The neighboring island of Boingo is very similar to that of Drongo, except that there are Mo old people and My young people; their endowments and utilities are the same as for the old and young in Drongo in parts 2a-2c. We first consider the case of no trade between islands. (a) What is the equilibrium price of period-1 cake in Boingo? Suppose now that a Polynesian invents an outrigger that permits costless trade between Boingo and Drongo. Suppose No/Ny #Mo/My. (b) Since costless trade between islands is possible, are the pre-trade competitive allocations in Boingo and Drongo Pareto efficient? (c) What is the competitive price and allocation, now that costless trade is possible? (d) Who is made worse off by the opening of trade? Reconcile this with the statement that com- petitive allocations are Pareto efficient. Question 2. In this question, we continue our exploration of intertemporal trade. On the island of Drongo, there is just one commodity, cake, and two time periods. There are two generations on this is- land. Each member of the old generation has an endowment of 1 pound of period-0 cake and no period-1 cake. Each member of the young generation has an endowment of 1 pound of period-1 cake and no period-0 cake. There are N, old people and N, young people. The consumption bundles are the pairs (Co. C₁), where co is cake in period 0 and c, is cake in period 1. All genera- tions, old and young, have identical utility functions U(co, c₁) log co +5log c₁, where & is a measure of impatience and satisfies 0 < 5 < 1. Period-0 cake is the numeraire, and P, is the price of period-1 cake. For each t=0, 1, period-r cake must be consumed in period t.
