Exercise 1. [45 Points] Consider a small open economy with 2 periods and a single non storable good. Preferences of the representative household are described by the following utility function: U(Cl,02)=11101 + 02 [n periods 1 and 2 households receive a constant endowment of Q1 = Q2 = Q Households have access to nancial markets' where they can lend or borrow at the international interest rate r'. The initial net foreign asset position of the representative household is BE = . Suppose that Q ) . (a) [10 Points] Set up the budget constraint of households for periods 1 and 2. Derive the intertemporal budget constraint. {b} [10 Points] Find the equilibrium levels of consumption and the current account for periods 1 and 2. Your answer should depend on the parameters 1\" and Q [c] [6 Points] \"'hat happens to consumption and the current account in period 1 when the interest rate 1" increases? Provide intuition for your results. Now suppose households have uncertainty regarding their future endowment. In par ticular' the endowment can be Q2 = Q 2:! with probability U3 or Q3 = Q + a with probability 2f3. Agents preferences are now given by 0101,02) = 11101+ ElCrlg where E indicates expected value. {d} [2 Points] Compute the expected value and variance of the endowment in period 2. (e) [10 Points] Set up the maximization problem for the households and nd equilibrium levels of consumption in periods 1 and 2 {there should be more than one consumption in period 2, depending on the realization of the endowment). [f] [8 Points] Are there precautionary savings in this economy? Why or why not? Provide intuition