(6) Consider a world where the governments of two countries interact, with populations n1 and n2. In each country i, the country-wide net payoff to population size is given by [An; - n;] + b(n; - n;), where n, is the population size of the other country. (a) There are two components in the payoff function. By drawing diagrams if needed, describe how these components vary with population size. Also interpret each component: what do you think each of them means in economic or political terms? (b) Prove that if each government chose its population independently of the other, then equilibrium population sizes would be A+b 01 = 12 2 (c) Is the above equilibrium efficient or not; i.e., is it possible to make both countries simul- taneously better off relative to the equilibrium by choosing other population sizes? Discuss this from both the specific perspective of the problem at hand, and from a broader intuitive perspective, emphasizing externalities (if any) that are involved. (d) Suppose that the two countries formed a union, and that they elected a representative who seeks to maximize the sum of their payoffs. Describe what nj and nz would look like