Consider a Cournot duopoly with the following inverse demand function: P = 100 - 2Q1 - 2Q2. The firms' marginal costs are identical and are given by MCi(Qi) = 2Qi. Based on this information, firm 1 and 2's reaction functions are:A.r1(Q2) = 24.5 - 0.5Q1 and r2(Q1) = 24.5 - 0.5Q2. B.r1(Q2) = 24.5 - 0.5Q2 and r2(Q1) = 24.5 - 0.5Q1. C.Q1 = 49 - 0.5Q2 and Q2 = 49 - 0.5Q1. D.Q1 = 49 - 0.25Q2 and Q2 = 49 - 0.25Q1. Please provide me with detail step by step process to get to the answer. coz no matter how many times I tried. my answer doesnt match the one in answer key

Inverse Demand Function: Firm's identical marginal cost: Where i = 1, 2

Answered: Consider a Cournot duopoly with the…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider a Cournot duopoly with the following inverse demand function: P = 100 - 2Q₁ - 2Q₂. The firms' marginal costs are identical and are given by MC_i(Q_i) = 2Q_i. Based on this information, firm 1 and 2's reaction functions are:

A.	r₁(Q₂) = 24.5 - 0.5Q₁ and r₂(Q₁) = 24.5 - 0.5Q₂.

B.	r₁(Q₂) = 24.5 - 0.5Q₂ and r₂(Q₁) = 24.5 - 0.5Q₁.

C.	Q₁ = 49 - 0.5Q₂ and Q₂ = 49 - 0.5Q₁.

D.	Q₁ = 49 - 0.25Q₂ and Q₂ = 49 - 0.25Q₁.

Please provide me with detail step by step process to get to the answer. coz no matter how many times I tried. my answer doesnt match the one in answer key

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