2. A perfectly competitive, constant-cost industry has a market demand curve P =

Question

2. A perfectly competitive, constant-cost industry has a market demand curve P = 50-(1 /7) Each firm has a U-shaped long-run average cost function with a minimum of $10. The efficient scale of production for these firms is 5 units. a What is the long-run equilibrium market price and quantity? b) What is the long-run number of firms in the industry? How much does each produce? What are their profits? c) Suppose that market demand drops so that the new demand curve is P = 40-( 1 /7)Q. If the short-run marginal cost of firms is SMC-2q-5, what is the short-run equilibrium price and quantity in the market? What is the output of each firm in the short run? Now find the new long-run equilibrium price and quantity. What is the new equilibrium number of firms? d)

Explanation / Answer

Solution:

Demand Curve:
P = 50 -(1/7)Q
a) At long run each firm will produce,
where P = AC, so price in market = $10
50 - (1/7)Q = 10
40 = (1/7)Q
So Q = 280
Long run equillibrium price = minimum ATC (Economic profit = 0)
Long run equillibrium price = $10
P = 10

b) Since efficiency scale of production is 5 units.
Let 'm' be the no. of firms.
So 280 = 5m
m = 280/5 = 56 firms

Each firm produces 5 units (efficient scale of production)

Profits = 0 (In long run profit are zero)

c)

Supply curve (firm) is same as the marginal cost curve (firm)

Supply curve (firm) : q = 0.5 x (P + 5)

Supply curve (market) : Q = 56q = 28 x (P + 5)

New market demand: P = 40 - Q/7

Q = 252 units

P = 4

Output of each firm = 4.5

d) Long run equillibrium price = $10 (minimum ATC)

which implies 40 - (1/7)Q = 10
30 = (1/7)Q
Q = 210
p = 10
n = 210/5
So n = 42 firms exist in long run

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