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long run market equilibrium price and output

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Q1. Ten competitive sawmills currently supply lumber to a market whose demand q,
depends on lumber price, p, as follows:
q = 3550 - 350p.
The cost function of each mill is identical:
Ci = 5qi + 0.05qi2 + 80 i = 1........10
(a) Determine the market supply curve.
(b) Determine the short run equilibrium market price and output.
(c) Is the equilibrium in (b) also a long run equilibrium? Why or why not?
(d) Technical development changes the cost function of new mills to:
Cj = 5qj + 0.1qj2 + 22.5
Ninety new competitive mills enter the market. What becomes the new short-run equilibrium market price and output? Assume the old mills still operate and that the entry and exit of mills do not affect individual mill cost functions.
(e) What will be the long run market equilibrium price and output? How many mills of what type - new or old - will survive?

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The long run market equilibrium price and output are determined.

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Problem 1
List the conditions than need to hold for a long run competitive equilibrium.

Problem 2
A number of stores offer film developing as a service to their costumers. Suppose that each store that offers this
service has a cost function C(q)=50+0.5q+0.08q2 .
(a) If the current rate for developing a roll of film is $8.5, is the industry in long run equilibrium? Explain.
(b) If the firm is not in a long run equilibrium, find the price associated with long run equilibrium.
(c) Suppose now that a new technology is developed which will reduce the cost of film developing (total cost) by
%25. Assuming that the industry is in long run equilibrium, how much would any one store be willing to pay
to purchase this new technology?

Problem 3
You are given the following information about a particular industry:
722 ) (
100 6500
2 q q C
p Q
p Q
+ =
- =
Where QD is the market demand, QS is the market supply and MC(q) is the firm total cost function.
Assuming that all firms are identical, and that the market is characterized by pure competition,
(a) Find the equilibrium price, the equilibrium quantity, the output supplied by each firm and the profit of the
firm in the short run.
(b) Would you expect to see entry into or exit from the industry in the long-run? Explain. What effect will entry
or exit have on market equilibrium?
(c) What is the lowest price at which each firm would sell its output in the long run? Is profit positive, negative
or zero at this price?

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