(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?
(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?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
d, e and f

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?
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