International macroe.. - Free

268CHAPTER 9. THE NEW INTERNATIONAL MACROECONOMICSIt follows that the home and foreign price levels, (9.4) and (9.9) simplifytoP t = [np t (z) 1−θ +(1− n)(S t p ∗ t (z∗ )) 1−θ ] 11−θ , (9.10)Pt ∗ = [n(p t (z)/S t ) 1−θ +(1− n)p ∗ t (z∗ ) 1−θ ] 11−θ , (9.11)and that PPP holds for the correct CES price indexP t = S t P ∗t . (9.12)Notice that PPP will hold for GDP deßators only if n =1/2.Asset Markets. The world capital market is fully integrated. There isan internationally traded one-period real discount bond which is denominatedintermsofthecompositeconsumption good C t . r t is thereal interest rate paid by the bond between t and t + 1. The bond isavailable in zero net supply so that bonds held by foreigners are issuedby home residents. The gross nominal interest rate is given by theFisher equation1+i t = P t+1(1 + r t ), (9.13)P tand is related to the foreign nominal interest rate by uncovered interestparity1+i t = S t+1(1 + i ∗ t ). (9.14)S tLet B t be the stock of bonds held by the domestic agent and Bt∗ bethe stock of bonds held by the foreign agent. By the zero-net supplyconstraint 0 = nB t +(1− n)Bt ∗ , it follows thatBt ∗ = −n1 − n B t. (9.15)(153)⇒The Government. For 0