Question

Suppose that the perfectly competitive for market for milk is made up of identical firms with long-run total cost functions given by:

TC = 4 q^{3} - 24 q^{2} + 40 q

Where, q = litres of milk. Assume that these cost functions are independent of the number of firms in the market and that firms may enter or exist the market freely.

If the market demand is :

Qd = 8,000 - 160 P

1. What is the long-run equilibrium price?

2. What is the quantity produced by each firm?

3. What is the number of firms in the industry?

4. Suppose that market demand increases to Qd = 12,000 - 171.43 P. What is the new long-run equilibrium number of firms?

Answer #1

We have TC = 4q^{3} - 24q^{2} + 40q

This gives MC = 12q^2 - 48q + 40 and AC = 4q^2 - 24q + 40

a) Long run price is given by MC = AC

12q^2 - 48q + 40 = 4q^2 - 24q + 40

8q^2 - 24q = 0

q = 3

Long run price is MC = 12*9 - 48*3 + 40 = $4.

b) Each firm produces 3 units

c) At this price, market quantity is 8000 - 160*4 = 7360. Number of firms = 7360/3 = 2453 firms

d) The long run price will remain $4 and each firm produces 3 units. Market quantity = 12000 - 171.43*4 = 11314.28. Number of firms = 11314.28/3 = 3771 firms

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