Assume a competitive firm faces a market price of 60 a cost

Assume a competitive firm faces a market price of ?$60?, a cost curve? of:

C? = 0.003q³+ 50q ?+ 500?,

and a marginal cost? of:

MC? = 0.009q2² + 50.

The? firm\'s profit maximizing output level is _____ units ?(enter your response rounded to two decimal places?), and the per unit profit at this output level is ?$ ____________ ?(enter your response rounded to two decimal placeslong dashinclude the minus sign if necessary?). This firm will ? _________ (produce/shut down) in the? short-run. The firm will realize _________- (economic loss / economic profit) ?, and ________ (may or may not) have a business profit. In the? long-run, if circumstances do not? change, this firm will _________(shut down/ produce)

Solution

Output level:

The equilibrium condition of a competitive firm is (P = MC).

P = MC

60 = 0.009q^2 + 50

0.009q^2 = 60 – 50

0.009q^2 = 10

q^2 = 10 / 0.009

q^2 = 1,111.1111

q = Square root (1,111.1111)

   = 33.3333

   = 33.33 (rounded to two decimal palces)

Answer: Required output is 33.33 units.

Profit per unit:

Total profit = Total sales – Total cost

                    = ($60 × 33.33) – (0.003q^3 + 50q + 500)

                    = 1,999.80 – {0.003 (33.33)^3 + 50 × 33.33 + 500}

                    = 1,999.80 – (111.08 + 1,666.5 + 500)

                    = 1,999.80 – 2,277.58

                    = - 277.78

Profit per unit = Total profit / Output

                        = -277.78 / 33.33

                        = -8.33 (Answer)

Produce or shutdown:

If the firm covers average variable cost (AVC) in the short-run, it will produce.

Total variable cost (TVC) = 0.003q^3 + 50q

                                           = 0.003 (33.33)^3 + 50 × 33.33

                                           = 111.08 + 1,666.50

                                           = 1,777.58

AVC = Total cost / Output

            = 1,777.58 / 33.33

            = 53.33

Since the price ($60) is higher than AVC ($53.33), the firm covers AVC; the price is higher than AVC; the firm should continue to produce.

Answer: produce.

Economic loss:

Total cost = 2,277.58

Average total cost (ATC) = Total cost / Output

                                          = 2,277.58 / 33.33

                                          = $68.33

Since price ($60) is smaller than ATC ($68.33), there would be economic loss.

Answer: Since price is below the ATC, there would be economic loss.

Answer: The firm may not have profit.

Answer: The firm will shutdown in the long-run.