Answer to Question #284631 in Economics for mara

Question

3. A cloth producing firm in a perfectly competitive market has the following short-run total cost function: TC = 6000 + 400Q – 20Q2 + Q3 . If the prevailing market price is birr 250 per unit of cloth, A) Should the firm produce at this price in the short-run? B) If the market price is birr 300 per unit, what will be the profit (loss) of the firm at equilibrium? Should the firm continue to produce or not? C) Calculate the shut-down price of this firm?

Answer 1

3.

A) The firm should produce at this price in the short-run if P > AVC.

B) If the market price is birr 300 per unit, then in equilibrium P = MC, so:

$MC = 400 - 40Q + 3Q^2 = 300,$

$3Q^2 - 40Q + 100 = 0,$

Q = (40 + 20)/6 = 10 units (another answer Q = 3.33 is too small).

The loss of the firm at equilibrium is:

$TP = 300×10 - (6000 + 400×10 – 20×10^2 + 10^3) = -6000.$

$AVC = 400 - 20×10 + 10^2 = 100,$

P > AVC (300 > 100), so the firm should continue producing.

C) The shut-down price of this firm is:

P = AVC,

$400 - 20Q + Q^2 = 250,$

$Q^2 - 20Q + 150 = 0,$

There are no real roots in this equation.