17. Using the information from the above question: is the market in which Firm A
ID: 1125835 • Letter: 1
Question
17. Using the information from the above question: is the market in which Firm A is selling its output currently in long run equilibrium? Questions 18-21 rely on the following prompt: Firm A and Firm B compete in the sale of a product with market inverse demand given by P(0) = 150-Q, where Q is market output, and Q = qA + qB (4a-Firm A's output, qB-Firm B's output). Firm A's Total Cost function is given by TCA qA) 10qA and Firm B's is given by 18. Find the value of Q when Firms A and B Cournot compete to maximize profits (i.e. when they simultaneously determine profit maximizing output). 19. At what price will Firms A and B sell their output? 20. Suppose that Firm A's total cost function were to change to TCA(A) 10qA 50, (so, a fixed cost of 50 has been added). How will Firm A's profit maximizing output level change as a result of this? How will Firm B's profit maximizing output level change as a result of this? 21. Suppose that Firm A's total cost function were to change to TCACqA) 20qA, (so, Firm A's marginal cost has increased from 10/unit to 20/unit). How will Firm A's profit maximizing output level change as a result of this? How will Firm B's profit maximizing output level change as a result of this?Explanation / Answer
18) Marginal costs are same for both at 10. Find the best response functions for both using the profit function
PrA = 150qA - qA^2 - qAqB - 10qA and PrB = 150qB - qB^2 - qAqB - 10qB
Maximize profits give best response functions
150 - 2qA - qB = 10 and 150 - 2qB - qA = 10
qA = 70 - 0.5qB and qB = 70 - 0.5qA
Solve them to get qA = qB = 46.67. Total Q = 46.67*2 = 93.34
19) Price = 150 - 93.34 = $56.67
20) New profit functions are
PrA = 150qA - qA^2 - qAqB - 10qA - 50 and PrB = 150qB - qB^2 - qAqB - 10qB
This does not change marginal profit or best response functions so the result is still qA = qB = 46.67
21) New profit functions are
PrA = 150qA - qA^2 - qAqB - 20qA and PrB = 150qB - qB^2 - qAqB - 10qB
Find the best response functions
150 - 2qA - qB = 20 and 150 - 2qB - qA = 10
qA = 65 - 0.5qB and qB = 70 - 0.5qA
Solve them to get qA = 40 and qB = 50
So firm A now produces less at 40 and firm B produces more at 50
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.