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


(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.

See Also This Related BrainMass Solution

Profit Maximization in perfectly competitive environment

Assume the following cost data are for a purely competitive producer:

a. At a product price of $56, will this firm produce in the short run? Why or why not? If it is preferable to produce, what will be the profit-maximizing or loss minimizing output? Explain. What economic profit or loss will the firm realize per unit of output?

b. Answer the relevant questions of 4a assuming product price is $41.

c. Answer the relevant questions of 4a assuming product price is $32.

d. In the table below, complete the short-run supply schedule for the firm (columns 1 and 2) and indicate the profit or loss incurred at each output (column 3).

Price Quantity Supplied Single Firm Profit Or Losse Quantity Supplied 1500 Firms

e. Explain: "That segment of a competitive firm's marginal cost curve that lies above its average-variable-cost curve constitutes the short-run supply curve for the firm." Illustrate graphically.

f. Now assume that there are 1500 identical firms in this competitive industry; that is, there are 1500 firms, each of which has the cost data shown in the table. Complete the industry supply schedule (column 4).

g. Suppose the market demand data for the product are as follows:
What will be the equilibrium price? What will be the equilibrium output for the industry? For each firm? What will profit or loss be per unit? Per firm? Will this industry expand or contract in the long run?

Total Product Average Fixed Cost Average Variable Cost Average Total Cost Marginal Cost
1 $60.00 $45.00 $105.00 $45
2 30.00 42.50 72.50 40
3 20.00 40.00 60.00 35
4 15.00 37.50 52.50 30
5 12.00 37.00 49.00 35
6 10.00 37.50 47.50 40
7 8.57 38.57 47.14 45
8 7.50 40.63 48.13 55
9 6.67 43.33 50.00 65
10 6.00 46.50 52.50 75

Price Total Quantity Demandad
$26 17,000
32 15,000
38 13,500
41 12,000
46 10,500
56 9,500
66 8,000

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