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9.1. THE REDUX MODEL 281money shock generates a home current account surplus (in (9.91)) andimproves the home wealth position and therefore the terms of trade.Home agents enjoy more leisure in the new steady state.From (9.89) it follows that the nominal exchange rate exhibits lessvolatility than the money supply. It also exhibits less volatility understicky prices than under ßexible prices since if prices were perfectlyßexible prices, money would be neutral and the effect of a monetaryexpansion on the exchange rate would be Ŝt = ˆM t − ˆM ∗ t .The short-run terms of trade decline by Ŝt since ˆp t (z) =ˆp ∗ t (z ∗ )=0. ⇐(172)Since there are no further changes in the exchange rate, it follows from(9.92) and (9.90) that the short-run increase in the terms of trade exceedsthe long-run increase. The partial reversal means there is overshootingin the terms of trade.To Þnd the effect of permanent monetary shocks on the real interestrate, use the consumption Euler equations (9.51) and (9.52) to getĈ w t = −(1 − β)ˆr t . (9.93)To solve for Ĉw t , use (9.73)—(9.74) to substitute out the short-run pricelevelchanges and (9.70)—(9.71) to substitute out the long-run price levelchanges from the log-linearized money demand functions (9.53)—(9.54) ⇐(173-174)Ĉ t +Ãβ²(1 − β)Ĉ − ² +β(1 − β)Ã! h iˆMt − (1 − n)Ŝt = βˆrt ,! hˆM∗t + nŜtĈt ∗ β+β)Ĉ∗ βi− ² += βˆrt .²(1 − (1 − β)Multiply the Þrst equation by n, the second by (1−n) then add togethernoting by (9.64) Ĉw =0. ThisgivesÃ!ββˆr t = Ĉw t − ² + ˆM t w .(1 − β)Now solve for the real interest rate gives the liquidity effectˆr t = −ò +β(1 − β)!ˆM w t . (9.94)A home monetary expansion lowers the real interest rate and raisesaverage world consumption. From the world demand functions (9.47)