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# Determining long run and short run equilibrium

Q5. Ten competitive widget makers each have the following cost structure:
Ci = 0.005qi2 + 4qi + 200 i = 1, 2,....,10
(a) What is the short-run supply curve for each firm?
(b) What is the industry supply curve?
(c) If market demand is:
Q = 6,500 - 500p
What are short-run equilibrium market price and quantity?
(d) At the price determined in (c), is the firm breaking even, making profits or losses?
(e) In the long-run, firms enter the industry -assume constant costs over long-run-what will be market price and quantity?
(f) How many firms will there be in the industry?

#### Solution Preview

Please refer attached file for better clarity of expressions.

Solution:

(a) What is the short-run supply curve for each firm?

Ci = 0.005qi^2 + 4qi + 200
Marginal cost of each firm = MCi=dCi/dqi=0.01qi+4
In equilibrium MC = Price =p
pi = 0.01qi+4
0.01qi=-4+p
qi= -400+100p

(b) What is the industry supply curve?
There are ten firms in market
Total supply will be Qs=10*qi=(-400+100p)*10
Qs =-4000+1000p

(c) ...

#### Solution Summary

Solution describes the steps to determine short term and long run equilibrium quantity and price for perfectly competitive firms.

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