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# Determining short and long run equilibrium price/quantity

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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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#### Solution Preview

Please refer attached word file for better clarity of algebraic expressions.

Solution:

(a) Determine the average fixed, average variable, average total and marginal cost functions.
Ci = 0.1qi2 + 2qi + 160

Here we can divide function into variable part and constant part. Variable part is variable cost and fixed part is fixed cost.
Total Cost = Ci = 0.1qi2 + 2qi + 160

Fixed Cost = TFC=160
Variable Cost= 0.1qi2 + 2qi

Average Total cost
= Total cost/qi
= (0.1qi2 + 2qi + 160)/qi
=0.1qi +2+(160/qi)

Average Fixed Cost=TFC/qi=160/qi

Average ...

#### Solution Summary

Solution describes the steps to determine market supply curve, short and long run equilibrium points for 15 competitive firms.

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