International macroe.. - Free

4.2. THE ONE-MONEY MONETARY ECONOMY 117To solve the model, aggregate the cash-in-advance constraints over thehome and foreign agents and use the adding-up constraints to getM t = P t (x t + q t y t ). (4.36)This is the quantity equation for the world economy where velocity isalways 1. The single money generates no new idiosyncratic countryspeciÞcrisk. The equilibrium established for the barter economy (constantand equal portfolio shares) is still the perfect risk-pooling equilibriumω xt = ω ∗ xt = ω yt = ω ∗ yt = 1 2 ,c xt = c ∗ xt = x t2 ,c yt = c ∗ yt = y t2 .The only thing that has changed are the equity pricing formulae, whichnow incorporate an ‘inßation premium.’ The inßation premium arisesbecause the nominal dividends of the current period must be carriedover into the next period at which time their real value can potentiallybe eroded by an inßation shock.Solution under constant relative risk aversion utility. Under the utilityfunction (4.22), the real exchange rate is q t = h i³1−θ xtθ y t´. Substituting ⇐(87)this into (4.36), the inverse of the gross inßation rate is PtP t+1= Mt x t+1M t+1 x t.Together, these expressions can be used to rewrite the equity pricingequations as" µCt+1e t= βE tx tC te ∗ " µCt+1t= βE tq t y t C t (1−γ)ÃMtM t+1+ e t+1x t+1!#, (4.37) (1−γ)Ã !#Mt+ e∗ t+1. (4.38)M t+1 q t+1 y t+1To price nominal bonds, you are looking for the shadow price of a hypotheticalnominal bond such that the public willingly keeps it in zero netsupply. Let b t be the nominal price of a bond that pays one dollar at theend of the period. The utility cost of buying the bond is u 1 (c xt ,c yt )b t /P t .