(3c) Solve for the Bertrand-Nash Equilibrium. (3d) Under the Betrand-Nash Equilibrium, how much does each supplier earn (раyoff)? (3e) Suppose Joe has the opportunity to invest and lower his costs as follows: C*(Qjoe) = 4 Qjoe If Joe invests in this new technology and Sarah is stuck with her current costs (constant marginal cost of $8), what would the new Bertrand-Nash Equilibrium be? (3f) How much does each supplier earn under the Bertrand-Nash Equilibrium in (2e) given that the investment cost for Joe is $500 ? Assuming that Sarah is stuck with her current costs, what is the most that Joe would have been willing to spend for the new technology? (3g) Suppose Sarah has the same opportunity to invest in the lower cost technology (at $500). If both Joe and Sarah make the investment and lower their marginal costs to $4, what is the new Bertrand-Nash Equilibrium?

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
icon
Related questions
Question

d, e and f

(3) Joe and Sarah's Investment Dilemma
Suppose Joe and Sarah each have a patent on their respective product: no other
supplier can provide their particular product. However, Joe and Sarah's products are
imperfect substitutes for each other. Consequently, they face the following respective
consumer demand
Qjoe = 300 – 15 Pjoe + 10 Psarah
Qsarah = 300 – 15 Psarah + 10 Pjoe
They face the following costs characterized by constant marginal cost and no fixed
costs
C(Qjoe) =
Qjoe
C(Qsarah) = 8 Qsarah
%3D
(3a) Assuming that each supplier charges marginal cost Pjoe = Psarah = $8, calculate
the own-price and cross-price elasticities for Joe. (Sarah's are the same due to
symmetry)
(3b) Solve for Joe's and Sarah's respective reaction curves, assuming a Bertrand
game.
(3c) Solve for the Bertrand-Nash Equilibrium.
(3d) Under the Betrand-Nash Equilibrium, how much does each supplier earn
(payoff)?
(3e) Suppose Joe has the opportunity to invest and lower his costs as follows:
C*(Qjoe) = 4 Qjoe
If Joe invests in this new technology and Sarah is stuck with her current costs
(constant marginal cost of $8), what would the new Bertrand-Nash Equilibrium be?
(3f) How much does each supplier earn under the Bertrand-Nash Equilibrium in (2e)
given that the investment cost for Joe is $500 ? Assuming that Sarah is stuck with her
current costs, what is the most that Joe would have been willing to spend for the new
technology?
(3g) Suppose Sarah has the same opportunity to invest in the lower cost technology
(at $500). If both Joe and Sarah make the investment and lower their marginal costs
to $4, what is the new Bertrand-Nash Equilibrium?
Transcribed Image Text:(3) Joe and Sarah's Investment Dilemma Suppose Joe and Sarah each have a patent on their respective product: no other supplier can provide their particular product. However, Joe and Sarah's products are imperfect substitutes for each other. Consequently, they face the following respective consumer demand Qjoe = 300 – 15 Pjoe + 10 Psarah Qsarah = 300 – 15 Psarah + 10 Pjoe They face the following costs characterized by constant marginal cost and no fixed costs C(Qjoe) = Qjoe C(Qsarah) = 8 Qsarah %3D (3a) Assuming that each supplier charges marginal cost Pjoe = Psarah = $8, calculate the own-price and cross-price elasticities for Joe. (Sarah's are the same due to symmetry) (3b) Solve for Joe's and Sarah's respective reaction curves, assuming a Bertrand game. (3c) Solve for the Bertrand-Nash Equilibrium. (3d) Under the Betrand-Nash Equilibrium, how much does each supplier earn (payoff)? (3e) Suppose Joe has the opportunity to invest and lower his costs as follows: C*(Qjoe) = 4 Qjoe If Joe invests in this new technology and Sarah is stuck with her current costs (constant marginal cost of $8), what would the new Bertrand-Nash Equilibrium be? (3f) How much does each supplier earn under the Bertrand-Nash Equilibrium in (2e) given that the investment cost for Joe is $500 ? Assuming that Sarah is stuck with her current costs, what is the most that Joe would have been willing to spend for the new technology? (3g) Suppose Sarah has the same opportunity to invest in the lower cost technology (at $500). If both Joe and Sarah make the investment and lower their marginal costs to $4, what is the new Bertrand-Nash Equilibrium?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

Blurred answer
Knowledge Booster
Financial Statements
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
ENGR.ECONOMIC ANALYSIS
Economics
ISBN:
9780190931919
Author:
NEWNAN
Publisher:
Oxford University Press
Principles of Economics (12th Edition)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
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)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
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-…
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education