Consider a two-period small open economy populated by a large number of households with preferences described by the lifetime utility function

ln(C₁^TC₁^N) + ln(C₂^TC₂^N) where C_t ^Tand C_t^N , for t = 1, 2, denote consumption of tradable and nontradable goods in period t, respectively. Households are endowed with Q₁^T = 1 and Q₂^T = 2 units of tradables and Q₁^N = Q₂^N = 1 units of nontradables in periods 1 and 2. Households start period 1 with no assets or debts. The world interest rate is zero.

1. Calculate the equilibrium levels of the current account and the relative price of nontradables in terms of tradable in period 1, denoted CA₁ and p₁, respectively.
2. Suppose now that suddenly the world interest rate increases from 0 to 10 percent. Calculate the new equilibrium levels of the current account and the relative price of nontradables in terms of tradables in period 1