MANKIW'SMACROECONOMICSMODULES.

CHAPTER17

Investment

APowerPointTutorial

ToAccompany

MACROECONOMICS,6th.ed.

N.GregoryMankiw

By

MannigJ.Simidian

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ChapterSeventeen2

3TypesofInvestmentSpeD

?Businessfixedinvestmentincludestheequipmentand

structuresthatbusinessesbuytouseinproduction.

?Residentialinvestmentincludesthenewhousingthat

peoplebuytoliveinandthatlandlordsbuytorentout.

?Inventoryinvestmentincludesthosegoodsthatbusinesses

putasideinstorage,includingmaterialsandsupplies,work

inprogress,andfinishedgoods.

ChapterSeventeen

BusinessFixedInvestment

Thestandardmodelofbusinessfixedinvestmentiscalledthe

neoclassicalmodelofinvestment.Itexaminesthebenefitsandcostsof

owningcapitalgoods.Herearethreevariablesthatshiftinvestment:

1)themarginalproductofcapital

2)theinterestrate

3)taxrules

Todevelopthemodel,imaginethattherearetwokindsoffirms:

productionfirmsthatproducegoodsandservicesusingthe

capitalthattheyrentandrentalfirmsthatmake^H4he

investmentsintheeconomy.

ChapterSeventeen4

TheRentalPriceofCapital

Toseewhatvariablesinfluencetheequilibriumrentalprice,lefs

considertheCobb-Douglasproductionfunction(recallinChapter3)as

agoodapproximationofhowtheactualeconomyturnscapitalandlabor

intogoodsandservices.TheCobb-Douglasproductionfunctionis:

Y=AKaL[a,whereYisoutput,Kcapital,Llabor,andaaparameter

measuringtheleveloftechnology,andaaparameterbetween0and1

thatmeasurescapitaPsshareofoutput.Therealrentalpriceofcapital

adjuststoequilibratethedemandforcapitalandthefixedsupply.

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d七

Capitaldemand(MPK)

ChapterSeventeen-5

KCapitalstock,K

ThemarginalproductofcapitalfortheCobb-Douglasproduction

functionisMPK=aA(L/K)'r。Becausetherealrentalpriceequalsthe

marginalproductofcapitalinequilibrium,

wecanwriteR/P-okA(L/K)y'a'Thisexpressionidentifiesthevariables

thatdeterminetherealrentalprice.Itshowsthefollowing:

?thelowerthestockofcapital,thehighertherealrentalpriceofcapital

?thegreatertheamountoflaboremployed,thehighertherealrental

priceofcapitals

?thebetterthetechnology,thehighertherealrentalpriceofcapital.

Eventsthatreducethecapitalstock,orraiseemployment,orimprove

thetechnology,raisetheequilibriumrealrentalpriceofcapital.

ChapterSeventeen6

TfcteCostofOeipiteLl

Lefsconsiderthebenefitandcostofowningcapital.

Foreachperiodoftimethatafirmrentsoutaunitofcapital,therental

firmbearsthreecosts:

1)Interestontheirloans,whichequalsthepurchasepriceofaunitof

capitalPKtimestheinterestrate,[soiPK.

2)Thecostofthelossorgainonthepriceofcapitaldenotedas-APK.

3)Depreciation8definedasthefractionofvaluelostperperiod

becauseofthewearandtear,so8PK.

Thereforethetotalcostofcapital=iPK-APK+8PKor

=PKAPJ尸K+3)

Finally,wewanttoexpressthecostofcapitalrelativetoothergoodsin

theeconomy.Therealcostofcapital-thecostofbuyingandrenting

outaunitofcapitalmeasuredintermsoftheeconomy'soutputis:

TheRealCostofCapital=(PK/P)(r+8),whereristherealinterest

rateandPK/Pequalstherelativepriceofcapital.Toderivethis

equation,weassumethattherateofincreaseofthepriceofgoodsin

generalisequaltotherateofinflation.

TheDeterminantsofInvestment

Nowconsiderarental行rm'sdecisionaboutwhethertoincreaseor

decreaseitscapitalstock.Foreachunitofcapital,thefirmearnsreal

revenueR/Pandbearstherealcost(PK/P)S+8).

Therealprofitperunitofcapitalis

Profitrate=Revenue-Cost

=R/P-(PK/P)(r+d)

Becausetherealrentalpriceequalsthemarginalproductofcapital,we

canwritetheprofitrateas

Profitrate=MPK-(PK/P)(r+8)

Thechangeinthecapitalstock,callednetinvestmentdependsonthe

differencebetweentheMPKandthecostofcapital.IftheMPKexceeds

thecostofcapital,firmswilladdtotheircapitalstock.IftheMPK

fallsshortofthecostofcapital,theylettheircapitalstockshrink,thus:

A7C=Zn[MP^-(PK/P)(r+8)L

where/n()isthefunctionshowinghowmuchnetinvestmentresponds

totheincentivetoinvest.

TheInvestmentFunction

Wecannowderivetheinvestmentfunctionintheneoclassicalmodelof

investment.Totalspendingonbusinessfixedinvestmentisthesumof

netinvestmentandthereplacementofdepreciatedcapital.

Theinvestmentfunctionis:

.I=/n[MPK-(PK/P)(r+5)7+

/''thecostofcapital

/dependson\amountofdepreciation

Investmentmarginalproductofcapital

Thismodelshowswhyinvestmentdependsontherealinterestrate.

Adecreaseintherealinterestratelowersthecostofcapital.

ChapterSeventeen9

Noticethatbusinessfixedinvestnientincreaseswhentheinterestrate

fall——hencethedownwardslopeoftheinvestmentfunction.Also,

anoutwardshiftintheinvestmentfunctionmaybearesultofan

increaseinthemarginalproductofcapital.

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ChapterSeventeen10

Finally,weconsiderwhathappensasthisadjustmentofthecapital

stockcontinuesovertime.Ifthemarginalproductbeginsabovethe

costofcapital,thecapitalstockwillriseandthemarginalproductwill

fall.Ifthemarginalproductofcapitalbeginsbelowthecostofcapital,

thecapitalstockwillfallandthemarginalproductwillrise.

Eventually,asthecapitalstockadjusts,theMPKapproachesthecost

ofcapital.Whenthecapitalstockreachesasteadystatelevel,

wecanwrite:

MPK=(PK/P)(r+6).

Thus,inthelongrun,theMPKequalstherealcostofcapital.The

speedofadjustmenttowardthesteadystatedependsonhowquickly

firmsadjusttheircapitalstock,whichinturndependsonhowcostly

itistobuild,deliver,andinstallnewcapital.

ChapterSeventeen11

InvestmentTaxCredit

Policymakersoftenchangetherulesgoverningcorporateincome

taxinanattempttoencourageinvestment,oratleastmitigatethe

disincentivethetaxprovides.

Aninvestmenttaxcreditisataxprovisionthatreducesafirm's

taxesbyacertainamountforeachdollarspentoncapitalgoods.

Becauseafirmrecoupspartofitsinvestmentincapitalgoodsinthe

formoflowertaxes,acreditreducestheeffectivepurchasepriceof

aunitofcapitalP.

ChapterSeventeen12

TheStockMarketandTobin'sq

Thetermstockreferstothesharesintheownershipofcorporations,and

thestockmarketisthemarketinwhichthesesharesaretraded.

TheNobel-Prize-winningeconomistJamesTobinproposedthatfirms

basetheirinvestmentdecisionsonthefollowingratio,whichisnow

calledTobin火q:

q=MarketValueofInstalledCapital

ReplacementCostofInstalledCapital

13

henumeratorofTobin'sqisthevalueofthe

economy'scapitalasdeterminedbythestockmarket.

Thedenominatoristhepriceofcapitalasifitwere

purchasedtoday.Tobinconveyedthatnetinvestment

shoulddependonwhetherqisgreaterorlessthan1.If

q>1,thenfirmscanraisethevalueoftheirstockby

increasingcapital,andifq<1,thestockmarketvalues

capitalatlessthanitsreplacementcostandthus,firms

willnotreplacetheircapitalstockasitwearsout.

Tobin'sqmeasurestheexpectedfuture

rofitabilityaswellasthecurrentprofitability.

ChapterSeventeen

1)Higherinterestratesincreasethecostofcapitalandreducebusiness

fixedinvestment.

2)Improvementsintechnologyandtaxpolicies,suchasthecorporate

incometaxandinvestmenttaxcredit,shiftthebusinessfixed-

investmentfunction.

3)DuringboomshigheremploymentincreasestheMPKandtherefore,

increasesbusinessfixedinvestment.

ChapterSeventeen15

i'ho:浙沁⑶M>?）由。4次,尸

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Efficient-MarketHypothesisethemarketpriceofacompany's

stockisthefullyrationalvaluationofthecompany'svalue,given

currentinformationaboutthecompany'sbusinessprospects..

Keynes'beautycontestisametaphorforstockspeculation.Inthis

view,thestockmarketfluctuatesfornogoodreason,andbecausethe

stockmarketinfluencestheaggregatedemandforgoodsandservices,

thesefluctuationsareasourceofshort-runeconomicfluctuations.

ChapterSeventeen16

ResidentialInvestment

Wewillnowconsiderthedeterminantsof

residentialinvestmentbylookingatasimple

modelofthehousingmarket.Residential

investmentincludesthepurchaseofnew

housingbothbypeoplewhoplantolivein

itthemselvesandbylandlordswhoplantorent

ittoothers.

Therearetwopartstothemodel:

1)themarketfortheexistingstockofhousesdeterminesthe

equilibriumhousingprice

2)thehousingpricedeterminestheflowofresidentialinvestment.

ChapterSeventeen

TheStockEquilibriumandtheJzlowSupply

Therelativepriceofhousinjuststoequilibratesupplyanddemand

fortheexistingstockofsingcapital.Therelativepricethen

determinesresident!vestment,theflowofnewhousingthat

constructionfiruild.

The

PH/P

Demand

Stockofhousingcapital,KHFlowofresident!1investment,/H

ChapterSeventeen18

ChangesinHgusingDemand

Whenthedemandforhousiifts,theequilibriumpriceofhousing

changes,andthischangejturnaffectsresidentialnvestment.

Anincreaseinhousiemand,perhapsduetoa11intheinterest

rate,raiseshousiricesandresidentialinvestment.

TheSupplyOfNewHousing

p，p

Demand

Demand

Stockofhousingcapital,KHFlowofresidentialinvestment,/H

ChapterSeventeen19

SummaryofResidentialInvestment

1)Anincreaseintheinterestrateincreasesthecostc

forhomebuyersandreducesresidentialhousinginv(

2)Anincreaseinpopulationandtaxpoliciesshiftth(

housing-investmentfunction.

3)Inaboom,higherincomeraisesthedemandforh

increasesresidentialinvestment.

ChapterSeventeen20

InventoryInvestment

Inventoryinvestment,thegoodsthatbusinessesputaside

instorage,isatthesametimenegligibleandofgreat

significance.Itisoneofthesmallestcomponentsof

spending—butitsvolatilitymakesitcriticalinthestudy

ofeconomicfluctuations.

ChapterSeventeen

ReasonsforHoldingInventories

Whensalesarehigh,thefirmproduceslessthatitsells

andittakesthegoodsoutofinventory.Thisiscalled

productionsmoothing.Holdinginventorymayallow

firmstooperatemoreefficiently.Ihus,wecanview

inventoriesasafactorofproduction.Also,firmsdon't

wanttorunoutofgoodswhensalesareunexpectedly

high.Thisiscalledstock-outavoidance.Lastly,ifa

productisonlypartiallycompleted,thecomponentsare

stillcountedininventory,andarecalled,workin

process.

ChapterSeventeen22

L

heAccel6I3orpfA1A

xUvru1F

bcV

Theacceleratormodelassumesthatfirmsholdastockof

inventoriesthatisproportionaltothefirm'slevelofoutput.Thus,if

Nistheeconomy'sstockofinventoriesandYisoutput,then

N=^Y

where0isaparameterreflectinghowmuchinventoryfirmswishto

holdasaproportionofoutput.InventoryinvestmentIisthechangein

thestockofinventoriesA/V.Therefore,I=AN=0AK

Theacceleratormodelpredictsthatinventoryinvestmentis

proportionaltothechangeinoutput.

?Whenoutputrises,firmswanttoholdalargerstockofinventory,

soinventoryinvestmentishigh.

?Whenoutputfalls,firmswanttoholdasmallerstockofinventory,

sotheyallowtheirinventorytorundown,andinventoryinvestment

isnegative.

Themodelsaysthatinventoryinvestmentdependsonwhetherthe

economyisspeedingupo