宏观经济学-我是宏经课件ing卢老师chap

MACROECONOMICS©2010WorthPublishers,allrightsreservedSEVENTHEDITIONPowerPoint®SlidesbyRonCronovichN.GregoryMankiwCHAPTEREconomicGrowthI:

CapitalAccumulationandPopulationGrowth7ModifiedforEC204byBobMurphyInthischapter,youwilllearn:theclosedeconomySolowmodel

封闭经济中的索洛模型howacountry’sstandardoflivingdependsonitssavingandpopulationgrowthrates

一个国家的生活水平如何依赖于储蓄和人口增长率howtousethe“GoldenRule”tofindtheoptimalsavingrateandcapitalstock

如何利用“黄金律”来找出最优的储蓄率以及资本存量水平3CHAPTER7

EconomicGrowthIWhygrowthmatters

为什么增长重要Dataoninfantmortalityrates:婴儿死亡率数据20%inthepoorest1/5ofallcountries最贫穷的1/5国家中为20%0.4%intherichest1/5最富的1/5国家为0.4%InPakistan,85%ofpeopleliveonlessthan$2/day.在巴基斯坦，有85%的人依靠每天2美元存活。One-fourthofthepoorestcountrieshavehadfaminesduringthepast3decades.过去三十年中，在最穷的1/4国家中有过饥荒Povertyisassociatedwithoppressionofwomenandminorities.贫穷和镇压妇女和少数民族有关联

Economicgrowthraiseslivingstandardsandreducespoverty….经济增长提升生活水平以及减少贫穷eandpovertyintheworld

selectedcountries,2000MadagascarIndiaBangladeshNepalBotswanaMexicoChileS.KoreaBrazilRussianFederationThailandPeruChinaKenyalinkstopreparedgraphs@notes:circlesizeisproportionaltopopulationsize,

colorofcircleindicatescontinent,press“play”onbottomtoseethecrosssectiongraphevolveovertime,clickhereforoneinstructionguideepercapitaandLifeexpectancyInfantmortalityMalariadeathsper100,000AdultliteracyCellphoneusersper100,0006CHAPTER7

EconomicGrowthIWhygrowthmattersAnythingthateffectsthelong-runrateofeconomicgrowth–evenbyatinyamount–willhavehugeeffectsonlivingstandardsinthelongrun.任何对经济的长期增长率有影响的因素（即使只有非常小的影响），都将会对长期的生活水平产生重大的影响。1,081.4%243.7%85.4%624.5%169.2%64.0%2.5%2.0%…100years…50years…25yearspercentageincreasein

standardoflivingafter…annualgrowthrateofepercapita人均收入年增长率7CHAPTER7

EconomicGrowthIWhygrowthmattersIftheannualgrowthrateofU.S.realGDPpercapitahadbeenjustone-tenthofonepercenthigherduringthe1990s,theU.S.wouldhavegeneratedanadditional$496billionofe

duringthatdecade.如果美国在90年代的人均实际GDP年增长率只比当时实际情况高千分之一，那么美国近十年来将会产生额外的4960亿美元收入。8CHAPTER7

EconomicGrowthIThelessonsofgrowththeory增长理论的研究…canmakeapositivedifferenceinthelivesofhundredsofmillionsofpeople.能够对数以百万计的人的生活产生积极的影响Theselessonshelpusunderstandwhypoorcountriesarepoor理解为什么穷国会穷designpoliciesthatcanhelpthemgrow制定出帮助其增长的政策learnhowourowngrowthrateisaffectedbyshocksandourgovernment’spolicies认识冲击以及政府政策如何影响增长率9CHAPTER7

EconomicGrowthITheSolowmodel索洛模型duetoRobertSolow,wonNobelPrizeforcontributionstothestudyofeconomicgrowth

由于罗伯特索洛对经济增长的贡献而赢得了诺贝尔奖amajorparadigm:widelyusedinpolicymaking广泛地运用于政策制定benchmarkagainstwhichmostrecentgrowththeoriesarecompared近年来的增长理论比较的基准looksatthedeterminantsofeconomicgrowthandthestandardoflivinginthelongrun观察长期经济增长和生活水平的决定因素10CHAPTER7

EconomicGrowthIHowSolowmodelisdifferentfromChapter3’smodel索洛模型和第三章的模型有哪些不同1.

Kisnolongerfixed:K不再固定不变

investmentcausesittogrow,投资导致K增长

depreciationcausesittoshrink折旧导致K减少2.

Lisnolongerfixed:L不再是固定不变

populationgrowthcausesittogrow人口增长导致L增长3. theconsumptionfunctionissimpler消费函数更加简单11CHAPTER7

EconomicGrowthIHowSolowmodelisdifferentfromChapter3’smodel4.

noGorT没有G和T

(onlytosimplifypresentation;

wecanstilldofiscalpolicyexperiments)5.

cosmeticdifferences形式上的差异12CHAPTER7

EconomicGrowthITheproductionfunction生产函数Inaggregateterms总量形式:Y=F(K,L)Define:y=Y/L=outputperworker人均产出

k=K/L=capitalperworker人均资本量Assumeconstantreturnstoscale:规模报酬不变

zY=F(zK,zL)foranyz>0Pickz=1/L.ThenY/L=F(K/L,1)y=F(k,1)y=f(k) wheref(k)=F(k,1)13CHAPTER7

EconomicGrowthITheproductionfunctionOutputper

worker,y

Capitalper

worker,k

f(k)Note:thisproductionfunctionexhibitsdiminishingMPK.1MPK=f(k+1)–f(k)14CHAPTER7

EconomicGrowthIThenationaleidentity国民收入恒等式Y=C+I (remember,noG)In“perworker”terms:

y=c+i

wherec=C/Landi=I

/L

15CHAPTER7

EconomicGrowthITheconsumptionfunction消费函数s=thesavingrate,储蓄率

thefractionofethatissaved(sisanexogenousparameter) Note:sistheonlylowercasevariablethat

isnotequalto

itsuppercaseversiondividedbyL储蓄率S是唯一的小写形式不代表大写形式除以L的变量Consumptionfunction:c=(1–s)y

(perworker)16CHAPTER7

EconomicGrowthISavingandinvestment储蓄和投资saving(perworker) =y–c =y–(1–s)y =syNationaleidentityisy=c+i Rearrangetoget:i=y–c=sy (investment=saving,likeinchap.3!)Usingtheresultsabove,

i=sy=sf(k)17CHAPTER7

EconomicGrowthIOutput,consumption,andinvestment

产出，消费和投资Outputper

worker,y

Capitalper

worker,k

f(k)sf(k)k1

y1

i1

c1

18CHAPTER7

EconomicGrowthIDepreciation折旧Depreciationperworker,k

Capitalper

worker,k

δk=therateofdepreciation=thefractionofthecapitalstockthatwearsouteachperiod1δ19CHAPTER7

EconomicGrowthICapitalaccumulation资本积累Changeincapitalstock =investment–depreciation k =i –k Sincei=sf(k),thises:k=s

f(k)

–k

Thebasicidea:Investmentincreasesthecapitalstock,depreciationreducesit.投资增加资本存量，折旧减少资本存量20CHAPTER7

EconomicGrowthITheequationofmotionfork资本存量的变动方程TheSolowmodel’scentralequation索洛模型的核心方程Determinesbehaviorofcapitalovertime…决定了资本的长期性状…which,inturn,determinesbehaviorofalloftheotherendogenousvariablesbecausetheyalldependonk.这又决定了其他所有内生变量的性状，因为它们都取决于kE.g.,eperperson:y=f(k) consumptionperperson: c=(1–s)f(k)k=s

f(k)

–k

21CHAPTER7

EconomicGrowthIThesteadystate稳定状态Ifinvestmentisjustenoughtocoverdepreciation

[sf(k)

=k],如果投资刚好可以弥补折旧thencapitalperworkerwillremainconstant:

k=0.

那么每个工人拥有的资本量保持不变

Thisoccursatonevalueofk,denotedk*,calledthesteadystatecapitalstock.此时，k*是一个常量，称为稳定状态的资本存量.k=s

f(k)

–k

22CHAPTER7

EconomicGrowthIThesteadystateInvestmentanddepreciationCapitalper

worker,k

sf(k)δkk*

23CHAPTER7

EconomicGrowthIMovingtowardthesteadystate向稳定状态变动Investmentanddepreciation投资和折旧

Capitalper

worker,k

sf(k)kk*

k=sf(k)-kdepreciationkk1investment24CHAPTER7

EconomicGrowthIMovingtowardthesteadystateInvestmentanddepreciationCapitalper

worker,k

sf(k)kk*

k1k=sf(k)-kkk225CHAPTER7

EconomicGrowthIMovingtowardthesteadystateInvestmentanddepreciationCapitalper

worker,k

sf(k)kk*

k=sf(k)-kk2investmentdepreciationk26CHAPTER7

EconomicGrowthIMovingtowardthesteadystateInvestmentanddepreciationCapitalper

worker,k

sf(k)kk*

k=sf(k)-kkk227CHAPTER7

EconomicGrowthIMovingtowardthesteadystateInvestmentanddepreciationCapitalper

worker,k

sf(k)kk*

k=sf(k)-kk2kk328CHAPTER7

EconomicGrowthIMovingtowardthesteadystateInvestmentanddepreciationCapitalper

worker,k

sf(k)kk*

k=sf(k)-kk3Summary:

Aslongask<k*,investmentwillexceeddepreciation,

andkwillcontinuetogrowtowardk*.只要k<k*,投资大于折旧，k将继续增加直到等于k*NOWYOUTRY:现在你来试一试：

Approachingk*fromabove大于k*趋向稳定状态DrawtheSolowmodeldiagram,labelingthesteadystatek*.画出索洛模型图，标出稳定状态k*Onthehorizontalaxis,pickavaluegreaterthank*fortheeconomy’sinitialcapitalstock.Labelitk1.在横轴，找出大于k*的一个值作为经济的初始资本存量，标为

k1Showwhathappenstokovertime.Doeskmovetowardthesteadystateorawayfromit?看随着时间的变化k发生什么变化。K是朝着稳定状态移动还是偏离稳定状态？30CHAPTER7

EconomicGrowthIAnumericalexample一个数字例子Productionfunction(aggregate):生产函数（总体）Toderivetheper-workerproductionfunction,dividethroughbyL:为得到人均生产函数，两边都除以LThensubstitutey=Y/Landk=K/Ltoget31CHAPTER7

EconomicGrowthIAnumericalexample,cont.Assume:s=0.3=0.1initialvalueofk=4.032CHAPTER7

EconomicGrowthIApproachingthesteadystate:

Anumericalexample接近稳定状态:一个数字例子Year

k

y

c

i

k

Dk1 4.000 2.000 1.400 0.600 0.400 0.2002 4.200 2.049 1.435 0.615 0.420 0.1953 4.395 2.096 1.467 0.629 0.440 0.1894 4.584 2.141 1.499 0.642 0.458 0.184…10 5.602 2.367 1.657 0.710 0.560 0.150…25 7.351 2.706 1.894 0.812 0.732 0.080…100 8.962 2.994 2.096 0.898 0.896 0.002…

9.000 3.000 2.100 0.900 0.900 0.000NOWYOUTRY:练习

SolvefortheSteadyState求解稳定状态

Continuetoassume

s=0.3,=0.1,andy=k1/2Usetheequationofmotion

k=sf(k)-k

tosolveforthesteady-statevaluesofk,y,andc.来求解稳定状态下的k,y,c.

ANSWERS:答案

SolvefortheSteadyState35CHAPTER7

EconomicGrowthIAnincreaseinthesavingrate储蓄率提高Investment

and

depreciationkdks1f(k)Anincreaseinthesavingrateraisesinvestment…储蓄率提高将增加投资……causingktogrowtowardanewsteadystate:促使资本存量达到一个新的高度:s2f(k)36CHAPTER7

EconomicGrowthIPrediction:Highershigherk*.Andsincey=f(k),

higherk*highery*.Thus,theSolowmodelpredictsthatcountrieswithhigherratesofsavingandinvestment

willhavehigherlevelsofcapitalandeperworkerinthelongrun.因此，Solow模型预言：从长期看，如果一国有更高的储蓄率和投资，则将有更高的人均资本存量水平和收入水平Internationalevidenceoninvestmentratesandeperperson投资率与人均收入的国际证据

eperpersonin2003

(logscale)Investmentaspercentageofoutput

(average1960-2003)38CHAPTER7

EconomicGrowthITheGoldenRule:Introduction黄金规则：简介Differentvaluesofsleadtodifferentsteadystates.Howdoweknowwhichisthe“best”steadystate?不同的s值有不同的稳定状态.哪个是“最优”的稳定状态呢?The“best”steadystatehasthehighestpossible

consumptionperperson:c*=(1–s)f(k*).最优的稳定状态有最高的人均消费水平Anincreaseinsleadstohigherk*andy*,whichraisesc*引致更高的k*，y*，c*可能随之升高reducesconsumption’sshareofe(1–s),whichlowersc*.消费占收入的比例(1–s)降低，则可能导致c*降低So,howdowefindthesandk*thatmaximizec*?因此，需要选择s和k*，以使c*最大化39CHAPTER7

EconomicGrowthITheGoldenRulecapitalstock

资本的黄金规则水平theGoldenRulelevelofcapital,资本的黄金规则水平

thesteadystatevalueofkthatmaximizesconsumption.最大化消费水平的稳定状态的k值.Tofindit,firstexpressc*intermsofk*: c* =y* -i* =f

(k*)-i*

=f

(k*)-

k*

Inthesteadystate: i*

=

k*becausek=0.40CHAPTER7

EconomicGrowthIThen,graph

f(k*)andk*,

lookforthe

pointwhere

thegapbetweenthemisbiggest.TheGoldenRulecapitalstocksteadystateoutputanddepreciationsteady-statecapitalper

worker,k*

f(k*)δ

k*41CHAPTER7

EconomicGrowthITheGoldenRulecapitalstockc*=f(k*)-

k*

isbiggestwheretheslopeoftheproductionfunction

equals

theslopeofthedepreciationline:steady-statecapitalper

worker,k*

f(k*)

k*MPK=

42CHAPTER7

EconomicGrowthIThetransitiontothe

GoldenRulesteadystate

向黄金规则稳定状态的过渡TheeconomydoesNOThaveatendencytomovetowardtheGoldenRulesteadystate.经济体系没有向黄金规则稳定状态移动的自发趋势AchievingtheGoldenRulerequiresthatpolicymakersadjusts.要达到黄金规则，要求政策制定者调整储蓄率s.Thisadjustmentleadstoanewsteadystatewithhigherconsumption.这种调整导致更高消费水平的新的稳定状态.Butwhathappenstoconsumption

duringthetransitiontotheGoldenRule?但在这个过渡中，将如何影响消费水平呢?43CHAPTER7

EconomicGrowthIStartingwithtoomuchcapital

从资本过多开始thenincreasingc*requiresafallins.消费c*增加要求储蓄s降低.InthetransitiontotheGoldenRule,consumptionishigheratallpointsintime.在向黄金规则的过渡过程中，消费水平都比原来高.timet0ciy44CHAPTER7

EconomicGrowthIStartingwithtoolittlecapital

从资本过少开始thenincreasingc*requiresanincreaseins.要使c*增加必须增加s.Futuregenerations

enjoyhigherconsumption,butthecurrentoneexperiencesaninitialdropinconsumption.将来有较高的消费水平，但最初要减少消费才能达到目的timet0ciy45CHAPTER7

EconomicGrowthIPopulationgrowth人口增长Assumethepopulationandlaborforcegrow

atraten(exogenous):假设人口，亦即劳动力，增长率为n.(n是外生的)EX:SupposeL=1,000inyear1andthepopulationisgrowingat2%peryear(n=0.02).例:假设第1年L=1000，人口增长率为2%/年(n=0.02).ThenL=nL=0.02×1,000=20,

soL=1,020inyear2.46CHAPTER7

EconomicGrowthIBreak-eveninvestment

收支相抵的投资(+n)k=break-eveninvestment,

theamountofinvestmentnecessary

tokeepkconstant.保持人均资本不变的投资Break-eveninvestmentincludes:ktoreplacecapitalasitwearsout弥补资本折旧nktoequipnewworkerswithcapital (Otherwise,kwouldfallastheexistingcapitalstockisspreadmorethinlyoveralargerpopulationofworkers.)为新工人提供人均资本(否则,人口的增长，而资本存量不变或增长较慢，k将会变小)47CHAPTER7

EconomicGrowthITheequationofmotionfork

k的运动方程Withpopulationgrowth,随着人口增长

theequationofmotionforkis:break-eveninvestmentactualinvestmentk=s

f(k)

-

(

+

n)

k48CHAPTER7

EconomicGrowthITheSolowmodeldiagramInvestment,break-eveninvestmentCapitalper

worker,k

sf(k)(

+

n

)

kk*

k

=

sf(k)-(+n)k49CHAPTER7

EconomicGrowthITheimpactofpopulationgrowthInvestment,break-eveninvestmentCapitalper

worker,k

sf(k)(+n1)

kk1*

(+n2)

kk2*

Anincreaseinncausesanincreaseinbreak-eveninvestment,人口增长率n的增加导致补偿投资增加leadingtoalowersteady-statelevelofk.进一步导致稳定状态k的降低50CHAPTER7

EconomicGrowthIPrediction:Highernlowerk*.Andsincey=f(k),

lowerk*lowery*.Thus,theSolowmodelpredictsthatcountrieswithhigherpopulationgrowthrateswillhavelowerlevelsofcapitalandeperworkerinthelongrun.因此，Solow模型预言：从长期看，人口增长率较高的国家，人均资本和收入水平较低.Internationalevidenceonpopulationgrowthandeperperson人口增长率与人均收入的国际证据

eperpersonin2003

(logscale)Populationgrowth

(percentperyear,average1960-2003)52CHAPTER7

EconomicGrowthITheGoldenRulewithpopulationgrowth

人口增长下的黄金规则TofindtheGoldenRulecapitalstock,

expressc*intermsofk*: c* =y* -i* =f

(k*) -(+n)k*

c*ismaximizedwhen

MPK=+n

orequivalently,

MPK-=nIntheGoldenRulesteadystate,themarginalproduct

ofcapitalnetofdepreciationequalsthepopulationgrowthrate.达到黄金规则稳定状态，资本边际产量减去资本折旧率等于人口增长率。53CHAPTER7

EconomicGrowthIAlternativeperspectivesonpopulationgrowth关于人口增长的其他观点TheMalthusianModel(1798)马尔萨斯模型Predictspopulationgrowthwillouts