Two firms compete in a homogeneous product market where the inverse demand funct
ID: 1114838 • Letter: T
Question
Two firms compete in a homogeneous product market where the inverse demand function is P = 20 -5Q (quantity is measured in millions). Firm 1 has been in business for one year, while Firm 2 just recently entered the market. Each firm has a legal obligation to pay one year’s rent of $0.4 million regardless of its production decision. Firm 1’s marginal cost is $2, and Firm 2’s marginal cost is $10. The current market price is $15 and was set optimally last year when Firm 1 was the only firm in the market. At present, each firm has a 50 percent share of the market. b. Determine the current profits of the two firms. Instruction: Enter all responses rounded to two decimal places.
Firm 1's profits: $ million
Firm 2's profits: $ million
c. What would each firm’s current profits be if Firm 1 reduced its price to $10 while Firm 2 continued to charge $15? Instruction: Enter all responses to two decimal places.
Firm 1's profits: $ million
Firm 2's profits: $ million
Explanation / Answer
(b) In the absence of any additional data, we will have to assume that Variable Cost (or operating cost) is equal to Marginal Cost (or the cost of producing any additional unit). We are assuming a long-run situation here.
Based on the inverse demand function
P = 20 - 5Q (Q is quantity in millions)
P = price = $15
Therefore,
For Firm 1
Q =20-p/5 = 3 million
Profit = Total Revenue - Total Cost
Total Revenue = Selling Price x Quantity = 15 x 1 million = $15 million
Total Cost = Fixed Cost + Variable Cost x Q
Fixed Cost for Firm 1 = 0.4 million
Variable Cost = $2
Total Cost = 0.4 + $2 x 1 million = $2.4 million
Therefore, Profit = $15 million - $2.4 million = $12.6 million
For Firm 2
Total Revenue = $15 x 1 million = $ 15 million
Total Cost = 0.4 million + $10 x 1 million = $10 million
Profit = $15 million - $10 million = $5million
(c) if P = $10 for Firm 1 and $15 for Firm 2 then,
For Firm 1
Q = (20-10)/5= 2 million
Total Revenue = $10 x 2 million = $20 million
Total Cost = $0.4 million + $2 x 2 million = $4,4 million
Profit = $20 million - $4.4 million = $15.6 million
For Firm 2
Q = (20-15)/5 = 1 million
Total Revenue = $15 x 1 million = $15 million
Total Cost = $0.4 million + $ 10x 1 million = $6.4 million
Profit = $15 milion - $6.4 million = $million8.6
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