1. (25 points total) Consider the inter-temporal model with two time periods t=0 and 1. Home is a small open economy that can borrow and lend in the first period at a fixed world real interest rate of 5%. In the first period output is X0=200. Because of a deteriorating environment, output in the second period is expected to fall to X1=150. The country wants to smooth consumption as much as possible. The country begins with no external assets or liabilities.

a. (5 points) Solve for the optimal level of consumption consistent with perfect consumption smoothing, the current account, and financial account in the first period (t=0).

b. (5 points) Solve for NFIA, the trade balance, and the current account in the second period (period 1).