Consider a single-good, two-period small open endowment economy populated by a representative household with preferences described by the lifetime utility function
ln C1 + ln C2, where C1 and C2 denote consumption in periods 1 and 2, respectively. The household receives exogenous endowments of the good of Q1 = Q2 = 10 in periods
1 and 2, respectively. The household enters period 1 with some debt, denoted by B0, inherited from the past. Let B0 be equal to −5. The interest rate r0 on these liabilities is 20 percent. Finally, suppose that the country enjoys free capital mobility and that the world interest rate r∗ on assets held between periods 1 and 2 is 10 percent.
(a) Derive the household’s intertemporal budget constraint.
(b) Compute the equilibrium levels of consumption, the trade balance, and the current account in periods 1 and 2.