Question

A frim selling in a perfectly competitive market has estimated total cost as TC = 3,645...

  1. A frim selling in a perfectly competitive market has estimated total cost as TC = 3,645 + 7Q + 0.2Q2.
  1. Currently the market price is $67 per unit. Find the firm’s optimal output:                         2 points

  1. If Price = 67, what is the perfect competitor’s economic profit?                                            1 point

  1. If Market demand is Qx = 4,085 - 5Px, the number of firms currently operating in the market is:

                                                                                                                                                 1 point

  1. What is your expectation for the future on this market? You must motivate your answer.

                                                                                                                                                 1 point

  1. Determine the firm’s long-run profit-maximizing output and price.                                   2 points

If Market demand is Qx = 4,085 - 5Px, determine the number of firms that will operate in this market in the long-run:

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Homework Answers

Answer #1

TC = 3645 + 7Q + 0.2Q2

dC/dQ = MC = 7 + 0.4Q

a) At Optimal choice  

P = MC  

67 = 7 + 0.4Q

67 - 7 = 0.4Q

60 = 0.4Q

Q = 60/0.4

= 150

b) Economic Profit = PQ - TC  

= 67(150 ) -3645 - 7(175) - 0.2(175)2  

= 10050 - 9195

= 855

c) Market demand Qx = 4085 - 5Px

= 4085 - 5(67)

= 4085 - 335

= 3750

Number of firms = Qx/Q  

= 3750/150

= 25

thus,currently there are 25 firms in the market

d) Since firms are making positive economic profits thus,firms will enter in the market in long run.

e) In long run equilibrium

P = MC = AC

AC = TC/Q

AC = ( 3645 + 7Q + 0.2Q2 )/Q

= 3645/Q + 7+ 0.2Q

MC = AC

7 + 0.4Q = 3645/Q + 7 + 0.2Q

0.4Q - 0.2Q = 3645/Q + 7 - 7

0.2Q = 3645/Q

Q2 = 3645/0.2

= 18225

Q = 135

Thus in long run each firm will produce Q = 135

P = MC  

= 7 + 0.4(135)

= 7 + 54

= 61

Thus, long run equilibrium price is 61

Qx = 4085 - 5(61)

= 4085 - 305

= 3780

Long run output Qx = 3780

Number of firms = 3780/135

= 28

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