nicholson微观经济理论（答案+ppt+习题库）-230-03-033593-0

CAPITALINTHISCHAPTERWEPROVIDEANINTRODUCTIONTOTHETHEORYOFCAPITALINMANYWAYSTHATTHEORYRESEMBLESOURANALYSISOFINPUTPRICINGINGENERALTHEPRINCIPLESOFPROTMAXIMIZINGINPUTCHOICEDONOTCHANGEBUTCAPITALTHEORYADDSANIMPORTANTTIMEDIMENSIONTOECONOMICDECISIONMAKINGOURGOALHEREISTOEXPLORETHATEXTRADIMENSIONWEBEGINWITHABROADCHARACTERIZATIONOFTHECAPITALACCUMULATIONPROCESSANDTHENOTIONOFTHERATEOFRETURNTHENWETURNTOMORESPECICMODELSOFECONOMICBEHAVIOROVERTIME23CHAPTERCAPITALANDTHERATEOFRETURNWHENWESPEAKOFTHECAPITALSTOCKOFANECONOMY,WEMEANTHESUMTOTALOFMACHINES,BUILDINGS,ANDOTHERREPRODUCIBLERESOURCESINEXISTENCEATSOMEPOINTINTIMETHESEASSETSREPRESENTSOMEPARTOFANECONOMYSPASTOUTPUTTHATWASNOTCONSUMED,BUTWASINSTEADSETASIDETOBEUSEDFORPRODUCTIONINTHEFUTUREALLSOCIETIES,FROMTHEMOSTPRIMITIVETOTHEMOSTCOMPLEX,ENGAGEINCAPITALACCUMULATIONHUNTERSINAPRIMITIVESOCIETYTAKINGTIMEOFFFROMHUNTINGTOMAKEARROWS,INDIVIDUALSINAMODERNSOCIETYUSINGPARTOFTHEIRINCOMESTOBUYHOUSES,ORGOVERNMENTSTAXINGCITIZENSINORDERTOPURCHASEDAMSANDPOSTOFCEBUILDINGSAREALLENGAGINGINESSENTIALLYTHESAMESORTOFACTIVITYSOMEPORTIONOFCURRENTOUTPUTISBEINGSETASIDEFORUSEINPRODUCINGOUTPUTINFUTUREPERIODSPRESENT“SACRICE”FORFUTUREGAINISTHEESSENTIALASPECTOFCAPITALACCUMULATIONRATEOFRETURNTHEPROCESSOFCAPITALACCUMULATIONISPICTUREDSCHEMATICALLYINFIGURE231INBOTHPANELSOFTHEGURE,SOCIETYISINITIALLYCONSUMINGLEVELC0ANDHASBEENDOINGSOFORSOMETIMEATTIMET1ADECISIONISMADETOWITHHOLDSOMEOUTPUTAMOUNTSFROMCURRENTCONSUMPTIONFORONEPERIODSTARTINGINPERIODT2THISWITHHELDCONSUMPTIONISINSOMEWAYPUTTOUSEPRODUCINGFUTURECONSUMPTIONANIMPORTANTCONCEPTCONNECTEDWITHTHISPROCESSISTHERATEOFRETURN,WHICHISEARNEDONTHATCONSUMPTIONTHATISPUTASIDEINPANELA,FOREXAMPLE,ALLOFTHEWITHHELDCONSUMPTIONISUSEDTOPRODUCEADDITIONALOUTPUTONLYINPERIODT2CONSUMPTIONISINCREASEDBYAMOUNTXINPERIODT2ANDTHENRETURNSTOTHELONGRUNLEVELC0626PARTVIIPRICINGININPUTMARKETSTWOVIEWSOFCAPITALACCUMULATIONINA,SOCIETYWITHDRAWSSOMECURRENTCONSUMPTIONSTOGORGEITSELFWITHXEXTRACONSUMPTIONINTHENEXTPERIODTHEONEPERIODRATEOFRETURNWOULDBEMEASUREDBYX/SH110021THESOCIETYINBTAKESAMORELONGTERMVIEWANDUSESSTOINCREASEITSCONSUMPTIONPERPETUALLYBYYTHEPERPETUALRATEOFRETURNWOULDBEGIVENBYY/SCONSUMPTIONCONSUMPTIONTIMETIMEAONEPERIODRETURNBPERPETUALRETURNC0T1T2T3T1T2T3C0XSSYFIGURE231SOCIETYHASSAVEDINONEYEARINORDERTOSPLURGEINTHENEXTYEARTHEONEPERIODRATEOFRETURNFROMTHISACTIVITYWOULDBEDENEDASFOLLOWSSINGLEPERIODRATEOFRETURNTHESINGLEPERIODRATEOFRETURNR1ONANINVESTMENTISTHEEXTRACONSUMPTIONPROVIDEDINPERIOD2ASAFRACTIONOFTHECONSUMPTIONFOREGONEINPERIOD1THATIS,R1H11005H11005H110021231IFXH11022SIFMORECONSUMPTIONCOMESOUTOFTHISPROCESSTHANWENTINTOIT,WEWOULDSAYTHATTHEONEPERIODRATEOFRETURNTOCAPITALACCUMULATIONISPOSITIVEFOREXAMPLE,IFWITHHOLDING100UNITSFROMCURRENTCONSUMPTIONPERMITTEDSOCIETYTOCONSUMEANEXTRA110UNITSNEXTYEAR,THEONEPERIODRATEOFRETURNWOULDBEH110021H11005010OR10PERCENTINPANELBOFFIGURE231,SOCIETYISASSUMEDTOTAKEAMORELONGTERMVIEWINITSCAPITALACCUMULATIONAGAIN,ANAMOUNTSISSETASIDEATTIMET1NOW,HOWEVER,THISSETASIDECONSUMPTIONISUSEDTORAISETHECONSUMPTIONLEVELFORALLPERIODSINTHEFUTUREIFTHEPERMANENTLEVELOFCONSUMPTIONISRAISEDTOC0H11001Y,WEDENETHEPERPETUALRATEOFRETURNASFOLLOWSPERPETUALRATEOFRETURNTHEPERPETUALRATEOFRETURNRH11009ISTHEPERMANENTINCREMENTTOFUTURECONSUMPTIONEXPRESSEDASAFRACTIONOFTHEINITIALCONSUMPTIONFOREGONETHATIS,RH11009H11005232IFCAPITALACCUMULATIONSUCCEEDSINRAISINGC0PERMANENTLY,RH11009WILLBEPOSITIVEFOREXAMPLE,SUPPOSETHATSOCIETYSETASIDE100UNITSOFOUTPUTINPERIODT1TOBEDEVOTEDTOCAPITALACCUMULATIONIFTHISCAPITALWOULDPERMITOUTPUTTOBERAISEDBY10UNITSFOREVERYPERIODINTHEFUTURESTARTINGATTIMEPERIODT2THEPERPETUALRATEOFRETURNWOULDBE10PERCENTWHENECONOMISTSSPEAKOFTHERATEOFRETURNTOCAPITALACCUMULATION,THEYHAVEINMINDSOMETHINGBETWEENTHESETWOEXTREMESSOMEWHATLOOSELYWESHALLSPEAKOFTHERATEOFRETURNASBEINGAMEASUREOFTHETERMSATWHICHCONSUMPTIONTODAYMAYBETURNEDINTOCONSUMPTIONTOMORROWTHISWILLBEMADEMOREEXPLICITSOONANATURALQUESTIONTOASKISHOWTHEECONOMYSRATEOFRETURNISDETERMINEDAGAIN,THEANSWERMUSTSOMEHOWREVOLVEAROUNDTHESUPPLYANDDEMANDFORPRESENTANDYH5007SDEFINITION110H5007100XH5007SXH11002SH5007SDEFINITIONCHAPTER23CAPITAL627FUTUREGOODSINTHENEXTSECTIONWEPRESENTASIMPLETWOPERIODMODELINWHICHTHESUPPLYDEMANDINTERACTIONISDEMONSTRATEDDETERMINATIONOFTHERATEOFRETURNINTHISSECTIONWEWILLDESCRIBEHOWOPERATIONOFSUPPLYANDDEMANDINTHEMARKETFOR“FUTURE”GOODSESTABLISHESANEQUILIBRIUMRATEOFRETURNWEBEGINBYANALYZINGTHECONNECTIONBETWEENTHERATEOFRETURNANDTHE“PRICE”OFFUTUREGOODSTHENWESHOWHOWINDIVIDUALSANDRMSARELIKELYTOREACTTOTHISPRICEFINALLY,THESEACTIONSAREBROUGHTTOGETHERASWEHAVEDONEFORTHEANALYSISOFOTHERMARKETSTODEMONSTRATETHEDETERMINATIONOFANEQUILIBRIUMPRICEOFFUTUREGOODSANDTOEXAMINESOMEOFTHECHARACTERISTICSOFTHATSOLUTIONRATEOFRETURNANDPRICEOFFUTUREGOODSFORMOSTOFOURANALYSISINTHISCHAPTER,WEWILLASSUMETHEREAREONLYTWOPERIODSTOBECONSIDEREDTHECURRENTPERIODTOBEDENOTEDBYTHESUBSCRIPT0ANDTHENEXTPERIODDENOTEDBYTHESUBSCRIPT1WEWILLUSERTODENOTETHEONEPERIODRATEOFRETURNBETWEENTHESETWOPERIODSHENCE,ASDENEDINTHEPREVIOUSSECTION,RH11005H110021,233WHEREWEUSETHEH9004NOTATIONTOREFERTOTHECHANGEINCONSUMPTIONINTHETWOPERIODSREWRITINGEQUATION233YIELDSH110051H11001R234ORH11005235BUTTHETERMONTHELEFTOFEQUATION235SIMPLYRECORDSHOWMUCHC0MUSTBEFOREGONEIFC1ISTOBEINCREASEDBYONEUNITTHATIS,THEEXPRESSIONREPRESENTSTHERELATIVE“PRICE”OFONEUNITOFC1INTERMSOFC0SOWEHAVEDENEDTHEPRICEOFFUTUREGOODS1PRICEOFFUTUREGOODSTHERELATIVEPRICEOFFUTUREGOODSP1ISTHEQUANTITYOFPRESENTGOODSTHATMUSTBEFOREGONETOINCREASEFUTURECONSUMPTIONBYONEUNITTHATIS,P1H11005H110052361H50071H11001RH9004C0H5007H9004C1DEFINITION1H50071H11001RH9004C0H5007H9004C1H9004C1H5007H9004C0H9004C1H5007H9004C0628PARTVIIPRICINGININPUTMARKETS1THISPRICEISIDENTICALTOTHEDISCOUNTFACTORINTRODUCEDINCONNECTIONWITHREPEATEDGAMESINCHAPTERS10AND20WENOWPROCEEDTODEVELOPADEMANDSUPPLYANALYSISOFTHEDETERMINATIONOFP1BYSODOINGWEALSOWILLHAVEDEVELOPEDATHEORYOFTHEDETERMINATIONOFR,THERATEOFRETURNINTHISSIMPLEMODELDEMANDFORFUTUREGOODSTHETHEORYOFTHEDEMANDFORFUTUREGOODSISONEFURTHERAPPLICATIONOFTHEUTILITYMAXIMIZATIONMODELDEVELOPEDINPARTIIOFTHISBOOKHERETHEINDIVIDUALSUTILITYDEPENDSONPRESENTANDFUTURECONSUMPTIONTHATIS,UTILITYH11005UC0,C1,ANDHEORSHEMUSTDECIDEHOWMUCHCURRENTWEALTHWTOALLOCATETOTHESETWOGOODS2WEALTHNOTSPENTONCURRENTCONSUMPTIONCANBEINVESTEDATTHERATEOFRETURNRTOOBTAINCONSUMPTIONNEXTPERIODASBEFORE,P1REECTSTHEPRESENTCOSTOFFUTURECONSUMPTION,ANDTHEINDIVIDUALSBUDGETCONSTRAINTISGIVENBYWH11005C0H11001P1C1237THISCONSTRAINTISILLUSTRATEDINFIGURE232IFTHEINDIVIDUALCHOOSESTOSPENDALLOFHISORHERWEALTHONC0,TOTALCURRENTCONSUMPTIONWILLBEWWITHNOCONSUMPTIONOCCURRINGINPERIOD2ALTERNATIVELY,IFC0H110050,C1WILLBEGIVENBYW/P1H11005W1H11001RTHATIS,IFALLWEALTHISINVESTEDATTHERATEOFRETURNR,CURRENTWEALTHWILLGROWTOW1H11001RINPERIOD23UTILITYMAXIMIZATIONIMPOSITIONOFTHEINDIVIDUALSINDIFFERENCECURVEMAPFORC0ANDC1ONTOTHEBUDGETCONSTRAINTINFIGURE232ILLUSTRATESUTILITYMAXIMIZATIONHEREUTILITYISMAXIMIZEDATTHEPOINTC0,C1THEINDIVIDUALCONSUMESC0CURRENTLYANDCHOOSESTOSAVEWH11002C0TOCONSUMENEXTPERIODTHISFUTURECONSUMPTIONCANBEFOUNDFROMTHEBUDGETCONSTRAINTASP1C1H11005WH11002C0238ORC1H11005239H11005WH11002C01H11001R2310INOTHERWORDS,WEALTHTHATISNOTCURRENTLYCONSUMEDWH11002C0ISINVESTEDATTHERATEOFRETURN,R,ANDWILLGROWTOYIELDC1INTHENEXTPERIODWH11002C0H5007H5007P1CHAPTER23CAPITAL6292FORANANALYSISOFTHECASEWHERETHEINDIVIDUALHASINCOMEINBOTHPERIODS,SEEPROBLEM2313THISOBSERVATIONYIELDSANALTERNATIVEINTERPRETATIONOFTHEBUDGETCONSTRAINTGIVENBYEQUATION237,WHICHCANBEWRITTENINTERMSOFTHERATEOFRETURNASWH11005C0H11001THISILLUSTRATESTHEFACTTHATITISTHE“PRESENTVALUE”OFC1THATENTERSINTOTHEINDIVIDUALSCURRENTBUDGETCONSTRAINTTHECONCEPTOFPRESENTVALUEISDISCUSSEDINMOREDETAILLATERINTHISCHAPTERC1H50071H11001REXAMPLE231INTERTEMPORALIMPATIENCEINDIVIDUALSUTILITYMAXIMIZINGCHOICESOVERTIMEWILLOBVIOUSLYDEPENDONHOWTHEYFEELABOUTTHERELATIVEMERITSOFCONSUMINGCURRENTLYORWAITINGTOCONSUMEINTHEFUTUREONEWAYOFREECTINGTHEPOSSIBILITYTHATPEOPLEMAYEXHIBITSOMEIMPATIENCEINTHEIRCHOICESISTOASSUMETHATTHEUTILITYFROMFUTURECONSUMPTIONISIMPLICITYDISCOUNTEDINTHEINDIVIDUALSMINDFOREXAMPLE,WEMIGHTASSUMETHATTHEUTILITYFUNCTIONFORCONSUMPTION,UC,ISTHESAMEINBOTHPERIODSWITHUH11032H110220,UH11033H110210,BUTTHATPERIOD1SUTILITYISDISCOUNTEDINTHEINDIVIDUALSMINDBYA“RATEOFTIMEPREFERENCE”OF1/1H11001H9254WHEREH9254H110220IFTHEINTERTEMPORALUTILITYFUNCTIONISALSOSEPARABLEFORMOREDISCUSSIONOFTHISCONCEPT,SEETHEEXTENSIONSTOCHAPTER6,WECANWRITEUC0,C1H11005UC0H11001H50071H110011H9254H5007UC12311MAXIMIZATIONOFTHISFUNCTIONSUBJECTTOTHEINTERTEMPORALBUDGETCONSTRAINTWH11005C0H110012312C1H50071H11001R630PARTVIIPRICINGININPUTMARKETSINDIVIDUALSINTERTEMPORALUTILITYMAXIMIZATIONWHENFACEDWITHTHEINTERTEMPORALBUDGETCONSTRAINTWH11005C0H11001P1C1,THEINDIVIDUALWILLMAXIMIZEUTILITYBYCHOOSINGTOCONSUMEC0CURRENTLYANDC1INTHENEXTPERIODAFALLINP1ANINCREASEINTHERATEOFRETURN,RWILLCAUSEC1TORISE,BUTTHEEFFECTONC0ISINDETERMINATEBECAUSESUBSTITUTIONANDINCOMEEFFECTSOPERATEINOPPOSITEDIRECTIONSASSUMINGTHATBOTHC0ANDC1ARENORMALGOODSFUTURECONSUMPTIONC1CURRENTCONSUMPTIONC0WH11005C0H11001P1C1U2U1U0W/P1C1C0WFIGURE232YIELDSTHEFOLLOWINGLAGRANGIANEXPRESSIONH5112H11005UC0,C1H11001H9261H20900WH11002C0H11002H20901,2313ANDTHERSTORDERCONDITIONSFORAMAXIMUMAREH11005UH11032C0H11002H9261H1100502314H11005UH11032C1H11002H50071H11001H9261RH5007H110050H11005WH11002C0H11002H110050DIVIDINGTHERSTANDSECONDOFTHESEANDREARRANGINGTERMSGIVES4UH11032C0H11005H500711H11001H11001H9254RH5007UH11032C12315BECAUSETHEUTILITYFUNCTIONFORCONSUMPTIONWASASSUMEDTOBETHESAMEINTWOPERIODS,WECANCONCLUDETHATC0H11005C1IFRH11005H9254,THATC0H11022C1IFH9254H11022RTOOBTAINUH11032C0H11021UH11032C1REQUIRESC0H11022C1,ANDTHATC0H11021C1FORRH11022H9254WHETHERTHISINDIVIDUALSCONSUMPTIONINCREASESORDECREASESFROMPERIOD0TOPERIOD1WILLTHEREFOREDEPENDONEXACTLYHOWIMPATIENTHEORSHEISALTHOUGHACONSUMERMAYHAVEAPREFERENCEFORPRESENTGOODSH9254H110220,HEORSHEMAYSTILLCONSUMEMOREINTHEFUTURETHANINTHEPRESENTIFTHERATEOFRETURNRECEIVEDONSAVINGSISHIGHENOUGHQUERYIFTWOINDIVIDUALSAREEQUALLYIMPATIENTBUTFACEDIFFERENTRATESOFRETURN,WHICHWILLEXHIBITTHEGREATESTINCREASEOFC1OVERC0EFFECTSOFCHANGESINRACOMPARATIVESTATICSANALYSISOFTHEEQUILIBRIUMILLUSTRATEDINFIGURE232ISSTRAIGHTFORWARDIFP1FALLSTHATIS,IFRRISES,BOTHINCOMEANDSUBSTITUTIONEFFECTSWILLCAUSEMOREC1TOBEDEMANDED,EXCEPTINTHEUNLIKELYEVENTTHATC1ISANINFERIORGOODHENCE,THEDEMANDCURVEFORC1WILLBEDOWNWARDSLOPINGANINCREASEINREFFECTIVELYLOWERSTHEPRICEOFC1,ANDCONSUMPTIONOFTHATGOODTHEREBYINCREASESTHISDEMANDCURVEISLABELEDDINFIGURE233BEFORELEAVINGOURDISCUSSIONOFINDIVIDUALSINTERTEMPORALDECISIONS,WESHOULDPOINTOUTTHATOURANALYSISDOESNOTPERMITANUNAMBIGUOUSSTATEMENTTOBEMADEABOUTTHESIGNOFH11128C0/H11128P1INFIGURE232SUBSTITUTIONANDINCOMEEFFECTSWORKINOPPOSITEDIRECTIONS,ANDNODENITEPREDICTIONISPOSSIBLEAFALLINP1WILLCAUSETHEINDIVIDUALTOSUBSTITUTEC1FORC0INHISORHERCONSUMPTIONPLANSBUTTHEFALLINP1RAISESTHEREALVALUEOFWEALTH,ANDTHEINCOMEEFFECTCAUSESBOTHC0ANDC1TOINCREASEPHRASEDSOMEWHATDIFFERENTLY,THEMODELILLUSTRATEDINFIGURE232DOESNOTPERMITADENITEPREDICTIONABOUTHOWCHANGESINTHERATEOFRETURNAFFECTC1H50071H11001RH11128H5112H5007H11128H92611H50071H11001H9254H11128H5112H5007H11128C1H11128H5112H5007H11128C0C1H50071H11001RCHAPTER23CAPITAL6314EQUATION2315ISSOMETIMESCALLEDTHE“EULEREQUATION”FORINTERTEMPORALUTILITYMAXIMIZATIONONCEASPECICUTILITYFUNCTIONISDENED,THEEQUATIONSHOWSHOWCONSUMPTIONCHANGESOVERTIMECURRENTPERIODWEALTHACCUMULATIONSAVINGAHIGHERRPRODUCESSUBSTITUTIONEFFECTSTHATFAVORMORESAVINGANDINCOMEEFFECTSTHATFAVORLESSULTIMATELY,THEREFORE,THEDIRECTIONOFTHEEFFECTISANEMPIRICALQUESTIONSUPPLYOFFUTUREGOODSINONESENSETHEANALYSISOFTHESUPPLYOFFUTUREGOODSISQUITESIMPLEWECANARGUETHATANINCREASEINTHERELATIVEPRICEOFFUTUREGOODSP1WILLINDUCERMSTOPRODUCEMOREOFTHEM,BECAUSETHEYIELDFROMDOINGSOISNOWGREATERTHISREACTIONISREECTEDINTHEPOSITIVELYSLOPEDSUPPLYCURVESINFIGURE233ITMIGHTBEEXPECTEDTHAT,ASINOURPREVIOUSPERFECTLYCOMPETITIVEANALYSIS,THISSUPPLYCURVEREECTSTHEINCREASINGMARGINALCOSTSORDIMINISHINGRETURNSRMSEXPERIENCEWHENATTEMPTINGTOTURNPRESENTGOODSINTOFUTUREONESTHROUGHCAPITALACCUMULATIONUNFORTUNATELY,DELVINGDEEPERINTOTHENATUREOFCAPITALACCUMULATIONRUNSINTOCOMPLICATIONSTHATHAVEOCCUPIEDECONOMISTSFORHUNDREDSOFYEARS5BASICALLY,ALLOFTHESEDERIVEFROMPROBLEMSINDEVELOPINGATRACTABLEMODELOFTHECAPITALACCUMULATIONPROCESSFOROURMODELOFINDIVIDUALBEHAVIORTHISPROBLEMDIDNOTARISE,BECAUSEWECOULDASSUMETHATTHE“MARKET”QUOTEDARATEOFRETURNTOINDIVIDUALSSOTHEYCOULDADAPTTHEIRBEHAVIORTOITWESHALLALSOFOLLOWTHISROUTEWHENDESCRIBINGRMSINVESTMENTDECISIONSLATERINTHISCHAPTERBUTTODEVELOPAN632PARTVIIPRICINGININPUTMARKETSDETERMINATIONOFTHEEQUILIBRIUMPRICEOFFUTUREGOODSTHEPOINTP1,C1REPRESENTSANEQUILIBRIUMINTHEMARKETFORFUTUREGOODSTHEEQUILIBRIUMPRICEOFFUTUREGOODSDETERMINESTHERATEOFRETURNVIAEQUATION2316FUTURECONSUMPTIONC1PRICEP1C1P1DDSSFIGURE2335FORADISCUSSIONOFSOMEOFTHISDEBATE,SEEMBLAUG,ECONOMICTHEORYINRETROSPECT,REVEDHOMEWOOD,ILRICHARDDIRWIN,1978,CHAPTER12ADEQUATEMODELOFCAPITALACCUMULATIONBYRMS,WEMUSTDESCRIBEPRECISELYHOWC0IS“TURNEDINTO”C1,ANDTODOSOWOULDTAKEUSTOOFARAELDINTOTHEINTRICACIESOFCAPITALTHEORYINSTEAD,WEWILLBECONTENTTODRAWTHESUPPLYCURVEINFIGURE233WITHAPOSITIVESLOPEONTHEPRESUMPTIONTHATSUCHASHAPEISINTUITIVELYREASONABLEMUCHOFTHESUBSEQUENTANALYSISINTHISCHAPTERMAYSERVETOCONVINCETHEREADERTHATTHISISINDEEDTHECASEEQUILIBRIUMPRICEOFFUTUREGOODSEQUILIBRIUMINTHEMARKETSHOWNINFIGURE233ISATP1,C1ATTHATPOINTINDIVIDUALSSUPPLYANDDEMANDFORFUTUREGOODSAREINBALANCE,ANDTHEREQUIREDAMOUNTOFCURRENTGOODSWILLBEPUTINTOCAPITALACCUMULATIONTOPRODUCEC1INTHEFUTURE6THEREAREANUMBEROFREASONSTOEXPECTTHATP1WILLBELESSTHAN1THATIS,ITWILLCOSTLESSTHANTHESACRICEOFONECURRENTGOODTO“BUY”ONEGOODINTHEFUTUREASWESHOWEDINEXAMPLE231,ITMIGHTBEARGUEDTHATINDIVIDUALSREQUIRESOMEREWARDFORWAITINGEVERYDAYADAGES“ABIRDINTHEHANDISWORTHTWOINTHEBUSH,”“LIVEFORTODAY”ANDMORESUBSTANTIALREALITIESTHEUNCERTAINTYOFTHEFUTUREANDTHENITENESSOFLIFESUGGESTTHATINDIVIDUALSAREGENERALLYIMPATIENTINTHEIRCONSUMPTIONDECISIONSHENCE,CAPITALACCUMULATIONSUCHASTHATSHOWNINFIGURE233WILLTAKEPLACEONLYIFTHECURRENTSACRICEISINSOMEWAYWORTHWHILETHEREAREALSOSUPPLYREASONSFORBELIEVINGP1WILLBELESSTHAN1ALLOFTHESEINVOLVETHEIDEATHATCAPITALACCUMULATIONIS“PRODUCTIVE”SACRICINGONEGOODTODAYWILLYIELDMORETHANONEGOODINTHEFUTURESOMESIMPLEEXAMPLESOFTHEPRODUCTIVITYOFCAPITALINVESTMENTAREPROVIDEDBYSUCHPASTORALACTIVITIESASTHEGROWINGOFTREESORTHEAGINGOFWINEANDCHEESETREENURSERYOWNERSANDVINEYARDANDDAIRYOPERATORS“ABSTAIN”FROMSELLINGTHEIRWARESINTHEBELIEFTHATTIMEWILLMAKETHEMMOREVALUABLEINTHEFUTUREALTHOUGHITISOBVIOUSTHATCAPITALACCUMULATIONINAMODERNINDUSTRIALSOCIETYISMORECOMPLEXTHANGROWINGTREESCONSIDERBUILDINGASTEELMILLORANELECTRICPOWERSYSTEM,ECONOMISTSBELIEVETHETWOPROCESSESHAVECERTAINSIMILARITIESINBOTHCASESINVESTINGCURRENTGOODSMAKESTHEPRODUCTIONPROCESSLONGERANDMORECOMPLEXANDTHEREFOREIMPROVESTHEOVERALLPRODUCTIVEPOWEROFOTHERRESOURCESUSEDINPRODUCTIONTHEEQUILIBRIUMRATEOFRETURNWECANNOWDENETHERELATIONSHIPOFTHERATEOFRETURNRTOWHATWEHAVECALLEDTHEPRICEOFFUTUREGOODSBYTHEFORMULAP1H110052316BECAUSEWEBELIEVETHATP1WILLBELESSTHAN1,THERATEOFRETURNRWILLBEPOSITIVEFOREXAMPLE,IFP1H110059,RWILLEQUALAPPROXIMATELY11,ANDWEWOULDSAYTHATTHERATEOFRETURNTOCAPITALACCUMULATIONIS“11PERCENT”BYWITHHOLDINGONEUNITOFCURRENTCONSUMPTION,THECONSUMPTIONOFFUTUREGOODSCANBEINCREASEDBY1111H50071H11001RCHAPTER23CAPITAL6336THISISAMUCHSIMPLIEDFORMOFANANALYSISORIGINALLYPRESENTEDBYIFISHER,THERATEOFINTERESTNEWYORKMACMILLAN,1907THERATEOFRETURNANDP1AREEQUIVALENTWAYSOFMEASURINGTHETERMSONWHICHPRESENTGOODSCANBETURNEDINTOFUTUREGOODSRATEOFRETURN,REALINTERESTRATES,ANDNOMINALINTERESTRATESTHECONCEPTOFTHERATEOFRETURNWEHAVEBEENANALYZINGSOFARINTHISCHAPTERISSOMETIMESUSEDSYNONYMOUSLYWITHTHERELATEDCONCEPTOFTHE“REAL”INTERESTRATEINTHISCONTEXT,BOTHARETAKENTOREFERTOTHEREALRETURNTHATISAVAILABLEFROMCAPITALACCUMULATIONTHISCONCEPTMUSTBEDIFFERENTIATEDFROMTHENOMINALINTERESTRATEACTUALLYAVAILABLEINNANCIALMARKETSSPECICALLY,IFOVERALLPRICESAREEXPECTEDTOINCREASEBYPH11080EBETWEENTWOPERIODSTHATIS,APH11080EOF10WOULDBEA10PERCENTINATIONRATE,WEWOULDEXPECTTHENOMINALINTERESTRATERTOBEGIVENBYTHEEQUATION1H11001RH110051H11001R1H11001PH11080E,2317BECAUSEAWOULDBELENDERWOULDEXPECTTOBECOMPENSATEDFORBOTHTHEOPPORTUNITYCOSTOFNOTINVESTINGINREALCAPITALRANDFORTHEGENERALRISEINPRICESPH11080EEXPANSIONOFEQUATION2317YIELDS1H11001RH110051H11001RH11001PH11080EH11001RPH11080E,2318ANDASSUMINGRH11080PH11080EISSMALL,WEHAVETHESIMPLERAPPROXIMATIONRH11005RH11001PH11080E2319IFTHEREALRATEOFRETURNIS4PERCENT04ANDTHEEXPECTEDRATEOFINATIONIS10PERCENT10,THENOMINALINTERESTRATEWOULDBEAPPROXIMATELY14PERCENT14THEDIFFERENCE,THEREFORE,BETWEENOBSERVEDNOMINALINTERESTRATESANDREALINTERESTRATESMAYBESUBSTANTIALININATIONARYENVIRONMENTSTHEFIRMSDEMANDFORCAPITALFIRMSRENTMACHINESINACCORDANCEWITHTHESAMEPRINCIPLESOFPROTMAXIMIZATIONWEDERIVEDINCHAPTER21SPECICALLY,INAPERFECTLYCOMPETITIVEMARKETTHERMWILLCHOOSETOHIRETHATNUMBEROFMACHINESFORWHICHTHEMARGINALREVENUEPRODUCTISPRECISELYEQUALTOTHEIRMARKETRENTALRATEINTHISSECTIONWERSTINVESTIGATETHEDETERMINANTSOFTHISMARKETRENTALRATE,ANDWEASSUMETHATALLMACHINESARERENTEDLATERINTHESECTION,BECAUSEMOSTRMSBUYMACHINESANDHOLDTHEMUNTILTHEYDETERIORATERATHERTHANRENTTHEM,WESHALLEXAMINETHEPARTICULARPROBLEMSRAISEDBYSUCHOWNERSHIPDETERMINANTSOFMARKETRENTALRATESCONSIDERARMINTHEBUSINESSOFRENTINGMACHINESTOOTHERRMSSUPPOSETHERMOWNSAMACHINESAY,ACARORABACKHOETHATHASACURRENTMARKETPRICEOFPHOWMUCHWILLTHERMCHARGEITSCLIENTSFORTHEUSEOFTHEMACHINETHEOWNEROFTHEMACHINEFACESTWOKINDSOFCOSTSDEPRECIATIONONTHEMACHINEANDTHEOPPORTUNITYCOSTOFHAVINGITSFUNDSTIEDUPINAMACHINERATHERTHANINANINVESTMENTEARNINGTHECURRENTAVAILABLERATEOFRETURNIFITISASSUMEDTHATDEPRECIATIONCOSTSPERPERIODAREACONSTANTPERCENTAGEDOFTHEMACHINESMARKETPRICEANDTHAT634PARTVIIPRICINGININPUTMARKETSTHEREALINTERESTRATEISGIVENBYR,THETOTALCOSTSTOTHEMACHINEOWNERFORONEPERIODAREGIVENBYPDH11001PRH11005PRH11001D2320IFWEASSUMETHEMACHINERENTALMARKETISPERFECTLYCOMPETITIVE,NOLONGRUNPROFITSCANBEEARNEDBYRENTINGMACHINESTHEWORKINGSOFTHEMARKETWILLENSURETHATTHERENTALRATEPERPERIODFORTHEMACHINEVISEXACTLYEQUALTOTHECOSTSOFTHEMACHINEOWNERHENCEWEHAVETHEBASICRESULTTHATVH11005PRH11001D2321THECOMPETITIVERENTALRATEISTHESUMOFFOREGONEINTERESTANDDEPRECIATIONCOSTSTHEMACHINESOWNERMUSTPAYFOREXAMPLE,SUPPOSETHEREALINTERESTRATEIS5PERCENTTHATIS,005ANDTHEPHYSICALDEPRECIATIONRATEIS15PERCENT015SUPPOSEALSOTHATTHE