g, h and I (3h) How much does each supplier earn under the Bertrand-Nash Equilibrium in (2g)(accounting for the investment cost)? Are payoffs lower or higher in this equilibriumthan in the other two Bertrand-Nash equilibria (considered above)?Consider the following two-stage game.1. First, each supplier simultaneously and independently decides whether to invest inthe new technology at a cost of $500.2. Second, with each supplier having made his/her investment decision (revealed toeach other), each supplier simultaneously and independently decides on the price tocharge for his/her product.So the second stage of this game is the Bertrand game, conditional on each supplier'sfirst stage investment decision.This two-stage game can be solved using backward induction ... first solve the secondstage game for each possible outcome of the first stage and then solve the first stage.You've actually done the first step of the induction in the earlier parts of this question...(3i) Fill-in the following payoff matrix for the first-stage “investment game" usingyour answers from (2d), (2f), (2h)SarahNot InvestInvestJoe Not Invest?,??, ??,??, ?InvestHINT: The payoffs from the Nash-Bertrand Equilibrium where Sarah invests but Joedoes not are symmetric to the case where Joe invests but Sarah does not.(3j) Solve for the pure strategy Nash equilibrium for this "investment game."(3k) Explain why this "investment game" is a “Prisoner's Dilemma" game. Whobenefits the most from the availability of this new low cost technology: Joe, Sarah, orconsumers? (3) Joe and Sarah's Investment DilemmaSuppose Joe and Sarah each have a patent on their respective product: no othersupplier can provide their particular product. However, Joe and Sarah's products areimperfect substitutes for each other. Consequently, they face the following respectiveconsumer demandQjoe = 300 – 15 Pjoe + 10 PsarahQsarah = 300 – 15 Psarah + 10 PjoeThey face the following costs characterized by constant marginal cost and no fixedcostsC(Qjoe) = 8 QjoeC(Qsarah) = 8 Qsarah(3a) Assuming that each supplier charges marginal cost Pjoe = Psarah = $8, calculatethe own-price and cross-price elasticities for Joe. (Sarah's are the same due tosymmetry)(3b) Solve for Joe's and Sarah's respective reaction curves, assuming a Bertrandgame.(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 QjoeIf 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 hercurrent costs, what is the most that Joe would have been willing to spend for the newtechnology?(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 coststo $4, what is the new Bertrand-Nash Equilibrium?

In Bertrand Nash Equilibrium, firms stand on prices rather than on quantities, which results in…

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 30015 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) = 8 Qjoe

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 30015 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) = 8 Qjoe

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter22: Frontiers Of Microeconomics

Section: Chapter Questions

Problem 6PA

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