Krugmanmodel文档格式.docx
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Krugmanmodel文档格式.docx
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Qship*t>
itcostsmoretoshipintothesmallerregionthantobuildafactoryinit.
InthiscaseonefirmmaychoosetosupplyEastwithafactoryinEastandWestwithafactoryinWest.
Oriftherearetwoindependentproducers–StanfieldsandPenmanstextilemills,eachcansurviveinitsownmarketandwillnotshipintotheother.
Krugmanapproach:
Krugmanmodel:
Determinantsofdistributionofmanufacturing:
Willacoreforminoneregion,orwillbothshareinmanufacturing?
mountains
40workerslocatewhereplantslocate.
UsingEquations:
ShareofpopulationintheWest=Sn
ShareofpopulationintheEast=(1-Sn)
Shareofworkers(manufacturing)inWest=Sm
Shareofworkers(manufacturing)intheEast=(1-Sm)
Shareoffarmers(agriculture)inWest=Sa
Shareoffarmers(agriculture)inEast=1-Sa
IfSm=1,allthemanufacturingisinWest,soWestisthecoreandEastisaperipherywith(1-Sm)=0
IfSm=0,noneofthemanufacturingisintheWest,soWestistheperipheryandEastisacorewith(1-Sm)=1
IfSm=.5,manufacturingisevenlydistributedbetweentheWestandEast.Thereisnocoreperipherypattern.
Therelationshipbetweentheshareofthepopulationandtheshareofmanufacturing.
RelationshipbetweenSnandSmcanbeexpressedalgebraically.Theshareofworkersinthepopulationandthedivisionoffarmersbetweentheregionscanbetakenasparametersthatcanbechanged.
π=shareofpopulationwhoareworkers
Sa=shareoffarmersinWest.(KrugmanassumesSa=½
)
Sn=(1-π)*Sa+π*SmTHISISAKEYEQUATION
InWords:
ShareofthepopulationinWest(Sn)equalstheshareoffarmersinthetotalpopulation(1-π)timestheshareoffarmersinWest(Sa)plustheshareofworkersinthetotalpopulation(π)timestheshareofworkersinWest(Sm).
Initialvalues:
Sa=.5;
π=.4
IfWestistheperipherySm=0andgiventheinitialvalues
Sn=(1-.4)*.5+.4*0=.3
Westhas.3ofthepopulation.
IfWestisthecore,Sm=1andgiventheinitialvalues
Sn=(1-.4)*.5+.4*1=.7
NoCorePeripheryPattern
Ifmanufacturingisevenlydistributed,eachuniqueproductwillbeproducedlocally,soeachfirmwillhaveaplantineachregionandnogoodswillbeshippedbetweenregions.Inthatcaseeachregionmanufacturesforitself,andmanufacturingmustbeinproportiontothepopulation.(Rememberinthissimplifiedandartificialworldwehaveassumed,allfirmshaveidenticalfixedcostsandtransportationcostsandconsumptionofgoodsisstrictlyproportionaltopopulation.)
IfWestmanufacturesforitselfonly,thenSm=Sn.ManufacturingproductionmustbegearedtothesizeofWest’spopulation.
Sn=(1-π)*Sa+π*Sm,butSm=Snso
Sn=(1-π)*Sa+π*Sn
Sn-(π*Sn)=(1-π)*Sa
(1-π)*Sn=(1-π)*Sa
Sn=Sa
Thenumberofworkersisproportionatetothenumberoffarmers.Ifeachregionmanufacturesonlyforitself,thentheratioofworkerstofarmersintheentireeconomymustbetheratioineachregion.
TheshareofthepopulationinWestequalsitsshareinagriculture.GivenKrugman’sassumptionofequalagriculturalresources,Sn=.5.
Butifagriculturewerenotevenlydivided,sayWesthad60%ofthefarmers,thenSn=.6whenmanufacturingisequallydivided.
TheKrugmanBox
IfthereisnomanufacturinginWest,Sm=0,thereareonlyfarmersinWest.TheshareofpopulationinWestisthefarmersinWestasashareofthetotalpopulation.AstheshareofmanufacturingincreasesinWest,theshareofpopulationinWestgrowsalongthelinePforpopulation.
WhenWesthasnomanufacturing(Sm=0)Easthasallthemanufacturing.AsWest’sshareofpopulationgrows,East’sshareofpopulationshrinks.WhenSm=1,Easthasonlyfarmersandnomanufacturing.
2.Manufacturingdependsonpopulation
IfthepopulationinWestissmall,becauseithasnomanufacturingthenitmaybethatitwillcostlesstoshipintoWestfromEastthantobuildafactorythere.Sm=0ispossible,andWestcanbeaperiphery.
IfSn<
F/txthenQshiptowest*t<
FCitcostslesstoshipintoWest,Alberta,thantobuildafactoryandproducethere.Sm=0ispossible
IfthepopulationinEastissmall,becauseallthemanufacturingisinWest,thanitmaybethatitwillcostlesstoshipintoEastfromWestthantobuildafactoryinEast.Westcancontinuetohaveallthemanufacturing.Sm=1ispossible,andWestcanbetheCoreandeastcanbetheperiphery.
If1-Sn<
F/txthenQshiptoeast*t<
FCFCitcostslesstoshipintoEast,thantobuildafactoryandproducethere.Sm=1and1-Sm=0ispossible;
EastwillhavenomanufacturingandWestwillhaveallofit.Sm=1ispossible.
1-Sn<
F/txisthesameasSn<
1-F/tx
IfevenwhenWesthasnomanufacturing,theshareofpopulationislargeenoughthatitpaystobuildafactoryinWestratherthantoshipintoit,thenSm=0isnotpossible.Westcannotbeaperiphery.
IfF/tx<
Snthenitcostslesstobuildafactorythantoshiptowest.Ifthatistrue,ifSm=0,firmswoulddecidetolocateinWestratherthanshipinandSmwouldrise.Sm=0,Westisaperipheryisnotpossible.
ThesameistrueforeastifF/tx<
(1-Sn)(East’sshareofpopulation)whenallthemanufacturingisinWestandnoninEast.ThatoccurswheneverSn<
(1-F/tx)evenwhenallthemanufacturingisinWest.
TheRedLineisSm=f(Sn);
Theshareofmanufacturingdependsontheshareofpopulation.
Thebluecirclesshowthethreeequilibriums.
IfSm=0,F/tx>
Sn,Westcanbeaperiphery
IfSm=1,1-F/tx<
Sn,Westcanbeacore;
Eastcanbeaperiphery
IfSm=Sn,EastandWestwilleachmanufactureforthemselves.Acoreperipherypatternisnotpossible.
Ifanyoneoftheseequilibriumsisestablisheditwillpersist.Anyonecouldbeestablished.
WHENISACOREPERIPHERYPATTERNLIKELY?
Whenwillitbeeconomicalforaregiontohaveallthemanufacturing,tohavenone,ortohavethesameproportionofmanufacturingasithaspopulation?
Theanswerdepends(surprise,surprise!
)ontherelationshipbetweenfixedcosts,transportcosts,thetotalsizeofthemarket–andSa.
Krugman’svalues
Fixedcosts=F=4
transportcostsperunit=t=1
unitssold=x=10
Sa=.5
π=.4
Wewilluseequationstoseethatwiththegivenvalues,threetypesofworldsarepossible.WestcouldbetheperipheryandEastthecore,EastcouldbetheperipheryandWestthecore,ormanufacturingcouldbedividedbetweenthetwo.
CanWestbeaperipherywithnomanufacturing?
DonotbuildaplantinWest
IfSn*tx<
FthatisifSn<
F/tx
ItcostslesstoshiptoWestthantobuildaplantinWest.
Therefore,Sm=0.
InourAndersonnotation,thisisthesituationwhenFC<
t*Qs;
ItcostsmoretoshipthegoodsthantobuildaplantinWest.Inthissituation,everyfirmwillwanttohaveaplantinWest.
Giventhecosts,ifWesthasonlyfarmers,Sm=0.
Sn=(1-π)*Sa+π*Sm;
Sn=(1-.4)*.5+.4*0=.3+0=.3
Sn=.3
F/tx=4/(1*10)=.4
Sn<
F/txbecause.3<
.4
Costofbuildingthefactoryis4(milliondollars)
CostofshippingthegoodsintoWestis3(milliondollars).Thatis$1perunit,times30(million)unitsshipped.Westhas.3ofthepopulationsobyourassumptionofpercapitalconsumption,itwillbuy.3ofthe10(million)unitsproduced.
Therefore,itisconsistentforWesttohavenomanufacturingandtobepopulatedonlybyfarmers.BuildingaplantwouldcostmorethanshippingfromWesttoEastifWesthadnomanufacturing,Snwouldbelowenoughthatitpaidtocontinuetohavenomanufacturing.
IfWestbeganasaperiphery,itwouldstayaperiphery.Westasaperipheryisoneequilibrium.
CanWestbeacore,withallthemanufacturinginWestandnoneinEast?
ThenEastmustbeaperiphery,andfirmsmustbeunwillingtolocateinEast.
IfWestisacore,thanSm=1;
Sn=(1-.4)*.5+.4*1=.3+0=.7
Sn=.7
(1-Sn)=.3;
Easthasonly.3shareofthepopulation
(1-Sn)<
InourAndersonnotation,FC>
t*Qs;
BuildingaplantinEastcostsmorethanshippingfromWesttoEast.
DonotbuildaplantinEast
If(1-Sn)*tx<
Fthatisif(1-Sn)<
F/txorSn>
IfitcostslesstoshiptoEastthantobuildaplantinEastthennofirmwillwanttolocateinEast.Westwillhaveallthemanufacturing,andWestwillbethecore.
Therefore,Sm=1.Westhasallthemanufacturing,Easthasnone.
Therefore,itisconsistentforWesttohaveallthemanufacturingandalltheworkers.BuildingaplantinEastwouldthencostmorethanshippingfromWesttoEast.IfWesthadallthemanufacturing,1-SnwouldbelowenoughthatitpaidtocontinuetohavenomanufacturinginEastandallthemanufacturinginWest.
IfWestbeganasacorewouldstayacore.Westasacoreisoneequilibrium.
Canmanufacturingbedivi
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