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ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015

Money,InterestandPrices

MoneyinGeneralEquilibriumModels,thePriceLevel,InterestRates

andInflation

ProfGeorgeAlogoskoufis,DynamicMacroeconomicTheory,2015 2

Money,thePriceLevelandNominalVariables

• Money,theexistenceofwhichinamoderneconomyisusuallytakenforgranted,performsthreemainfuncJons.

• First,itisaunitofaccount,seconditisauniversallyacceptedmeansofpayment,andthirdly,itisastoreofvalue.

• WhileinmodelswithoutmoneyonecanonlyanalyzethedeterminaJonofrealvariables,suchasthequanJJesofgoodsandservicesproducedandconsumed,andtheirrela9veprices,inmodelswithmoneyonecanalsodeterminenominalvariablessuchasthepricelevel,nominalincome,thelevelofnominalwages,nominalinterestratesandinfla9on.Thesenominalvariablesareexpressedintermsofmoney.

MoneyasaUnitofAccount• Inamonetaryeconomyallpricesaredeterminedandquotedintermsofthe

monetaryunit.Otherwise,economicagentswouldhavetocalculatealltherelaJvepricesofgoodsandservicesinordertoconducttheirtransacJons.

• InaneconomywithNgoodsplusmoney,thereareNmoneyprices.Withoutmoney,economicagentswouldneedtocalculateN(N+1)/2relaJvepricesinordertomaketheirtransacJons.Asthenumberofgoodsandservicesincreases,thenumberofrelaJvepricestobecalculatedgrowsexponenJally.Forexample,ifthereare5goodsandservices,therearefivemoneyprices,and15relaJvepricesofgoodsbetweenthem.With1000goodsandservices,thereare1000moneyprices,and500,500relaJvepricesbetweengoodsandprices.

• MoneythereforehelpstosimplifythecalculaJonofpricesandvalues,andthusfacilitateseconomictransacJonsthroughitsunitofaccountfuncJon.

MoneyasaMeansofPayment• Beingacceptedbyall,moneygreatlyfacilitateseconomictransacJons

anddrasJcallyreducestheircosts.

• Withoutmoney,inordertocompleteatransacJonthesellerofaproductorservicewouldhavetofindabuyerwhowouldbepreparedtoofferinreturnanothergoodorservicethatthesellerwishestoacquire.ThisrequiresthatthereisadoublecoincidenceofwantsinalleconomictransacJons.TransacJonsorthiskindarecalledbarter,whichimplieshugecostsonthepartofeconomicagentsinordertofindsuitablecounter-parJestotheirtransacJons.

• AmoderneconomywouldimmediatelyceasefuncJoningiftherewasnotagenerallyacceptedmediumofexchangeandpayments,becausetransacJoncostswouldbecomeprohibiJve.

MoneyasaStoreofValue• Moneyisastoreofvalue,i.e.ameansofholdingwealth,andis

indeedtheassetthatischaracterizedbygreaterliquidity,asitcanbeuseddirectlyforpaymentsfortheacquisiJonofgoodsandservices.

• Thisisakeyfeatureofmoney,becauseifmoneywerenotastoreofvalue,andlostitsvaluequickly,itwouldnotbegenerallyacceptedasameansofpaymentseither.Thenagain,sincemoneyistheonlystoreofvaluewhichisalsoameansofpayments,bydefiniJonitisthemostliquidstoreofvalue.

• However,asameansofholdingwealth,moneyhastheweaknessthatitdoesnotpayinterest,unlikeotherlessliquidassets.

DefiningtheMoneySupply• Wedefineasmoneythesumofbanknotes,coinsanddepositsin

currentaccountsincommercialbanksheldbyhouseholdsandfirms.

• ThisdefiniJonofmoneysupplyisusuallyknownasM1.Itemphasizesthemoreliquidassetsofhouseholdsandfirms,whichusuallydonotyieldinterest.However,therearebroaderdefiniJonsofthemoneysupply,thatincludelessliquidassetssuchasJmedepositsandotherlessliquiddepositsandsecuriJes(M2,M3etc).

• DepositsofcreditinsJtuJonsandotherinsJtuJonsparJcipaJngintheinterbankmarketandtheforeignexchangemarketarenotconsideredaspartofthemoneysupply.ThesedepositsarenotusedforthetransacJonsofthegeneralpublic.

TheSupplyofMoney• MonetarycondiJonsinmoderneconomiesaredeterminedbycentral

banks.

• Thecentralbankmayaffect,throughavarietyofpolicyinstrumentsatitsdisposal,boththequanJtyofbanknotes(andcoins)incirculaJon,and,indirectly,theamountofdepositsincommercialbanks,whicharealsopartofthemoneysupply.

• AlternaJvely,acentralbankmayfollowaninterestraterule,interveninginthemoneymarketandpeggingnominalinterestrates.Inthisla[ercase,thestockofmoneyintheeconomyisdeterminedbythedemandformoney,andthemoneysupplyadaptstodemandinordertoachievethegoalofthecentralbankregardingthenominalinterestrate.

TheRolesofCentralBanks• CentralbanksarepublicinsJtuJonsthatmanageastate’smoney

supply,interestratesandregulatethecommercialbankingsystem.Inmostcountriesthecentralbankpossessesamonopolyonprin9ngnotes,andmin9ngcoins,whichserveasthestate’slegaltender.InaddiJon,centralbanksusuallyactaslendersoflastresorttothebankingsystemand,inmanycases,thegovernment.CentralbankscanthusdirectlydeterminethecirculaJonofnotes(andcoins)andindirectlytheamountofdepositsincommercialbanks.

• ThedeterminaJonofthemoneysupplybycentralbanksisnotasimpleprocess.ItdependsontherulesunderwhichthecentralbankparJcipatesinmoneyandassetmarketsandregulatesthefinancialsystem,onitsrelaJonswiththegovernment,andonthegoalsenvisagedinitscharter.

TheGoalsandPolicyInstrumentsofCentralBanks

• Themaingoalsofacentralbankarethecontrolofinfla9on,thestabilityofthefinancialsystem,andinsomecases,thesupportofthegeneraleconomicpoliciesofthegovernment.

• InwhatfollowsweshallignoremanyoftheinsJtuJonaldetailsthatrelatetohowacentralbankoperates,andwillmaketwoalternaJvesimpleassumpJons.

• First,weshallassumethatthecentralbankhasfullcontrolofthemoneysupply.ThisisanassumpJonwithalonghistoryinmacroeconomicanalysis,althoughnotparJcularlyrealisJc,ascentralbankshaveimperfectcontroloverthemoneysupply.

• AlternaJvelyweshallassumethatthecentralbankfollowsapolicyofpeggingthenominalinterestrateandcommi^ngtoprovidingunlimitedcredittohouseholds,businessesandcommercialbanksatthisrate.

TheDemandforMoney• Thedemandformoneydependsonthreemainfactors.

• Thefirstfactoristhepricelevel.Thehigherthelevelofprices,thehigherwillbetheamountofmoneythathouseholdsandfirmswouldwanttoholdfortheircurrentandfuturetransacJons.ThedemandformoneyisusuallyassumedtobeproporJonaltothepricelevel.

• ThesecondfactoristhevolumeoftransacJons.WhenthevolumeoftransacJons,usuallymeasuredbyaggregaterealoutput,increases,householdsandfirmswillneedmoremoneytocarryouttheirincreasedtransacJons.

• Thethirdfactoristhelevelofinterestrates.Banknotespaynointerest.Ontheotherhand,demanddepositsandcurrentaccounts,evenwhentheypayinterest,payaverylowratecomparedtotheyieldsoflessliquidassetssuchasJmedeposits,treasurybillsorbonds.Consequently,thedemandformoneywilldependnegaJvelyonthenominalinterestrate,asthenominalinterestratemeasurestheopportunitycostofholdingmoney.

TheMoneyDemandFuncJon

M d = P ×m(Y ,i)

whereMdisthequanJtyofmoneydemanded,Pisthepricelevel,Yreal

aggregateoutputandincome(GDP)andithenominalinterestrate.misafuncJonincreasinginrealaggregateincomeanddecreasinginthenominalinterestrate.

ThedemandformoneyisproporJonaltothepricelevel,inthesensethatanincreaseinthepricelevelrequiresanincreaseinthequanJtyofmoneybythesameproporJon,inordertocompletethesamenumberoftransacJons.

TheDemandforRealMoneyBalances

P= m(Y ,i)

SincethedemandformoneyisproporJonaltothepricelevel,itcanbeexpressedasademandforrealmoneybalances.Holdingmoneyisusefulforitspurchasingpower.

TherelaJonshipbetweenrealmoneydemandandthenominalinterestrateisnegaJve,becauseholdingmoneybecomesmoreexpensiveasinterestratesrise,sincemoneydoesnotpayinterest.Therefore,householdsandfirmsreducetheamountofmoneyholdingsandincreaseholdingsofsecuriJesandotherinterestyieldingassets.

TheDemandforRealMoneyBalances,theNominalInterestRateandRealIncome

ShortRunEquilibriumintheMoneyMarket

P= M d

P= m(Y ,i)

TheequilibriumcondiJoninthemoneymarketisforthemoneysupplytobeequaltomoneydemandbyhouseholdsandfirms.

Intheshortrun,withpricesandincomegiven,howthemoneymarketequilibratesdependsonthemodusoperandiofthecentralbank.

Ifthecentralbankfixesthemoneysupply,theequilibraJngmechanismisthenominalinterestrate.Ifthecentralbankfixesthenominalinterestrate,theequilibraJngmechanismisthemoneysupply.

ShortRunEquilibriumintheMoneyMarketwhentheCentralBankFixestheMoneySupply

AnIncreaseintheMoneySupplyandNominalInterestRates:TheLiquidityEffect

AnIncreaseinMoneyDemandandNominalInterestRates:TheLiquidityEffect

ShortRunEquilibriumintheMoneyMarketwhentheCentralBankFixestheNominalInterest

LongRunEffectsoftheMoneySupply

P = M s

m(Y ,i)

• Inthelongerterm,thepricelevelalsoadjusts.WecanseethedirecJonofthisadjustmentbyrearrangingtheequilibriumcondiJoninthemoneymarket,andsolvingforthepricelevel.Wethenget,

• Inlongrunequilibrium,aggregaterealincomeandtherealinterestrateareontheirbalancedgrowthpaths.WithconstantinflaJon,nominalinterestratesarealsoconstant.Thus,thefactorsaffecJngthedemandformoneyaregiven,andthemoneysupplydeterminesthepricelevel,withoutaffecJngtheevoluJonofrealvariables.Thispropertyiscalledlong-runneutralityofmoney.

TheNeutralityofMoneyinStaJcGeneralEquilibriumModels

• TheneutralityofmoneyappliestoallstaJcgeneraleconomicequilibriummodelswithflexibleprices.

• Whatdeterminesthelevelofequilibriumrealincome,andotherrealvariablesaretheavailableresources,technology,preferences,thefuncJoningofmarkets,aswellaseconomicinsJtuJonsthatdeterminetotalfactorproducJvityandtheproducJvityofspecificfactors.

• InstaJcgeneralequilibriummodelsrealoutputandincomeandotherrealvariablesdonotdependonthemoneysupply.Moneyismerelya“veil”whichcoverstheeconomy,simplydeterminingnominalvariablessuchasthepricelevel.

TheNeutralityandSuper-neutralityofMoneyinDynamicGeneralEquilibriumModels

• IndynamicgeneralequilibriummodelsweusuallydisJnguishbetweenthe“neutrality”andthe“super-neutrality”ofmoney.

• The“neutrality”ofmoneyreferstotheeffectsofaoneoffchangeinthemoneysupply,andthe“super-neutrality”ofmoneytotheeffectsoftherateofchangeofthemoneysupply.

• Theneutralityofmoneyappliestoalldynamicgeneraleconomicequilibriummodelswithflexibleprices.

• However,asthegrowthrateofmoneysupplyaffectsinflaJonandlong-termnominalinterestrates,itthusaffectsrealmoneydemand.

• The“super-neutrality”ofmoneyholdsinrepresentaJvehouseholdmodels,asmoneydoesnotaffectotherrealvariables,butdoesnotholdinoverlappinggeneraJonsmodels.

LongRunNeutralityofMoneyandMonetaryReforms

• AnalternaJvewaytothinkabouttheneutralityofmoney,istoconsiderwhatwouldbetheimpactofaveryradicalchangeinthemoneysupply.SuchradicalchangestakeplaceinJmesofmonetaryreforms.Anumberofsuchhistoricalexamplesexist,whichsuggestthat,aderamonetaryreform,thepriceleveladjustsimmediatelytothenewmonetarystandard.

• Forexample,inMay1954,therewasaradicalmonetaryreforminGreece.Anewdrachmawascreated,whichamountedto1,000olddrachmas.EssenJallythisamountedtoadirectreducJoninthemoneysupplytoonethousandthoftheoldmoneysupply.AsonewouldexpectonthebasisofourmoneydemandfuncJon,thepricelevelinGreecefellimmediatelytoonethousandthofthepricelevelbeforethereform.Nothingelsechanged,otherthanthelevelofprices.

• Gradualincreasesinthemoneysupplyinthelongrunhaveeffectssimilartosuchmonetaryreforms.Thetriplingofthemoneysupplyinadecade,inthelongrunhasthesameeffectasamonetaryreforminwhichacurrencyunitisreplacedwiththreeunitsofa“new”currency.

DynamicGeneralEquilibriumModelswithMoney

• TheSamuelson(1958)overlappinggeneraJonsmodel.

• RepresentaJveHouseholdModelswithMoneyintheUJlityFuncJon(PaJnkin1956,Sidrauski1967)

• OverlappingGeneraJonsModelswithMoneyintheUJlityFuncJon(Weil1987).

• Cash-in-AdvanceRepresentaJveHouseholdModels(Clower1967,GrandmontandYounes1972,Lucas1980,1982,Svensson1985).

• Cash-in-AdvanceModelsofOverlappingGeneraJons(Samuelson-Lucas).

TheSamuelsonOverlappingGeneraJonsModel:MoneyasaStoreofValue

• WeassumethattheeconomyconsistsofsuccessivegeneraJonsofhouseholds,eachofwhichlivesfortwoperiods.

• Everyhouseholdhasexogenousincomey1inthefirstperiodoflifeandy2inthesecondperiodoflife.

• Thisincomeisintheformofanonstorablegood,whichcannotbetransferredfromperiodtoperiod.

• Theonlynon-perishablecommodityismoney,whichcanbeusedasameansofholdingwealth.

TheInter-temporalOpJmizaJonProblemofHouseholds

ΤhehouseholdborninperiodtmaximizestheuJlityfuncJon,

Ut = u(C1t )+ βu(C2t+1) = lnC1t + β lnC2t+1

PtC1t +Mt = PtY1

Pt+1C2t+1 = Mt + Pt+1Y2

undertheconstraints,

DefiniJonsofVariablesandParameters

C1ishouseholdconsumpJoninthefirstperiodoflifeandC2consumpJoninthesecondperiodoflife.

uisaconcaveuJlityfuncJonandβ=1/(1+ρ)thediscountfactor,whereρisthepurerateofJmepreference.

Mtisthemoneysupply,carriedoverbythehouseholdfromthefirsttoitssecondperiodoflife.Themoneysupplyisequaltothesavingsofhouseholdsintheirfirstperiodoflife.

PtisthemoneypriceoftheconsumpJongoodinperiodtandPt+1themoneypriceoftheconsumpJongoodinperiodt+1.

ConsumpJonofYoungandOldHouseholdsinPeriodt

PtC1t =1

1+ βPtY1 + Pt+1Y2( )

PtC2t = M + PtY2

GoodsMarketEquilibriumandMoneyDemand

C1t +C2t = Y1 +Y2

= 11+ β

βY1 −Pt+1PtY2

⎛⎝⎜

⎞⎠⎟

EquilibriumPriceLevel

= 11+ β

βY1 −Y2( )

P*> 0⇔ βY1Y2

Thedemandformoney,andhencethepricelevel,willbeposiJveonlyifthediscountedfirstperiodincomeofhouseholdsexceedssecondperiodincome.Itisonlythenthatsavings,andhencemoneydemand,willbeposiJve.

PriceAdjustmentEquaJon

Pt+1 − P*=βY1Y2(Pt − P*)

• Sincethepricelevelisanonpredeterminedvariable,thecondiJonforthestabilityofthedynamicadjustmenttotheequilibriumpricelevelP*isthattherootofthedifferenceequaJonaboveisgreaterthanone.Consequently,thecondiJonfortheexistenceofaposiJveequilibriumpricelevelcoincideswiththecondiJonforthestabilityoftheequilibrium.IfβY1/Y2>1,thenaposiJveequilibriumpricelevelexists,andinaddiJontheequilibriumisasaddlepoint,i.e.dynamicallystable.

ImplicaJonsoftheSamuelsonModel

• TheSamuelsonmodelhasastrikingimplicaJon:Moneyimproveswelfare,becauseitallowshouseholdstoengageininter-temporaltradeandsmoothconsumpJonoverJme.

• Intheabsenceofmoney,consumpJonineachperiodwouldhavetobeequaltocurrentincomeforallgeneraJons.ThisequilibriumisclearlysubopJmalcomparedwiththeequilibriumofamonetaryeconomywhichallowsforconsumpJonsmoothing.

• TheSamuelsonmodelofoverlappinggeneraJonsisoneofthefirstdynamicgeneralequilibriummodelsthatgenerateaposiJvedemandformoneyasastoreofvalue.TheneutralityofmoneyfollowsimmediatelyfromthemoneydemandfuncJon.Moreover,inthismodel,sincethepricelevelisanonpredeterminedvariable,theincreaseinthepricelevelwouldhappenimmediately.

WeaknessesoftheSamuelsonModel

• Thefirstweaknessisthattheequilibriumwehavejustdescribed,whichentailsaposiJvedemandformoney,isnotunique.Thereisasecond,subopJmal,equilibrium,withzeromoneydemand.Thusthedemandformoneyinthismodelisextremelyfragile.

• AsecondweaknessofthismodelisthatthereisnoalternaJvestoreofvalue.Theonlywaytosaveinthismodelisbyholdingmoney.However,ifthereisanalternaJveassetwhichpaysinterest,forexamplebondsorcapital,thenmoneywouldbeostracizedfromthiseconomy,becauseitsonlyroleisasastoreofvalue,andmoneydoesnotpayinterest.

MulJplicityofEquilibriumintheSamuelsonModel

Twolong-runequilibria:

Y2βY1 − (1+ β ) M / Pt( )

= 11+ β

βY1 −Y2( ) andMP**

MulJplicityofEquilibriumintheSamuelsonModel

UniqueEquilibriumiftheOldHavenoIncome

IfY2=0thenthereisauniqueequilibrium,

= β1+ β

MoneyintheUJlityFuncJonofaRepresentaJveHousehold

ThereisarepresentaJvehouseholdmaximizinganinter-temporaluJlityfuncJonoftheform,

Ut = β s−tu(Cs ,Ms

∞∑

undertheconstraint,

Cs +Ms

Ps+ BsPs

= Ys −Ts +Ms−1

Ps+ (1+ is−1)Bs−1

LagrangeFuncJonandFirstOrderCondiJon

Et β s−t u(Cs ,Ms

Ps)+ λs

Ms−1

Ps+ (1+ is−1)Bs−1

Ps+Ys −Ts −Cs −

Ps− BsPs

⎛⎝⎜

⎞⎠⎟

⎝⎜⎞

⎠⎟s=t

∞∑

λt =∂u∂Ct

= β(1+ it )Etλt+1Pt+1

⎛⎝⎜

⎞⎠⎟

∂u∂Mt

+ βEtλt+1Pt+1

⎛⎝⎜

⎞⎠⎟

InterpretaJonofFirstOrderCondiJons

• First,isthestaJcfirstordercondiJon,accordingtowhich,themarginaluJlityofconsumpJonshouldinanyperiodisequaltothe“shadowvalue”ofmarginalsavings.EssenJally,thehouseholdshouldbeindifferentatthemarginbetweenconsumpJonandsavings.

• SecondisthedynamicfirstordercondiJon,accordingtowhichthetotalexpectedrealreturnonsavingsshouldbeequaltothepurerateofJmepreferenceofthehousehold.

• ThirdisthedynamicfirstordercondiJonaccordingtowhichthemarginaluJlityofrealmoneybalancesisequaltothedifferenceofthepurerateofJmepreferencefromtheexpectedrealreturnofmoney,takingintoaccountexpectedinflaJonandexpectedcapitalgainsfromachangeinλ.

TheUJlityFuncJonandtheMoneyDemandFuncJon

u = ln γ Ct( )ε + (1− γ ) Mt

⎛⎝⎜

⎞⎠⎟

⎝⎜

⎠⎟

Pt= γ1− γ

it1+ it

⎛⎝⎜

⎞⎠⎟

− 11−εCt =

γ1− γ

it1+ it

⎛⎝⎜

⎞⎠⎟

− 11−εYt

AssumingthattheperiodicuJlityfuncJonutakestheform,

ImposingthegoodsmarketequilibriumcondiJonCt=Yt,thefirstordercondiJonsimplythat,

TheCash-in-AdvanceConstraintandMoneyDemand

• Thebasicideaofmodelsinwhichmoneyistheonlymeansofpayment,isthatinordertocompleteanyeconomictransacJon,paymentmustbeinmoney,andinparJcularcash,whichthebuyerholdsinadvanceofthecompleJonofthetransacJon.

• ThisideaisduetoClower(1967),anditsintegraJonintogeneralequilibriummodelsleadstoaclassofmodelsknownascash-in-advancemodels.

• TherestricJonthatthetransacJonmustbepaidwithmoneyheldinadvance,imposesacostofholdingmoney,because,alternaJvely,economicagentscouldholdanotherasset,suchasbonds,whichpaysinterest.

AlternaJveCash-in-AdvanceModels

• ThecashinadvancerestricJoncantakeseveralforms,dependingontheassumpJonsmadeaboutthesequencingoftransacJons.AsimpletradiJonalwayofexpressingthisconstraintistoassumethatspendingcannotexceedthemoneybalancescarriedoverfromtheendofthepreviousperiod(Svensson1985).

• AnalternaJvehypothesisisthateachperiodconsistsoftwodifferentsub-periods.Inthefirstsub-periodagentsvisitafinancialmarket,sayabank,wheretheycanswapinterestbearingassetswithmoney,orborrowcash,andinthesecondsub-periodtheydealinmarketsforgoodsandservices,whichareliabletothecash-in-advanceconstraint(seeHelpman1981,Lucas1980,1982).

TheCash-in-AdvanceConstraintwhenHouseholdsCanVisitFinancialMarketspriorto

MakingPurchases

At = Mt + Bt

PtCt ≤ Mt

At+1 = Mt + (1+ it )Bt + Pt (Yt −Tt −Ct ) = (1+ it )At − itMt + Pt (Yt −Tt −Ct )

Inthefirstsub-periodagentsvisitafinancialmarket,sayabank,wheretheycanswapinterestbearingassetswithmoney,orborrowcash.Inthesecondsub-periodtheydealinmarketsforgoodsandservices,whichareliabletothecash-in-advanceconstraint.Inthesecondsub-period,householdsalsoreceivetheirexogenousrealincomeYandpaytheirtaxes(netoftransfers)Τ.

TheLagrangianoftheRepresentaJveHouseholdandtheFirstOrderCondiJons

Et β s−t u(Cs )+ν tMt

Pt−Ct

⎛⎝⎜

⎞⎠⎟+ λt (1+ it )

+Yt −Tt −Ct − itMt

Pt− At+1Pt

⎛⎝⎜

⎞⎠⎟

⎝⎜⎞

⎠⎟s=t

∞∑

λt +ν t =∂u∂Ct

= ′u (Ct ) ν t = λtitλtPt

= βEt (1+ it+1)λt+1Pt+1

⎛⎝⎜

⎞⎠⎟

InterpreJngtheFirstOrderCondiJonsoftheRepresentaJveHouseholdwithaCash-in-

AdvanceConstraint• FirstisthestaJcfirstordercondiJonaccordingtowhichtheopJmal

consumpJonequatesthemarginaluJlityofconsumpJonwiththe“shadowvalue”ofsavingsλ,plustheshadowvalueofmoneyν.TheshadowvalueofmoneyresultsfromtherestricJonforcashinadvanceinordertobuyconsumergoods.

• Secondisthedynamicfirst-ordercondiJon,accordingtowhichthetotalexpectedrealreturnonsavings,includingexpectedinflaJonandexpectedcapitalgains,shouldbeequaltothepurerateofJmepreferenceofthehousehold.

• ThirdisthestaJcfirstordercondiJonaccordingtowhich,theshadowvalueofmoneyshouldbeequaltotheshadowvalueofsavingsJmestheopportunitycostofholdingmoney,whichisnoneotherthanthenominalrate,sincemoneypaysnointerest.

TheEulerEquaJonandtheMoneyDemandFuncJonintheCash-in-AdvanceRepresentaJve

HouseholdModel

′u (Ct )Pt

= β(1+ it )Et′u (Ct+1)Pt+1

⎛⎝⎜

⎞⎠⎟

FromthefirstordercondiJonwecanderivetheEulerequaJonforconsumpJoninamonetaryeconomy.

Pt= Ct

ThemoneydemandfuncJonisderivedfromthecash-in-advanceconstraint.

TheEulerEquaJonforConsumpJonandtheNominalInterestRatewithLogarithmic

Preferences

= β(1+ it )Et1

Pt+1Ct+1

⎛⎝⎜

⎞⎠⎟

Assuminglogarithmicpreferences,theEulerequaJonforconsumpJoncanbewri[enas,

11+ it

= βEtMt

⎛⎝⎜

⎞⎠⎟

FromtheEulerequaJonaboveandthemoneydemandfuncJonitfollowsthatthenominalinterestrateisdeterminedby

Cash-in-AdvanceinanOverlappingGeneraJonsModel

WefinallyexaminetheimplicaJonsformoneydemandofacashinadvanceconstraintinavariantoftheSamuelsonoverlappinggeneraJonsmodels.Inthismodel,moneyfuncJonsbothasameansofpaymentsandastoreofvalue.

Thehouseholdborninthebeginningofperiodtlivesfortwoperiods,periodtandperiodt+1.ItreceivesincomeYtandpaystaxesTt,inthefirstperiodoflife,andconsumesinbothperiods.

Itmaximizesaninter-temporaluJlityfuncJonundertheconstraintsthatthepresentvalueofconsumpJonmustbeequaltothepresentvalueofincomenetoftaxes,andthecash-in-advanceconstraintsforeachperiod.

Ut = lnC1t + β lnC2t+1

PtC1t ≤ M1t Pt+1C2t+1 ≤ M 2t+1PtCt +11+ it

Pt+1C2t+1 = Pt (Yt −Tt )

AggregateconsumpJonandaggregatemoneybalancesineachperiodaregivenby,

Ct = C1t +C2t Mt = M1t +M 2t

TotalassetsofhouseholdsareequaltoA,andweassumethatyounghouseholdsarebornwithoutassets.Asaresult,allassetsbelongtotheoldhouseholds.ForsimplicityweassumethattaxesTareonlypaidbyyounghouseholds.

Giventhatoldhouseholdsreceivenocurrentincome,theirconsumpJonisequaltotheirassets,which,however,theyneedtoconvertintomoney,inordertopurchaseconsumergoods.

ConsumpJonofoldhouseholdsisthusgivenby,

C2t =AtPt

Giventhatyounghouseholdsholdnoassets,theyneedtoborrowandconverttheirloanintomoney,inordertofinancetheirconsumpJon.Asaresult,foryounghouseholdsthefollowingconstraintsmusthold,

M1t = PtC1t = −B1t

At+1 = M1t + (1+ it )B1t + Pt Yt −Tt −C1t( ) = Pt Yt −Tt − (1+ it )C1t( )

IntroducingassetsinplaceofsecondperiodconsumpJonintheuJlityfuncJon,wefindthatyounghouseholdswillchooseconsumpJonintheirfirstperiodoflifeinordertomaximize,

Ut = lnC1t + β lnPt Yt −Tt − (1+ it )C1t( )

⎛⎝⎜

⎞⎠⎟

C1t =1

1+ βYt −Tt1+ it

FromthefirstordercondiJonsitfollowsthat,

AggregateconsumpJoninperiodtisgivenby,

Ct = C1t +C2t =1

1+ βYt −Tt1+ it

+ AtPt

Yt = Ct =1

1+ βYt −Tt1+ it

+ AtPt

Fromequilibriuminthemarketforgoodsandservicesandmoneyitfollowsthat,

Thesecanbesolvedforthepricelevelandthenominalinterestrate.Theneutralityofmoneyholdssincerealincomeisexogenous.

Mt = PtYt

NominalandRealInterestRates:MoneyintheUJlityFuncJon

Withlogarithmicpreferences,thefirstordercondiJonsforthemaximizaJonoftheuJlityfuncJonoftherepresentaJvehouseholdaregivenby,

λt =γCt

FromthesecondiJons,itfollowsthat,

= β(1+ it )Etλt+1Pt+1

⎛⎝⎜

⎞⎠⎟

= 1− γMt

+ βEtλt+1Pt+1

⎛⎝⎜

⎞⎠⎟

= β(1+ it )Et1

Pt+1Ct+1

⎛⎝⎜

⎞⎠⎟

= 1− γγ

+ βEt1

Pt+1Ct+1

⎛⎝⎜

⎞⎠⎟

ThelastfirstordercondiJoncanbesolvedas.

= 1− γγ

β s−tEt1Ms

⎛⎝⎜

⎞⎠⎟s=t

∞∑

GiventhatCt=Ytwhichisexogenous,thisequaJondeterminestheequilibriumpricelevel,asafuncJonofexpectaJonsaboutthefutureevoluJonofthemoneysupply.SubsJtuJnginthemoneydemandequaJonforε=0,andsolvingforthenominalinterestrate,

1+ itit

= γ1− γ

= β s−tEtMt

⎛⎝⎜

⎞⎠⎟s=t

∞∑

ThenominalinterestratesisdeterminedbythecurrentmoneysupplyandexpectaJonsaboutthefuturedevelopmentofthemoneysupply,atarateofdiscountthatdependsonthepurerateofJmepreferenceofthehousehold.Supposetheexpectedgrowthrateofthemoneysupplyisconstantandequaltoμ.

1+ itit

= β s−t 11+ µ

⎛⎝⎜

⎞⎠⎟s=t

∞∑s−t

= 11+ ρ( ) 1+ µ( )

⎛⎝⎜

⎞⎠⎟s=t

∞∑s−t

= (1+ ρ)(1+ µ)(1+ ρ)(1+ µ)−1

Itfollowsthat,

it = (1+ ρ)(1+ µ)−1! ρ + µ

Thehigherthegrowthrateofmoneysupplyμ,thehigherwillbethenominalinterestratei,astheexpectedfutureinflaJonratewillbehigher.

ItisworthnoJngthattherealequilibriuminterestrateinthemodelisequaltoρ.Forμ=0,i=ρ.Inthiscase,becausetheexpectedfutureinflaJonrateisequaltozero,thenominalinterestrateequalstheequilibriumrealinterestrate,i.e.thepurerateofJmepreferenceoftherepresentaJvehousehold.

ItisworthnoJngthatifμ=-ρ/(1+ρ),i.e.ifthemoneysupplyisreducedatthisrate,thenominalinterestrateisdriventozero.Azeronominalinterestratehasa[racJveproperJesandleadstotheop9malmoneydemandbyhouseholds.

it = (1+ ρ)(1+ µ)−1! ρ + µ

NominalandRealInterestRates:Cash-in-Advance

IntherepresentaJvehouseholdmodelinwhichmoneydemandresultsfromthecash-in-advanceconstraint,undertheassumpJonoflogarithmicpreferences,thenominalinterestrateisdeterminedby,

it = (1+ ρ)(1+ µ)−1! ρ + µ

11+ it

= βEtMt

⎛⎝⎜

⎞⎠⎟= β 1

1+ µ⎛⎝⎜

⎞⎠⎟= 1(1+ ρ)(1+ µ)

FromthiscondiJon,itfollowsthat,

TheIndeterminacyofthePriceLevelwhentheCentralBankpegstheNominalInterestRate:

MoneyintheUJlityFuncJon

FromtheequilibriumcondiJonsinthegoodsandmoneymarkets,ifthecentralbankpegsthenominalinterestrateattheleveli0,thentherepresentaJvehouseholdmodelwithmoneyintheuJlityfuncJon,impliesthat,

Pt= 1− γ

γ1+ i0i0

Giventhatrealincomeisexogenous,thiscondiJonissaJsfiedforaninfinitenumberofcombinaJonsofΜandP.IfitissaJsfiedforM0andP0,itisalsosaJsfiedforλM0andλP0,foranyλ.

TheIndeterminacyofthePriceLevelwhentheCentralBankpegstheNominalInterestRate:

Cash-in-Advance

FromtheEulerequaJonforconsumpJonandtheequilibriumcondiJoninthegoodsmarket,itfollowsthat,

Pt+1Yt+1 = β(1+ i0 )PtYt

Giventhatrealincomeisexogenous,thiscondiJonissaJsfiedforaninfinitenumberofcombinaJonsofPtκαιPt+1.IfitsaJsfiedforP0andP1,thenitisalsosaJsfiedforλP0andλP1,foranyλ.

InterestRatePeggingandPriceLevelIndeterminacy

ThisindeterminacywasfirstdemonstratedbySargentandWallace(1975)inthecontextofanadhocmacromodelwithraJonalexpectaJons.ThisindeterminacydoesnotonlyariseinrepresentaJvehouseholdmonetarymodels,butinmoneymodelswithraJonalexpectaJons.

Thereasonfortheindeterminacyisthat,underinterestratepegging,thereisnomonetaryanchorwhichcandeterminethepricelevel,asinthecasewherethecentralbankdeterminesthemoneysupply.

Sincethecentralbankiscommi[edtoprovidingunlimitedcreditatanominalinterestratei0,thenthemoneysupplyisdeterminedbythedemandformoney.Neitherthepricelevel,northemoneysupplycanbeidenJfieduniquely.

TheequilibriumcondiJonsforprivateconsumpJonandmoneydemandcanbesaJsfiedwithbothhighpricesandaconsequenthighstockofmoney,andwithlowpricesandaconsequentlowstockofmoney,i.e.virtuallyforanylevelofprices.

DealingwithPriceLevelIndeterminacyunderInterestRateRules:TheWicksellandTaylorRules

Oneofthefirstanswerstothisproblemwasprovidedbythemonetaryeconomistwhofirstrealizeditsexistence,namelyWicksell(1898).Wicksellproposedthat,“Solongaspricesremainunaltered,thebanks’rateofinterestistoremainunaltered.Ifpricesrise,therateofinterestistoberaised;andifpricesfall,therateofinterestistobelowered;andtherateofinterestishenceforthtobemaintainedatitsnewlevelunJlafurthermovementofpricescallsforafurtherchangeinonedirecJonortheother.”(p.189).Thus,Wicksellproposedthatcentralbanksshouldhaveapriceleveltarget,andchangeinterestrateswhenthepriceleveldeviatesfromthistarget.

AlternaJvewaystosolvetheproblemofpricelevelindeterminacywhenthepolicyinstrumentofthecentralbankisthenominalinterestrate,havebeenproposed:InflaJontargeJngrules,nominalincomerules,andmorerecentlytheTaylor(1993),whichisageneralizaJonofWicksell’srule.WeshallexaminetheproperJesofsuchrulesinthelecturesonaggregatefluctuaJonsandmonetarypolicy.

TheFiscalTheoryofthePriceLevel

OnetheoreJcaldevelopmentworthmenJoningistheso-calledfiscaltheoryofthepricelevel(see.Leeper1991,Sims1994andWoodford1994,1995).

Thistheoryarguesthatevenifmonetarypolicyisnotsufficienttodeterminethepricelevel,asunderinterestratepegging,thepricelevelcanbedeterminedatthelevelwhichensuresthatpublicdebt,whichisdefinedinnominalterms,doesnotfollowanexplosivepath.

ApathforthepricelevelthatensuresapathofnominalpublicdebtthatsaJsfiestheinter-temporalbudgetconstraintofthegovernmentissufficientinthosemodelstodeterminethepricelevel.

PriceLevelDeterminacyinOverlappingGeneraJonsModelsandthePigouEffect

ItisalsoworthstressingthattheproblemofpricelevelindeterminacydoesnotariseinoverlappinggeneraJonsmodels.UnliketherepresentaJvehouseholdmodel,whereboththecurrentandthefuturepricelevelarenonpredeterminedvariables,intheoverlappinggeneraJonsmodel,thepricelevelisdeterminedthroughthepredeterminednominalfinancialassetsof“old”households.ThesefuncJonasamonetaryanchorandhelpindeterminingthepricelevel.

IntradiJonalmonetarymodels,thedependenceofconsumpJononthefinancialwealthofhouseholdswascalledthePigoueffect(seePigou1943),ortherealbalanceeffect(seePaJnkin1956).AsSargentandWallace(1975)hadindicatedintheiroriginalanalysisofpricelevelindeterminacy,inthepresenceofaPigouorrealbalanceeffect,theproblemdoesnotariseevenifthecentralbankpegsthenominalinterestrate.

SeigniorageandInflaJon• If the growth of the money supply translates into higher inflation in the longer

term, why don’t governments and central banks keep the rate of growth of the money supply low and stable in order to control and eliminate inflation?

• The answer is that governments often have other policy motives besides the motive of tackling inflation. Perhaps the most important incentive for the issuance of new money by governments is to finance expenditure that they cannot, or do not want to, finance through other methods, such as higher taxes or higher government debt.

• The main cause of all the episodes of high inflation or hyperinflation appears to have been the need of governments to use revenue from money creation (seigniorage) to finance wars and war reparations, revolutions, extraordinary costs related to natural disasters or sudden reductions in their borrowing capacity from financial markets and their capacity to raise revenue from taxes and customs revenues.

HighInflaJonandHyperinflaJon

• WeexploretherelaJonshipbetweenthegrowthrateofmoneysupply,inflaJonandtheneedsofgovernmentstoraiserevenuethroughseigniorage.

• Weexamineboththecaseinwhichtherequiredincomefromseignioragecanberaisedonthebalancedgrowthpath,asituaJoninwhichequilibriumturnsouttobecharacterizedbyhighinfla9on,andthesituaJoninwhichtherequiredrevenuefromseigniorageissohigh,thatitcannotberaisedinsteadystateequilibrium,whichcanleadtohyperinfla9on.

• ThegenerallyaccepteddefiniJonofhyperinflaJonisduetoCagan(1956).CagandefinedaaperiodofhyperinflaJonasone“beginninginthemonthinwhichtheriseinpricesexceeds50%andasendinginthemonthbeforethemonthlyriseinpricesdropsbelowthatamountandstaysbelowforatleastayear.”

EpisodesofHighInflaJonandHyperinflaJon

• ThefirstmodernepisodesofhyperinflaJonoccurredinEuropeintheadermathofWorldWarI,aswellasduringandintheadermathofWorldWarII.

• InthelastfortyyearsveryhighinflaJonandhyperinflaJonreappearedinsomeLaJnAmericancountries,insometransiJoneconomiesaderthecollapseoftheSovietUnionandinsomebelligerentcountriesofAsiaandAfrica.

• Moreover,manycountries,withoutreachingthelevelsofhyperinflaJon,haveexperienceswithhighinflaJonfrom100%to1000%peryearforquitelongperiods.

MonetaryGrowth,InflaJonandSeigniorage:TheDemandforMoneyFuncJon

InordertostudytherelaJonbetweentherateofgrowthofthemoneysupply,inflaJonandrevenuefromseigniorage,weshallstartfromalinearlogarithmicformofthemoneydemandfuncJon.Inequilibrium,thedemandformoneyequalsthesupplyofmoney,soitfollowsthat,

κisaconstant,ethebasisofnaturallogarithms,καιη>0thesemi-elasJcityofmoneydemandwithrespecttothenominalinterestratei.

=κYe−ηi

MonetaryGrowth,InflaJonandSeigniorage:NominalandRealInterestRates

ThenominalinterestrateisdefinedbytheFisherequaJon,

whereristherealinterestrate,andπeexpectedinflaJon.

RealOutputYisconsideredexogenous,withagrowthrateg+n>0,whiletherateofgrowthofthenominalmoneysupplyMisdenotedbyμ>0.

UndertheseassumpJon,inflaJononthebalancedgrowthpath,saJsfies,

i = r +π e

π = µ − (g + n)

TheDemandforMoneyandtheRateofGrowthoftheMoneySupply

AssumingraJonalexpectaJons,themoneydemandfuncJoncanthusbewri[enas,

Tofurthersimplifyma[ers,weshallassumethatthegoldenruleappliesonthebalancedgrowthpath,whichimpliesthatr=g+n.UnderthisaddiJonalassumpJon,

=κYe−η(r+µ−(g+n))

=κYe−ηµ

SeigniorageRevenueandRateofGrowthoftheMoneySupply

Seignioragerevenueisequalto,

AsaproporJonoftotaloutput,seignioragerevenueisdefinedby,

S = M•

= µ MP

= µκYe−ηµ

s = SY= µ M

PY= µκ e−ηµ

MaximizingSeigniorageRevenueSeignioragerevenuesasaproporJonoftotaloutput,dependonμ,accordingto,

ThisdependenceisposiJveinμ,uptothepointwhereμ=1/η.Whenμ>1/ηthedependencebecomesnegaJve.Seignioragerevenue,asaproporJonoftotaloutputisthusmaximizedwhenμ=1/η.Maximumseignioragerevenueinsteadystateisthusgivenby,

∂s∂µ

= (1−ηµ)κ e−ηµ

smax =κλe

TheSeigniorageLafferCurve

TheRateofGrowthoftheMoneyandMaximumSeigniorageRevenue

• Cagan,usingannualdata,esJmatedthatηliesbetween1/2and1/3.Consequently,heesJmatedthegrowthrateofthemoneysupplythatmaximizesrevenuesfromseigniorage,asapercentageoftotaloutput,andthecorrespondinginflaJon,atbetween200%and300%peryear.

• Assumingthatκ=0.10,themaximumrevenuefromseigniorageasapercentageoftotaloutputisbetween7-11%.ThisisroughlytheesJmateofCagan(1956).

• Fortheperiod1975-1985,SachsandLarrain(1993)esJmatedactualrevenuefromseigniorageatabout5to6.5%forhighinflaJoncountriessuchasItaly,Bolivia,TurkeyandPeru,andmuchlowerforaseriesofothercountries.

HighInflaJonBalancedGrowthPath

• LetusnowconsideragovernmentwhichneedstofundaproporJonofitspublicspendingthroughseigniorage.Wewillassumethatthisfinancingrequirement,asaproporJonoftotaloutputisequaltosE,whichislessthanthemaximumseignioragesmaxthatthegovernmentcanachievebyse^ngthegrowthrateofthemoneysupplyatμ=1/η.

• TherearetwoopJonstoachieverevenueequaltosE.OneiswithagrowthrateofthemoneysupplyμE<1/η,andtheotheriswithagrowthrateofthemoneysupplyμE΄>1/η.

• AssumingthatthegovernmentdislikesinflaJon,itwillchoosethelowestgrowthrateofthemoneysupplythatiscompaJblewiththeobjecJveofraisingrevenuesEfromseigniorage.

• ForaslongasthegovernmentneedstofinanceaproporJonsEofitsoutputthroughseigniorage,theeconomyistrappedinanequilibriumwitharateofgrowthofthemoneysupplyequaltoμEandthecorrespondinghighinflaJon.Forexample,ifthegovernmentwantstoraiseseignioragecorrespondingto6%oftotaloutput,assumingη=1/2,thisimpliesanannualgrowthrateofthemoneysupply(andcorrespondingsteadystateinflaJon)equaltoabout100%.

AHighInflaJonBalancedGrowthPath

SeigniorageRevenueOutsidetheBalancedGrowthPath:GradualAdjustmentofMoney

DemandorGradualAdjustmentinExpectaJons• Supposenowthatthegovernmentneedstoraiseseigniorage

which,asaproporJonoftotaloutput,ishigherthanthemaximumthatcanberaisedinthesteadystate.WeassumesE>smax.

• Obviouslytherecanbenobalancedgrowthpathinwhichthegovernmentcanraiserevenuesfromseignioragetoexceedssmax.

• However,foraJme,andastheeconomyadjuststowardsthebalancedgrowthpath,thegovernmentmaybeabletoraiseseignioragerevenuesgreaterthansmax.Thiscouldhappenifforexamplethereisgradualadjustmentinthedemandformoney,orgradualadjustmentininflaJonaryexpectaJons.

SeigniorageRevenueOutsidetheBalancedGrowthPath:GradualAdjustmentofMoney

Demand• Supposethatthedemandformoneydoesnotadjustimmediatelytoitssteady

stateleveladerachangeinthenominalinterestrate,butonlyadjustsgradually.Thus,whenthenominalinterestrateincreases,moneydemandistemporarilyhigherthaninthesteadystate.

• Inthiscase,duringtheadjustment,themonetarybaseuponwhichtheinflaJonarytaxisimposedishigherthanthesteadystatemonetarybase.Consequently,duringtheadjustment,asμincreases,seignioragerevenueswillexceedsmaxbecauserealmoneybalancesarehigherthanonthebalancedgrowthpath.

• Asthedemandformoneydecreasesgradually,thegovernmentshouldconstantlyincreasetherateofmonetaryexpansionandtheconsequentinflaJon,tobeabletohavetherequiredhighrevenuesfromseigniorage.Thiscanleadtoanexplosivepathfortherateofgrowthofthemoneysupply,andaconsequenthyperinflaJon.

GradualAdjustmentinMoneyDemand

Assumethat,intheshortrun,realmoneydemandadjustsgraduallytowardsitssteadystatevalueaccordingto,

d lnm(t)dt

= m•(t)

m(t)=ψ lnm*− lnm(t)( )

where,ψisthespeedofadjustment,and,

m(t) = M (t)P(t)Y (t)

m*= MPY

=κ e−ηµ

MonetaryGrowthandtheGradualAdjustmentinMoneyDemand

SubsJtuJngforthedeterminantsofsteadystatemoneydemandm*,theadjustmentofmoneydemandtakestheform,

m•(t)

m(t)=ψ lnκ −ηµ(t)− lnm(t)( )

InordedtoachieveaconstanttargetsEforseignioragerevenue,therateofgrowthofthemoneysupplymustbeequaltotherateofreducJonofthedemandforrealmoneybalances

sE = µ(t)m(t) µ•(t)

µ(t)= − m

•(t)

m(t)and

DynamicAdjustmentoftheRateofGrowthoftheMoneySupply

inordertomaintainrevenuesfromseigniorageconstantasapercentageoftotalincomeatthelevelsE,thegrowthrateofthemoneysupplymustkeepincreasingconJnuously,atthesamerateasthedeclineofrealmoneydemandrelaJvetooutput.FromthepreviousequaJonsthisimpliesthat,

µ•(t)

µ(t)= −ψ lnκ − ln sE + lnµ(t)−ηµ(t)( )

sE = µκ e−ηµ ≤ smax

AnecessaryandsufficientcondiJonforstabilizingtherateofgrowthofthemoneysupplyisthat,

TransiJontoHyperinflaJon

IfsE>smaxthentherateofgrowthofthemoneysupplyincreasesconJnuously.Aderapointitstartsincreasingatanincreasingrate,withtheresultanexplosivepathfortherateofgrowthofthemoneysupplyandinflaJon.TheresultishyperinflaJon.

µ•(t)

µ(t)= −ψ lnκ − ln sE + lnµ(t)− λµ(t)( )

HighInflaJonandHyperinflaJonwithParJalAdjustmentinMoneyDemand

RequiredSeigniorageRevenue,MoneySupplyGrowthandInflaJon• Inthecasewherethefinancingneedsofthegovernmentfromseigniorage

arelessthanorequaltothemaximumpossibleonthebalancedgrowthpath,thentherateofgrowthofthemoneysupplystabilizesataratethatmayindeedentailsignificantinflaJon,butinflaJonisstableanddoesnotevolveintohyperinflaJon.

• However,ifthefinancingneedsofgovernmentexceedthemaximumthatissustainableonthebalancedgrowthpath,then,asthegovernmenttriestoraisethenecessaryrevenuefromseigniorage,therateofgrowthofthemoneysupplygraduallyaccelerates,inordertokeepupwiththedecliningmonetarybase,andtheeconomyfallsintoastateofhyperinflaJon.ThereasonisthatinflaJongraduallyreducesthedemandformoneyrelaJvetototaloutput,andthegovernmentneedsaneverincreasinggrowthrateofthemoneysupplyinordertobeabletocollecttheneededseignioragerevenue.

ConclusionsontheDeterminantsofHighInflaJon

• Ourbasicanalysisexplainswhy,inmanycases,inflaJonmaybedriventoveryhighlevels.Thisisduetotheinabilityofagovernmenttofinanceitsspendingfromotherrevenuesources,suchastaxaJonorborrowingfromthemarkets,anditsneedtouseseigniorage,i.erevenuefrommoneycreaJon.

• TheanalysisalsoexplainswhyeventhoughinflaJonmayreachveryhighlevels,itisnotnecessarythatitwillevolveintoanexplosivehyperinflaJon.Forthistohappen,thefinancingneedsofthegovernmentmustbesohighthattheyexceedthemaximumlevelthatcanbefinancedthroughseigniorageonthebalancedgrowthpath.

• Finally,theanalysisemphasizesthecentralroleoffiscalproblemsasthemainrootcausesofbothhighinflaJonandhyperinflaJon.AsignificantprecondiJonfortacklinghighinflaJonorhyperinflaJonistopursuereformsthataddresstheunderlyingfiscalproblems(Sargent1982).

FinalConclusions• InthislecturewehaveanalyzedtheroleandfuncJonsofmoney.Moneyperformsthree

funcJons.First,itisaunitofaccount,second,itisagenerallyacceptedmeansofpayment,and,thirdly,itisastoreofwealth.

• WefirstreviewedthebasicfuncJonsofmoneyandthefactorsthatdeterminethedemandforandsupplyofmoney.Weanalyzedtheconceptofshortrunequilibriuminthemoneymarket,assumingthatthecentralbankfollowsapolicyofeithertargeJngthemoneysupplyorpeggingnominalinterestrates,andalsodefinedthenoJonofthelong-termneutralityofmoney.

• Wethenfocusedonanumberofdynamicgeneraleconomicequilibriummodelswithmoney,inordertoanalyzethedeterminaJonofthepricelevelandnominalinterestratesandalsoanalyzedthelongrelaJonshipbetweenthemoneysupply,thepricelevelandinflaJon.

• FinallyweexaminedthefiscalincenJveforincreasingthemoneysupplyanditseffectsoninflaJon.ThemostimportantmoJveforsustainedlargeincreasesinthemoneysupplybygovernmentshasbeentheincenJvetouseseigniorageinordertofinancegovernmentexpenditurethatcouldnotbefinancedbyothermethods,suchasaddiJonaltaxesorgovernmentbonds.

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