Determining Equilibrium output and profits
2 companies produce the same item. The companies each determine their own output and the combined output of the two is sold at the market price. Company A has controls its costs better than its competitor, B. The demand curve is P=280-2(Q1+Q2) and the cost function is C1(Q1)=3Q1 and C2(Q2)=2Q2
Find out the followings
1) Marginal revenue for both,
2) Reaction function for both,
3) Equilibrium output,
4) Equilibrium profits.
https://brainmass.com/economics/general-equilibrium/determining-equilibrium-output-profits-277883
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Solution:
It is given that Company A has better control over costs,
So, cost function for company A=C2(Q2)=2Q2
cost function for company B=C1(Q1)=3Q2
1) figuring out the marginal revenue for both,
Company B
Total Revenue=Price*Output of company=P*Q1
TR1={280-2(Q1+Q2)}*Q1
TR1=280Q1-2Q1^2-2Q1Q2
To get Marginal Revenue differentiate TR1 w.r.to Q1,
MR1=d(TR1)/dQ1=280-4Q1-2Q2
Company A
Total Revenue=Price*Output of company=P*Q2
TR2={280-2(Q1+Q2)}*Q2
TR2=280Q2-2Q1Q2-2Q2^2
To get Marginal Revenue differentiate TR2 w.r.to ...
Solution Summary
The solution depicts the steps to find reaction functions, equilibrium output and equilibrium profits in a oloigopoly model.
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
$26
32
38
41
46
56
66
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