Using the assumptions and answers from the previous question, complete the following:
a. Write an expression for the future value of the stock of external wealth in period N (WN). This should be written as a function of the economy’s trade balance (TB) each period, the real interest rate r*, and initial external wealth.
b. Using the answer from (a), write an expression for present value of the stock of external wealth in period N (WN).
c. The “no Ponzi game” conditions force the present value of WN to tend to 0 as N gets large. Explain why this implies that the economy’s initial external wealth is equal to the present value of future trade deficits.
d. How would the expressions in (a) and (b) change if the economy had net labor income (positive or negative) to or from abroad or net unilateral transfers? Explain briefly.