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In a Cournot duopoly, we find that Firm 1's reaction function is Q1 = 50 - 0.5Q2, and Firm 2's reaction function is Q2 = 75 - 0.75Q1. What is the Cournot equilibrium outcome in this market?

Question

In a Cournot duopoly, we find that Firm 1's reaction function is Q1 = 50 - 0.5Q2, and Firm 2's reaction function is Q2 = 75 - 0.75Q1. What is the Cournot equilibrium outcome in this market?

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Solution

To find the Cournot equilibrium, we need to solve these two reaction functions simultaneously.

Step 1: Substitute Q2 from Firm 2's reaction function into Firm 1's reaction function:

Q1 = 50 - 0.5*(75 - 0.75Q1)

Step 2: Simplify the equation:

Q1 = 50 - 37.5 + 0.375Q1

Step 3: Rearrange the equation to solve for Q1:

0.625Q1 = 12.5

Step 4: Solve for Q1:

Q1 = 12.5 / 0.625 = 20

Step 5: Substitute Q1 into Firm 2's reaction function to find Q2:

Q2 = 75 - 0.75*20 = 75 - 15 = 60

So, the Cournot equilibrium in this market is Q1 = 20 and Q2 = 60.

This problem has been solved

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