disutilityhttp

RESEARCHOpenAccessEmissiontradingorproportionalcarbontax:aquestformoreefficaciousemissioncontrolMasayukiOtakiAbstractBackground:Twoalternativeprocedurescurrentlyexistforefficientcarbondioxide(CO2)emissionscontrol:carbonemissiontradingandproportionalcarbontax.
Thisarticleexploreswhichofthetwoismoredesirableandefficacious.
Results:Comparedtoemissiontrading,theequilibriumunderauniversalproportionalcarbontaxachievesParetosuperiorallocation.
Inaddition,thepriceofaunitofCO2emissionsismuchhigherinthecaseofauniversalproportionalcarbontaxthanforbilateralemissionstrading.
Conclusions:ThispaperrevealsthesuperiorityofauniversalproportionalcarbontaxovertheemissionstradingintermsoftheefficiencyofCO2emissionscontrol.
However,decidingandabidingbyauniversaltaxrateislikelytorequiregreatpoliticalwill.
Inthissense,viewedinthecurrentcontext,suchataxschemeisvisionary.
Gradualismisunavoidable.
Itisfarmoredesirabletoexpandthenetworkoftheupcomingtrilateralcarbontradingnetworksteadilyratherthanleavingtheglobaleconomytothelaissez-fairesituation.
Keywords:CO2emissions;Proportionalcarbontax;Emissionstrading;ModifiedSamuelsonRule;NonlinearcarbontaxBackgroundCarbonmarketsarejerry-builtinnaturea.
Theycannotbesufficientlysustainedwithoutgovernmentassistanceandintervention.
AccordingtoLovinsandCohen(2011),p.
227,"Inthewakeoftheworld'sfailuretoagreeonanewtradinglegislationinCopenhagenandtheU.
S.
Senatefailuretopassbindinglegislation,thepriceofcarbonfelldrastically.
IntheUnitedStatesitfellalmosttonothing.
InEurope,thepriceofcarbonfellfromahighof25to8aton.
ByOctober2010,priceshadstartedtorebound,hitting12.
Subsequentmeasureshaveonlystrengthenedthepriceperton".
First,thisarticleexploresthesourceofsuchfragility.
Wefindthatthedecisionsofeconomicagentsemittingcarbondioxide(CO2)areisolatedfromdirectandindirectdamagesduetosuchemissions,owingtothegenuinepropertyoftheirexternaldiseconomyoftheemission;therefore,attheveryleast,themarketcannotremainsustainablewithoutexpectationsofstrengthenedregulationinthefuture.
Second,weexaminethepropertiesofbilateraloffsetcarbontrading,whichiscurrentlythemostpopulartradingschemeandisnotsubjecttoregulationconcerningtotalemissionamounts.
UnlikeOtaki(2013),althoughtheanalysisisstatic,theextensiontodynamicanalysisisnotimpossible,sincethelatterisanapplicationofcaptradingwhichregulatestotalemissions.
Moreover,analysispertainingtocaptrading,whichseemstobepopularwithintheEuropeanmarket,requirestheconsiderationofonlyoneadditionalconstraintconcerningtotalemissionsinthemodel.
Finally,wecomparethefunctionofbilateralcarbontradingwiththatofauniversalproportionalcarbontax.
Thearticleconcludesthatalthoughawide-rangeduniversalproportionalcarbontaxissuperiortobilateralcarbontrading,thetaxratebecomesextremelyhighandimpractical,andhence,expandingthenetworkofbilateraloffsetemissiontradingisanefficaciousmeasureforemissiontrading.
ResultsanddiscussionsThemodelAssumethattwotypesofcountriesexist.
OneofthecountriesisanadvancedindustrializedordevelopedCorrespondence:ohtaki@iss.
u-tokyo.
ac.
jpInstituteofSocialScience,UniversityofTokyo,7-3-1HongoBunkyo,Tokyo,113-0033,Japan2013Otaki;licenseeSpringer.
ThisisanopenaccessarticledistributedunderthetermsoftheCreativeCommonsAttributionLicense(http://creativecommons.
org/licenses/by/2.
0),whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
OtakiEnvironmentalSystemsResearch2013,2:8http://www.
environmentalsystemsresearch.
com/content/2/1/8countrywhichemitsCO2.
Theothercountryisadevel-opingcountrythatdoesnotemitCO2.
Therearenpairsofadevelopedandadevelopingcountry(dj,uj)betweenwhichtheemissionrightistraded,wheredjandujarethejthdevelopedanddevelopingcountryrespectively,comprisingthejthblockofemissiontrading.
EachcountryhasthesameutilityfunctionUij:Uij≡cijΨed1;;edj;;edn;eu1;;euj;;eun≡cijΨed→;eu→;1wherecijandeijdenotetheconsumptionandCO2emis-sionlevelofthejthcountrythatbelongstotypei(i=d,u),respectively.
ΨrepresentsthedisutilityfromtheCO2emissionviatheproductionprocessofaconsumptiongood.
WeassumethatΨislinearhomogenousb,quasiconcaveandsymmetricinthefol-lowingsense.
Thatis,Ψ;ekl;;ek0l0≡Ψ;ek0l0;;ekl;k;k0;l;l0:2Thissymmetricassumptionimpliesthatthedisutilityderivedfromtheemissiondoesnotdependonwhereitisemitted.
ItisaplausibleassumptionwhenweconsiderthediffusionspeedofCO2intheatmosphere.
Thesemi-reducedformproductionfunction,whichrepresentstherelationshipbetweentheconsumptioncandtheadjoinedemissione,isc=αF(e),αissomepositiveconstant.
F0>0;F00http://www.
environmentalsystemsresearch.
com/content/2/1/8developingcountry.
TheaboveconstrainedmaximizationproblemmeansthatanadvancedcountrymaximizesitseconomicwelfareguaranteeingtheminimalutilitylevelofthecounterpartdevelopingcountryatthelevelofU.
Thefirsttermof(6)isthedeveloped-country'sutilityderivedfromthisemissiontrading,andthetermwithinthesquarebracketsofthesecondtermisthenetwelfaregainofthedevelopingcountry.
Letusdenoteεlj≡eljXnl;k1elk≡eljE:7ByusingεljandE,ΨcanbetransformedintoΨψεd;→εu→E≡ψε→E:8ThenbythesymmetryofΨ,theoptimalityconditionfortheabovecontractproblemunderperfectinforma-tionandsymmetricequilibriumcanberepresentedasF0ekl2αψcl1jεlj1n≡θ2α:j;l:9PUΨe→Uθ2neUθ2en1θ2e≡UT2n1θ2e:10θ2≡2ψcl1εlj1nistheunitcarbonpriceinthistradingscheme.
Thisschemecanberegardedastheidealoffset-tradescheme.
Thecarbonpriceshouldbedeterminedasthesumofthemarginaldisutilityfromtheglobalwarmingoftwocountrieswithpartnership.
Thetransferfromadevelopedcountryis,asidefromthedirectpaymentforcarbonemissionsT(2),thesumofthereservationutilityofthedevelopingcountryinconcernUandthepecuni-arynuisancefromemissionsofotherdevelopedcoun-triesasawhole[n1]θ(2)e*.
Wemustnotethatsuchanidealsystemdoesnotre-quiresettingthebaselineoftheproject,whichisun-avoidableinthecurrentsystem.
Sincetheproceduresforsuchsettingisverymuchcomplicatedandlapsesmuchtime,itseemstobedesirabletotransformtheexistingoffsettradingschemetothatbasedonthefor-mulae(9)and(10).
UniversalproportionalcarbontaxFormattingauniversalproportionalcarbontaxschemeAuniversalproportionalcarbontaxisformattedbythefollowingoptimizationproblem:maxε→αFed1Ψε→EXl;k≠1;dλklαFeklΨε→EUmhi2435:11TheaboveproblemmeansthatanadvancedcountrymaximizesitseconomicutilitypresumingitprovidestherestoftheworldwiththeminimalutilityU.
ItisclearthattheattainedallocationundersuchaschemeisParetoeffi-cientbydefinition.
Bythesymmetryoftheproblem,itisalsoclearthateveryLagrangeanmultiplierunderoptimalplanningtakesthevalueunityc.
Thus,weobtainthefollow-ingformulaconcerningtheoptimalemission:F0enαψcd1jεlj1n:12ThisisthemodifiedSamuelson(1954)ruleconcerningtheoptimalpublicgood(bad)provision:Themarginalbenefitaccruedfromthecountry'semissionsαF'(e*)shouldbeequalizedtothesumofthemarginaldisutilitydiffusedallovertheworld,nψcd1jεlj1n.
Theright-handsideof(12)istheoptimaltaxratecommontoallconstituents.
WelfareorderingforvariousemissionsuppressingmeasuresAlthoughitisclearthataproportionalcarbontax,withtherateexpressedby(12),isthefirst-bestpolicy,itisimportanttounderstandthemannerinwhichtheothertwomeasuresareorderedintermsofParetoefficiency.
WecandealwiththisproblembyusingthesymmetryandlinearhomogeneityofΨ.
TheutilityofeachcountryUklcanbewrittenasUkljαFejψcl1jεkl1nEjαFejnψcl1jεkl1nej:13Employingtheenveloptheorem,dUkljdjψcl1jεkl1nej>0;1≤jhttp://www.
environmentalsystemsresearch.
com/content/2/1/8unilateralcarbontaxscheme,wherebyacountrycansetaproportionalcarbontaxrateatitsdiscretion.
Thisfactimpliesthatalthoughaproportionalcarbontaxpossiblyattainsthefirst-bestallocation,emissiontradingisthesecond-bestmeasure,unlessallcountriesconcurabouttheseriousnessofglobalwarming,inwhichcaseamuchhighercarbontaxratethanthatintheunilateralcasecanbeadopted.
Inaddition,sincenislikelytofarexceedtwo,thesuppressioneffectofemis-siontradingisestimatedtoberatherrestrictivefromtheviewpointofthefirst-bestallocation.
Welfareanalysisofemission-savingtechnologicalprogressConsidertheeffectofemission-savingtechnologicalpro-gresstotheworldeconomyasawhole.
Thisprogressisexpressedbyanincreaseinαinthismodel.
Beforepro-ceedingtothegeneralequilibriumanalysis,wemustnotethateverytradingpairincreasesemissionsincon-junctionwithtechnologicalprogress.
Althoughitseemstobecounterintuitive,ifwenotethefactthattechno-logicalprogressmakestheimputedpriceofCO2cheaperasshownbytheright-handsidesof(5),(9),and(12),itisnaturalthatemission-savingtechnologicalpro-gressconverselyheightenstheaccumulationofCO2.
Withthisprecautioninmind,weshallproceedwiththegeneralequilibriumanalysis,intowhichthemutualnegativeexternalitiesbetweentradingpairsarewoven.
Then,from(13)andtheenveloptheorem,weobtaindUdjdαFenjψed1jεkl1ndedα>1ααFeηΨ;η≡de=edα=α;j;dUdndα>0;15whereηistheelasticityoftheemissionvolumetotheunitofthetechnologicalprogress.
SinceαF(e*)Ψ>0,ifηissmallenoughandtheincreaseintheemissiongeneratedbythetechnologicalprogressisnotsoseriousd,theadvanceintheemission-savingtechnologyimprovesworldwideutility,althoughthisadvancealsoincreasesthetotalamountofCO2emissions.
Thisfactisunderscoredinthatwhenweextendthescopeofanalysistodynamicandintergenerationalemissionallocation(e.
g.
,Otaki2013),wemayhavetomodifytheobtainedresult,becausetheaccelerationinemissionsdiffusesthenegativeexternalitytofuturegenerations.
Inotherwords,althoughtheemission-savingtechno-logicalprogresslowerstheimputedpriceofCO2andstimulatesthecurrentgeneration'sconsumption,suchcurrentprosperitymayconverselyworsenthede-scendants'utilityviatheresultingmassiveemissions.
However,suchadynamicprospectisbeyondofthescopeofthisarticle,anditselfrequiressolvingthesimul-taneousoptimizationconcerningintertemporalandinternationalemissionproblems.
Onincomedistributionbetweencountries:thepossibilityofnonlinearpricingThusfar,thisarticlehasassumedthatadevelopedcoun-trydirectlyinvestsinthecorrespondingdevelopingcountryandthatitreceivesrevenuesafterdeductingthecarbontax.
Thus,αFejjψel1jεkl1nej≡αFeτjej;16whereτjisthecarbontaxrate,whichisidenticaltotheunitcarbonpriceinemissiontrading.
Hence,thedevelopingcountryobtainstaxrevenuesR(j),whichamounttoRj≡τjej;17fromtheinvestingdevelopedcountry.
Sinceeveryconstraintconcerningthejointutilityfromsuchatradingschemebindswheneverplanningisopti-mal(seeUzawa1958),thenetsurplusfromthetradingintermsofconsumptionbecomesUme.
Althoughwehavenotyetanalyzedthepossibilityofadditionallump-sumtransferfromtheinvestingdevelopedcountrytoitscounterpartdevelopingcountry(orthetransferinverteddirection,whichispossibleifthetaxpaymentistooheavyforthedevelopedcountry),onecannotenvisageauniversalproportionalcarbontaxwithoutsomefairdiv-isionofthesurplusearnedbydirectinvestmentthroughthislump-sumtransfer,specificallybecausethestandardoflivingoftheremitting/recipientcountrydependsde-cisivelyonitsshareofthissurplus(Uzawa2003).
Hereafterthisarticleanalyzesbothdirectionsofthetransferandclarifieshowthedirectionaffectstheeffect-ivetaxrate.
First,considerthetransferfromthedevel-opedcountrytothedevelopingcountry.
Thisisanapplicationofnonlinearpricing,whichappearsinbasicmicroeconomics(e.
g.
,seeTirole1988).
Letthesumofthetransferbes.
Then,thetotalpaymentofadevelopedcountrytohercounterpartTbecomesT≡τjejsτjsej!
ej:18Thetermwithinthesquarebracketsistheeffectivetaxrate,whichisillustratedbyFigure1.
Thus,theeffectivetaxrateisdigressivealthoughsuchatransferenrichesthedevelopingcountry.
Thisisowingtotheeconomyofscalefromthede-factomassivepurchaseoftherightofemission.
OtakiEnvironmentalSystemsResearch2013,2:8Page4of6http://www.
environmentalsystemsresearch.
com/content/2/1/8Figure2illustratesthelocusoftheeffectivetaxratefortheinvertedtransferfromthedevelopingcountrytothedevelopedcountry(s0).
Figure2Theeffectivetaxrate(DigressiveCase:shttp://www.
environmentalsystemsresearch.
com/content/2/1/8requestseachaffiliatetocalculatetheworldwidedisutil-itycausedbyitsemissions.
EndnotesaUnitedStatesEnvironmentalProtectAgency(2003)classifiedemissiontradingintothreecategories:(i)capandtrade,(ii)project-basedtrade,(iii)rate-basedtrade.
Theoff-settradeiscorrespondstothesecondcategory.
Myanalysisconcentratesandtheorizesthiscategoryofemissiontrade.
OffsetQualityInitiative(2008)indicateshowthequalityofemissionoffsettingmeasureisassessed.
UnitedNationsFrameworkConventiononClimateChange(2012)figuresouthowthecleandevelopmentmechanism(CDM)actuallyworks.
bThelinearhomogeneityassumptionisintroducedbyfacilitatingthecalculation.
WecaneasilyextendtheclassofΨintothehomotheticfunction.
However,weneedadditionalinformationonΨ.
cThefirst-orderconditionrequiresthatαλklF0ekl1Xj≠l;kλkj"#Ψεd1εkj1n.
Accordingly,λkj1;j;ksatis-fiesthiscondition.
Ifλk0j0≠1forsomeppairsof(j",k"),1λk00s001Xj;kλkj"#1npXj0;k0≠j00;k00λk0j0λk00s00holdsfor(j",k").
Otherwise1λkl1Xj≠l;kλkj"#npXl0;k0λk0s0holds.
LetusdefineSp≡Xl00;k00λk00s00.
Then,thesymmetricassumptionrequires1npSpλk00s00λk00s00npSpλk00s001.
Thisisacontradiction.
Therefore,λkl1;l;k.
dOtherwise,thewelfareisconverselyaggravatedbytheemission-savingtechnologicalprogressundersecond-bestemissioncontrolsystems.
Thisisafallacyofcomposition.
eSinceourutilityfunctionisquasilinear,thesurplusisequivalenttothatintermsoftheutility.
Inaddition,sincewepresumethattheequilibriumissymmetric,thereservationutilityUmisendogenouslydetermined.
ThisresultcomesfromtherequiredpropertythatalloptimalLagrangeanmultipliersshouldtakethevalueunity.
fThisarticlestudieshowfaremissionsofCO2arepermis-siblewiththeremaininggivenvolumeofCO2intheatmos-phere.
Assuch,estimatingthedynamicandcumulativeeffectsofCO2isbeyondthescopeofthisarticle.
WhileOtaki(2013)consideredthisproblem,heneglectedtheproblemoftheefficientallocationofemissionsonaninter-nationalbasis.
CompetinginterestsTheauthordeclaresthathehasnocompetinginterests.
AcknowledgementsTheauthoristhankfultoSusumuCatoandMorioKuninorifortheirincisiveandconstructivecomments.
Received:3August2013Accepted:15October2013Published:18October2013ReferencesLovinsL,CohenB(2011)Climatecapitalism:capitalismintheageofclimatechange.
HillandWang,NYOffsetQualityInitiative(2008)Ensuringoffsetquality:integratinghighqualitygreenhousegasoffsetsinNorthAmericancap-and-tradepolicy.
http://www.
offsetqualityinitiative.
org/pdfs/OQI_Ensuring_Offset_Quality_Exec_Sum_7_08.
pdfOtakiM(2013)Endogenoussocialdiscountrate,proportionalcarbontax,andsustainability:dowehavetherighttodiscountfuturegenerations'utilityEnvironSystRes2:10.
1186/2193-2697-2-1SamuelsonP(1954)Thepuretheoryofpublicexpenditure.
RevEconStat36:387–389,10.
2307/1925895TiroleJ(1988)Thetheoryofindustrialorganization.
MITPress,MassachusettsUnitedStatesEnvironmentProtectionAgency(2003)Toolsofthetrade:aguidetodesigningandoperatingacapandtradeprogramforpollutioncontrol.
EPA430-B-03-002.
http://www.
epa.
gov/airmarkets/resource/docs/tools.
pdfUnitedNationsFrameworkConventiononClimateChange(2012)CleanDevelopmentMechanism:ExecutiveBoardAnnualReport2012.
http://unfccc.
int/resource/docs/publications/pub_cdm_eb_annual_report_2012.
pdfUzawaH(1958)TheKuhn-Tuckertheoreminconcaveprogramming.
In:ArrowK,HarwichL,UzawaH(eds)Studiesinlinearandnonlinearprogramming.
StanfordUniversityPress,California,pp129–134UzawaH(2003)Economictheoryandglobalwarming.
CambridgeUniversityPress,Cambridgedoi:10.
1186/2193-2697-2-8Citethisarticleas:Otaki:Emissiontradingorproportionalcarbontax:aquestformoreefficaciousemissioncontrol.
EnvironmentalSystemsResearch20132:8.
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comOtakiEnvironmentalSystemsResearch2013,2:8Page6of6http://www.
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