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244 CHAPTER 8. THE MUNDELL-FLEMING MODELNow equate the coefficients on the variables to geta 1 = 1 η = −a 3,a 2 = 0,a 4 = γ à !σ.η η + σThe ßexible-price solution for the real exchange rate is˜q t = y t − d tη+ γ ηÃση + σ!δ t , (8.27)where indeed nominal (monetary) shocks have no effect on ˜q t .Therealexchange rate is driven only by real factors—supply and demand shocks.Since both of these shocks were assumed to evolve according to unitroot process, there is a presumption that ˜q t alsoisaunitrootprocess.A permanent shock to supply y t leads to a real depreciation. Sinceγσ/(η(η + σ)) < (1/η), a permanent shock to demand δ t leadstoarealappreciation. 8To get the shadow price level, start from (8.18) and (8.19) to get˜p t = m t − y t + λE t (s t+1 − s t ). If you add λ˜p t to both sides, add andsubtract λE t˜p t+1 to the right side and rearrange, you get(1 + λ)˜p t = m t − y t + λE t (˜q t+1 − ˜q t )+λE t˜p t+1 . (8.28)By (8.27), E t (˜q t+1 − ˜q t )=[γ/(η + σ)]δ t , which you can substitute backinto (8.28) to obtain the stochastic difference equation˜p t = m t − y t1+λ + λγ(η + σ)(1 + λ) δ t + λ1+λ E t˜p t+1 . (8.29)Now solve (8.29) by the MUC. Let˜p t = b 1 m t + b 2 y t + b 3 d t + b 4 δ t , (8.30)be the guess solution. Taking expectations conditional on time-t informationgivesE t˜p t+1 = b 1 m t + b 2 y t + b 3 (d t − γδ t ). (8.31)8 Here is another way to motivate the null hypothesis that the real exchange ratefollows a unit root process in tests of long-run PPP covered in Chapter 7.