International macroe.. - Free

278CHAPTER 9. THE NEW INTERNATIONAL MACROECONOMICSShort-Run Adjustment under Sticky PricesWe assume that there is a one-period nominal rigidity in which nominalprices p t (z) andp ∗ t (z ∗ ) are set one period in advance in the producer’scurrency. 7 This assumption is ad hoc and not the result of a clearlyarticulated optimization problem. The prices cannot be changed withinthe period but are fully adjustable after 1 period. It follows that thedynamics of the model are fully described in 3 periods. At t − 1, theeconomy is in the 0-steady state. The economy is shocked at t, andthevariable X responds in the short run by ˆX t .Att + 1, we are in the newsteady state and the long-run adjustment is ˆX t+1 = ˆX ' ln(X/X 0 ).Date t + 1 variables in the linearized model are the new steady statevalues and date t hat values are the short-run deviations.From (9.45) and (9.46), the price-level adjustments areˆP t = (1− n)Ŝt, (9.73)ˆP t ∗ = −nŜt. (9.74)(161-163)⇒In the short run, output is demand determined by (9.47) and (9.48).Substituting (9.73) into (9.47) and (9.74) into (9.48) and noting thatindividual goods prices are sticky ˆp t (z) =ˆp ∗ t (z ∗ )=0,youhaveŷ t (z) = θ(1 − n)Ŝt + Ĉw t +ĝ w , (9.75)ŷ ∗ t (z ∗ ) = −θ(n)Ŝt + Ĉw t +ĝ w . (9.76)The remaining equations that characterize the short run are (9.51)-(9.54), which are rewritten asĈ = Ĉt +(1− β)ˆr t , (9.77)Ĉ ∗ = Ĉ∗ t +(1− β)ˆr t, (9.78)ˆM t − ˆP t = 1 ²"ˆM ∗ t − ˆP ∗t = 1 ²Ĉ t − β"ÃĈ ∗ t − βˆr t + ˆP − ˆP t1 − βÃ!#ˆr t + ˆP ∗ − ˆP t∗1 − β, (9.79)!#. (9.80)(164)⇒Using the consolidated budget constraints, (9.40)—(9.41) and the pricelevel response (9.73) and (9.74), the current account responds by