Problem 11.3 Two countries, 1 and 2, are located next to one another. Export production in Country 1 emits a pollutant which has a negative impact on welfare in Country 2. Similarly, the export production in Country 2 emits a pollutant which has a negative impact on welfare in Country 1 More precisely, annual welfare in the two countries is given by

V₁ (q₁,q₂) = (60-q₂)q₁-(q₁)² in Country 1, and

V₂(q₁,q₂) = (60-q₁)q₂-(q₂)² in Country 2,

where q₁ is the export production in Country 1 and q₂ is the export production in Country 2.

a) Suppose the countries only interact once. Derive each country's best-response function and find the Nash equilibrium of that static game. What is the level of annual welfare in each country in this equilibrium?

b) Suppose the countries could negotiate an outcome where export production is set such that combined annual welfare in the two countries is maximized and each country produces the same amount of exports. What is the level of exports in each country that achieves this? How does this outcome compare to the Nash equilibrium in (a) in terms of welfare?

c) Now take into consideration that the countries interact every year. Assume that export production in each year is decided at the start of the year. What strategies can the countries employ to support the negotiated level of quantities in (b) as an equilibrium in an infinitely repeated game? For which levels of discount factors is this possible?