Question

Leila runs a firm in a perfectly competitive market with many other firms. Her short-run cost function is

given by C(q) = q2 + 25q + 144. Answer the following questions.

How much is Leila’s fixed cost of running the firm?

If the market price is $75, how much profit will Leila make?

Below which price will Leila need to shut down in the short-run?

How much output will Leila produce in the long-run? What will the market price be in the long-

Answer 1

(a) Fixed cost = 144 (Since fixed cost does not depend on output)

(b) Leila will maximize profit by equating price with Marginal cost (MC).

MC = dC(q)/dq = 2q + 25

Equating P and MC,

2q + 25 = 75

2q = 50

q = 25

Total revenue (TR) = P x q = $75 x 25 = $1875

C(q) = (25 x 25) + (25 x 25) + 144 = 625 + 625 + 144 = $1394

Profit ($) = TR - C(q) = 1875 - 1394 = 481

(c) Leila will shut down when Price falls below minimum point of AVC.

AVC = TVC/q = (q2 + 25q)/q = q + 25

AVC is minimum when q = 0.

Shut-down price = AVC = 0 + 25 = $25

(d) In long run, P = MC = AC

AC = C(q)/q = q + 25 + (144/q)

Equating with MC,

q + 25 + (144/q) = 2q + 25

144/q = q

q² = 144

q = 12

Price = MC = (2 x 12) + 25 = 24 + 25 = $49