a, b and c (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) =QjoeC(Qsarah) = 8 Qsarah%3D(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(payoff)?(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?

Answered: Image /qna-images/answer/28af2a4f-1911-48eb-b6e9-7faf82941c0f.jpg

(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) = 8 Qjoe C(Qsarah) = 8 Qsarah (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.

(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) = 8 Qjoe C(Qsarah) = 8 Qsarah (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.

Principles of Microeconomics (MindTap Course List)

8th Edition

ISBN:9781305971493

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter17: Oligopoly

Section: Chapter Questions

Problem 9PA

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