroeconomics for Aziz

Question

4.   A perfectly competitive firm has total revenue and

total cost curves given by:

            TR = 100Q                           TC = 5,000 + 2Q +

0.2 Q²

a.         Find the profit-maximizing output for

this firm.

b.         What profit does the firm make?

Answer 1

a.The equality of MR and MC is a condition for maximizing profits for any firm, regardless of the market structure in which it operates (perfect or imperfect competition).

$MR=TR'=(100Q)'=100$

$MC=TC'=(5000+2Q+0.2Q^2)'=2+0.4Q$

100=2+0.4Q

98=0.4Q

Q=245

P=MC

MC=2+0.4Q

MC=P=100

b.

$Profit=TR-TC=100\times245-(5000+2\times245+0.2(245)^2)=24500-17495=7005$