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P = 100 - 2Q, where Q is total quantity demanded for both firms 1 and 2, respectively. The firms 1' marginal cost is given by MCi(Qi) = 2Qi. The firms 2' marginal cost is given by MC2(Q2)=4Q2. Based on this information firm 1 and 2's reaction functions are

Sagot :

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The reaction functions of the equations that we have here are given as Q1 = 16.7 - 0.33Q₂ and Q₂ = 12.5 - 0.25Q₁

How to solve for the reaction functions

We have

P = 100 - 2Q

= 100 - 2Q1 - 2Q2

MCi(Qi) = 2Qi

while,

MC2(Q2)=4Q2

δπ₁/δQ₁ = 100Q₁ - 2Q₁² - 2Q₁Q₂ - Q₁²

= 100 - 4Q₁ - 2Q₂ - 2Q₁

= 100 - 6Q₁ - 2Q₂

6Q₁ = 100 - 2Q₂

divide through by 6

Q₁ = 16.7 - 0.33Q₂ ⁻⁻⁻⁻⁻⁻⁻ This is the reactant function for Q₁

δπ₂/δQ₂ = 100Q₂ - 2Q₁Q₂ - 2Q₂² - 2Q₂²

= 100 - 2Q - 4Q₂ - 4Q₂

= 100 - 2Q - 8Q₂

8Q₂ = 100 - 2Q₁

divide through by 8

Q₂ = 12.5 - 0.25Q₁ --------- This is the reactant function for Q2

Hence the reactant functions for these two equations are given as

Q₁ = 16.7 - 0.33Q₂ and Q₂ = 12.5 - 0.25Q₁

Read more on reactant functions here:

https://brainly.com/question/24384825

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