ISSN CNPJ / Working Paper Series Brasília n. 315 July 2013 p. 1-50

Transcription

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2 IN CNPJ / Wokng Pe ees Bsíl n 35 July 03-50

3 Wokng Pe ees Eded by Reseh Demen Dee E-ml: Edo: Benmn Mnd Tbk E-ml: Edol Asssn: Jne of Mo E-ml: Hed of Reseh Demen: Edudo José Aúo m E-ml: edudolm@bbgovb The Bno Cenl do Bsl Wokng Pes e ll evlued n double blnd efeee oess Reoduon s emed only f soue s sed s follows: Wokng Pe n 35 Auhozed by Clos Hmlon Vsonelos Aúo Deuy Goveno fo Eonom Poly Genel Conol of Publons Bno Cenl do Bsl Comun/Dv/Cov B Qud 3 Bloo B Edfío-ede 4º nd C Posl Bsíl DF Bzl Phones: nd F: E-ml: edo@bbgovb The vews eessed n hs wok e hose of he uhos nd do no neessly efle hose of he Bno Cenl o s membes Alhough hese Wokng Pes ofen eesen elmny wok on of soue s equed when used o eodued As onões eesss nese blho são elusvmene dos uoes e não efleem neessmene vsão do Bno Cenl do Bsl And que ese go eesene blho elmn é equed ção d fone mesmo qundo eoduzdo lmene Czen eve Dvson Bno Cenl do Bsl De/De B Qud 3 Bloo B Edfío-ede º subsolo Bsíl DF Bzl Toll Fee: F: Inene: <h//wwwbbgovb/?contactu>

4 Pe Dffeenon nd Menu Coss n Ced Cd Pymens Mos Vll Joge * Wlfedo ev Mldondo ** Abs The Wokng Pes should no be eoed s eesenng he vews of he Bno Cenl do Bsl The vews eessed n he es e hose of he uhos nd do no neessly efle hose of he Bno Cenl do Bsl We buld model of ed d ymens whee he eles e llowed o hge dffeenl es deendng on he nsumen of ymen hosen by he onsume We follow he Rohe nd Wgh 00 oh bu ssumng ed d sysem whou no-suhge ule o ny ye of e dffeenon dsnenve In Hoellng omeon fmewok he eles level he omeve equlbum es e omued ssumng h he soe ed ovded by he ele s less os effen hn he one ovded by he ed d In odne wh he leue we obn h he nehnge fee beomes neul f we elmne he nosuhge ule when he nehnge fee loses s bly o dso he ndvdul onsume s desons dslng he ggeged onsumes welfe fom s mmum We ove h he vege e obned unde e dffeenon s smlle hn he sngle el e unde he nosuhge ule dese he ele s mgns beng he sme n boh senos Fuhemoe we show how some oss subsdes e elmned when e dffeenon s llowed In ddon we nodue menu oss o ove h hee s heshold vlue fo he nehnge fee suh h e dffeenon s equlbum f h fee s bove hs vlue The heshold my be neeed s n endogenous fo he nehnge fee fed by he ed d ndusy Fnlly we onlude h even wh menu oss ssoed o e dffeenon he onsumes welfe n be gee n he e dffeened equlbum hn n he sngle e equlbum unde he non-suhge ule Keywods: Ced ds ymens wo-sded mkes JE Clssfon: ; E4; G8 * Bno Cenl do Bsl Demen of Bnkng Oeons nd Pymens ysem E-ml ddess: mosvll@bbgovb ** Chol Unvesy of Bsl Gdue hool of Eonoms E-ml ddess: wlfedo@osubb 3

5 Inoduon Thee s n nensve nenonl debe nvolvng ndusy membes mke egulos nd onsumes eesenves bou he suue of he ed d mke he behvo of s lyes nd he onsequenes on omeveness nd mos monly on he sol welfe Wene nd Wgh 005 Bdfod nd Hysh 008 Aully he sol welfe mmzon should be he ulme gol of ny egulo Howeve hs s dfful hllenge h enomsses he ssessmen of dsbuve ses lke defnng elve mone of he welfe of eh segmen of he soey Among he mos nsgng ssues n he debe bou he ed d mke egulon s he one onenng he effes of he no-suhge ules o ny ohe dsnenve on e dffeenon on onsume s welfe We n fnd n he leue h suhgng my hve osve effes fo mehns nd onsumes Chkvo nd Emmons 003 Bol nd Chkvo 008 s well s sudes showng mbguous o osve ms on he sysem Rohe 003 Rohe nd Tole 008 A dsnve feue of he d ymen sysem s h dese he f h he dholdes mke he hoe of he ymen nsumens he nson oss s only nued by he mehns whh n genel eove hose oss hough he sngle e segy In e he fee suue hs ggeed he use of mehn fees o ewd he ssune nehnge fee nd he usge of ds d ewds whh s yl behvo n wo-sde mke suues The enl queson s f he ed d ndusy n ee mke owe by mosng sheme ules ohbng suhgng of ed d uhses by mehns In ohe wods no-suhge ules ould even e sgnlng o dholdes bou he elve oss of dffeen ymen mehods enfong he en whee he hghe he mehn fee he gee he y o ewd dholdes ledng o less effen lloon of esoues n he ymen sysem eess of d usge Anohe mon ssue s h unde he no-suhge ule mehns eove he vege os of dffeen nsumens of ymen hgng ll onsumes eqully Consequenly onsumes who do no use ed ds y moe hn hey would 4

6 ohewse In ohe wods onsumes who use ed ds e subsdzed n he uhses Chkvo nd Emmons 003 Chkvo nd To 007 Thee e eml sudes h mesue hese oss subsdes n some usdons genelly ndng h hese e no neglgble Beuse of s n-omeve nue he no-suhge ule hs been ohbed n some usdons Fo nsne n Uned Kngdom sne 99 n he Nehelnds sne 994 n weden sne 995 nd n Ausl sne 003 The uhoes udged h mehn ng feedom s essenl fo n effeve e omeon n ul fo he omeon beween ymen shemes In Ausl he ohbon on no-suhge ules s sed n he ndds s Nehe he ules of he heme no ny n n he heme shll ohb mehn fom hgng ed dholde ny fee o suhge fo ed d nson Fuhe n ssessmen of nehnge-fee ng n hs ouny showed h ssues hd eoveed of he loss of nehnge fees n he sho un Chng e l 005 Those uhos lso showed h mehns defnely hd benef whh ws no subsnlly ssed o he onsumes Dese ll hs egulos sll eognze h he suhgng efoms n Ausl hve been suessful nd hve ovded sgnfn ubl benefs Nowhsndng hey hve beome onened bou ses whee suhges seem o be hghe hn he ene oss ne he evdene obned shows h n some nsnes suhgng hs develoed n wy h oenlly omomses e sgnls nd edues he effeveness of he efoms egulos e uenly evewng he no-suhge sndds n ode o ovde d shemes wh he bly o onsn he level of suhges o somehng lose o he mehn ene oss whose mn omonen s he mehn fees 3 When nlyzng he onvenene of elmnng he no-suhge ule fo ed d ymens s que esonble o ffm s we ove n hs e h some mehns wll hve nenves o unlelly suhge ed d nsons bove huh ; vns J 00 nd Cenl Bnk of Bzl 0 nd 0b e emles of eml sudes h esme oss subsdes n he Uned es nd Bzl esevely ee esevely Uned Kngdom Plmen 990 Vs E;Toh J 000 MA Mke Develomen AB 000 nd Reseve Bnk of Ausl 0 3 Consulon doumens of he Reseve Bnk of Ausl 0 nd 0b 5

7 he sngle e level whou ny eduon of es of ohe yes of nsons Nowhsndng s f fom beng vld gumen gns dffeenon beuse hs sseon should ssume he mehn hs mke owe The oe nlyss should need o ke no oun he esene of new equlbum es n he bsene of he no-suhge ule s well s o ome onsume welfes n boh equlb Ths s ely one of he mn gols of hs e As we wll lluse n he ne seon hough ou heoel nlyss of smle model he f h eh mehn hs he ossbly o obn n e of when he ndvdully deves fom he sngle e does no gunee h suh segy s susnble Aully omlee nd oheen nlyss needs fs of ll o fnd he new equlbum es whh wll deend on he sef omeve envonmen nd he effes on of ossbles Then we n o mesue he welfe gns o losses when omng boh equlb In he leue we n fnd es fousng on he eonom ole of he ed d nehnge fee s well s on s deemnon nd ossble egulon In eonom envonmen of of-seekng fms whh e mefely omeve hmlensee 00 onludes h he nehnge fee shfs he oss beween ssues nd ques nd s onsequene lso shfs he dsbuon of hges on mehns nd onsumes Ths llows enhnng he vlue of he ymen sysem s whole o s ownes due o he newok eenly Rohe nd Tole 00 nlyze he welfe mlons of ooeve deemnon of he nehnge fee by membe bnks n fmewok n whh bnks nd mehns my hve mke owe s well s onsumes nd mehns dede onlly on whehe o buy o e ymen d Wgh 003 evlues he sol omly of vely se nehnge fees unde he no-suhge ule n wo eemes of mehn ng nmely monools ng nd efe omeon In ddon he osve se of he no-suhge ule n evenng he eessve mehn suhgng s ssessed Rohe nd Tole 006 nlyze he welfe effes of he eenles nheen n he d ymen sysem nd dsuss whehe onsume sulus o sol welfe s he oe benhmk fo he sudy of he egulon n he d ymen ndusy They bng ll he heoel nlyss o unvel he een nus ons ken by egulos nd mehns gns 6

8 d ssoons n Ausl he UK nd U Wng 00 suggess h he d newoks demnd hghe nehnge fees o mmze membe ssues ofs s d ymens beome moe effen nd onvenen He lso dsusses osve nd negve feues of oly nevenons Ou wok s losely eled o Rohe nd Wgh 00 They model he ed d elly llowng see ole fo he ed funonly of ed ds whh s modeled fom ohe ymen ds e deb ds They ssume mossbly o lk of nenves of eles o dffeene es odng o he nsumen of ymen hosen by onsumes Unde hose ssumons hey showed how monooly d newok ould sele n nehnge fee hgh enough o omoe he ulzon of ed ds n level h eeeds he one h mmzes he ggeged onsume sulus They show how eguloy fo he nehnge fee ould be used o nese onsume sulus Ou wok ms o eend he Rohe nd Wgh 00 model gvng dsnve subsdy o he debe nd helng o lfy hough smle heoel model he mlons of e dffeenon nd of menu oss nued by mehns n ed d ymens Wh hs eenson we e ble o lluse how he bsene of no-suhge ule ould genee equlbum es ble of movng onsume welfe nd edue he mke owe of bnks hough he nehnge fee 4 even unde he ssumon h eles fe menu oss ssoed o e dffeenon In hs se we ove h eles wll dffeene es s long s he menu oss e no hgh enough The e s dvded no fou seons eon desbes he model In eon 3 we esen he mn esuls of he e fs onsdeng he bsene of fon gven by he menu oss of e dffeenon nd seondly nludng suh oss o nlyze he effes of h mke mefeon In seon 5 we summze he mn onlusons The Aend onns he deled oofs of ll he esuls enuned n he e 4 ee Gns nd Kng 003 bou he neuly of he nehnge fee unde e dffeenon 7

9 The model wh e dffeenon Two dsnve hnges n he model oosed by Rohe nd Wgh 00 e nodued In fs veson of ou model we only llow eles o dffeene he e of ed d ymens fom he e of he ohe ymen nsumens soe ed sh deb ds nd ohes The seond sefon nodues n he fome veson of he model menu oss nued by mehns whh eesen ny oss euny o no ssoed o he doon of he e dffeenon by he mehn As n Rohe nd Wgh 00 we ssume hee h hee s onnuum of onsumes ll dsbued unfomly n uny lengh nevl All onsumes hve denl qus-lne efeenes sendng he nome on el goods osng γ fo he mehn 5 Thee e wo ymen ehnologes The fs one oesonds o gou of sh ymen ehnologes whh ould nlude money heks deb ds o ohe nsumens no nvolvng ny ed funonly The seond one oesonds elusvely o he ed ds ymen ehnology As n lenve o boh ehnologes eh ele n dely ovde ed o he onsume whh s lled soe ed Ced ds e held by onsn fon of onsumes nd ssumed o be moe osly hn sh Whou loss of genely he oss of ll ymens e eessed elvely nomlzed o he os of he sh ymen whh s ssumed o hve zeo os Ced ds llow onsumes o uhse on ed nd enl os o benef f negve fo he onsume buye 6 whh s eeved o d by he ssue nd enl os mehn fee fo he ele selle 7 5 As usul n l equlbum models qus-lney llows us o mesue he uly n money ems 6 Thee mgh be ohe ne oss/benefs ssoed o ed d ymens wh ese o sh nd no lnked wh he elonsh wh he ssue fo nsne hose omng fom he vy gly sfey fnnl lnnng If suh oss/benefs e lowe hn hen he qulve nlyss emns unhnged 7 If eles eeve he ymens fom he que wh some dely hey wll nu os of he me vlue of money nees e on ned eevbles If hs os s lowe hn he mehn fee he qulve esuls obned hee emn unhnged 8

10 The soe ed s n lenve o he ed funon of he ed d nd enls ndom nson sef os o benef f negve B fo he onsume nd os o he ele Eh onsume uhses one un of he el good lled odny uhses ovdng hm uly eeves uly u 0 > γ bu n ddon wh obbly he lso u > γ fom onsumng nohe un of he el good lled ed uhses I s ssumed h mehns nno bundle he wo nsons no dsngush beween odny nd ed uhses When mkng odny uhses ll onsumes n hoose beween sh o soe ed bu only fon of hem hve he ossbly o hoose ed ds On he ohe hnd when mkng ed uhse sh s no n oon fo ny onsume Addonlly s ssumed h eh onsume lwys hs suffen sh o y fo hs odny uhses bu mus ely on ed fo ed uhses The nson sef os B of soe ed s obseved by he onsume only when he s n he soe 8 whh s dwn fom onnuous dsbuon wh he umulve dsbuon funon H We ssume he dsbuon hs full suo ove some nge B B whee B s suffenly negve suh h dholdes wll somemes hoose o use soe ed even f sh n be used nsed nd B s osve bu no oo hgh n omson wh u γ suh h onsumes wll lwys efe o mke he ed uhse even f hey hve o y wh soe ed he hn no buy ll The dw B s he ne os of usng soe ed he hn ed ds o sh A negve dw of B ould eesen suon whee dholde needs o eseve hs sh o ed d blne fo some ohe onngenes nd hus vlues he use of soe ed The ssumon h hee e suons when onsumes see moe benefs n usng he soe ed hn ed ds s key se of ou model sne wll usfy 8 In ons he oss/benefs of ed d ymen e ssumed o be known by he onsumes befoe vng o he soe Aully he ed d seve s onul ondons e nees nnul fees nd ewds e usully osed n dvne o ed d uses 9

11 he esene of dffeenl e equlb even n he esene of menu oss ssoed wh he dffeenon If he mehn fee m of ed d uhse s smlle hn he os of soe ed m< eng ed ds s oenl men fo mehns o edue he nson oss of eng ed uhses Bu f d neses he mehn s nson oss m> ene of ed In genel onsumes wll efe ed ds o soe ed when B > f fo boh odny nd ed uhses In ul when ssues gve benefs f < 0 e hough ewds o sh bk bonuses o onsumes n eh ed d uhse onsumes wll efe o use he ed ds he hn sh fo odny uhses I ws oved n Rohe nd Wgh 00 h fom he on of vew of ggeged onsumes eessve nenves fo ed d use ould be solly wseful The bnk of he mehn o que of he nson nus n n qung os A s well s nu n n nehnge fee whh s d o he bnk of he onsume fo eh ed d nson I s ssumed whou loss of genely h only ques e efely omeve whh mles h he mehn fee m s equl o he sum of he qung os A nd he nehnge fee m A The bnk of he dholde o ssue of he d nus n n ssung os I nd eeves he nehnge fee fom he que 9 I s ssumed h ssues e mefely omeve whh mles h he dholde fee f s equl o he ssue os h eeed he nehnge fee evenue I lus onsn of mgn π 9 Besde he nehnge fee nd he nnul fees he nees evenue mgh be n mon omonen of he ssues ol evenues Ths s he se n some usdons s n Bzl Noe h he nnul fees nd he nees evenues my be nluded n he ne dholde fee f 0

12 f I π Thus he ol os of ed d nson s A I : 3 Denoe by δ he eess os of he soe ed wh ese o he ol os o ovde ed d nson nludng ssue s of whh s defned by δ π : 4 We wll es ou nlyss o he suon whee fom he on of vew of he sules of he eds mehns o ed d ndusy ed d nson s moe os effen hn he soe ed o equvlenly δ > 0 Fgue Pes oss nd fees of nsumens of ymen γ Mehn m A B Consume f I π - ndom wh df H ooon of ed d ownes Aque A I Issue oe ed Ced d Comeon beween eles ous s n he sndd Hoellng model: onsumes e unfomly dsbued on n nevl of un lengh wh one ele

13 loed eh eemy of he nevl Thee s nsoon os fo onsumes e un of dsne Unlke Rohe nd Wgh 00 we e neesed hee n he suon whee eles hve he oon o hge dffeen el es odng o he nsumens of ymen To smlfy we es ouselves o he ul suon whee he ele s llowed o hge e fo ed d nson whh my be dffeen fom he e hged fo sh o soe ed nson We denoe by he sed beween hese wo es nmely: : 5 Fgue lluses he neonneon beween ns of he ed d mke s well s he eseve es oss nd fees hged by eh one The mng of he desons s s n he model of Rohe nd Wgh 00 whh n be dvded no 9 ses goued n wo eods: 5 ses befoe he vl of he onsume o he soe nd 4 ses one he onsume s n he soe Befoe vng he soe: The d newok ses he nehnge fee ; Bnks se he fees: f fo dholdes nd m fo eles; 3 Reles ndeendenly hoose he d ene oles: f ele es ed ds 0 ohewse; 4 Reles ndeendenly se el es nd ; 5 Consumes sele one ele o onze fe obsevng he obseved el es el s ene oles ssue s fee he dsbuon of soe ed os nd nsoon os One he onsume s n he soe: 6 Consume buys fs un of he el good odny uhse nd ys fo usng sh o ed d f he hs one;

14 7 Nue dedes whehe he onsume hs n oouny fo n ddonl ed uhse whh wll ou wh obbly ; 8 The os B of usng soe ed fo he buye s dwn odng o he df H wh full suo on B B ; 9 Cdholdes hen sele he mode of ymen We se f he onsume efes ed ds ove sh when buyng he ele o 0 ohewse In ohe wods: f f 0 : 6 0 ohewse 3 Anlyss nd esuls Assumng he mehn hges e fo sh nd soe ed nd hges n ddonl sed seflly on ed d nsons we obn see Aend h he eeed mgn of he ele s gven by M γ H0 Γ 7 whee [ H 0] [ H f ] m Γ : 8 The fs wo ems he gh hnd sde of 7 oesond o he eeed evenue of he ele when hee e no ed d uses 0 o he ele dedes no o e ed ds 0 These ems e esevely he ne os of he odus nd he ne os of he nsumens of ymen The hd em oesonds o he eeed mgn eduon ssoed o he use of ed ds by ed d ownes 3

15 We obn see Aend h he uly of he onsume h hooses o uhse he good fom he ele s gven by U 0 u u dh E 9 0 B B B B whee B B : B f dh B B dh B 0 f 0 The fs fve ems he gh sde of 9 oesond o he ne eeed uly of he onsumon kng no oun he odu os nd he soe ed os when hee e no ed d uses o he ele dedes no o e ed ds The ls em oesonds o he ddonl welfe ssoed elusvely o he use of ed ds The mke she of boh eles s deemned by omung he oson of he ndffeen onsume n he egon nevl of sze one whee ll onsumes e unfomly dsbued ne hee s os fo evey un of dslemen he uly mnus he dslemen os of onsume who dedes o uhse he good fom ele s U s Theefoe he dsne s beween he ndffeen onsume nd he ele s equl o he ooon of onsumes hoosng ele Fgue shows ne ules nd he mke shes of boh eles 4

16 Fgue Indffeen onsume n he Hoellng model U s U s Indffeen Consume Rele Rele s s s Then he mke she s of he ele deends on he nehnge fee es nd seds nd s gven by he followng eesson s Noe h fo fed nehnge fee he Nsh equlbum e when dffeenon s no llowed s defned by equon 5 n Rohe nd Wgh 00 ssfes he followng equon γ H 0 φ 0 Γ 0 3 whee φ : Γ 3 s he dffeene beween he ddonl welfe of he onsume nd he ddonl os of he ele ssoed o eh ed d nson Fo eh δ > 0 s defned n 4 onsde he followng mee defnon 5

17 B B φ δ : B δ dh B B dh B 4 δ 0 nd noe h φ δ φ A Noe h f we φ > 0 nd he sed s equl o m he δ A benef of he ed d nsons fo onsumes s gee hn he os of he sme nsons fo eles Noe h f δ > 0 s suffenly smll he ssumon φ > δ 0 s equvlen o he ondon B B B dh B > π dh B whee he lef-hnd sde em bove oesonds o he oss svngs n usng ed ds fo eodny uhses nd he gh-hnd sde em oesonds o he os of usng ed ds n boh yes of uhses The esuls n hs e e obned unde he fou bs ssumons defned below The fs one eles he non-suhge ule llowng eles o hge dffeen es fo ed d nsons nd eesens he mn ssumon Assumon : Pe dffeenon of ed ds nsons s llowed The seond ssumon s eled o he os effeny of he ed d ndusy omed o he soe ed nsumen Assumon : The mee δ defned by 4 s sly osve Assumon bove mens h fom he on of vew of he lendes he sum of he ol bnk oss nd ofs of ed d nsons π s lowe hn A I he ele s os of ovdng soe ed In hs sef sense he ed d ndusy s moe os effen hn eles n ovdng ed 6

18 As demonsed n Rohe nd Wgh 00 unde he no-suhge ule f he onsume s benef of ed d nson s equl o he os svngs of geneng ed hough ed d nson nsed of soe ed f δ onsumes obn he mmum ggege welfe They oved h ny ohe level of ed ds oss/benefs f whh deends on he nehnge fee sne f I π wll genee loss n onsumes welfe In ohe wods dese onsumes e ndvdully dedng he nsumens of ymens n n oml wy fom he ggege on of vew hose desons genee n ollevely neffen level of ed d usge f omed o he oml suon when f δ The hd ssumon hs moe sohsed neeon nd essenlly moses esons on he eles vege os nd he onsumes vege benefs of ed d nson Assumon 3: The mee φ δ defned n 4 s sly osve As noed fomely Assumon 3 bove s equvlen o mosng h when he sed hged by boh mehns s equl o m he onsumes vege benef fom ed d nsons s gee hn he eles vege os fom he sme ed d nsons Noe h f eles eove hose oss hough he vege e d by onsumes Assumon 3 mles h onsumes hve osve vege benefs n usng ed ds δ Assumon 4: The nsoon os s gee hn δ dh b B B Assumon 4 bove gunees h he nsoon os s gee hn δ ε : δ B dh B 6 δ A 7

19 fo ll vlues of gee hn Noe h ε A oesonds o he ggege welfe benefs of ll onsumes nd eles obned fom dffeenon equlbum f omed wh he non suhge sngle e equlbum The ondon mens h he nsoon os s gee hn he benef obned fom he e dffeenon We ove Pooson h gee he nsoon os gee he of of ele when he deves unlelly fom dffeenl es equlbum We lso ove h hs mke she nd he mgn e boh zeo when ε sne even hs mos loses onsume wll efe o nu n nsoon oss sne hese oss e omensed by he benefs of hoosng he dffeenl es offeed by he ohe ele 3 Equlbum es unde e dffeenon In hs subseon we ovde some esuls h llow us o nlyze he ms of ulng ou he no-suhge ules n he ed d sysems All he esuls below e obned unde Assumons 3 nd 4 Pooson : If boh eles hge he sngle e s defned n equon he mehn fee s gee hn he os of he soe ed m > nd he densy of onsumes h e ndffeen o he os of soe ed o ed d B f s osve h f > 0 eles hve nenves o mose suhge ove he sngle e Poof: ee Aend The fs ddonl ondon n Pooson m > s ssfed f he nehnge fee s hgh enough > sne gves us he equlbum mehn fee An mmede onsequene of Pooson bove s h he sngle e hged fo evey nsumen of ymen s no he Nsh equlbum e unde e dffeenon A 8

20 The oof of Pooson emloys he f h he of funon s sly nesng n he e sed n neghbohood of 0 menng h s desble fo he mehn o suhge ed d nsons bove Howeve s woh nong h hs esul s only omve s ssessmen whose uly s elusvely o ove h he sngle e segy nno be susned n equlbum unde he e dffeenon ssumon Any oly ssessmen needs o ddess moe elevn quesons lke: s hee omeve equlbum wh h e dffeenon hes? And f he esonse s osve how does he onsume welfe n h equlbum fe when omed o h of sngle e? The esuls n he followng heoem hel us o lfy hese quesons Theoem : Fo eh nehnge fee defned by he bnks hee s of es esevely he e hged fo sh/soe ed nsons nd he one hged elusvely fo ed d nsons whee hs s Nsh equlbum eflly f boh eles e hgng hose es none of hem hs nenves o deve fom hose es The es e gven by [ H 0 H0 ] γ 7 nd m 8 Poof: ee Aend Noe h he e does no deend on nehnge fee Aully only he e of ed ds nsons deends on hough nd ny nese of he nehnge fee s olly nsfeed o he odu e when he ymen s mde usng he ed d 9

21 Fom equons 8 nd we obn h he equlbum sed s gven by A 9 nd onsequenly usng 9 nd we onlude h f δ In ohe wods he nehnge fee loses s bly of ffeng he onsumes ne benef of ed d nson f unde dffeenon whh beomes onsn nd equl o he oml benef vlue δ unde he no-suhge ule Ths s emkble dffeene wh ese o he Rohe nd Wgh 00 fndngs The vege equlbum e s m α α 0 whee α : [ H f ] s he ooon of d ownes h unde e dffeenon efe o use ed ds he hn soe ed o sh Coolly : The e s onve ombnon of he es nd Moe seflly α 0 α 0 whee α : [ H ] oesonds o he ooon of ed d ownes h 0 f unde no-suhge ule efe ed ds o ny ohe nsumen Poof: ee end An mon nd mmede onsequene of Coolly s h unde sly osve suhge > 0 we hve α [ H f ] < [ H f ] α0 Theefoe usng 0 nd we obn h he vege e m unde e dffeenon s lowe hn he sngle e unde he no-suhge ule 0

22 To fnlze he es nlyss we show how he oss subsdes sng n fmewok wh he no-suhge ule e elmned unde hs new seno wh e dffeenon Fgue 3 below lluses how he e n be deomosed no he new equlbum es nd he subsdy omonens h e elmned In ses nd he ems n he gh sde of boh equles no nluded n he gy boes oesond o he e hged usng sh o he soe ed In se 3 he ems n he gh sde of he equly no nluded n he gy bo oesond o he e hged usng ed d Noe h of he ol subsdy s elmned wh he e dffeenon of ed d nsons bu one omonen of he subsdy emns Ths omonen s ssoed o he gou of onsumes whou ed ds fed ooon h hs no benef usng he soe ed Thus hey use sh Ths ul gou of onsumes ys subsdy o he ohe onsumes The subsdy ous beuse hey hve fewe oons of ymen nsumens nd s onsequene less omeveness n he ymen ehnology Fgue 3 Deomosons of he sngle e equlbum Csh: [ H 0] γ Podu os Tnsoon mku ubsdy d oe ed: γ [ H 0] [ H f ] m [ H f ] m Elmned wh e dffeenon oe ed os ubsdy eeved ubsdy d 3 Ced d: [ H 0] γ m { [ H f ]} m Mehn fee ubsdy eeved ubsdy eeved Noe h he emnng subsdy fom sh uses o he ohes s elmned f we suose h evey onsume hs ed d Howeve sne we e no

23 llowng fo e dffeenon beween sh nd soe ed nsons subsdy beween hem esss Ths s beuse he e s n vege e does no efle he dffeen oss of eh nsumen sh hs zeo os nd soe ed hs os The followng heoem shows h hee s osve m on onsume welfe s onsequene of he elmnon of bes o e dffeenon of ed d nsons Theoem : The onsume welfe n he equlbum unde e dffeenon s gee hn he oesondng unde he no-suhge ule They e equl only f he nehnge e s equl o A Poof: ee end Wh ese o he mehns ofs he followng oolly shows h eles e ndffeen wh ese o he no-suhge ule In model whh onsdes boh onvenene uses nd nees-yng uses of ed ds Chkvo nd Emmons 003 showed h eles efe o hge dffeen es Coolly : The equlbum mehn of s he sme unde e dffeenon nd unde he no-suhge ule Poof: ee end

24 Fgue 4 Rele unlel movemen o sngle e segy Rele Rele ed ds sh/soe ed * Rele ed ds sh/soe ed Rele To nlyze he effe of he nehnge fee fed by bnks on he nenves of eles o deve o sngle e wll be useful o omue he of of ele esulng fom hs devon whls he ohe ele onnues o hge he dffeened es nd Fgue 4 lluses he suon whee Rele moves unlelly o he sngle e segy whls Rele onnues o hge wo es The followng ooson shows h ovded h boh mehns e hgng dffeened es none of hem hs nenve o unlelly hnge he mmum of sngle e * whh s no neessy equl o he no suhge sngle e equlbum In he ne subseon he sme ye of nlyss s evsed bu n one of esene of menu oss when onsdeng he ossbly of dffeened es see Theoem 3 Pooson : Assume h boh eles e nlly hgng dffeened es nd wh osve sed If one of hem dedes o hge he sngle e * h mmzes s of omed wh ll lenve sngle es he of of hs 3

25 ele wll deese he moun ε ε whees he of of he omeo wll ugmen n he moun ε Poof: ee he oof of Theoem 3 n end he se whou menu oss s ul se of he moe genel demonson esened hee A onsequene of Coolly nd Pooson s h dese boh eles hvng he sme of unde e dffeenon nd unde sngle e no one hs whou ooeon nenves o move unlelly o he sngle e Fgue 5 lluses he ofs of boh eles whee he seges e ly suhge nd ly sngle e As usul eh eny of he m eesens he ofs of eh ele oesondng o he doed seges Thus he gy ell ndes he equlbum ofs of Rele nd Rele whh e equl o / when boh dede o ly suhge The ofs of boh eles e / gn f hey ly he sngle e Howeve h segy ofle s no equlbum Fgue 5 Pofs unde e dffeenon ssumon Reles ofs Dffeenl es Rele ngle e Rele Dffeenl es ngle e / ; / / ε ε/ ; / ε/ / ε/ ; / εε/ / ε/ ; / ε ε/ / εε/ ; / ε/ / ; / Noe h f boh eles e he dffeenl e equlbum nd Rele unlelly dedes o hge he sngle e hs of flls fom / o / ε ε / nd Rele of gows fom / o / ε / Howeve f boh eles e hgng sngle es nd Rele ndvdully dedes o hge he dffeenl es hs of neses fom / o 4

26 / / ε ε nd Rele of deese fom / o / ε / Theefoe sne eh movemen eesens unlel devon fom sef nl e seno eh one genees dsn ofs senos The esonng s nlogous fo when Rele moves unlelly fom sngle e o dffeenl es segy nd when Rele moves unlelly fom dffeenl es o sngle e segy 3 Menu oss In hs ls subseon we nlyze he effes of he noduon of he menu oss n he model of e dffeenon h we e onsdeng In hs fmewok we wll ll menu os o ny os euny o no fed by he ele s onsequene of hgng dffeen es odng o he nsumen of ymen hoosed by he onsumes As usul he esons o onsde hs ye of fon nlude: he oss of develong ng seges fo dffeenon o he oss of mlemenng nd udng he sysems wh he nfomon of dffeened es Anohe eson fo nludng menu oss n be eled o he legl nd eguloy nseuy egdng evenul enles h he ele ould suffe s esul of lyng e dffeenon In usdons whee hee s no le ule wh ese o he e dffeenon o even whee hee e nsuonl onfls egdng o n esng ule he selles bue hgh oss o e dffeenon 0 uose h eles fe menu oss e nson μ nd μ o he mgn of he Rele s gven by M μ γ H0 Γ I : μ 0 The ynde of Reles of Belo Hozone he l of he e of Mns Ges Bzl eled o he Cou of Juse gns fnes led by he Insue of Consume Poeon of Mns Ges Poon/MG o eles who dffeene es of ed ds nsons In July 9 h 0 he 6 h Chmbe of Cou of Juse nnouned he senenng n fvo of he ynde In f hee s no el legl bss fo he led fnes; howeve he Poon/MG gues h he ohbon s suoed n eguloy ssued by he Mnsy of Fnne No 8 of Mh h 998 Indeed h eguloy efes o he mlemenon of he nson ules fo new ueny un of h e ne s no fnl senene he Poon/MG s elng o he Cou of Juse of he e of Mns Ges 5

27 0 whee I : ; f ; f 0 0 The followng heoem sses h even n he esene of menu oss he e dffeenon segy emns s Nsh equlbum The seds e he sme obned n he se whou menu os The equlbum es e gee hn he ones whou menu oss s well s hey e dffeen f he eseve menu oss e dffeen μ Theoem 3: If μ μ μ 3 nd μ ε > hen he suhges on ed d uhses emn beng equlbum whee he equlbum seds e equl he one fo he se whou menu os μ μ nd he equlbum bse es μ μ μ μ μ μ nd 3 3 e gee hn oesondng one fo he se whou menu oss Poof: ee end μ Pully when hee s no menu os dseson s esy o see μ h dese he esene of os ssoed o dffeenon he eles e ble o eove he full menu oss nesng he es sne μ > μ μ μ μ μ μ 3 3 Howeve f hee s menu os dseson when Rele s no ble o μ μ μ eove s full menu os sne < μ Howeve Rele eove moe 3 μ μ hn s menu os sne > μ As onsequene see he oof of Theoem 3 3 end Rele loses mke she nd mgn nd Rele neses hs eseve mke she nd mgn f omed wh he oesondng ones n se whou menu os dseson 6

28 Fgue 6 below genelzes he esuls Fgue 5 bove I shows he ofs of boh eles deendng on he ndvdul desons of ng seges when we μ ssume he esene of menu oss We defne : μ α nd 3 μ β : ε Noe h Assumon 4 nd he ddonl ssumons of Theoem 3 bove e suffen o gunee h 0 α < nd h fo evey nehnge fee 0 < α < fo β Fgue 6 shows he effes of he menu oss on he eles deson bou he lon o no of suhges on ed d uhses Noe h s onsequene of he unlel devon fom he dffeenl e o he sngle e he Rele s of deeses by β { [ α ] β } By he ohe sde he unlel devon of Rele fom he dffeenl e o he sngle e deeses hs of by β { [ α] β } Essenlly he gee he nehnge fee he gee s he of loss nd onsequenly he moe sble s he equlbum wh dffeenl es Addonlly he gee he menu oss he less sble s he equlbum wh dffeenl es Fgue 6 Pofs unde e dffeenon nd menu oss ssumons Reles ofs Dffeenl es Rele ngle e Rele Dffeenl es ngle e /-α-αβ ; / α-β /-α ; /α / β ; / -β / -α-β ; /ααβ / ; / / -β ; / β In hs ven Rohe 003 gued h suhgng s seldom used by selles obbly beuse of nson oss even when he sysem does no ohb Ou esuls evel h f hee e no mny onsumes obnng benefs fom he use of 7

29 soe eds hen β ould be negve fo o nd onsequenly he dffeenl e segy s no equlbum Theefoe n neesng o of led eseh ould be o ssess he dsosbly nd onvenene fo onsumes of he soe ed omed wh he ed of ed d n ode o nlyze f hs ould eln why n some eonomes dese suhge s elly llowed eles do no hge dffeenl es The oolly below shows h dese he esene of menu oss due o e dffeenon onsumes nd eles obn gee welfe nd ofs esevely when he non-suhge ule s voded In ul when hee s no menu oss dseson beween eles he oolly shows h he onsumes nd eles ggeged welfe gn wh dffeenon s he dffeene beween he ne welfe benefs of he elng soe ed fo ed ds by of onsume s esul of he mlemenon of he e dffeenon mnus he menu os nued by ele Coolly 3: The ggeged onsume s welfe nd he ggeged eles ofs n he dffeenl e equlbum wh menu oss e gee hn he oesondng ones obned unde he non-suhge sngle e equlbum In ul f boh oss e equl whee μ : μ μ he ggeged gn of welfe of onsume nd eles wh he dffeenon s gven by ε μ Poof: ee end Theefoe ou esuls desbed heoel suon whee he bolshmen of he non-suhge ule n edue he mke owe of he ed d sysem nd nese he ggeged welfe of onsumes nd eles These esuls hve n mon lnk wh he fndngs of Rohe nd Wgh 00 e ~ : mn{ ε μ /; ε μ /} If he bnks dede o se hgh nehnge fee sy > ~ he eles would be wllng o se he equlbum dffeenl es see Fgue 6 In ul suose h he heshold vlue ~ s lowe hn he nehnge fee h mmzes he bnks of unde he no-suhge ule s obned n Rohe nd Wgh 00 In hs suon s ossble h some ele dedes o 8

30 dffeene es whh n desblze he fome equlbum e enfong bnks o se he nehnge fee ~ In hs wy he mke owe nd he ofs of he ed d ssues e edued Consequenly he onsumes nd eles welfe e ugmened f omed wh he no-suhge sngle e equlbum 4 Conlusons In hs e we d he fmewok of Rohe nd Wgh 00 o he bsene of no-suhge ules fo es of ed ds nsons In hs seng we ove h he equlbum es fo he uhses usng ed ds nd usng sh o soe ed e no he sme In ul we obn h he equlbum suhge sed s he dffeene beween he mehn fee nd he os he hs o ovde he soe ed The esul egdng he equlbum e sed s emkble eselly n usdons whee he debe gend s he neessy of defnng mehn s suhge s n Ausl Ou esuls sse h he suhge should no eeed he omeve equlbum e sed h we found nmely h he suhge mus be lowe o equl o he dffeene beween he mehn fee nd he soe ed os fed by mehns In ul hs esul mles h only f he os fo he eles of soe ed nson s equl o o gee hn he ed d mehn fee he no-suhge ule should be eble fom he on of vew of hose who seek o eseve he welfe of he onsumes Ths s onsng esul wh he model nlyzed n Rohe 003 Inlly we ove h he sngle e s no equlbum when he dffeenon s llowed I s onsequene of eh ele beng wllng o unlelly suhge he ed d ymens nd deve fom he sngle e equlbum sed by he no-suhge ules The esul gven bove leds us o he followng queson: f e dffeenon s llowed mgh ovde some degee of mke owe o he mehns so h hey 9

31 would be ble o kee suhge on ed d nsons wh n vege e of ll nsons gee hn he sngle e found unde he no-suhge ule? The nswe s defnely no In ode o show h we omued he new equlbum es when e dffeenon of ed d ymens s llowed nd oved h he vege e s lowe hn he sngle e unde he no-suhge ule Moeove he new ggeged onsume welfe n he e dffeenon equlbum s n genel gee hn he oesondng one n he sngle e equlbum Equly would only ke le f he nehnge fee ws he level h mmzes he onsumes sulus unde he no-suhge ule fmewok We lso obn h he mehns ofs unde e dffeenon e equl o hose unde he sngle e equlbum Ths esul sed he followng queson: would he ele hve nenves o unlelly deve owds he sngle e? We found suons whee he would no In f we oved h f eesenve gou of onsumes see benefs n usng soe ed nsed of ed ds none of he eles hve nenves o unlelly deve fom he equlbum wh e dffeenon o he sngle e In he ls eese we nodue menu oss ssoed wh he e dffeenon o nlyze whehe hs so of fon my nhb eles nenves o dffeene es In hs new one we onlude h hee e suons when he segy of dffeenl ng my un ou o be equlbum In f f boh eles hge equlbum dffeenl es he of of he ele h nus n he gee smlle menu os wll fll below nese bove he levels ned unde sngle e Consequenly we deny suons when dese he esene of menu oss f boh eles e hgng dffeenl es none of hem hs nenves o unlelly hnge o he sngle ng segy Aully f only one mehn hges he sngle e he loses mke she nd mgn edung hs of Theefoe hee wll be loss of eles welfe ssoed o he deson of unlelly movng owd he sngle e segy 30

32 If he menu oss e he sme he boh eles ofs e equl he one ned unde he dffeenl es equlbum whou menu oss whh s he sme one unde non suhge sngle e equlbum Theefoe eles e ndffeen beween hese hee senos Dese of hs ndffeene of he eles onsumes n hve hghe ggeged uly omed wh he one obned unde no suhge sngle e equlbum In summy by usng smle ed d mke model we wee ble o lluse how he bsene of no-suhge ule ould genee equlbum es ble of movng onsume welfe Ths my edue he mke owe h bnks hve usng he nehnge fee even n he esene of menu oss ssoed o e dffeenon h he eles my fe We lso lluse suon when eles h fe smlle menu oss ssoed o e dffeenon hve omeve dvnge n one whee dffeenon s llowed Thus ould be ossble heoel usfon fo he eml evdenes of eles h efuse o e he moson of non-suhge ules Aknowlegemens The uhos hnk Alende Moody lve Fábo Mns Tno de Aud Mdlson Fenndez Queoz nd Rdo Tee ee Mouão fo ll he houghovokng dsussons nd fuful ommens onenng hs veson of he e The uhos en full esonsbly fo ny emnng eos Mos knowledges he PhD sholsh gned by CAPE-Bzl Mldondo s wok ws suoed n by CNPq Bzl hough gns /009-8 nd 4046/009- He lso knowledges h hs wok ws odued dung hs dem vs o he Reseh hool of Eonoms of he Ausln Nonl Unvesy 3

33 Refeenes BOT W; CHAKRAVORTI 008 Consume hoe nd mehn ene of ymen medthe Fedel Reseve Bnk of Chgo Wokng e BRADFORD T; HAYAHI F 008 Develomens n nehnge fees n he Uned es nd bod Fedel Reseve Bnk of Knss Cy Wokng e CENTRA BANK OF BRAZI 0 Relóo sobe Indús de Cões de Cédo Bno Cenl do Bsl <h://wwwbbgovb/pom/b/ing/pymen_ Cds_Reodf> CENTRA BANK OF BRAZI 0b O subsído uzdo no uso dos ões de édo Bno Cenl do Bsl Aend A of he 00 sl Addendum of he Reo on he Bzln Pymen Cd Indusy <h://wwwbbgovb/hms/sb/ Reloo_Coes_Adendo_00df> CHANG H; EVAN D; GARCIA-WARTZ DG 005 The effe of eguloy nevenon n wo-sded mkes: n ssessmen of nehnge-fee ng n Ausl Revew of Newok Eonoms Vol4 4 Ago 5 CHAKRAVORTI ; EMMON W 003 Who ys fo ed ds? Jounl of Consume Affs Vol CHAKRAVORTI ; To T 007 A heoy of ed ds Inenonl Jounl of Indusl Ognzon Vol GAN J ; KING P 003 The Neuly of Inehnge Fees n Pymen ysems Tos n Eonom Anlyss & Poly Vol3 Issue Ale Bekeley Eleon Pess MA MARKET DEVEOPMENT AB 000 udy Regdng he Effes of he Abolon of he Non-dsmnon Rule n weden fo Euoen Commsson Comeon Deoe Genel ITM Reseh Fnl Reo REERVE BANK OF AUTRAIA 0 Revew of d suhgng: onsulon doumen Reseve Bnk of Ausl <h://wwwbgovu/ublons/onsulons/ 006-evew-d-suhgng/df/006-evew-d-suhgngdf> REERVE BANK OF AUTRAIA 0b A Von o he suhgng sndds: onsulon doumen Reseve Bnk of Ausl h://wwwbgovu/ ublons/onsulons/0-von-suhgng-sndds/df/0- von-suhgng-snddsdf> REERVE BANK OF AUTRAIA 0 A Von o he uhgng ndds: Fnl Refoms nd Regulon Im emen Reseve Bnk of Ausl June <h://wwwbgovu/ymens-sysem/efoms/ds/006-v-suhgng-sndsfn-ef-s/ndehml> 3

34 ROCHET J-C 003 The heoy of nehnge fees: synhess of een onbuons Revew of Newok Eonoms Vol Ago 4 ROCHET J-C; WRIGHT J 00 Ced d nehnge fees Jounl of Bnkng & Fnne Vol ROCHET J-C; TIROE J 00 Cooeon mong omeos: some eonoms of ymen d ssoons Rnd Jounl of Eonoms Vol ROCHET J-C; TIROE J 006 Eenles nd Regulon n Cd Pymen ysems Revew of Newok Eonoms Vol5 Issue -4 ROCHET J-C; TIROE J 008 Mus-ke ds: Mehn dsouns nd voded oss Toulouse hool of Eonoms Wokng e CHMAENEE R 00 Pymen sysems nd nehnge fees Jounl of Indusl Eonoms Vol50 03 CHUH ; TAVIN J 00 Why e some onsumes fnlly wng fewe heks? The ole of ymen hess Jounl of Bnkng nd Fnne Vol WANG Z 00 Mke suue nd ymen d ng: Wh dves he nehnge? Inenonl Jounl of Indusl Ognzon Vol WEINER ; Wgh J 005 Inehnge fees n vous ounes: Develomens nd deemnns Revew of Newok Eonoms Vo 4 4 Ale 3 WRIGHT J 003 Oml d ymen sysems Euoen Eonom Revew Vol UNITED KINGDOM PARIAMENT 990 The Ced Cds Pe Dsmnon Ode 990 Uned Kngdom Plmen uoy Insumens No 59 <h://wwwlegslongovuk> VI E; TOTH J 000 The Abolon of he No-dsmnon Rule Reo fo Euoen Commsson Deoe Genel Comeon Vol <h://e euoe/omm/omeon/nus/ses/973/sudes/nehelnds/eodf> 33

35 Aend To ove h unde e dffeenon he sngle e s no equlbum nd o fnd he new equlbum es we fs deve he mehn mgn he onsume uly nd mehn mke she nd use hem o fnd he of funon ubsequenly we omue he devves of he of funon wh ese o he bse e nd he sed Fgue A shows deomoson of he mehn s eeed mgn no sevel omonens The fs gou of omonens oesonds o he mgn obned by mehns fom onsumes h nno use ed ds ehe by no hvng hem o beuse he ele dd no dhee o he ed d sysem The seond gou of omonens oesonds o he ele mgns fom he onsumes who hve ed d ondoned o hs dheene o he ed d sysem Fgue A Mehn s eeed mgn soe ed sh Cnno use ed ds H 0 γ H 0 M odny uhse soe ed γ ed uhse soe ed n use ed ds H γ f γ H f γ m soe ed [ H f H f m ] γ γ ed d nd sh odny uhse ed d ed uhse The fomul n Fgue A n be smlfed o deve equon 7 Then he l devves wh ese o he bse e nd he sed e gven by 34

36 M A nd M { h f m [ H f ]} A Consumes dede whh ele o onze omung s uly nd subng he nsoon oss of eh hoe To lule he mke she we need o denfy he ndffeen onsume n he nevl Anlogously Fgue A below shows deomoson of he onsumes eeed uly The fs gou of omonens oesonds o he uly obned by onsumes h nno use ed ds ehe by no hvng hem o beuse he ele dd no o dhee o he ed d sysem The seond gou of omonens oesonds o he uly of onsumes h hve ed d nd he hosen ele dheed o he sysem Fgue A Consume s uly U u nno use ed d 0 u uly of os of onsumon odu 0 B B dh B E B os of soe ed odny nd ed uhses n use ed d u0 u uly of os of onsumon odu f B dh B B B f dh f B f B B B dh B os of soe ed odny uhses f f dh os of ed d odny uhse B os of soe ed ed uhse os of ed d ed uhse 35

37 The eesson n Fgue A n be smlfed o deve equon 9 whh s used o obn he mke she equon The devves of he mehn s mke she wh ese o he bse e nd he sed e gven by nd s s A3 [ H f ] A4 The mehn s eeed of s he odu of he mgn nd he mke she As we n see below he eessons A5 o A8 e useful o omue he devves of he of funon We n use he equons 7 A nd A3 o deve he eessons below: nd M s M s γ H 0 Γ A5 A6 We n use he equons 7 A nd A4 o deve he eessons below: s M [ H f ] [ γ H 0 Γ ] A7 nd M s { h f m [ H f ]} { } A8 36

38 ummng u A5 nd A6 we obn he devve of he of funon wh ese o he bse e Γ 0 H γ π A9 Anlogously we fnd he devves of he of funon wh ese o he sed fom A7 nd A8 [ ] [ ] [ ] { } { } Γ 0 f H m f h H f H γ π A0] Poof of Pooson : ubsung n A0 wh 0 nd we obn h he devve of he mehn s eeed of wh ese o he sed ssfy he followng equon m f h π A whee h eesens he densy funon of he umulve dsbuon funon H Noe h he gh hnd sde of A s osve f ll he followng ondons e ssfed: Thee e nsoon oss 0 > ; Thee e d uses 0 > ; 37

39 The densy of onsumes h e ndffeen o he os of soe ed o ed d f B s osve 0 > f h ; The mehn fee s gee hn he os of he soe ed m > We onlude h f e dffeenon s llowed mehns hve nenves o suhge nd onsequenly he sngle e s no equlbum Poof of Theoem : The fs ode ondons wh ese o he bse e nd he sed usng equons A9 nd A0 e gven esevely by 0 H Γ γ A nd [ ] { } [ ] { } { } 0 f H m f h H f H Γ γ A3 ubsung A n A3 we obn 0 m f h nd he sed n equlbum s m Usng A we obn he followng eessons onnng he bse es of boh eles ; 0 H Γ γ 38

40 Inehngng nd nd mullyng by wo we obn 4 γ H 0 Γ ummng u he equons bove nd engng we obn h he equlbum e ssfes he followng equon φ 3 γ H 0 Γ A4 Fom equon A4 bove we obn φ 3 Γ whh n be nluded n he mke she equon o obn s φ 6 A5 If φ φ > 0 we onlude fom fomul A5 h n equlbum boh δ eles dhee o he ed d sysem Ths ous beuse f one of hem dedes he ony he wll lose mke she Consequenly he mke she of boh eles e he sme s s s Theefoe usng nd m we onlude fom A4 nd 8 h he equlbum vlue fo he bse e s gven by equon 7 Aully o onlude he oof nd show h hose es e no only lol equlbum bu elly globl Nsh equlbum we need o ssess he of von 39

41 when eh one of he eles dedes o deve fom he dffeenl es equlbum o nohe se of es ne we do hs demonson n moe genel one n he Poof of Theoem 3 below we om hee hs of he oof bu we ommen hee how nlyze hs se whou menu oss s ul se of he moe genel se Poof of Coolly : Fom nd A3 sne nd m we onlude h [ H f ] m A6 whh n be enged usng equon 7 o obn equon Poof of Theoem : We n use equon 9 o show h he dffeene beween he onsumes ggeged ules sulus n boh equlb s gven by U [ ] B f dh B H f f f ubsung equon A6 no he equon bove we obn U [ H f H f ] f f B f dh B Rewng he equon bove we obn h U f f f dh B B 0 > 0 f f

42 o > A A B B dh U A f 0 f 0 δ δ δ Poof of Coolly : We use equon 7 o show h he dffeene beween he eles mgns n boh equlb s gven by [ ] { } f H M whh s equl o zeo by equon A6 ne he mke shes e equl n boh equlb / s we onlude h he mehns ofs e lso he sme In ohe wods mehns e ndffeen beween boh equlb Poof of Theoem 3: Fom equon we obn h f boh eles hge dffeenl es he menu oss μ wll deese he mgns The fs ode ondons wh ese o he bse e nd he sed e gven esevely by 0 I H Γ μ γ nd [ ] { } [ ] { } { } 0 f H m f h I H f H Γ μ γ 4

43 Denong by μ μ μ nd μ he seds nd es h solve he fs ode ondons bove We use he sme ehnque led o ove Theoem o ove h μ μ μ μ μ 3 μ μ μ : m nd h nd 3 Assumng whou loss of genely h μ μ he ele h nus n gee menu os hge equlbum e gee hn ele Moe esely we μ μ μ μ obn h 0 3 If he nsoon os of one dsne uny s bgge o equl he one hd of he dffeene beween he e of goods of boh eles μ μ nd 3 μ μ f we defne α : we hve 0 < α < Unde ll he ondons bove nd 3 usng equon we lso ove h he equlbum mke shes e esevely μ μ s α nd s α Addonlly we use equon o ove h he μ μ equlbum mgns e esevely M α nd α We onlude h he equlbum ofs unde menu oss e esevely π α nd π α Noe h π π 4 α > 0 menng h of of he ele wh he bgges menu os s smlle he of of ele wh he smlle menu os M Afe solvng he fs ode ondons we now need o ove h he eles do no hve nenves o unlelly deve fom hose dffeenl es Noe h he funon f ε : f B dh f B 4

44 s genelzon of he funon of ε sne 0 ε ε nd h [ ] Γ Γ ε All he omuons below n be eodued n n nlogous wy fom he on of vew of eh ele Pully we f he e hged by he ele nd boh seds nd we n we he of of he ele s [ ] Γ Γ I H I H 0 0 μ γ μ γ π Noe h he e h mmze globlly he of funon bove ssfes he followng equon [ ] 0 m I H Γ μ γ We n use he eesson bove o defne s μ he e of mmum of fo he ele when he deves unlelly fom bse e μ nd he sed so he ele sy hgng bse e μ nd he sed nd dede o hge he sed Consequenly he e von s gven by [ ] I ε μ μ 43

45 μ Defnng s μ nd M esevely s he mke she nd he mgn fe he movemen we n omue he oesondng mke she von nd mgn von eevely nd s s μ I ε μ μ M M μ I μ μ ε ne ε > 0fo ll s nd gmn{ ε } nd we onlude fom he eessons bove h he mmum of s globlly ned by he ele he sed nd bse e μ onludng hee he oof of Theoem 3 Noe h he esul bove hs s ul se whh s he se whou menu oss Then he oof of he esene of globl equlbum of Theoem n be onluded usng he esuls bove ssumng μ μ 0 Below we wll use he eessons bove o ove Pooson nd o omue he ofs n Fgue 5 nd 6 Pully we n use he sme eessons bove o obn he mke she nd mgn vons when ele dedes o hge sngle e esevely s β μ 0 nd μ μ M 0 M β μ s μ whee unde ou ssumon we hve 0 < β : ε < Theefoe we n onlude he of von gven by π μ 0 π μ β [ α β ] 44

46 whh s negve sne unde ou ssumons 3 : 0 < μ μ α Usng he sme ehnque we n omue he mke she nd mgn vons when ele deves fom he non suhge sngle e equlbum esevely 0 0 I s s μ ε μ nd 0 0 I M M μ ε μ Now sne { } 0 gm ε we obn osve mke she nd mgn vons esevely 0 0 > s s β μ nd 0 0 > M M β μ nd onsequenly osve of von 0 0 > β β π π μ Fom hose eessons bove fo he of vons s sghfowd o omue he ofs n he Fgue 6 s well s ssumng μ μ o demonse Pooson nd o omue ll he ofs showed n Fgues 5 Poof of Coolly 3: Denoe by U nd μ U he uly of he onsumes h hoose ele esevely unde he non suhge sngle e equlbum nd unde dffeenl 45

47 e equlbum wh menu oss To ome boh senos we omue he uly von μ μ μ U U ε 3 Anlogously fo onsumes h hoose ele The dffeene beween boh ules μ μ μ μ efles he dffeenes on es nd s gven by U U 3 ne he mke shes e dffeen deendng on he equlbum he ggeged uly von s gven by U μ U α μ α U U μ U U We n ewe he ggeged uly von s U μ U α β β μ whee : μ μ α > 0 nd β : ε > 0 Thus we onlude h he uly 3 nese Howeve o onlude he onsume welfe nlyss we lso need o omue he ggeged nsoon os von α / / s ds s ds s ds s ds 0 α / 0 / 46

48 whh s equl o α 4 Fnlly f we sub nsoon os von fom he uly von we obn he ol onsume welfe von whh s lso osve α β β 4 Now we nlyze he ele s welfe We omue he of von α α whh s equl o α Then hee s of nese f he eles menu oss e dffeen Pully ssumng h eles hve he sme menu oss we n defne μ : μ μ nd β : β β In hs se s neesng o noe h summng u he ggeged welfe von of onsumes uly mnus nsoon os nd eles of omued bove we obn he ol welfe gn of onsume nd eles wh he dffeenon s gven by [ β] ε μ 47

49 Bno Cenl do Bsl Tblhos Dsussão Os Tblhos Dsussão do Bno Cenl do Bsl esão dsoníves downlod no webse h://wwwbbgovb/?trabdicita Wokng Pe ees The Wokng Pe ees of he Cenl Bnk of Bzl e vlble fo downlod h://wwwbbgovb/?workingpaper 84 On he Welfe Coss of Busness-Cyle Fluuons nd Eonom- Gowh Von n he 0h Cenuy Osmn Tee de Cvlho Gullén João Vo Issle nd Afonso Anos de Mello Fno-Neo 85 Asse Pes nd Money Poly A ky-dsesed Infomon Model M Aeos nd Wldy Aeos 86 Infomon n Chns: nfomon nsmsson hough oduon hns Wldy Aeos nd M Aeos 87 ome Fnnl bly Indos fo Bzl Adn oes les Wldy D Aeos nd M B M Aeos 88 Foesng Bond Yelds wh egmened Tem uue Models Co Almed Ael monsen nd José Vene 89 Fnnl bly n Bzl uz A Pee d lv Adn oes les nd Wgne Pzz Gglnone 90 lng hough he Globl Fnnl om: Bzl's een eeene wh money nd moudenl oles o len gns he fnnl yle nd del wh sysem sks uz Awzu Pee d lv nd Rdo Eye Hs 9 O Desemenho Reene d Polí Moneá Bsle sob Ó d Modelgem DGE Buno Fes Boynd de Vsonelos e José Angelo Dvno 9 Cong wh Comle Globl Envonmen: Bzln eseve on emegng mke ssues Adn oes les nd João B Rbeo Blno Boso 93 Congon n CD Bnkng nd Equy Mkes Rodgo Cés de Cso Mnd Benmn Mnd Tbk nd Muo Medeos Juno 93 Conágo nos Medos de CD Bnáo e de Ações Rodgo Cés de Cso Mnd Benmn Mnd Tbk e Muo Medeos Juno Jul/0 Jul/0 Jul/0 Jul/0 Jul/0 Aug/0 Aug/0 e/0 O/0 O/0 Ou/0 48

50 94 Pesqus de Esbldde Fnne do Bno Cenl do Bsl olnge M Gue Benmn Mnd Tbk e Rodgo Cés de Cso Mnd 95 The Eenl Fnne Pemum n Bzl: eml nlyses usng se se models Fenndo Nsmeno de Olve 96 Um Avlção dos Reolhmenos Comulsóos eondo Alen Tony Tked Buno Mns e Pulo Evndo Dwd 97 Avlndo Volldde Dá dos Avos: ho d negoção mo? José Vlenm Mhdo Vene Gusvo lv Aúo Pul Bão Fshe de Cso e Fele Noonh Tves 98 Aução de Bnos Esngeos no Bsl: medo de édo e de devvos de Rquel de Fes Olve Rfel Fele hoze e égo eão 99 ol Mke uue nd Bnk Comeon: evdene fom he Bzln uo lon mke Buno Mns 99 Esuu de Medo ol e Começão Bná: evdêns no medo de fnnmeno de veíulos Buno Mns 300 Conevdde e Rso sêmo no sem de Pgmenos Bsleo Benmn Mnd Tbk Rodgo Cés de Cso Mnd e ego Rubens no de ouz 300 Connevy nd ysem Rsk n he Bzln Nonl Pymens ysem Benmn Mnd Tbk Rodgo Cés de Cso Mnd nd ego Rubens no de ouz 30 Deemnnes d Cção íqud dos Deósos de Pounç Clodoldo Aedo Annbl 30 ess Tesng qudy Rsk: he se of he Bzln Bnkng ysem Benmn M Tbk olnge M Gue Rodgo C Mnd nd ego Rubens de ouz 303 Usng DGE Model o Assess he Moeonom Effes of Reseve Requemens n Bzl Wldy Du Aeos nd Chsno Agon Coelho 303 Ulzndo um Modelo DGE Avl os Efeos Moeonômos dos Reolhmenos Comulsóos no Bsl Wldy Du Aeos e Chsno Agon Coelho 304 Ced Deful nd Busness Cyles: n nvesgon of hs elonsh n he Bzln ooe ed mke Jquelne Te Mou Mns nd Myn Bez Es ds Neves Ou/0 O/0 Ou/0 Nov/0 Nov/0 Nov/0 Nov/0 Nov/0 Nov/0 Dez/0 De/0 Jn/03 Jn/03 M/03 49

51 304 Indmlên de Cédo e Clo Eonômo: um eme d elção no medo bsleo de édo oovo Jquelne Te Mou Mns e Myn Bez Es ds Neves 305 Peços Admnsdos: oeção e esse mbl Pulo Robeo de mo Alves Fnso Mos Rodgues Fgueedo Anono Negomone Nsmeno Juno e eondo Po Peez 306 Comle Newoks nd Bnkng ysems uevson Theohlos Pdmou Pekls Gogs nd Benmn M Tbk 306 Redes Comles e uevsão de sems Bnáos Theohlos Pdmou Pekls Gogs e Benmn M Tbk 307 Rso sêmo no Medo Bnáo Bsleo Um bodgem elo méodo CoVR Gusvo lv Aúo e égo eão 308 Tnsmssão d Polí Moneá elos Cns de Tomd de Rso e de Cédo: um nálse onsdendo os seguos ondos elos bnos e o sed de édo no Bsl Debo Pee Tves Gbel Clds Mones e Osmn Tee de Cvlho Gullén 309 Conveng he NP Ro no Comble ong Tem Me Rodgo Pno Coelho nd Glneu Fnso Asolf Vvn 30 Bnks Asse Mngemen o Consulnes Inflon Foess: s hee bee foese ou hee? To Nís Tee d lv Flho 3 Esmção não-mé do so de ud Co Ibsen Rodgues Almed José Vlenm Mhdo Vene e Osmn Tee de Cvlho Gullen 3 A Influên d Assme de Infomção no Reono e n Volldde ds Ces de Ações de Vlo e de Cesmeno M endo Fee Tves Cludo Henque d lve Bbedo e Gusvo lv Aúo 33 Qunve Esng nd Reled Cl Flows no Bzl: mesung s effes nd nsmsson hnnels hough goous ouneful evluon João B R B Boso uz A Pee d lv nd Adn oes les 34 ong-run Deemnns of he Bzln Rel: lose look ommodes Emnuel Kohlsheen M/03 M/03 My/03 Mo/03 Jul/03 Jul/03 Jul/03 Jul/03 Jul/03 Jul/03 Jul/03 Jul/03 50