The marginal costs of climate changing emissions

Transcription

1 Instituut voor Milieuvrgstukken / Institute for Environmentl Studies The mrginl costs of climte chnging emissions Richrd S.J. Tol nd Thoms E. Downing b b Institute for Environmentl Studies, Vrije Universiteit, Amsterdm, The Netherlnds nd Center for Integrted Study of the Humn Dimensions of Globl Chnge, Crnegie Mellon University, Pittsburgh, PA, USA Environmentl Chnge Unit, University of Oxford, Oxford, United Kingdom D-00/08 September 2000

2 IVM Institute for Environmentl Studies Vrije Universiteit De Boeleln HV Amsterdm Tel Fx E-mil: Copyright 2000, Institute for Environmentl Studies All rights reserved. No prt of this publiction my be reproduced, stored in retrievl system or trnsmitted in ny form or by ny mens, electronic, mechnicl, photocopying, recording or otherwise without the prior written permission of the copyright holder.

3 The mrginl costs of climte chnging emissions i Contents 1. Introduction 2 2. Models Open Frmework FUND FUND Conventions for vlution nd reporting Discounting Aggregtion 7 4. Crbon dioxide, methne nd nitrous oxide 9 5. Uncertinty Ozone nd sulphte erosols Conclusion 20 References 22 Appendix I. Uncertinty in FUND I.1 Bsic ssumptions 24 I.2 Excerpts from Tol (1999) 25 I.3 Excerpts from Tol (1999b) 26 I.4 Excerpts from Tol (1999c) 28

4 The mrginl costs of climte chnging emissions 2 1. Introduction This pper presents the mrginl costs of the emissions of selected number of rditivelyctive gses, three uniformly-mixed gses crbon dioxide, methne, nitrous oxide nd two region-specific gses nitrogen (from ircrft) nd sulphur, which influence ozone nd sulphte erosol concentrtions, respectively. Eyre et l. (1997) extensively discuss the literture on climte chnge impct estimtion nd vlution, nd estimte the mrginl costs of CO 2, CH 4 nd N 2 O, including substntil sensitivity nd uncertinty nlyses (cf. Perce et l., 1996; Tol, 1999). This pper does not repet Eyre et l. (1997), but rther complements it by dding third model (FUND2.0), dding region-specific gses, nd by presenting n lterntive ccounting frmework.

5 The mrginl costs of climte chnging emissions 3 2. Models Three models re used in this nlysis, viz. the Open Frmework for Economic Vlution of Climte Chnge (OF), developed by Downing et l. (1995, 1996), nd two versions of the Climte Frmework for Uncertinty, Negotition nd Distribution (FUND), developed by Tol (1995, 1996) nd Tol (1999b,c), respectively. The models re briefly presented here. 2.1 Open Frmework The Open Frmework for Economic Vlution of Climte Chnge (Downing et l. 1995, 1996) follows sequence of steps in clculting economic dmges. A reference scenrio, bsed on the IPCC 1992 scenrio, is used to project economic conditions, sensitivity to climtic vritions nd the climte forcing ofglobl GHG emissions. Globl-verge temperture chnge nd se level rise re clculted by the 1995 version of MAGICC (Wigley et l., 1993). MAGICC is reltively simple upwelling-diffusion, energy blnce climte model tht distinguishes between lnd nd ocen nd between hemispheres. In ll cses, MAGICC s defult prmeters re used. Sptil scenrios of climte chnge re bsed on the 2xCO 2 equilibrium run of the generl circultion model experiment from the Goddrd Institute of Spce Sciences (GISS). The GCM scenrio ws scled to the globl-verge temperture projection from MAGICC. This results in time-dependent climte chnge scenrio consistent with the ssumptions of the globl emissions. The sptil pttern of nomlies from the GISS equilibrium scenrio is retined, however. Simple impct models re run for the current climte nd for the scenrio of climte chnge. The bseline climte is bsed on the 0.5 degree ltitude by longitude climtology of Crmer nd Leemns (1994). Climte prmeters for the bseline re men monthly temperture nd precipittion for the period of record. These methods of creting scenrios re common in climte chnge impct ssessment (see Viner nd Hulme, 1994). The impct vribles include heting nd cooling degree dys, griculturl suitbility, nd wter blnce. They re extrcted to provide country-verge vlues. The model clcultes costs for seven time slices from 1990 to However, the sptil impcts re only clculted for 1990 (the bse yer) nd 2100, scling the simple impct indictors for intervening time periods ccording to chnges in the globl men temperture. For costl impcts (costl protection, loss of wetlnds, loss of drylnds, migrtion nd biodiversity), griculture, energy demnd nd wter, country-level economic impcts re derived from the reference projections, simple impct models, nd climte sensitivity-cost equtions. The equtions vry in form, depending on the vilbility of previous sectorl studies. Most include chnges in supply (from the simple impct models), projected prices (or vlue of production) nd the sensitivity of demnd to chnges in supply or price. The impcts of nturl dissters re only clculted t globl-verge level.

6 The mrginl costs of climte chnging emissions 4 The country-level direct costs re summed to globl totl. An dditionl globl cost, representing higher order, non-mrket effects, is clculted s multiplier on the net dmges (i.e. not including the positive impcts of climte chnge). This is done to provide n estimte of the totl cost of climte chnge, rther thn only the costs tht hve been cptured by the sectorl models. The used sclr corresponds to the rtio of non-mrket to mrket costs in other models (such s FUND), but is still subjective estimte of the potentil dmges to other 2.2 FUND 1.6 The Climte Frmework for Uncertinty, Negotition nd Distribution (FUND) is model tht closes the loop popultion economy technology greenhouse gs emissions tmospheric composition climte climte chnge impcts emission btement. Using simple representtions of these components, the model runs in time steps of one yer from 1950 to 2200, for nine mjor world regions. The fct tht FUND is ble to perform cost-benefit nlysis -- with multiple ctors nd under uncertinty implies tht the impct module is subject to strict demnds on computtionl speed. FUND ws developed to compre the impcts of climte chnge ginst the impcts of greenhouse gs emission btement. Here, the min interest is in the climte chnge impct module. This is described in Tol (1995, 1996), nd pplied to estimte the mrginl costs of greenhouse gs emissions in Eyre et l. (1998) nd Tol (1999). A stndrd five-box crbon cycle model (cf. Hmmitt et l., 1992) is used for crbon dioxide concentrtions in the tmosphere. The influence of methne nd nitrous oxide emissions on concentrtions geometriclly declines over time, with life-times ccording to Schimel et l. (1996). Other humn disturbnces of climte re omitted. Chnges in rditive forcing follow from Shine et l. (1990). Rditive forcing drives the equilibrium chnge in the globl men temperture, to which ctul temperture geometriclly converges. Actul temperture determines equilibrium se level rise, to which ctul se level rise geometriclly converges. Equilibrium sensitivities nd convergence rtes re clibrted to the typicl outcomes of simple climte models (cf. Kttenberg et l., 1996). Impct of climte chnge I t t time t is modelled s either: or I = α W + β W 2 t t t t t I t = αt Wt + βt W 2 t + ρi t 1 with W n pproprite climte vrible, nd α, β nd ρ prmeters. W my be the globl men surfce ir temperture, or the globl men se level. The prmeters α nd β differ per impct ctegory, nd depend on griculturl production, per cpit income, nd urbnistion (cf. Tol, 1996). Impct I is mesured either in percentge of Gross Domestic Product, or in percentge of popultion. In the ltter cse, climte chnge induced mortlity is vlued t 200 times the per cpit income in the relevnt region t the relevnt time for ech csulty.

7 The mrginl costs of climte chnging emissions FUND 2.0 The impct module of FUND1.6 reflects the insights into the effects of climte chnge of the first hlf of the 1990s, s lid down in the Second Assessment Report of the IPCC (Perce et l., 1996; Wtson et l., 1996). These insights hve substntilly chnged since. Wheres erlier studies emphsised the negtive impcts of climte chnge, lter studies incresingly found positive spects s well (Mendelsohn nd Neumnn, 1999), for exmple in energy consumption nd griculture. Other developments include the extension of studies to new sectors nd new countries, better inclusion of dpttion, better integrtion of sectors, nd the ddition of more dynmics. These chnges re reflected in the climte chnge impct module of FUND2.0, which is complete revision of the impct module of FUND1.6. FUND2.0 is described in Tol (1999b,c). There re four resons why version 2.0 is plced longside version 1.6, rther thn replcing it: 1. FUND2.0 is currently being peer-reviewed wheres FUND1.6 ws published in the scientific literture; 2. FUND1.6 is known, inter li from previous ExternE pplictions; 3. the revision of FUND2.0 ws so extensive tht it is lmost completely different model; nd 4. lthough FUND1.6, reflecting erlier impct literture, my be too pessimistic bout climte chnge, FUND2.0, reflecting more recent literture, my be too optimistic.

8 The mrginl costs of climte chnging emissions 6 3. Conventions for vlution nd reporting 3.1 Discounting Climte chnge is problem of the long term. Discounting is therefore of utter importnce (cf. Arrow et l., 1996). There re four resons to discount the future: 1. Imptience, or myopi. People prefer current consumption over lter consumption. 2. Economic growth. If people re richer in the future, dollr now hs greter (reltive) vlue thn dollr lter. 3. Chnging reltive prices. Certin impcts, such s on humn helth, my well be vlued higher in the future. 4. Uncertinty. Becuse future consumption is less certin, it is worth less. Arguments 1, 2, nd 4 cll for positive discount rte (i.e., one tht plces more weight on the ner thn on the fr future). Argument 3 my cll for negtive discount rte. Arguments 3 nd 4 re improper rguments for discounting. Chnges in reltive prices re better explicitly modelled thn included in the discount rte, primrily for resons of trnsprency. Similrly, it is better to include uncertinty explicitly, rther thn to short cut it through tinkering with the discount rte. The Open Frmework nd FUND model chnges in reltive prices. FUND includes uncertinty, the OF reports low, middle nd high estimtes. The discount rte thus consists of the first two elements only. In the stndrd neo-clssicl formultion the discount rte r follows from: r = ρ + η g, with ρ the pure rte of time preference, η the consumption elsticity of mrginl utility, nd g the growth rte of per cpit consumption. Here, η=1, tht is, utility is proportionl to the nturl logrithm of consumption. The growth rte of per cpit consumption g is ssumed to equl the growth rte of per cpit income. The pure rte of time preference ρ vries between 0%, 1%, nd 3% per yer. 0% is preferred on morl grounds (Rmsey, 1928; Koopmns, 1967) nd in line with sustinbility (Broome, 1992; Brown, 1997). 3% is observed on mrkets (Nordhus, 1994). 1% is n rbitrry vlue in between, tht will be used for our centrl estimtes below. Tble 1 displys the ssumed growth rtes per region. Although ll nlyses re bsed on the IS92 scenrio, the different models hd to mke different ssumptions to fit this to their different sptil nd temporl resolutions. In ddition, the feedbck of climte chnge on economic nd popultion growth is different cross the models.

9 The mrginl costs of climte chnging emissions 7 Tble 1 Assumed regionl per cpit income growth rtes. FUND1.6 b FUND2.0 Open Frmework vg. min. mx. vg. Min. mx. vg. min. mx. OECD-A OECD-E OECD-P CEE&fSU ME LA S&SEA CPA AFR World The tble shows verge, minimum nd mximum growth rtes per decde for the period b FUND llows for different growth rtes s prt of its uncertinty nlysis, ssuming Norml distribution with coefficient of vrition of 20%. 3.2 Aggregtion Impcts of climte chnge re vlued t ntionl or regionl prices in both the Open Frmework nd FUND. When ggregted, this my be objectionble becuse, for exmple, life lost in Bngldesh counts less thn life lost in Germny. Altering vlues, however, would undermine the theoreticl foundtions of monetiztion nd yield inconsistencies between ntionl nd interntionl environmentl policies (Fnkhuser et l., 1998). Therefore, the ggregtion of monetized impcts is chnged, using so-clled equity weights (Fnkhuser et l., 1997). The frmework of Fnkhuser et l. (1997) ssumes globl decision mker. The udience of the ExternE project, however, is Europen decision mker. The economic theory of how one decision mker vlues impcts in other thn her own country is underdeveloped. An d hoc solution is therefore chosen, inspired by the equity-weights of Fnkhuser et l. (1997). Four lterntives re reported here: 1. EU impcts only, with EU vlues ( EU only ); 2. 1, plus impcts in other regions with locl vlues ( regionl vlues ); 3. 1, plus impcts in other regions with globlly verged vlues ( world verge ); 4. 1, plus impcts in other regions with EU vlues ( EU vlues ). The lterntives re ordered in terms of estimted severity of the mrginl cost estimtes. Alterntive 1 ignores impcts outside the EU, closest to relpolitik. Alterntive 2 is bsed on the expressed willingness-to-py of people outside of the EU, but suffers from the welfreeconomic inconsistencies induced by ggregting money mesures over people with very different incomes. Alterntive 3 rgues from the perspective of benevolent world leder. Alterntive 4 rgues from the morl perspective of Europen decision mker inclined to Knt. We reject lterntive 2 s internlly inconsistent (but do report the outcomes), nd use lterntive 3 in between lterntives 1 nd 4 for our centrl estimtes below.

10 The mrginl costs of climte chnging emissions 8 Alterntives 3 nd 4 re pproximted to void expensive reprogrmming of FUND. Impcts in other regions re vlued t locl levels. In ggregting, impcts re weighted with the rtio of world nd EU per cpit income, respectively, over regionl per cpit income. Open Frmework estimtes re pproximted using the period, sector nd region impcts for slightly different reporting conventions.

11 The mrginl costs of climte chnging emissions 9 4. Crbon dioxide, methne nd nitrous oxide Tble 2 presents the mrginl costs of crbon dioxide emissions. Ptterns re cler nd obvious. The more weight one plces t impcts outside the Europen Union, the higher the mrginl cost. The higher the discount rte, the lower the mrginl cost. The regionl nd temporl ptterns of the three models re quite different. FUND1.6 finds lowest mrginl costs for the EU, FUND2.0 highest, nd the Open Frmework lies somewhere in between. This pttern chnges if more weight is plced on the rest of the world, depending on the discount rte. Tble 2 The mrginl costs of crbon dioxide emissions (in $/tc). EU only regionl vlues world verge EU vlues FUND1.6 0% PRTP % PRTP % PRTP FUND2.0 0% PRTP % PRTP % PRTP Open Frmework 0% PRTP % PRTP % PRTP Emissions re in the period Costs re discounted to Time horizon is Scenrio is IS92. Morbidity risks re vlued bsed on the vlue of sttisticl life. Tble 3 The mrginl costs of nitrous oxide emissions (in $/tn 2 O). EU only regionl vlues world verge EU vlues FUND1.6 0% PRTP , , , % PRTP , , , % PRTP , , ,155.2 FUND2.0 0% PRTP , , , % PRTP , , % PRTP Open Frmework 0% PRTP 1, , , , % PRTP , , , % PRTP , , ,256.4 Emissions re in the period Costs re discounted to Time horizon is Scenrio is IS92. Morbidity risks re vlued bsed on the vlue of sttisticl life. Tble 3 displys the results for nitrous oxide. The ptterns re similr to those for crbon dioxide. However, FUND2.0 finds positive mrginl impct for 3% discount rte for regionl vlues: Short-term benefits to reltively rich regions outside the EU dominte the

12 The mrginl costs of climte chnging emissions 10 globl estimte. Exmples re the positive impct of climte chnge on griculture in the USA nd Chin. Tble 4 presents the mrginl cost estimtes for methne. The Open Frmework now finds the highest mrginl costs to the EU. FUND2.0 finds mrginl benefits in number of cses, reflecting its ssumption tht climte chnge is, in the short run, good for number of sectors nd countries. Tble 4 The mrginl costs of methne emissions (in $/tch 4 ). EU only regionl vlues World verge EU vlues FUND1.6 0% PRTP , % PRTP , % PRTP ,086.5 FUND2.0 0% PRTP % PRTP % PRTP Open Frmework 0% PRTP , % PRTP % PRTP Emissions re in the period Costs re discounted to Time horizon is Scenrio is IS92. Morbidity risks re vlued bsed on the vlue of sttisticl life. Tble 5 The mrginl costs of greenhouse emissions ccording to FUND2.0. EU only Regionl vlues World verge EU vlues Crbon dioxide ($/tc) 0% PRTP % PRTP % PRTP Nitrous oxide ($/tn 2 O) 0% PRTP , , % PRTP , % PRTP ,163.6 Methne ($/tch 4 ) 0% PRTP % PRTP % PRTP Emissions re in the period Costs re discounted to Time horizon is Scenrio is IS92. Morbidity risks re vlued bsed on the vlue of yer life lost. Tble 5 presents the results of FUND2.0 if mortlity is vlued not on the bsis of vlue of sttisticl life (200 times per cpit income) but rther t vlue of life yer lost (10 times per cpit income, per yer). Crdiovsculr nd respirtory diseses, for which reltively little life-time is lost, dominte in the rich regions, do YOLL methodology leds to substntilly lower mrginl costs thn does the VOSL methodology. The gp closes if more

13 The mrginl costs of climte chnging emissions 11 weight is plced on developing countries, where vector-borne diseses, for which more lifetime is lost, dominte. The sectorl brekdown of the mrginl costs of crbon dioxide is given in Tble 6. Tble 6 Sectorl brekdown of the estimted mrginl costs of crbon dioxide (cf. Tble 5). EU only Regionl vlues World vlues EU vlues 0% Wter 15.4% 178.0% 71.6% 77.2% Forestry -1.2% -0.9% -0.5% -0.5% Energy 60.5% -34.7% 31.3% 28.1% Agriculture 22.2% 1.8% -0.4% -1.9% Cost 2.8% 3.2% 2.6% 2.5% Migrtion 0.2% 0.1% 0.1% 0.1% Species 0.0% -0.1% 0.0% 0.0% Mortlity 0.0% -47.5% -4.6% -5.5% 1% Wter 15.3% 129.2% 68.9% 74.5% Forestry -1.2% -0.7% -0.6% -0.5% Energy 63.2% -28.9% 30.9% 27.6% Agriculture 19.2% 1.0% -0.9% -2.2% Cost 3.2% 2.8% 3.3% 3.2% Migrtion 0.2% 0.1% 0.1% 0.1% Species 0.0% -0.1% 0.0% 0.0% Mortlity 0.0% -3.5% -1.7% -2.7% 3% Wter 15.0% 66.9% 62.7% 68.0% Forestry -1.2% -0.4% -0.6% -0.6% Energy 67.9% -19.0% 27.6% 24.3% Agriculture 14.2% 0.3% -1.7% -2.7% Cost 3.9% 2.0% 4.8% 4.7% Migrtion 0.3% 0.1% 0.1% 0.1% Species -0.1% -0.1% 0.0% 0.0% Mortlity 0.0% 50.1% 7.2% 6.3%

14 The mrginl costs of climte chnging emissions Uncertinty Uncertinties bound in climte chnge. The uncertinties bout the impct of climte chnge re estimted in Tol (1999,b). These re confounded by uncertinties bout the scenrios (which expnd through time) nd bout the workings of the climte system. The exct specifiction cn be found in the Appendix. The uncertinty nlysis is restricted to prmetric uncertinty. The uncertinties reflect the rnges found in the literture. Thus, the uncertinty clculted below is lower bound to the true uncertinty. This prticulrly holds for the uncertinties bout the impcts of climte chnge. The literture on tht is thin (excepting griculture), nd rnges re therefore nrrow. Tble 7 The uncertinty bout the mrginl costs of crbon dioxide (in $/tc) ccording to FUND2.0. EU only Regionl vlues World verge EU vlues 0% PRTP Centrl est Men Medin Std. Dev Geom. Men b 1.2 n Geom. Std. Dev. c 1.8 n % PRTP Centrl est Men Medin Std. Dev Geom. Men 0.7 n Geom. Std. Dev. 1.8 n % PRTP Centrl est Men Medin Std. Dev Geom. Men 0.3 n Geom. Std. Dev. 1.8 n Emissions re in the period Costs re discounted to Time horizon is Scenrio is IS92. Morbidity risks re vlued bsed on the vlue of yer life lost. The sttistics re bsed on Monte Crlo experiment with 1,000 runs. The ssumed probbility density functions re given in the Appendix. b The geometric men is the exponent of the men of the nturl logrithms of the observtions. n.. stnds for not pplicble becuse there re negtive mrginl costs in the smple. c The geometric stndrd devition is the exponent of the stndrd devition of the nturl logrithm of the observtions. If the observtions re lognormlly distributed, the 95% confidence intervls rnges from the geometric men divided by twice the geometric stndrd devition Tble 7 displys the results for crbon dioxide for Monte Crlo nlysis with 1,000 runs. All results re bsed on the yers of life lost methodology for morbidity risks. Figure 1 de-

15 The mrginl costs of climte chnging emissions 13 picts the uncertinty bout the mrginl costs of crbon dioxide emissions for 1% PRTP nd world verge vlues. The uncertinty is lrge nd right-skewed. The probbility density cn be resonbly pproximted with lognorml distribution (the line in Figure 1). In cse regionl vlues re used, the mrginl costs my be negtive (i.e., benefits). In this cse, the positive impcts of climte chnge on the USA, the former Soviet Union nd Jpn my dominte the negtive impcts on other regions frequency dollr per tonne of crbon Figure 1 Uncertinty bout the mrginl costs of crbon dioxide emissions for 1% PRTP nd world verge vlues. Source: FUND2.0; see Tble 7. As sensitivity nlysis, nd to emphsise the rel uncertinties, Tble 8 displys wht hppens if the time horizon is extended from 2100 to The uncertinties get relly lrge in the 22 nd century, prtly becuse of the uncertinty bout the scenrios nd prtly becuse prmeter uncertinties ccumulte over time. The result is tht it cnnot be excluded tht some economies collpse, for climte chnge or other resons. If per cpit income shrply declines, the discount rte becomes negtive, nd smll chnges in impcts re mplified in the net present vlue. This effect cn be quite drmtic, nd substntilly increse the estimted mrginl cost. However, the model ws not designed for such extreme scenrios, so this result is model rtefct rther thn genuine finding. Compring the centrl estimtes of Tbles 7 nd 8, we see tht there re substntil impcts of emissions in the period in the 22 nd century. The outcomes of the Monte Crlo experiment re trimmed, tht is, the highest nd lowest 5% re removed. Nevertheless, we observe n even lrger increse in the men estimte, nd substntil increse in the uncertinty, prticulrly for world vlues nd EU vlues nd low discount rte.

16 The mrginl costs of climte chnging emissions 14 Tble 8 Uncertinty bout the mrginl costs of crbon dioxide emissions (in $/tc) with time horizon up to 2200, ccording to FUND2.0. EU only Regionl vlues World vlues EU vlues 0% PRTP Centrl est Men Medin Std. Dev Geom. Men b Geom. Std. Dev. c % PRTP Centrl est Men Medin Std. Dev Geom. Men Geom. Std. Dev % PRTP Centrl est Men Medin Std. Dev Geom. Men 0.3 n Geom. Std. Dev. 1.6 n Emissions re in the period Costs re discounted to Time horizon is Scenrio is IS92. Morbidity risks re vlued bsed on the vlue of yer life lost. The sttistics re bsed on Monte Crlo experiment with 1,000 runs. Results re trimmed for the top nd bottom 5%. The ssumed probbility density functions re given in the Appendix. b The geometric men is the exponent of the men of the nturl logrithms of the observtions. n.. stnds for not pplicble becuse there re negtive mrginl costs in the smple. c The geometric stndrd devition is the exponent of the stndrd devition of the nturl logrithm of the observtions. If the observtions re lognormlly distributed, the 95% confidence intervls rnges from the geometric men divided by twice the geometric stndrd devition to the geometric men times twice the geometric stndrd devition. Tble 9 nd Figure 2 disply the results for nitrous oxide. The findings re similr s those for crbon dioxide in Tble 7.

17 The mrginl costs of climte chnging emissions 15 Tble 9 The uncertinty bout the mrginl costs of nitrous oxide (in $/tn 2 O) ccording to FUND2.0. EU only Regionl vlues World verge EU vlues 0% PRTP Centrl est , ,242.1 Men , ,010.6 Medin , ,613.2 Std. Dev , ,213.0 Geom. Men b n.. 1, ,872.8 Geom. Std. Dev. c 1.8 n % PRTP Centrl est ,967.7 Men ,826.5 Medin ,129.8 Std. Dev ,639.9 Geom. Men 61.8 n ,276.1 Geom. Std. Dev. 1.8 n % PRTP Centrl est ,163.6 Men ,366.6 Medin ,181.3 Std. Dev Geom. Men 24.9 n ,212.6 Geom. Std. Dev. 1.8 n Emissions re in the period Costs re discounted to Time horizon is Scenrio is IS92. Morbidity risks re vlued bsed on the vlue of yer life lost. The sttistics re bsed on Monte Crlo experiment with 1,000 runs. The ssumed probbility density functions re given in the Appendix. b The geometric men is the exponent of the men of the nturl logrithms of the observtions. n.. stnds for not pplicble becuse there re negtive mrginl costs in the smple. c The geometric stndrd devition is the exponent of the stndrd devition of the nturl logrithm of the observtions. If the observtions re lognormlly distributed, the 95% confidence intervls rnges from the geometric men divided by twice the geometric stndrd devition to the geometric men times twice the geometric stndrd devition.

18 The mrginl costs of climte chnging emissions frequency dollr per tonne of nitrous oxide Figure 2 Uncertinty bout the mrginl costs of nitrous oxide emissions for 1% PRTP nd world verge vlues. Source: FUND2.0; see Tble 9. Tble 10 nd Figure 3 disply the results for methne. The uncertinty is lrge nd rightskewed, but the lognorml pproximtion is not very good.

19 The mrginl costs of climte chnging emissions 17 Tble 10 The uncertinty bout the mrginl costs of methne (in $/tch 4 ) ccording to FUND2.0. EU only Regionl vlues World verge EU vlues 0% PRTP Centrl est Men Medin Std. Dev Geom. Men b 5.8 n Geom. Std. Dev. c 1.7 n % PRTP Centrl est Men Medin Std. Dev Geom. Men 3.9 n Geom. Std. Dev. 1.7 n % PRTP Centrl est Men Medin Std. Dev Geom. Men 2.1 n Geom. Std. Dev. 1.7 n Emissions re in the period Costs re discounted to Time horizon is Scenrio is IS92. Morbidity risks re vlued bsed on the vlue of yer life lost. The sttistics re bsed on Monte Crlo experiment with 1,000 runs. The ssumed probbility density functions re given in the Appendix. b c The geometric men is the exponent of the men of the nturl logrithms of the observtions. n.. stnds for not pplicble becuse there re negtive mrginl costs in the smple. The geometric stndrd devition is the exponent of the stndrd devition of the nturl logrithm of the observtions. If the observtions re lognormlly distributed, the 95% confidence intervls rnges from the geometric men divided by twice the geometric stndrd devition to the geometric men times twice the geometric stndrd devition.

20 The mrginl costs of climte chnging emissions frequency Figure dollr per tonne of methne Uncertinty bout the mrginl costs of methne emissions for 1% PRTP nd world verge vlues. Source: FUND2.0; see Tble 10.

21 The mrginl costs of climte chnging emissions Ozone nd sulphte erosols The methodology to estimte the costs of region-specific climte chnge is described in Grewe nd Tol (1999). Geogrphicl climte chnge ptterns resulting from regionl nitrogen nd sulphur emissions re derived from the DLR tmospheric chemistry model nd the MPIM generl circultion model (for nitrogen nd ozone) nd from the UIUC tmospheric chemistry nd generl circultion model (for sulphur nd sulphte erosols). Chnges in the regionl climte ptterns re imposed on FUND1.6 so s to estimte the regionl dmges. Tble 11 presents the estimted mrginl costs of nitrogen emissions from ircrft flying over Europe. The effects on Europe re positive t first, nd negtive ltter. The pulse of nitrogen emissions cuses temporry wrming, which brings the positive effects of climte chnge on Europen griculture forwrd. Although the direct climtic effect ends with the pulse, the rte of wrming is slightly lower fterwrds. This brings costs to Europe, becuse its cold-relted deths fll less. Nitrogen emissions over Europe lso wrm the rest of the world. Here, generlly negtive effects ensue. Tble 11 The mrginl costs of nitrogen emissions from Europen ircrft ($/kgn). EU only Regionl vlues World verge EU vlues FUND1.6 0% PRTP , % PRTP , % PRTP ,233.5 Notes: Emissions re in the period Costs re discounted to Scenrio is FUND. Tble 12 displys the mrginl costs of sulphur emissions in Europe. Sulphte erosols hve short-lived cooling effect, so the pttern of the mrginl costs of sulphur emissions is opposite to the pttern of the mrginl costs of nitrogen emissions. Tble 12 The mrginl costs of sulphur emissions from Europe ($/kgs). EU only Regionl vlues World verge EU vlues FUND1.6 0% PRTP % PRTP % PRTP Notes: Emissions re in the period Costs re discounted to Scenrio is FUND.

22 The mrginl costs of climte chnging emissions Conclusion This pper ressesses the mrginl costs of greenhouse gses, viz. crbon dioxide, methne, nd nitrous oxide, nd estimtes the mrginl costs of sulphur emissions (vi sulphte erosols) nd nitrogen emissions from ircrft (vi ozone.). The recommended vlues for ExternE re given in Tble 13. The discounting nd vlution procedures for mrginl cost estimtion were refined, but the estimtes for the three greenhouse gses do not substntilly differ from those in Eyre et l. (1999), Perce et l. (1996), nd Tol (1999). The currently recommended vlues (Tble 13) re lower thn those of Eyre et l. (1999), though, reflecting the more optimistic tone of recent impct literture. The older models, FUND1.6 nd the Open Frmework, re unble to estimte mrginl costs on the bsis of the vlue of life yer lost. With comprble vlution methods, these models estimte the mrginl costs of CO 2 nd N 2 O to be fctor 5-7 higher thn does FUND2.0. It should be noted tht with the inclusion of new insights into the impcts of climte chnge, it cn no longer be excluded tht mrginl costs re negtive, prticulrly for methne. The sign of the costs is model nd region dependent. Despite their short life-time, the mrginl costs of nitrogen nd sulphur emissions re reltively lrge, primrily becuse they re not much discounted. The results presented here should not be tken s finl estimtes. The impcts covered by the models used re only frction (of unknown size) of ll climte chnge impcts. Prticulrly, lrge scle disruptions, such s brekdown of North Atlntic Deep Wter formtion or collpse of the West-Antrctic Ice Sheet, re excluded from the nlysis. The methodologies to estimte climte chnge impcts in different future remin wek. Adpttion is not included in its full complexity. Vlution of impcts is still troublesome, prticulrly for nture nd helth. Our knowledge of tmospheric chemistry nd climte hs substntil gps. The estimtes reflect our current best knowledge, nd indicte stimulting reserch gend. Tble 13 Recommended mrginl costs for ExternE. Minimum b Low c Centrl estimte d High c Mximum b CO 2 ( /tco 2 ) e N 2 O ( /tn 2 O) e , ,242.1 CH 4 ( /tch 4 ) e N ( /kgn) f ,270.2 S ( /kgs) f Emissions re in the period Costs re discounted to b Minimum nd mximum re s in Tbles 5, 11 nd 12. c High nd low pproximtely spn the 67% confidence intervl. d PRTP equls 1%. Vlues re world verges. e Model is FUND2.0. Time horizon is Scenrio is IS92. Morbidity risks re vlued bsed on the vlue of life yer lost. Note tht the mrginl costs of crbon dioxide re here expressed per tonne of CO 2, rther thn per tonne of crbon s in erlier tbles.

23 The mrginl costs of climte chnging emissions 21 f Model is FUND1.6. Time horizon is Scenrio is FUND. Morbidity risks re vlued bsed on the vlue of sttisticl life. Uncertinty is bsed on n ssumed geometric stndrd devition of 1.7, in line with CO 2, N 2 O nd CH 4. Nitrogen emissions re from ircrft only. Acknowledgements This pper benefited from the generous finncil support of the Europen Commission, DG12, through its Fourth Frmework Progrmme. Comments by the ExternE tem, prticulrly Peter Bickel nd Kees Dorlnd, helped improve the exposition. Nick Eyre lso commented on n erlier version, nd ws very instrumentl in formulting the vlution nd reporting section.

24 The mrginl costs of climte chnging emissions 22 References Arrow, K.J., W.R. Cline, K.G. Meler, M. Munsinghe, R. Squitieri nd J.E. Stiglitz (1996). Intertemporl Equity, Discounting, nd Economic Efficiency. In J.P. Bruce, H. Lee nd E.F. Hites (eds.), Climte Chnge 1995: Economic nd Socil Dimensions - Contribution of Working Group III to the Second Assessment Report of the Intergovernmentl Pnel on Climte Chnge, pp , Cmbridge University Press, Cmbridge. Broome, J. (1992). Counting the Cost of Globl Wrming. White Horse Press, Cmbridge. Brown, P.G. (1997). Stewrdship of Climte - An Editoril Comment, Climtic Chnge, 37, pp Downing, T.E., N. Eyre, R. Greener nd D. Blckwell (1996). Projected Costs of Climte Chnge for Two Reference Scenrios nd Fossil Fuel Cycles. Environmentl Chnge Unit, Oxford. Downing, T.E., R.A. Greener nd N. Eyre (1995). The Economic Impcts of Climte Chnge: Assessment of Fossil Fuel Cycles for the ExternE Project. Oxford nd Lonsdle, Environmentl Chnge Unit nd Eyre Energy Environment. Eyre, N., T.E. Downing, R. Hoekstr nd K. Rennings (1997). Globl Wrming Dmges. ExternE, Brussels. Fnkhuser, S., R.S.J. Tol nd D.W. Perce (1998). Extensions nd Alterntives to Climte Chnge Impct Vlution: On the Critique of IPCC Working Group III's Impct Estimtes, Environment nd Development Economics, 3, pp Fnkhuser, S., R.S.J. Tol nd D.W. Perce (1997). The Aggregtion of Climte Chnge Dmges: A Welfre Theoretic Approch, Environmentl nd Resource Economics, 10, pp Hmmitt, J.K., R.J. Lempert nd M.E. Schlesinger (1992). `A Sequentil-Decision Strtegy for Abting Climte Chnge, Nture, 357, pp Kttenberg, A., F. Giorgi, H. Grssl, G.A. Meehl, J.F.B. Mitchell, R.J. Stouffer, T. Tokiok, A.J. Wever nd T.M.L. Wigley (1996). `Climte Models - Projections of Future Climte, in J.T. Houghton, L.G. Meiro Filho, B.A. Cllnder, N. Hrris, A. Kttenberg nd K. Mskell (eds.), Climte Chnge 1995: The Science of Climte Chnge - Contribution of Working Group I to the Second Assessment Report of the Intergovernmentl Pnel on Climte Chnge, pp , Cmbridge University Press, Cmbridge. Koopmns, T.C. (1967). Objectives, Constrints, nd Outcomes in Optiml Growth Models, Econometric, 35, pp Leemns, R. nd W.P. Crmer (1991). The IIASA Dtbse for Men Monthly Vlues of Temperture, Precipittion nd Cloudiness on Globl Terrestril Grid. RR-91-18, Interntionl Institute for Applied Systems Anlysis, Lxenburg. Mendelsohn, R. O. nd J. E. Neumnn (eds.) (1999). The Impct of Climte Chnge on the United Sttes Economy. Cmbridge University Press, Cmbridge. Nordhus, W.D. (1994). Mnging the Globl Commons: The Economics of Climte Chnge. The MIT Press, Cmbridge. Perce, D.W., W.R. Cline, A.N. Achnt, S. Fnkhuser, R.K. Pchuri, R.S.J. Tol nd P. Velling (1996). `The Socil Costs of Climte Chnge: Greenhouse Dmge nd the Benefits of Control', in J.P. Bruce, H. Lee nd E.F. Hites (eds.), Climte Chnge 1995: Economic nd Socil Dimensions - Contribution of Working Group III to the Second Assessment Report of the Intergovernmentl Pnel on Climte Chnge, pp , Cmbridge University Press, Cmbridge.

25 The mrginl costs of climte chnging emissions 23 Rmsey, F. (1928). A Mthemticl Theory of Sving, Economic Journl, 38, pp Schimel, D., D. Alves, I. Enting, M. Heimnn, F. Joos, M. Rynud, R. Derwent, D. Ehhlt, P. Frser, E. Snhuez, X. Zhou, P. Jons, R. Chrlson, H. Rodhe, S. Sdsivn, K.P. Shine, Y. Fouqurt, V. Rmswmy, S. Solomon, J. Srinivsn, D.L. Albritton, I. Isksen, M. Ll nd D.J. Wuebbles (1996). `Rditive Forcing of Climte Chnge', in J.T. Houghton, L.G. Meiro Filho, B.A. Cllnder, N. Hrris, A. Kttenberg nd K. Mskell (eds.), Climte Chnge 1995: The Science of Climte Chnge - Contribution of Working Group I to the Second Assessment Report of the Intergovernmentl Pnel on Climte Chnge, pp , Cmbridge University Press, Cmbridge. Shine, K.P., R.G. Derwent, D.J. Wuebbles nd J.J. Morcrette (1990). Rditive Forcing of Climte', in J.T. Houghton, G.J. Jenkins nd J.J. Ephrums (eds.), Climte Chnge - The IPCC Scientific Assessment, pp , Cmbridge University Press, Cmbridge. Tol, R.S.J. (1995). The Dmge Costs of Climte Chnge Towrd More Comprehensive Clcultions, Environmentl nd Resource Economics, 5, pp Tol, R.S.J. (1996). The Dmge Costs of Climte Chnge Towrds Dynmic Representtion, Ecologicl Economics, 19, pp Tol, R.S.J. (1999) The Mrginl Costs of Greenhouse Gs Emissions, Energy Journl, 20 (1), pp Tol, R.S.J. (1999b). New Estimtes of the Dmge Costs of Climte Chnge, Prt I: Benchmrk Estimtes, D99/01, Institute for Environmentl Studies, Vrije Universiteit, Amsterdm. Tol, R.S.J. (1999c). New Estimtes of the Dmge Costs of Climte Chnge, Prt II: Dynmic Estimtes, D99/02, Institute for Environmentl Studies, Vrije Universiteit, Amsterdm. Tol, R.S.J. nd V. Grewe (1999). Climte-Relted Externl Costs of Nitrogen nd Sulfur Emissions (drft). Viner, D. nd M. Hulme (1994). The Climte Impcts LINK Project - Providing Climte Chnge Scenrios for Impcts Assessment in the UK. Climte Reserch Unit, University of Est Angli, Norwich. Wtson, R. T., M. C. Zinyower, nd R. H. Moss (eds.) (1996) Climte Chnge 1995: Impcts, Adpttion, nd Mitigtion of Climte Chnge - Scientific-Technicl Anlysis - Contribution of Working Group II to the Second Assessment Report of the Intergovernmentl Pnel on Climte Chnge. Cmbridge University Press, Cmbridge. Wigley, T.M.L., M. Hulme nd S.C.B. Rper (1993). MAGICC: Model for the Assessment of Greenhouse Induced Climte Chnge. University Consortium for Atmospheric Reserch, Boulder.

26 The mrginl costs of climte chnging emissions 24 Appendix I. Uncertinty in FUND2.0 I.1 Bsic ssumptions Tble A1. Assumptions in the uncertinty nlysis. Set of prmeters Distribution Men Spred Scenrios (economy, popultion, Norml IS92 Grows over time emissions (other thn in- dustril CO 2 ), technology) Atmospheric life-time CH 4 nd Inverse tringulr Tol (1999) Tol (1999) N 2 O Atmospheric life-time CO 2 Inverse norml knotted t 0 Tol (1999) Tol (1999) Temperture nd se-level sensitivity Gmm Tol (1999) Tol (1999) Temperture nd se-level rection Inverse tringulr Tol (1999) Tol (1999) time Elsticity of WTP to per cpit Norml knotted t 0 Tol (1999b) Tol (1999c) income Elsticity of impct to per cpit Norml knotted t 0 Tol (1999c) Tol (1999c) income Linerity of impct Norml knotted t 0 Tol (1999c) Tol (1999c) Sensitivity of impct to level of Norml Tol (1999b) Tol (1999b) climte chnge Sensitivity of impct to rte of Norml knotted t 0 Tol (1999b) Tol (1999b) climte chnge Sensitivity of impct of se Exponentil Tol (1999b) Tol (1999b) level rise Adpttion time Inverse norml knotted t 0 Tol (1999c) Tol (1999c) Threshold income vector-borne Norml Tol (1999c) Tol (1999c) disese Mximum crdiovsculr disese Norml knotted t 0 Tol (1999c) Tol (1999c) Elsticity bse crdiovsculr Norml knotted t 0 Tol (1999c) Tol (1999c) disese to per cpit income Ecosystem vlue Norml knotted t 0 Tol (1999b) Tol (1999c) Mortlity vlue Norml knotted t 0 Tol (1999b) Tol (1999c) Agriculturl climte optimum Norml Tol (1999c) Tol (1999c) Intke of migrnts Stndrdised norml knotted t Tol (1999b) Tol (1999b) 0 Migrtion vlue Norml knotted t 0 Tol (1999b) Tol (1999b)

27 The mrginl costs of climte chnging emissions 25 I.2 Excerpts from Tol (1999) Methne nd nitrous oxide re tken up in the tmosphere, nd then geometriclly depleted: where C denotes concentrtion, E emissions, t yer, nd pre pre-industril. Tble 1 displys the prmeters for both gses. The crbon cycle is five-box model: with Ct = C Box t-1 ( ) + α Et - β Ct-1 - C pre (A1) = ρ Boxi,t i Et (A2) i, t i α 5 Ct = α i Box i, t (A2b) i=1 where á i denotes the frction of emissions E (in million metric tonnes of crbon) tht is llocted to box i -rte of the boxes (ñ = exp(-1/lifetime), with verge life-times infinity, 363, 74, 17 nd 2 yers, respectively). Tble A2. Prmeters of Eqution (A2). b Gs á â b Pre-industril concentrtion Methne (CH 4 ) / ppb Nitrous oxide (N 2 O) / ppb 4 or N 2 O) into concentrtions (in prts per billion by volume). -industril (nd ssumedly equilibrium) concentrtions; 1/â is the tmospheric life-time (in yers) of the gses. The globl men temperture T is governed by geometric build-up to its equilibrium (determined by rditive forcing RF), with life-time of 50 yers. In the bse cse, globl men temperture rises in equilibrium by 2.5 C for doubling of crbon dioxide equivlents, so: T t = T t RF 6.3ln(2) t (A3) Globl men se level is lso geometric, with its equilibrium determined by the temperture nd life-time of 50 yers.

28 The mrginl costs of climte chnging emissions 26 Tble A3. Description of prmeter uncertinty; units re given in brckets. Prmeter distribution chrcteristics prmeters Climte sensitivity gmm Mode 2.50 á ( C/doubling CO 2 ) Men 2.85 â std.dev se level sensitivity gmm Mode 0.31 á (m/ C) Men 0.36 â std.dev tm. Life-time CH 4 Tringulr Mode (yer) Men 10.2 b 16.0 std.dev. 1.3 c 8.6 tm. Life-time N 2 O Tringulr Mode (yer) Men 130 b 170 std.dev. 15 c 120 life-time temperture Tringulr Mode life-time se level Men 58 b 100 (yer) std.dev. 16 c 50 tm. Life-times CO 2 norml Men 363; 74; 17; 2 ì men (yer) std.dev. hlf men ó std.dev. Knotted (truncted) t zero. I.3 Excerpts from Tol (1999b) Tble A4. Impcts of climte chnge on griculture. Region rte of chnge (%GAP/ C) Level of chnge (%GAP/1 0 C) Optiml temperture ( 0 C wrt 1990) OECD-A (0.031) (0.530) 2.29 (1.32) OECD-E (0.025) (0.450) 0.45 (0.50) OECD-P (0.038) (0.648) 2.71 (0.33) CEE&fSU (0.027) (0.452) 2.96 (0.43) ME (0.011) (0.193) 3.08 (0.49) LA (0.015) (0.280) 2.14 (0.26) S&SEA (0.007) (0.132) 2.16 (0.33) CPA (0.023) (0.403) 3.41 (1.01) AFR (0.006) (0.111) 3.00 (0.48) Tble A5. Impct of 1 C wrming on current dy forestry, wter, heting, nd cooling, in million US dollr. Region forestry wter heting cooling OECD-A 218 (24) -3 (3) 22 (22) -11 (11) OECD-E 134 (16) -2 (2) 13 (13) -20 (20) OECD-P 93 (20) -0 (0) 7 (7) -1 (1) CEE&fSU -136 (17) -76 (76) 46 (46) -19 (19) ME 0 (0) -1 (1) 8 (8) -1 (1) LA -10 (2) -1 (1) 3 (3) -2 (2) S&SEA 140 (34) -2 (2) 4 (4) -4 (4) CPA 0 (0) 2 (2) 17 (17) -12 (12) AFR 0 (0) -2 (2) 0 (0) -5 (5)

29 The mrginl costs of climte chnging emissions 27 Tble A6. Impct of one metre se level rise. level drylnd loss drylnd vlue wetlnd loss wetlnd vlue protection emigrnts prot. costs % 10 3 km $/km km $/km $ 10 6 OECD-A (2.4) 1.3 (0.6) 12.0 (8.6) 5.4 (2.7) 83 (74) 0.13 (0.07) OECD-E (0.4) 13.1 (6.6) 4.0 (2.3) 4.3 (2.2) 136 (45) 0.22 (0.10) OECD-P (0.4) 13.7 (6.7) 1.0 (1.1) 5.9 (2.9) 63 (38) 0.04 (0.02) CEE&fSU (2.7) 0.9 (0.5) 0.0 (0.0) 2.9 (1.5) 53 (50) 0.03 (0.03) ME (1.2) 0.5 (0.3) 0.0 (0.0) 1.3 (0.7) 5 (3) 0.05 (0.08) LA (7.1) 0.3 (0.2) 50.2 (36.4) 0.9 (0.5) 147 (74) 0.71 (1.27) S&SEA (9.6) 0.5 (0.3) 54.9 (48.0) 0.3 (0.2) 305 (158) 2.30 (1.40) CPA (15.1) 0.3 (0.2) 15.6 (17.1) 0.2 (0.1) 171 (126) 2.39 (3.06) AFR (18.4) 0.4 (0.2) 30.8 (14.8) 0.4 (0.2) 92 (35) 2.74 (2.85)

30 The mrginl costs of climte chnging emissions 28 TbleA7 Additionl deths due to vector-borne diseses for 1ºC globl wrming. Region Mlri Schistosomisis dengue fever OECD-A 0 (0) 0 (0) 0 (0) OECD-E 0 (0) 0 (0) 0 (0) OECD-P 0 (0) 0 (0) 0 (0) CEE&fSU 0 (0) 0 (0) 0 (0) ME 155 (112) -64 (13) 0 (0) LA 1,101 (797) -114 (22) 0 (0) S&SEA 8,218 (5949) -116 (3) 6,745 (1,171) CPA 0 (0) -128 (25) 393 (68) AFR 56,527 (40,919) -503 (99) 343 (60) Tble A8 Additionl deths (in thousnds) due to crdiovsculr nd respirtory diseses for 1 C globl wrming. Region Crdiovsculr cold Crdiovsculr - het Respirtory OECD-A (4.4) 11.4 (5.9) 3.0 (9.7) OECD-E (2.6) 11.7 (4.0) -2.8 (5.7) OECD-P (2.2) 3.5 (2.8) 1.0 (4.8) CEE&fSU (5.2) 10.7 (4.4) 4.5 (11.0) ME -8.9 (1.3) 2.5 (0.4) 9.9 (2.6) LA (3.5) 8.1 (1.8) 11.1 (7.0) S&SEA (16.9) 17.5 (2.9) (34.1) CPA (21.7) 24.3 (4.6) 62.8 (44.4) AFR (3.0) 4.7 (0.5) 24.8 (6.0) I.4 Excerpts from Tol (1999c) The ssumed model for griculture is: β r Tt r t, r = r + ρt 1, r 0.04 (A4) r denotes the chnge in griculturl production due the rte of climte chnge; t denotes time; r denotes region; T denotes the chnge in the globl men temperture; α is prmeter, denoting the benchmrk chnge in griculturl production; β is prmeter, denoting the non-linerity of the rection to temperture; β=2 ( ); ρ is prmeter, denoting the speed of dpttion; ρ=10 (5-15). l t, r B opt B 2Ar Tr Ar 2 = T opt t + T opt t (A5) 1 2T 1 2T r r l denotes the chnge in griculturl production due to the level of climte chnge; t denotes time; r denotes region; T denotes the chnge in globl men temperture reltive to 1990; A B is prmeter, denoting the benchmrk chnge in griculturl production; T opt is prmeter, denoting the optiml temperture.

31 The mrginl costs of climte chnging emissions 29 For T opt <0.5, (2) is replced by biliner form. If T=T opt, l =2A B. If T=0, l =0. If T=1, l =A B. The shre of griculturl production in totl income flls with per cpit income: GAP Y t, r t, r GAP = Y 1990, r 1990, r y y 1990, r t, r ε (A6) GAP denotes gross griculturl product; Y denotes gross domestic product; y denotes gross domestic product per cpit; t denotes times; r denotes regions; ε = 0.31 ( ). Forestry follows: F = y ε T t, r β t, r r t y (A7) 1990, r where F denotes the chnge in forestry consumer nd producer surplus (s shre of totl income); t denotes time; r denotes region; y denotes per cpit income; T denotes the globl men temperture; ε = 0.31 ( ); β = 1 ( ). The impct of climte chnge on wter resources follows: W = Y β T r, t γ r, t r t Y (A8) r,1990 where W denotes the chnge in wter resources, expressed in billion dollrs; t denotes time; r denotes region; Y denotes income; T denotes the globl men temperture; β = 0.85 ( ); γ = 1 ( ). The model for spce heting is: ε y t t, r Pt, r β t, r = rt t y t,1990 P t,1990 sπ= 1990 SH AEEI, s r (A9) SH denotes the mount of money spent less on spce heting; t denotes time; r denotes region; T denotes the chnge in the globl men temperture reltive to 1990; y denotes per cpit income; P denotes popultion size; β = 1 ( ); ε = 0.8 ( ); AEEI is bout 1% per yer in 1990, converging to 0.2% in 2200; its stndrd devition is set t qurter of the men. The model for spce cooling is: ε y t t, r Pt, r β t, r = rt t y t,1990 P Π t,1990 s= 1990 SC AEEI, s r (A10)

32 The mrginl costs of climte chnging emissions 30 SC denotes the mount of money spent dditionlly on spce cooling; t denotes time; r denotes region; T denotes the chnge in the globl men temperture reltive to 1990; y denotes per cpit income; P denotes popultion size; β = 1 ( ); ε = 0.8 ( ). Lnd loss is ssumed to be liner function of se level rise. The vlue of drylnd is ssumed to be liner in income density ($/km 2 ), with n verge vlue of $4 million per squre kilometre for the OECD. Wetlnd vlue is ssumed to be logistic in per cpit income, with n verge vlue of $5 million per squre kilometre for the OECD. If drylnd gets lost, the people living there re forced to move. The number of forced migrnts follows from the mount of lnd lost nd the verge popultion density in the region. The vlue of this is set t three times the regionl per cpit income per migrnt. The level of protection, tht is, the shre of the costline protected, is: 1 PC + WL L = mx 0,1 (A11) 2 DL L is the frction of the costline to be protected. PC is the net present vlue of the protection if the whole cost is protected. WL is the net present vlue of wetlnd lost due to full costl protection. DL is the net present vlue of drylnd lost without protection. PC t = Σ 1 1+ PC = t g = 1 1+ ρ + ρ ρ + g PC + g where PC is the verge nnul costs of protection; ρ=1%. (A12) 1 1 g WL = Σ + ρ + t WL0 = WL 2 t g ( + g ) = ρ ρ t where WL 0 denotes the vlue of wetlnd loss in the first yer. 1 DL = Σ t DL t 0 1 ρ g = + + t 0 = ( 1+ g )( 1+ ρ + g) where DL 0 is the vlue of drylnd loss in the first yer. Ecosystems loss is vlued s E y P y / y ρ 2 0 DL 0 (A13) (A14) t, r t, r b t, r = t, r (A15) y1990, r 1+ yt, r / yb where E denotes the vlue of the loss of ecosystems; t denotes time; r denotes region; y denotes per cpit income; P denotes popultion size; α is prmeter such tht E equls $50 per person if per cpit income equls the OECD verge in 1990; y b = $20,000 (10,000).