Question

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

C(q)=2q^{2} +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 = 2q ^{2} + 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**

**2q ^{2} + 3q + 400 = q ( 4q + 3 )**

**2q ^{2} + 3q + 400 = 4q^{2} +
3q**

**400 = 2q ^{2}**

**200 = q ^{2}**

**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.**

**Thankyou, hope it helped.
Do leave a thumbsup**

**Cheers**

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