Question

Suppose a representative perfectly competitive firm has the
following cost function: TC = 100 + 5Q^{2}. The short-run
market demand and supply are given by: Q^{D} = 600 - 40P
and Q^{S} = 20P. How many firms are in the market in the
**short-run?**

Answer #1

Answer : At market equilibrium, Demand = Supply occur. So,

600 - 40P = 20P

=> 600 = 20P + 40P

=> 600 = 60P

=> P = 600 / 60

=> P = 10

From demand function we get,

Q = 600 - (40 * 10)

=> Q = 200

So, here the market price is $10 and market quantity is 200 units.

Firm's MC (Marginal Cost) = TC / Q = 10Q.

For perfectly competitive firm the profit maximizing condition is, P = MC. So,

10 = 10Q

=> Q = 10 / 10

=> Q = 1

So, each firm produces 1 unit.

Number of firms in the market = Market quantity / Each firm's quantity = 200 / 1 = 200

Therefore, in short run the market has 200 firms.

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