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9.1. THE REDUX MODEL 27966)⇒ ˆbt = ŷ t (z) − (1 − n)Ŝt − Ĉt − ĝ t , (9.81)ˆb∗ t = ŷ ∗ t (z∗ )+nŜt − Ĉ∗ t − ĝ∗ t = −n1 − nˆb t . (9.82)We have not speciÞed the source of the underlying shocks, which mayoriginate from either monetary or government spending shocks. Sincethe role of nominal rigidities is most clearly illustrated with monetaryshocks, we will specialize the model to analyze an unanticipatedand permanent monetary shock. The analysis of governments spendingshocks is treated in the end-of-chapter problems.Monetary ShocksSet G t = 0 for all t in the preceding equations and subtract (9.78) from(9.77), (9.80) from (9.79), and use PPP to obtain the pair of equationsĈ − Ĉ∗ = Ĉt − Ĉ∗ t , (9.83)ˆM t − ˆM t ∗ − Ŝt = 1 β² (Ĉt − Ĉ∗ t ) −²(1 − β) (Ŝ − Ŝt). (9.84)Substitute Ŝ from (9.72) into (9.84) to getŜ t =(ˆM t − ˆM t ∗ ) − 1 ² (Ĉt − Ĉ∗ t ). (9.85)This looks like the solution that we got for the monetary approachexcept that consumption replaces output as the scale variable. Comparing(9.85) to (9.72) and using (9.83), you can see that the exchangerate jumps immediately to its long-run valueŜ = Ŝt. (9.86)Even though goods prices are sticky, there is no exchange rate overshootingin the Redux model.(9.85) isn’t a solution because it depends on Ĉt − Ĉ∗ t which is endogenous.To get the solution, Þrst note from (9.83) that you only need7 z-goods prices are set in dollars and z ∗ -goods prices are set in euros.