Consider the model in Lecture 1 about the intertemporal approach to the current account. Suppose the consumers have an income of 1 in period 1 and 2 in period 2, their preference is given by (1,2) = ln (1) + ln (22), where 0 < < 1 is the discount rate. They face a given interest rate r in the international capital market for lending or borrowing. Suppose they are born without debts or inheritance and die without debts or heritage. (a) Write down the intertemporal budget constraint faced by consumers. (b) Write down the Euler Equation. (hint: ln(x) = 1 ) (c) Solve for 1 and 2. (note: we do not assume = 1/1 + ) (d) Solve for the current account 1 in period 1. What happens to 1 when goes up? Can you provide the intuition?