Question

1. Suppose a perfectly competitive firm has a cost function described by TC = 200Q + Q^2 + 225 Each firm’s marginal revenue is $240. a. Find the profit maximizing level of output. b. Is this a short-run or long-run situation? How do you know? c. Assuming that this firm’s total cost curve is the same as all other producers, find the long-run price for this good.

Answer 1

Answer
a)
the firm maximizes profit at MC=P=MR
MC=dTC/dQ=200+2Q
200+2Q=240
2Q=40
Q=20
P=240
b)
the firm is in short-run because the total cost function has some fixed cost which is the constant term in the cost function.
c)
In the long run, the firm charges the price equal to the min(ATC)
which will be found by first-order condition equal to zero.
ATC=TC/Q=200+Q+225/Q
dATC/dQ=1-225/Q^2=0
225/Q=1
Q=225
Q=15
ATC=200+15+225/15
=230
the long run price is $230 which is equal to min(ATC).