International macroe.. - Free

124 CHAPTER 4. THE LUCAS MODELTable 4.1: Notation for the Lucas Modelx Thedomesticgood.y The foreign good.q Relative price of y in terms of x.c x Home consumption of home good.c y Home consumption of foreign good.C Domestic Cobb-Douglas consumption index, c θ x c(1−θ) y .C ∗ Foreign Cobb-Douglas consumption index, c ∗θx cy ∗(1−θ) .c ∗ x Foreign consumption of home good.c ∗ y Foreign consumption of foreign good.ω x Shares of home Þrm held by home agent.ω y Shares of foreign Þrm held by home agent.ωx∗ Shares of home Þrm held by foreign agent.ωy∗ Shares of foreign Þrm held by foreign agent.s Nominal exchange rate. Dollar price of euro.e Price of home Þrm equity in terms of x.e ∗ Price of foreign Þrm equity in terms of x.P Nominal Price of x in dollars.P ∗ Nominal Price of y in euros.M Dollars in circulation.N Euros in circulation.λ t Rate of growth of M.λ ∗ t Rate of growth of N.m Dollars held by domestic household.m ∗ Dollars held by foreign household.n Euros held by domestic household.n ∗ Euros held by foreign household.r t Price of claim to future dollar transfers in terms of x.rt ∗ Price of claim to future euro transfers in terms of x.ψ Mt Shares of dollar transfer stream held by home agent.ψ Nt Shares of euro transfer stream held by home agent.ψMt∗ Shares of dollar transfer stream held by foreign agent.ψNt∗ Shares of euro transfer stream held by foreign agent.Price of one-period nominal bond with one-dollar payoff.b t