曼昆《宏观经济学》(第五版)课堂讲义PPT(英文)Ch07优质PPT.ppt

曼昆《宏观经济学》(第五版)课堂讲义PPT(英文)Ch07优质PPT.ppt

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ChapterSevenAPowerPointTutorialtoAccompanymacroeconomics,5thed.N.GregoryMankiwMannigJ.SimidianCHAPTERSEVENEconomicGrowthI1ChapterSevenTheSolowGrowthModelisdesignedtoshowhowgrowthinthecapitalstock,growthinthelaborforce,andadvancesintechnologyinteractinaneconomy,andhowtheyaffectanationstotaloutputofgoodsandservices.Letsnowexaminehowthemodeltreatstheaccumulationofcapital.2ChapterSeven3ChapterSevenTheproductionfunctionrepresentsthetransformationofinputs（labor（L）,capital（K）,productiontechnology）intooutputs（finalgoodsandservicesforacertaintimeperiod）.Thealgebraicrepresentationis:

@#@Y=F（K,L）TheProductionFunctionIncomeIncomeisissomefunctionofsomefunctionofourgiveninputsourgiveninputsLetsanalyzethesupplyanddemandforgoods,andseehowmuchoutputisproducedatanygiventimeandhowthisoutputisallocatedamongalternativeuses.KeyAssumption:

@#@TheProductionFunctionhasconstantreturnstoscale.zzz4ChapterSevenThisassumptionletsusanalyzeallquantitiesrelativetothesizeofthelaborforce.Setz=1/L.Y/L=F（K/L,1）OutputOutputPerworkerPerworkerisissomefunctionofsomefunctionoftheamountoftheamountofcapitalperworkercapitalperworkerConstantreturnstoscaleimplythatthesizeoftheeconomyasmeasuredbythenumberofworkersdoesnotaffecttherelationshipbetweenoutputperworkerandcapitalperworker.So,fromnowon,letsdenoteallquantitiesinperworkertermsinlowercaseletters.Hereisourproductionfunction:

@#@,wheref（k）=F（k,1）.y=f（k）5ChapterSevenMPK=f（kk+1）f（kk）ykf（k）Theproductionfunctionshowshowtheamountofcapitalperworkerkdeterminestheamountofoutputperworkery=f（k）.Theslopeoftheproductionfunctionisthemarginalproductofcapital:

@#@ifkincreasesby1unit,yincreasesbyMPKunits.1MPK6ChapterSevenconsumptionconsumptionperworkerperworkerdependsdependsononsavingssavingsraterate（between0and1）（between0and1）OutputOutputperworkerperworkerconsumptionconsumptionperworkerperworkerinvestmentinvestmentperworkerperworkery=c+i1）c=（1-s）y2）y=（1-s）y+i3）4）i=syInvestment=savings.Therateofsavingssisthefractionofoutputdevotedtoinvestment.7ChapterSevenHerearetwoforcesthatinfluencethecapitalstock:

@#@Investment:

@#@expenditureonplantandequipment.Depreciation:

@#@wearingoutofoldcapital;@#@causescapitalstocktofall.Recallinvestmentperworkeri=ssy.Letssubstitutetheproductionfunctionfory,wecanexpressinvestmentperworkerasafunctionofthecapitalstockperworker:

@#@i=ssf（kk）Thisequationrelatestheexistingstockofcapitalktotheaccumulationofnewcapitali.8ChapterSevenInvestment,sf（k）Output,f（k）c（perworker）i（perworker）y（perworker）Thesavingratesdeterminestheallocationofoutputbetweenconsumptionandinvestment.Foranylevelofk,outputisf（k）,investmentissf（k）,andconsumptionisf（k）sf（k）.yk9ChapterSevenImpactofinvestmentanddepreciationonthecapitalstock:

@#@DDkk=iddkChangeinCapitalStockInvestmentDepreciationRememberinvestmentequalssavingsso,itcanbewritten:

@#@DDk=ssf（kk）ddkddkkkddkDepreciationisthereforeproportionaltothecapitalstock.10ChapterSevenInvestmentandDepreciationCapitalperworker,kki*=ddkk*kk*kk1kk2Atkk*,investmentequalsdepreciationandcapitalwillnotchangeovertime.Belowk*,investmentexceedsdepreciation,sothecapitalstockgrows.Investment,ssf（kk）Depreciation,ddkkAbovek*,depreciationexceedsinvestment,sothecapitalstockshrinks.11ChapterSevenInvestmentandDepreciationCapitalperworker,kki*=ddkk*kk11*kk2*Depreciation,ddkkInvestment,ss11f（kk）Investment,ss2f（kk）TheSolowModelshowsthatifthesavingrateishigh,theeconomywillhavealargecapitalstockandhighlevelofoutput.Ifthesavingrateislow,theeconomywillhaveasmallcapitalstockandalowlevelofoutput.Anincreaseinthesavingratecausesthecapitalstocktogrowtoanewsteadystate.12ChapterSevenThesteady-statevalueofkthatmaximizesconsumptioniscalledtheGoldenRuleLevelofCapital.Tofindthesteady-stateconsumptionperworker,webeginwiththenationalincomeaccountsidentity:

@#@andrearrangeitas:

@#@c=y-i.Thisequationholdsthatconsumptionisoutputminusinvestment.Becausewewanttofindsteady-stateconsumption,wesubstitutesteady-statevaluesforoutputandinvestment.Steady-stateoutputperworkerisf（k*）wherek*isthesteady-statecapitalstockperworker.Furthermore,becausethecapitalstockisnotchanginginthesteadystate,investmentisequaltodepreciationdk*.Substitutingf（k*）foryanddk*fori,wecanwritesteady-stateconsumptionperworkerasc*=f（k*）-dk*.y-c+i13ChapterSevenc*=f（k*）-dk*.Accordingtothisequation,steady-stateconsumptioniswhatsleftofsteady-stateoutputafterpayingforsteady-statedepreciation.Itfurthershowsthatanincreaseinsteady-statecapitalhastwoopposingeffectsonsteady-stateconsumption.Onthe