International macroe.. - Free

9.2. PRICING TO MARKET 297From the money demand functions it follows that the steady statechange in the nominal exchange rate isŜ = ˆM − ˆM ∗ − 1 ²hĈ− Ĉ ∗i . (9.171)Adjustment to Monetary Shocks under Sticky PricesConsider an unanticipated and permanent monetary shock at time t,where ˆM t = ˆM, and ˆM t∗ = ˆM ∗ . As in Redux, the new steady state isattained at t +1,sothatŜt+1 = Ŝ, ˆP t+1 = ˆP, and ˆP t+1 ∗ = ˆP ∗ .Date t nominal goods prices are set and Þxedone-periodinadvance.By (9.10) and (9.11), it follows that the general price levels are alsopredetermined, ˆPt = ˆP t∗ =0. The short-run versions of (9.141) and(9.142) areˆM = 1 β² Ĉt +²(1 − β) ˆδ t , (9.172)ˆM ∗ = 1 ² Ĉ∗ t + β²(1 − β) [ˆδ t + Ŝ − Ŝt]. (9.173)Subtracting (9.173) from (9.172) givesˆM t − ˆM ∗ t = 1 ² (Ĉt − Ĉ∗ t ) − β²(1 − β) (Ŝ − Ŝt). (9.174)From (9.153) and (9.154) you getĈ t = ˆδ t + Ĉ + ˆP, (9.175)Ĉ ∗ t = ˆδ t + Ĉ∗ + ˆP ∗ + Ŝ − Ŝt. (9.176)At t +1PPPisrestored, ˆP = ˆP ∗ + Ŝ. Subtract (9.176) from (9.175)to getĈ − Ĉ∗ = Ĉt − Ĉ∗ t − Ŝt. (9.177)The monetary shock generates a short-run violation of purchasing powerparity and therefore a short-run international divergence of real interestrates. The incompleteness in the international asset market results inimperfect international risk sharing. Domestic and foreign consumptionmovements are therefore not perfectly correlated.