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Question 1 (20 points) Consider the standard neoclassical growth model in discrete time. There is a large number of identical households normalized to 1. Each household wants to maximize life-time discounted utility U((a).) = _Bu(a), BE (0, 1). Each household has an initial capital ko at time 0, and one unit of productive time in each period that can be devoted to work. Final output is produced using capital and labor, according to a CRS production function F. This technology is owned by firms (whose measure does not really matter because of the CRS assumption). Output can be consumed (c) or invested (i,). Households own the capital (so they make the investment decision), and they rent it out to firms. Let & E (0, 1) denote the depreciation rate of capital. Households own the firms, i.e., they are claimants to the firms' profits, but these profits will be zero in equilibrium. The function u is twice continuously differentiable and bounded, with u'(c) > 0, u"(c) 0, f"(x) wn What is the economic meaning of this result? h) Without going into detail, provide a strategy to solve for the steady state equi- librium. More precisely, explain how you would combine the various equilibrium con- ditions derived so far in order to characterize the five equilibrium variables.Question 2 (20 points) Consider an economy that consists of two islands, i = (1, 2). Each island has a large population of infinitely-lived, identical agents, normalized to the unit. There is a unique consumption good, say, coconuts, which is not storable across periods. Although within each island agents have identical preferences over consumption, across islands there is a difference: Agents in island 2 are more patient. More precisely, the lifetime utility for the typical agent in island i is given by where 8, E (0, 1), for all i, and & > A. Due to weather conditions in this cconomy, island 1 has a production of e >0 units of coconuts in even periods and zero otherwise, and island 2 has a production of e units of coconuts in odd periods and vero otherwise. Agents cannot do anything to boost this production, but they can trade coconuts, so that the consumption of the typical agent in island i, in period f, is not necessarily equal to the production of coconuts on that island in that period (which may very well be xero). Assume that shipping coconuts across lulands is cout less. al Describe the Arrow-Debree equilibrium (ADE) allocations in this economy. You can use any method you like, but I strongly recommend that you exploit Negishi's method. by Describe the ADE prices in this economy. c Plot the equilibrium allocation for the typical agent in bland i, ie., tap f = [1, 2), against t. Is there any period & in which & - ed If yes, please provide a closed form solution for that value of t.&quot