1. Consider the following Cournot game: . There are n ≥ 1 firms. • Firm i, i = 1, 2, ..., n, chooses an output qi € [0, ∞]. • The market inverse demand is P = a - bq, where a, b>0 and q = Σ₁_19i. =1 • Firm i's cost function is ci(qi) = cqi, where c > 0. (a) Solve the monopoly problem, in which there is only one firm in the market. (b) Find the Nash equilibrium outputs with n firms. Find the price in the equilibrium. (c) Show that the Nash equilibrium of the above game covers cases of market outcomes arranging from monopoly (n = 1) to perfect competition (n →∞).
1. Consider the following Cournot game: . There are n ≥ 1 firms. • Firm i, i = 1, 2, ..., n, chooses an output qi € [0, ∞]. • The market inverse demand is P = a - bq, where a, b>0 and q = Σ₁_19i. =1 • Firm i's cost function is ci(qi) = cqi, where c > 0. (a) Solve the monopoly problem, in which there is only one firm in the market. (b) Find the Nash equilibrium outputs with n firms. Find the price in the equilibrium. (c) Show that the Nash equilibrium of the above game covers cases of market outcomes arranging from monopoly (n = 1) to perfect competition (n →∞).
Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.4P
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![1. Consider the following Cournot game:
• There aren>1 firms.
• Firm i,
i
1, 2,
· , n, chooses an output q; E [0, 0).
..
• The market inverse demand is P = a – bq, where a, b > 0 and q = E=1 9i.
• Firm i's cost function is ci(qi)
cqi, where c > 0.
||
(a) Solve the monopoly problem, in which there is only one firm in the market.
(b) Find the Nash equilibrium outputs with n firms. Find the price in the equilibrium.
(c) Show that the Nash equilibrium of the above game covers cases of market outcomes
arranging from monopoly (n = 1) to perfect competition (n →).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd24795d2-8b0e-4e05-9bba-3c3739829edd%2F00cbbd20-6962-460f-a97f-af84b0940554%2Fpavqyp_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider the following Cournot game:
• There aren>1 firms.
• Firm i,
i
1, 2,
· , n, chooses an output q; E [0, 0).
..
• The market inverse demand is P = a – bq, where a, b > 0 and q = E=1 9i.
• Firm i's cost function is ci(qi)
cqi, where c > 0.
||
(a) Solve the monopoly problem, in which there is only one firm in the market.
(b) Find the Nash equilibrium outputs with n firms. Find the price in the equilibrium.
(c) Show that the Nash equilibrium of the above game covers cases of market outcomes
arranging from monopoly (n = 1) to perfect competition (n →).
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