Using the notation from the text, answer the following questions. You may assume that net labor income from abroad is zero, there are no capital gains on external wealth, and there are no unilateral transfers.
a. Express the change in external wealth (ΔW0) at the end of period 0 as a function of the economy’s trade balance (TB), the real interest rate (a constant, r*), and initial external wealth (W–1).
b. Using (a), write an expression for the stock of external wealth at the end of period 0 (W0). This should be written as a function of the economy’s trade balance (TB0), the real interest rate, and initial external wealth (W–1).
c. Using (a) and (b), write an expression for the stock of external wealth at the end of period 1 (W1). This should be written as a function of the economy’s trade balance (TB) each period, the real interest rate, and initial external wealth (W–1).
d. Using your answers from (a), (b), and (c), write an expression for the stock of external wealth at the end of period 2 (W2). This should be written as a function of the economy’s trade balance (TB) each period, the real interest rate, and initial external wealth (W–1).
e. Suppose we require that W2 equal 0. Write down the condition that the three trade balances (in periods 0, 1, and 2) must satisfy. Arrange the terms in present value form.