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(C,C) = In C + C In periods 1 and 2 households receive a constant endowment of Q = Q = Q. Households have access to financial markets, where they can lend or borrow at the international interest rater. The initial net foreign asset position of the representative household is B = 0. Suppose that Q>. (a) [10 Points.] Set up the budget constraint of households for periods 1 and 2. Derive the inter-temporal 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 r* and Q. (c) [8 Points.] What happens to consumption and the current account in period 1 when the interest rate r increases? Provide intuition for your results. Now suppose households have uncertainty regarding their future endowment. In par- ticular, the endowment can be Q = Q- with probability 2/3 or Q = Q + 20 with probability 1/3. Agents preferences are now given by U(C, C2) = ln C+E[C]. where E[] indicates expected value. (d) [2 Points.] Compute the expected value of the endowment in period 2. (e) [10 Points.] Set up the maximization problem for the households and find 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.