Suppose in a Cournot duopoly that two firms, Firm 1 and Firm 2, face market demand $P = 50 -$ $Q$ and both have marginal cost, $M C = \$ 20$. The equilibrium price in this market will be:
A) $P = 10$
B) $P = 20$
C) $P = 30$
D) $P = 40$

Question

Quizplus · Accepted Answer

To find the equilibrium price, we first need to find the equilibrium quantity. 
The total quantity demanded in the market, Q, is equal to the sum of the quantities produced by Firm 1 and Firm 2. 
Each firm's quantity produced depends on the other firm's quantity produced, according to the Cournot model. 
The best response function for Firm 1 is: 
Q1 = (1/2)(50 - Q2 - 20) 
where Q1 is Firm 1's quantity produced and Q2 is Firm 2's quantity produced. 
The best response function for Firm 2 is: 
Q2 = (1/2)(50 - Q1 - 20) 
where Q2 is Firm 2's quantity produced and Q1 is Firm 1's quantity produced. 
To find the equilibrium, we need to solve these two equations simultaneously.

If we substitute the second equation into the first equation to eliminate Q1, we get: 
Q1 = (1/2)(50 - (1/2)(50 - Q1 - 20) - 20)
Simplifying this, we get: 
Q1 = 15 
Similarly, we can find that Q2 = 15. 
Therefore, the total quantity demanded in the market is Q = 30.

To find the equilibrium price, we can substitute Q = 30 into the demand equation: 
P = 50 - Q 
P = 50 - 30 
P = 20

Therefore, the equilibrium price in this market is $20, which corresponds to choice (C). To find the equilibrium price in a Cournot duopoly, we first need to find the equilibrium quantity for each firm. Since both firms have the same marginal cost, they will produce an equal quantity. To find this quantity, we can use the reaction function:

Q1 = (50 - Q2 - 20)/2 = 15 - Q2/2
Q2 = (50 - Q1 - 20)/2 = 15 - Q1/2

Setting these two reaction functions equal to each other, we get:

15 - Q2/2 = 15 - Q1/2
Q1 = Q2 = 20

So each firm will produce 20 units of the good, for a total market quantity of 40 units. Plugging this into the demand function, we get:

P = 50 - 40 = 10

Therefore, the equilibrium price in this market is $10. However, this option is not available in the answer choices. The closest option available is C, which is $30. This is not the correct answer, but it is the closest option available.

Suppose in a Cournot Duopoly That Two Firms, Firm 1 P=50−P = 50 -P=50−

Suppose in a Cournot Duopoly That Two Firms, Firm 1 $P = 50 -$