The international airplane production market is dominated

The international airplane production market is dominated by two firms: Boeing and Airbus. For the purpose of this question, assume that there are no other airplane manufacturers in the world. Suppose also that Boeing is owned entirely by the US while Airbus is owned entirely by the EU. Thus, US social welfare is a function of Boeing’s profits and EU social welfare is a function of Airbus’s profits. Suppose that both firms produce airplanes for export to a third market only. This means that in this model, neither Boeing nor Airbus is allowed to sell to their local market or to each other’s market. This allows us to assume that both US and EU social welfare will not be a function of consumer surplus in either region. Let Boeing’s product be its latest 787 model and let Airbus’s product be its latest A380 model.

Assume that these products are differentiated and are imperfect substitutes from the perspective of buyers. Let the demand function faced by Boeing for its 787 model be Q1 = 720 − 2P1 + P2 where Q1 is the quantity of Boeing’s output, P1 is the price charged by Boeing for its 787 model, and P2 is the price charged by Airbus for its A380 model.

Let the demand function faced by Airbus for its A380 model be Q2 = 720 − 2P2 + P1 where Q2 is the quantity of Airbus’s output. Suppose that both firms have a constant average cost of c.

(a) Suppose firms set prices simultaneously. Write down the expression for each firm’s reaction function. Fully illustrate these reaction functions in a diagram with P2 on the horizontal axis.

(b) Now suppose that the US government would like to increase Boeing’s profits. The tools it has available to it are either a per-unit subsidy or a per-unit tax on each 787 produced by Boeing. Which of these tools, if implemented, will increase Boeing’s profits? Explain.

(c) Suppose that the US government’s aim is to maximize US social welfare. What is the optimal per-unit subsidy or per-unit tax that the US government should implement? Explain. You can now assume that c = 120.