Two firms, Boors and Cudweiser, are Cournot competitors selling identical beer. Market demand is $P = 5 - 0.001(QB + QC)$. Boors' marginal revenue is $MR_B = 5 - 0.001(2QB + QC)$ and Cudweiser's is symmetrical. Boors' marginal cost is $MC_B = 2$, and Cudweiser's is $MC_C = 1$. We want to find how many units of beer Cudweiser will produce.

1. Problem Description

Two firms, Boors and Cudweiser, are Cournot competitors selling identical beer. Market demand is $P = 5 - 0.001(QB + QC)$. Boors' marginal revenue is $MR_B = 5 - 0.001(2QB + QC)$ and Cudweiser's is symmetrical. Boors' marginal cost is $MC_B = 2$, and Cudweiser's is $MC_C = 1$. We want to find how many units of beer Cudweiser will produce.

2. Solution Steps

Since the firms are Cournot competitors, we can use the profit-maximizing condition where $MR = MC$.

For Boors:

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

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

$3 = 0.001(2QB + QC)$

$3000 = 2QB + QC$

For Cudweiser, we know that the marginal revenue function is symmetrical to Boors, so we can infer that

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

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

$4 = 0.001(2QC + QB)$

$4000 = 2QC + QB$

Now we have a system of two equations with two unknowns:

(1) $2QB + QC = 3000$

(2) $QB + 2QC = 4000$

Multiply equation (2) by 2:

(3) $2QB + 4QC = 8000$

Subtract equation (1) from equation (3):

$(2QB + 4QC) - (2QB + QC) = 8000 - 3000$

$3QC = 5000$

$QC = \frac{5000}{3} = 1666.67$

Substitute $QC = 1666.67$ into equation (1):

$2QB + 1666.67 = 3000$

$2QB = 3000 - 1666.67$

$2QB = 1333.33$

$QB = \frac{1333.33}{2} = 666.67$

Rounding $QC$ to the nearest integer we get $QC = 1667$

3. Final Answer

a. 1,667