Two firms produce a homogenous product. Let p denote the product's price. The output levelof firm 1 is denoted by q1, and the output level of firm 2 by q2. The aggregate industryoutput is denoted by Q, Q = q1 + q2. The aggregate industry demand curve for this productis given by p = 200 – Q.a. Assuming that firms are homogeneous with cost function C(qi) = 2qi, derive the bestresponse function for each firm. Show that Cournot-Nash equilibrium output for eachfirm is symmetric. Find the Cournot-Nash equilibrium aggregate output and price. Verifythat given similar cost functions, equilibrium profits for each firm is symmetric as well.

The demand curve refers to the inverse relationship between the price and quantity demanded. The…

Two firms produce a homogenous product. Let p denote the product's price. The output level of firm 1 is denoted by q1, and the output level of firm 2 by q2. The aggregate industry output is denoted by Q, Q = q1 + q2. The aggregate industry demand curve for this product is given by p = 200 – Q. a. Assuming that firms are homogeneous with cost function C(q1) = 2qi, derive the best response function for each firm. Show that Cournot-Nash equilibrium output for each firm is symmetric. Find the Cournot-Nash equilibrium aggregate output and price. Verify that given similar cost functions, equilibrium profits for each firm is symmetric as well.

Two firms produce a homogenous product. Let p denote the product's price. The output level of firm 1 is denoted by q1, and the output level of firm 2 by q2. The aggregate industry output is denoted by Q, Q = q1 + q2. The aggregate industry demand curve for this product is given by p = 200 – Q. a. Assuming that firms are homogeneous with cost function C(q1) = 2qi, derive the best response function for each firm. Show that Cournot-Nash equilibrium output for each firm is symmetric. Find the Cournot-Nash equilibrium aggregate output and price. Verify that given similar cost functions, equilibrium profits for each firm is symmetric as well.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter12: Price And Output Determination: Oligopoly

Section: Chapter Questions

Problem 5E

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