Two firms are competing in a Bertrand setting. The demand and costs equations are: Q1 = 88–4P1+2P2, Q2 = 88–4P2+2P1; MC1 = 9; and MC2 = 10. Instructions: Use two decimal for part a. a. Determine the reaction function for each firm. Firm 1: P1 =  + P2 Firm 2: P2 =  + P1 Instructions: Use no decimals. Do not round values if used to complete other calculations. Use commas (30,000 instead of 30000) b. P1 = $ and P2 = $ c. Q1 =  and Q2 =  d. Profits Firm 1 = $ and profits Firm 2 = $ e. If Firm 1 instead produces P1 = 16, the optimal P2 = . f. When one of the firms set a P < P-Duopoly, the best strategy for the other firm is to set:  A. a P-BRF, and continue with this strategy afterward with the risk of economic profits = 0. B. a P-BRF, and after this one time, then continue with P-Duopoly. C. a P > P-Duopoly from now on, until the market reaches P-Monopoly. D. also P < P-Duopoly one time, then set P-Monopoly

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
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Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.1P
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  1. Two firms are competing in a Bertrand setting. The demand and costs equations are: Q1 = 88–4P1+2P2, Q2 = 88–4P2+2P1; MC1 = 9; and MC2 = 10.

    Instructions: Use two decimal for part a.

    a. Determine the reaction function for each firm.
    Firm 1: P1 =  + P2

    Firm 2: P2 =  + P1

    Instructions: Use no decimals. Do not round values if used to complete other calculations. Use commas (30,000 instead of 30000)

    b. P1 = $ and P2 = $

    c. Q=  and Q2 = 

    d. Profits Firm 1 = $ and profits Firm 2 = $

    e. If Firm 1 instead produces P1 = 16, the optimal P2 = .

    f. When one of the firms set a P < P-Duopoly, the best strategy for the other firm is to set: 

    A. a P-BRF, and continue with this strategy afterward with the risk of economic profits = 0.

    B. a P-BRF, and after this one time, then continue with P-Duopoly.

    C. a P > P-Duopoly from now on, until the market reaches P-Monopoly.

    D. also P < P-Duopoly one time, then set P-Monopoly. 

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