Question

Consider a perfectly competitive market where each firm’s total cost function is TC = q^3 – 10q^2 + 50q.

a) What is the long run equilibrium price and quantity for each firm?

b) The industry demand function is Qd=2000-10p. How many firms are there in the industry in the long run?

c) The demand has changed to Qd=4000-18p. Describe the industry’s response to the demand shock and calculate the change in the number of firms in the long run equilibrium.

Answer 1

a) In the long run equilibrium, ATC=MC=Price. So, we can find MC & ATC with the help of TC.

  

To find equilibrium price and quantity, we will put ATC=MC

In order to find the equilibrium price, we will put q=5 in MC equation because we know that a firm produces at the point where P=MR=MC.

Therefore, the equilibrium price is 25 and equilibrium quantity is 5.

b) We know the market price is 25, so we can determine the market quantity from industry demand function.

Qd=2000-10p

Qd=2000-10X25

Qd=1750

Therefore, the number of firms in the industry in the long run will be

Since each firm is identically sized, so all of them will be producing 5 units (equilibrium quantity), therefore, the number of firms in the long run will be 350.

c) Due to increase in demand, the number of firms will increase in the industry. Entry of new firms will take place as long as firms are making economic profits.

Qd=4000-18p

Qd=4000-18X25=3550

Therefore, the number of firms will be

Change in the number of firms in the long run equilibrium=710-350=360.