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304CHAPTER 9. THE NEW INTERNATIONAL MACROECONOMICSProblems1. Solve for effect on the money component of foreign welfare followinga permanent home money shock in the Redux model.(a) Begin by showing that∆U ∗3tµ M∗= −γP ∗ 0 1−² ·ˆP ∗t +β ˆP∗¸1 − βNext, show that ˆP ∗ t= −nŜt andFinally, show that∆U ∗3t ="ˆP ∗ = rn(θ2 − 1)²[r(1 + θ)+2θ]Ŝt.−(θ 2 # µM− 1)∗ 1−²²[r(1 + θ)+2θ] − 1 P0∗ nγŜtThis component of foreign welfare evidently declines followingthe permanent M t shock. Is it reasonable to think that it willoffset the increase in foreign utility from the consumption andleisure components?2. Consider the Redux model. Fix M t = M ∗ t = M 0 for all t. Begin inthe ‘0’ equilibrium.(a) Consider a permanent increase in home government spending,G t = G>G 0 =0. at time t. Show that the shock leads to ahome depreciation ofŜ t =(1 + θ)(1 + r)r(θ 2 − 1)+²[r(1 + θ)+2θ]ĝ,andaneffect on the current account of,What is the likely effect on ˆb?ˆb =(1 − n)[²(1 − θ)+θ 2 − 1]²[r(1 + θ)+2θ + r(θ 2 − 1)]ĝ.