consto www.consto.u D On-Accss-Publkatonssv d ZBW Lbn-Infomatonsntum Wtschaft Th On Accss Publcaton Sv of th ZBW Lbn Infomaton Cnt fo Economcs Echn, Thomas; Pthg, Rüdg Wokng Pa Intnatonal cabon mssons tadng and statgc ncntvs to subsd gn ngy Volkswtschaftlch Dskussonsbtäg // Unvstät Sgn, Fachbch Wtschaftswssnschaftn, Wtschaftsnfomatk und Wtschaftscht, No. 142 Povdd n Cooaton wth: Fakultät III: Wtschaftswssnschaftn, Wtschaftsnfomatk und Wtschaftscht, Unvstät Sgn Suggstd Ctaton: Echn, Thomas; Pthg, Rüdg (2010) : Intnatonal cabon mssons tadng and statgc ncntvs to subsd gn ngy, Volkswtschaftlch Dskussonsbtäg // Unvstät Sgn, Fachbch Wtschaftswssnschaftn, Wtschaftsnfomatk und Wtschaftscht, No. 142 Ths Vson s avalabl at: htt://hdl.handl.nt/10419/41083 Standad-Nutungsbdngungn: D Dokumnt auf EconSto düfn u gnn wssnschaftlchn Zwckn und um Pvatgbauch gscht und kot wdn. S düfn d Dokumnt ncht fü öffntlch od kommll Zwck vvlfältgn, öffntlch ausstlln, öffntlch ugänglch machn, vtbn od andwtg nutn. Sofn d Vfass d Dokumnt unt On-Contnt-Lnn (nsbsond CC-Lnn) u Vfügung gstllt habn solltn, gltn abwchnd von dsn Nutungsbdngungn d n d dot gnanntn Ln gwähtn Nutungscht. Tms of us: Documnts n EconSto may b savd and cod fo you sonal and scholaly uoss. You a not to coy documnts fo ublc o commcal uoss, to hbt th documnts ublcly, to mak thm ublcly avalabl on th ntnt, o to dstbut o othws us th documnts n ublc. If th documnts hav bn mad avalabl und an On Contnt Lcnc (scally Catv Commons Lcncs), you may cs futh usag ghts as scfd n th ndcatd lcnc. bw Lbn-Infomatonsntum Wtschaft Lbn Infomaton Cnt fo Economcs
Fachbch 5 Wtschaftswssnschaftn, Wtschaftsnfomatk und Wtschaftscht Volkswtschaftlch Dskussonsbtäg Dscusson Pas n Economcs No. 142-10 May 2010 Thomas Echn Rüdg Pthg Intnatonal cabon mssons tadng and statgc ncntvs to subsd gn ngy
Unvstät Sgn Fachbch 5 Wtschaftswssnschaftn, Wtschaftsnfomatk und Wtschaftscht Fachgbt Volkswtschaftslh Höldlnstaß 3 D-57068 Sgn Gmany htt://www.un-sgn.d/fb5/vwl/ ISSN 1869-0211 Avalabl fo f fom th Unvsty of Sgn wbst at htt://www.un-sgn.d/fb5/vwl/sach/dskussonsbtag/ Dscusson Pas n Economcs of th Unvsty of Sgn a ndd n RPEc and can b downloadd f of chag fom th followng wbst: htt://das.c.og/s/s/sgn.html
Intnatonal cabon mssons tadng and statgc ncntvs to subsd gn ngy * Thomas Echn Datmnt of Economcs, Unvsty of Hagn Rüdg Pthg Datmnt of Economcs, Unvsty of Sgn Abstact Ths a amns statgc ncntvs to subsd gn ngy n a gou of counts that oats an ntnatonal cabon mssons tadng schm. Wlfa-mamng natonal govnmnts hav th oton to dscmnat aganst ngy fom fossl fuls by subsdng gn ngy, although n ou modl gn ngy omoton s not ffcncy nhancng. Th cass of small and lag counts tun out to hbt sgnfcantly dffncs. Whl small counts fan fom subsdng gn ngy and thus mlmnt th ffcnt allocaton, lag mt-motng counts subsd gn ngy n od to nflunc th mt c n th favo. JEL Classfcatons: H21, Q42, Q48 Kywods: mssons tadng, black ngy, gn ngy, ngy subsds * Echn: Datmnt of Economcs, Unvsty of Hagn, Unvstätsst. 41, 58097 Hagn, Gmany, mal: thomas.chn@fnun-hagn.d; Pthg: Datmnt of Economcs, Unvsty of Sgn, Höldlnst. 3, 57068 Sgn, Gmany, mal: thg@vwl.ww.un-sgn.d.
1 Intoducton In 2005 th Euoan Unon stablshd an EU-wd CO 2 mssons tadng systm to duc ts gnhos gas mssons by 8 % n 2012 fom ts basln mssons n 1990. Smlaly, n August 2007 th Wstn Clmat Intatv, launchd by svn US stats and fou Canadan ovncs, lannd to lay th foundaton fo an ntnatonal mssons tadng schm that nvolvs both th Untd Stats and Canada and usus th goal of ducng gnhous gas mssons by 15 % fom 2005 lvls by 2020. Counts und th umblla of an ntnatonal mssons tadng schm,.g. th EU mmb stats, a obsvd to omot gn ngy by fd-n taffs o gn tadabl ctfcats. Fd-n taffs (o nwabl ngy taffs) a outut subsds unt of oducd ngy (Mnantau t al. 2003) and gn ctfcats a tadabl commodts 'and' by gn ngy oducs fo ach unt of th outut whch oducs of black ngy a thn oblgd to uchas n som ooton to th outut. Fd-n taffs a n oaton n 63 usdctons aound th wold, ncludng Canada, Fanc, Gmany, and n a don stats n th Untd Stats. Natonal tadng schms of gn ctfcats a n us n.g. th UK, Italy and som US stats. Intnatonal mssons tadng schms am at cong wth clmat chang by cubng gnhous gas mssons, but th conomc atonal fo omotng gn ngy s lss cla. Th ltatu suggsts two ustfcatons fo combnng mssons contol wth gn ngy omoton olcs. In th snc of lanng sllovs 1 subsdng th us of nwabl ngy s ffcncy nhancng scally n th nnovatoy has n od to su lanng ffcts that a bnfcal fo nwabl ngy oducs as wll as fo socty at lag (Bläs and Rquat 2007, Fsch and Nwall 2008, Lhmann 2009). Th scond ustfcaton s ngy scuty,.. th ducton of th dndnc fom nscu fossl ful mots. Assumng unctanty about th mot c of fossl ful, Echn and Pthg (2009b) show that sk avs govnmnts of small on conoms may choos to subsd gn ngy to duc th c unctanty. Th snt a suggsts and nvstgats anoth atonal fo subsdng gn ngy. Counts may hav a statgc ncntv to us (ostv o ngatv) gn subsds 1 Lanng sllovs a latd to tchnologcal o R&D sllovs. Fo an analyss of tchnologcal sllovs n th nvonmntal contt w f to Gould and Matha (2000). 2
n od to manulat n th favou th mt c. To mak ths thss cs, w consd a gou of counts oatng ont mssons tadng schm. Each county oducs gn ngy wth a domstc souc and black ngy by mans of fossl ful motd fom th st of th wold. Th domstc souc s also usd fo th oducton of an ntnatonally tadabl comost consum good. Focussng on comttv conoms and wlfa-mamng govnmnts, w show that t s ffcnt fo th gou of counts to fan fom subsdng gn ngy. Th govnmnts of small on counts who tak as gvn th c n th ntnatonal mt makt fnd t otmal not to subsd gn ngy and thus also scu ffcncy fom th vwont of th gou of counts. In contast, govnmnts of lag counts a awa that th olcy affcts th mt c and thfo fnd t otmal to us th subsdy fo dstotng th mt c n th favo whl bhavng Nash wth gad to th oth counts subsds. Th statgc ncntvs to omot gn ngy dff makdly btwn mt-otng and mt-motng counts. In th fld of ntnatonal nvonmntal conomcs statgc choc of nvonmntal olcy nstumnts has bn nvstgatd.g. by Batt (1994), Rausch (1994) and Ulh (1996). Th s only a small ltatu, howv, that nvstgats statgc ncntvs of natonal gulaton n th contt of ntnatonal mssons tadng. In Bécht and Palta (2008) and Echn and Pthg (2009a) natonal govnmnts lvy ngy o mssons tas to manulat th mt c n th favo. In Santo t al. (2003) natonal gulatos mos mssons tas and taffs to affct th mt c n a modl wth sllovs. W a not awa of contbutons to th ltatu that lo as w am to do n th snt a th ntacton of ntnatonal mssons tadng and natonal gn ngy omoton olcs. Th snt a s ogand as follows. Scton 2 sts u th modl. Scton 3 chaacts th ffcnt allocaton and th fst-bst olcy-suotd comttv qulbum fo th gou of counts. Scton 4 analys subsdy comtton fo th smallcounty cas of govnmnts whch gno th mact of th olcy on th mt c and fo th lag-county cas of govnmnts whch account fo th mact of th olcs on th mt c. Scton 6 concluds. 3
2 Th modl Consd a gou of n counts mbddd n th wold conomy. All counts n that gou atcat n an ntnatonal CO 2 mssons tadng schm to b scfd blow. County = 1,..., n mloys th souc nut to oduc th amount s of a consum good (good X), th sam n all counts, accodng to th oducton functon s X =. (1) Moov, county oducs ngy, = b + g s, (2) s s consstng of black ngy b s and gn ngy g s. Both knds of ngy a consdd n (2) to b fct substtuts, fo smlcty. Black ngy s gnatd fom fossl ful, bs B =, (3) and gn ngy s oducd wth th souc nut g va gs = G g. (4) Th oducton functons X, B andg a stctly ncasng and stctly concav n th agumnts. Th sntatv consum of county dvs utlty (, ) u U = (5) fom consumng unts of good X and th amount of ngy. Th utlty functon U s stctly ncasng n both agumnts and quas-concav. CO 2 mssons a ootonal to th nut of fossl ful and thfo w smly us to dnot th ful nut as wll as CO2 mssons. Th gou of counts as a whol has commttd to stct ts total cabon mssons to som lvl c > 0. To mt that mssons tagt c, th counts tak at n a ont mssons tadng schm. Each county s assgnd a natonal mssons ca c such that = c. Th natonal mssons cas c a takn as gvn thoughout th snt a. Th qulbum on th mt makt, c 4
= c, (6) s bought about by th mt c π. Good X and fossl ful a tadd on wold makts at cs and, sctvly, whch all counts tak as gvn. Engy and th souc a tadd on domstc makts n ach county at cs, sctvly. Th condtons fo clang thos makts a and = s and + g =, (7) wh s th souc ndowmnt of county ownd by ts sntatv consum. Wth ths nfomaton, county 's balanc of aymnts (cunt account) s ( c ) ( ) 0. π + = (8) s 3 Allocatv (n)ffcncy and gn subsds In ths scton w dtmn th Pato ffcnt allocaton va mamng th wghtd s =. sum of utlts und th constants (1) (4), (6), (7) and ( ) 0 Th last quaton s th gou s consoldatd tad balanc vs-à-vs th st of th wold. W us that constant ath than all counts' tad balancs (8) to chaact th ffcnt allocaton, bcaus owng to (6) summng (8) ov all counts ylds π ( c ) + ( s ) = ( s ) = 0 Th ffcnt allocaton s a soluton to th Lagangan. α (, ) ( g) ( λ λ ) + λt ( X ) + λ( g ), L= U + B + G + c + wh c, and a ostv constants, λ, λ, λ t and λ a Lagang multls and α dnot constant ostv wlfa wghts. Sml calculatons show that th allocaton of th mult-county conomy (1) (8) s ffcnt, f and only f U U µ =, G X µ =, and µ B = µ + fo = 1,..., n, (9) 5
t t wh µ : = λ λ and µ : = λ λ. Th fst quaton n (9) s th ul fo ffcnt consumton, th scond and thd quatons a uls fo ffcnt oducton. Th quaton µ B = µ + flcts th wll-known ffcncy qumnt of qualng magnal abatmnt costs acoss counts. Nt w assss th ffcncy ots of comttv makts whn th mssons tadng schm s n oaton and gn ngy s subsdd. Fo that uos, w ntoduc a gn ngy subsdy 2 (subsdy, fo shot) n ach county at at 3, and consd th c takng agnts' otmaton lans: Th oducs of good X, gn ngy and black ngy mam ofts φ φ = X, = + s G, g g g 4 s φ b B ( ) ( c ) = π, sctvly, and th consum mams h utlty (5) subct to th budgt constant + * * * + φ + φg + φb sg s, wh φ *, * φ g and φ * b a mamum ofts and wh sg s s a lumsum ta lvd on th consum and usd to subsd gn ngy oducton. Th tanng fst-od condtons a U U =, G = X + s and B = π +. (10) Fom comang th quatons (9) and (10) mmdatly follows s s s1 =... = s n = 0. Pooston 1. Th comttv qulbum of th n-county conomy wth mssons tadng and subsdy ats ( 1,..., n ) s ffcnt, f and only f 2 As mntond abov (Scton 1), n actc gn ngy omoton oftn taks th fom of fd-n taffs o gn ctfcats schms. Howv, at th hgh lvl of abstacton of ou modl th ncdnc of ths olcy schms s th sam as that of govnmnt subsds. 3 Th at s s not sgn-constand. To avod clumsy wodng, w f to s not only f s > 0, but also f s < 0, n whch cas t s a ta on gn ngy ath than a subsdy (n th naow sns). 4 Accodng to th dfnton of φ th oduc of black ngy gts th mt ndowmnt c fo f. Th b altnatv assumton of auctonng mts would lav th sults unchangd at th hgh lvl of abstacton of ou modl. 6
Th cla mssag of Pooston 1 s that fo th gou of counts as a whol, subsds a dstotonay and nd nffcnt th qulbum allocaton. That sult dos not com as a sus bcaus, gvn th mssons tadng schm, th a no tnalts o oth makt mfctons n ou n-county conomy and thfo any subsdy o ta (basd on ndognous conomc vaabls) s bound to duc th wlfa of th gou of counts. If cubng mssons s consdd th only olcy tagt and f gou ffcncy s an agd-uon tagt, Pooston 1 advss govnmnts to abstan fom subsdng gn ngy altogth. It s not cla, though, whth gn ngy subsds a also unfavoabl fom th vwont of ndvdual counts whos govnmnts (also) consd cubng mssons as th only olcy tagt but focus on natonal wlfa ath than on gou ffcncy. W wll addss that ssu n th nt scton. 4 Subsdy comtton Th small county cas. Consd fst a small on county whos govnmnt has at ts dsosal a gn ngy subsdy, taks th mt c π as gvn and ams at mamng ts county s wlfa dfnd as ts sntatv consum s utlty. Th comaatv statc ffcts of a chang n and π (dvd n th And A) on county s wlfa a s du λ = sα ds + c sβ d π, (11) 2 wh 5 2 1 2 G 1 c B G α : = + B σb > 0, β : = + B D D, 1 2 X G D : B σb γ = + + BG > 0, γ : = X ( + s) G > 0. Th govnmnt of county taks th mt c as gvn (whch mans that w st dπ = 0 n (11)) and chooss ts subsdy such that du = 0. Th staghtfowad concluson fom (11) s 5 W ntoduc ths tms (and som mo blow) to mov th adablty of th a. Th lst of all aulatoy tms dfnd s ovdd n th And B. 7
Pooston 2. (Small county cas). If th govnmnt of county sks to mam natonal wlfa takng th mt c as gvn, t fans fom subsdng gn ngy. Accodng to Pooston 2, th comttv qulbum wthout subsds s thfo not only ffcnt fom th vwont of th gou of counts (Pooston 1) but also wlfa mamng fom th vwont of ndvdual govnmnts of small counts (Pooston 2) caabl to subsd gn ngy. Th lag county cas. Now w tun to gn ngy subsds n a gou of lag on counts whos wlfa mamng govnmnts account fo th nflunc of th olcy on th mt c π. Analogous to ou ocdu n th small county cas, w nvsag an ndvdual county and lo that county's chang n wlfa whn subsdy ats vay. In contast to (11), howv, th govnmnt now taks nto account n ts otmaton calculus how th qulbum mt c changs n sons to vaatons n ts own subsdy and n th oth counts' subsds. Fomally, (11) s lacd by du dπ sαds ( c sβ) λ = +. (12) ds To dtmn th dffntal quotnts d π /d w nd to -consd th fossl ful consumton, = E ( π, s ), of a county that taks as gvn both th subsdy s and th mt c π 6, and w thn nd to scfy how vas n sons to small ognous changs n s and π. In th And A w show that s E s X G G = = + B = δ < 0 s D = : δ > 0 B and (13) ( ) X G G σ c B γ Eπ = + = ( δ + D D = : δ = : ζ ζ ). (14) π s th qulbum - 6 E ( π, s mt c. ) s th qulbum quantty of fossl ful consumton, f and only f 8
Fom (14) t s staghtfowad that ζ 0 and hnc E π < 0, f c. Howv, fo mt-otng counts th sgn of ζ s uncla. Lat w wll amn n som dtal th dtmnants of th sgn of E π fo mt-otng counts bcaus that sgn wll lay an motant ol fo th conclusons to b dvd. Nt w wt quaton (6) as ( π, s ) = c and obsv that aft som E (small) ognous vaatons n subsds a nw qulbum s attand, f and only f d= E π dπ + s d s = 0 o E δ d ( δ + ζ ) Es ds B s dπ = = E π, (15) wh δ and ζ a dfnd n (13) and (14). W nst (15) nto (12) and obtan du ( c sβ ) δ B = sα + λ ( δ + ζ ) ds ( δ + ζ ) ( β ) c s δ B ds. (16) st To chaact govnmnt 's bst ly to gvn subsdy ats of all oth counts w s = 0 fo all. That convts (16) nto d du sη + c δ B = ds λ δ ζ ( + ), (17) = + B = ( ) wh : η α δ ζ βδ 2 δbg α δ + ζ ζ γ o η = α ( δ + ζ ) + θζ wth 2 αγ δbg θ : = > 0. (18) γ Th fst-od condton fo th bst ly s du λ ds = 0 whch mls n vw of (17) s ( ) c δb =. (19) η 9
Th concluson to b dawn fom (19) cucally dnds on th sgn of η. As α, δ and θ a ostv fo all, whl ζ may but nd not b ngatv fo mt-otng counts, th sgn of η s uncla. ζ > 0 fo all s an obvous suffcnt condton fo η > 0 (and fo E π < 0 as wll). Howv, w wsh to mak us of wak condtons fo η > 0. Fst w mos th constant E π ( δ ζ ) 0 = + < fo all ath than ζ > 0 fo all and w wll dmonstat lat that E π < 0 dos not aa to b an unasonably stong stcton. Clos nscton of (14) shows that E π < 0 fo all s quvalnt to c X G G σ < + + γ B B fo = 1,, n. (20) Th ght sd of that nqualty s ostv so that (20) s satsfd fo all mtotng counts fo whch ( c )/ s not too lag. ( c )/ s th mt ot as a sha of domstc mt us. Unfotunatly, (20) stll lavs th sgn of η ambguous. W thfo nd to ntoduc " η > 0 fo = 1,, n" as a scond constant whch can b shown to b quvalnt to th nqualty c ( ) σ α D δ + ζ < + B γ Bθ fo = 1,, n. (21) Whn combnd wth (20) whch s quvalnt to δ ζ > 0, th ght sd of (21) s os- + tv and gat than σ / B. Fom ths obsvaton combnd wth (19) follows mmdatly Pooston 3. (Lag county cas). Suos th govnmnts of all counts sk to mam natonal wlfa and account fo th mact of th gn ngy subsdy on th mt c. If th Nash qulbum n subsdy ats of th n-county conomy satsfs (20) and (21), th qulbum subsdy of county s chaactd by sgn s = sgn ( c ). (22) 10
Accodng to (22) th govnmnt of county chooss s > 0 [ s < 0] f and only f county mots [ots] mts. Th mt-motng county has an ncntv to subsd gn ngy ( s > 0 ) to dscouag ts black ngy oducton as wll as ts fossl ful consumton and gnaton of mssons. Th do n th dmand fo mts lows both th mt c and th nd fo mts and thus th county's mt mot bll. That s wlfa nhancng u to som ont wh th dstoton n oducton comnsats th advantag of asng th subsdy. Convsly, th mt-otng county als a ngatv subsdy (= ta) on gn ngy ( s < 0 ) to stmulat black ngy oducton and wth t th county's mt dmand. Th ntnton s to as th mt c whch thn ncass natonal ncom va sng vnus fom mt ots. Th nt advantag of succssv ncass n th ta at dmnshs bcaus of sng dstotons n oducton. Not that oducton nffcncs sult whnv s 0, and that th dstotons a atculaly sv bcaus s s ngatv fo som counts and ostv fo oths. Ngatv gn ngy subsds (= tas) do not aa to b a lvant ssu n actcal olcy although thy may b found as (ossbly unntndd) sd ffcts of coml gulaton. Assumng that ngatv subsds a not vabl,.g. bcaus of stong sstanc fom gn lobby gous, th govnmnts of mt-otng counts can b concvd to mam wlfa und th addtonal constant would thn b s = 0. In oth wods, f tang gn ngy s not fasbl mt- otng counts hav stong statgc ncntvs not to omot gn ngy. s 0. Th otmal choc 5 How stctv a th condtons of Pooston 3? It s not asy to s how gnal th sult of Pooston 3 s,.. how sv th stctons (20) and (21) a fo th sult (22). To assss that ssu t s convnnt to focus on condton (20) ath than on (21) o on both condtons - and amn th od of magntud of th ght sd of th nqualty (20) whch ads X G G B B σ + + γ. (23) W am at offng som thumb stmats of all comonnts of (23). Th tansfomatons: 11
X G 1 + s + + = X + G = 1+ = ( s) + + s. γ : = X + s G = + g g g ε ε X G g g, wth ε : = and ε : =. X G g G g ε b b g ε B tun (23) nto g G g b B =, wth ε : = and ε : =. g b g + s + 1 ε 1 g 1 g b + σ b ( + s ) ( g / ) ε + ε ε b ε b [1] [2] [3] [4] [5] [6] [7] [8] (24) What do w know about th od of magntud of th tms [1] though [8] n (24)? Th tm [1] s much lag than on, bcaus th valu of ngy, than th valu + s, s fa lss = of th comost consum good X. In tm [2] th ato ( g/ ) g s sgnfcantly small than on, and th lastcts ε and ε a n th ntval ] 0,1 [ fo so-lastc oducton functons. Hnc [2] can b ctd to b gat than o clos to on, and [3] 1 s also lausbl. To dtmn a low bound fo [4] w mak us of s s > (ostv oft) and fnd that ξ = wth ] 0,1[ ξ w hav ξ 1 1 ξ >. Fo an so-lastc oducton functon s =. Snc tnds to gow wth ncasng souc ndowmnt,, [4] wll b lag than on fo suffcntly lag. Summng u, th oduct [ 1][2][3][4] can b safly assumd to b much lag than on. Howv, th tm [5] s fa small than on whch maks t vy dffcult to lac a labl numb on th nt oduct [ 1][2][3][4][5]. Nonthlss ou abov agumnts lad us to consd [1] [2] [3] [4] [5] 1 a asonabl and ath low stmat. b Consd nt th oduct [6] [7] [8]. Snc ε 0,1, th tm [6] n (24) s claly ] [ gat than on. Th tm [7] s sgnfcantly lag than on bcaus good X snts all consum goods n ou modl whas th valu of black ngy s a faly small sha of 12
GDP only 5-8% (EAI 2008). 7 Consquntly, vn f w allow fo small valus of σ, say valus wll blow on, th oduct [6] [7] [8] s stll lkly to b lag than on. Hnc w consd [ 1][2][3][4][5] + [6] [7] [8] 2 a vy coas but faly consvatv stmat fo th nt tm n (24). If w consd X G G B B σ + + γ = 2 n (20), w fnd that Pooston 3 covs Nash qulba n whch mt-otng counts do not ot mo than two thds (67%) of th mt ndowmnt,. In th mssons tadng schm of th Euoan Unon no county coms vn clos to an ot sha of mts cdng 60%. (Totgnon and Dlbosc 2008). In lght of ths lausblty agumnts (gudd by styld mcal stmats) th condton (20) dos not aa to b unasonably stctv at all. So fa w hav stctd ou attnton on th constant (20). Obvously, f (21) ath than (20) s bndng fo som mt-otng counts, Pooston 3 s somwhat lss gnal than suggstd by ou dscusson of (24) abov. Nonthlss, vn n that cas th nqualts (20) and (21) a stll lss stctv than th altnatv constant that s suffcnt fo achng th concluson (22), namly th condton ζ > 0 fo = 1,, n o c σ < fo = 1,, n. B c Th cdng dscusson showd that E π ( δ ζ ) 0 = + < s not unalstc fo mt- otng counts. To nfoc that assssmnt w wsh to dntfy th conomc dvs of th sgn of E π by fnc to th comaatv statcs of th small on conomy cad out n th And A. Accodng to that analyss, n mt-otng and -motng counts alk 8 π > 0 stmulats gn ngy oducton, ducs th oducton of good X, and ass th consum c of ngy,, whl th consum good c mans constant by assumton. Total ngy consumton and wth t ncssaly black ngy oducton shnks unambguously only, whn th county mots mts. Und th lausbl assumton that th ncom lastcts of ngy and good X a ostv, 7 EIA (2008) ots that ov 2000-2008 n th US th total ngy ndtus GDP l btwn 6 and 9 %. Snc th sha of black ngy s 90%, th black ngy sha of GDP amounts to 5 to 8%. 8 ndcats a fnt chang of a vaabl. 13
> 0 follows fom π > 0 n mt-otng counts, f and only f th followng condtons a satsfd: (a) Natonal ncom must s to gnat a ostv ncom ffct I > 0 ; (b) Th ngatv substtuton ffct < 0 du to S 0 nsat 9 I S th ostv ncom ffct: = + > 0. / > must not ovcom- Evn f ths condtons hold 10, black ngy and mssons nd not ncssaly ncas, howv, bcaus = b + g > 0 may b bought about by g > 0 and b < 0. Thfo, E π < 0 aas to b lkly fo all mt-otng counts. 6 Concludng maks Th snt a suggsts that statgc ncntvs may b a atonal fo subsdng gn ngy whn counts oat a ont mssons tadng schm. Wlfa mamng govnmnts of lag counts ut a ostv o ngatv subsdy on gn ngy n od to manulat th mt c. Subsdy comtton of small counts tuns out to b ffcnt fom th sctv of th gou of counts, snc all counts fan fom gn ngy subsds. In contast, subsdy comtton of lag counts nds th mult-county conomy nffcnt. In that cas th olcy mlcaton s 'subsdy hamonaton at th lvl o'. Fnally, t must b kt n mnd that th sml assumtons of ou styld modl ut som lmts on th gnalty of sults. E.g., ngy oducton taks lac und fct comtton whch s n stak contast to ngy makts n th al wold. Th analyss of monoolstc o olgoolstc ngy oducs s thfo an motant task fo futu sach. Also, w assum that ngy s tadd on domstc makts only and no fossl ful s suld n any county of th gou. Ths assumtons may b consdd acctabl as a fst aomaton,.g. fo th Euoan Unon, but t s ncssay to amn 0 9 Fo any gvn c chang / >, th substtuton ffct < 0 s th small n absolut tms th small s th lastcty of substtuton n dmand, σ. 10 It s ntstng to obsv that f th ncom lastcts of ngy and good X a ostv and th condtons (a) and (b) hold, thn th consumton of good X ncass along wth ngy consumton and thfo th wlfa of th county ss. 14 S
th obustnss of ou sults wth sct to dvatons fom ths assumtons n od to mov ou undstandng of statgc ncntvs fo o aganst omotng gn ngy. And A: Comaatv statcs of th small on conomy Fo convnnc of notaton, w suss th nd, whn th s no sk of confuson, and w st qual to on th c of good X ( 1). Fo gvn c,,, 1 and π an qulbum of th small on conomy 11 s consttutd by cs, and an allocaton ( bs,, gs, g,, s, s,, s) such that ( s,, s, g,,, s,, s) b g s a soluton to th agnts otmaton oblms and th constants (6) and (7) hold. Th 12 vaabls b,, g,,,,,,, λ,,and bs s s g s s = B, s bs g a dtmnd by th 12 quatons = + s, X ( ) =, ( c ) ( ) 0 π + =, s g s ( g ) = G, s =, ( ) ( g) + =, (, ) s G U = λ, s = X, = +, B = π +, (, ) g U = λ. To obtan nfomaton on how that qulbum dnds on th subsdy s and on th mt c π, w wll consd th mact of small changs n thos aamts on th qulbum. Fo that uos w lmnat th vaabls b, g,,,,, and λ n th 12 s s s s quatons lstd abov though substtuton thus condnsng th 12 quatons nto th fou quatons ( c ) + X ( ) = 0, π g (A1), X = + s G (A2) g g π, B = + (A3) 11 Not that th qulbum of th small on conomy s not an qulbum of th n-county conomy. Th latt would qu th addtonal constant (6) to hold and th mt c π to b ndognously dtmnd. 15
+ ( g) + ( g) U, B G 1 =, U, B G (A4) that dtmn th ndognous vaabls,, and. Total dffntaton of ths quatons ylds g Bd+ Xd + d= c dπ, (A5) g γ d G d = G d s, (A6) g B d+ B d = dπ, (A7) B G d σ d+ dg + d = 0, (A8) U d U wh σ : = U d U γ : = X + sg > 0. s th substtuton lastcty and Aft nstng d fom (A8) n (A5), th quatons (A5), (A6) and (A7) ad n mat notaton ( c ) σ 1 X G + B + d d π G 0 γ d = Gd s. (A9) B B 0 d g dπ W solv th quaton systm (A9) by usng Cam s ul and obtan aft som aangmnts of tms 1 γ B dπ = γ B + ( c ) D d X G d s + GB +, D (A10) γ B γσ X G dπ = ( c ) + G X G d s + BG, D D d (A11) 16
1 dπ dg = + BG GB( c ) D 1 2 d s + + BG σ GB, D (A12) wh 1 D γb σγb X G G B 2 : = + + > 0. Nt, w nst (A11) and (A12) n ds = d = Bd+ Gd g to obtan aft aangmnts of tms 2 2 2 2 2 1 sbg dπ sbg d s ds = d = γ B ( c ) ( c ) G B γσb. D D (A13) Makng us of (A10) and (A13) n d d d = + σ w obtan ( c ) γ B ( c ) 2 2 d 2 sbg = G B σ ab σ ab d + ( c ) π D 2 2 X G sbg d s + σ GB +. (A14) D Th comaatv statc sults of th small on conomy a summad n Tabl 1: d d,d b s d g, dgs d d s d,d s d ds > 0 + dπ > 0, c> +? +?? dπ > 0, c< + +? Tabl 1: Th comaatv statcs of th small on conomy (Assumton: B + B > 0 12 ) Fnally, w nst d fom (A5) and d = B d+ G nto du = U d+ U d and us U = U = λ and (A2) to obtan d g m = ] 0,1[ 12 If th oducton functon taks th fom B wth m, thn ( B B ) + = m > 0. Th functonal fom b = aas to b a mld stcton only on (3). θ 17
du = sg dg + ( c ) d π. (A15) λ Wth d g fom (A12) w tun (A15) nto (11). B: Tms dfnd to as th oston α 1 G 2 2 : = + B σb > 0 D 1 β : = + B 2 ( c ) B G D : X G G γ = X ( + s) G > 0 δ : = + D ( ) σ c B ζ : = D γ η : = α ( δ + ζ ) + θζ 2 αγ δbg θ : = > 0 γ 1 2 X G D : = + B σb γ + BG > 0 Rfncs Batt, S (1994): Statgc nvonmntal olcy and ntnatonal tad. Jounal of Publc Economcs 54, 325 338. Bläs, A. and T. Rquat (2007): Subsds fo wnd ow: sufng down th lanng cuv? CAU Economc Wokng Pa 2007 28, Kl. Bécht, T. and S. Palta (2008): Th ac fo ollutng mts. CEPR dscusson a No. 6209, London. EIA (2008): Engy consumton, ndtus and mssons ndcatos, Tabl 1.5, US. Echn, T. and R. Pthg (2009a): CO 2 mmssons contol wth natonal mssons tas and an ntnatonal mssons tadng schm. Euoan Economc Rvw 53, 625 635. 18
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