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'{Question 2. in this question. we continue our exploration of intertemporal trade. [in the island of Drongo. there is just one commodity. cake. and two time periods. There are two generations on thls ls- iand. Each member of the old generation has an endowmmt of 1 pound of period-[I cake and no period-l cake. Each member of the young generation has an endotmnent of 1 pound of period-l cake and no period-II) cake. There are No old people and N}. young people. The consumption bundles are the pairs (cu. cl}, where Fe is cake in period ii and Cl is cake in period 1. All genera tions. old and voting. have identical utility functions Ute\". cl]: logcg+5logch where 5 is a measure of impatience and satises Ill 4:: 5 c: 1. PeriodI] cake is the numeraire. and p] is the price ofperiod-l cake. For each t = [in]. periodI 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-l cake p]. [b] What is the equilibrium price of periodl cake [in general. this will depend on the parame ters describing Drongo's economy. N... My. and 5]. lci Compare the equilibrium price of periodvl cake 1Isu'hen Na = My with the price 1when Na c N... What are the implications for the consumption of period- cake by the vcung genera- tion in each case? Provide some intuition. no intrepid explorer discovers a cache of period- cake of size N . Suppose N = N... = N... 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- cake. [d] Suppose the cache is awarded to the old generation so that each member of the old genera- tion now has an endowment of 2 pounds of period-I] cake. Compare the equilibrium price and allocation before and after the discovery. [e] Suppose the cache ls awarded to the young generation so that each member of the young generation now has an endowment of 1 pound of period-ti cake and 1 pound of period-l cake. Compare the equilibrium price and allocation with that of part 2d