posted by sleepy on .
This is going to be really long, but I want to see if my answers are correct. This is problem number 10.10 in my Intermediate Microeconomics book. A perfectly competitive painted necktie industry has a large number of potential entrants. Each firm has an identical cost structure such that long-run average cost is minimized at an output of 20 units. The minimum average cost is $10 per unit. Total market demand is given by Q=1500-50P.
a. What is the industry's long-run supply schedule?
b. What is the long-run equilibrium price? The total industry output? The output of each firm? The profits of each firm?
c. The short-run total cost curve associated with each firm's long-run equilibrium output is given by
where SMC=q-10. Calculate the short-run average and marginal cost curves. At what necktie output level does short-run average cost reach a minimum?
d. Calculate the short-run supply curve for each firm and the industry short-run supply curve.
e. Suppose now painted neckties become more fashionable and the market demand function shifts upward to Q=2000-50P. Using this new demand curve, answer part b for the very short run when firms cannot change their outputs.
f. In the short run, use the industry short-run supply curve to recalculate the answers to part b.
g. What is the new long-run equilibrium for the industry?
Yesterday, a person under the user-name of "timmy" posted a very similiar question. Questions a and b were addressed in that post.
c) You are given the short run MC curve. AC is simply TC divided by Q.
So, SAC = .5Q - 10 + 200/Q
To find the minimum, take the first derivitive, then set the equation to zero. Hint: I get Q=20.
d) the short run supply curve for a firm is simply its MC curve. The industry supply curve is the sum of the firm supply curves, (ignoring any constants) I get supply is N*Q - 10, where N=number of firms (50 in this example)
Take it from here.
thank you economyst. I have been doing it correctly :) except for industry supply curve as 50q-500. Is that correct?
The industry supply curve could be written as Q = 500+50P
Alternative, using some algebra, industry supply curve is also: P = Q/50-10
(where Q = industry supply)
Check it out, solve for P when 500 + 50P = 1500-50P
(my bad, I used a big Q instead of a small q in my original post.
Could you please clarify how did you derive the answer for (a) supply schedule = 500+ 50P? Thanks,
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For industry supply I got P = 50Q - 500?
intermediate micro economic