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 T0  on these liabilities is 20 percent. Finally, suppose that the country enjoys free capital mobility and that the world interest rate T* 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.

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 inancial assets carried over from period 0 worth 1.1 bushels of wheat including interest at rate T0  = 0.1 (i.e., (1 + T0 )B0  = 1.1). The country enjoys free capital mobility and the world interest rate T*  be- tween periods 1 and 2 is 10 percent. Financial assets are denominated in units of wheat.