FoundationsofInternationalMacroeconomics1

Workbook2

MauriceObstfeld,KennethRogo ,andGitaGopinath

Chapter8Solutions

1.Firstthinkaboutthecontinuous-timecase.Attimet=0themarketbelievesthegovernment’spromisethatitwillpegtheexchangerateatitst=TlevelfromtimeTonward.Inthatcase,wecanshowthattheexchangerateisindeterminate,sothatthegovernment’spolicyisnotcoherent(inthatitdoesnottiedownauniquemarketequilibrium).Letperfect-foresightequilibriumbedescribedbythecontinuous-timeCaganmodel[eq.(70)onp.559ofthebook],

mt=et ηeút.

LeteaTbeanarbitrarytime-TexchangerateandsupposethemarketÞrmlyexpectsthatratetoprevail.ThentheprecedingCaganequation,coupledwiththeterminalconditioneT=eaT,showsthattheexchangeratepath

1ZTet=exp[(t s)/η]msds+exp[(t T)/η]eaTηt

willequilibratemarketsfort∈[0,T].

Nextconsiderthemonetaryauthority’spositionattimeTwhencon-frontedwiththisexchangeratepath.Theauthorityhasnochoice,inviewofitsvowofaconstantexchangeratefromTon,buttosetthefundamental

amT=eaTandtoholdmt=eTforallt>T.Why?Weretheauthorityto

actotherwise,theexchangeratewoulddeviatefromeaTatsomepointintheByMauriceObstfeld(UniversityofCalifornia,Berkeley)andKennethRogo (Prince-

cMITPress,1996.tonUniversity).°

2c°MITPress,1998.Version1.1,February27,1998.Foronlineupdatesandcorrec-tions,seewww.51wendang.com Book.html1

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