International macroe.. - Free

288CHAPTER 9. THE NEW INTERNATIONAL MACROECONOMICSprice of the bond is1δ t ≡(1 + i t ) .The foreign nominal interest rate is given by uncovered interest parityà !(1 + i ∗ t )=(1+i Stt) .S t+1(181)⇒Households. We need to distinguish between hours worked, whichis chosen by the household, and output which is chosen by the Þrm.The utility function is similar to (9.2) in the Redux model except thathours of work h t (z) appears explicitly in place of output y t (z)⎡∞XU t = β j ⎣ln C t+j +γà ! ⎤1−²Mt+j− ρ 1 − ² P t+j 2 h2 ⎦t+j(z) . (9.107)j=0The associated price indices for the domestic and foreign householdsareP t =P ∗t =·Z n0·Z n0p t (z) 1−θ dz +q ∗ t (z) 1−θ dz +Z 1nZ 1nq t (z ∗ ) 1−θ dz ∗¸1/(1−θ) , (9.108)p ∗ t (z ∗ ) 1−θ dz ∗¸1/(1−θ) . (9.109)W t is the home country competitive nominal wage. The householdderives income from selling labor to Þrm z, W t h t (z). Household-z alsoowns Þrm-z from which it earns proÞts, π t (z). Nominal wealth takeninto the next period consists of cash balances and bonds (M t + δ t B t ).This wealth is the result of wealth brought into the current period(M t−1 + B t−1 ) plus current income (W t h t (z)+π t (z)) less consumptionand taxes (P t C t + P t T t ). The home and foreign budget constraints aregiven byM t + δ t B t = W t h t (z)+π t (z)+M t−1 + B t−1 − P t C t − P t T t , (9.110)M ∗ t +δ tB ∗ tS t= W ∗t h ∗ t (z)+π ∗ t (z)+M ∗ t−1 + B∗ t−1S t− P ∗t C ∗ t −P ∗t T ∗t . (9.111)Households take prices and Þrm proÞts as given and choose B t ,M t ,and h t . To derive the Euler-equations implied by domestic household