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Domestic Stock and International Stock. There are two different \"types\" of stock that the representative consumer can buy: \"domestic" stock and \"intemational\" stock. Denote by oi, the represenmtive consumer's holdings of domestic stock at the beginning of period t and by \":4 the representative consumer's holdings of international stock at the beginning of period I. Similarly. let S,\" and S,' denote, respectively, the nominal price of domestic and international stock in period t. and D,\" and D,' denote, respectively, the per-share nominal dividend that domestic and international stock pay in period t. The period-I budget constraint of the domestic representative consumer is thus RC, + Sfa: + Sf'a,D = Y, + (S: +13: )af,l +(S,D +D,D)a:1, in which all of the other notation is standard: Yr denotes nominal income (over which the domestic consumer has no control) in period t, c, is real units of consumption, and I: is the nominal price of each unit of consumption. Also as usual, the lifetime utility of the consumer starting from period t onwards is u(c{)+u(cm)+2u(cm) +3u(cm) +... , in which [3 e (0.1] is the usual measure of consumer impatience. A restriction that is known to everyone (i.e., is common knowledge) at the beginning of period t is that international stock will pay zero dividends through (and including) period r+6 and will begin paying dividends in period 1+7. Starting in period 1+7, the nominal dividend based on a unit of international stock will be identical to the nominal dividend based on a unit of domestic stock. More precisely, the dividend payment schedule that is known to everyone is i_ l _ i _ I _ l' _ f _ n' _ D! _Dr+l D!+2 _DH3_DH4_DHS _Dr46 _O' .r _ D r _ D r _ n r _ n r _ D Di+1 _Dr+7'DH-E _D.'+E'Dr+9 _'Dr+9'\""Dr+41 _Dl+47'Dr+48 _Di+48' """ Regarding domestic stock, it is known to all parties that D? >0 VTZI 7 that is, nominal dividends based on domestic stocks will always be strictly positive. Macroeconomic Theory and Policy | Sanjay K. Chugh '- a. Based on the common knowledge at the beginning of period I, determine whether or not it is the case that S,\" =5] '3 If it is. clearly and carefully explain why; if it is not, clearly and carefully explain Why not. (Note: It is left to you to determine the most relevant steps of logic andfor mathematics andior graphical analysis that support(s) the conclusion. A conclusion, even if correct, will be awarded ZERO points if there is no or very little support behind it or if the logic/explanation is not sufciently clear.) b. At the beginning of period t+5, a completely unexpected \"government coup\" occurs abroad, and the new government announces that the dividend restriction on international stock will last forever. More precisely, the restricted dividend payment schedule announced in the beginning of period t+5 is r I r r r J r I D Due Dr+7 Dun DH; DMD DH,\" Dmu 0' {+5 Supposing that this announcement by the new government is believed by everybody, provide ONE equation for the period 1+5 nominal price of international stock and ONE equation for the period t+5 nominal price of domestic stock, which should be written as Si 1+5 :"' 3" :+5 _ in which the pair of rightihand sides are for you to determine. (Note 1: As in part a, it is left to you to detennine the most relevant steps of logic and/or mathematics anda'or graphical analysis that support(s) the conclusion. The conclusion, even if correct, will be awarded ZERO points if there is no or very little support behind it or if the logic/explanation is not sufciently clear.) (Note 2: The solution for 31:: is a precise numerical solution; if your solution for Sis is not a precise numerical solution, you may be awarded ZERO points.)
