Question

In a competitive market the cost function is given by: C(q) = 800 + 40q + 2q 2 . Demand is given by QD = 520 − p.

(a) What is a firm’s marginal cost?

(b) Below which price should a firm shut down in the short run?

(c) In the short run there are 28 firms. How much does each firm sell?

(d) Below which price should a firm shut down in the long run?

(e) What is the number of firms in the long run?

Answer 1

C(q) = 800 + 40q + 2q²

(a) Marginal cost (MC) = dC(q) = 40 + 4q

(b) Firm will shut down when price falls below minimum AVC.

Total variable cost (TVC) = 40q + 2q²

AVC = TVC / q = 40 + 2q

AVC is minimized when q = 0, Therefore Shut-down price = Minimum AVC = 40

(c) Since firm's supply curve is its MC curve, the firm supply curve is

P = 40 + 4q

Since there are 28 firms, Market supply (QS) = 28 x q

q = QS / 28

P = 40 + 4 x (QS / 28)

P = 40 + (QS / 7)

QS / 7 = P - 40

QS = 7P - 280 (Market supply function)

Equating QD & QS,

520 - P = 7P - 280

8P = 800

P = 100

Q = 520 - 100 = 420

q = 420 / 28 = 15

(d) In long run, Price = AC = MC where AC = C(q) / q = (800 / q) + 40 + 2q

Equating AC & MC,

(800 / q) + 40 + 2q = 40 + 4q

2q = 800 / q

q² = 400

q = 20

Shutdown price = AC = MC = 40 + (4 x 20) = 40 + 80 = 120

(e) In long run, P = 120

From demand function, QD = 520 - 120 = 400

Number of firms = QD / q = 400 / 20 = 20