1. Suppose there are 100 firms in a perfectly competitive industry. Short run ma
ID: 1113266 • 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-q2 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 equi- librium for each firm in part a is also the long run equilibrium. Determine the consumer and producer surplus for the industry (in this case, the areas of the triangles) d. Suppose now the market demand shifts upward to O-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) SMC is MC = q + 2, so supply function is p = q + 2 or q = p - 2. Supply function of the market is 100q = Qs = 100P - 200. Market demand is Qd = 1000 - 20P
Market equilibrium is at
1000 - 20P = 100P - 200
1200 = 120P
P* = 10
Q* = 1000 - 20*10 = 800 units
Each firm produces 800/100 = 8 units. This gives SMC = 8 + 2 = 10 which is justified as P = MC = 10
b) Long run price is minimum of ATC. Here LRAC is minimum at $10. Hence long run price is $10. When price is $10, quantity in the market, is Q = 1000 - 20*10 = 800.
c) Long run equilibrium output for each firm is found when LRAC is minimized and P = LRMC = minimum LRAC. We know that LRAC is $10, so LRMC is also $10. This makes LRMC = 10 = q +2 or q* = 8 units.
We therefore see that q* = 8 is also the short run equilibrium (part a) and is the long run equilibrium (found above)
CS = 0.5*(Max price - current price)*current qty = 0.5*(50 - 10)*800 = $16000
PS = 0.5*(current price - minimum price)*qty = 0.5*(10 - 2)*800 = $3200
d) New demand is Q = 1200 - 20P
We know that long run price is fixed at $10. Hence long run quantity is 1200 - 20*10 = 1000 units. In the long run each firm was prodiucing 8 units so now there are 1000/8 = 125 firms in the long run.
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