Answer to Question #145906 in Microeconomics for Isa

Question

A firm has two companies Firm 1 and Firm 2, each with the following cost function:TC(qi)=400qi+4000 where qi is the output of an individual firm(i=1,2). The market inverse demand function is P=1000+4Q where Q=qi+q2. What output and profit would each firm produce if the two firms are proce takers acting independently?

Answer 1

The profit is maximized at such output level, for which MR = MC.

$MR = TR'(Q) = 1000 - 8Q,$

$MC = TC'(q) = 400,$

1000 - 8Q = 400,

Q = 75 units,

So, every firm will produce 75/2 = 37.5 units.

P = 1000 - 4×75 = 700.