Question

1. Perfectly competitive market. An individual firm has the following cost function:

TC = 36 + 2q +q2.  

1. Find the firm’s supply curve.

2. If there are 100 identical firms in the market, what is the market supply curve?

3. In the long run, how many units would each firm produce? What is the price in the long run?

4. What is each firm’s profit? Show this.

5. If the market demand= Qd = 614 - p, how many firms would be in the market?

Answer 1

TC = 36 + 2q + q2  

MC = 2 + 2q  

firm’s supply curve is given as
P = MC  

P = 2 + 2q  

P - 2 = 2q  

q = P/2 - 1  

Therefore firm’s supply curve is q = P/2 - 1  

Now n = 100  

so market supply curve is Qs = nq

= 100(P/2 - 1)  

= 50P - 100

LONG RUN EQUILIBRIUM

P = MC = AC  

AC = TC/q  

= (36 + 2q + q2 )/q  

= 36/q + 2 + q

MC = AC

2 + 2q = 36/q + 2 + q

2q - q + 2 - 2 = 36/q

q = 36/q

q2 = 36  

q = 6

So each firm will produce 6 units in long run

P = MC

= 2 + 2q = 2 + 2(6)  

P = 14

Long run equilibrium price is P = 14

Profit of each firm  

= Pq - TC  

= 14(6) - 36 - 2(6) - (6)2

= 84 - 36 - 12 - 36  

= 84 - 84 = 0  

so each firm just earns zero profits or normal profits in the long run.

Qd = 614 - P  

Q = 614 - 14 = 600

Number of firms n = Q/q = 600/6 = 100