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{"ops":[{"insert":"a.\u00a0First, suppose we have a representative individual living for two periods and has utility, U = ln C"},{"attributes":{"script":"sub"},"insert":"1"},{"insert":" + ln C"},{"attributes":{"script":"sub"},"insert":"2"},{"insert":". Let his\/her labour income in the first period to be Y"},{"attributes":{"script":"sub"},"insert":"1"},{"insert":" and zero in the second period. Let the rate of return to savings, r, to be influenced by a random shock, find the first-order condition for his\/her choice of C"},{"attributes":{"script":"sub"},"insert":"1."},{"insert":" Explain how, if at all, does consumption respond to the uncertainty in the rate of return? \n\nb.\u00a0Second, suppose we extend the time horizon to infinitely lived agents, and let the individual also supply capital to a representative firm in the economy. Formulate and solve the firm\u2019s profit maximization problem. You can assume price level to be fixed and normalized to one, but you should explain the economic intuitions of the first-order conditions.\n\nc.\u00a0Third, let \u03b2>0 be the discount factor, present and solve for both the competitive equilibrium and the steady state of the two-sector economy. With the use of phase diagram, identify the saddle path.\n\n"}]}

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