International macroe.. - Free

4.3. THE TWO-MONEY MONETARY ECONOMY 121We know that in equilibrium, the cash-in-advance constraints bind.The cash-in-advance constraints for the foreign agent arem ∗ t = P t c ∗ xt, (4.52)n ∗ t = P ∗t c∗ yt (4.53)In addition, we have the adding-up constraints1 = ψ Mt + ψMt,∗1 = ψ Nt + ψNt ∗ ,x t = c xt + c ∗ xt ,y t = c yt + c ∗ yt,M t = m t + m ∗ t ,N t = n t + n ∗ t .Together, the adding-up constraints and the cash-in-advance constraintsgive a unit-velocity quantity equation for each countryM t = P t x tN t = P ∗t y t,which can be used to eliminate the endogenous nominal price levelsfrom the Euler equations.The equilibrium where people are able to pool and insure againsttheir country-speciÞc risks is given by⇐(93)ω xt = ω ∗ xt = ω yt = ω ∗ yt = ψ Mt = ψ ∗ Mt = ψ Nt = ψ ∗ Nt = 1 2 .Both the domestic and foreign representative households own half of thedomestic endowment stream, half of the foreign endowment stream,half of all future domestic monetary transfers and half of all futureforeign monetary transfers. In short, they split the world’s resourcesin half so the pooling equilibrium supports the symmetric allocationc xt = c ∗ xt = x tand c 2 yt = c ∗ yt = yt. 2To solve for the nominal exchange rate S t , we know by (4.47) thatthe real exchange rate isu 2 (c xt ,c yt )u 1 (c xt ,c yt ) = S tPt∗P t= S tN t x tM t y t. (4.54)