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 →∞).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![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 →).
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps with 32 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
![ENGR.ECONOMIC ANALYSIS](https://compass-isbn-assets.s3.amazonaws.com/isbn_cover_images/9780190931919/9780190931919_smallCoverImage.gif)
![Principles of Economics (12th Edition)](https://www.bartleby.com/isbn_cover_images/9780134078779/9780134078779_smallCoverImage.gif)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
![Engineering Economy (17th Edition)](https://www.bartleby.com/isbn_cover_images/9780134870069/9780134870069_smallCoverImage.gif)
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
![ENGR.ECONOMIC ANALYSIS](https://compass-isbn-assets.s3.amazonaws.com/isbn_cover_images/9780190931919/9780190931919_smallCoverImage.gif)
![Principles of Economics (12th Edition)](https://www.bartleby.com/isbn_cover_images/9780134078779/9780134078779_smallCoverImage.gif)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
![Engineering Economy (17th Edition)](https://www.bartleby.com/isbn_cover_images/9780134870069/9780134870069_smallCoverImage.gif)
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
![Principles of Economics (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305585126/9781305585126_smallCoverImage.gif)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
![Managerial Economics: A Problem Solving Approach](https://www.bartleby.com/isbn_cover_images/9781337106665/9781337106665_smallCoverImage.gif)
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
![Managerial Economics & Business Strategy (Mcgraw-…](https://www.bartleby.com/isbn_cover_images/9781259290619/9781259290619_smallCoverImage.gif)
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education