曼昆《宏观经济学》第五版课堂讲义英文ChPPT课件.ppt

1 CHAPTERSEVENEconomicGrowthI 2 TheSolowGrowthModel TheSolowGrowthModelisdesignedtoshowhowgrowthinthecapitalstock growthinthelaborforce andadvancesintechnologyinteractinaneconomy andhowtheyaffectanation stotaloutputofgoodsandservices Let snowexaminehowthemodeltreatstheaccumulationofcapital 3 TheAccumulationofCapital 4 Theproductionfunctionrepresentsthetransformationofinputs labor L capital K productiontechnology intooutputs finalgoodsandservicesforacertaintimeperiod Thealgebraicrepresentationis Y F K L TheProductionFunction Let sanalyzethesupplyanddemandforgoods andseehowmuchoutputisproducedatanygiventimeandhowthisoutputisallocatedamongalternativeuses 5 ConstantReturnstoScale Thisassumptionletsusanalyzeallquantitiesrelativetothesizeofthelaborforce Setz 1 L Y L F K L 1 Constantreturnstoscaleimplythatthesizeoftheeconomyasmeasuredbythenumberofworkersdoesnotaffecttherelationshipbetweenoutputperworkerandcapitalperworker So fromnowon let sdenoteallquantitiesinperworkertermsinlowercaseletters Hereisourproductionfunction wheref k F k 1 y f k 6 MarginalProductofCapital MPK TheSlopeoftheProductionFunction MPK f k 1 f k Theproductionfunctionshowshowtheamountofcapitalperworkerkdeterminestheamountofoutputperworkery f k Theslopeoftheproductionfunctionisthemarginalproductofcapital ifkincreasesby1unit yincreasesbyMPKunits DiminishingMarginalProductofCapital 7 TheDemandforGoodsandtheConsumptionFunction Investment savings Therateofsavingsisthefractionofoutputdevotedtoinvestment 8 GrowthintheCapitalStockandtheSteadyState Herearetwoforcesthatinfluencethecapitalstock Investment expenditureonplantandequipment Depreciation wearingoutofoldcapital causescapitalstocktofall Thisequationrelatestheexistingstockofcapitalktotheaccumulationofnewcapitali 9 Output ConsumptionandInvestment Thesavingratesdeterminestheallocationofoutputbetweenconsumptionandinvestment Foranylevelofk outputisf k investmentissf k andconsumptionisf k sf k 10 Depreciation Impactofinvestmentanddepreciationonthecapitalstock Dk i dk Rememberinvestmentequalssavingsso itcanbewritten Dk sf k dk Depreciationisthereforeproportionaltothecapitalstock 11 Thelong runequilibriumoftheeconomy InvestmentandDepreciation Capitalperworker k i dk k k1 k2 Atk investmentequalsdepreciationandcapitalwillnotchangeovertime Belowk investmentexceedsdepreciation sothecapitalstockgrows Investment sf k Depreciation dk TheSteadyState k Abovek depreciationexceedsinvestment sothecapitalstockshrinks 12 HowSavingAffectsGrowth InvestmentandDepreciation Capitalperworker k i dk k1 k2 Depreciation dk Investment s1f k Investment s2f k TheSolowModelshowsthatifthesavingrateishigh theeconomywillhavealargecapitalstockandhighlevelofoutput Ifthesavingrateislow theeconomywillhaveasmallcapitalstockandalowlevelofoutput Anincreaseinthesavingratecausesthecapitalstocktogrowtoanewsteadystate 2020 2 4 13 14 TheGoldenRuleLevelofCapital 15 c f k dk Accordingtothisequation steady stateconsumptioniswhat sleftofsteady stateoutputafterpayingforsteady statedepreciation Itfurthershowsthatanincreaseinsteady statecapitalhastwoopposingeffectsonsteady stateconsumption Ontheonehand morecapitalmeansmoreoutput Ontheotherhand morecapitalalsomeansthatmoreoutputmustbeusedtoreplacecapitalthatiswearingout Steady stateConsumption Theeconomy soutputisusedforconsumptionorinvestment Inthesteadystate investmentequalsdepreciation Therefore steady stateconsumptionisthedifferencebetweenoutputf k anddepreciationdk Steady stateconsumptionismaximizedattheGoldenRulesteadystate TheGoldenRulecapitalstockisdenotedk gold andtheGoldenRuleconsumptionisc gold 16 17 PopulationGrowth ThebasicSolowmodelshowsthatcapitalaccumulation alone cannotexplainsustainedeconomicgrowth highratesofsavingleadtohighgrowthtemporarily buttheeconomyeventuallyapproachesasteadystateinwhichcapitalandoutputareconstant Toexplainthesustainedeconomicgrowth wemustexpandtheSolowmodeltoincorporatetheothertwosourcesofeconomicgrowth So let saddpopulationgrowthtothemodel We llassumethatthepopulationandlaborforcegrowataconstantraten 18 TheSteadyStatewithPopulationGrowth Likedepreciation populationgrowthisonereasonwhythecapitalstockperworkershrinks Ifnistherateofpopulationgrowthanddistherateofdepreciation then d n kisbreak eveninvestment whichistheamountnecessarytokeepconstantthecapitalstockperworkerk Fortheeconomytobeinasteadystateinvestmentsf k mustoffsettheeffectsofdepreciationandpopulationgrowth d n k Thisisshownbytheintersectionofthetwocurves Anincreaseinthesavingratecausesthecapitalstocktogrowtoanewsteadystate 19 Anincreaseintherateofpopulationgrowthshiftsthelinerepresentingpopulationgrowthanddepreciationupward Thenewsteadystatehasalowerlevelofcapitalperworkerthantheinitialsteadystate Thus theSolowmodelpredictsthateconomieswithhigherratesofpopulationgrowthwillhavelowerlevelsofcapitalperworkerandthereforelowerincomes TheImpactofPopulationGrowth Anincreaseintherateofpopulationgrowthfromn1ton2reducesthesteady statecapitalstockfromk 1tok 2 20 PopulationGrowth n Thechangeinthecapitalstockperworkeris Dk i d n k Now let ssubstitutesf k fori Dk sf k d n kThisequationshowshownewinvestment depreciation andpopulationgrowthinfluencetheper workercapitalstock Newinvestmentincreasesk whereasdepreciationandpopulationgrowthdecreasek Whenwedidnotincludethe n variableinoursimpleversion wewereassumingaspecialcaseinwhichthepopulationgrowthwas0 21 Inthesteady state thepositiveeffectofinvestmentonthecapitalperworkerjustbalancesthenegativeeffectsofdepreciationandpopulationgrowth Oncetheeconomyisinthesteadystate investmenthastwopurposes Someofit dk replacesthedepreciatedcapital Therest nk providesnewworkerswiththesteadystateamountofcapital Capital perworker k k k TheSteadyS