Moral considerations in trading pollution permits. Johan Eyckmans and Snorre Kverndokk

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1 Moral consdratons n tradng olluton rmts Johan yckmans and Snorr Kvrndokk HUB RSARCH PAPR 2008/12. FBRUARI 2008

2 Frst draft. Fbruary 2008 Moral consdratons n tradng olluton rmts 1 by Johan yckmans uroan Unvrsty Collg Brussls Stormstraat 2, B-1000 Brussls, Blgum. 2 and Katholk Unvrstt Luvn Cntrum voor conomsch Studën and Snorr Kvrndokk Ragnar Frsch Cntr for conomc Rsarch Gaustadallén 21, 0349 Oslo, orway 3 Abstract In ths ar w nvstgat how moral consdratons, modlld as dntty ffcts, affcts an ndognous olluton rmt tradng qulbrum, n whch govrnmnts choos n a non-cooratv way th amount of rmts thy allocat to thr domstc ndustrs. Poltcans mght fl rluctant to allow unlmtd rmt tradng and/or may rfr that abatmnt s undrtakn domstcally du to thcal motvaton. Howvr, onc govrnmnts hav chosn rmt allocatons, frms trad ths rmts n an ntrnatonal comttv rmt markt wthout moral rstrants. W show that govrnmnts moral concrns may actually ncras global mssons but ths rsult dnds on th rcs formulaton of th dntty functon. Fnally, w xlor how xognous tchnologcal chang affcts ndognous rmt tradng qulbra undr dntty consdratons. W show that dcrasng costs of abatmnt tchnologs may lad countrs to ovrcom thr rluctanc to tradng msson rmts. Kywords: Tradabl msson rmts, noncooratv gam thory, moral motvaton, dntty, tchnologcal chang. 1 W ar ndbtd to commnts from Kll Arn Brkk, Karn vlyn Haug, Karn yborg, Alstar Ulh and othr artcants at th Frsch Cntr Klækkn smnar (May 2007) and th CAS Worksho n Askr (August 2007). 2 Johan.yckmans@hsal.b 3 Snorr.Kvrndokk@frsch.uo.no 1

3 1. Introducton In ths ar w tak a closr look at olluton rmts whn arts ar rluctant to trad. conomsts tycally rfr trad n olluton rmts ovr convntonal, non markt-basd nvronmntal olcy nstrumnts bcaus of cost ffcncy consdratons. Both n thory (s,.g. Montgomry, 1972) and n ractc (s,.g. Schmalns t al., 1998), markt-basd olcy nstrumnts ar known to fostr cost ffcncy n nvronmntal olcy makng. Howvr, rmt trad has bn oosd by many obsrvrs such as nvronmntal organsatons and oltcal arts. Som consdr trad n olluton rmts as a way to try to avod on s oblgatons, to ay othrs to clan u, or to ay ndulgnc, s Goodn (1994). In th Kyoto rotocol for nstanc, trad n olluton rmts s allowd, but only as a sulmnt to natonal mtgaton. 4 Ths mchansm may hav bn ntroducd as a consqunc of th maorty of th sgnators bng rluctant to rmt tradng. Also n th uroan msson Tradng Schm (TS), accss to buyng msson rductons n thrd arty countrs (JI Jont Imlmntaton for conoms n transton and CDM - Clan Dvlomnt Mchansm for dvlong countrs) can b lmtd by mmbr stats 5. Thus, th cost-ffctv trad volum may not b wthn th ossblty rang. Howvr, t sms to us that tradng wth olluton rmts s mor acctabl now than t was ust yars back. In orway for nstanc, nvronmntal organsatons ar now tradng carbon offsts on th ntrnt (to offst carbon mssons from arln flghts), vn f thy argud aganst olluton trad ust a fw yars ago. W wll study th mlcatons n a tradabl rmt markt f thr ar moral concrns aganst rmt tradng. scally, w focus on a norm sayng that on should not ngag too much n rmt tradng and to do most of th abatmnt at hom, but w assum that countrs ar wllng to trad off th norm f th bnfts from dong so ar larg nough. Frst, w study how moral concrns may affct global mssons. Scond, w wll try to com u wth an xlanaton why thr sms to b a largr ntrst n rmt trad now comard to som yars ago. A largr ntrst n olluton rmt trad may b du to a chang n th norm so that t s mor acctabl than bfor. 6 But thr may also b anothr xlanaton. Although thr may contnu to xst som rluctanc to trad, th bnfts from trad may b hghr than bfor. Ths ar wll focus on th lattr xlanaton. If w comar th conomy today and yars back, on strkng dffrnc s th chang n mtgaton tchnology. Tchnology mrovs ovr tm, n such a way that mtgaton bcoms char. Thrfor, w want to study how mrovmnts n mtgaton tchnology may affct th markt for olluton rmts trad f thr s a norm that you should not trad rmts. In othr words w wll study how a chang n tchnology wll affct th bnfts from trad, and f th bnfts may b largr than th costs of trsassng th norm. 4 Artcl 6.1 of th orgnal Kyoto Protocol txt stats Th acquston of msson rducton unts shall b sulmntal to domstc actons for th uross of mtng commtmnts undr Artcl 3. Howvr, latr mtngs of th Confrnc of th Parts (CoP) hav not bn abl to fnd a consnsus on a mor rcs or quanttatv manng of ths sulmntarty rqurmnt. 5 Mor dtals on th latst roosd changs n th U TS 3 rd has ( ) can b found at htt://uroa.u/rad/rssrlassacton.do?rfrnc=mmo/08/35&format=html&agd=0&lan guag=&gulanguag=n. Although svral scnaros ar crculatng (January 2008), t s clar that accss to CDM and JI rocts wll not b unlmtd. 6 S,.g., yborg and Rg (2003) for a study on changs n smokng norms. 2

4 Som forms of moral concrns about rmt trad, but not all as shown n ths ar, rrsnt addtonal costs of tradng and thus gv rs to lowr wlfar from trad comard to th cas n whch ths concrns ar absnt. Thus, ntroducng ths moral concrns shars smlarts wth a rmt trad systm wth transacton costs 7, s,.g., Stavns (1995). Wth transacton costs, th volum of trad s lowr and wlfar s lowr comard to a systm wthout transacton costs. Also th ntal allocaton of rmts may affct th outcom of tradng. Howvr, th rsnc of moral consdratons about rmt trad s dffrnt than transacton costs n svral rscts, whch wll b outlnd n mor dtal blow. Ths ar s organsd n th followng way. W frst dscuss ossbl rasons bhnd th rluctanc to trad olluton rmts. In scton 3, w rsnt th modl and drv conclusons on how dntty consdratons followng from a norm aganst msson rmt tradng, chang govrnmnts bhavour n th rmt tradng markt. Scton 4 studs how a chang n tchnology affcts th dcsons for countrs to nvolv n mssons tradng. Scton 5 concluds. 2. thcal rasonng, norms and dntty In conomc thory, t s assumd that most goods can b bought or sold n a markt. Howvr, ths may not always b th cas and dstast, or vn rugnanc, for crtan transactons may b a ral constrant n many markts, s Roth (2008) for a survy. 8 Ths can b dscrbd as norms aganst tradng crtan goods. A norm s dfnd as a standard of rght or wrong, and n all culturs thr ar goods that ar consdrd to b rclss or sacrd n such a way that w cannot st a rc on thm. xamls may b lf, frdom, lov, frndsh, chldrn, rlgon, dmocracy and th nvronmnt. Som of ths goods ar calld taboo goods (Fsk and Ttlock, 1997) whr a taboo s dfnd as a artcular owrful knd of normatv rohbton. Taboos ar mant to rotct ndvduals and socts from bhavour dfnd or rcvd to b dangrous (Tannnwald, 1999), and brakng a taboo s usually mt by socal sanctons or rrcussons. Incommnsurablty may also b a roblm, manng that thr may not b a common masur to comar th goods (O ll, 1993, chatr 7). Som xamls may b frndsh or lov. A markt may dstroy ths goods, as sttng a rc on thm may rduc thr valu. Howvr, thr ar goods that may b tradd, not mt by th sam strngth of sanctons whl tradd as taboo goods, but stll thr s a norm aganst such trad. xamls may b lgalzd rosttuton, body organs and mltary duty (Bénabou and Trol, 2007; Roth, 2008). Som knds of transactons ar consdrd rugnant n som tms and lacs, but not n othrs, thus th boundars btwn th scular and th sacrd ar volvng ovr tm. For nstanc slavry s an xaml of a markt that usd to xst n larg arts of th world, but s now rugnant and llgal n most lacs. On th othr hand, thr has bn mor ostv atttuds ovr tm towards lf nsuranc (Zlnr, 1999), lgalzd rosttuton and also olluton rmts. Polluton rmts has bn rcognsd by svral authors as a markt whr thr may xst som rluctanc or vn rugnanc aganst transactons, s,.g., Goodn 7 Roth (2008) comars rugnanc to trad crtan goods to a dffcult tchnologcal barrr. 8 Frank (1985), chatr 10, also gvs svral xamls of why trad n crtan goods should not b allowd. 3

5 (1994), Bénabou and Trol (2007) and Roth (2008). Why may thr b rluctanc or a norm aganst trad n crtan goods such as olluton rmts? In thcal rasonng, thr ar two ways to ustfy f an acton s good or bad. Th frst s to rfr to th consquncs (tlology or substantv farnss). Basd on ths, an acton s good f t s th bst way to attan th am w strv for (.g, maxms wlfar, rduc grnhous gas mssons). Brkk t al. (2003) gvs an xaml of moral rasonng basd on tlology wr ol can ay an organsaton nstad of dong voluntary work. If thy thnk that th aymnt s nough to ay rofssonals to do th ob, thy do not fl rsonsbl anymor, and thy may choos th markt soluton. But, f thy thnk that th aymnt s not nough, thy fl that thy stll ar rsonsbl for havng th task don. Howvr, thr may also b stuatons whr w dslk gvng othrs ths rsonsblty, ndndnt of th consquncs for our wlfar. Ths lads us to anothr way of moral thnkng sayng that consquncs alon do not gud us whthr somthng s rght or wrong (dontology or rocdural farnss). It s not nough to know that th acton s th most ffctv way to attan th am. On can for nstanc argu that ndustralsd countrs hav cratd th global warmng roblm, and that s our duty to rduc th consquncs of t by clanng u our own backyard, vn f ths s not th way that mnmss ovrall costs of takng acton. Ths could also b usd as an argumnt aganst sllng rmts by dvlong countrs as sllng quotas to ndustralsd countrs would not lad to abatmnt n th countrs rsonsbl for th roblm. Anothr argumnt s basd on unfar background condtons (s Kvrndokk, 1995, and yckmans and Schokkart, 2004). vn f two arts agr to trad rmts, th trad may not b ustfd on thcal rasons. A voluntary agrmnt btwn two arts s not ncssary far f s ntrd nto condtons that ar not far (Pogg, 1989). Background ustc s not rsrvd whn som artcant s basc rghts, oortunts or conomc ostons ar grossly nfror. Undr th Kyoto Protocol, for nstanc, on may argu that ths s th cas for som CDM contracts. conomcs s bascally about consquncs. If th consquncs of th us of a olcy nstrumnt s ostv (ncrasng wlfar), w rcommnd t. Ths s th cas wth msson rmts. Th basc argumnt of quota trad s that t s cost-ffctv (Montgomry, 1972), thus arts nvolvd n rmt trad would gt lowr abatmnt costs than f thy had to mtgat th mssons wthn thr gograhcal boundars. Thus, cost-savngs wll b wlfar mrovng, vrythng ls gvn. On ossbl xlanaton of th rsstanc of rmt trad s thrfor, that wlfar mrovmnts followng from rmt trad hav not bn communcatd wll nough,.., th standont s basd on lack of nformaton. 9 Howvr, othr xlanatons may also b lausbl. Thr may b ngatv consquncs of a rmt markt, consquncs that may b rlatd to th am of rsrvng th global nvronmnt, or t may b rlatd mor broadly to othr aras of th socty concrnng,.g., rsonsblty. Buyng, va th CDM mchansm, grnhous gasss olluton rmts n countrs that dd not subscrb to bndng msson lmts n th Kyoto Protocol, may hav som advrs ffcts basd on lack 9 On xaml basd on lack of nformaton ontd out to us by Alstar Ulh s as follows. If a country has xtrmly hgh margnal abatmnt costs (n th lmt nfnt:.., t cannot abat) thn wantng to do all th abatmnt at hom s ust not snsbl (thcally); t would sm mor arorat, for a country to us ts rsourcs to ay a country whch can abat chaly to do so. 4

6 of an msson basln, moral hazard, lack of ncntvs to undrtak mssons rductons by th dvlong countrs, transacton costs and carbon lakags. Thr s also som dscusson whthr CDM s hav th xctd ffct on msson rductons as som obsrvrs argu that th markt s floodd by rocts of qustonabl qualty (Harvy, 2006, and Davs, 2007). Hot ar, manng that som countrs gt ntal msson quotas that ar hghr than thr actual mssons, has also bn mntond as a rason to avod msson tradng as tradng hot ar wll not rduc mssons. Othr argumnts that hav bn rasd n ths dbat ar th ostv sllovr ffcts of tchnology dvlomnt by natonal abatmnt as wll as th ancllary bnfts (rducton n local mssons, traffc accdnts, congston tc.) of abatng at hom. Abatng at hom nstad of buyng msson rmts, shars som smlarts wth unlatral actons takn by a country. Unlatral actons may b dfndd as a contrbuton n th rght drcton or as sttng a good xaml. Hol (1991) analyss ffcts of unlatral actons on harmful mssons, and concluds that n absnc of a ngotatd agrmnt, such a olcy wll tycally lad to lowr aggrgatd mssons than a slfsh olcy. But ths olcy may also affct th outcom of ngotatons on msson rductons. Hol concluds that th outcom may vry wll mly hghr total mssons. Howvr, f th unlatral acton s announcd as a commtmnt to rduc mssons n xcss of th outcom of th ngotaton, total mssons wll lkly b lowr than only comard to th cas whr all countrs act slfshly. Som argumnts not analysd by Hol and whch may b n favour of unlatral acton ar that th acton may lad to smlar bhavour by othr countrs, t may affct th clmat n ntrnatonal agrmnt ostvly, and t may rduc th conflct of ntrst wthn a country as t actually shows th tru costs of abatmnt. Th dscusson abov rovds argumnts, basd on both rocdural farnss and consquntalst thcs, aganst rmt tradng. W wll summarz ths dscusson by rducng t to two basc statmnts that w wll formalz n our modl: 1) countrs mght dslk rmt tradng, and 2) countrs mght rfr to do all th abatmnt at hom. Th frst statmnt s wakr than th scond as ths dos not ncssary man that countrs car about th nvronmnt. Howvr, rasons to avod tradng ar oftn basd on a rfrnc for nvronmntal valus, and n th scond clam, th maor motvaton s to sav th nvronmnt, and to do that ndndnt of ntrnatonal agrmnts and quota trad. W do not clam that ths statmnts ar tru or that thr ar good thcal argumnts aganst rmt tradng. Howvr, w thnk that ths statmnts may dscrb som of th rluctanc that w obsrv n th oltcal dbat on rmt tradng. Th statmnts abov may form a norm aganst tradng olluton rmts. orms ar closly rlatd to th rsrvaton of dntty, and by modllng a norm aganst rmt trad, w buld on th thory of dntty and moral motvaton (Akrlof and Kranton, 2000, 2005; Brkk, t al., 2003). In ths way w can modl both th rluctanc to trad wth olluton rmts, and gvn that th agnt dos not follow th norm, th wsh to rduc th trad vn f t s conomcally roftabl. 10 As th rasons for trad rluctanc may b basd on both rocdural farnss as wll as consquncs, w do not try to ndogns th norm n th modl, manng that w do not dtrmn why a socty chooss a crtan norm aganst trad. 10 An xaml of th last rorty can for nstanc b th sulmntary condton n th Kyoto Protocol whr th arts agrd that rmt trad should only b a sulmnt to natonal abatmnt. 5

7 3. Th rmt trad modl Our framwork s basd on Hlm (2003) who rsntd a modl of ntrnatonal mssons tradng n whch countrs choos th amount of rmts thy allocat to thr domstc ndustry n an ndognous and non-cooratv way. W xand Hlm s modl by ntroducng xlct dntty consdratons. Countrs ar assumd to b rluctant to trad (larg quantts of) mssons rmts and/or may dslk th fact that thy mt mor than what thy dally thnk that thy should do. Th modl works n th followng way. Thr ar n countrs or govrnmnts ngagd n ngotatons on a futur ntrnatonal nvronmntal agrmnt ncludng rovsons for olluton rmt tradng. Th govrnmnts rrsnt th vw of th votrs who ar, to som xtnt, rluctant to trad rmts. Howvr, thy ar wllng to trad f th bnfts from trad ar larg nough. As n Hlm (2003), w mak th assumton that th rmt tradng rgm s stablshd only by unanmous aroval of all countrs. Allowng for ndognous coalton formaton would substantally comlcat th analyss as th countrs ar not symmtrc n our analyss. Rathr th dffrnc btwn countrs s ssntal hr. 11 Howvr, n scton 4 w wll study th dcson to ntr th tradng club and how ths s affctd by tchnologcal chang. In th frst stag, govrnmnts choos n a non-cooratv way thr ntal mssons allocaton. ot that ths stu rsmbls closly th ralty of ntrnatonal clmat ngotatons, n artcular n th run u to th 1997 Kyoto Protocol and n th comng ngotatons on a follow u agrmnt for th ost-kyoto rod. Anothr xaml s th Us msson tradng systm (TS) n th rods (.., bfor th start u of th global Kyoto rmt markt rod) and (.., th frst commtmnt rod of th Kyoto Protocol). U mmbr stats had to draft atonal Allocaton Plans (APs) suggstng a rmt allocaton for all nstallaton covrd by th TS drctv on thr trrtory. In th last stag of th gam, ndvdual frms trad mssons n a comttv rmt markt. Thy hav no othr oton than to oby th msson clng and thy do not hav any othr goal than maxmzng roft. Thus, w assum that frms do not hav moral concrns about tradng. 12 Ths gam s solvd by backwards nducton,.., w start b solvng th last stag frst. 3.1 STAG 2: Frms tradng mssons W assum that n vry country = { 1, 2,,n } thr s a larg numbr of dntcal frms that maxmzs rofts takng as gvn th mssons tradng schm: 11 Symmtrc or homognous countrs s a common assumton n studs of coalton formaton, s,.g., Barrtt (2005). 12 Ths s consstnt wth Sbrt (1992,. 130) and Rauschr (2006) who argu that a frm sndng rsourcs on socal actvts not rwardd by th markt wll not rman comttv and wll b drvn out of th markt. Howvr, f frms hav markt owr, non-roft motvs can survv. 6

8 ( ) B ( ) [ ] max π ;,, = ; + (1) Th bnfts of mssons, B, can b ntrrtd as a roducton functon. Producng valu addd rqurs, among othrs, nut of carbon mssons. Th bnft of mssons functon s assumd strctly ncrasng and strctly concav n mssons: B > 0 and B < 0. Bnfts ar dndng also on a tchnology shft aramtr n such a way that B < 0 and B < 0, hnc margnal bnfts of mssons dcras n th tchnology aramtr and, thrfor, an ncras n can b ntrrtd as an ffcncy mrovmnt or a rducton of margnal msson abatmnt costs. ot that th tchnology aramtr s not country scfc, thus w assum that thr ar tchnology sllovrs btwn countrs. In Andx 1, th rorts of th bnft functon ar drvd. From th frst-ordr condton for roft maxmzaton, w can drv th dmand for mssons: 13 1 B ( ; ) ( ; ) ( B ) ( ; ) = = = (2) Proft maxmzng bhavour by frms lads to cost-ffctvnss: margnal bnfts of mssons ar qualsd across frms. Thus, ths condton s vald vn f countrs hav moral argumnts aganst rmt tradng, as such consdratons ar not takn nto account by th comttv frms. Ths would not hav bn th cas wth transacton costs rlatd to th volum of trad (Stavns, 1995). Comaratv statcs of ths xrssons shows that mssons ar dcrasng n th rmt rc and n th tchnology aramtr: 1 = = < 0 B B d + B d = d B = = < 0 B (3) W dnot by 0 th ntal allocaton of rmts to frm. Usng (2), w can dfn a nt suly of rmts functon that s ncrasng n th rc of rmts and n th tchnology aramtr: S = S = > 0 S ( ; ) = ( ; ) wth S = S = > 0 (4) 13 W assum that bnfts of mssons ar such that an ntror soluton to th frm s maxmzaton lm B, = + and that, n th comlt roblm always xsts. In artcular, w assum that ( ) 0 absnc of nvronmntal consdratons, thr xsts an msson lvl > 0 dfnd by th condton ( ) B, = 0. 7

9 A olluton rmt markt qulbrum s dfnd as a rc lvl such that total nt suly of rmts s nonngatv: ( ) = ( ) (5) o o o such that S ; ; 0 Ths markt qulbrum condton mlctly dfns a rc functon mang a o = ρ,. vctor of msson allocatons nto th markt clarng rc lvl: ( ) W assum that th margnal bnft functons ar such that for vry vctor of msson allocatons, thr xsts a unqu qulbrum rmt rc 14. Th rmt rc functon can b shown to b dcrasng n th ntal allocatons of rmts to a country and n th tchnology aramtr. ρ d * 1 ρ (, ) = = = < 0 d ρ d* ρ (, ) = = = < 0 d (6) Hnc, corrsondng to ntuton, hghr allocatons of rmts and lowr margnal msson abatmnt costs lad to a dcras n th qulbrum rmt rc. 3.2 STAG 1: Govrnmnts choosng ntal rmt allocatons Gvn th smoothly workng rmt markt n stag 2, govrnmnts ngotat on th ntal allocaton of rmts and w assum that thy choos a numbr of rmts as to maxmz th followng wlfar functon: (, ;, ) ( ; ) [ ] ( ) (, S, ; ) W = B + D + + I (7) Th functon D dnots olluton damags ncurrd by country. Ths damags ar convx n global mssons, whch s dfnd by th total amount of rmts dstrbutd (country s rmts ar, whl all othr countrs msson rmts ar ). Thus, th nvronmntal roblm s causd by a unformly mxng ollutant as n th cas of global clmat chang. W assum that country maxmzs ts mssons, takng as gvn th rmt allocatons by all othr countrs ( = ). Hnc, w ar lookng for a ash qulbrum among natonal govrnmnts n rmt allocatons. Ths st-u s smlar to th modl ntroducd by Hlm (2003). Howvr, n addton to th aroach by Hlm, w assum that countrs xrnc an dntty ffct of thr msson and rmt tradng bhavour, I, whch adds ostvly to thr wlfar functon. Idntty s usually dfnd as a rson s slf mag as an ndvdual or as a art of a grou (Akrlof and Kranton, 2003). Idntty has bn rcognsd as 14 If mor rmts would b allocatd than th nt dmand for mssons, w assum that th o qulbrum rc s zro: > ( 0; ) = 0. 8

10 mortant for ndvdual bhavour n flds as socal sychology and socology, but has only rcntly bn adotd n formal conomc modls. In ths ar, howvr, w dfn a country s dntty n th sam way as th dntty of an ndvdual. Ths s ustfd by assumng that govrnmnts rform th moral rasonng of ts votrs. If a substantal shar of votrs has moral rflctons on olluton rmt tradng, ths wll b rflctd n th govrnmnt s dcson f rulng oltcans car about thr rlcton chancs. Basd on th statmnts mad n scton 2, th dntty of a country s a functon of S t s actual mssons,, t s rmt allowancs as wll as t s dal mssons,. Th lattr s dfnd as th msson lvl that th country would lk to am for basd on thcal rasonng. Ths dal s consdrd xognous. Th rcs way ths dal s dtrmnd, wll b dscussd latr n th ar. Usng th notaton ntroducd bfor, w can wrt th obctv of th govrnmnt of country, takng nto account comttv rmt tradng by frms n stag two, as: ( ( ) ) ( ) ( ( ) ) S ( ) ( ρ ( ; ); ),, ; ( ) ( ) W, = B ρ ; ; ; + ρ ; ρ ; ; ( ) D + + I ach country thn wants to st ts ntal rmt allocaton,, n ordr to maxms wlfar. Th frst-ordr condton for an ntror soluton s thrfor (all varabls and functons ar valuatd n th ash qulbrum of rmt allocatons), whr I s th chang n dntty for a chang n : [ ] 1 0 B ρ + ρ + ρ ρ D + I = (9) Or, aftr smlfyng (usng th frst-ordr condton B = ρ of comttv rmt tradng among frms n stag 2), th followng condton should b satsfd for all countrs : [ ] D I 0 ρ ρ (8) + + = (10) Th frst trm on th lft hand sd (LHS) stands for th ffct of addtonal rmt allocatons on th msson tradng rvnu through th ffct on th rmt rc. A mor gnrous rmt allocaton s bnfcal for rmt mortrs (as th markt rc at whch thy sll gos down), a mor rstrctd rmt allocaton s bnfcal for rmt xortrs (as th markt rc at whch thy buy gos u). W wll labl ths ffct th stratgc rmt tradng ffct. Th scond trm s th drct rc ffct of a mor gnrous rmt allocaton. vry addtonal rmt s worth th rvalng markt rc ρ. Th thrd trm stands for th addtonal olluton damag ffct causd by a mor gnrous rmt allocaton. Mor rmts lad, ctrs arbus, to hghr global mssons and hnc hghr olluton damags. Ths ffct s thrfor ngatv. Fnally, th last trm caturs th chang n dntty of xtra rmts. Ths ffct can b ostv or ngatv dndng uon th rcs scfcaton of th dntty functon. W wll frst drv rsults for a gnral formulaton of th dntty ffct bfor turnng to mor rcs scfcatons of th dntty functons. 9

11 Rarrangng (10) and usng agan th frms roft maxmzng frst-ordr condton B = ρ, w obtan: [ ] B = D ρ I (11) Hnc, vry country chooss an ntal rmt allocaton such that ts margnal bnft from th last ton of mssons quals ndvdual margnal damags, corrctd for a stratgc rmt trad ffct and an dntty ffct. In th followng aragrah w wll frst study th ndognous rmt allocaton qulbrum gnorng dntty ffcts. W wll thn turn to ntroducng dntty consdratons. As a rfrnc ont, w can also asly fnd th standard non-cooratv ash qulbrum n mssons whn frms do not trad. Sttng = n quaton (11), w fnd: whr ˆ ˆ = If dntty dos not mattr B ( ˆ ) = D ( ˆ ) I (12) If dntty dos not mattr (.., I = 0 ), th modl bols down to a stratgc mssons tradng modl. Hahn (1984) was on of th frst dscrbng non-comttv bhavour n mssons rmt markts but on mortant dffrnc btwn our aroach and Hahn s modl s that w do not start from an xognously fxd total amount of rmts n th markt. W follow Hlm (2003) who was th frst to study th mlcatons of ndognously dtrmnd rmt allocatons n an ntrnatonal rmt markt modl. Although both n Hlm s and our modl, frms ar assumd to b rc takrs on th rmt markt, thr natonal govrnmnts act stratgcally on thr bhalf whn dcdng on th total amount of rmts t wll allocaton to ts domstc ndustrs. If I = 0, quaton (10) s rducd to: [ ] D ρ ρ + = (13) In th stratgc msson tradng modl, ntutvly, nt rmt sllng countrs ( > 0 ) tnd to undr allocat thr domstc frms as ths maks rmts scarc and drvs u th qulbrum markt rc (rcall that ρ < 0 ). On th othr hand, nt rmt buyng countrs tnd to ovr allocat thr domstc frms bcaus ths maks rmts mor abundant and lowrs th markt rc. As shown by Hlm (2003), th nt ffct on global mssons cannot b sgnd n gnral snc t dnds on th rlatv wght of rmt xortrs vrsus mortrs. Ths s statd mor formally n th followng rooston. Prooston 1 (Prooston 2 n Hlm, 2003): If dntty consdratons do not mattr (.., I = 0 ), th ovrall amount of mssons rmts ssud n th ndognous rmt allocaton qulbrum mght b hghr or lowr thn n th ash qulbrum wthout tradng. In artcular: 10

12 ˆ ˆ B ( ) B ( ˆ ) = = (14) o o o Proof: Sttng I = 0 and usng th frst-ordr condtons n (11) and (12), convxty of damag and concavty of bnft functons, t follows: ( ) ( ) ( ) ( ) o o o o o ˆ ˆ ˆ D D B + ρ B ( ; ; ) o o whr ( ) = ρ dnots th qulbrum msson lvl for rmt o allocaton vctor, whn dntty s not takn nto account. Summng ovr all countrs and usng th rmt markt clarng condton ylds th dsrd rsult n (14). Q..D. If damags from global mssons wr lnar, thn th rsult bcoms mor clar cut. Th total amount of mssons s th sam and vry rmt mortr (xortr) allocats lss (mor) n th ndognous rmt allocaton qulbrum comard to th non-cooratv ash mssons qulbrum wthout rmt trad. Corollary 1 If damags of global mssons ar lnar ( D ( x) d x 0 = ) and f dntty consdratons do not mattr (.., I = 0 ), th ovrall amount of mssons rmts ssud n th ndognous rmt allocaton qulbrum s qual to th global amount of mssons n th ash qulbrum wthout tradng. Morovr, rmt mortrs (xortrs) allocat lss (mor) n th ndognous rmt allocaton qulbrum comard to th non-cooratv ash mssons qulbrum wthout rmt trad. Th roof of ths corollary follows trvally from th frst-ordr condtons (11) and (12). Howvr, t can n gnral b shown that th total amount of rmts ssud n th ndognous rmt allocaton qulbrum wll always xcd th frst-bst otmal amount of rmts. Th frst-bst allocaton of mssons,, rsults from maxmzng a utltaran socal wlfar functon and can b charactrzd by th Samulson rul (s for nstanc yckmans t al., 1993): * * ( ) ( ) B = D (15) * Prooston 2: If dntty consdratons do not mattr (.., I = 0 ), th global amount of mssons rmts ssud n th ndognous rmt allocaton qulbrum s hghr than th frst bst amount of mssons. 11

13 o Proof: Assum, on th contrary, that * *. Usng th frst-ordr condtons of th ndognous rmt allocaton qulbrum (10) and th frst-bst allocaton of mssons, B = ρ, t follows that: * * ( ) = ρ < ρ = ( ) ( ) = ( ) for all B n D D B o o o o. Bcaus of o * concavty of th bnft functon, t follows that > and hnc o * = > whch contradcts th ntal assumton. Q..D. Although th ndognous rmt allocaton qulbrum can lad to mor or lss mssons comard to th standard ash qulbrum wthout tradng (s Prooston 1), w know for sur that th rmt tradng qulbrum s globally nffcnt. Global mssons ar too hgh or, quvalntly, too lttl abatmnt s undrtakn If dntty mattrs How dos th ntroducton of dntty consdratons altr th rsults rortd so far? Clarly, th dstortons causd by ntroducng dntty consdratons wll dnd uon th rcs scfcaton of th dntty functon. W wll consdr two man factors dtrmnng dntty basd on th statmnts n scton 2: Countrs mght dslk rmt tradng, and countrs mght rfr to do all th abatmnt at hom. Howvr, for as of xoston, w wll start by studyng th two statmnts saratly bfor combnng both argumnts Rluctanc to trad W start by studyng th statmnt that countrs dslk rmt tradng. Assum frst a symmtrc formulaton of rluctanc to trad,.., countrs dslk both sllng and buyng rmts: I (, ; ) 2 ( ( ) ) ( ) ( ) F δ ρ, ; f ρ ; = 0 othrws Involvng n rmt tradng rrsnts a cost, both for buyrs and sllrs, du to th fact that on dos not act n accordanc wth on s moral convcton. Ths loss n dntty conssts of a fxd cost, F, ndndnt of th amount of rmts tradd, and a varabl cost. Th fxd cost rrsnts th loss of gong from on rgm to anothr, hr rrsntd by gong from a non-trad rgm to a tradng rgm. Howvr, th volum of trad also mattrs. If a country dcds to trad, t fls lss comfortabl th hghr th volum of rmt tradng s as long as δ > An xaml of th last rorty can for nstanc b th sulmntary condton n th Kyoto Protocol as wll as rcnt oltcal dscussons,.g., n orway, on sttng a lmt on how much on can rduc abatmnt abroad. Ths dntty functon only taks nto (16) 15 In th cas whr δ = 0,.., thr s an dntty cost of not followng th norm, whch s ndndnt on th volum of trad as long as th volum s ostv, w wll actually gt th sam frst ordr condtons as whn dntty dos not mattr,.., = 0. I 12

14 account olluton rmt transactons, and not xlctly th natonal abatmnt lvl. Idntty from natonal abatmnt wll b studd n dtal blow. Fnally, not that ths dntty functon has a maxmum at zro n th absnc of mssons tradng. Th dscusson on th acctablty of rmt tradng s manly a toc n countrs that ar otntal rmt buyrs. W wll, thrfor, also consdr a cas wth an asymmtrc dntty functon, whr countrs only suffr an xtra dntty loss f thy buy mssons: 2 ( ( ) ) ( ) ( ) F δ ρ, ; f < ρ ; I (, ; ) = F f > 0 othrws As mntond n th ntroducton, ths dntty consdratons, both th fxd and th varabl trm rrsnt costs of tradng and thus lowr wlfar n th tradng systm comard to whn dntty consdratons ar not rsnt. Thus, ths shars smlarts wth a rmt trad systm wth transacton costs as n Stavns (1995). Wth transacton costs, th volum of trad s lowr and wlfar s lowr comard to a systm wthout transacton costs. Also th ntal allocaton of rmts may affct th outcom of tradng. Howvr, moral consdratons affct rmt tradng dffrntly than transacton costs n svral rscts. Frst, th fxd dntty trm affcts th dcson whthr th country wants to tak art n th rmt tradng markt (s scton 4 blow), and scond, th ndognous art of th dntty functon affcts th allocaton of ntal allowancs as countrs do not want th allowanc allocatons to b vry dffrnt from actual mssons. Ths mans that th volum of trad wll b lowr. Howvr, for a gvn lvl of aggrgatd allowancs (global mssons targt), th outcom of tradng s not affctd by th ntal allowanc allocaton. In our modl, frms fac no transacton costs n trad so thy trad cost-ffctvly,.., margnal abatmnt costs among sourcs ar qual (s stag 2 abov). Ths s not th cas n modls wth transacton costs as ths costs ar modlld as a functon of th volum of trad. Usng ths xlct dntty functon, w can drv th followng rsult: Prooston 3: If countrs ar rluctant to trad rmts, and f dntty s symmtrc t can b shown that: f country s a rmt sllr ( > ) t follows that B > D ; f country s a rmt buyr ( < ) t follows that B < D. Proof: Th chang n th dntty ffct n frst-ordr condton (11) from a margnal ncras n th ntal rmt allowanc s gvn by: I = 2δ 1 ρ [ ]. Ths chang s ostv for rmt buyrs and ngatv for rmt sllrs for th symmtrc dntty functon bcaus 0 ρ = 1. Thrfor, t follows that: (17) 13

15 and thrfor B [ ] [ ] 2 1 [ ] B D = ρ + δ ρ D f = ρ δ ρ +. Q..D. Th ntuton s as follows. t rmt sllng countrs tnd to undr allocat thr domstc frms as ths maks rmts scarc and drvs u th qulbrum markt rc. In addton, th undr allocaton has ostv dntty ffcts as th volum of trad gos down, or n othr words, th ga btwn rmt allocaton and actual mssons shrnks. On th othr hand, nt rmt buyng countrs tnd to ovr allocat thr domstc frms bcaus ths maks rmts mor abundant and lowrs th markt rc. Furthr, th sam dntty mchansm as dscrbd for sllrs s also vald for buyrs; ovr allocatng rmts has ostv dntty ffcts as th volum of trad gos down. Summarzng, th dntty ffct, f t only stms from rluctanc to trad, confrms th rsults obtand by Hlm (2003). Th dntty ffct rnforcs th stratgc trad ncntvs for both sllrs and buyrs of rmts. How dos th ntroducton of dntty consdratons affct th global amount of rmts ssud nto th markt? In ordr to fnd th global ffct, w tak th sum ovr all countrs of thr frst-ordr condtons to obtan: { ρ ρ D δ ρ } = 0 { } ρ + nρ D 2δ + 2δρ = 0 nρ D + 2δρ = 0 Hnc, (18) nρ = D 2δρ As th followng rsults show, th outcom dnds on th balanc of owr btwn rmt xortrs and mortrs. Prooston 4: If countrs ar rluctant to trad, dntty s symmtrc and > ( < )0, global mssons wll b lowr (hghr) and vry country wll mt lss (mor) than n th ndognous rmt allocaton qulbrum wthout dntty consdratons. I o Proof: Assum th clam wr fals,.., > 0 and >,.., global mssons ar hghr wth th ntroducton of th dntty functon. Bcaus of I o D > D convxty of th damag functons f follows that: ( ) ( ). Usng 14

16 th arorat frst-ordr condtons for both qulbra,.., (13) and (18), t can b shown that: I o nρ + 2δρ > nρ I o 2δρ ρ ρ > > 0 n Hnc, th qulbrum rmt rc wth dntty consdratons would b hghr than th rc wthout. Gvn that th qulbrum rc functon s dcrasng n th global I o rmt allocaton, ths would mly < whch contradcts th ntal assumton. Fnally, as w hav ust shown that f > 0, t follows that th global mssons wll b lowr and, hnc, qulbrum rc of rmts wll b hghr n cas of dntty consdratons and thrfor, vry country s rrsntatv frm wll mt B I = ρ I > ρ o = B o I < o du to concavty of th bnft lss: ( ) ( ) functons. Q..D. Hnc, f > 0, rluctanc to trad shfts th ndognous rmt allocaton qulbrum n th drcton of th frst-bst Parto ffcnt soluton but w cannot tll whthr w wll fall short or ovrshoot th ffcnt soluton. But how should w ntrrt th condton > 0? Ths sum can b ntrrtd as a wghtd avrag of all th rmt trads (ostv and ngatv) whr th wghts ar gvn by th nvrs of th slo of th margnal bnft of mssons functon (rcall that = 1 B < 0 ). Hnc, n ordr for th sum to b ostv, rmt xortrs should, on avrag, hav hghr valus of than rmt mortrs. ot that hgh absolut valus of B (.., st margnal msson abatmnt cost functons) mly hgh valus (.., small ngatv numbrs) of. Thrfor, th trm s ostv f rmt sllrs ar rdomnantly countrs wth st margnal abatmnt cost functons. ot that ths s not vry lkly to aly to th Kyoto rmt markt n th frst commtmnt rod Most mrcal carbon msson markt modls rdct on th contrary that t ar scally low abatmnt cost countrs (.., countrs wth flat margnal bnft functons B ) that wll xort carbon mssons rmts, s Böhrngr (2002), Dn lzn and d Moor (2002) or yckmans and Hagm (2008). Thrfor, n th cas of th Kyoto rmt markts, t s mor lkly that dntty consdratons would shft ndognous rmt allocaton qulbrum away from th ffcnt soluton. Ths mans that th soluton wth dntty consdratons mght b lss ffcnt than wthout thos consdratons. 15

17 Prooston 5: If only buyrs ar rluctant to trad (asymmtrc dntty functon (17)), thn th ndognous rmt allocaton qulbrum s shftd furthr away from th ffcnt soluton and vry ndvdual country wll mt mor than n th ndognous rmt allocaton qulbrum wthout dntty consdratons. Proof: Th frst-ordr condtons for govrnmnts ssung rmts ar dffrnt for rmt mortrs ( < ) and xortrs ( ): [ ] [ ] [ ] 0 B ρ 2δ 1 ρ D + = 0 f < B D + ρ = f Summng ovr both tys of countrs and usng th markt clarng condton from (5), t follows that: { } B 2δ mn 0, 1 ρ D = 0 Th mnmum functon mn{ 0, } allows us to sum ovr all countrs whl takng nto account th dntty ffct for rmt mortrs only. I o Assumng, n contrast to th clam n Prooston 5, < and usng convxty of I o th damag functons f follows that: D ( ) < D ( ). Usng th arorat frst-ordr condtons for both qulbra, t can b shown that (rcall that 0 1 ρ 1): I o 2δ ρ ρ < mn{ 0, } 1 ρ < 0 n Hnc, th qulbrum rmt rc would b lowr wth asymmtrc dntty consdratons than wthout. Gvn that th qulbrum rc functon s dcrasng n I o th global rmt allocaton, ths would mly > whch contradcts th ntal I o assumton. Thrfor, t must b that,.., takng nto account dntty consdratons wll lad to hghr global mssons than wthout dntty consdratons, and thrfor, th total mssons ar shftd furthr away from th frst bst lvl of global mssons. As w hav ust shown that th qulbrum rc of rmts wll b lowr n cas of asymmtrc dntty consdratons, t follows that vry country s rrsntatv frm B I = ρ I < ρ o = B o I > o du to concavty of th wll mt mor: ( ) ( ) bnft functons. Q..D. Prooston 5 s ntutvly clar. W know that rmt buyrs hav an ncntv to ovr allocat thr domstc ndustrs bcaus of (1) stratgc trad consdratons (.. for drvng down th qulbrum rmt rc), and (2) dntty consdratons (.. ovr allocatng domstc frms rducs th amount of rmts that has to b mortd). Snc only buyrs dntty consdratons ar takn nto account n th 16

18 asymmtrc dntty functon (17), t obvously follows that global mssons wll b hghr than n th scnaro wthout dntty consdratons Ga btwn actual and dal ffort lvl Rluctanc to trad s on asct of a country s dntty, but th country could also car about ts actual lvl of mssons. To modl ths, w assum that dntty also dnds on th rlatonsh btwn actual mssons and th morally dal mssons, S. Followng Brkk t al. (2003) w assum that th dal mssons ar found by maxmzng a utltaran wlfar functon whr vrybody follows th sam gnral rul, namly mt th amount that maxmzs th utltaran wlfar functon. Thus S * * * ths gvs =, whr follows from (15). ot also that s only a functon of, and s thrfor consdrd xognous n all analyss w rform aart from n scton 4 whr w consdr a chang n. Ths nw dntty functon can b scfd n th followng way: (, ; ) γ ( ρ (, ); ) * * I = (19) Frst of all, w show that vry country wll mt mor than what s consdrd as th dal mssons lvl,.., th frst-bst Parto ffcnt mssons allocaton. Prooston 6: If countrs car only about th dal, vry ndvdual country wll mt mor than ts frst-bst mssons lvl: * and thrfor, total amount of rmts allocatd wll xcd th frst-bst lvl *. Proof: Assum, on th contrary, that : < *. From th strct concavty of th mssons bnft functon, t follows that ( ) > ( * ) frst-ordr condtons, (2) and (15), ths mls: ( ) ( ) ( ) ( ) ( ) 2 B B. Usng th arorat ρ = B > B = D = ρ < At th sam tm, w can drv: * * * * * * * ( ) + 2γ ρ = ( ) > ( ) = ( ) D B B D ( ) ( ) ( ) ( ) > 2 0 * * D D D D γ ρ > Whch contradcts th rvously stablshd nqualty. W can thrfor conclud that : *. Gvn that vry country mts mor than th dal lvl, t follows obvously that total mssons n th ndognous rmt allocaton qulbrum wll xcd th frstbst lvl: * >. * 17

19 Q..D. Gvn that w now know from Prooston 6 that vry country always mts mor than ts dal, w can asly sgn th drvatv of th dntty functon wth rsct to : * I = 2γρ < 0 (20) Takn n solaton, th dntty ffct that rfrs to th dal ffort lvl shfts th ndognous rmt allocaton qulbrum towards th Parto ffcnt frst-bst allocaton of mssons. Prooston 7: If countrs car only about th dal, thn th ndognous rmt allocaton qulbrum s shftd n th drcton of th ffcnt soluton and vry ndvdual country wll mt lss than n th ndognous rmt allocaton qulbrum wthout dntty consdratons. Proof: Assumng, n contrast, that I > f countrs car about th dal. Usng o I o convxty of th damag functons f follows that: D ( ) > D ( ). Usng th arorat frst-ordr condtons for both qulbra, t can b shown that: ρ 2γρ I * ρ o > > n Hnc, th qulbrum rmt rc would b hghr wth dntty consdratons than wthout. Gvn that th qulbrum rc functon s dcrasng n th global rmt I o allocaton, ths would mly < whch contradcts th ntal assumton. I o Thrfor, t must b that. As w hav ust shown that th qulbrum rc of rmts wll b hghr n cas of dntty consdratons, t follows that vry country s rrsntatv frm wll mt B I = ρ I > ρ o = B o I < o du to concavty of th bnft lss: ( ) ( ) functons. 0 Q..D. Abov w hav comard th dntty costs from rmt tradng to transacton costs. ot, howvr, that th dntty functon n (19) dos not ncras costs of rmt tradng. If trad rducs th dstanc btwn actual mssons and dal mssons, th country may also bnft n dntty trms from trad Both dntty ffcts takn togthr W ar now abl to combn th rsults of th rvous sctons on th dntty ffcts saratly. Takn togthr, th full dntty functon can b wrttn as follows: 18

20 I * (,, ; ) 2 * 2 ( (, ); ) [ ( (, ); ) ( )] ( ( ) ; ) * 2 ( ( ) ) (21) F δ ρ γ ρ f ρ = γ [ ρ, ; ( )] othrws ot that th nw dntty functon dscrbs an ntrnal conflct; w can hav but stll. =, * Th rsults abov wll nabl us to charactrz th condtons undr whch global mssons mght volv nto th drcton of frst-bst Parto ffcnt mssons. Prooston 8: If countrs ar rluctant to trad rmts and f thy car about th dal, thn th ndognous rmt allocaton qulbrum s shftd n th drcton of th ffcnt soluton f, thr: condton > 0 holds, or, th dntty ffct rgardng th dal s valud suffcntly strongly to comnsat th dntty ffct rgardng rluctanc to trad. Proof: Th roof s trval by combnng Proostons 4 and 7. Ths rsult dscrbs th condtons undr whch dntty consdratons mght fostr global msson rducton and hnc, rduc th ga btwn th ndognous rmt tradng qulbrum and th Parto ffcnt frst-bst lvl of mssons. At frst sght, on mght thnk t s obvous that dntty consdratons would lad to lowr global mssons. Howvr, Prooston 8 shows that t dnds crucally on both th form of th dntty functon and th balanc of owr btwn rmt mortrs and xortrs. What dos ths analyss so far larn us whn w try to aly t to th ntrnatonal clmat ngotatons that should lad to a follow-u agrmnt for th ost-kyoto rod aftr 2012? As w hav argud abov, most smulaton modls rdct that rmt xortrs ar rdomnantly countrs wth rlatvly flat margnal msson abatmnt cost curvs. Ths mls that s lkly to b ngatv. From Prooston 8, w can thrfor conclud that th ovrall msson lvl rsultng from th ntrnatonal clmat ngotatons outcom wll b closr to th frst-bst lvl of mssons only f thr s a rlatvly strong dntty ffct basd on th ga btwn actual and dal mssons lvls. If ths dntty ffct s wak, th ga btwn th ngotatd rmt allocaton and frst-bst mssons lvls wll b hghr than n a scnaro whr dntty consdratons would not lay a rol n govrnmnts dcson makng rocss. Anothr way of ntrrtng our rsult s as follows. Prooston 8 (and 4) can b ntrrtd as argumnts to say that on should b carful wth mosng constrants on global rmt tradng. Although thcally motvatd, ths constrants on rmt trad mght lad to an advrs ffct n th sns that thy lad to hghr global mssons f rmts allocatons ar th rsult of a non-cooratv ngotaton rocss btwn sovrgn countrs. Hnc, ths can b sn as a warnng aganst thos 19

21 argung for lmtng accss to ntrnatonal flxblty mchansms n ntrnatonal clmat olcy. Thy mght nd u wors n nvronmntal trms, n st of thr thcal motvaton. 4. Th dcson to nvolv n rmt tradng From quaton (12), w know that wthout tradng, govrnmnts would choos mssons clngs qual to ˆ such that: ( ˆ ; ) ( ˆ ) B = D I (22) Margnal bnfts from a small mssons ncras should qual th country s ndvdual margnal damag of ths ncras n addton to th chang n dntty. As thr s now trad, th ffct on dntty only xsts bcaus of a dvrgnc from th * dal lvl,.., I 2 [ ˆ = γ ]. ot that (22) assums that all countrs hav chosn not to trad, w ar n a non-trad rgm. W dnot ths as th busnss-asusual (BAU) cas. A tradng rgm s rfrrd ovr a non-trad rgm f and only f th wlfar n th tradng rgm s hghr than th wlfar wth no trad,..: ( ( ( ) )) ( ) ( ) 2 ( ( ) ) ( ) ( ) ( ) ( ) ( ) B ρ ; ; + ρ ; ρ ; ; D + ( ) F δ ρ, ; γ ( ρ, ; ( )) * 2 B ˆ ; D ˆ γ ( ˆ ( )) * 2 Ths condton mls an ur bound on th fxd dntty trm: ( ( ( ) )) ( ˆ ) ( ) ( ) 2 ( ( ) ) ( ) (23) ( ) ( ) ( ˆ ) F B ρ ; ; B ; + ρ ; ρ ; ; D + + D * 2 * 2 ( ) ˆ ( ) δ ρ, ; γ ( ρ, ; ( )) + γ ( ( )) φ (24) Thus, f F, th dntty cost of movng to a tradng rgm, s largr than φ ( ), whch s th bnft from a tradng rgm, country rfrs a rgm wth no trad. In Prooston 1, w showd that ovrall mssons wth trad can b hghr or lowr than ovrall mssons wthout trad f thr ar no dntty consdratons. Hlm (2003), Prooston 4, also shows that a tradng rgm may b wlfar mrovng vn f mssons ar hghr. ot that th dntty consdratons ntroducd by th fxd trm and by δ > 0 n our ar rrsnt costs of tradng and thus lowr wlfar n th tradng systm comard to whn dntty consdratons ar not rsnt. 16 Basd on ths, w can drv th followng rsult: 16 Ifγ > 0, w cannot rul out th ossblty that dntty costs wll b lss wth tradng. As notd abov and as sn from quaton (24), f < ˆ th dntty from dvatng from th dal wll mrov from tradng. 20

22 Prooston 9: Wthout dntty consdratons ovrall mssons may b lowr and wlfar may b hghr n th tradng stuaton than wthout trad. Thus f dntty consdratons ar ncludd that nducs a cost to tradng, countrs may rfr no trad and hghr mssons to a systm wth trad and lowr mssons. Howvr, f ovrall mssons as wll as wlfar ar hghr wth trad, ncludng dntty consdratons may nduc a systm wth no trad and lowr ovrall mssons. Proof: S th txt abov as wll as roof for Prooston 4 n Hlm (2003). 4.1 Th ffcts of tchnologcal mrovmnts As notd n th ntroducton as wll as n Bénabou and Trol (2007),. 20, thr sms to b a changd atttud towards olluton rmts th last fw yars. A largr ntrst n olluton rmt trad may b du to a chang n th norm so that t s mor acctabl than bfor to trad rmts, but thr may also b anothr xlanaton; th transactons may stll b rugnant so that th norm s constant, but th bnfts from trad may b hghr than bfor. Comarng th conomy today and a fw yars ago, on rlvant dffrnc s th chang n mtgaton tchnology. Tchnology mrovs ovr tm, n such a way that mtgaton bcoms char. Basd on ths, w consdr how an xognous tchnologcal chang may altr th dcsons of a country on whthr to rfr a trad rgm to a non-trad rgm. I.., w wll study how a shft n th tchnology aramtr wll altr th bnfts from a trad rgm rrsntd by ( ) φ. Assum frst that γ = 0, so that only th norm on rmt tradng mattrs. Th drvatv of th RHS of (24) wth rsct to s gvn by: ρ φ ( ) = B ρ + + B B + B [ ] ρ + ρ + ρ ( ρ + ) D + + D + [ ] ρ 2 δ ( ρ + ) (25) Or, usng th frms tradng FOC,.., B = ρ : φ = + ( ) B B B [ ] + + [ ] ρ ρ D + + D + ρ 2 δ ( ρ + ) (26) And usng th ash qulbrum FOC n th no-trad stuaton for γ = 0,.., B ( ˆ ) ( ˆ ˆ = D + ), and substtutng ρ for B, w gt: 21

23 ( ) B B [ ] φ = + ρ + B D [ ] ρ 2 δ ( ρ + ) D + D (27) Assum now that D D + 0,.., th ffcts on damag of a margnal chang n allowanc choc and BAU mssons n othr countrs du to an ncras n th tchnology aramtr ar about th sam 17, or that th total ffct s small whch may b a rasonabl assumton. Ths lavs four dffrnt ffcts on th bnfts from trad: B : Th frst trm rflcts that abatmnt has bcom char as a rsult B of tchnologcal chang. W know that B B = C > 0, s Andx 1. Thus, th bnft n dvatng from th BAU qulbrum has ncrasd. Ths holds for both otntal buyrs and sllrs. ρ : Th scond trm rflcts th ffcts of a chang n rc. As [ ] ρ < 0, ths ffct s ostv for buyrs, [ ] sllrs, [ ] > 0. < 0, and ngatv for B D : Th thrd trm rflcts th ffcts of a chang n th ntal allocaton. As sn, ths s dndnt on th ga btwn margnal bnft and margnal damag. As sn from Prooston 3, ths ga s ostv ( B > D ) for a rmt sllr and ngatv for a rmt buyr ( B [ ] < D ). ρ 2 δ ( ρ + ) : Th fnal trm rflcts th mact on dntty of a chang n tchnologcal chang. Ths ffct s ambguous for sllrs and buyrs as dscussd blow. Assum frst that < 0,.., th country may want to dcras ts ntal msson allocaton f thr s a ostv chang n tchnology. Ths may sm as a rasonabl assumton as countrs wll b lss dndnt of fossl fuls. Blow w wll also tak a look at othr ossblts. 18 Consdr frst th cas whr only th fxd dntty trm mattrs (δ = 0),.., thr ar no dntty ffcts from th volum of trad. In ths cas w s that th frst thr ffcts ar ostv for a otntal buyr, whl th last on s zro. Thus, a tchnologcal chang wll mak t mor bnfcal to trad and th otntal buyrs may b wllng to not follow th norm. 17 Ths assums that th sgns of and ar qual. It rovs that ths drvatvs ar dffcult to sgn wthout scfc functonal forms. S Andx 2 for th drvaton of th drvaton of. and Andx 3 for 18 Th sgn of s ambguous wthout choosng scfc functonal forms, s Andx 3. 22

24 For otntal sllrs, th rsult s lss clar. As for buyrs, sllrs wll also bnft from char abatmnt (th frst trm), but th scond and th thrd trm s not favourabl for otntal sllrs. Thus, th ncntv to mov to a rmt tradng rgm may b lss or hghr. Ths lads us to th followng rsult: Prooston 10: If < 0 and γ = 0 and δ = 0, otntal buyrs wll hav a hghr ncntv to nvolv n trad f thr s a tchnologcal chang, vn f thr s a norm aganst rmt tradng. For otntal sllrs, th ncntvs ar ambguous, but w cannot rul out th cas whr otntal sllrs also wll hav a hghr ncntv n tradng wth rmts f thr s a tchnologcal chang. Proof: S txt abov. Assum now that δ > 0 such that dntty s fallng n th volum of trad. If thr s a tchnologcal chang, th ffct on dntty s as follows: For a otntal sllr [ ] [ ] ρ I = 2 δ ( ρ + ) (28) > 0, and dntty wll only ncras f ( ρ ρ + ) < 0,.., f mssons ncrass mor than ntal allocatons for a chang n tchnology. If < 0, ths mans that th ntal allocaton of rmts has to fall mor than th actual mssons. ot that th ffct of tchnologcal chang on mssons s ambguous as th frst art n th arnthss s ostv whl th scond s ngatv. For a otntal buyr th concluson s th othr way around. Ths lads to th followng rsult: Prooston 11: If δ > 0 and γ = 0, th dntty from th volum of trad s affctd by an mrovmnt n tchnology. Ths may rduc th ncntv to trad rmts for a tchnologcal chang. Howvr, thr s also a ossblty that ths dntty ffct ncrass th ncntvs to trad rmts. Proof: S txt abov. Th last art of ths rsult s ntrstng. If a country consdrs transactons n olluton rmts as rugnant, but n addton rfrs a small volum of trad to a hgh volum f t chooss to trad, ths last dntty ffct may actually mak th country mor wllng to start tradng f thr s a tchnologcal chang. Th rason s that th volum of trad wll b lowr wth th nw tchnology, whch wll rduc th dntty loss from trad. Th cas whr dntty mattrs only for buyrs (asymmtrc dntty functon), wll not chang th rsults abov. Buyrs can b wllng to trad rmts f th volum of trad wll b rducd wth th nw tchnology. Consdr now th full dntty functon from (21),.. th cas whr δ > 0 and γ > 0, so that thr s also a norm to do abatmnt at hom. Th dntty ffcts thn bcom 23

25 [ ] * * * * ρ ρ I = 2 δ ( ρ + ) 2 γ + ( ρ + ) (29) Th scond trm n ths quaton s th ffct from γ > 0. In gnral ths ffct s ambguous too, whch mans that th concluson n Prooston 8 stll holds. Th rason for ths s that w cannot say n gnral whthr a tchnology chang movs th actual mssons closr or furthr away from th dal mssons. Prooston 12: If dntty dnds on both from th volum of trad (δ > 0) and on th dstanc btwn actual and dal mssons (γ > 0), th dntty s affctd by an mrovmnt n tchnology. Ths may rduc th ncntv to trad rmts for a tchnologcal chang. Howvr, thr s also a ossblty that ths dntty ffct ncrass th ncntvs to trad rmts. Proof: S txt abov. So far w hav consdrd th cas whr < 0. Howvr, as sn from Andx 3, w cannot rul out th othr ossblts. If = 0 ths would lav out th thrd ffct on ( ) φ, but would stll lav th ffct on dntty uncrtan. If > 0, ths would mak th ncntv for a otntal buyr mor uncrtan. Stll thr s an dntty ffct as found n Proostons 11 and Dscusson and conclusons In ths ar w analysd how dntty consdratons affct an ndognous olluton rmt tradng qulbrum, n whch govrnmnts choos n a non-cooratv way th ovrall nvronmntal obctv and rgonal rmt allocatons. Wth dntty consdratons w man two thngs. Frst, countrs may fl rluctant to trad rmts bcaus thy fl t s a way to sca ons moral rsonsblty or bcaus of th assumd ngatv consquncs th trad may hav n dvlong countrs. Hnc, both consquntalst and rocdural thcs argumnts ar usd to ustfy lmts on accss to flxbl mchansms lk CDM n th framwork of th Kyoto Protocol or uroan msson Tradng Schm for nstanc. Onc govrnmnts hav chosn rmt allocatons, frms ar assumd to trad ths rmts on an ntrnatonal comttv rmt markt wthout takng nto account moral rstrants. Our man conclusons ar th followng. Gvn an ntrnatonally ngotatd rmt tradng systm, dntty consdratons may ncras or rduc global mssons dndng on th rcs formulaton of th dntty. W consdrd two man formulatons of dntty. Th frst on caturs th da that countrs mght b rluctant to trad. For that formulaton w showd that f dntty s asymmtrc,.., f only rmt rmt mortrs fl rluctant to buy, global mssons wll b hghr than n an ndognous rmt tradng qulbrum wthout moral motvaton. Th rason s that rmt mortrs ovr allocat thr domstc frms n ordr to ra stratgc rmt trad gans (bcaus of lowr global rmt rcs) and to rduc th amount of rmts thy hav to mort and hnc thr loss of dntty. Howvr, for symmtrc dntty functons, th oost ffct may tak lac and global mssons 24