[n the text we derived the expression for the stock of external wealth for any time period N . That is, WN = TBN + (l + r*}WN_|., where WN, TEN. and 1"\" denote external wealth at the end of period N , the trade balance at the end of period N, and the real interest rate, respectively. Using this expression, we can write the stock of external wealth at the end of periods 0 and 1. W0 2 T30 + (l + r*}W_. WI : TB]+(1+ r*}% 3. Based on the notation from the text, which of the following equations express the stock of external wealth at the end of period 2'? At the end of period 2. Owa=r3.+(1+r*}% Om=rsg+n+mw2 Om:r3.+(1+r*}% OH:TBg+(l+r*}WJ l). Which of the following express the stock of external wealth at the end of period 1 written as a function of the trade balance in each period, the real interest rate, and initial external wealth HQ] only'.J Hint: substitute the expressioufbr W0 in the expression for IV. . At the end of period I. O w. = rsJ + (1 + ens.) + (1 + #13111. O w. = (1 + r*)(TBu + TBJ} + (1 + r*]2W_| 0 "'1 = T31 +(1+ r*}TBo + (l + r*)W_. O w. = rsJ + (1 + r*}W0 (3. Which of the following express the stock of external wealth at the end of period 2 written as a function of the trade balance in each period, the real interest rate, and initial external wealth Hi] only? Hint: substitute your answer in the previous questions in your answer in part a. At the end of period 2. O "/2 : TB; + T3. + (1 + r")TB.;. + (1 + FEW1 0 W2 = r32 + (1 + ears] +(1+ r*l2T30 +(1+ r*)2W1 0 w2 : mg + (1 + ns] + (1 + frso + (1 + #13111. 0 W2 = r30 + (1 + Hare] + (1 + #121132 +(1+ r*)3W_1 d. Suppose we require that the stock of external wealth at the end of period 2 equal zero. Which of the following conditions must be satisfied? Hint: substitute W2 = 0 on your previous answer. At the end of period 2, O-(1 +r)W_1 =(TB2 + TB, + TBo)(1 + r*) O-(1+rPW_1 = TB2+ (1 + r* )TB,+ (1+ r* )TBo O - W_1 = TB2+ (1 + r* )TB, + (1 +r)TBo O-(1+r*PW_1 = TBo+ (1 + r* )TB, + (1+r* )TBz e. Which of the following equations express your answer in part d in present value form? Hint: divide your answer in part d by (1 + r* )2 . In present value form, O - (1 +r)WI = TB TBI ( It * * ) 2 + ( Itr# ) + T Bo O - W_1 = TB2 + (Itr") TBI + + T Bo (Itr)2 O - (1 + r ) W_1 = TB2+ (Itr) TBI T Bo O - (1 + r )W-1 = TB2 TBI + + (Itr* )2 ( Itr* ) 2 (Itr# ) + T Bo