Problem 1 (Small Open Economy)
Consider a single-good, two-period small open endowment economy popu-
lated 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 house hold 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.
Problem 2 (The Terms of Trade and the Current Account)
The following table shows commodity prices in world markets. In the table,
prices of oil are expressed in dollars per barrel, prices of wheat are expressed in
dollars per bushel.
Price
Commodity Period 1 Period 2
Wheat 1 1
Oil 1 2
Kuwait is a two-period economy that produces oil and consumes wheat. Con-
sumers have preferences described by the lifetime utility function
U(C1, C2) = ln C1 + ln C2,
where C1 and C2 denote consumption of wheat in periods 1 and 2, respectively,
measured in bushels. Kuwait’s per-capita endowment of oil is 5 barrels in each
period. Kuwait starts period 1 with net financial assets carried over from period 0 worth 1.1 bushels of wheat including interest at rate r0 = 0.1 (i.e., (1 + r0)B0 =
1.1). The country enjoys free capital mobility and the world interest rate r∗ be-
tween periods 1 and 2 is 10 percent. Financial assets are denominated in units of
wheat.
(a) What are the terms of trade faced by Kuwait in periods 1 and 2?
(b) Calculate consumption, the trade balance, the current account and national savings in periods 1 and 2.
[Hint: In this economy, there is no investment technology (e.g. capital accu-
mulation). Therefore, the investments are zero, I1 = I2 = 0.)]
