economics
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 longrun 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=150050P.
a. What is the industry's longrun supply schedule?
b. What is the longrun equilibrium price? The total industry output? The output of each firm? The profits of each firm?
c. The shortrun total cost curve associated with each firm's longrun equilibrium output is given by
STC=.5q^210q+200
where SMC=q10. Calculate the shortrun average and marginal cost curves. At what necktie output level does shortrun average cost reach a minimum?
d. Calculate the shortrun supply curve for each firm and the industry shortrun supply curve.
e. Suppose now painted neckties become more fashionable and the market demand function shifts upward to Q=200050P. 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 shortrun supply curve to recalculate the answers to part b.
g. What is the new longrun equilibrium for the industry?

Yesterday, a person under the username 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 50q500. 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/5010
(where Q = industry supply)
Check it out, solve for P when 500 + 50P = 150050P
(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,
SB 
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For industry supply I got P = 50Q  500?

intermediate micro economic