The Self-Organizing Economy - Krugman, Paul

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Firstpublished1996
Copyright© PaulR. Krugman,1996
CompositionbyMeganH. Zuckerman
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PART I
Embryos,Earthquakes,andEconomics
Self-Organization in Space
The vonThiinen-Mills Model
CentralPlaceTheory
Schelling'sSegregationModel
EdgeCity Dynamics
Complex Landscapes
The Emergenceof Order
An Urban Mystery
Meteorites,Earthquakes,andCities
Simonon Zipf
Principles of Self-Organization
OrderfromInstability
OrderfromRandomGrowth
Where We Stand
Contents
PART II
Self-Organizationin Time andSpace
Dynamics in Self-Organizing Systems
Temporal Self-Organization
Two QuestionsabouttheBusinessCycle
NonlinearBusinessCycleTheory
PercolationEconomics
PhaseLockingandtheGlobalBusinessCycle
Models of Spatial Self-Organization
Preface
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TheEdgeCityModel
A CentralPlaceModel
Simon'sUrbanGrowthModel
9 ConcludingThoughts
10 Appendix:The Evolutionof CentralPlaces
UrbanMorphogenesis:TheEdgeCityModel
A CentralPlaceModel
References
Index
IV SELF-ORGANIZING ECONOMY
76
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119 Preface
Every oncein a while theworld economyplungesinto a severe
recession.Someof theseinternationalslumpsappearto be caused
by particularnoneconomicevents:wars,disruptionsof oil supply.
Others,however,haveno obviouscause- andtheirglobalscaleis
hardto explainin termsof theconventionallymeasuredlinkages
amongnationaleconomies.
Everyoncein a (muchlonger)while, thepaleontologiststellus,
theworld experiencesmassextinctionsthatwipe out mostof the
extantspecies.Someextinctionsappeartohaveexternalcauses,like
the comet whose impact coincided with the demiseof the
dinosaurs.Others, however,havenot beentied to any obvious
cause.Sometheoristswho simulateevolutionon theircomputers
claimthatthisis asit shouldbe: theirmodelspredictoccasional,
spontaneousmassextinctionsevenin theabsenceof anyexternal
shocksto thesystem.
Can thesetwo paragraphshaveanythingto do with eachother?
Is therea sensein which a globalslumpis somethinglike a mass
extinction?
Here is anotherparallel.When you look at thesizes(however
measured)ofmanyenormouslycomplexphysicalorbiologicalphe-
nomena,thedistributionof thosesizesfor somereasonturnsoutto
bewelldescribedbyaverysimplepower law: thenumberof objects
(earthquakes,meteorites,species,and - perhaps- extinctions)
whosesizeexceedsS is proportionalto s-a,wherea is not only a
mysteryparameterbutoftenturnsout,weirdly,tobearoundnum-
ber,like 1 or 2. Amongthemostspectacularexamplesof apower
law,however,is onethatinvolveseconomicsratherthanphysical
science:the sizedistributionof cities.In the United States,the
"
numberof citieswhosepopulationexceedsS is, simply,propor-
tionalto l/S: thereare40citieswith morethanamillionpeople,20
with morethan2 million, and9 (Houstonfell a bit short)with
morethan4 million!
Socialscientistsarenormallysuspiciousof peoplewho wantto
importconceptsfromphysicalorbiologicalscience,andwith good
reason:thehistoryof suchefforts,fromsocialDarwinismtosystems
dynamics,hasbeenlittleshortof disastrous.Nonetheless,thistime
thingsmaybedifferent;thereis agenuinelyinterestinginterdisci-
plinarymovementofwhicheconomicsoughttobeapart.
In thelastfewyearstheconceptofself-organizingsystems- ofcom-
plexsystemsinwhichrandomnessandchaosseemspontaneouslyto
evolveinto unexpectedorder- hasbecomeanincreasinglyinflu-
entialideathatlinkstogetherresearchersin manyfields,fromarti-
ficial intelligenceto chemistry,from evolutionto geology.For
whateverreason,however,thismovementhassofarlargelypassed
economictheoryby. It is timeto seehow thenew ideascanuse
fullybeappliedto thatimmenselycomplex,but indisputablyself-
organizingsystemwe calltheeconomy.
In thisbookI trytoshowhowmodelsof self-organizationcanbe
appliedto manyeconomicphenomena- how the principleof
"orderfrom instability,"which explainsthegrowthof hurricanes
andembryos,canalsoexplaintheformationof citiesandbusiness
cycles;how the principle of "order from randomgrowth" can
explainthestrangelysimplerulesthatdescribethesizesof earth-
quakes,meteorites,andmetropolitanareas.I believethattheideas
of self-organizationtheorycanaddsubstantiallytoourunderstand-
ingof theeconomy;whatevertheirultimateusefulness,theseideas
areveryexciting,andplayingaroundwith themis tremendousfun.
Finally,anoteon style.This bookbeganastheMitsui lectures,
which I gaveat the Universityof Birminghamin March 1994.
Although I havenot triedto maintainthe lectureformat,I have
allowedmyselfto retainsomeof thelicenseusuallygrantedin such
alectureseries:thisbookiswrittenin aninformalstyleandcontains
morethanafewwild speculations.Nonetheless,I havetriedtoget
thingsrightwhenI can;andI amgratefulfordiscussionswith par-
ticipants in seminarsat Birmingham, UCLA, Chicago, and
Stanfordthathelpedmecorrectsomeseriouserrors.In particular,I
wouldlike to thankMike WoodfordatChicagofor pushingmeto
testapethypothesisto itswell-deserveddestruction.
vi SELF-ORGANIZING ECONOMY
PART-----1-----
Embryos,Earthquakes,andEconomics
Isaneconomicslumplikeahurricane,or isit morelikeanearth-
quake?Is a growing city like an embryo,or is it more like a
meteorite?
Thesequestionsmaysoundlike children'sriddles,to whichthe
answeris somekind of badpun; or maybetheysoundlike Zen
koansalongthelinesof "What is thesoundof onehandclapping?"
in which theabsurdityof thequestionis meanttojolt thelistener
intoahigherstateof awareness.But myaimis neitherto telljokes
nor tohelpyouachieveanenlightenmentthattranscendsrationali-
ty.On thecontrary,in thecourseof thisbook I hopeto convince
you thattheseareperfectlyreasonablequestionsto ask,thatthere
maywellbeamorethanpoeticsensein whichadeepeningslump
resemblesanemerginghurricane,in whichagrowingcityisquitea
lot likeadevelopingembryo.
In makingthesekindsof analogiesI am not, of course,being
completelyoriginal.Thereis abroadandgrowinginterdisciplinary
movementin thephysicalandbiologicalsciences- oftenreferredto
as the studyof complexity- that looks for exactlysuchparallels
betweenseeminglydisparatephenomena.For example,in the
courseof my preparationsfor thisbook I ranacrossanarticleon"percolationtheory"thatcasuallylisted15areastowhichthebasic
approachapplied,rangingfromatomicnucleitogalaxies.But sofar
thismovementhaslargelypassedeconomicsby.
Actually,letmequalitythatstatement.Peoplewho writebooks
or conveneconferenceson complexityalmostinvariablyassertthat
the emergingfield will makegreatcontributionsto the studyof
thatimmenselycomplicatedsystemwe calltheeconomy.Indeed,
theSantaFe Institute,oneof thehotbedsof thisstyleof research,
wasinitiallyfundedby Citibank largelybecauseJohn Reed, the
bank's CEO, hoped that researchon complexsystemswould
improveeconomicforecasting.For whateverreason,however,the
authorsof articlesandbookson complexityalmostnevertalk to
seriouseconomistsor readwhat seriouseconomistswrite; as a
result,claimsabouttheapplicabilityof thenewideasto economics
areusuallycoupledwith statementsabouthow economieswork
(andwhateconomistsknow)thatseemsoill-informedasto make
anyeconomistwho happensto encounterthemdismissthewhole
enterprise.
But it doesnot haveto be thatway.What I amgoingto claim,
andI hopedemonstrate,in theselecturesis thatsomeof theideas
thatcomeout of theinterdisciplinarystudyof complexsystems-
the attemptto find commonprinciplesthatapplyacrossa wide
varietyof scientificfields,fromneuroscienceto condensedmatter
physics- are,in fact,usefulin economicsaswell.That is,you can
understandandrespecttheeconomictheorywe alreadyhaveand
stillfindwaysbothto improveit andtobuildbridgestootherfields
bytakingintoaccounttheideasof theseinterdisciplinarytheorists.
BeforeI goanyfurther,I hadbetterexplainalittlebetterwhatI
amtalkingabout.What is this interdisciplinaryeffortthatI have
beenalludingto,andhowcanit teacheconomistsanythingnew?
Manyof thepeoplewho thinkthatearthquakes,embryos,cycles,
andcitieshaveall got somethingto do with oneanotherdescribe
theirfield asthestudyof "complexity,"basedon theinsightthat
complicatedfeedbacksystemshavesurprisingproperties.If that
wereall therewereto theprogram,however,economistswouldbe
entitledto changethechannel.If economistsdo understandone
thingmuchbetterthanthelaypublic,it is thesheercomplexityof
the economicsystemandtheimportanceof feedbacks.After all,
whatisgeneralequilibriumtheorybutaformalizationofthepropo-
sitionthateverythingin theeconomyaffectseverythingelse,in at
leasttwo ways?If you haveevertriedto explainto a roomfulof
engineerswhy highermanufacturingproductivitywill probably
reduce,not increase,manufacturingemployment- andwhy high-
er productivitywill not necessarilyreducethe tradedeficit- you
quicklyrealizethateconomistsarebetter,not worse,thanmost
physicalscientistsatunderstandingtheimportanceof feedbackin
complexsystems.
A seconddefinition,by Philip Anderson,the Nobel laureate
physicistwho mayperhapsberegardedasthefatherof thefield, is
thatcomplexityis thescienceof "emergence."That is, it is about
how largeinteractingensembles- wheretheunitsmaybewater
molecules,neurons,magneticdipoles,or consumers- exhibitcol-
lectivebehaviorthatisverydifferentfromanythingyoumighthave
expectedfrom simplyscalingup the behaviorof the individual
units.(Thebehaviormayalsobeoddlysimilarto thatof ensembles
ofotherwiseverydifferentunits:collectionsofneuronsmaybehave
alot likecollectionsof magneticdipoles.)Anderson'sprimeexam-
pleof anemergentpropertyis theliquidnessof water,which is in
no senseanextrapolationof someprimordialliquidnessof individ-
ualwatermolecules.
Hereagain,however,we haveadefinitionthatsoundslikewhat
economistsalreadyunderstandprettywell. When Adam Smith
wroteof thewaythatmarketsleadtheirparticipants,"asif by an
invisiblehand,"to outcomesthatnobodyintended,whatwashe
describingbutanemergentproperty?And examplesof emergence
aboundin economictheory- weneedonlynotethewaythatcom-
petitivemarkets,in whicheachindividualis strivingonlyforhisor
herownprofit,actasif theparticipantswerecollectivelytryingto
maximizethesumof consumerandproducersurplus,conceptsof
whichtheyaregenerallyunaware.(Nor is thisonlytheory:experi-
mentalmarketsin which theparticipantsareassignedpayoffsand
thenmakebidsforandoffersof unitsof anotionalcommoditydo,
in practice,comeverycloseto maximizingaggregatesurplus,even
thoughthe participantsnot only are not trying to achievethat
objective,theydonotevenknowwhateachothers'payoffsare.)
There is, however,a thirddefinitionof thisfield thatdoesnot
soundlike somethingthateconomistsalreadydo, or at leastnot
whattheydoroutinely.This istheviewthatwhatlinksthestudyof
embryosandhurricanes,of magneticmaterialsandcollectionsof
neurons,is thattheyareallself-organizingsystems:systemsthat,even
when theystartfrom an almosthomogeneousor almostrandom
state,spontaneouslyformlarge-scalepatterns.One daytheairover
aparticularpatchof tropicaloceanis no differentin behaviorfrom
theairoveranyotherpatch;maybethepressureis abit lower,but
2 SELF-ORGANIZING ECONOMY Embryos,Earthquakes,andEconomics 3
thedifferenceisnothingdramatic.Overthecourseof thenextfew
days,however,that slight dip in pressurebecomesmagnified
throughaprocessof self-reinforcement:risingairpullswatervapor
up to analtitudeatwhichit condenses,releasingheatthatreduces
thepressurefurtherandmakesmoreair rise,until thatparticular
pieceof theatmospherehasbecomeahuge,spinningvortex.Early
in theprocessof growthanembryois acollectionof nearlyidenti-
calcells,but(oratleastsomanybiologistsbelieve)thesecellscom-
municatewith eachotherthroughsubtlechemicalsignalsthatrein-
forceandinhibiteachother,leadingto the"decision"of somecells
tobecomepartsof awing,otherspartsof aleg.
Is theeconomya self-organizingsystemin thissense?Of course
it is.Think aboutametropolitanarea- even,or ratherespecially,a
modernmetropolitanarealikegreaterLosAngeles,with no clearly
definedcenter.Is anurbansprawllike LA ahomogeneous,undif-
ferentiatedmass?No - it is a patchworkof areasof verydistinct
character,rangingfromKoreatowntoHollywood,WattstoBeverly
Hills. And it contains(accordingto therecentbook Edge City by
Joel Garreau)no fewerthan16"edgecities,"newlyemergedbusi-
nesscenters,eachof whichincludesatleast5 million squarefeetof
office spaceand20,000workers,wherethelow-rise sprawlsud-
denlygivesway to tall buildingsandmultistoryparkinggarages.
What issostrikingaboutthisdifferentiationisthatit issoindepen-
dentofphysicalgeography:therearenoriverstosetboundaries,no
bigdowntowntodefineagradientofaccessibility.(OK, thebeach-
esandthefreewayscreateabitofexogenousstructure,butgrantme
alittlelicense.)The strongorganizationof spacewithin metroLos
Angelesis clearlysomethingthathasemerged,notbecauseof any
inherentqualitiesofdifferentsites,butratherthroughself-reinforc-
ing processes:Koreansmoveto Koreatownto be with Koreans,
beautifulpeoplemoveto BeverlyHills to bewith otherbeautiful
people.And whenanobserverlikeGarreautracesthedevelopment
of edgecities,heis immediatelydrawnto metaphorslike "sponta-
neouscombustion"and"criticalmass"- clearindicatorsthatheis
tryingto describea self-organizingsystem.
I havestartedwith thewaythatcitiesspontaneouslyevolveapat-
ternof sharplydistinctdistricts,becausetheeconomicself-organi-
zationof spaceis somethingwe can all relateto our immediate
experience.But I wouldassertthatthereareprocessesin theecon-
omy thatproducetemporalself-organizationaswell. I referto the
businesscycle:thepulsesofexpansionandcontractionaroundarel-
ativelystablelong-run trend.(No, I don'tbelievein Kondratieff
waves.)Somerecessionsandrecoveriesareclearlysetoffby specif-
ic, essentiallyexogenouseventslikeoil crises.Overthelongsweep
of history,however,mostboomsandslumpshavehadno obvious
externalcause.Most notably,themotherof all economicslumps,
thecontractionfrom 1929to 1933,cameasit wereout of a clear
bluesky.But then,sodohurricanes.
In fact,letmeexplainwhyaslumpmaybequitealot likeahur-
ricane.A hurricaneisaself-reinforcingprocess,in whichanupdraft
thatpullswatervaportoalevelatwhichit condensestherebyreleas-
esheat,which in turn reinforcestheupdraft.Aslumpis alsoself-
reinforcing:fallingoutputcausesfirmstoslashtheirinvestmentand
consumersto reducetheirspending,therebyreducingoutputstill
further.But wait,thereismore.A hurricanecannotgoon forever.
The fuel for its violenceis thewatervaporthatexistsin relative
abundanceabovea warmtropicalocean.But the hurricaneitself
coolsthatoceansurface- indeed,in awaythewholepointof trop-
icalstormsis thattheyareNature'swayof transferringsolarenergy
fromthetropicstohigherlatitudes.And sohurricanes,eventhough
theyareself-reinforcingin the shortrun, areself-limitingin the
longrun.What aboutaneconomicslump?Well, it leadsto falling
prices,or at leastdisinflation,which graduallyincreasesthe real
moneysupply.The low or negativenetinvestmentin adeepslump
mayalsoleadtoagrowingbacklogofpotentiallyprofitableprojects.
And sowemayarguethataneconomicslumpisalsoaself-limiting
process,evenif thereis no deliberateor effectivegovernmentpoli-
cytogettheeconomymovingagain.
By theway,Americanswho watchtheweathernewsknow that
hurricanessustainthemselvesby moving,gainingstrengthwhen
theypassoverfreshtractsof warmwater;if thishasanyanalogyin
businesscycles,I amunawareof it. But I didnotclaimthatthepar-
allelwasperfect.And you mayarguethatmy descriptionof what
goeson in atypicalrecessionisnottooaccurate- ormaybethereis
no suchthingasa "typical"recession,in which caserecessionsare
morelikeearthquakesthanlikehurricanes.But we shallgetto that
in PartII.
While I ammakingasides,let mealsotakethe opportunityto
makeanotherpoint: self-organizationis not necessarily,or even
presumptively,agoodthing.I think it is fairto accusemanyof the
4 SELF-ORGANIZING ECONOMY Embryos,Earthquakes,andEconomics 5
t
"
writerson complexity,especiallybut not only the morepopular
ones,of fallingintothisfallacy.Book titleslikeOrderoutif Chaos(by
Nobel laureateIlyaPrigogineandI. Stenger,butwith a Foreword
by,believeit or not,Alvin Toffler),or Complexity:Life at theEdgeif
Chaos(byR. Lewin) comeperilouslycloseto makingself-organi-
zationa kind of mysticalgoal.Even StuartKauffman,whoseThe
Originsif Orderis a seriousandstimulatingtract(if we ignorethe
inevitablycarelessandill-informedsectionon economics),talksfar
too casuallyaboutcoevolutionarysystemsthatmaximize"average
fitness"- a surelymeaninglessconceptwhen the fitnessof each
speciesis definedatleastpartlyin termsof howwell it copeswith
competitionandpredationfromothers.Luckily,if weareatallseri-
ousabouttheeconomicsof self-organizationweimmediatelyreal-
ize thatno valuejudgmentis implied.An economywith a strong
businesscycleexhibitsmore temporalself-organizationthan an
economythatgrowssmoothly,butmostof uswouldratherlivein
the latter.A city whoseraciallyintegratedcommunitiesunravel,
producinghugesegregateddomains,becomesmorespatiallyorga-
nized,butnotbetter,in theprocess.Self-organizationis something
we observeandtry to understand,not necessarilysomethingwe
want.
I haveassertedthatthestudyof self-organizationis something
thateconomistsdo notdo, or atleastdo not do routinely.What I
havejust saidabouteconomicslumpsis,however,notatallnewor
original.On thecontrary,I havejust givenyou a looseversionof
thenonlinearbusinesscycleliteraturethatflourishedin the 1940s
and1950s,with contributorsincludingeconomistsof thestatureof
John Hicks,RichardGoodwin,andJamesTobin. For thatmatter,
urbaneconomistshavehardlybeenunawareof theself-organization
of metropolitanareas,andtherehavebeensomenotableeffortsto
modelthecreationof urbansubcenters,asedgecitiesarecolorless-
ly knownamongtheprofessionals.(I havein mindparticularlythe
pioneeringwork of FujitaandOgawa.)
And yetI thinkit is fairto saythatfeweconomistshaveexplicit-
ly realizedthattheyweretrying to modelself-organization;few
havetriedto drawtheparallelbetweenself-organizationin space
and self-organizationin time;few havetried to usesomeof the
techniquesforunderstandingself-organizationthathaveevolvedin
otherfields.Furthermore,althoughsomedeeplyinsightfulthinkers
moreor lessconsciouslyhavewrittenaboutself-organizationin the
economy,theirwork hasbeenneglectedby theprofession(andis
completelyunknownoutsideof it). Nonlinearbusinesscycletheo-
ry, for example,wastechnicallyfaraheadof itstimeandmakesthe
latereffortsto shoehorn"catastrophetheory"intoeconomicslook
primitive.But who remembersit? (I maybetheonlyeconomistin
mygenerationwho hasevenheardof it.) ThomasSchellingwrotea
remarkableessayon thedynamicsof segregationin hiswonderful
1978book MicromotivesandMacrobehavior,but thebook hadlittle
impactatthetimeandis stillunderappreciated.
I thinkthatI canexplainwhythepioneersof self-organizationin
economicshavebeeneitherneglectedor forgotten,andI will talk
aboutthosereasonslaterin theselectures.For now,however,letus
putintellectualhistoryasideandturnto doingsomeeconomics.
Here is myplanof action.In thisfirstpart,I amgoingto do a
quickrun-throughof stories- I do not want to dignifythemby
callingthemmodels- aboutwaysin whichtheeconomyorganizes
itselfin space.(I startwith spatialself-organizationfor two main
reasons.First,asanempiricalmatterI amonmoresolidground:the
self-organizingspatialcharacterof theeconomyisobvioustoevery-
one,althoughnotusuallyunderthatname.Second,I knowwhatI
believeaboutspatialeconomics,but I amstillfairlyagnosticabout
the macroeconomicsof businesscycles.)Along the way I shall
describetwo broad,andseeminglyparadoxical,principlesof self-
organizationthataresuggestedby thesestoriesandthatarealso
commonin much of the literatureon self-organizationin other
fields.Just towhetyourappetite,letmegivetheseprinciplesnames:
"orderfrominstability"and"orderfromrandomgrowth."
In thesecondpart,I will startby showinghow theseprinciples
mayapplynot only to spacebut to time: in particular,how we
might think of the businesscycleas temporalself-organization.
Thenweshallcomebacktothespatialeconomy.I will describetwo
moreorlessfull-fledgedmodelsthatillustratetheprincipleoforder
frominstabilityandonethatillustratestheprincipleof orderfrom
randomgrowth.EventhereI will golighton theequations,stress-
inganintuitiveexplanation.But therewill beatechnicalappendix,
whichderivestheresultsin all thegorydetailI canmanage(which
isnotmuch).
So letusbeginour tourwith a look atthewaythateconomies
organizespace,particularlythespacewithinmetropolitanareas.
6 SELF-ORGANIZING ECONOMY Embryos,Earthquakes,andEconomics 7
-----1-----
Self-Organizationin Space
THE VON THUNEN-MILLS MODEL
How do economistsroutinelydealwith thequestionof how the
economyorganizesitsuseof space?The shortansweris thatmost-
ly theydo not dealwith thequestionatall. Indeed,thereis some-
thingstrangeabouttheway thatmostof our professionneglects
anythinghavingto dowith whereeconomicactivitieshappen.For
example,theverypopular(andalmost900-page-Iong)economics
principlestextbookbyWilliam BaumolandAlanBlindercontains
notasinglereferenceto "cities,""location,"or "space"in itsindex.
The rival,1100-pagetextbyJosephStiglitzdoescontainonerefer-
enceto cities,which turnsout to occurin a brief discussionof
rural-urbanmigrationin less-developedcountries.Considering
how muchtimemostpeoplespendin trafficjams,how manyfor-
tunesaremadeandlostin realestate,thewaythatwe turnablind
eyetospatialeconomicsislittleshortofeerie.I stronglysuspectthat
thisneglectiscloselyrelatedto thethemeof thisbook:asaprofes-
sionwe areimplicitlyawarethatto understandcitiesandspatial
economicsgenerallywe mustcopewith issuesof self-organization
andthatratherthanfacewhatseemtobeintractableissueswesim-
plyavertourgaze.
Anyway,whenwe do dealwith thequestionof theorganization
of space,asurbaneconomistsatleastmust,we generallyturn to a
classofmodelspioneeredin theearly19thcenturybyvonThiinen.
Manyofyouareprobablyfamiliarwith thevonThiinenmodel,but
I wantto run throughit brieflyto makea coupleof pointsabout
complexity,emergence,andself-organization.
9
Von Thiinen envisagedanisolatedtownsuppliedby farmersinthesurroundingcountryside.He supposedthatcropsdifferin both
theiryieldperacreandtheirtransportationcosts,aswell asallow-
ingfor thepossibilitythateachcropcouldbeproducedwith differ-
entintensitiesofcultivation.And heaskedtwoquestionsthatmight
seemtobeverydifferent:How shouldthelandaroundthetownbe
allocatedto minimizethecombinedcostsof producingandtrans-
portinga givensupplyof food to the town?How will the land
actuallybe allocatedif thereis an unplannedcompetitionamong
farmersandlandowners,with eachindividualactingin his or her
perceivedself-interest?
We all know the answerto the secondquestion.Competition
amongthefarmerswill leadtoagradientoflandrentsthatdeclines
from amaximumatthetowntozeroattheoutermostlimit of cul-
tivation.Each farmerwill be facedwith a tradeoffbetweenland
rentsandtransportationcosts;sincetransportationcostsandyields
differamongcrops,theresultwill beapatternof concentricrings
of production.In equilibriumthelandrentgradientmustbe such
asto inducefarmersto growjust enoughof eachcropto meetthe
demand,andit turnsoutthatthisconditiontogetherwith thecon-
ditionthatrentsbezerofor theoutermostfarmersufficesto fully
determinetheoutcome.
Figure1.1illustratesschematicallythetypicaloutcomeof avon
Thiinenmodel.The upperpartof thefigureshowstheequilibrium
"bid-rent" curves,therentthatfarmerswouldbewilling topayat
anygivendistancefromthetown,for threecrops.The heavyline,
the envelopeof the bid-rent curves,definesthe rent gradient.
Along eachof thethreesegmentsof thatlinegrowersof oneof the
cropsarewillingtopaymoreforlandthantheothers.Thusonegets
concentricringsof cultivation,with a quartersectionof thelayout
shownin thebottomhalfof thefigure.
It isworththinkingaboutthisoutcomeforamomentin termsof
thevariousdefinitionsthathavebeenofferedof whatcomplexity
theoryisallabout.If it is reallyjust aboutcomplexity,vonThiinen
modelsareprobablycomplicatedenoughto qualify.After all, the
problemof whichcropstogrowwhereis not thateasy:byallocat-
ing anacreof landnearthecity to someonecrop,you indirectly
affectthecostsof deliveringallothercrops,becauseyouforcethem
tobegrownfurtheraway.Exceptin thecasewherethereisnopos-
sibilityofvaryingthelandintensityof cultivation,it isbynomeans
Figure1.1 The Von ThiinenModel. Competitionfor landarounda
townleadsto theemergenceofconcentricringsofproduction
11
Cattle
Bidrent
Distance
from
center
Wheat
Vegetables
Self-Organizationin Space
trivialtodetermineeitherwhatshouldbedoneorwhatwill happen
in anunplannedmarket.
SupposethatyouinsteaddefinethesubjectasAndersondoes,as
astudyofemergence.Then surelythevonThiinenmodelqualifies.
At the mostobviouslevel,the concentricring patternis hardly
somethingthatis immanentin themotivesof thefarmers.Indeed,
theconcentricringswill emergeevenif no farmerknowswhatany-
oneelseisgrowing,sothatnobodyisawarethattheringsarethere.
Evenmorestrikingis theresultthateconomicshastrainedusto
expectbut that remains startling (and implausible)to most
noneconomists:theunplannedoutcomeis efficient,is indeedthe
sameastheoptimalplan.More specifically,unplannedcompetition
will allocatecropsto landin a waythatminimizesthetotalcom-
SELF-ORGANIZING ECONOMY10
binedcostof producingandtransportingthecrops- notincluding
thelandrent.This is surelyasniceanexampleof emergenceasyou
couldwant.All farmersaretryingtomaximizetheirincomeandare
thereforeverymuchconcernedwith landrents,yettheircollective
behaviorminimizesafunctionin whichlandrentsdo notappear.
On two of thecriteriathathavebeenusedto definethisenter-
prisecalledcomplexity,then,thevon Thiinen modelqualifies.And
yetI doubtthatmanycomplexitytheoristswouldagreethatthiswas
thekind of economicstheyhadin mind.Avon Thiinen modelis
not like a hurricane,or an embryo,or a neuralnetwork.Why?
Becauseit isnotself-organizing.The concentricringsofproduction
formaroundatownwhoseexistenceis simplyassumed.That does
notmakeit abadmodel,butit doesmakeit alimitedone.If your
questionisnotsimplyhowlanduseisdeterminedgivenapre-exist-
ing town,butratherhowlanduseis determinedwhenthelocation
of thetownor towns- indeed,theirnumberandsize- arethem-
selvesendogenous,thevonThiinen modeloffersno help.
This limitationbecamepainfullyclearwhen the von Thiinen
modelwaspresentedin a newform in the1960sby Edwin Mills,
who substitutedcommutersfor farmersand the centralbusiness
districtfor theisolatedtown,toarriveathisnow classicmodelof a
monocentriccity.
Again, you areprobablyfamiliarwith thebasicideaif not the
details.We imagineacitypopulatedby commuterswho wantland
to liveon butmustwork in acentralbusinessdistrict;theremaybe
differenttypesof peoplewho varyin thevaluetheyplaceon the
timetheyspendcommuting,theamountof landtheywantto live
on, theirwillingnessto substitutefancyhousesfor largebackyards,
andsoon. As in thevonThiinen model,competitionestablishesa
landrentgradient,which sortspeopleout into a structureof con-
centricrings;andasin thatmodel,decentralizedlocationchoices
lead,throughnobody'sintention,to anefficientoutcome.
Mills's 1967paper introducingthe monocentric city model
launchedahugetheoreticalandempiricalliterature.And yetin the
end thatliteratureprovedrathersterile.Part of theproblemwas
purelyaesthetic:amodelthatsimplyassumesthatthereis acentral
businessdistrictisdeeplyunsatisfYingif youwanttoexplaincitiesas
opposedto describingthem.But urbaneconomistsmight have
swallowedtheirdisappointmentif it hadnotbeenforanotherprob-
CENTRAL PLACE THEORY
Economicsaswe knowit is largely,thoughnotentirely,anAnglo-
Saxontradition.Locationtheory,however,waslongaGermantra-
dition, containingatleastthreestreams.One streamfollowsfrom
lem:cities,donot look like that,andtheylook lesslike thatwith
everypassingdecade.
Rememberwhat I saidaboutgreaterLos Angeles,with its 16
edge cities far overshadowingits two traditionaldowntowns.
Sophisticatedpeopleusedto turnuptheirnosesatCaliforniacities,
with theirlackof clearlydefinedcenters- GertrudeSteindeclared
of Oaklandthat"there'sno therethere."Shewaswrong,ofcourse:
therearelotsof quitedistincttheresthere,justno onebigthereyou
cancall thecenter.And increasinglythatis thewayall our cities
look. I wrotethedraftof thisbookin PaloAlto, whichispartof the
SanFranciscometropolitanarea.SanFranciscoproperisacompact
city,whichstillepitomizesacertainkindof urbanity.But PaloAlto
haslittletodowith thatcenter.One thinksof oneselfasbeing,not
aSanFranciscan,butaresidentof SiliconValley;onereadstheSan
JoseMercuryNews ratherthantheSanFranciscoChronicle(it is abet-
terpaperanyway),andpeoplewho livein PaloAlto aremuchmore
likelyto commuteto theedgecityin Sunnyvalethanto thevicini-
tyof theGoldenGate.The monocentriccitymodelpicturesamet-
ropolitanareaassomethinglike a slicefrom an onion,with rings
arrayedaroundasinglecenter.The realityof all largemetropolitan
areasin the United Statestoday,eventhoselike New York or
Chicagothatstillhavehuge,vitaldowntownofficedistricts,is that
theyarelesslike anonion sliceandmorelikeJack Horner'splum
pudding,in whichedgecitiescorrespondto theplums.
The problemof modelingthestructureof themodernpolycen-
tric urbanareais in largepartoneof eXplainingtheformationand
locationof theseplums.That is, we cannotavoidtheproblemof
understandingtheurbanarea'sself-organization.Partof theprocess
bywhichthatself-organizationtakesplaceis,of course,acompeti-
tion for landthatestablishesa land rentsurfaceacrosstheurban
landscape;in thatsensethevon Thiinen-Mills approachremains
essential.But it isatbesthalfthestory- andarguablythelessinter-
estinghalf
13Self-Organizationin SpaceSELF-ORGANIZING ECONOMY12
15Self-Organizationin Space
The answer,I believe,is thatanyeconomistwho thinkshard
aboutcentralplacetheory realizesthat it doesnot quite hang
togetherasaneconomicmodel.What do we look for in aneco-
nomicmodel- or toputit differently,whatconstitutesan"expla-
nation"fromthepointof view of economists?I do not thinkyoucansumit up betterthanThomasSchellingdid in thetitleof his
book, Micromotivesand Macrobehavior.We feel thatwe havereally
managedto shedlighton aphenomenonwhenwe showhow that
phenomenon,the"macrobehavior,"emerges(thereis oneof those
wordsagain)fromtheinteractionofdecisionsbyindividualfamilies
or firms;themostsatisfyingmodelsarethosein which theemer-
gentbehavioris mostsurprisinggiventhe "micromotives"of the
players.What is thereforedeeplydisappointingaboutcentralplace
theoryis thatit givesno accountalongtheselines.Loschshowed
thata hexagonallatticeis efficient;he did not showthatit would
tendto emergeout of anydecentralizedprocess.Christallersug-
gestedtheplausibilityofahierarchicalstructure;hegavenoaccount
of how individualactionswouldproducesuchahierarchy(oreven
sustainoneonceit hadbeensomehowcreated).
What,then,is centralplacetheory?It is notacausalmodel.It is
probablybestto thinkof it asaclassificationscheme,awayof orga-
nizingourperceptionsandour data.Seenin thatlight,it is awor-
thyenterpriseindeed.After all, in thephysicalandbiologicalsci-
encesclassificationschemeshaverepeatedlyservedasthebasisfor
greatinsights- thinkof theLinnaeanclassificationof speciesor the
periodictable.The point,however,isthatclassificationschemesare
onlyastepon theway:theytellyouwhat,but theydonottellyou
why.So centralplacetheoryis adescriptionbut not reallyanexpla-
nationof self-organization.
SCHELLING'S SEGREGATION MODEL
The twoapproachesto theorganizationof spacejust describeddo
not quite makeit: the von Thiinen-Mills approach,which is a
modelof spatialorganizationbutnotof self-organization,andcen-
tralplacetheory,which is a usefulclassificationschemebut not a
causalmodel.Well, enoughof frustration:nowletusturnto some
approachesthat do help explainthe self-organizationof spatial
econormes.
Thiinen analysisofland rentandlanduse,whichwe have
lussed.A secondstream,associatedwith AlfredWeberand
ers,focusedontheissueofoptimalplantlocation;thatlit-
"11playno rolein mydiscussion.But thereisathirdtradi-
ichatfirstsightseemstoofferananswerto theproblemof
If-organization:thecentralplacetheoryof Christallerand
SELF-ORGANIZING ECONOMY
asicideasof centralplacetheoryseempowerfullyintuitive.
a featurelessplain,inhabitedby anevenlyspreadpopula-
"rmers.Imaginealsothattherearesomeactivitiesthatserve
ersbutcannotbeevenlyspreadbecausetheyaresubjectto
o[lliesof scale- manufacturing,administration,and so on.
seemsobviousthatthetradeoffbetweenscaleeconomies
r~[lllsportationcostswill leadto theemergenceof a latticeof
places,"eachservingthesurroundingfarmers.
bvious,but still intuitivelypersuasiveoncepresented,are
en~ementsintroducedby ChristallerandLosch.Christaller",I~ndproducedevidencein support,thatcentralplacesform
hy: therearealargenumberof markettowns,everygroup
t townsis focusedon alargeradministrativecenter(which
arkettown),andsoon. Loschpointedoutthatif alattice
o minimizetransportationcostsforagivendensityofcen-
s, the marketareasmustbe hexagonal.And thusevery
on locationtheorycontainsapictureof anidealizedcen-
systemin whichahierarchyofcentralplacesoccupiesaset
hexagons.
iginalcentralplacetheorystoryappliedto townsservinga
ketoBut it isobviousthata similarstorycanbeappliedto
districtswithin a metropolitanarea.Smallneighborhood
districtsarescatteredacrossthebasinsthatsurroundlarg-
tswith morespecializedstores,alleventuallycenteringon
townwith itsgreatdepartmentstoresandhigh-endbou-
Illdeed,thehierarchicalimageis sonaturalthatit is hardto
.cribingthingsthatway.
\MHyis centralplacetheorynot a standardpartof theecono-
lkit?Why do theintroductorytextsfind no room for a
In thatusescentralplacetheoryto explainwhy we havecenters,thenusesthevonThiinen-Mills modeltoexplain
n ofland usearoundthosecenters?
14
1. You shouldnot,bytheway,concludethatI prefer"commonsense"toaca-
demicdiscourse.In the realworld of affairs,an economicideais mostlikelyto
succeedif it isnaivelywrong- onlythencanit appealto theprejudicesof impor-
tantpeople.
I havealreadyexpressedmyadmirationfor thework of Thomas
Schelling.He is bestknown for his famoustreatiseon non-zero-
sumgames,TheStrategyof Conflict.But I thinkthathisbestbookis
MicromotivesandMacrobehavior,anunderappreciatedclassicthathada
deepimpacton mewhen I first readit asa wet-behind-the-ears
assistantprofessor.The firstchapterof thebook is surelythebest
essayon what economicanalysisis about,on the natureof eco-
nomicreasoning,thathaseverbeenwritten.And thetwochapters
on "sortingandmixing"areawonderfulintroductiontotheideaof
self-organizationin economics.
If thereis anyflaw in Schelling'swork, it is thathe is socleara
thinkerthathecanoftenreachdeepconclusionswith almostnovis-
ible technicalapparatusandsogracefulawriter thathe canoften
maketheseconclusionsseemintuitivelyobvious.Thesevirtues,I
believe,haveworkedagainsthim. As an amateuranthropologist
who haslongstudiedthatpeculiarcultureknownasacademiceco-
nomics,it seemstomethataneconomicideaflourishesbestif it is
expressedin arathertechnicalway,evenif thetechnicaldifficultyis
largelyspurious.!After all,a teacherwantssomethingto do atthe
blackboard,and a cleverstudentwantssomethingon which to
demonstratehisor hercleverness.If a deepideais conveyedwith
simpleexamplesandelegantparables,ratherthanwith hardmath,
it tendsto getignored.
In anycase,however,in MicromotivesandMacrobehaviorSchelling
presenteda simpleyetprofoundmodelof segregation.The basic
ideasoundstrivial:segregationresultswhenpeopleprefernot to
havetoo manyneighborswho aredifferentfrom themselves.But
Schellingmadetwo muchlessobviouspoints.First,mild prefer-
encesaboutthecolor or cultureof your neighbors- preferences
thatseemon thefaceof themtobeconsistentwith maintainingan
integratedresidentialpattern- in facttypicallyleadtoahighdegree
of segregation.Why?Because,evenwhenpeoplehavemildprefer-
encesof theform"I don'tmindhavingsomeneighborsof adiffer-
entcolor,aslongasI'm not toomuchin theminority,"integrated
2. An equivalentstatementof therule is thateachindividualrequiresthatat
least37percentof theneighborsbeof hisor herown type.
17Self-Organizationin Space
residentialpatternstendtobeunstablein thefaceof randompertur-
bations.Second,evenif theconcernsof individualsareverylocal-
theycareaboutonlytheirimmediateneighbors- whatemergeare
largesegregatedneighborhoods.Thus Schellingderived,without
anyfanfare,a themeof manywriterson complexity:local,short-
rangeinteractionscancreatelarge-scalestructure.
Characteristically,hemadethesepointswith afewsimpleexam-
plesratherthanafullyworked-outmathematicalmodel.It ispossi-
ble to setup suchamodel,andI amsurethatonecanevenprove
theoremsaboutit. I shallreservemylimitedmathematicalfirepow-
er, however,for my own models. For our current purposes,
Schelling'sapproachwill begoodenough.
Let us,then,imaginea "city" thatconsistsof anumberofloca-
tionslaidout in a squarelattice,like achessboard.For illustration,
indeed, let us actuallyuse an 8-by-8 chessboard-sizelattice,
althoughthesameprincipleswouldapplytoamuchlargerdomain.
And letus supposethattherearetwo kindsof people- callthem
blackandwhite,buttheycouldrepresentanykind of racialor cul-
turalgroups,orforthatmatterdifferenttypesofbusinessesthattend
to repeleachothers'customers,like boutiquesand auto supply
stores.
We now assumethatblacksandwhitescareaboutthecolor of
theirimmediateneighbors.(Thatmeanstheabuttingsquaresonthe
chessboard.)Their preferencesareassumedtobenotsomuchalik-
ing for neighborsthe samecolor as a fear of being isolated.
Specifically,Schellingsuggestedthe followingrule: an individual
with oneneighborwill try to moveif thatneighboris a different
color;onewith twoneighborswantsatleastoneof themtobethe
samecolor;onewith threetofiveneighborswantsatleasttwotobe
hisor hercolor;andonewith six to eightneighborswantsatleast
threeof themtobelikehim or her.2
Thesepreferencesareconsistentwith an integratedresidentialpattern.ConsiderFigure1.2,in which#and@ signifYthetwodif-
ferentgroups.Herewe havemanagedto place60 individualsin a
completelyintegratedpattern,without violatinganyone'scon-
straints.That is,completeintegrationisanequilibrium.
SELF-ORGANIZING ECONOMY16
But arewelikelyto geta resultlike thisin practice?No, argued
Schelling.Althoughhedidnotputit quitethisway,anequilibrium
like theone shownin Figure1.2will be unstablewith respectto
somerandomshufflingandwill thereforetendto unravel.
To showthis,Schellingtookthepatternin Figure1.2andmessed
it up a bit. (His instinctwasunerring.My first inclinationwould
havebeento startfromacompletelyrandomallocationof peopleto
locations.It turnsout, however,thatself-organizingspatialsystems
yieldthegreatestorderwhentheinitialconditionis a smallpertur-
bationawayfromtheunstableintegratedorflatequilibrium.Wewill
seewhyin thesecondpart.)Specifically,heextracted20individuals
atrandom,bothdisruptingthepatternandfreeingupsomeroomfor
discontentedindividualsto move,thendisruptedthepatternabit
moreby filling fiveemptysquaresatrandomwith #sor @s.Figure
1.3showstheresultwhenI andmyrandomnumbergeneratordoit.
It isprettyobviousthatin Figure1.3someof thepeopleareno
longercontentwith their locationsand will move.When they
move,however,theywill in turnoftenmakethosewho stayunhap-
py- eitherby deprivingsame-colorindividualsof neighborsor by
shiftingthebalanceagainstnewneighborsof adifferentcolor.Soa
chainreactionbegins.To simulatethatchainreactiononacomput-
eryouwouldneedto specifytheorderin whichpeoplemoveand
how theypick amongavailablelocations.If you aredoing it by
hand,you canbe looseraboutit - it doesnot mattermuch.Like
Schelling,I did thisbyhand(usingaspreadsheetinsteadof pennies
and dimeson a realchessboard)andjust watchedthe structure
evolve.When thingssettledown,yougetFigure1.4.
Guesswhat: eventhough individualsare tolerantenoughto
acceptan integratedpattern,theyendup with moreor lesstotal
segregation.And, eventhoughindividualscareaboutonly their
PerturbingtheEquilibrium.If thepatternis givensome
randomscrambling,someindividualsareno longercontent
withtheirlocation.
19Self-OrganizationinSpace
#@ @#@
#
@#@#@#
@
#@#@#@#
#
##@#
@
@@@@@#
#
@ @#@#@
@
# #
@
@ @
Figure1.3
#@#@#@
#
@#@#@#@
@
#@#@#@#
#
@#@#@#@
@
#@#@#@#
#
@#@#@#@
@
#@#@#@#
@
#@#@#
An IntegratedCity. Evenif peopleinsistthataminimum
fractionoftheirneighborsresemblethemselves,it ispossibleto
createanequilibriumresidentialpatternthatishighlyintegrat-
SELF-ORGANIZING ECONOMY
Figure1.2
18
21Self-Organizationin Space
Asyoucantell,I loveSchelling'smodel.It isaperfectexampleof
how to wearyour sophisticationlightly;thewaythatbig conclu-
sionsarederivedfromplayingwith coinsonachessboardhasaspe-
cialcharm.As amodelof theself-organizationofurbanareas,how-
ever,it hassomelimitations.Someof themareproblemsthatI will
nottrytofix in thisbook;forexample,thereisnoexplicithandling
of themarketfor land,which surelyplaysacrucialrolein mediat-
ingthechoicesofhouseholdsandfirmsaboutwheretolocate.One
problemthatI do want to dealwith, however,is thatSchelling's
model is too one-sided:it tellsus why birds of a featherflock
togetherbut offersno reasonwhy thereshouldeverbemorethan
twoflocks.
To seewhat I mean,askwhatwould happenif I replacedmy
8-by-8chessboardwith amuchbiggerone,say1000by1000.What
wouldaSchelling-typemodelpredictasanoutcome?Well, ahuge
literaturein physicsdealswith systemsnot too differentfrom
Schelling'smodel,calledspin-glasses,andanumberof formalresults
havebeenderived;but I havetoadmitthatI havenotyettakenthe
timeto try to masterthisliterature.Still, a few thingsseemfairly
obvious.The tendencyof Schelling'smodelis alwaysto dividethe
whole city into two vast#and@territories.That doesnot mean
thatwewill necessarilygetthere:if we startwith arandompattern,
the chainreactionof movinghouseholdswill typicallydie out at
somepoint,leavingthecity"frozen"into#and@ domainsofvary-
ing sizes.(If we settheparametersright, thesizedistributionwill
surelyobeyapowerlaw- butmoreaboutthatkind of thinglater.)
We can,however,"melt"thesedomainsif weaddabit of "temper-
ature"tothestory,bygivingevencontentedhouseholdssomesmall
probabilityof movingjust for the hell of it. In thatcasewe will
indeedeventuallyfind ourselveswith atwo-neighborhoodcity.
Now thatis too stronga result.Let usgo backto Los Angeles.
Therearesomewaysin whichthecityhasatwo-zonestructure:all
thebeautifulpeoplelivein BeverlyHills, all thenonbeautifulpeo-
plesomeplaceelse.But whatissostrikingaboutLA comparedwith
atraditionalcityispreciselyitsmultipolarity.Thereisno dominant
downtownofficedistrict:instead,thereare16edgecities,spreadin
a not-too-irregularfashionacrossthe metropolitanarea- and,
accordingto Garreau,8 morein theprocessof coalescing.
# # ####
#
## ###
#
###@@ #
#
##@@@@
@
@@@@@@
@
@@@@@@
@
@
@
@ @
SELF-ORGANIZING ECONOMY
1.4 A SegregatedCity.Theresultisachainreaction,in which
eachmoveprovokesothermoves;intheendmildconcernsabout
beinginalocalminorityproduceacompletelysegregatedcity.
20
calneighborhood,thewholechessboardgetsorganizedinto
eareaandablackarea.
and@ reallydorepresentwhiteandblack,it isanastyoutcome.
That, owever,isbesidethepointforthisbook(exceptasareminder
that . anizeddoesnot mean"good").What I wantto emphasizeis
thatt ischessboardcityhasengagedin aprocessof self-organization.
Larg scaleorder- not a nice order,but ordernonetheless- has
emeredfromabasicallydisorderedinitialcondition.
T .s large-scaleorderemergesbecausea disorderedstate,in
whicl #'sand@'sareevenlymixed,is unstable:scrambleit abitand
yous .rt adynamicprocessthatproducessegregation.This isthere-
fore y firstillustrationof theprincipleof orderfrominstability-
butd notworry,therewill bealot more.
r··
II
DGE CITY DYNAMICS
23Self-Organizationin Space
3. Alternatively,one canimaginea city of infinite extent.Los Angelesmay
approximatethiscondition.
theends.Thatisnotsimplyaformalissue:in realityanofficecom-
plexnearthemiddleof a metropolitanareawill be differentfrom
onenearthepointwheresubdivisionsbegintobemixedwithfarm-
land.BecauseI do notwantto dealwith thatissue,I needto make
asillyassumption:mycityisnotonlyonedimensionalbutcircular,
sothereareno ends.3
A secondissueis thetreatmentof landandlandrents.Modern
urbaneconomistsaregenerallywilling to playgameswith geome-
try,but theytendto be quitefanaticalaboutexplicitlymodeling
landrent- when I presenteda modelwithout landrentsto one
group,adisgruntledurbantheoristtoldmethatasfarashewascon-
cerned,urbaneconomicswasessentiallyaboutlandrent.It is obvi-
ous where thatattitudecomesfrom: in the von Thiinen-Mills
modellandrentis indeedthecrucialingredient.But I amaskinga
differentquestionandwill askyou to bearwith anapproachthat
recognizeslandscarcityatbestin animplicit,reduced-formway.
A thirdissueis thetreatmentof expectations.I will be tellinga
dynamicstory;it isastoryabouthowedgecitiesevolve.But I donot
wantto worry aboutforward-lookingbehavior.To manyecono-
mists,raisedin anenvironmentof rationalexpectationstheory,that
byitselfdisqualifiesamodel.Most ofyouprobablydonotcare,but
for thoseofyouwho do, I urgeyoutoputyourprejudicesonhold.
Finally,I haveapersonalrulethatI amabouttobreak.In gener-
al, I do not like simply assumingthe existenceof external
economiesanddiseconomies.It oftenseemstoocloseto assuming
your conclusions.(I know of oneeconomistwho triedto explain
hisworktoagroupofphysicists,oneofwhomsarcasticallysaid,"So
whatyou'retellingusis thatfirmsagglomeratebecauseof agglom-
erationeconomies.")Most ofmyworkoneconomicgeographyhas
focusedon tryingto deriveexternaleconomiesout of theinterac-
tions among scaleeconomies,transportationcosts,and factor
mobility- to makeexternaleconomiesan emergentproperty.I
actuallyarrivedattheapproachI amgettingto in thecontextof
suchamodel,onethatI shallpresentin thesecondpart.But it turns
out thatit is easiestto explainthebasicideasimplyby assuming
externaleconomies,andsoI will temporarilysuspendmyrule.
SELF-ORGANIZING ECONOMY
So if we wanta storyaboutthe self-organizationof theurban
l~ndscapethatreflectsthepolycentric,plum-puddingmetropolitan
reaswe increasinglyinhabit,we needamodelthatspontaneously
roducesnot only orderbut somekind of more or lessregular
epetitivepattern.Let usseeif wecanconstructone.
IinamomentI will describeanapproachthat,it seemstome,sheds
onsiderablelightonhowofficedistricts- edgecities- mayemerge
ih a polycentricmetropolitanarea.I believeand hope that the
pproachwill provideausefulmetaphorfor theemergenceof spa-
tlal structurein a varietyof othercontexts.But anyexperienced
conomistknowsthatin presentinganewapproachonemustbegin
with somepreemptiveexcusesfor thequestionablesimplifications
nehasmade.SobeforeI evenstartto describemyframework,let
eoffersomejustificationsfor thewayit is done.
The modelsthatI will describelooselynow andpresentmore
lly in thenextpartwill, not surprisingly,representakind of ide-
allizationof reality.This will not shockanyone:bothvon Thiinenandcentralplacetheorybeginwith theidealizationof ahomoge-
eousagriculturalplain,which neverboremuchresemblanceto
alityandbearsevenlessnow thanit did whentheywrote.What
ind of idealizationseemslegitimateis,however,in theeyeof the
eholder.My guessis thatthereareatleastfourwaysin whichthe
a~proachI amabouttopresentwill botherpeople.
First, thereis the issueof geometry.The Germantraditionin
locationtheorywascheerfulaboutassumingawayrivers,roads,and
ariationsin landqualitybutrigorousaboutfacingupto theconse-
uencesof thefactthattheEarth'ssurfaceis twodimensional.It is
cfmmon in modernurbaneconomictheory,however,to analyze
"long, narrow"citiesthatareeffectivelyone dimensional(as,for
ebmple, in Fujita1988),a simplificationthatseemsreasonableto
ebutthatwouldprobablyhavehorrifiedmanyof theGermans.
Well, it turnsout thatformypurposeseventheone-dimension-
cityis notquitesimpleenough,becauseI wantto focuson self-
0rganizat.•ion:theemergenceof structurethatarisesnotfrominher-
e t differencesamonglocationsbut from theinternallogicof the
s stem.And evenin a one-dimensionalcity locationsaredistin-
g ishedfromoneanotherbyonecrucialaspect:theirdistancefrom
4. Joel Garreauwrites:"Fivemillionsquarefeetis a pointof spontaneous
combustion.It turnsouttobeexactlyenoughtosupportthebuildingofaluxu-
ryhotel.It causessecondaryexplosions;businessesbegintoflocktothelocation
toservethebusinessesalreadythere."
Now thattheexcusesareout of theway,letusgetto thesub-
stance.
Imagineametropolitanarea,whichwe canthink of asahomo-
geneousexpanseof identicalhousingdevelopments- exceptthat,
ratheroddly,thepopulationisdistributednotin atwo-dimension-
alsprawlbutin anarrowring,andtravelispossibleonlyalongthat
ring'scircumference.And supposethatthereissomebusinessactiv-
ity- it couldbeofficework,it couldberetailing- thatdependsOn
thespread-outpopulationbothasamarketandasasourceoflabor.
Let usalso,unobjectionably,supposethatthedecisionsbybusi-
nessesaboutwhereto locateareinterdependent.That is, thedesir-
abilityof anyonesiteasabusinesslocationdependsOnwhereallof
theotherbusinessesarelocated.And we mayalsosafelysuppose
thatbusinessesmigrateovertimefromlessto moredesirablesites.
Clearlythedynamicsof thisprocessdependOnthenatureof this
interdependence.One canimaginetwogeneralsortsof interdepen-
dence.On the Onehand,businessesmight dislikehavingother
businessesnearby,becausetheycompeteforcustomers,workers,or
land.Call theseconsiderationscentrifugalforces,forcesthatpromote
dispersionof business.On theotherhand,businessesmightlike to
haveotherbusinessesclose,becausetheyattractcustomersto the
areaor helpsupporta greatervarietyof localservices.4Call these
centripetalforces,forcesthattendto makebusinessesclumptogeth-
er.If onlycentrifugalforcesexisted,businesseswouldspreadthem-
selvesevenlyacrossthe landscape.If therewereonly centripetal
forces,theywouldrushtogetherinto Onebigclump.
But whatexplainsthepolycentric,plum-puddingpatternof the
modernmetropolis?In general,amodelthatwouldexplainthispat-
ternmustmeettwo criteria:
Criterion 1.Theremustbe a tensionbetweencentripetaland
centrifugalforces,with neithertoostrong.
Criterion 2. The rangeof thecentripetalforcesmustbeshorter
thanthatof thecentrifugalforces:businessesmustliketohave
otherbusinessesnearby,but dislikehavingthema littleway
away.(A specialtystorelikesit whenotherstoresmoveinto its
25Self-Organizationin Space
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shoppingmall,becausetheypull in morepotentialcustomers;
it doesnot like it whenstoresmoveinto a rivalmall10miles
away.)
And that'sall thatwe need.In anymodelmeetingthesecriteria,
anyinitialdistributionof businessacrossthelandscape,nOmatter
howeven(orrandom),will spontaneouslyorganizeitselfintoapat-
ternwith multiple,clearlyseparatedbusinesscenters.
Doesthispropositionsoundobvious?Maybeso (althoughI did
nothaveit clearin myOWnminduntil afterI startedplayingwith
mathematicalmodels).But thereismore.For awidevarietyof spe-
cific modelsin which criteria1and2 aremet,anyinitialdistribu-
tion of businessacrossthelandscapewill evolvenot merelyinto a
patternwith severalbusinesscentersbut into a patternin which
thesecentersareroughlyevenlyspaced,with a characteristicdis-
tancethatdependsOnthedetailsandparametersof themodelbut
notOntheinitialdistribution.And thesmootheris theinitialspa-
tial distributionof the businesses,the more eventheir eventual
spacmg.
Figure1.5 The Evolutionof EdgeCities.An ititiallyalmostuniform
distributionof businessaccrossthelandscapeevolvessponta-
neouslyintoa higWystructuredmetropoliswith twoconcen-
tratedbusinessdistricts.
SELF-ORGANIZING ECONOMY24
5. Eachlocationreceivedaweight5 +Ui, whereUi wasalocation-specificran-
domvariablebetween0 and1, ands wasa"smoothing"parameter,setequalto 5
forthisrun.Then eachlocationwasassignedashareofthebusinessesproportional
to itsweight,
6. Robert Gordonof NorthwesternUniversityhasdubbedFigure1.5the'59
Cadillacmodel.
At thispoint I hadbettershowyou anillustration.It turnsout,
not too surprisingly,thatcomputersimulation- and computer
graphics- arean invaluableaid to thinkingaboutself-organizing
systems.Figure1.5isasamplerun of amodelof a "city" consisting
of 24 locationsaroundacircle.The locationsareshownon theX
axis;bearin mindthatlocation24isnexttolocation1.I startedthe
runwith afairlybutnotperfectlyevenallocationof businessacross
theselocations,5thenlet it evolveaccordingto a rule thatcaused
businessesto movetowardlocationsthatwere highly desirable.
"Desirability"of a locationwas both positivelyand negatively
affectedby thenumberof businessesatotherlocations,with both
effectsdecliningwith distancebutwith thepositiveeffectsdeclin-
ing fasterthanthenegativeeffects.The Y axisof thefigureshows
thepassageof time;theZ axisshowstheshareof thebusinessesin
eachlocationateachpointin time.Thus thefiguregivesyouasort
of frozenportraitof thewholesimulatedhistory.
Let uslook abit atFigure1.5;thepicturecontainsquitea lot of
information.The rightedgeof thecalculatedsurface,whichrepre-
sentsthe initial geographicaldistributionof business,is almosta
horizontalline.That is, I havestartedmy"city" offwith almostno
spatialorganization.But eventuallythesurfacerearsup into apair
of dorsalfins:6 all of thebusinessesendup in locations8 and20.
The cityhasspontaneouslydevelopedastrongspatialstructure.
This maynotbesurprising.But now noticewhich locationsget
thebusinesses.In a24-locationcircularcity,locations8 and20are
exactlyoppositeoneanother.That is notanartifactof theparticu-
lar startingposition:ifyou run the modelrepeatedlywith these
parameters,butwith a differentinitial spatialdistributionof busi-
nesseachtime,you will consistentlygettwo businessconcentra-
tionsoppositeeachother.
By theway,I do notwantyouto gettheimpressionthatthereis
somethingspecialaboutcitieswith twobusinessdistricts.Figure1.6
showsa typicalrun of the samemodelwith somewhatdifferent
27Self-Organization in Space
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parameters.In thiscasewegetfourbusinessdistricts,equallyspaced
aroundthecircle.The generalprinciple,then,is thatthecityorga-
nizesitselfinto a structurewith a characteristicdistancebetween
businessdistricts;if thereareonly two, thisimpliesthattheyface
eachother.
Letusgobackto Figure1.5andlook atonemorething.Look at
how thealmostflat initial surfaceevolvesovertime.Althoughin
theendonly twowidelyseparatedlocationsendup with business
concentrations,in theearlystagesof self-organizationit doesnot
look asif thewinninglocationsaregrowingattheexpenseof their
neighbors.On thecontrary,initiallynotonlythewinninglocations
butthosenearbygrow.The surfaceseemsto undulate,with waves
risingupoutof theplain.Only aftersometimehaspasseddothese
wavesgatherthemselvesinto dorsalfins,with theeventualcenters
cannibalizingtheirneighbors.Again,thisimpressionis notunique
toaparticularrun:it isaconsistentfeature,whatevertheinitialdis-
tribution.
Figure1.6 SameStory,DifferentParameters.With somewhatdiffer-
entparameters,themetropolisevolvesfour businessdistricts.
SELF-ORGANIZING ECONOMY26
7. Rememberthatthesearespatialfrequencies:thesearewobblesin space,not
time.
It turnsout thatthis imageof an undulatingsurface,with the
wavesgrowingovertime,isthekeytounderstandingtheprocessof
self-organization.To fullyexplainwhywill takealittletime,andI'll
reservethatforthesecondpart(andthetechnicalappendix).But let
meofferapreliminaryview.
RememberthatI startedthe simulationin Figure1.5with an
almostbutnotexactlyflatdistributionofbusinessesaroundthecir-
cle.The deviationof thatdistributionfromperfectflatnessmaybe
representedasanirregular,wobblyline.But it isgenerallytruethat,
to usetechnicallanguage,anirregularwobblecanbethoughtof as
thesumofmanyregularwobblesatdifferentfrequencies.In partic-
ular,anirregularwobblearoundacirclecanbeexpressedasthesum
of oneline thatwobblesonceasit goesaroundthecircle,another
thatwobblestwice,a third thatwobblesthreetimes,andso on.
(Someofyouknow thatI amtalkingaboutaFourierseries.)
Now hereis thepoint:in anymodelthatsatisfiesmytwocrite-
ria, someof thesecomponentwobbles- wobblesthatgo certain
particularnumbersof timesaroundthecircle- will tendto grow
overtime(althoughwobblesatotherfrequencies7maytendto die
out).And, becausethedecompositionof anirregularwobblewill
ordinarilycontainwobblesof allpossiblefrequencies,anevendis-
tributionofbusinessaroundthecircleisunstable.Someof thecom-
ponentwobbleswill grow,creatinganincreasinglyunevenspatial
distributionof business.Orderfrominstability!
Why, however,is theeventualspacingof businessso regular?
Becausewobblesthatgodifferentnumbersof timesaroundthecir-
clewill growatdifferentrates.If theinitialdistributionof business
is sufficientlysmooth,afterawhile thedeviationfromsmoothness
will bedominatedbywhicheverfrequencywobblegrowsthefastest
- bythemostunstablewobble.And thefrequencyof thiswobble,the
numberof timesit goesaroundthecircle,will determinewherethe
peakbusinessconcentrationsarelocated.The undulationsyou see
in Figures1.5and1.6arethatmostunstablewobbletakingoverthe
distributionof businesses.For the parametersusedto generate
Figure1.5,themostunstablewobblegoesaroundthecircletwice;
for thoseusedto generateFigure1.6,themostunstablewobble
goesaroundthecirclefour times.Not only doesinstabilitycreate
order,theform of thatorderis dictatedby a sortof principleof
maximuminstability.
Whataboutthelastpartof thefigures,wherethewobblesgath-
erthemselvesup intospikes?Well, theformalansweris thatevery-
thingthatI havesaidisvalidonlyforalinearapproximationto the
model,whichbreaksdownwhenthespatialdistributionofbusiness
getstoouneven.Lessformally,in theearlystagesof self-organiza-
tionthemostfavoredlocationscangrowbypullingbusinessesaway
from distantlocations.Once thereareno morebusinessesin the
largegapsbetweenbusinesscenters,theycancontinuetogrowonly
byeatingtheirneighbors.The importantpoint,however,isthatthe
locationsof thewinnersaredeterminedin theearlierstage:thedis-
tancebetweenedgecitiesis determinedby thewavelengthof the
mostunstablewobble.
OK, letusstopandtakeadeepbreath.EventhoughI haveavoid-
ed any formal modeling,you may at this point havesuddenly
realizedhow seeminglyabstract,how unrelatedto the detailsof
freewaysandshoppingmalls,skyscraperconstructionandfastfood
consumption,thishasgotten.That isverymuchthestyleof com-
plexitytheorists:indeed,thewholerationaleof thefieldis theidea
thatcommonprinciplesmayapplyto subjectswith verydifferent
details.Still, hastheabstractionled us into a storythatconflicts
badlywith reality?
My guessis thatmanyreaderswill objectto theimpliedregular-
ity of theresult- thoseequal-size,regularlyspacedbusinesscon-
centrations.In realityedgecitiesarenotallthesamesizeor equally
spacedacrossthe landscape.That doesnot worry me, however.
Mter all, thereallandscapeis not homogeneous.Therearehigh-
ways,whoseintersectionsmakeparticularlyfavorablesitesforbusi-
ness,variationsin thepleasantnessor buildabilityof sites,andfor
thatmatterrealmetropolitanareasdo havecentersandedgesand
thusareprimafacienot undifferentiated.Furthermore,theresult
thatbusinessdistrictsareevenlyspacedistrueonlyforanimaginary
historyinwhichbusinessstartsoutspreadalmostevenlyacrossloca-
tions;becausetherealhistoriesarenotlikethat,we shouldexpecta
moreirregularresult.
But if realcitiesdo not evolvein thewayI havejust described,
doesthatmeanthatthewholeapproachis irrelevant?I think not,
but I needto introducesomemore conceptsand examplesto
explainwhy.
29Self-Organizationin SpaceSELF-ORGANIZING ECONOMY28
-----2-----
ComplexLandscapes
In hiswonderfulbookNature'sMetropolis:ChicagoandtheGreatWest,
thehistorianWilliamCronondistinguishesbetweentwolandscapes
in whichurbanevolutiontakesplace.One is thenaturallandscape:
themountainranges,rivers,andlakesthataregivensof theenvi-
ronment.The secondis the createdlandscapeof railroadlines,
canals,farmingpatterns,and citiesthemselvesthat resultsfrom
humandecisions.Crononarguesthatin themodernworldthecre-
atedlandscape,which he refersto assecondnature,hasbecomefar
moreimportantasadeterminantoflocationthanthe"firstnature"
in which it is embedded:Chicago'sroleasa GreatLakesportwas
quicklyovershadowedbyitsroleasarailhub.And secondnatureis
oftenself-reinforcing:railroadsaimedatChicagobecauseit wasthe
economiccenterof itsregionandtherebymadeitscentralityallthe
greater.That is, the landscapeof secondnature is inherently
dynamic.
But how doesonevisualizea landscapethatchangesovertime?
One answeris ahistoricalatlas:a sequenceof mapsthattracesout
thechanges.In somecasesit maybepossibleto do abit betterby
drawingakindof temporalreliefmapinwhichthetimedimension,
andthustheevolutionof thelandscape,ismoreor lessimperfectly
represented.Indeed,Figures1.5and 1.6arejust that:theyshow
how someimaginarylandscapeschangeoverthe courseof their
imaginaryhistories.But evenwhenyoucandothis,allthatyouget
isadescriptionofwhathappened;whyit happenedisatbestimplic-
it.
Sowhatdoyoudo?Anyonewho hasworkedon formalmodels
of dynamicsystemsknowstheanswer:youtryto drawapictureof
11
1. Strictlyspeaking,onecanrepresentatwo-dimensionaldynamicsystemasa
three-dimensionalreliefmaponlyif thesystemactsasif it werefollowingthegra-
dientof somepotentialfunction.This is sometimesreasonable,but not always:
theevolutionof asinglespeciesisin effectmaximizingsomethingwecancallfit-
ness,but thecoevolutionofpredatorsandpreyis not.Nonetheless,thelanguage
commonlyusedtodescribephasespace,with itsbasinsof attraction,saddlepaths,
andsoon, drawsheavilyon thereliefmapmetaphor;andI atleastviewthepoet-
ry asworth thepotentialconfusion.
2. See,for example,theinfluentialpaperby Hopfield (1982)andcompareit
with the"NK model"ofKauffinan (1993).
yetathirdlandscape,a "phasespace"in whicheachpointsumma-
rizesthepositionof thesystematapointin timeandin whichthe
rulesthatgovernthesystem'sevolutionaretranslatedinto "lawsof
motion"in thatabstractlandscape.
Phasespacerepresentationsof dynamicsystemsareextremely
commonin moderneconomicanalysis.In general,however,we
tendtofocuson onlyanarrowrangeofpossibletypesoflandscapes
- indeed,basicallyononlytwofairlysimpleforms.Beforethemid-
1970snearlyalldynamicmodelsin economicsweregloballystable;
thatis, thephaselandscapewasassumedto belikeabowl,a single
basinof attractionin which all pointsdrainto a singlelong-run
equilibrium.Sinceabout1975it hasbecomecommonalsotowork
with modelsin whichthephaselandscapelookslikeasaddle- and
in whichsomesetof forward-lookingvariables,suchasassetprices,
is determinedbytheassumptionthattheeconomyisalwayson the
ridgethatis theonlypathto long-runequilibrium.1
The literatureon complexity,however,is largelyconcernedwith
systemsin which thedynamiclandscapelookslike neitherabowl
norasaddle;indeed,it isoftenconcernedwith "ruggedlandscapes"
(asStuartKauffmanputsit) thatlook like theSouthDakotabad-
lands.
What aspectsof a dynamicsystemleadto a ruggedphaseland-
scape?I haveno generalanswer,andI do notknow if thereis one.
Many of themodelsin thecomplexityliterature,however,havea
similarsetup.2The modelerrepresentshis or her systemas an
ensembleof manycomponents,eachof which is atanyparticular
timein oneof severalstates:magneticdipolesthatareorientedup
or down,neuronsthatarefiring or quiescent,genesthathaveone
characteror theother,andso forth.And futurechangesin these
statesarelinkedin someway:theenergyofaspin-glass,andthusits
likelydirectionof change,dependson whethernearbydipolesare
orientedin thesamedirectionornot;neuronsexciteor inhibiteach
other;theeffectof changingan individualgeneon anorganism's
fitness,and thus the likelihood that a mutationwill survive,
dependsonwhatothergenesit has.Suchasystem,it turnsout,will
produceacomplexdynamiclandscapeaslongastwoconditionsare
met:theresponsesof theindividualunitsmustbediscrete(neurons
eitherfiring or not),andtheremustbe a mixtureof positiveand
negativefeedback(neuronsbothexciteandinhibiteachother).
Now think aboutspatialeconomies.They aresystemsin which
manycomponents(firms)areat anyparticulartime in particular
states(locations)and in which changesin thesestatesarelinked
(throughagglomerationeconomiesanddiseconomies).If thereare
significanteconomiesof scale,firmswill chooseonlyafewdiscrete
locations;andtherewill usuallybeamixtureof positiveandnega-
tive feedbackbetweenthesechoices.Thereforewe might well
expectspatialeconomiesto havecomplex,ruggeddynamicland-
scapes.
And indeedthatis whatyou find whenyou look atevenquite
simplemodelsof spatialeconomies.Over thelastfewyears,I have
spenta lot of time tryingto understandthebehaviorof a model
almostasminimalistasthe edgecity model I introduceda little
while ago.(In fact,asI shallexplainin Part II, the two models
behavein verysimilarways.)In thisstructureweimaginethatthere
aretwo factorsof production:immobileagriculturalworkersand
mobilemanufacturingworkers.Manufacturingisamonopolistical-
ly competitivesectorcharacterizedbybothincreasingreturnsatthe
levelof thefirm andtransportcosts.The interactionamongfactor
mobility,increasingreturns,andtransportcostsgeneratesforcesfor
agglomeration:firms tendto concentrateproductionin locations
with goodaccesstomarkets,butaccesstomarketsisgoodprecisely
whereotherfirmsareconcentrated.Working againstthese"cen-
tripetal"tendencies,however,is the"centrifugal"pull providedby
thegeographicallydispersedagriculturalsector.
If weaddsomerudimentarylawsof motion,saytheassumption
thatmanufacturingworkerstendtomovetolocationsthatofferrel-
ativelyhigh realwages,we geta dynamicstoryin a phasespace
33Complex LandscapesSELF-ORGANIZING ECONOMY32
3. The kind of complexlandscapethatcanarisein modelsof economicgeog-
raphycan,of course,arisein manyothereconomiccontextsaswell.Mostnotably,
thechoiceamongseveraltechnologiessubjecttonetworkexternalitieswill present
averysimilarpicture,with thelandscapecomplexif noneof thetechnologieshas
too stronganinherentadvantageandtheexternalitiesaresufficientlypowerful.
definedbytheallocationofmanufacturingworkersacrosslocations.
And thisdynamiclandscapecaneasilybeverycomplex.3
An easilyshownexampleis thethree-regioncase.Supposethat
therearethreeequidistantlocations,with equalagriculturallabor
forces.The allocationof themanufacturingwork forceamongthe
threelocationscanberepresentedasapointon the"unit simplex":
atrianglewhosecornersareatthepoints(1,0, 0), (0, 1,0),and(0,
0, 1)in a spacewhoseaxesaretheshareof manufacturingin each
locationbut thatcanconvenientlybe pastedonto a two-dimen-
sionalpage.Startingatanygivenpointon thatsimplex,onecanlet
themodelevolveandseewhereit endsup.To drawthepictureana-
lyticallyis extremelydifficult,but it is straightforwardto compute
numericalexamples.
Figure2.1showswhatI getforthemostinterestingrangeofpara-
meters.(Thereareonlythreeparametersin themodel:theelastici-
ty of substitutionamongproductsin themanufacturingsector,set
for thisexampleat4; theshareof manufacturesin expenditure,set
at0.2;andthetransportcostbetweenanytwolocations,setatOA.)
At eachof anumberof pointson thesimplex,representinganini-
tialallocationofmanufacturingworkers,I drawanarrowrepresent-
ing thedirectionandspeedof "flow". It turnsout thatthereare
fourequilibria:threein whichallmanufacturingis concentratedin
onelocation,onein whichthereis anequaldistributionof manu-
facturingacrossthelocations.Therearecorrespondinglyfourbasins
of attraction:a centralbasinthatleadsto theequaldivisionout-
come,andthreeflankingbasinsthatleadto concentration.
The landscapecanbecomefar morecomplexwhen thereare
morelocations.Suppose,forexample,thatweconsideranexample
in whichthereare12locations,laidoutin acirclelikethenumbers
on aclock.(Twelveis aparticularlyconvenientnumberbecauseit
is a fairly smallnumberwith a largenumberof divisors.)The
dynamicsonceagaintakeplaceon aunitsimplex- butthistimean
ll-dimensionalone.This is hardfor mostof us to visualize.We
can,however,getagoodideaof thepropertiesof themodelexper-
Figure 2.1 Basins of Attraction. A three-regioneconomicmodelcanend
up with four differentlocationalpatterns,dependingon initial
conditions.
35
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Complex Landscapes
'"
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imentally,bystartingwith anumberof randomallocationsof man-
ufacturingacrosslocationsandseeinghow theyevolve.
Figure2.2illustratesa typicalrun. The initialrandomallocation
ofmanufacturingeventuallyorganizesitselfintotwomanufacturing
concentrations,atlocations6 and11;thatis,5 apart.In thecourse
of anumberof runswith theseparametervalues,I gottwoconcen-
trations5 apartabout60percentof thetime,twoconcentrations6
aparton almostall otheroccasions.At rareintervalsa run would
leadto threeequallyspacedconcentrations.
On a circlewith 12locations,thereare12waysto placetwo
markers5 apart,6waystoplacethem6apart,and4waystoplace3
equidistantmarkers.So it appearsthatwith theseparametersthe
modelimpliesalandscapewith 22basinsofattraction- ruggedter-
rainindeed.In suchaworld thelocationof economicactivity,and
to someextenteventhestructureof theresultingeconomicgeog-
raphy,woulddependcruciallyon initialconditions,whichisto say
on historicalcontingency.
Now, finally,we getbackto thequestionthatledusoff on this
sidetrip throughphasespace.The beautifullysimple,aesthetically
pleasing"'59 Cadillac"picturesin Figures1.5and1.6werebased
SELF-ORGANIZING ECONOMY34
THEEMrnRGENCE OF ORDER
37ComplexLandscapes
Let us look againatwhat I saidaboutthe 12-regionmodelof
economicgeographywhoseoutcomeis representedin Figure2.2.
The modelappearsto havea dynamiclandscapewith 22basinsof
attraction.And yet,lookedata differentway,the resultsaresur-
prisinglyordered.Startingwith arandomallocationofmanufactur-
ing acrossspace,the modelalwaysorganizesitselfinto a highly
orderedstructurein whichmanufacturingisconcentratedin twoor
threeequal-sizeconcentrations.Furthermore,althoughthereare
manysuchequilibriumstructures,theysharestrongsimilarities:all
involveroughlyequidistantcitylocations,withafairlynarrowrange
of typicaldistancesbetweencities.
Whatwe sawin theedgecitymodelwasthesecharacteristicfea-
turesofequilibriumstructuresin anextremeform:ifwestartedthat
modelfromanalmostuniforminitialdistributionofbusiness(cor-
respondingto a startingpoint nearthe centerof the simplexin
Figure2.1),we gotbusinessconcentrationsexactlyevenlyspaced
aroundthe circle,with an invariantdistancebetweenconcentra-
tions.The sameoccursin thismodel:if I taketheparametersused
to generateFigure 2.2 but restrictmyselfto initial positionsin
which thedistributionof manufacturingis sufficientlyflat, I will
consistentlygetapicturelike Figure1.5- theeconomyorganizes
itselfinto astructurewith twocities,exactlyoppositeoneanother.
Whatthissuggeststomeis thatthefakehistory,in whichahigh-
lyregularspatialstructureemergesfromanalmostunstructuredini-
tialposition,canbeviewedasasortofmodelof themodel.Thatis,
thepreciseregularitiesof thatspecialcasehelpusunderstandthe
roughregularitiesof themoregeneralcase.
Nor do I think thatthis insightis merelyaboutmodeling.It
seemsreasonableto speculatethatthe immenselymorecomplex
landscapethatdeterminestherealgeographyof theworldeconomy
hasitsownunderlyingapproximatesimplicities.That is, theremay
be manypossibleoutcomes,dependingon initial conditions-
SiliconValleymight,givena slightlydifferentsequenceof events,
havebeenin LosAngeles,Massachusetts,or evenOxfordshire.But
somebroaderfeaturesmaybemoreor lessindependentof histori-
calcontingency.
And in factoneregularityin spatialeconomicsissospectacularin
itsexactnessanduniversalitythatit ispositivelyspooky.Thatregu-
larityinvolvesthesizedistributionof cities,andit leadsus to our
otherprinciple:orderfromrandomgrowth.
SELF-ORGANIZING ECONOMY
0.0
2 3 4 5 6 7 8 9 10 II 12
Location
I_Initial _Final I
Figure 2.2. Exploring a Complex Landscape. Models with more
regionscanbeexploredviasimulations;hereisatypicalrunfor
a12-regionexample.
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36
on theassumptionthatthespatialeconomystartedwith analmost
uniformdistributionof businessacrossspace.But thatis not how
realeconomichistoryworks- andwe havejust seenthatspatial
economiestypicallymust havecomplexdynamiclandscapesin
whichwhereyouendupdependsalotonwhereyoustart.Soisthe
simplepicturebasicallyirrelevant?
I think not - becausealthoughspatialmodelseasilygenerate
complexdynamics,lurkingwithin thatcomplexitywe oftenfind
surprisingsimplicity.
The mostprovocativeclaimof theprophetsof complexityis that
complexsystemsoftenexhibitspontaneouspropertiesof self-orga-
nization,in atleasttwo senses:startingfromdisorderedinitialcon-
ditionstheytendtomovetohighlyorderedbehavior,andatleastin
astatisticalsensethisbehaviorexhibitssurprisinglysimpleregulari-
ties:forexample,apowerlawdistributionrelatingthesizesandfre-
quenciesof earthquakes.
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-----3-----
An UrbanMystery
Let usstartwith apicture.Supposethatyou takeallof themetro-
politanareaslistedin theStatisticalAbstractif theUnitedStates,130in
number,andrankthembypopulation.And supposethatyouplot
theranksof theseareasagainsttheirpopulations,usingalogarith-
micscale.Whatyougetis Figure3.1.
What is interestingaboutthisfigure?Of coursetheline relating
rankto populationis,by definition,downwardsloping.But there
aretwo thingsaboutthatline thatdid nothaveto betrue.First,it
isprettyclosetoastraightline:thereseemstobesomethingcloseto
alog-linearrelationshipbetweenrankandpopulation.Thatin itself
isprettyinteresting;surelyit suggeststhatsomehiddenprincipleis
at work. But evenmoreinterestingis the slopeof thatapproxi-
matelylinearrelationship:it isverycloseto-1.
Thereisanotherwayofputtingtheseresults,whichisalsoanoth-
er nameforwhatis sometimescalledZipj's law: it is the rank-size
rule.This rulesaysthatthepopulationof acityis inverselypropor-
tionalto its rank.If therule heldexactly,thenumber2 city in a
countrywould havehalf the populationof the biggestcity, the
number3 cityone-thirdthatpopulation,andsoon. Obviouslythe
ruledoesnotholdexactly.If youlook atonlythelargestmetropol-
itanareas,you maybe unconvinced:Los Angelesis considerably
morethanhalfaspopulousasNew York. But onceyou getdown
therankingabit, thefit startstobecomealmostterrifyinglyexact.
For example,the 10thrankedmetropolitanareain the United
StatesisHouston,with 3.85millionpeople.The 100thrankedarea
is Spokane,Washington,with 370,000people- closeenoughto
39
Figure3.1Zipt~sLaw:Thesizedistributionofmetropolitanareasin the
UnitedStatesisstartlinglywelldescribedbyapowerlaw,withan
exponentverycloseto1.
Source:StatisticalAbstractif theUnitedStates,1993.
7.0
41
6.56.05.55.0
An UrbanMystery
4.5
In(S)
I • 1990 +1940 * 1890 I
4.0
1
3.5
3
6
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Zipfs law is not quiteasneatin othercountriesasit is in the
UnitedStates,butit stillseemsto holdin mostplaces,if youmake
one modification:manycountries,for example,Franceand the
United Kingdom,havea single"primatecity" thatis muchlarger
thanalinedrawnthroughthedistributionofothercitieswouldlead
you to expect.Theseprimatecitiesaretypicallypoliticalcapitals;it
is easyto imaginethattheyareessentiallydifferentcreaturesfrom
therestof theurbansample.
What couldexplaintheexistenceof somethingthatlookssuspi-
ciouslylikeauniversallawoncitysizes?Bearin mindthatthereare
two thingswe needto explain.We needto understandwhy the
rank-sizerelationshipis nearlylinearin thelogs,andwe needto
understandwhy it stayssooddlyclosetoaslopeof -1.
When urbaneconomistsattemptto explaintherank-sizerule,
theyusuallyarguethatit reflectssomesortof hierarchyof central
places.Hereis how thisreasoninggoes.First,wepointout thatan
Figure3.2Zipf'sLawoverTime. Thesamepowerlawhasworkedrea-
sonablywellforatleastacentury.
Source:HistoricalStatisticsif theUnitedStates.
2~------------------------------------------------------------------------
109.0 9.57.0 7.5 8.0 8.5
Log of citysize
SELF-ORGANIZING ECONOMY
5.0
4.54.0~
3.5
c '" 3.0
L..
~·u 2.5.•....
0
tl() 2.00...J 1.5
1.00.50.0
5.5
6.06.5
40
one-tenthof Houstonto bewell within reasonableuncertaintyof
definitionandmeasurement.If you regressthelog of rankon the
log of population,you geta coefficientof -1.003,with a standard
errorof only0.01- aslopeverycloseto 1andverytightlyfitted.
We areunusedto seeingregularitiesthisexactin economics- it
is so exactthatI find it spooky.The picturegetsevenspookier
whenyou find out thatthe relationshipis not somethingnew-
indeed,therank-sizerule seemsto haveappliedto u.s.citiesat
leastsince1890!Figure3.2showsdatatakenfromHistoricalStatistics
of theUnitedStates,whichreportsthenumberof "urbanplaces"in
specifiedsizeranges;I showthenumberwith morethan100,000,
morethan250,000,morethan500,000,andmorethan1million
for 1890,1940,and1990.(Thesedataarenot quitecomparableto
thosein Figure3.1,becauseof thedifferencein definitionbetween
anurbanplaceandametropolitanarea.)The pictureis notperfect,