What is the bertrand equilibrium in the given market

Question

Problem

United Airlines and American Airlines both fly between Chicago and San Francisco. Their demand curves are given by Q_A = 1000 - 2P_A  +P_U and Q_U = 1000 - 2P_U + PA. Q_A and Q_U stand for the number of passengers per day for American and United, respectively. The marginal cost of each carrier is $10 per passenger.

a) If American sets a price of $200, what is the equation of United's demand curve and marginal revenue curve? What is United's profit-maximizing price when American sets a price of $200?

b) Redo part (a) under the assumption that American sets a price of $400.

c) Derive the equations for American's and United's price reaction curves.

d) What is the Bertrand equilibrium in this market?

The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.