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# Cournot problem

(See attached file for full problem description)

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Reconsider the attached problem (prior problem), except suppose American and United take each other's quantity as given rather than taking each other's price as given. That is, assume that American and United act as Cournot competitors rather than Bertrand competitors. The inverse demand curves corresponding to the demand curves in the attached problem (prior problem) are

PA= 1000-2QA/3-QU/3

PU= 1000-2QU/3-QA/3

a) Suppose that American chooses to carry 660 passengers per day (i.e., QA=660). What is United's profit maximizing quantity of passengers? Suppose American carries 500 passengers per day. What is United's profit maximizing quantity of passengers?

b) Derive the quantity reaction function for each firm.

c) What is the Cournot equilibrium in quantities for both firms? What are the corresponding equilibrium prices for both firms?

d) Why does the Cournot equilibrium in this problem differ from the Bertrand equilibrium in the attached problem (prior problem)?

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United Airlines and American Airlines both fly between Chicago and
San Francisco. Their demand curves are given by QA=1000-2PA+PU and
QU=1000-2PU+PA.
QA and QU stand for the number of passengers per day for American and United, respectively. The marginal cost of each carrier is \$10 per passenger.
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#### Solution Summary

Cournot problem is solved.

\$2.19