Question

Suppose the market consist of 300 identical firms, and the market demand is given by ? = 60 − ?. Each firm has a short-run total cost curve ??? = 0.1 + 150?².
1) What is the short-run equilibrium price in this market?
2) What is the profit-maximizing quantity for each firm?

Answer 1

Answer : 1) Given,

Demand :

Q = 60 - P

=> P = 60 - Q

Total cost of each firm is,

TC = 0.1 + 150Q^2

MC = TC / Q

=> MC = 300Q

At equilibrium condition for each identical firm, P = MC.

=> 60 - Q = 300Q

=> 60 = 300Q + Q

=> 60 = 301Q

=> Q = 60 / 301

=> Q = 0.2

Now, the market price is,

P = 60 - 0.2

=> P = 59.8

Therefore, the market equilibrium price is $59.8 because each identical firm always face the market equilibrium price.

2) The profit maximizing quantity of each firm is 0.2 unit.