Suppose a representative perfectly competitive firm has the following cost function: TC = 100 + 5Q2. The short-run market demand and supply are given by: QD = 600 - 40P and QS = 20P. How many firms are in the market in the short-run?
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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