Consider a twoperiod intertemporal choice model. Lut has utility over consumption in period 1 (c1) and consumption in period 2 (2) given by: L U(C1, (:2) = 111(01) + 1.03 111(62) where the It? captures his subjective discount factor, )3. He can borrow and lend at the real interest rate r. (a) Suppose that Lut will receive equal income in both periods of y1 = y; = 1. Also suppose that the real interest rate r = 0.03. Solve for Lut's optimal consumption plan. Interpret this result, briey. Suppose now that Lut knows his income in the initial period, y1 = 1. However, there is uncertainty about what next period's income will be. It could be high, yf = 1.5 with probability 0.5, or low, y? = 0.5 with probability 0.5. His problem now is to choose the initial period consumption c1, consumption in the event that future income is high 62\" , and consumption in the event that future income is low cg, to maximize expected utility. That is, we can assume his preferences satisfy G1G6. (b) Set up the optimization problem and derive the rstorder conditions. Hint: You should have two budget constraints. So either you need a Lagrangian with two A's, or since we know both budget constmints will.r hold with equality, you can substitute in for of and cg in the utility function. (c) Will Lut choose the same consumption c1 from part (a) when faced with this uncertainty? If not, how will it change? Explain your intuition