The problem describes a Cournot duopoly with two firms, Boors and Cudweiser, producing identical nonalcoholic beer. The market demand is given by $P = 5 - 0.001(QB + QC)$, where $QB$ is the quantity produced by Boors and $QC$ is the quantity produced by Cudweiser. Boors' marginal revenue is $MR_B = 5 - 0.001(2QB + QC)$, and Cudweiser's marginal revenue is symmetrically $MR_C = 5 - 0.001(QB + 2QC)$. Boors has a constant marginal cost of $2, and Cudweiser has a constant marginal cost of $1. We need to find Cudweiser's reaction function.

1. Problem Description

The problem describes a Cournot duopoly with two firms, Boors and Cudweiser, producing identical nonalcoholic beer. The market demand is given by $P = 5 - 0.001(QB + QC)$, where $QB$ is the quantity produced by Boors and $QC$ is the quantity produced by Cudweiser. Boors' marginal revenue is $MR_B = 5 - 0.001(2QB + QC)$, and Cudweiser's marginal revenue is symmetrically $MR_C = 5 - 0.001(QB + 2QC)$. Boors has a constant marginal cost of $2, and Cudweiser has a constant marginal cost of$

1. We need to find Cudweiser's reaction function.

2. Solution Steps

Since the firms behave as Cournot competitors, each firm maximizes its profit by setting its marginal revenue equal to its marginal cost.

For Cudweiser, we have:

$MR_C = MC_C$

$5 - 0.001(QB + 2QC) = 1$

$4 = 0.001(QB + 2QC)$

$4000 = QB + 2QC$

Now we solve for $QC$:

$2QC = 4000 - QB$

$QC = 2000 - 0.5QB$

For Boors, we have:

$MR_B = MC_B$

$5 - 0.001(2QB + QC) = 2$

$3 = 0.001(2QB + QC)$

$3000 = 2QB + QC$

Now we can solve for $QB$:

$2QB = 3000 - QC$

$QB = 1500 - 0.5QC$

The problem asks for Cudweiser's reaction function, which we derived earlier:

$QC = 2000 - 0.5QB$

3. Final Answer

c. QC = 2,000 - .5QB