In Problem 6, suppose that two Cournot duopolists serve the Peoria-Dubuque route, and the demand curve for tickets per day is Q = 160 - 2p (so p = 80 - ). Total costs of running a flight on this route are 400 + 20q, where q is the number of passengers on the flight. Each flight has a capacity of 80 passengers. In Cournot equilibrium, each duopolist will run one flight per day and will make a daily profit of
A) $800.
B) $400.
C) $200.
D) $160.
E) $1,600.

Question

In Problem 6, suppose that two Cournot duopolists serve the Peoria-Dubuque route, and the demand curve for tickets per day is Q = 160 - 2p (so p = 80 -  ). Total costs of running a flight on this route are 400 + 20q, where q is the number of passengers on the flight. Each flight has a capacity of 80 passengers. In Cournot equilibrium, each duopolist will run one flight per day and will make a daily profit of
A) $800. 
B) $400. 
C) $200. 
D) $160. 
E) $1,600.

Quizplus · Accepted Answer

To find the Cournot equilibrium, we need to set up the profit function for each duopolist. Let q1 be the number of passengers served by the first duopolist and q2 be the number of passengers served by the second duopolist. Then, the total quantity of passengers served is Q = q1 + q2. The market price is given by the demand curve, which can be rewritten as p = 40 - 0.5Q = 40 - 0.5q1 - 0.5q2.

The profit function for each duopolist is:

π1 = pq1 - (400 + 20q1)
π2 = pq2 - (400 + 20q2)

In Cournot equilibrium, each duopolist maximizes their profit taking the output of the other firm as given. Therefore, we need to find the Nash equilibrium of this game, which is a pair of output levels (q1*, q2*) such that no player has an incentive to deviate unilaterally.

To find the equilibrium output levels, we need to solve the first-order conditions of each duopolist's profit maximization problem:

∂π1/∂q1 = p - 20 - 0.5q2 = 0
∂π2/∂q2 = p - 20 - 0.5q1 = 0

Substituting p = 40 - 0.5q1 - 0.5q2 in each equation and solving for q1 and q2, we obtain:

q1* = q2* = 40

Therefore, each duopolist will serve 40 passengers per day and charge a price of p* = $20 per ticket. The total profit of each firm is:

π1* = (20)(40) - (400 + 20(40)) = $400
π2* = (20)(40) - (400 + 20(40)) = $400

Therefore, the total daily profit of the duopolists is $800. The correct answer is option B.

In Problem 6, Suppose That Two Cournot Duopolists Serve the Peoria-Dubuque