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- X j=1 PijtCijt As well explained in Obstfeld and Rogo (1996), this is the price index de…ned as the minimal expenditure in terms of country i’ s domestic currency needed to purchase one unit of consumption index. A.1.2 Household’ s optimization problem Country i representative household has a budget constraint of the form: PitCit + Et (Qit+1Bit+1) Bit + Wit(h)Lit(h) + Tit (24) where Bit+1 is the nominal payo in period t + 1 of portfolio held at the end of period t whereas Qit+1 is the asset market price of nominal bonds. Wit(h) is the nominal wage and Tit denotes a lump-sum taxe or transfer. Formally, Qit+1 = Rn it = 1 + iit where iit denotes country i’ s one period nominal interest rate that prevails on date t. Representative household chooses a string of variables fCit+k; Lit+k(h); Bit+k+1g1 k=0 that maximize a string of discounted future value of its utilities given by: Et X k=0 k ln(Cit+k Hit+k) L1+ it+k(h) 1 + # subject to budget constraint (24).
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