Question

Suppose a perfectly competitive market consists of identical firms with the same cost function given by

C(q)=2q² +3q + 400

The market demand is

Q_D= 5800 - 4p

How many firms will operate in this market in the long run?  

Round your answer to the nearest whole number.

Answer 1

TC = 2q² + 3q + 400 , MC = dTC/ dq = 4q + 3

ATC = TC/q = 2q + 3 + 400/q

# In long run ATC = MC, thus the quantity the firm will produce in the long run can be calculated as:-

ATC = MC

2q + 3 + 400/q = 4q + 3

2q² + 3q + 400 = q ( 4q + 3 )

2q² + 3q + 400 = 4q² + 3q

400 = 2q²

200 = q²

q = 14.14

# We can figure out the market price by remembering that in the long run this firm's MC = MR = P, so we get:-

P = 4q + 3

P = 4(14.14) + 3

P = 59.56

# We can use this price and the market demand curve to find the market quantity:-

Q = 5800 - 4(59.56)

Q = 5800 - 238.24

Q = 5561.76

#Since each firm produce 14.14 units and Q = 5561.76, the total no of firms operating are:-

= 5561.76 / 14.14 = 393.33 = 393

Hence total 393 firms will operate in the long run.

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