International macroe.. - Free

296CHAPTER 9. THE NEW INTERNATIONAL MACROECONOMICSRecall that world demand for home goods is y(z) = [p(z)/P ] −θ C wand world demand for foreign goods is y ∗ (z ∗ )=[p ∗ (z ∗ )/P ∗ ] −θ C w . Thechange in steady-state demand isŷ(z) = −θ[ˆp(z) − ˆP ]+Ĉw , (9.160)ŷ ∗ (z ∗ ) = −θ[ˆp ∗ (z ∗ ) − ˆP ∗ ]+Ĉw (9.161)(197-198)⇒By (9.151) and (9.152), the optimal labor supply changes byŷ(z) = ˆp(z) − ˆP − Ĉ, (9.162)ŷ ∗ (z ∗ ) = ˆp ∗ (z ∗ ) − ˆP ∗ − Ĉ∗ . (9.163)(9.157)—(9.163) form a system of 6 equations in the 6 unknowns(Ĉ,Ĉ∗ , ŷ(z), ŷ ∗ (z ∗ ), (ˆp(z) − ˆP ), (ˆp ∗ (z ∗ ) − ˆP ∗ ), which can be solved toget 13 β(1 + θ)Ĉ = − ˆb, (9.164)2θĈ ∗ =β(1 + θ)2θµ n ˆb, (9.165)1 − nŷ(z) = β (9.166)2ˆb,ŷ ∗ (z ∗ )=− β µ n ˆb, (9.167)2 1 − nˆp(z) − ˆP = −2θˆb, β (9.168)ˆp ∗ (z ∗ ) − ˆP ∗ = β µ n ˆb. (9.169)2θ 1 − n(199)⇒(200)⇒By (9.164) and (9.165), average world consumption is not affectedĈ w = 0, but the steady-state change in relative consumption isβ(1 + θ)Ĉ − Ĉ∗ = − (9.170)2θ(1 − n)ˆb.13 The solution looks slightly different from the redux solution because the internationallytraded asset is a nominal bond whereas in the redux model it is a realbond.