Suppose that firms A and B are Cournot duopolists in the salt industry. The market demand curve can be specified $P = 200 - Q _ { A } - Q _ { B }$ The marginal cost to each firm is $40. Suppose that firm A is producing 100 units. What is firm B's profit-maximizing quantity?
A)100.
B)60.
C)30.
D)20.

Question

Quizplus · Accepted Answer

To find firm B's profit-maximizing quantity, we need to use the concept of reaction function. The reaction function shows how one firm will respond to changes in the other firm's output.

First, let's find the total quantity produced in the market when firm A produces 100 units:

Q = QA + QB
Q = 100 + QB

Using the demand equation, we can find the market price:

P = 200 - Q
P = 200 - (100 + QB)
P = 100 - QB

Now, we can find firm B's marginal revenue:

MR = P' * QB + P
MR = (-1) * QB + (100 - QB)
MR = 100 - 2QB

Setting MR equal to marginal cost (MC = $40), we get:

100 - 2QB = 40
2QB = 60
QB = 30

Therefore, firm B's profit-maximizing quantity is 30 units.

Suppose That Firms a and B Are Cournot Duopolists in the Salt