Climate change control: the Lindahl solution

Transcription

1 Mtg Adapt Strateg Glob Change (2018) 23: DOI /s ORIGINAL ARTICLE Clmate change control: the Lndahl soluton Loek Groot 1 & Jula Swart 2 Receved: 24 March 2017 /Accepted: 14 July 2017 /Publshed onlne: 19 August 2017 # The Author(s) Ths artcle s an open access publcaton Abstract The man purpose of ths paper s to evaluate dfferent burden sharng rules wth respect to abatement of carbon emssons. We evaluate seven dfferent rules both n terms of ther redstrbutve mpact and by the extent to whch they realze the am of optmal abatement. We show that the Lndahl soluton, where the burden sharng rule of carbon abatement s determned by each regon s wllngness to pay, s to be preferred above the non-cooperatve Nash outcome. Poor regons however would prefer the socal planner outcome wth a global permt market, because then the burden sharng rule has a secondary role of ncome redstrbuton by means of transfers from rch to poor, on top of ts prmary role of assgnng abatement burdens. Based on these fndngs, we argue that n order to control global greenhouse gas emssons, the level of ndvdual country emsson abatement effort should be a functon of ther wllngness to pay to curb clmate change, rather than ther hstorcal emssons or ablty to abate. Keywords Nash. Lndahl. Tradable permts. Equty. Effcency. Burden sharng rule JEL classfcaton D610. D63. H410. Q01. Q5 1 Introducton Artcle 2 of the 2015 Unted Natons Clmate Change Conference Pars Agreement ams at lmtng global warmng to well below 2 C and BMakng fnance flows consstent wth a pathway towards low greenhouse gas emssons and clmate-reslent development.^1 Contrary 1 See * Loek Groot L.F.M.Groot@uu.nl; Utrecht Unversty School of Economcs, P.O. Box 80125, 3508 TC Utrecht, The Netherlands Utrecht Unversty School of Economcs, P.O. Box 80125, 3508 TC Utrecht, The Netherlands

2 758 Mtg Adapt Strateg Glob Change (2018) 23: to the Kyoto protocol, there s no detaled country- and tme-specfc path to reach these goals, but nstead a bottom-up approach where each country can set ts own Bnatonally determned contrbutons^ to cut greenhouse gas (GHG) emssons, wthout an enforcement mechansm. Apparently, the specfcs of burden sharng s relegated to the 5-yearly perodcal global stocktake specfed n Artcle 14, startng n 2023, although Artcle 4 states that developed countres should make absolute reductons, aganst for the near future just mtgaton efforts for developng countres and of moblzng USD $100 bllon per year to fund clmate polces fnanced by the developed countres. Long before Pars 2015, there has been an ongong and flourshng debate among scentsts about the tme path to contan global warmng. The tmng ssue s largely concerned wth the choce of approprate dscount rates (Wetzman 2001;Nordhaus 2007;Heath 2013) and how to assess the rsk of unlkely but potentally dsastrous outcomes, e.g., reversal of the Bthermohalne crculaton,^ also known as the BGreat Ocean Conveyor Belt^ of the Gulf Stream and the exacerbated release of methane due to global warmng from the Arctc permafrost. Here, we abstract from the tme path and concentrate on how the abatement burdens should be allocated across regons n the world at a gven pont n tme. Gven the urgency to reduce GHG emssons worldwde, the most dffcult ssue s how the burdens are dstrbuted across regons. Snce clmate change s a global publc good, t requres a global burden sharng rule. The two domnant gudng prncples for far burden sharng are the polluter pays prncple and the ablty to pay prncple. For nstance, the Stern Revew (Stern 2007, p. 23) states that based on ncome, hstorc responsblty, and per capta emssons, rch countres should take the prmary responsblty to combat clmate change. However, the lterature on burden sharng emphaszes the free-rdng problem as a consequence of clmate change beng a publc good (Gupta 1997). Thus, one mportant strand n the lterature has analyzed the challenge of relatng damage caused by clmate change to economc actvtes, whch are often occurrng n dstnct places (see, for example, Edwards and Mller 2001; Vogt 2008 and Dellnk et al. 2009). Ths paper contrbutes to ths lterature by avodng the problem of havng to establsh the causaton from polluter to damage experenced, by turnng nstead to countres own nterest. In ths paper, we derve the burden sharng rule followng the Lndahl equlbrum (hereafter LE), where burden shares are not so much determned by ablty to pay or (hstorcal) emssons, but by countres nterest, e.g., due to expected damages, to combat global warmng. To llustrate the LE by means of a smple example, suppose two persons share a household n whch the cleanlness of the house s consdered a publc good. The problem of burden sharng s how many hours every member of the household has to spend on cleanng. A smple splt wll not do, because one person may prefer to have the ktchen or closet much cleaner than the other, so even at frst glance, far splt wll not solve the queston how many hours n total wll have to be spent on cleanng, that s, the provson level of the publc good. The LE wll dentfy a unque level of the publc good wth shares assgned to each household member n such a way, that gven the assgned shares, each member wll choose the same (Lndahl) level of publc good provson wth the shares summng up to unty. However, snce shares are proportonal to margnal wllngness to pay (WTP), household members have an ncentve not to reveal ther true preferences n order to easy- or free-rde on the efforts of the other. Although one may queston how plausble t s that people durably lvng n a household are able and wllng to hde true preferences to get an advantage n burden sharng at the expense of the other member, wth many agents sharng a publc good strategc msrepresentaton of

3 Mtg Adapt Strateg Glob Change (2018) 23: preferences can ndeed be a serous problem. Wth respect to an agreement nvolvng many states, the dentfed LE from the scentst drawng table s therefore only useful as long as the analyss s based on easly observable varables such as GDP, populaton sze, GDP per capta, energy consumpton, GHG emssons, and to be expected damages from clmate change that are not easy to manpulate. In the burden sharng debate of clmate change, surprsngly lttle attenton s pad to the LE. 2 In the LE, each country s assgned an abatement share n such a way that gven ther assgned share, they all want the same level of the global publc good n ths case global carbon emsson abatement (for the dervaton of Lndahl equlbra n publc goods models, see Sandler and Murdoch 1990; Mas-Colell 1989; Shtovts and Spegel 1998, 2003). In such a LE, each country contrbutes to the global provson level accordng to ts WTP. The salency of WTP s that any Internatonal Envronmental Agreement n whch some countres have to contrbute less than ther WTP s a pty, because they are prepared to abate more. At the same tme, a country wll be reluctant to contrbute n excess of ts WTP, for nstance, f t s prescrbed to do so by nvokng the polluter pays prncple or ablty to pay prncple. Therefore, any devaton from the LE would mean that ether some countres contrbute less than ther actual WTP, whch s undesrable f we are to realze the am of mtgatng GHG emssons, or that some countres are supposed to contrbute more than they are wllng to, makng the agreement unstable. Therefore, t s mportant to assess the burden sharng rule accordng to the LE and to check how t fares compared to other burden sharng rules. Buchholz and Peters (2007, 2008) have dentfed the man farness propertes of the LE. They show not only that the LE s effcent (.e., satsfyng the Samuelson condton for the optmal supply of the publc good) but also that the beneft prncple (descrbed as Beveryone pays what he gets^) and the axom of proportonal contrbutons (meanng that cost shares are proportonal to margnal WTP) are satsfed. Despte these attractve propertes, the neglect of the LE should not come as a surprse, snce n the economc lterature on burden sharng to provde a publc good, the LE s sad to be merely of theoretcal nterest, manly for two reasons: frst, the dffculty to assess objectvely for each country ts WTP and second, the ncentve to strategcally msrepresent preferences. The best llustraton of the practcal nsgnfcance of the LE n the debate on clmate change s that as far as we know, there s no study wth an emprcal smulaton of the abatement burdens across countres or regons n a LE, a lacuna we hope to fll n ths paper. The structure of ths paper s as follows. Secton 2 presents the sub-optmal noncooperatng Nash model. Secton 3 presents the model wth a socal planner but wthout the nstrument of redstrbuton, whch, together wth the Nash model, are used as benchmarks for the LE. Secton 4 dentfes the LE n the global burden sharng of abatement. The emprcal part s presented n Secton 5. In the frst smulaton, the world s dvded nto two blocks of rch (Annex I) and poor (Annex II) countres; n the second, fve regons are dstngushed. The dfferent burden sharng rules are evaluated by two crtera, the extent to whch global abatement s optmal and the requred degree of redstrbuton by means of transfers from rch to poor countres. The fnal secton summares and concludes. 2 Gersch (2007, p. 1), comparng Lndahl wth the Nash outcome, also mentons that although the Lndahl equlbrum s consdered as one of the cornerstones of publc fnance, t s also Bdsmssed as unconvncng.^

4 760 Mtg Adapt Strateg Glob Change (2018) 23: Non-cooperatve Nash wth and wthout permt markets In modelng clmate change and abatement, many choces have to be made. Does one take a statc or a dynamc perspectve, s the externalty arsng n consumpton or producton or both, s the approach rooted n welfare economcs or game theory, what s the approprate dscount rate, and so on. In general, many of the choces made here are motvated by keepng the model as smple as possble n order to derve burden sharng rules of abatement under dfferent regmes. In the frst regme, servng as a benchmark for the models presented n subsequent sectons, countres are assumed to follow ther self-nterest n a non-cooperatve way. Followng the wthdrawal of the USA on 1 June 2017 from the Pars agreement, ratfed on 5 October 2016 and due to the absence of a burden sharng rule and enforcement mechansm, t s not exaggerated to clam that the Nash model, where each country pursues ts own nterest takng nto account the behavor of others, mght stll be an approprate workhorse carryng a sense of realsm n case the bottom-up Pars approach fals. Cramton and Stoft (2010) go so far to say that after Kyoto, BIn fact there s no clear evdence that we have done even as well as the publc-goods Nash equlbrum.^ Frst, we model non-cooperatve behavor wthout and wth a permt market. 2.1 Non-cooperatve Nash wthout a permt market In the model, utlty (u ) s a functon of per capta ncome avalable for consumpton (y c )and the level of worldwde abatement (A), the former beng a prvate good and the latter a global publc good. The chosen abatement level n country under Nash behavor (A ), takng the abatement effort of others as gven (A _ ), can be thought of as ts emsson under a busness-asusual (BAU) scenaro mnus ts actual emsson. Country wth populaton P s endowed wth resources R, whch can be devoted to ether consumpton (P y c ) or to fnance abatement costs (C (A )). The endowment R can be nterpreted as GDP wthout any cost of abatement, n whch case per capta ncome for consumpton equals resources per capta. The Lagrange functon for country canbestatedas Ly c ; A ¼ P u y c ; A þ A þ λ R P y c C ða Þ ð1þ wth the frst term on the rght-hand sde (RHS) the objectve and the second term the resource constrant and λ the Lagrange multpler. Dfferentatng wth respect to per capta consumpton and abatement, where varables n subscrpts denote dervatves, gves as frst-order condtons: P ¼ λ P ¼ λ ð2aþ P u ;A ¼ λ C A ð2bþ These two optmum condtons can be summarzed as P u ;A ¼ C N A MSB ;A ¼ C N A MU y c ð2cþ Equaton 2c states that the Samuelson rule for the optmal provson of the publc good the sum (P ) of the margnal rate of substtuton (u ;A = ) between abatement and per capta

5 Mtg Adapt Strateg Glob Change (2018) 23: consumpton must be equal to the margnal cost of abatement (C N A ) s only appled at the natonal level. Expressed dfferently, each country only abates up to the pont at whch ther natonal margnal socal benefts (MSB) are equal to the margnal cost of abatement tmes the margnal utlty of per capta ncome (MU). The sub-optmalty arsng under Nash s twofold. Frst, the postve externaltes of abatement n one country for the rest of the world are not taken nto account. Second, margnal abatement costs dffer between countres, so total abatement s not produced aganst mnmum cost (as shown by Chchlnsky and Heal 1994; Sandmo 2003, 2007; Eyckmans et al. 1993; Sheeran 2006). Overall, abatement levels wll be too low and the margnal cost of abatement (hence the abatement level) n a country wll be hgher the larger ts populaton sze and the lower ts margnal utlty of per capta ncome. Note that t s assumed that abatement s decded on the natonal level. If governments would not be n charge to (negotate and) mpose domestc abatement levels, then we would have an atomstc world and under Nash everyone would only mtgate ts contrbuton to global warmng up to the pont where the prvate margnal benefts equals prvate margnal costs Non-cooperatve Nash wth a permt market The second sub-optmalty can be removed by adoptng a worldwde cap-and-trade system so for each country, the optmal actual abatement (A ) wll be determned by where ther margnal cost of abatement equals the global permt prce (q) whle at the same tme allowng countres to choose ther own target abatement levels (T ). To see how ths works out, the resource constrant changes nto R ¼ P y c þ C ða ÞþqT ð A Þ ð3þ Accordng to Eq. 3, f the actual abatement n a country s lower than ts chosen target level of abatement, then t has to buy addtonal emsson permts aganst a unform permt prce of q. Substtutng the world abatement constrant A = T + T _ n the utlty functon and ncludng the new resource constrant of Eq. 3 n the Lagrange functon gves Ly c ; A ; T ¼ P u y c ; T þ T þ λ R P y c C ða Þ qðt A Þ ð4þ Dfferentaton wth respect to per capta ncome and abatement gves ¼ λ ð5aþ λ ½C A q ¼ 0 C A ¼ q ð5bþ For total abatement, whch wll equal the global sum of the natonal target abatement levels, the chosen target levels are crucal. Each country wll choose ts target level accordng to 3 Ths can be can be modeled as L = u j (y j, A _j + a j )+λ(r j y j c j (a j )), where subscrpt j refers to ndvduals. The optmum condton s u j;a =u y j ¼ c N a j wth a j abatement by j. In that case, the prvate margnal rate of substtuton between abatement and consumpton s equated aganst prvate margnal cost of abatement. Compared wth the outcome of Eq. 2c, even the postve externaltes wthn one s own country are gnored.

6 762 Mtg Adapt Strateg Glob Change (2018) 23: L y c ; A ; T A ¼ P u A λ T T A C A þ q ðt A Þþq 1 A T T T ¼ 0 ð5cþ Usng the optmum condton of Eq. 5a, dvdng by and snce A/ T =1, 4 the optmum condton of Eq. 5c can be rewrtten as P u A ¼ A T ðc A qþþq þ q T ðt A Þ ð6þ Because of the global permt market, margnal cost wll be equalzed everywhere to the permt prce q (see Eq. 5b), so the frst term n brackets wll be zero and Eq. 6 reduces to u A P ¼ q þ q T ðt A Þ ð7þ Equaton 7 expresses that n choosng the optmal target level, each country equates ts margnal socal beneft (LHS) to the permt prce plus the effect of a hgher chosen target level on the permt prce (q T ) tmes the volume of permts bought or sold by country (the same result s obtaned by Cramton and Stoft 2010). In a global permt market q/ T = q/ T j = q/ T = q T and summng both sdes of Eq. 7 over all countres results n n ¼1 P u A ¼ nq þ q T n ¼1ð T A Þ ð8þ By defnton, the last term s zero when the permt market clears, so Eq. 8 bolsdowntothe global sum of margnal benefts of abatement (the LHS) to be equal to the permt prce tmes the number of countres (the RHS). Although the second sub-optmalty of the noncooperatng Nash soluton wthout a global permt market s removed now that the same good abatement s produced at unform nstead of dfferentated margnal costs, the frst suboptmalty s stll there; the prce of abatement s, from a world pont of vew, much too low 5 because the LHS of Eq. 7 does not contan the global but only the natonal margnal benefts of abatement. 3 A socal planner wthout and wth a permt market Now, suppose countres agree to nstall a socal planner (labeled S) to redress the suboptmaltes of the Nash outcome. If S s gven not only the power to set the burden sharng rule for abatement but also the power to redstrbute ncome, the global welfare maxmzng outcome wll be equalty of margnal utltes of ncome across countres and unform margnal cost of abatement to ensure producton effcency (see Appendx 1). Although equty and effcency are acheved smultaneously, t s not realstc to assume that n order to solve the global warmng problem, however serous t may be, soveregn rch countres are prepared to equalze ther per capta ncomes to that of the rest of the world. Therefore, a more realstc verson of S s that t lacks the nstrument of ncome redstrbuton but s stll gven the 4 Under the zero Nash conjecture, each country takes the chosen target levels by others as gven, so a change n ts own target level wll lead to an equal change n total abatement. 5 The socal optmum would be that the prce of the permt equals the LHS of Eq. 8.

7 Mtg Adapt Strateg Glob Change (2018) 23: restrcted mandate to devse an optmal burden sharng abatement rule. We wll see that the optmal rule requres the margnal welfare cost of abatement to be equal across countres. We dstngush S wthout and wth the power to nstall a global permt market. 3.1 A socal planner wthout a permt market A dstncton can be made whether or not S has to operate under an external global abatement constrant. Suppose that all countres agreed that a requred level of global abatement (A ), e.g., stpulated by the IPCC relatve to BAU emssons, has to be met. Ths wll add a polluton constrant to the exercse, and the only decson by S s to assgn the abatement burdens A such that ther sum equal A. Thus, S maxmzes welfare over all countres subject to the global abatement constrant and all natonal resource constrants: Ly c ; A ; A ¼ n ¼1 P u y c ; A þ μ ½ A A þ λ R P y c C ða Þ ð9þ Note that the only dfference of ths Lagrange functon wth the one of S wth the power to make cross country lump sum ncome transfers (see Appendx 1) s that for the former, there s a resource constrant for each country (see the last term n Eq. 9), nstead of just one world resource constrant (λ R P y c C ða Þ ) under a socal planner wth ncome redstrbutve powers. Dfferentatng Eq. 9 wth respect to y c, A and A gve ¼ λ ð10aþ μ ¼ λ C A ð10bþ P u A ¼ μ ð10cþ Accordng to Eq. 10a, margnal utlty of per capta ncome s country specfc. Because there s no ncome redstrbuton, margnal utlty of per capta ncome n poor countres wll be hgher than n rch countres, 6 and therefore, the margnal cost of abatement wll be set lower n poor countres (see Eq. 10b). Note that f no external global abatement restrant s mposed, S wll maxmze Eq. 9 also wth respect to global abatement, ensurng the optmal level of total abatement as specfed by Eq. 10c. The external global abatement level A may have been set too hgh, too low, or just rght, and only n the latter case s the shadow cost of global abatement (μ) equal to the global sum of margnal abatement benefts ( P u A ), as specfed by Eq. 10c. Thus, only f the global abatement level s set at the rght level, the optmum condtons of Eqs. 10a c can be summarzed as the followng Samuelson rule: n P j u j A j¼1 ¼ C ;S A MSB w ¼ MC ;S A MU y : ð11þ The numerator n the LHS of Eq. 11, the global sum of margnal benefts of abatement (MSB w ), s a world total and so not country specfc. The denomnator, margnal utlty of per capta ncome, s country specfc. As a consequence, margnal cost of abatement (the RHS) s 6 Wth lump sum redstrbuton, ¼ λ, so margnal utlty of ncome per capta s unform across countres (see Appendx 1).

8 764 Mtg Adapt Strateg Glob Change (2018) 23: also country specfc. As the alternatve expresson of Eq. 11 shows, S dstrbutes the burden of abatement n such a way that, for each country, ts margnal cost of abatement tmes the margnal utlty per unt of ncome ths product can be nterpreted as the margnal welfare cost of abatement s equalzed to the global margnal benefts of abatement. All other thngs equal, poor countres, havng a hgh margnal utlty of per capta ncome, wll be assgned a low abatement level so that ther (margnal) cost of abatement wll be low. Summarzng, n comparson to the non-cooperatve case, S s guded by two rules n the maxmzaton of world welfare. Frst, by allocatng abatement burdens to ndvdual countres, the global abatement benefts are relevant, not the natonal. Second, nstead of natonal margnal abatement cost equated to (margnal) benefts of abatement, now the margnal welfare cost per unt of abatement s equalzed across countres. Comparng Eqs. 11 and 2c shows that the frst Nash sub-optmalty of not takng postve externaltes of abatement n one country to the rest of the world nto account s now removed, but the second sub-optmalty of dfferentated, country-specfc, margnal cost of abatement s stll present due to the absence of a global permt market. Ths sub-optmalty can be removed by empowerng S to nstall a global permt market. 3.2 A socal planner wth a global permt market To remove the second sub-optmalty of non-unform margnal cost of abatement, assume that countres allow the socal planner to mplement a global permt market (labeled as SP), 7 whch solves the producton neffcency of abatement produced n dfferent countres aganst dfferent margnal costs. As before, actual abatement levels n each country wll be unquely determned by the equalty of margnal cost of abatement (C A ) and the global permt prce (q), rrespectve of the partcular choce by SP of the burden sharng rule T. The global permt prce wll ether be determned by the chosen level of global abatement A by the IPCC or by the planner s optmal choce of the global abatement level, agan rrespectve of the sharng rule T. Hence, f the SP can operate wthout any constrant n settng T, to maxmze global welfare, the planner wll choose T n such a way that gven the optmal domestc abatement levels determned by where margnal abatement costs equals the global permt prce, the resultng transfer payments q(t A ) wll equalze margnal utlty of per capta ncomes, mplyng unform per capta ncome as under the lump sum socal planner wth unconstraned power to redstrbute. 8 Instead of lump sum redstrbuton, the same redstrbuton s establshed by transfer payments followng the chosen target abatement levels. 9 Therefore, a more constraned mandate for SP has to be adopted. For practcal reasons (see also the emprcal secton), we chose to constran SP n such a way that for each country or regon, the target abatement level s set equal to the actual abatement level under S. As a consequence, under SP, the same global abatement level as under planner S wthout permt market results. The advantage for the rch countres s that ther cost wll declne, snce the global permt prce s below ther margnal cost of abatement wthout emsson tradng. Poor countres wll beneft because ther target levels are ptched at the low abatement levels stpulated by Eq. 11 and they become consequently sellers of 7 Alternatvely, SP may mpose a unform global carbon tax, wth the tax equal to the equlbrum permt prce. 8 SP wll assgn target abatement levels such that y c ¼ ½R C ða Þ qðt A Þ =P ¼ y c w, whle at the same tme, the global sum of abatement equals the exogenously gven or optmal global abatement target, wth large negatve target levels for poor and large postve target levels for rch countres. 9 On the same footng, Shell (2003, p. 44) notes that BIf negatve allocatons were permtted for some countres, then the system would be equvalent to unrestrcted lump sum transfers.^

9 Mtg Adapt Strateg Glob Change (2018) 23: permts on the permt market. Swtchng to a permt market requres that at the country level, the consumpton constrant s adjusted to nclude ts dealngs on the permt market, so each country now faces the Lagrangan: Ly c ; A ¼ P u y c ; A þ λ R P y c þ C ða Þ qðt A Snce the SP s gven the authorty to set the burden sharng rule T, each country takes ts assgned burden T as gven, whch gves frst-order condtons: Þ ð12þ ¼ λ ð13aþ C A ¼ q ð13bþ Thus, although SP s constraned n settng the target-level abatements at the actual abatement levels f there would be no permt market, so T SP ¼ A S, the global permt market ncentvzes ndvdual countres to abate up to the pont where ther margnal cost are equal to the permt prce. Both neffcences of the non-cooperatve Nash outcome are then removed. Because of the permt market, the producton neffcency s removed and the IPCC or SP can mpose the requred global abatement level A. 4 The Lndahl soluton From a moral pont of vew, the acceptablty of the Lndahl soluton s hampered because t s n conflct wth both the polluter pays prncple and ablty to pay prncple. Gardner (2004,p. 590) concludes that: B there s a great deal of convergence on the ssue of who has prmary responsblty to act on clmate change. The most defensble accounts of farness and clmate change suggest that the rch countres should bear the brunt, and perhaps even the entrety, of the costs.^ In the same ven, the Executve Summary of the Stern Revew (Stern 2007, p. 23) states that BSecurng broad-based and sustaned co-operaton requres an equtable dstrbuton of effort across both developed and developng countres. There s no sngle formula that captures all dmensons of equty, but calculatons based on ncome, hstorc responsblty and per capta emssons all pont to rch countres takng responsblty for emssons reductons of 60 80% from 1990 levels by 2050.^ Apparently, both Gardner and Stern favor a burden sharng rule n whch the rch countres bear the lon share of the costs due to ther hgher ablty to pay and to the polluter pays prncple. However, assessng burdens to combat clmate change s not merely a moralty play. Countres are soveregn and a burden sharng rule based on moral prncples such as the polluter pays prncple or the ablty to pay prncple s only as strong as the commtment of countres to these prncples. 10 The ablty to pay or payng as polluter may not be n lne wth a countres wllngness to pay. 11 Our proposed burden sharng rule s based on countres 10 Elzen and Lucas (2003, Sect. 5) provdes an overvew of ten dfferent burden rules based on four equty prncples, namely, egaltaran (equal caps), soveregnty (grandfatherng), polluter pays, and capablty (ablty to pay). 11 In terms of a two-person household and the cleanlness of the house as the publc good, t mght be that one member has a hgher ablty to clean or s more pollutng than the other, but at the same tme has a much lower preference for a clean house, so a lower wllngness to clean.

10 766 Mtg Adapt Strateg Glob Change (2018) 23: wllngness to contrbute to combat clmate change, whch naturally leads to the Lndahl soluton to the optmal publc good provson level. The Lndahl soluton has two major dsadvantages. Frstly, the wllngness to pay s not only nfluenced by the expected damage but also by the adaptaton costs, whch puts many poor countres n a precarous poston f they lack the resources and know-how for adaptaton. Secondly, contrbutons accordng to wllngness to pay may be squarely at odds wth contrbutons based ether on the ablty to pay and the polluter pays prncple. For the sake of argument, suppose that the USA s protected from any consequences of clmate change and that only the rest of the world would suffer damages. Accordng to ablty to pay and the polluter pays prncple, the USA would have to contrbute heavly, but ts wllngness to pay mght be low. Analogous, the burden assgned to a poor country at sea level accordng to ablty to pay and polluter pays wll be low, but relatvely hgh accordng to wllngness to pay. In theory, countres that would beneft from global warmng (e.g., Russa, Canada, and Greenland) may have a negatve wllngness to pay, whch mples that they have to be compensated for ther partcpaton n an nternatonal agreement to abate greenhouse gases. Ths suggests that concerns of redstrbuton between rch and poor should be excluded n consderatons of how to assess far burden sharng to combat clmate change. What we propose s therefore that clmate change polcy must be evaluated on ts own merts, and the same goes for polces to address global ncome nequalty (see, e.g., Mlanovc 2016). 4.1 Lndahl soluton wthout permt market In the lterature, the LE s mostly nterpreted n terms of cost shares, but here nstead, each country s share s defned relatve to the total abatement level, 12 so wllngness to pay has to be nterpreted as wllngness to abate or contrbute. As before, we make a dstncton between the Lndahl soluton wthout (labeled L) and wth a permt market (LP). Under the former, countres are assgned abatement burdens a L such that these shares sum up to unty: a L ¼ AL A L ; a L ¼ 1 ð17þ Gven a country s assgned abatement share, to arrve at the LE, each country chooses the same global abatement level A L. Each country maxmzes Ly c ; AL ¼ P u y c ; AL þ λ R P y c C a L AL ð18þ wth respect to per capta ncome and total abatement, gvng ¼ λ ð19aþ P u A ¼ λ C A a L ð19bþ 12 Also, Gersch (2007, p. 18) consders ths approach of focusng on abatement rather than cost shares more realstc.

11 Mtg Adapt Strateg Glob Change (2018) 23: Combnng both gves P u A ¼ C A a L P u A ¼ a L u C A ð19cþ y c Takng summatons on both sdes of Eq. 19c results n the global sum of margnal benefts to be equal to the weghted sum of margnal cost of abatement: n ¼1 P u A ¼ a L C A ð19dþ whch s akn to the Samuelson condton. Note that wthout a permt market, margnal cost of abatement may dffer between countres. The Lndahl planner wll assgn abatement shares to countres, takng nto account that each one maxmzes Eq. (18), n such a way that gven ther assgned abatement shares, they wll choose the same global abatement level. 13 In the emprcal secton, we show that there s a global abatement level compatble wth the constrant that the sum of the abatement shares s unty and that gven these shares, each country wll choose that level of global abatement as beng optmal. However, there s a producton neffcency due to the dfferentated, countryspecfc, margnal cost of abatement, whch can be solved by mplementng a global permt market. 4.2 Lndahl soluton wth permt market A planner mposng the Lndahl burden rule wll ensure that for each country, the wllngness to pay equals the margnal burden of abatement. A Lndahl planner, also equpped wth the power to nstall a global permt market (LP), wll assgn target abatement shares t L, and gven these target shares, countres choose the same global abatement level A L. Gven a country s assgned target abatement t A L = T, each country maxmzes Ly c ; A ; A L ¼ P u y c ; AL þ λ R P y c C ða Þ q t A L A ð20þ wth respect to consumpton, domestc abatement, and global abatement, gvng ¼ λ ð21aþ L y c ; A ; A L A ¼ λ ½C A q ¼ 0 ð21bþ L y c ; A ; A L A A L ¼ P u A λ C A A L þ q A L t A L A þ q t A A L ¼ 0 ð21cþ 13 In terms of the 2015 Pars agreement, the man achevement s the commtment of all countres to lmt global warmng to well below 2 C, whch corresponds to a global abatement level. In our approach, n the fve yearly global stocktakes, the Bnatonally determned contrbutons^ have to be compared wth the contrbutons specfed by the Lndahl soluton to see where they do not come up to the mark.

12 768 Mtg Adapt Strateg Glob Change (2018) 23: Substtuton of the frst and second nto the thrd frst-order condton and rearrangng gves P u A ¼ A A L ð C A qþþqt þ q A L t A L A whch s smlar to Eq. 7 above. Due to the permt market, the margnal cost of abatement wll never be hgher than the permt prce, so the frst term on the RHS s zero. Therefore, for each country, the margnal rate of substtuton between consumpton and abatement (the LHS of Eq. 22) s proportonal to ts target Bcost^ share (qt ) plus the prce effect of a change n the global abatement level. Takng sums on both sdes gves n ¼1 P u A ¼ q n ¼1 u t þ q y c A L n ¼1 t A L A The last summaton term s zero f the permt market clears, so the Lndahl soluton s effcent f the sum of the target shares sum to unty, n whch case the populaton-weghted sum of the margnal rates of substtuton between abatement and consumpton s equal to the permt prce. Summarzng, the Lndahl soluton algns each country s wllngness to pay and optmal global abatement by adjustng burdens t, but the prce to be pad s that t dsregards any reference to polluter pays or ablty to pay consderatons. To address the queston of farness n terms of contrbutons of rch and poor, we need to look at the optmum condton for each country, gven by Eq. 22. Gven that under a permt market the frst term s zero and that for countres where actual abatement s close to the assgned target abatement level, the last term wll be small and therefore only be of secondary mportance, Eq. 22 can approxmately be wrtten as ð22þ ð23þ P u A t q MSB L MCL T MU L y C ð22 Þ The lower per capta ncome y c s, the hgher margnal utlty of ncome s; so all other thngs equal, the lower the margnal cost share t q s and gven the global permt prce, the lower the assgned target abatement share t ¼ T L =AL s. Therefore, poor countres have to abate lttle, whch s consdered as far accordng to the ablty to pay prncple. Now consder a country wth a hgh margnal socal beneft of abatement (e.g., located at sea level), as gven by the LHS of Eq. 22. The hgher t s, the hgher the assgned target share s, agan gven the permt prce and per capta ncome, so countres more affected or concerned wth clmate change have to abate more, all other thngs equal. Ths s remnscent of the problem of the LE that all countres want to hde ther true preferences wth respect to abatement f assgned shares are proportonal to margnal wllngness to pay. Ths problem however wll not arse f the margnal wllngness to pay for abatement can be assessed on an objectve bass at the country level. 14 In so far as expected damages from clmate change are unrelated to (hstorcal) emssons, the Lndahl soluton s volatng the polluter pays prncple. 14 For nstance, Tol (2002) provdes estmates of the damage of clmate change for nne world regons for the perod of Although the negatve mpacts domnate, for some regons at some ntervals, the total mpact s postve. Also, the Stern Revew (2007, p. 8) states that BIn hgher-lattude regons, such as Canada, Russa, and Scandnava, clmate change may lead to net benefts for temperature ncreases of 2 or 3 C, through hgher agrcultural yelds, lower wnter mortalty, lower heatng requrements, and a possble boost to toursm. But these regons wll also experence the most rapd rates of warmng, damagng nfrastructure, human health, local lvelhoods, and bodversty.^

13 Mtg Adapt Strateg Glob Change (2018) 23: In general, wth heterogeneous preferences, countres that stand to gan from global warmng, so u A < 0, are enttled to a compensaton, e.g., arable land benefts forgone (e.g., n Canada or Russa) f clmate change s contaned and wll have a negatve target share. Countres partcularly vulnerable to clmate change (e.g., the Netherlands, Bangladesh, and slands n the Pacfc Ocean all threatened by a sea level rse) wll be assgned a hgher target contrbuton because of ther hgher values of u A. These country characterstcs, whch determne the country-specfc functon u A, should be assessed on an objectve bass to avod strategc manpulaton of assgned burdens as far as possble. Takng stock, the Lndahl soluton enables the IPCC to secure the achevement of the overall abatement objectve whle at the same tme to assess whether the contrbuton of each country s n lne wth ts wllngness to pay for the global publc good of lmtng global warmng. 5 Smulaton results In ths secton, we compare the outcomes of dfferent regmes of burden sharng rules, especally wth respect to the extent that optmal global abatement levels are acheved and to the amount of transfer payments relatve to the total cost of abatement. For each regme, we measure the level of abatement relatve to the optmal abatement level under lump sum (LS; see Appendx 1). The operatonalzaton of the equlbrum condtons for each regme are explaned n Appendx 2.We measure redstrbuton by the share of the transfer payments made by countres wth a hgher target abatement level than ther actual abatement n global abatement costs. It s measured as TP ¼ q n ¼1;T >A ðt A Þ n ¼1 C ða Þ ð24aþ TP s an ndcator of the share of global abatement costs fnanced by other countres payments on the permt market. For regme LS, n whch per capta ncomes across countres are equalzed and where t does not matter who pays how much, we set TP equal to unty to express that all costs of abatement are shared. If there s no permt market and every country fnances ts own abatement, the ndcator TP s zero by defnton. We also calculate whch part of the total cost of abatement s shouldered by the rch countres 15 (e.g., Annex I, or Europe, Oceana, and North Amerca n case of the fve regons; see below), measured as TC ¼ n ¼1;rch½ q ð T A ÞþC ða Þ n ¼1 C ða Þ ð24bþ Compared to TP, the measure TC also ncludes actual abatement costs. If there s no permt market, then t smply measures the abatement cost shares. We have chosen the parameter α for the relatve mportance of abatement relatve to consumpton and the cost parameter c (see Appendx 2) so that the smulaton results smultaneously yeld plausble margnal abatement cost (n the range of $20 to $80 per tonne CO 2 ), total abatement cost as a share of GDP, and total abatement efforts (e.g., the Stern Revew (Stern 2006) recommends a sgnfcant reducton of 60 80% by the rch countres n 15 Both ndcators overestmate n what they purport to measure, because under the assumpton of ncreasng margnal cost of abatement, the average cost wll always be below the permt prce.

14 770 Mtg Adapt Strateg Glob Change (2018) 23: Table 1. Annex I and II Regon Pop GDP y c E e c e r Annex I , , ,098 Non-Annex I , , ,564 Total (Avg) , , A I A II A T I T II R I R II R N % 40% 38% NP % 50% 42% S % 47% 61% SP % 73% 61% L % 60% 61% LP % 84% 70% LS % 84% 70% y I y II u I u II W q AC TP TC N 37,892 4,934 3,6478 1,6093 1,960 0,017 0% 45% NP 37,832 4,940 3,6476 1,6118 1,962 0,039 0,018 40% 67% S 37,248 4,926 3,6388 1,6158 1,964 0,051 0% 84% SP 37,561 4,940 3,6471 1,6185 1,968 0,064 0,029 59% 85% L 37,650 4,907 3,6495 1,6117 1,962 0,033 0% 58% LP 37,593 4,899 3,6510 1,6131 1,964 0,077 0,034 32% 59% LS 10,525 10,525 2,3779 2,3779 2,378 0,077 0, % 100% BAU N NP S SP L LP LS A 0% 54% 60% 88% 88% 88% 100% 100% TP 0% 0% 40% 0% 59% 0% 32% 100% TC 0% 45% 67% 84% 85% 58% 59% 100% 2050 relatve to 1990). 16 All data are for 2014 and obtaned from CAIT Clmate Data Explorer (Washngton DC, World Resources Insttute 2016) and from EDGAR (2009, European Commsson Jont Research Centre, Netherlands Envronmental Assessment Agency). Table 1 gves an overvew of the scores on salent varables f the world s dvded nto only two blocks, Annex I and Annex II. The Annex I countres comprse the regons Europe and Oceana (EU) and North Amerca (NA). The non-annex I countres comprse the regons sub-saharan Afrca and Mddle East and North Afrca (AF), South Amerca and Central Amerca and Carbbean (SA), and Asa (AS). In Table 2, the results are presented f the world s dvded nto fve regons. The top panel n Table 1 contans the descrptve statstcs: populaton (n mllons), GDP (n bllons USD), ncome per capta, emssons (n Mt.), emsson per capta (n tonnes), emsson ntensty, and the margnal cost adjustment parameter r (see Appendx 2, Eq. 26). Income per capta n Annex I countres s more than seven tmes as hgh as n Annex II countres and emssons per capta s more than three tmes as hgh. In the second panel, (target) levels of abatement and reducton rates are 16 The value for α s set equal to The cost parameter c s set equal to 0.101, double the value used by Nordhaus (1991) and Bohm and Larsen (1994). They use a value for c of 185.2, but snce we express emssons n carbon doxde, where 1 kg carbon corresponds to 3.67 kg CO 2, we get 185.2/3.67 = Snce we measure abatement n Mt. and GDP n bllons, we have to dvde 50.5 by 1000, and doublng (to adjust for nflaton snce the early 90s and ncreasng cost of abatement) gves our chosen value of More specfcally, gven the specfcatons of the utlty functon n Eq. 27 and the margnal cost functon n Eq. 26 n Appendx 2, the choce of the parameters s such that total cost of abatement wll be a small share of GDP, n lne wth the Stern Revew. The Report of the Hgh-Level Commsson on Carbon Prces (2017, p. 3) recommends a carbon prce n the range of $40 $80 by 2020.

15 Mtg Adapt Strateg Glob Change (2018) 23: Table 2. Fve regons (Asa = AS, North Amerca = NA, Europe and Oceana = EU, Afrca and Mddle East = AF, Central and South Amerca = SA) Regon Pop GDP y c E e c e r AS , , ,59 NA , , ,00 EU , , ,14 AF , , ,47 SA , , ,06 All , ,7 443 A AS A NA A EU A AF A SA A N NP S SP L LP LS R AS R NA R EU R AF R SA R N 32% 17% 19% 8% 6% 23% NP 23% 14% 12% 21% 13% 19% S 53% 98% 75% 34% 48% 63% SP 77% 48% 42% 71% 45% 63% L 59% 65% 62% 63% 63% 61% LP 85% 53% 46% 78% 50% 70% LS 85% 53% 46% 78% 50% 70% y AS y NA y EU y AF y SA q AC N 5,650 53,865 28,154 3,655 9,955 0,0105 NP 5,647 53,814 28,103 3,693 10,042 0,0156 0,0076 S 5,621 52,391 27,779 3,646 9,911 0,0501 SP 5,634 53,106 27,913 3,662 9,911 0,0664 0,0296 L 5,610 53,424 27,936 3,621 9,870 0,0328 LP 5,600 53,352 27,892 3,616 9,856 0,0771 0,0337 LS 10,525 10,525 10,525 10,525 10,525 0,0771 0,0337 u AS u NA u EU u AF u SA W TP TC N 1,740 3,995 3,346 1,304 2,306 2,001 0% 28% NP 1,738 3,992 3,342 1,313 2,313 2, % 177% S 1,748 3,980 3,346 1,315 2,315 2,008 0% 80% SP 1,751 3,994 3,351 1,320 2,315 2,011 53% 78% L 1,746 3,999 3,351 1,308 2,311 2,006 0% 53% LP 1,747 4,001 3,352 1,309 2,312 2,007 32% 53% LS 2,378 2,378 2,378 2,378 2,378 2, % 100% T AS T NA T EU T AF T SA T NP SP LP BAU N NP S SP L LP LS A 0% 33% 27% 90% 90% 88% 100% 100% TP 0% 0% 238% 0% 53% 0% 31,7% 100% TC 0% 28% 177% 80% 78% 53% 53% 100%

16 772 Mtg Adapt Strateg Glob Change (2018) 23: gven, where we take the actual emsson levels n 2014 as the busness-as-usual outcome (whch mples that the Nash outcome s the one where Annex I and I operate as blocks). Frstly, total abatement wth a permt market under the same regme s always hgher or equal (total abatement under S and SP are set equal by assumpton) than wthout. Secondly, n the shft from N to NP, the Annex II target abatement level under Nash wth a permt market s even below ts actual abatement wthout a permt market. Ths result can be explaned by polarzaton, also descrbed by Cramton and Stoft (2010, p. 6), where the rch wll choose an even hgher target level because abatement can be bought more cheaply under a permt market, whle the poor regon wll choose an even lower target level of abatement to beneft from permt tradng. Thrdly, total abatement under the socal planner, wthout (S) or wth (SP) a permt market, s hgher than under Lndahl (L). Ths s because assgnng abatement burdens has a dual role for the socal planner SP, not only to mtgate global warmng but also to redstrbute ncome or welfare. In case of S, Annex I s assgned a very hgh abatement burden (a reducton rate of 84%, aganst only 47% for Annex II), because the welfare cost of abatement for the rch countres are relatvely small, whle the benefts of abatement are global. The thrd panel gves nformaton about per capta ncomes (y), utlty (u), world welfare (W), the permt prce (q), average abatement cost (AC), the share of total abatement cost pad for by transfers (TP), and the share n total cost of buyers on the permt market (TC). Not surprsngly, global per capta welfare s at maxmum n the lump sum case, but t would not be acceptable for Annex I. Departng from regme N, Annex I would even not be n favor to move to regme NP (due to the polarzaton effect), nor to S or SP. The only transtons that ncrease utlty for Annex I are the Lndahl regmes L and LP. For Annex II, all other regmes than N are better n utlty terms,wheresandsparepreferredtolandlp.takentogether,departngfromn, only L and LP are Pareto mprovements and LP Pareto domnates L, so LP would be a vable outcome. 17 The equlbrum permt prce under LP s bllon per Mt. CO 2, whch corresponds to $77 per tonne, whle average abatement cost per tonne s $34 (due to ncreasng margnal costs of abatement, average cost s below margnal cost). The last panel gves total abatement relatve to (optmal) abatement (A), the share of total abatement cost fnanced by permts (TP), and the share of the total cost of abatement taken care of by the rch countres (TC). The frst two of these measures are llustrated n Fg. 1a, b. Apart from LS, there are four regmes that delver abatement equal or close to the optmal level under LS. Producton effcency requres the regmes wth permt markets. Among the permt market choce set {NP, SP, LP}, LP combnes that abatement s at the optmal level and transfer payments as a share of total costs are at mnmum. Takng stock, LP (L) are the only regmes 17 Buchholz et al. (2006, p. 33) show that a move from Nash to Lndahl does not necessarly ental a Pareto mprovement because of two countervalng effects. Frst, all countres wll gan n terms of benefts derved from overcomng the sub-optmal low Nash provson level of the publc good. Second, the move from Nash to Lndahl mght however ental hgher costs for some (poor) countres, notably f under the Nash outcome they were free-rdng on the contrbutons of others (often manfested n the form of explotaton of the rch by the poor). The second effect may outwegh the frst effect, whch s more lkely the poorer the country s (the more t was easy-rdng under Nash) and the hgher ts margnal preference for abatement (the hgher ts assgned burden under Lndahl), but as the number of partcpatng countres ncrease, t becomes more lkely that the frst effect wll be domnant.

17 Mtg Adapt Strateg Glob Change (2018) 23: Fg. 1 a Abatement versus net transfer payments. b Abatement versus total abatement cost, Annex I that are Pareto-superor to N and combnng (near) optmal abatement levels wth modest (zero) redstrbuton payments. In Table 2, the world s dvded n fve blocks. CAIT standardly provdes a dvson nto the eght geographcal regons, Asa (AS), Europe (EUR), Mddle East and North Afrca (ME), sub-saharan Afrca (AFR), North Amerca (NA), Central Amerca and Carbbean (CAM), South Amerca (SAM), and Oceana (OC). In Table 2, ME and AFR are merged nto AF, CAM, and SAM nto SA and OC and EUR nto EU. In ths dvson, two are rch (North Amerca and Europe wth Oceana) and two are poor (Asa and Afrca), wth Central and South Amerca n between. Because there are now more players, total abatement levels under Nash are almost halved compared to when Annex I and II operate as blocks. Departng from N, agan only L and LP are Pareto mprovements for all regons and LP Pareto domnates L. A strkng outcome n Table 2 s that for both Afrca and South Amerca, t s optmal to choose negatve target abatement levels. The extreme polarzaton leads here to the stuaton that under NP total abatement s even lower than under N, despte the effcency gans of a permt market. Note

18 774 Mtg Adapt Strateg Glob Change (2018) 23: Fg. 2 a Abatement versus net transfer payments. b Abatement versus total abatement cost, EU and North Amerca that under regme NP, each player s free to choose ts optmal target level. Net revenues from the permt market equals q(a T ), so although South Amerca abates 240 Mt., by choosng a target level of 3333 Mt. and sellng permts for the equlbrum prce of $15.6 per tonne, t receves $55.7 bllon on the permt market, whle Afrca receves $60.6 bllon. 18 Asa (due to ts hgh populaton), North Amercan, and Europe and Oceana (due to ther hgh per capta ncomes) together pay n total bllon (ther combned target abatement levels of 13,022 Mt. mnus ther combned actual abatement of 5558 Mt., tmes $15.6 per tonne), whereas total abatement cost s only 49 bllon (total abatement under NP equal to 6451 Mt. tmes average cost of $7.6 per tonne). The man reason for the outler poston of regme NP n Fg. 2a, b s that transfer payments under NP outwegh total abatement cost, whch s not so much due that the average cost of abatement s below the permt prce or margnal cost, but because of polarzaton. 18 Hof et al. (2010) argue that these net transfers can be consdered as compensaton for more severe clmate change damages and hgher adaptaton costs n, for nstance, Afrca.

19 Mtg Adapt Strateg Glob Change (2018) 23: Not surprsngly, total reducton levels (R) for the other regmes are almost equal compared to under Annex I and II. Apart from the locaton of N, shftng downwards and NP, shftng downwards and to the rght, Fg. 2a, b therefore gves the same confguraton of regmes as n Fg. 1a, b, where regme LP combnes optmal abatement wth modest transfer payments as a percentage of total cost Summary and conclusons The Pars agreement of 2015 entals that both developed and developng countres lmt ther emssons, wth 5-yearly revews to ensure that natonal contrbutons are n lne wth the overall goal to reach at maxmum 2 C global warmng, wth an aspraton of 1.5 C. In ths paper, the abatement burden sharng rules emergng under dfferent regmes, wth and wthout permt markets, were derved. The sub-optmal level under Nash wthout permt market s due to both producton neffcences n abatement and not takng global externaltes of natonal abatement nto account. The frst sub-optmalty can be removed by nstallng a permt market, but the second requres cooperaton or coordnaton between countres. A socal planner wthout the power to redstrbute and wthout a permt market wll mpose the rule that the product of the margnal cost of abatement and the margnal utlty of ncome be equalzed across countres. Ths mples hgh abatement burdens and (margnal) costs for rch and low burdens and costs for poor countres, wth the overall abatement level close to optmal. The same socal planner but equpped wth a permt market can organze transfer payments from rch to poor by assgnng hgh target levels to rch and low target levels to poor regons. The burden sharng rule then has a secondary role of redstrbuton and wthout any constrant the socal planner s outcome wll be the same as under an omnpotent socal planner wth lump sum redstrbuton. In the smulatons, we showed that the transton to a permt market under Nash can lead to polarzaton, eventually leadng to lower overall abatement as shown for the world dvded nto fve regons. Although poor countres prefer the socal planner regme wth permts the most, only the Lndahl regmes Pareto domnate the Nash regmes, wth or wthout a permt market. Moreover, of all permt regmes, the Lndahl permt market entals the lowest degree of redstrbuton n the form of net transfer payments from rch to poor. Our preferred burden sharng rule can be summarzed as that every country or regon shares n the burden to combat clmate change n proporton to ts benefts, whch are determned by the expected damages and adaptaton costs. The burden sharng rule mpled by the Lndhahl soluton therefore provdes a crteron to assess the natonal contrbutons to curb clmate change. The Lndahl soluton smultaneously acheves an optmal global abatement level and that each country s expected to contrbute accordng to ts wllngness to pay, but the prce to be pad s to dsregard competng prncples such as ablty to pay and the polluter has to pay. In our analyss, we only dfferentated countres by ther ncome per capta and populaton sze. Avenues for further research are to relate the Lndahl soluton and the correspondng abatement burdens to country- or regon-specfc expected damages and assocated adaptaton costs from 19 Although t s possble to further dsaggregate the smulaton to the ndvdual country level, under the assumptons made the shft from N to LP wll be a Pareto mprovement because the postve effect of the hgher abatement level under Lndahl compared to Nash wll be even stronger than when the world s dvded nto two or fve regons.