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Determining long run and short run equilibrium

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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?

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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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Fifteen competitive gadget makers each have the following cost structure:
Ci = 0.1qi2 + 2qi + 160 i = 1,2,3.....15
(a) Determine the average fixed, average variable, average total and marginal cost functions.
(b) What is the short-run supply curve for each firm?
(c) What is the market supply curve?
(d) If market demand is q = 850 - 25p show that the equilibrium market price and quantity is both a long and short run equilibrium.
(e) If market demand shifts down to q = 650 - 25p what will be the short run market equilibrium price and quantity?
(f) What will market price and quantity be in the long run under the lower demand as in (e) above?

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