d. Graph your restuits. nerfectly competitive painted necktie industry has a ber
ID: 1119121 • Letter: D
Question
d. Graph your restuits. nerfectly competitive painted necktie industry has a ber of potential entrants. Each firm has an cal cost structure such that long-run average cost is minimized at an output of 20 units minimum a demand is given by verage cost is $10 per unit. Total market 9. Q 1,500-50P hat is the industry's long-run supply schedule? b. What is the long-run equilibrium price (P") The total industry output (Q) The output of each firm (qi)? The number of firms? The profits of each firm? c. The short-run total cost curve associated with each firm's long-run equilibrium output is given by STC = .5q2-10q + 200 where SMC = q-10. Calculate the short-run aver- age and marginal cost curves. At what necktie out put level does short-run average cost real minimum? d. Calculate the short-run supply curve and the industry short-run supply curveExplanation / Answer
a) The minimum level of long run average cost is $10. Therefore, the industry’s long run supply curve is: P = 10.
b) The long run equilibrium price is $10, because the long run equilibrium price equals the minimum level of long run average cost.
Substitute 10 for P in the demand equation to calculate total industry output.
Q = 1,500 – 50(10) = 1,000
Total industry output is 1,000 units.
It is given that the individual firm’s output level at the minimum average cost of $10 is 20. The number of firms is 50 (= 1000/20).
In the long run, firms each no economics profits. The profit level is zero.
c) Short run average cost:
SAC = STC/q = (0.5q2 – 10q + 200)/q
SAC = 0.5q – 10 + (200/q)
Short run marginal cost:
SMC = q – 10
To calculate the output level at which the SAC reaches a minimum, equate SMC and SAC.
q – 10 = 0.5q – 10 + (200/q)
0.5q = 200/q
q2 = 400
q = 20
d) Substitute P at the place of SMC in the short run marginal cost function to get the short run supply curve of a single firm.
p = q – 10
q = p + 10
From part b, we know that the number of firms is 50. The industry short run supply curve is:
Q = 50q = 50 (p + 10)
Q = 50p + 500
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