Answer to Question #282102 in Economics for daniel

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?

4. Assume a wheat producing farmer engaging in selling its product under perfect competition market faces cost functions as TC= Q3 -2Q2 +8Q and Average revenue of the farmer is given as Birr 8 . Having this information, A) Determine the optimal level of output and price in the short run.

B) Calculate the economic profit (loss) the farmer will obtain (incur)

C) What will be the minimum price level the farmer gets to continue in wheat production?

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.

4.

A) The optimal level of output and price in the short run is at P = MC = MR = AR.

$MC = TC'(Q) = 3Q^2 - 4Q + 8 = 8,$

$3Q^2 - 4Q = 0,$

Q = 0 (not acceptable) or Q = 4/3 units.

P = 8.

B) The economic profit the farmer will obtain is:

$TP = 8×4/3 - ((4/3)^3 - 2×(4/3)^2 + 8×4/3) = 1.19.$

C) The minimum price level the farmer gets to continue in wheat production is at P = AVC.