1)Suppose there are 100 firms in a perfectly competitive industry. Short run mar
ID: 1114401 • Letter: 1
Question
1)Suppose there are 100 firms in a perfectly competitive industry. Short run marginal costs for each firm are given by SMC = q + 2 and market demand is given by Qd = 1000 20P
a)Calculate the short run equilibrium price and quantity for each firm.
b)Suppose each firm has a U-shaped, long-run average cost curve that reaches a minimum of $10. Calculate the long run equilibrium price and the total industry output.
c)What is the long-run equilibrium output for each firm? What are the profits of each firm in the long run? Show that the short run equilibrium for each firm in part a is also the long run equilibrium.
d)Determine the consumer and producer surplus for the industry (in this case, the areas of the triangles)
e)Suppose now the market demand shifts upward to Qd’ = 1200 20P, what will be the price and the total industry output in the new long run equilibrium? Will the shift in market demand change the number of firms in the long run? If so, how many firms will there be in the new long run equilibrium?
Explanation / Answer
a)
Market supply curve: Qs = 100qs
Individual firm's supply curve is the same as its marginal cost curve.
Qs = 100 x (P - 2)
Qd = 1000 - 20P
At equillibrium: Qd = Qs
P = $10 , Q = 800 and q = 800/100 = 8 units
b)
Long run equillibrium price = min ATC = $10
Total industry output = 800 units
c)
Long run equillibrium output (firm) = 800/100 = 8 units
Profits = 0 (Long run, P = ATC)
It can be seen clearly that P obtained in a) is the same as the long run equillibrium price. (SR eq = LR eq)
d)
CS = (Y intercept of the demand curve - Peq) x Qeq/2 = 800/2 x (50 - 10) = $16000
PS = (Peq - Y intercept of the supply curve) x Qeq/2 = 800/2 x (10 - 2) = $3200
e)
Price in the long run remains the same = $10 (= min ATC)
Total industry output = 1200 - 200 = 1000
Yes, the number of firms would increase.
Number of firms = 1000/8 = 125 firms
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