Question

Suppose you are given the following information about a particular industry in the short run (perfect competition):

Q^D = 200 − 2P                                      Market demand

Q^S = −120 + 6P                                     Market supply

C(q) = 4 + 30q + q²                 Firm total cost function for an individual firm

1. (10 pts) Find the equilibrium price & quantity in the market in the short run.
2. (20 pts) Find the output supplied by the individual firm, and the number of firms in the market in the short run.
3. (10 pts) What is the firm’s percentage markup of price over marginal cost (Lerner Index) in the short run?
4. (20 pts) What is the long run price in this market (long run equilibrium price)?

Answer 1

Q^D = 200 − 2P                                      Market demand

Q^S = −120 + 6P                                     Market supply

Equilibrium arises where:

Q^D = Q^S

200-2P = -120+6P

320= 8P

P*= 320/8= 40 Equilibrium price

Put P*= 40 in Q^S :

Q*= -120+6(40)= 120 Equilibrium quantity

C(q) = 4 + 30q + q²

MC= Differentiation of C wrt q= 30+2q

For firm's quantity:

MC=P

30+2q = 40

2q =10

q*= 5 Equilibrium quantity for a firm

Number of firms= Q*/q*= 120/5= 24

In perfect competition, firm choose the profit maximizing quantity where Price is equals to MC. So

P-MC= 0

The firm’s percentage markup of price over marginal cost (Lerner Index) in the short run = (P-MC)/P= 0

In the long run, equilibrium arises where:

MC= AC=P

30+2q = (4 + 30q + q² )/q

30q+2q² = 4 + 30q + q²

2q² -q² = 4

q² = 4

q**= 2

As even in long run:

MC=P

30+2q** = P

30+2(2)= P

P**= 34 Long run equilibrium price