(4) Firm l's cost function is C1(qı) = 41 and firm 2's cost function is C2(q2) = 2q2. Consider a duopoly selling in a market with inverse demand function p = 12-q. (a) Assume firms choose output simultaneously (Cournot model). Compute the equilibrium quantities and the market price in a Nash equilibrium. (b) Now assume that firm 1 is a leader and chooses its output q1 first. Then, firm 2 chooses its output q2 after observing q1 (Stackelberg model). Find a subgame-perfect Nash equilibrium of this game. Carefully specify the strategies for firm 1 and firm 2. What quantities are produced in equilibrium and what is the market price in equilibrium?
(4) Firm l's cost function is C1(qı) = 41 and firm 2's cost function is C2(q2) = 2q2. Consider a duopoly selling in a market with inverse demand function p = 12-q. (a) Assume firms choose output simultaneously (Cournot model). Compute the equilibrium quantities and the market price in a Nash equilibrium. (b) Now assume that firm 1 is a leader and chooses its output q1 first. Then, firm 2 chooses its output q2 after observing q1 (Stackelberg model). Find a subgame-perfect Nash equilibrium of this game. Carefully specify the strategies for firm 1 and firm 2. What quantities are produced in equilibrium and what is the market price in equilibrium?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![(4)
Firm l's cost function is C1(q1) = q1 and firm 2's cost function is C2(q2) = 2q2.
Consider a duopoly selling in a market with inverse demand function p = 12 q.
(a) Assume firms choose output simultaneously (Cournot model). Compute the equilibrium
quantities and the market price in a Nash equilibrium.
(b) Now assume that firm 1 is a leader and chooses its output q1 first. Then, firm 2
chooses its output q2 after observing q1 (Stackelberg model). Find a subgame-perfect
Nash equilibrium of this game. Carefully specify the strategies for firm 1 and firm 2.
What quantities are produced in equilibrium and what is the market price in equilibrium?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8acc7dc3-2265-4174-a01d-a23e0b8a230a%2Fdc018721-d447-48ac-91de-cc22d414ccac%2F5c6ns5p_processed.png&w=3840&q=75)
Transcribed Image Text:(4)
Firm l's cost function is C1(q1) = q1 and firm 2's cost function is C2(q2) = 2q2.
Consider a duopoly selling in a market with inverse demand function p = 12 q.
(a) Assume firms choose output simultaneously (Cournot model). Compute the equilibrium
quantities and the market price in a Nash equilibrium.
(b) Now assume that firm 1 is a leader and chooses its output q1 first. Then, firm 2
chooses its output q2 after observing q1 (Stackelberg model). Find a subgame-perfect
Nash equilibrium of this game. Carefully specify the strategies for firm 1 and firm 2.
What quantities are produced in equilibrium and what is the market price in equilibrium?
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