BanksorFintechs?ARoadmapforRegulation

FranciscoJesúsGuerreroLópez(UniversidaddeSanAndrés)

PaulaMargaretic(UniversidaddeChile)

LucíaQuesada(UniversidaddeSanAndrés)

FedericoSturzenegger(UniversidaddeSanAndrés)

DOCUMENTODETRABAJON°327

Juniode2024

LosdocumentosdetrabajodelaRedNIEsedifundenconelpropósitode

generarcomentariosydebate,nohabiendoestadosujetosarevisióndepares.LasopinionesexpresadasenestetrabajosondelosautoresynonecesariamenterepresentanlasopinionesdelaRedNIEosuComisiónDirectiva.

TheRedNIEworkingpapersaredisseminatedforthepurposeofgeneratingcommentsanddebate,andhavenotbeensubjectedtopeerreview.TheopinionsexpressedinthispaperareexclusivelythoseoftheauthorsanddonotnecessarilyrepresenttheopinionsoftheRedNIEoritsBoardofDirectors.

Citarcomo:

GuerreroLópez,Francisco,PaulaMargaretic,LucíaQuesada,FedericoSturzenegger(2024).BanksorFintechs?ARoadmapforRegulation.DocumentodetrabajoRedNIEN°327.

BanksorFintechs?ARoadmapforRegulation

FranciscoJesusGuerreroLopez*PaulaMargaretic?LucíaQuesada?

FedericoSturzenegger§February2024

Abstract

Inrecentyears,traditionalbankshavefacedincreasingcompetitionfromdigitalbanks,fin-techs,andbigtechcompanies.Thispaperbuildsaframeworktodiscussoptimalregulationwithinthismorecomplexcompetitivelandscape.Toachievethis,weestablishamodelwherebankscompetewithasinglefintech.Allplayerschoosethedegreeofspecialization.Banksholdageographicaladvantageforsomecustomers,whilethefintechreachesallcustomersequally.Duetofixedcosts,themarketoperatesunderimperfectcompetition,leadingtopa-rametervalueswheretheregulatormayseektoexcludenon-bankintermediariesandotherswheretheregulatormayprefertoexcludebanks,shiftingintermediationexclusivelytobigtechcompanies.Thesedistinctpatternsalignwithobservedcompetitioninfinancialmarkets,wherecompetitionwithbigtechcompaniesisintenseinthecustomerbusinessandlesssoincorporatelending.Ourmodelcontributestotheargumentthat,forcertaintypesoflending,bankingregulationtendstobeoverlyrestrictivetowardsnon-bankintermediaries,resultinginsignificantwelfarelosses.

*UniversidaddeSanAndrés

?UniversidaddeChile(FacultaddeEconomíayNegocios,DepartamentodeAdministración)?UniversidaddeSanAndrés

§UniversidaddeSanAndrés,fsturzenegger@.ar.

1

1Introduction

Inrecentyears,traditionalbankshavefacedincreasingcompetitionfromdigitalbanks,fintechs,andbigtechcompanies

.1

Thishasledtosignificant(sometimesheated)debatesonbankingreg-ulation.Thecentralquestioniswhethernon-bankinginstitutionsshouldbepermittedtoacceptdepositsandextendcredit,oriftheseactivitiesshouldberestrictedexclusivelytotraditionalbank-inginstitutions.Thewayregulatorshaverespondedtothesedevelopmentsvariesacrosscountries.Ingeneral,themantrainthesectoristhatonlyregulatedbanksshouldbeallowedtocapturede-positstobeusedforfinancialintermediation.Insomecountries,fintechlawshavebeenissued,restrictingfinancialintermediationonlytobanks.Insomecases,non-bankinginstitutionsareforcedtokeeptheirassetsfullyliquid,notonlyinhibitinglendingbutvirtuallyknockingofftheirprofitability.Inothercases,regulatorshavebeenmoreopentonewformsofcompetitionopeningthedoorforfintechstobecomefinancialinstitutions(asinChina)throughabankinglicense(insomecaseswithhighercapitalrequirements,asintheUSorEurope,

ZamilandLawson

(2022))

.

Thispaperbuildsaframeworktodiscussoptimalregulationinthisrichercompetitiveenviron-ment.Todoso,weestablishamodelinwhichfinancialintermediariesofferadifferentiatedprod-uct.Inoursetup,traditionalbankspositionthemselvessymmetricallyaroundaSalopcircle.Theinnovation(following

MaddenandPezzino

(2011))istheintroductionofafintechinsidethecircle

thatisequidistantfromallclientsontheperimeter.Financialintermediarieshavetopayafixedcost,whichdeviatesfromtheconditionsofperfectcompetition.Also,themarketequilibriummaydeviatefromthesocialoptimum.Becauseintermediariesencounteradownward-slopingdemandcurve,themarketequilibriumleadstoexcessiveentrybytraditionalbanksandlowerspecializationlevels.This,inturn,providesconsumerswithlessutility.Fromasocialplanningperspective,amorefavorableoutcomewouldinvolvefewerbanksandhigherspecialization.

WeshowthatthereareparametervaluesforwhichthePlannerwantstoexcludenon-bank

1Fintechsaretypicallyassociatedwithfirmsthatprovidespecificfinancialservices,suchaslendingorpayments,whilebigtechcompanies,suchasAmazon,Google,Meta,MercadoLibre,haveenormousscaleeconomiesandincorporatefinancialproductsalongsidetheirprimaryactivities.Forbrevity,inwhatfollows,wewillrefertofintechscollectivelyasnon-bankfinancialintermediaries.

2

intermediariesfromthemarket.Butwealsoshowthatforotherparametervalues,thePlannerwantstoexcludebanksandshiftintermediationexclusivelytofintechs.Thedifferenceplaysoutasatradeoffbetweenspecializationgainsprovidedbythebanksandthecostofintermediation(largerfortraditionalbanks,aseachonepaysanindependentfixedcostofoperation).Infact,thereareregionswherethefixedcostsofbanksaresolargethatthemarketisunderservedbytraditionalbanksbutcouldbenaturallyservedbythefintech.Inthisparameterregion,thereisasignificantwelfarelossfromnotallowingthefintechtoparticipateinfinancialintermediation.

Whileourmodelfocusesonthewelfaregainofthesenewformsofcompetition,itprovidesanicefitwithcurrentcompetitionpatternsintheindustry.Wherespecializationismorerelevantforcustomers,itismoredifficultforfintechstodisplacetraditionalbanks.Forexample,inlargecorporatelending,bankshaveaspecializationadvantagerelativetofintechsinthattheyprovideaverylargesuiteofproducts:lending,payroll,specialaccountsforemployees,internationaltradepayments,etc.Additionally,largecorporatesdonotrelyonbigtechsforsales.Therefore,theknowledgeofthesecompaniesbybigtechsislimited.Infact,thesefirmsaretypicallyservedbytraditionalbanks.Theoppositeoccursforsmallfirmsandretailcustomers.Forthesetypesofclients,bigtechsknowmoreaboutthem,enablingthemtooffersuperiorproductstotheirclients.Consequently,inourmodel,itisreasonabletoexpectthatfintechcompetitionismorelikelytooccurintheseareas.

Whilenotthefocusofthispaper,thedebateonthenatureofinstitutionsprovidingfinancialintermediationextendsbeyondcompetitionintheproductmarket.Asubstantialbodyofliteratureprovidesreasonswhyregulatedbankinginstitutionsshouldexclusivelyparticipateinthismarket.

Thesereasonsrangefromtheimperativetopreventbankingcrisestoaddressingliquidityneedsand

managingchallengesassociatedwithasymmetricinformation(FreixasandRochet

(2008);

Bolton

etal.

(2007);

Hellwig

(2000);

Freixasetal.

(2000);

DiamondandDybvig

(1986);

Goldsteinand

Pauzner

(2005),amongothers)

.2

Theargumentsforregulation,byextension,havebeeninterpretedasanaturaljustificationforexcludingnon-bankinginstitutionsfromfinancialintermediation,asif2Inourmodel,weassumetheexistenceofbanksandfintechsbasedontheliteraturethatjustifiestheirpresence.

3

non-banks(ornon-regulatedentities)shouldbemorepronetoasymmetricinformationorliquidityruns.However,wefindnoempiricalsupportforsuchclaims,orithasnotyetbeenprovided.Consider,forexample,MercadoLibre,abigtechcompanyinLatinAmericathatofferspaymentservicesthroughawallet.Itsassetslackdepositinsurance,yet,MercadoLibre’snetworthexceedsthetotaldepositsinArgentina’sfinancialsector.Thus,anargumentneedstobemadetoarguethatthemoneyintheseaccountsisatahigherriskthanintraditionalbanks.

Thepaperisstructuredasfollows.Section

2

reviewstheliterature,whileSection

3

intro-ducesthemodel.Section

4

comparesthemarketequilibriumwiththeonewherethereareonlybanks.Inturn,Section

5

examinesthesocialoptimumandthedecentralizedequilibriuminthegeneralsetting.Section

6

connectstheheterogeneityofcommercialborrowersinfinancialmarketswithourmodelresultstoderivesomepolicyimplications.Section

7

examineswhetherourmainfindingsremainrobustwhennotassuminganexplicitfunctionforthereturnsoftheinvestmentproject.Finally,Section

8

concludeswithsomepolicyimplicationsofthemodel’sresults.Proofsarerelegatedtotheappendix.

2Literaturereview

Ourpaperisbuilton

MaddenandPezzino

(2011)whostudyanoligopolisticmarketinwhichcon

-sumerslocatedaroundtheperimeterofaSalopcirclebuyeitherfromfirmsaroundthisperimeterorfromafirmlocatedatthecenterofthecircle.Intheirmodel,perimeterfirmscompetelocallywiththecentralfirmandwithneighboringfirmsontheperimeter;incontrast,thecentralfirmcompeteswithalltheperimeterfirms.Thispaperdivergesfrom

MaddenandPezzino

(2011)ina

fundamentalaspect:inourmodel,bothbanksandfintechs,whichlendtoentrepreneursforfinanc-ingtheirinvestmentprojects,endogenouslydeterminetheirdegreeofspecialization.Inourmodel,specializationenhancesentrepreneurs’returnsoninvestments

.3

Weallowfordifferentcombina-tionsoffixedcostsandmarginalcostsassociatedwithspecialization.Thisparameterdiversitynot

3Whilegeographicallocalizationisanaturalwaytoconceptualizespecialization,itcanalsoencompassthetypesofclientsservedorthenatureofactivitiesinwhichclientsareengaged.

4

onlyresultsinamoreintricatearrayofequilibriumconfigurationsandpotentialmarketfailuresbutalsoenablesustotailorourregulatoryrecommendationsbasedonthespecifictypesofclientsinvolved.

Ourpaperconnectstotwostrandsofliterature.First,itislinkedtothegrowingtheoreticalliteratureonfintechdisruption.Second,itisconnectedtotheliteratureexaminingtheregula-toryframeworkforfintechsandbigtechs.Regardingthefirststrand,consider

Heetal.

(2023);

VivesandYe

(2021);

Parlouretal.

(2022),whoinvestigatethecompetitiveenvironmentoffintech

companiescompetingwithtraditionalbanksinoriginatingloansandinpaymentsystems(Vives

(2019);

Bergetal.

(2022)offerreviewsofdigitaldisruptioninbanking)

.4

Heetal.

(2023)studyhowopenbanking,thatis,sharingbanks’customertransactiondata,

affectslendingcompetitionbetweenatraditionalbankandafintech.Intheirmodel,bankandfin-techconductindependentcreditworthinesstestsbeforeofferingloanstoborrowers,whocanbeofhighorlowcreditquality.Thefintechhaslimitedcustomerdatacomparedtobanks.However,itisequippedwithsuperiordataanalyticalalgorithms.Assumingthatopendataimprovesthefintech’s

screeningability,5

thepapershowsthatthehigherscreeningabilityofthefintechfollowingopenbankinghelpshigh-creditqualityborrowers.However,itcanalsohindercompetitionandleaveallborrowersworseoffifthescreeningabilitygapbetweenbankandfintechaugmentssignificantlythecompetitiveadvantageoffintech.Insuchascenario,thefintechendsupenjoyingagreatermarketpowerthanthebankhadbefore;bothtypesofborrowersareworseoffwhereasindustryprofitsincrease.

Inturn,

Parlouretal.

(2022)investigatetheimpactoffintechcompetitioninpaymentservices

whenamonopolisticbankintheloanmarketusespaymentdatatolearnaboutconsumers’creditquality.Competitionfromfintechpaymentprovidersdisruptsthisinformationspillover.Thepaperdemonstratesthatfintechcompetition:i)mayleadtoanincreaseinthebank’spriceforpayment4Forempiricalevidence,consider

GopalandSchnabl

(2022);

Buchaketal.

(2018);

Fusteretal.

(2019);

Liuetal.

(2022);

Babinaetal.

(2022)

.

5Intheirmodel,screeningabilityreferstothejointoutcomeofdataavailabilityanddataanalysistechniques.Opendataprovidesthefintechwithpreviousfinancialandcredittransactionsofcustomers.This,combinedwiththefintech’ssuperioralgorithms,leadstothefintech’senhancedscreeningability.

5

services;ii)promotesfinancialinclusionforconsumersofpaymentservicesthatwerepreviouslyunbanked;iii)mayhurtborrowerswithastrongbankpreferencebutwithlowcreditquality;iv)hasanambiguouseffectintheloanmarket.Themodeldescribedin

Parlouretal.

(2022)isinteresting

asitapplieswelltothepaymentservicesthatbigtechsprovide,suchasAmazonorMercadoLibreinLatinAmerica,thankstowhichtheylearninformationaboutconsumers’creditquality(mainlysmallandmedium-sizedenterprises).

Thisliteraturetypicallyhasanon-perfectlycompetitivemarketstructure.Inthiscontext,theimpactoffintechentrymayhaveambiguouseffectsonconsumersandwelfare.Ourmodelyieldssimilarconclusions.Inourcase,theentryofafintechmayresultinreducedcompetitioninequi-libriumbydiminishingthemarketfortraditionalbanks.However,asintheirsetups,thereareparametervaluesforwhichconsumerwelfareisenhancedbytheintroductionoffintechfirms.Furthermore,wesharewiththisliteraturetheconclusionthatcompetitionbetweenbanksandfin-techcompaniescriticallyhingesonthemarketstructureandthefixedandvariablecostsamongparticipants.Thesefactorsexplainthevariouscompetitiveenvironmentsobservedindifferentcountries.Weexpandupontheexistingresearchbyhighlightingthatthereexistsnouniversallyoptimalchoiceofpoliciestoregulatefintechs.Indeed,wedemonstratethatinregionswherebanksdonotoperate(e.g.whentheirfixedcostsofoperationaretoolarge),allowingfintechstoprovidefinancialintermediationiswelfare-improving.

Second,ourpaperisconnectedtotheliteraturesearchingforaregulatoryframeworkfor

fintechsandbigtechs(Zingalesetal.,

2022;

ZamilandLawson,

2022;

Ehrentraudetal.,

2022;

Carstensetal.,

2021)

.Ontheonehand,thisliteraturedocumentsthatintherecentpast,bigtechsandlargediversifiedfintechshaveobtainedbankinglicensesinvariousjurisdictions(mainly,Asia,andinparticular,China;theUnitedKingdom,andtoalesserextent,theEuropeanUnionandthe

UnitedStates),facilitatedbyanenablingregulatoryenvironment(ZamilandLawson,

2022)

.Table

A1,intheAppendix,summarizestheseregulatorydevelopmentsbycountry.

Ontheotherhand,thesestudiesemphasizethatwhilefintechsandbigtechsofferseveralbenefitsforconsumers(su-periortechnology,user-friendlycustomerinterfacesthatimproveusers’experiences,andfinancial

6

inclusion),theirbusinessmodelsmayentailsomerisks(stemmingfrompotentialanti-competitivebehaviorandimpedimentstoconsolidatedsupervision,

ZamilandLawson

(2022))

.Theserisksmayjustifythesearchforregulationforthesefirms.

Inthisregard,theliteraturetendstorecommendtwospecificregulatoryapproachesforbigtechsandfintechs.Thefirstapproachissegregation,whichconsistsofminimizingrisksarisingfromgroupinterdependenciesbetweenfinancialandnon-financialactivitiesbyimposingspecificring-fencingrules.Thesecondapproachisinclusion,whichaimsatcreatinganewregulatorycategoryforbigtechgroupsandlargerfintechswithsignificantfinancialactivities.Regulatoryrequirementswouldbeimposedforthegroupasawhole,includingthebigtechparent.Moreover,

somescholarscallforaninternational(Zingalesetal.,

2022)oratleastregionalregulation(Ehren-

traudetal.,

2022)forbigtechsandlargeanddiversifiedfintechs

.Therationaleforthisisthatthesefirmstendtooperateataglobalscale;therefore,itisnecessarytohaveasupranationalau-thoritytoregulatethem.Weaddtothisliteraturebyproposingatheoreticalframeworktodiscusstheoptimalregulationforfintechsandbigtechsthatisflexibleenoughtoaccommodateimperfectcompetition,anddifferencesinfirms’technological,spatial,andinformationalfeatures.

3Themodel

Wemodelthebankingindustryassumingtwotypesofsuppliersoffinancialservices:“traditionalbanks"anda“fintech".Themaincharacteristicofthefirstgroupisthatbanksprovideasortofspecialization.Whilegeographicallocalizationisanaturalwayofthinkingaboutspecialization,itcanalsorefertothetypesofclientsservedorthetypeofactivitiesinwhichclientsareengaged.Thefintechordigitalbank,onthecontrary,accessesallclientsidentically(typicallyviathephoneorotherelectronicmeans).

ThewaywemodelthisdichotomyisbyplacingtraditionalbanksalongaSalopcirclewithaperimeterequaltoonewhilethefintech(ordigitalbank)isaninnercirclethatcanbecloserorfartherawayfromtheoutercircle.WeassumethereareNbanksandeitheroneornofintech(we

7

denotethisasc=1orc=0,respectively).Thereisamassequalto1ofentrepreneursthatareuniformlydistributedontheperimeterofthecircle.Figure

1

showsthespatialconfigurationofour

bankingindustry.

Figure1:TheSalopcirclewithsixperimeterbanksandafintechintheinnercircle

EachentrepreneurhasanideaforaninvestmentprojectwithareturnofAinautarky.However,entrepreneurslackthefundstocosttheunitamountthattheprojectentails,sotheyneedtoborrowfromafinancialintermediaryi.Financialintermediariesprovideservicestoentrepreneursthatincreasetheproject’sreturn.Theseservicesareincreasinginthefinancialintermediary’sdegreeofspecialization,whichwedenoteasθiandwillbeendogenouslychosen.

Eachentrepreneurhastheoptionofundertakingornotaproject.Weassumethatthebenefitofundertakingtheproject(whichisAinautarky)issufficientlyattractivesoentrepreneursalwayspreferimplementingit.Consideranentrepreneurjthatdecidestoborrowfromafinancialinter-mediaryiwhichislocatedatadistancexijfromherlocation.Weassumethattheentrepreneur’sutilityifsheborrowsfromthisfinancialintermediary,is:

Thefirstterminequation(1)representstheentrepreneur’sgrossreturnfromundertakingthe

projectandborrowingfromafinancialintermediary,whichequalsthereturninautarkyAmul-

8

tipliedbythevalueofthebank’sspecializationservices,(1+√θi).Thesecondtermistheinterestratethattheentrepreneurhastopaytothefinancialintermediary,ri.Thethirdonecorrespondstothedis-utilityortransportationcostoftravelingthedistancexij.

Intuitively,equation(1)indicatesthatthehigherthedegreeofspecialization

θi,thebetterthefinancialintermediarysatisfiestheneedsoftheentrepreneurslocatedclosertoitsownlocation.However,thisalsoimpliesthatthebankisapoorerintermediaryforentrepreneurssituatedfartheraway.Thisisbecausetheutilityofentrepreneursdecreaseslinearlywiththedistancefromthefinancialintermediaryatarategivenbythebank’sdegreeofspecialization.Figure

2

showshowthechoiceofspecializationworks.Ahighlevelofspecializationimpliesalargerincreasein

productivityforcontiguousentrepreneurs,butarelativelyfasterdeclineforthoselocatedfurtheraway.

Figure2:Projectreturnswithdifferentvaluesofθ

Banksareidenticaland,inequilibrium,willbelocatedsymmetricallyonthecircle’sperimeter.Wedenotearepresentativebankwithsubindexi=p

.6

Assaid,thefinancialservicestheyprovide

6Weusethesubindexpforbankstoindicatetheyarelocatedintheperimiteroftheproductspace.

9

arelocationallyspecialized,thatis,theyaremorevaluableforentrepreneurslocatedclosetothebankthanforclientslocatedfurtheraway.WeinterpretthedistributionofbanksaroundtheSalopcircleasspatialproductdifferentiation.Intuitively,thisisconsistentwithbankbranchingand

regionallocationoffinancialinstitutions(SchargrodskyandSturzenegger,

2000)

.7

Conversely,thefintech,denotedwithsubindexi=f,islocatedatadistanceδfromallen-trepreneurs.Weconceptualizethefintechasanon-traditionalfinancialinstitutionthatusesalter-nativecommunicationchannelswiththeclient,andhasdifferentscorecardsandcosts.Givenitspositioninthecircle,itisperceivedequallybyallentrepreneurs.

Weassumethereisfreeentryintothebankingindustry;incontrast,atmostonefintechcanexistinthemarket

.8

Afinancialintermediaryilendstoanentrepreneurataninterestrateri(rpifthelenderisthebankorrfifitisthefintech).Inturn,financialintermediariesobtainfundingfromanexternalmarketatanexogenousrateρ

.9

Toenterthemarket,financialintermediariesmustpayafixedcost:banksincurthefixedcostofF,whereasthefintechpaysG.Specializationisanendogenousdecision;however,weassumethattherearecoststospecialization.Inparticular,weassumethatfinancialintermediarieshavemarginalspecializationcosts,whichwedenoteasτpforbanksandτfforthefintech.Forsimplicity,wesupposethatthesemarginalcostsareconstant.

Withtheseassumptions,theprofitfunctionsforbanksandthefintech,πpandπf,respectively,become

πp=2(rp-τpθp-ρ)x-F(2)

Startingwithequation(2),itsfirstparenthesiscorrespondstothenetincomethatabankobtains

fromlendingtoeachentrepreneur,whichisformedbytheinterestraterpitchargesnetofthecostofspecialization,τpθp,andthecostithastopayfortheexternalfundsitborrows.Definingxas

7Nevertheless,themodelisequallyapplicabletofinancialintermediariesthatconcentratetheirlendinginspecificeconomicsectors.Inthatsituation,locationinthecirclewouldcorrespondtoparticularactivitiesandthesewouldbechangingsmoothlyaroundthecircle.

8

EntryofmorethanonefintechwouldleavethemwithoutincomeduetoBertrandcompetition(Bouckaert,

2000)

.9Notethatwedonotmodeltheexistenceoffinancialintermediaries,wesimplyassumethattheyexist.Thereisex- tensiveliteraturejustifyingtheirexistenceforseveralreasons:asymmetricinformationandmaturitytransformation,

amongothers,(GortonandWinton,

2003;

Dowd,

1996)

.

10

thesolutionto

i.e.asthelocationoftheconsumerwhoisindifferentbetweenborrowingfromitsnearestbankorfromthefintech,2xisthefractionofthetotaldemandservedbyagivenbankandFisthefixedcostthateachbankhastopay.Knowingthat2Nxisthetotalloandemandservedbybanks,totalbanks’profitsare

2N(rp-τpθp-ρ)x-NF.(5)

Inturn,equation(3)showstheprofitfunctionofthefintechwhichdiffersfromtheprofitofa

typicalbankinthatitsdemandisnow2N,whichistheresidualdemandprovidedthebanksdonotservethewholecreditmarket.ThefintechhastopaythefixedcostG.

3.1TheCentralPlanner’sproblem

TheCentralPlannerwantstomaximizetotalwelfare,whichisobtainedbyaddingtheconsumerandproducersurpluses.Theendogenousvariablesinthisproblemarethedegreesofspecialization,θpandθf,thenumberofbanks,N,andwhetherthefintechshouldbeallowedtointermediate,c.

Todeterminethesocialoptimum,wefirstsolvetheCentralPlanner’sproblemassumingthatonlybanksprovidefinancialintermediation.Wethenintroducethefintech.Finally,wecompare

thetwooptimalsolutionsdependingonthevaluesofFandG.

3.1.1TheCentralPlanner’sproblemwithonlybanks

TosolvetheCentralPlanner’sproblem,westartbydefiningtheconsumerandbanksurpluses,whichwedenoteasCSpandPSp.Notethattominimizetransportationcosts,itissociallyoptimal.Thus,fromthespecificationsabove,consumerandproducersurplusesare

11

CSp=2N(6)

and

Totalwelfarewithonlybanks,whichwedenoteasWOB,canbeexpressedas,

ThevaluesofθpandNthatmaximizetotalwelfareare,

(10)

and

(11)

ThisisindeedthesolutionfortheCentralPlanneraslongasthenumberoffirmsinEquation

(11)isgreaterthan1

.

Indeed,Equations(10)and(11)showthatboththeoptimaldegreeof

specializationθpandtheoptimalnumberofbanksNdecreasewiththemarginalcostofprovidingspecialization,τpandwiththefixedcostF.Intuitively,whenF(orτp)increases,theCentralPlannerprefersasmallernumberofbanks.Withfewerbanks,alowerdegreeofspecializationisoptimal,aseachbankneedstoservecustomerswhoarelocatedrelativelyfareraway.NoteinadditionthatifFissufficientlylarge,Nbecomessmallerthan1,whichmakesnosenseineconomicterms

.10

ThelatterhencesuggeststhatthereisalimitonFabovewhichtheCentralPlannerprefersthatnofinancialintermediationisprovided.WecomebacktothislimitinSection

3.1.3.

SubstitutingtheoptimalvaluesofθpandN

(equations(10)and(11),respectively)inthetotal

10ThisisbecauseafractionofabankwouldimplyatotalfixedcostthatissmallerthanF.

12

welfare,theoptimalwelfarewithonlybanks,WOB,becomes:

WOB=A+N>1.

Whenthenumberofbanksinequation(11)issmallerthan1,theCentralPlannerhastochoose

whethertohaveonlyonebankornobankatall.Itprefersonlyonebankinthesystemaslongasthe