(10) Two firms compete by choosing price. Their demand functions are Q₁ 20-P₁+P₂ and Q₂ = 20+ P₁-P₂ where P₁ and P₂ are the prices charged by each firm, respectively, and Q₁ and Q₂ are the resulting demands. Note that the demand for each good depends only on the difference in prices; if the two firms colluded and set the same price, they could make that price as high as they wanted, and earn infinite profits. Marginal costs are zero. a. Suppose the two firms set their prices at the same time. Find the resulting Nash equilibrium. What price will each firm charge, how much will it sell, and what will its profit be? (Hint: Maximize the profit of each firm with respect to its price.) b. Suppose Firm 1 sets its price first and then Firm 2 sets its price. What price will each firm charge, how much will it sell, and what will its profit be? c. Suppose you are one of these firms and that there are three ways you could play the game: (i) Both firms set price at the same time; (ii) You set price first; or (iii) Your competitor sets price first. If you could choose among these options, which would you prefer? Explain why.
(10) Two firms compete by choosing price. Their demand functions are Q₁ 20-P₁+P₂ and Q₂ = 20+ P₁-P₂ where P₁ and P₂ are the prices charged by each firm, respectively, and Q₁ and Q₂ are the resulting demands. Note that the demand for each good depends only on the difference in prices; if the two firms colluded and set the same price, they could make that price as high as they wanted, and earn infinite profits. Marginal costs are zero. a. Suppose the two firms set their prices at the same time. Find the resulting Nash equilibrium. What price will each firm charge, how much will it sell, and what will its profit be? (Hint: Maximize the profit of each firm with respect to its price.) b. Suppose Firm 1 sets its price first and then Firm 2 sets its price. What price will each firm charge, how much will it sell, and what will its profit be? c. Suppose you are one of these firms and that there are three ways you could play the game: (i) Both firms set price at the same time; (ii) You set price first; or (iii) Your competitor sets price first. If you could choose among these options, which would you prefer? Explain why.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Please help me with this question

Transcribed Image Text:(10) Two firms compete by choosing price. Their demand functions are
Q₁ = 20 P₁+ P₂ and Q₂ = 20+ P₁-P₂
where P₁ and P₂ are the prices charged by each firm, respectively, and Q₁ and Q₂
are the resulting demands. Note that the demand for each good depends only on the
difference in prices; if the two firms colluded and set the same price, they could
make that price as high as they wanted, and earn infinite profits. Marginal costs
are zero.
a. Suppose the two firms set their prices at the same time. Find the resulting Nash
equilibrium. What price will each firm charge, how much will it sell, and what
will its profit be? (Hint: Maximize the profit of each firm with respect to its
price.)
b. Suppose Firm 1 sets its price first and then Firm 2 sets its price. What price will
each firm charge, how much will it sell, and what will its profit be?
c. Suppose you are one of these firms and that there are three ways you could play
the game: (i) Both firms set price at the same time; (ii) You set price first; or (iii)
Your competitor sets price first. If you could choose among these options, which
would you prefer? Explain why.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps

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


Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON

Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON


Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON

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)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning

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-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education