Question

The perfectly competitive golfball industry consists of 100 golfball-producing firms with the short-run total cost function ST C=q2+ 20q+ 200−N, where q represents the number of pallets of golfballs produced per day and N represents the number of firms in the industry. Firm marginal cost function is M C= 2q+ 20.

- Find the long-run equilibrium price of a pallet of golfballs, the number of pallets produced by each firm in equilibrium, firm profit, and the market quantity of pallets bought and sold in equilibrium.

- Suppose that the price of golf clubs, a complementary good, decreases, causing a demand increase in the golfball market. Suppose 19 new firms enter the industry in the long run,and that the market subsequently returns to long-run equilibrium. Find the new long-run market equilibrium price and quantity, and the number of pallets produced by each firm. How much profit do firms earn?

Answer 1

The perfectly competitive market has currently 100 firms.

Cost function is STC=q2+ 20q+ 200 - 100 or STC = q^2 + 20q + 100

MC = 2q + 20 and ATC = TC/q = q + 20 + 100/q

In the long-run equilibrium the price of a pallet of golfballs is AC = MC,

This implies 2q + 20 = q + 20 + 100/q

q = 100/q

q = 10

Hence, the number of pallets produced by each firm in equilibrium is 10,

Firm has a profit of $0 since P = AC

Market quantity of pallets bought and sold in equilibrium = 10*100 = 1000

Now there is a  demand increase in the golfball market and 19 new firms enter the industry in the long run

This makes the cost function STC = q^2 + 20q + 119

MC = 2q + 20 and ATC = TC/q = q + 20 + 119/q

In the long-run equilibrium the price of a pallet of golfballs is AC = MC,

This implies 2q + 20 = q + 20 + 119/q

q = 119/q

q = 10.91

Hence, the number of pallets produced by each firm in equilibrium is 10.91,

Firm has a profit of $0 since P = AC

Market quantity of pallets bought and sold in equilibrium = 10.91*119 = 1298