International macroe.. - Free

270CHAPTER 9. THE NEW INTERNATIONAL MACROECONOMICSG t =G ∗ t =·Z 10·Z 10g t (u) θ−1θ du¸ θθ−1,gt ∗ (u) θ−1θ du¸ θθ−1.It follows that home government demand for individual goods are givenby replacing c t with g t and C t with G t in (9.5)—(9.6). The identicalreasoning holds for the foreign government demand function.Governments issue no debt. They Þnance consumption either throughmoney creation (seignorage) or by lump—sum taxes T t ,andTt ∗ .Negativevalues of T t and Tt∗ are lump—sum transfers from the government toresidents. The budget constraints of the home and foreign governmentsareG t = T t + M t − M t−1, (9.16)P tG ∗ t = T t ∗ + M t ∗ − Mt−1∗ . (9.17)Aggregate Demand. Let average world private and government consumptionbe the population weighted average of the domestic and foreigncounterpartsPt∗Ct w = nC t +(1− n)Ct ∗ , (9.18)G w t = nG t +(1− n)G ∗ t . (9.19)Then C w t + G w t is world aggregate demand. The total demand for anyhome or foreign good is given by" # −θyt d (z) = pt (z)(Ct w + G w t ), (9.20)P ty ∗dt (z ∗ )="p∗t (z ∗ # −θ)(Ct w + G w t ). (9.21)P ∗tBudget Constraints. Wealth that domestic agents take into the nextperiod (P t B t + M t ), is derived from wealth brought into the currentperiod ([1 + r t−1 ]P t B t−1 + M t−1 ) plus current income (p t (z)y t (z)) less