Consider a two- period model of a small open economy with a single good each period. Let preferences of the representative household be described by the utility function

lnC1+lnC2,

whereC1andC2denote consumption in periods 1 and 2, respectively. In pe- riods 1 and 2, the household receives profits from the firms it owns, denoted 1and 2, respectively. Households and firms have access to financial mar- kets where they can borrow or lend at the interest rater1. The production technologies in periods 1 and 2 are given by

Q₁=A₁I₀^alpha

and

Q₂=A₂I₁^alpha

where Q₁ and Q₂ denote output in periods 1 and 2 I₀ and I₁ denote the

capital stock in periods 1 and 2,A1andA2denote the productivity factors

in periods 1 and 2, andalphais a parameter. Assume that I0=16 A1= 10/3

A2= 3.2,

andalpha=3/4.

At the beginning of period 1 households haveB₀^h= 8 bonds. The interest rate on bonds held from period 0 to period 1 isr₀= 0.25 In period 1, firms borrow the amountD₁^{f t}o purchase investment goods that become productive capital in period 2,I₁. Assume that there exists free international capital mobility and that the world interest rate, denotedr^*, is 20 percent.

1. Compute output and profits in period 1.

2. Compute the optimal levels of investment in period 1 and output and profits in period 2.

3. Solve for the optimal levels of consumption in periods 1 and 2.

4.) Find the country's net foreign asset position at the end of period 1, denotedB₁^*, saving,S₁, the trade balance,TB₁, and the current account,CA₁.

5 Now consider an interest-rate hike in period 1. Specifically, assume that as a result of turmoil in international financial markets, the world interest rate increases from 20 percent to 50 percent in period 1. Find the equilibrium levels of saving, investment, the trade balance, the current account, and the country's net foreign asset position in period 1. Provide intuition.

6 Suppose that the interest rate is 20 percent, and thatA1increases to 4. Calculate the equilibrium values of consumption, saving, investment, and the current account in period 1. Explain.

7 Suppose that the interest rate is 20 percent, thatA₁= 10/3 A₂increases from 3.2 to 4. Calculate the equilibrium values of con- sumption, saving, investment, and the current account in period 1. Explain.