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 island. 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 No old people and Ny young people. The consumption bundles are the pairs (c0 , c1 ), where c0 is cake in period 0 and c1 is cake in period 1. All generations, old and young, have identical utility functions U (c0 , c1 ) = log c0 + log c1 , where is a measure of impatience and satisfies 0 < < 1. Period-0 cake is the numeraire, and p1 is the price of period-1 cake. For each t = 0, 1, period-t cake must be consumed in period t .

(a) Set up the maximization problem for a representative agent from each generation. For each generation, solve for the representative agent's demand for cake in period 1 in terms of the price of period-1 cake p1 .

(b) What is the equilibrium price of period-1 cake (in general, this will depend on the parameters describing Drongo's economy, No , Ny , and ).

(c) Compare the equilibrium price of period-1 cake when No = NY with the price when No < Ny . What are the implications for the consumption of period-0 cake by the young generation in each case? Provide some intuition. An intrepid explorer discovers a cache of period-0 cake of size N . Suppose N = No = Ny . In order to investigate how the discovery of this cache affects the equilibrium price and allocation, we need to assign ownership of the discovered cache of period-0 cake.

(d) Suppose the cache is awarded to the old generation so that each member of the old generation now has an endowment of 2 pounds of period-0 cake. Compare the equilibrium price and allocation before and after the discovery.

(e) Suppose the cache is awarded to the young generation so that each member of the young generation now has an endowment of 1 pound of period-0 cake and 1 pound of period-1 cake. Compare the equilibrium price and allocation with that of part 2d.