It's year 2017, and Boeing is launching the B797 while Airbus is launching the A360. Assume that the companies stop selling their other planes, and there are no other plane makers in the world (sorry, Bombardier).

Airline companies view B797's and A360's as perfect substitutes, and the demand for these planes is: Q(P) = 5500 - 10P, where P is in millions of US dollars.

Airbus and Boeing have the same cost function: C(q) = 40000 + 100q + 0.05q2 , where the cost is in millions of US dollars. Assume that the $40 billion constant in the cost function is the sunk cost of developing the aircraft, so it is borne even if q=0.

5. Suppose Airbus and Boeing simultaneously choose price (Bertrand competition), and each company gets half the market if they choose the same price.

a) Let P_m be your answer to 3a [P=400]. What is Boeing's best response if Airbus chooses a price above P_m? Answer this question without calculations.

b) What is the socially efficient quantity of airplanes? Derive society's cost function carefully.

c) What is the price P_eff such that if both Airbus and Boeing charge it, the market outcome is efficient?

d) Show that it is a Nash Equilibrium for both firms to charge P_eff.

e) Show that it is a Nash Equilibrium for both firms to charge $270 million for each plane.

f) [OPTIONAL] Verify that if both firms charge $270 million, they are both pricing above marginal cost. Why is that a Nash Equilibrium here, while in class we got P=MC under Bertrand competition?