Suppose that the income balance is currently zero and that there is no capital gain or current transfer transaction arising from external assets. a. Express the future value of the foreign asset (WN) as a function of the trade balance (TB), the real interest rate (r), and the initial foreign asset (W-) based on period N. b. Use the answer in (a) to express the present value of the Nth foreign asset (Wx). c. According to the conditions of 'no Ponzi game', the present value of WN must converge to zero as N increases. Explain why, if this condition is true, the size of the initial external asset should match the present value of the future trade deficit. d. If the income balance or current transfer balance is not zero, (a) Explain how the expressions derived from and (b) differ.