A homogenous product is produced by n rival firms. They have the same costs. The market demand is: P = 80 – Q where: Q = q1 + q2 + ... + qn %3D - The firms' total cost equations are: TC; = 50qi (I = 1, 2, .., n) a. In estimating its marginal revenue, each firm takes all its rivals' output as given and maximizes profit subject to that assumption. Write firm 1's total revenue and marginal revenue equations. TR1 = MR1 = b. Set MR1 = MC; to derive the equation of firm l's reaction curve, Q:*(Q2, Q3, write the reaction curve equation for firm 2. Qn). Also Qi*(q2, q3, 94, - qn) = ... q2*(qı, q3, q4, . qn) = %3D ... c. Solve for the profit-maximizing price and output per firm as functions of n. (Check your earlier result for the monopoly and duopoly cases: n = 1 and n = 2.) q* : %3D P* =

A homogenous product is produced by n rival firms. They have the same costs. The market demand is: P = 80 – Q where: Q = q1 + q2 + ... + qn %3D - The firms' total cost equations are: TC; = 50qi (I = 1, 2, .., n) a. In estimating its marginal revenue, each firm takes all its rivals' output as given and maximizes profit subject to that assumption. Write firm 1's total revenue and marginal revenue equations. TR1 = MR1 = b. Set MR1 = MC; to derive the equation of firm l's reaction curve, Q:(Q2, Q3, write the reaction curve equation for firm 2. Qn). Also Qi(q2, q3, 94, - qn) = ... q2(qı, q3, q4, . qn) = %3D ... c. Solve for the profit-maximizing price and output per firm as functions of n. (Check your earlier result for the monopoly and duopoly cases: n = 1 and n = 2.) q : %3D P* =

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 3E

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