Exploring Interaction Effects of Climate Policies: a Model Analysis of the Power Market

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University of Groningen

Exploring Interaction Effects of Climate Policies

Mulder, Machiel; Zeng, Yuyu

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Resource and Energy Economics

DOI:

10.1016/j.reseneeco.2018.09.002

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Citation for published version (APA):

Mulder, M., & Zeng, Y. (2018). Exploring Interaction Effects of Climate Policies: a Model Analysis of the

Power Market. Resource and Energy Economics, 54 , 165–185.

https://doi.org/10.1016/j.reseneeco.2018.09.002

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Contents lists available atScienceDirect

Resource

and

Energy

Economics

j o u r n a l h o m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / r e e

Exploring

interaction

effects

of

climate

policies:

A

model

analysis

of

the

power

market

夽

Machiel

Mulder

∗

,

Yuyu

Zeng

DepartmentofEconomics,EconometricsandFinance,FacultyofEconomicsandBusiness,UniversityofGroningen,TheNetherlands

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received20December2016

Receivedinrevisedform24July2018

Accepted6September2018

Availableonline26September2018

Keywords: Climatepolicy Electricitymarket Interactioneffects Renewables Carbontax

a

b

s

t

r

a

c

t

Theeffectivenessofclimatepolicystronglydependsonhowthesemeasuresare imple-mented.Nationalpolicymeasuresmayhaveinternationalspillovereffectswhichpartly neutralizedomesticemissionreduction,whiledifferenttypesofpolicymeasuresmay off-seteachotheraswell.Thispaperexplorestheconditionsfortheseinteractioneffectsby usingaconcisepartial-equilibriumtwo-countrymodeloftheelectricitymarketwhichalso includesasystemforemissionstrading.Weﬁndthattheinternationalspillovereffects notonlydependontheintegrationofelectricitymarkets,butalsoonthetightnessofthe emissions-tradingsystem.Weshowthatthistightnessisnegativelyrelatedtothedegree thesupplyofrenewableenergyisstimulated.Weﬁndthatthemorerenewableenergyis stimulated,thelessdomesticreductionincarbonemissionsisoffsetbyspillovereffects.A morebindingcapintheemissions-tradingsystemmakesnationalpolicieslesseffective. Hence,ifclimate-policymeasuressuchassubsidiesforrenewableenergymakethecapin thetradingschemelessbinding,theseclimate-policymeasuresbecomemoreeffective.

1. Introduction

Inordertoreducecarbonemissionsinthepowersector,governmentsareimplementingasetofpolicymeasures.These

measuresvaryfromsubsidiesforrenewable-energytechniquestotaxesonfossil-fuelelectricityproductionandmechanisms

fortradinginemissionrights.Whilesomemeasuresaretakenonnationallevel,othershaveaninternationalcharacter.

WithintheEU,theimplementationofclimatepoliciesispursuedbytheEuropeanCommission.TheRenewableEnergy

Directive(2009/28/EC),forinstance,setsabindingtargetof20percentﬁnalenergyconsumptionfromrenewablesources

by2020.EachEUMemberStatehastorealizetherenewable-energytarget,butthesecountriesarefreetochoosetheirown

policiestostimulatedeploymentofrenewable-energysources.EUcountriesutilizedifferentmeasuresforthispurpose,

suchasfeed-in-tariffsubsidiesandquotasystems(Haasetal.,2010).Inadditiontothis,severalcountriesareconsidering

toimposeconstraintsonconventional powerplants,in particularcoal-ﬁredpowerplants(EIA,2014; EZ,2015).These

measuresvaryfromimplementingadditionalenvironmentalstandards(e.g.onfuelefﬁciencyoremissionsperunit)making

夽 Thispaperiswrittenaspartoftheresearchproject“Redesigningtheelectricitymarketinordertofacilitatethetransitiontowardsasustainable

energysystem”,ﬁnancedbyNWOandvariousstakeholdersintheDutchenergyindustry(EnergieNederland,TenneT,NetbeheerNederland,VEMWand

Consumentenbond)andendorsedbyACMandStatkraft.TheauthorsthankthemembersoftheProjectgroup,theValorisationBoardaswellastheScientiﬁc

AdvisoryBoardfortheirinputduringthisproject.Theauthorsarealsogratefultoseminarparticipantsatthe39thIAEEconferenceinBergen,Norway.The

authors,however,arefullyresponsibleforthecontentsofthispaper.

∗ Correspondingauthorat:FacultyofEconomicsandBusiness,Nettelbosje2,9747AEGroningen,TheNetherlands.

E-mailaddress:machiel.mulder@rug.nl(M.Mulder).

https://doi.org/10.1016/j.reseneeco.2018.09.002

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itcomplicatedifnotimpossiblefor(old)coal-ﬁredpowerplantstooperateorimposingacarbontaxwhichinparticular

raisethegenerationcostsofcoal-ﬁredpowerplants.Besidesthissetofdifferentnationalpolicymeasurestoreducecarbon

emissionsbythepowersector,anemissions-tradingsystemhasbeenimplementedonEUlevel.ThisEUEmissionTrading

System(ETS)isthelargestcapandtrademechanismforCO2emissionsintheworld.Itsetsupacaponthetotalamount

ofCO2emittedbyinstallationsofﬁrmssubjecttothisscheme.Thiscapisannuallyreducedinordertorealizeanoverall

reductionincarbonemissions.Theinitialallocationofthecaptoparticipantswasinitiallydonebygrandfathering,butmore

andmoreauctioningisusedasallocationmethod(EuropeanCommission,2012).Inthesecondarymarket,participants

cantradeinpermitswhichresultsinacarbonprice.Meanwhile,theEuropeanCommissionispromotingtheintegration

ofnationalelectricitymarketstofacilitateborder-freetradingacrossEurope,see(Keay,2013).Asaresult,nationalpower

marketshavebecomemorecloselyintegratedwitheachother,whichmayincreasetheinternationalspilloversofnational

climatepolicies.

Itiswellestablishedineconomicliteraturethatthecoexistenceofdifferenttypesofclimatepoliciesmayhave

coun-teractingeffects(Schmalensee,2012;Goulder,2013;Böhringeretal.,2016).Thisholdsinparticularwhenacap-and-trade

emissionsschemeisimplemented.Inthatcase,theoretically,thelevelofemissionsisonlydeterminedbythecapinthe

emissions-tradingscheme(Tietenberg,2006).Ifthecapremainsthesame,otherinstrumentsonlyaffectthecostsofreaching

thattarget,butnottheamountofemissions.Ifanemissionstradingschemeiscombinedwithsubsidiesforsolarpanels,

forinstance,itcanbeexpectedthattheemissionswithinthepowersectorarereducedwhichlowerstheoveralldemand

forand,hence,thepriceofemissionspermits,whichinturncanstimulateotherﬁrmsparticipatingwithintheemissions

tradingschemetoraisetheiremissionssinceemittinghasbecomecheaper(seee.g.vandenBerghetal.,2013;Böhringer

andRosendahl,2011).Thiseffectiscalledthewaterbedeffectofclimatepolicy.

Inthispaper,weexploretheconditionsfortheinteractioneffectstooccur.Forthatpurpose,weanalyzetheinteraction

ofthreetypesofpolicymeasurestorealizeatransitionoftheelectricityindustrybasedonfossilfuelstowardsanindustry

withalowerlevelofcarbonemissions.Thesepolicymeasuresaresubsidiesforrenewableelectricity,acarbontaxfor

fossil-fuelpowerplantsandaninternationalemissionstradingscheme.Thechoiceforthesethreetypesofpolicymeasures

(emissionstrading,subsidiesrenewablesandcarbontax)isbasedonthefactthatallthreetypesofmeasuresarecurrently

implementedordiscussed,albeittoadifferentextentinseveralEuropeancountries.IntheNetherlands,forinstance,the

governmentrecentlydecidedtoimplementa carbontaxontopoftheEuropeanemissiontradingschemeandseveral

domesticsupportschemesforrenewableenergyinordertorealizeaminimumpriceforcarbon.Inthispaperwedonot

discusstheprosandconsoftheindividualclimate-policyinstrumentsassubsidies,taxesandemissionstrading.Although

onecandiscusswhichinstrumentisbestequippedtorealisecarbonreductioninacost-effectiveway(seee.g.Aldyetal.,

2010),inpracticegovernmentsusepackagesofdifferenttypesofinstruments(HughesandUrpelainen,2015;Kauttoetal.,

2012;DelRioandMir-Artigues,2014;Sijm,2005).Thereforeitisalsoimportanttounderstandhowtheyinﬂuenceeach other.

Aswewanttoanalyzetheinteractionamongvariousclimate-policymeasures,webuildaconcisestylizedmodeloftwo

connectedelectricitymarketscombinedwitharegionalemissions-tradingmarket.Inthismodel,someelectricityproducers

areperceivedasstrategicplayers,hencetheycanexercisemarketpowerandinﬂuencethewholesaleprices.Suchamodel

isfairlywellequippedtosimulatethesituationwithafewcentralizedpowerproducers,asitexistsinseveralEuropean

countriessuchastheDutchandGermanelectricitymarket(seealsoWillemsetal.,2009;Mulderetal.,2015;tenCateand

Lijesen,2004).Wetakethestochasticnatureofbothsupplyanddemandintoaccount.Firmsbasetheirdecisionsregarding

investmentsandthedispatchofplantsonexpectedvaluesforweatherconditions,loadlevelsandscarcitylevels.Including

probabilitydistributionsforwindanddemandallowsustocontrolforthevolatilityofmarketconditionsinthepower

market.Internationaltradeisbasedonprice-arbitrageopportunities.Thesizeofthecross-bordertransmissioncapacity

determinesthepotentialmagnitudeofinternationaltradeand,hence,thepotentialcross-borderspillovereffects.Thetwo

countriesinthismodeldifferinsize,sowehavealargeandasmallcountry.Differencesinscaleofcountriesareimportant

toconsiderinordertobetterassessinternationalspillovereffectsfrompoliciesimplementedinthedifferentcountries.One

mayexpectthatthemagnitudeofthespillovereffectsarehighestwhentheyoriginatefromalargecountryandaffecta

neighboringcountrysmallerinsize.Asaninternationalcarbonpermitmarketisaddedtotheelectricitymarket,thecarbon

priceispartofthevariablegenerationcostsoffossil-fuelproducers.Inaddition,countriesmayimplementacarbontaxon

electricityproducers.Inordertoalsoanalyzetheinternationalspillovereffectsofdifferentnationalpolicies,weassume

thatthecarbontaxisonlyimplementedinonecountryatthesametime.Countriesarealsoabletostimulate

renewable-electricitygenerationbygivingsubsidieswhichareﬁnancedbyataxonelectricityconsumption.Themodeliscalibrated

tomoreorlessreﬂectthecurrentcharacteristicsoftheGermanandDutchpowermarket.Theobjectiveofthiscalibration

isjusttohaveareasonablebenchmarkforthenumericalanalysis,nottomakerealisticsimulationsofthepowermarkets

inthesecountries.Thenumericalanalysisremainsofastylizednaturewiththepurposetoexploretheconditionsforthe

occurrenceofinteractioneffectsamongclimate-policyinstruments.

Usingthenumericalapplicationofourmodel,weﬁndthatcombiningthethreedifferentclimate-policymeasures,

includ-inganemissions-tradingsystem,mayhaveaneteffectonthelevelofcarbonemissions,despiteoftheabove-mentioned

waterbedeffect.Thisresultcomesfromthefactthatthecarbonpriceinthetradingschemehasaﬂoor,i.e.itcanneverbe

lowerthanzero.Thismeansthatwhenotherclimate-policymeasuresareeffectiveinreducingthedemandforpermits,they

mayalsoneutralizethewaterbedeffect.Ourﬁndingsshowthatimplementingnationalpoliciesontopofaninternational

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taxontopofanemissionstradingschememayresultinmoreemissionsreductionsasthewaterbedeffectdoesnotalways

work,thisdoesnotmeanthatsuchapolicyisefﬁcient.

Theremainderofthispaperisorganizedasfollows.WereviewrelevantliteratureinSection2.InSection3,wedescribe

thekeyelementsofthepartialequilibriummodelofthewholesaleelectricitymarketanddeﬁnehowthemarketequilibrium

isdetermined.Section4presentstheresultsforthepolicyvariants.Section5,ﬁnally,concludes.

2. Literature

Thispaperbuildsonandcontributestotheliteratureofpowermarketmodelingandinteractioneffectsofclimatepolicies.

Akeyquestionregardingthemodellingoftheelectricitymarketishowtodealwithstrategicbehaviour.Willemsetal.(2009)

comparetwooligopolisticmodelsoftheelectricitymarket:CournotandSupplyFunctionEquilibrium.1_They_show_that_both

modelsexplainroughlythesamefractionoftheobservedpricevariationsintheGermanelectricitymarket.Furthermore,

theysuggesttouseCournotmodelforshort-termmodelanalysisassuchamodelcaneasilyaccommodateadditionalmarket

conditionssuchasnetworkconstraints.Mulderetal.(2015)applytheCournotmodeltotheDutchelectricitymarkettaking

boththeintermittentwindenergysupplyandfringesuppliersbyCombinedHeatandPower(i.e.,CHP)intoaccount.Asa

resultoftheintermittentandfringesupplies,thewholesalepricestendtobelower.Usingacompetitiveequilibriummodel

withoutstrategicbehavioramongpowergenerators,SaguanandMeeus(2014)investigatetheinteractionbetween

cross-bordertransmissioninvestmentsandrenewable-energypolicies.Theirmainconclusionisthatrenewableenergytradein

ordertocomplywitheachmemberstatetargetsisbeneﬁcialforbothzones,butthatanimperfectregulatoryframeworkfor

transmissioninvestmentcreatesasigniﬁcantcostforrealisingrenewable-energytargets.Inourmodel,some“big”producers

areperceivedasstrategicplayers,hencetheycanexercisemarketpowerandinﬂuencethewholesaleprices.Suchamodel

fairlywellresemblesthesituationwithafewcentralizedpowerproducers,suchasintheDutchandGermanelectricity

market.

Usingseveraldifferentmodelsincludingpartialequilibriummodelsandgeneralequilibriummodels,Calderónetal.

(2016)ﬁndsigniﬁcantCO2reductionsthroughhighcarbonpricesandabatementtargetsinColombia.Benavente(2016)

usesacomputablegeneralequilibriummodeltoexaminetheimpactofacarbontaxinChile.Theyconcludethatsucha

policyiseffectiveatreducingcarbonemissionsbutatthecostofGDPlosses.EllertonandFullteron(2014)ﬁndthatacarbon

taxonelectricityintheU.S.cangeneratenetnegativedomesticleakageasitraisesthecostsforotherindustries,which

resultsinlowerdemandand,hence,lowerproductionlevelsandcarbonemissionsbytheseindustries.Thisimpactofhigher

costsinthepowerindustryonoverallcarbonemissionswasalsofoundbyMcKibbinetal.(2014).Theseauthorsconclude

thatthedomesticcarbonemissionsoutsidethepowersectordecreaseashigherelectricitypricesslowoveralleconomic

activity.Notethattheabove-mentionedpapersonlyconsiderdomesticcarbontaxtoreducedomesticcarbonemissions.In

amorethanonecountrysetting,Elliottetal.(2010)conﬁrmsthatauniformtaxamongallmembercountriesiseffectiveat

reducingcarbonemissions.

Intheabovementionedliterature,theanalysisofinteractionofcarbontaxeswithotherclimatepoliciesisnottakeninto

account.Fromliteratureonemissionstradingweknowthatthecoexistenceofdifferenttypesofclimatepoliciesmayhave

counteractingeffects.Whenacap-and-tradeemissionsschemeisimplemented,thelevelofemissionsisdeterminedbythe

capintheemissions-tradingscheme(Tietenberg,2006).Ifthecapremainsthesame,otherinstrumentsonlyaffectthecosts

ofreachingthattarget,butnotnecessarilytheamountofemissions(seee.g.vandenBerghetal.,2013).Asaresult,theﬁnal

levelofemissionsremainsunchangedwhilethecontributionofdifferentemitterstothisoveralllevelhaschanged,which

raisesthecostsofreachingthecap.BöhringerandRosendahl(2011)ﬁndthatthecostsofrealisingaCO2reductiontargetof

25%increasebymorethan60%ifthepercentagerenewableenergyisstimulatedbymorethan10%.Inotherwords:incaseof

anemissions-tradingscheme,othermeasuresdirectedatrealisingemissionreductionmerelyaffectthelevelaswellasthe

allocationofcostsofreachingtheemissioncapamongtheparticipantsofthetradingschemewithoutaffectingtheoverall

levelofemissions(i.e.thebeneﬁtsintermsofreductionsofemissionsremainthesame).Becauseofthisinteractioneffect,

Böhringer(2014)concludesinhisoverviewoftwodecadesofEuropeanClimatepolicy,thatrenewable-energysubsidies

andenergy-efﬁciencymandatescanresultinhighercostsforrealisingenergysavings,energyefﬁciencyimprovements,and

fuelswitchingthanincaseofastand-alonecap-and-tradesystem.Theeffectivenessofclimatepolicycanalsoseriouslybe

reducedthroughcarbonleakage.Caronetal.(2015),forinstance,showthatthecap-and-tradeemissionstradingscheme

inCaliforniamayresultinanincreaseofemissionsinneighboringmarketswhichmayneutralizeabouthalfoftherealized

reductionbythescheme.

Fromthesepapers,welearnthatcombiningdifferenttypesofclimate-policymeasuresreducesthecost-effectivenessof

climatepolicy.Thisstrandofliteraturealsostatesthataddingotherpolicyinstrumentstoasystemofemissionstradingdoes

notresultinanyadditionalemissionsreduction(Sijm,2005;SorrellandSijm,2003).Theargumentsinfavourofotherpolicy

measures,suchassubsidiesforrenewableenergy,arederivedfromtheperceivedbeneﬁtsintermsoflearningeffectsor

securityofenergysupply.Thecontributionofourpaperisthatweanalysetheconditionsunderwhichtheinteractionoccurs

ordoesnotoccur.Inparticular,weanalyseinwhichcircumstancesclimate-policymeasuressuchassubsidiesforrenewables

1_Cournot_equilibrium_assumes_that_producers_compete_in_the_production_quantity_while_the_Supply_Function_Equilibrium_assume_that_producers_compete

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Fig.1.Frameworkofatwo-countrymodeloftheelectricitymarketwithclimate-policyinstruments.

andtaxesonfossil-fuelusehaveanadditionalreducingeffectoncarbonemissionswhenalsoanemissions-tradingscheme

exists.

3. Concisemodeloftheelectricitymarket

Inordertoanalysetheinteractionofdifferenttypesofclimate-policymeasures,wedevelopandapplyaconcisestylized

two-countrymodeloftheelectricitymarketplusaregionalemissions-tradingscheme.Theframeworkofthismodelis

depictedinFig.1.Inthefollowingsections,weintroducethecorrespondingcomponentsindetail.

3.1. Supplyside

Onthesupplyside,theelectricitymarketiscomposedofbothcentralizedanddecentralizedpowerproducers.Theset

ofcentralizedpowerproducersincountrycisdenotedasNc={1,2,...,nc}.Ingeneral,ncistakentobeasmallnumber.For

example,intheDutchelectricitymarket,thereareonlyafewmajorelectricityproducers(ENGIE,E.ONBenelux,Essent(part

ofRWE)andNuon(nowsubsidiaryofVattenfall)).Inmostcases,thepowermarketisoperatedonahourlybasis.Therefore,

wemodeltheelectricitymarkethourlyandh∈{1,2,...,24}denoteshoursinadaythroughoutthewholeyear.Theyears

areindexedbyy∈{1,..., ¯y}.Themodelissimulatedsuchthat“1”representsthecurrentsituationand“ ¯y”denotestheend

year.Notethatpcyhisthewholesalepriceperhourincountrycyeary.

Theenergymixemployedbyproducersconsistsoffossil-fuelﬁredplants(F)includinggasandcoal-ﬁredplants,wind

turbines(W),solarcells(S)andcombinedheatandpower(H).Theenergyresourcesforcentralizedpowerproducersinclude

fossil-fuelplantsandwindturbines.Notethatthedifferencebetweenfossil-fuelplantsandwindturbinesisthatthecosts

onthemarginforthewindturbinesarealmostzero,whilethemarginalcostsforfossil-fuelplantsarenotzeroandalso

includeCO2prices.Wedonotconsidertechnologyupgradestoreducethemarginalcostsoffossil-fuelplantsaswemay

assumethattheseareconstantintheshortterm.

Assumption1. Eachcentralizedpowerproduceri∈Nchasthesameconstantmarginalcostmc ∈R+forfossil-fuelplants

overyearyincountryc.

Notethatwedoallowdifferentfossil-fuelproductiontechniquesinthesetwocountries.Hence,theconstantmarginal

costsmightdifferbetweenthem.Thedeploymentofwindenergymainlydependsontheweatherconditionsandisstochastic,

exante.Letw_hdenotethecapacityfactorathourhtoexploitthewindenergycapacity.Becauseofthegeographicalproximity

ofneighboringcountries,weassumethattheproductionbywindturbinesissubjecttothesamestochasticpatterninboth

countries.

Assumption2. Weassumethatwhfollowsacertaindiscretedistribution,withrealizationsjh ∈R+andeachrealization

j_hhasaprobabilityj_h ∈R+.Notethat

j

j h=1.

Notethatqi

cyhiscomposedoftheproductionamountbyfossil-fuelplantsandalsowindturbines,hence

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NotethatqiF_cyhandqiW_cyharetheproductionpartbyfossil-fuelplantsandwindturbines,respectively.Andtherealizedwind

energyproductioniscalculatedbasedontherealizedcapacityfactorandtheinstalledgenerationcapacity,

qiW cyh= j h×Q iW cy . (2)

Atthebeginningofacertainyear,eachcentralizedpowerproducer’swindenergycapacityQiW

cy isgivenandisassumed

tobecommonknowledge.NotethattheproductionamountisconstrainedbythegenerationcapacityQiF

cyandQcyiW,hence wehaveqiF cyh≤Q iF cyandqiWcyh≤Q iW

cy .TheaggregatefossilfuelgenerationcapacityincountrycyearyisdenotedasQcyF and

QF

cy=

i∈NcQ

iF

cy.Theﬁrmscaninvestinfossil-fuelgenerationcapacityeachyearandwedenoteQcyF astheinvestmentin

fossil-fuelplantsincountrycyeary.

Becauseofthelargenumberofdecentralizedpowerproducers,theyaremodeledasprice-takerswhichcannotexercise

marketpowertoinﬂuencewholesalemarketprices.Hence,thedecentralizedpowerproducerequalizestheirmarginal

beneﬁtstotheirmarginalcosts.Theaggregatedecentralizedpowerproduction(D)onlyusescombinedheatandpower

(DH),andsolarcells(DS).Costsonthemarginfromwindandsolarenergiesproductionareassumedtobezerowhile

combinedheatandpowerisasideproductofthehorticulturalsuppliers,whosemainobjectiveistoproduceheatfortheir

greenhouses.Weassumethattheyhaveincreasingmarginalcosts(seealsoMulderetal.,2015).

Assumption3. TheproductionamountbycombinedheatandpowerqDH

cyhisassumedtobealinearfunctionofelectricity

prices,

qDH

cyh=˛D+ˇDpcyh,

where˛D>0andˇD>0.

Inaddition,theexpectedproductionamountbysolarcellsistheproductofthehourlycapacityfactorandtheinstalled

generationcapacities.Letuhbetheexpectedcapacityfactorofsolarcellsathourh.Hence,wehavethefollowing,

qDS_cyh=uh×QcyDS,

whereQDS

cy denotestheyearlygenerationcapacityforsolarcells.ThesumofCHPandsolarcellscomposestheaggregated

productionamountbyfringesuppliers,

qD_cyh=˛cyh+ˇpcyh, (3)

where˛cyh=˛D+uh×QcyDSandˇ=ˇD.

3.2. Demandside

Thedemandsideofthewholesaleelectricitymarketconsistsoflargeelectricityusers(L)andretailers(R).Retailerssell

electricityfurthertoconsumersandprosumers.Weassumealineardemandfunctionforlargeelectricityusersasfollows:

pcyh+tL+h=aLh−bLhqLcyh, (4)

whereaL

handbLhareparameterstobecalculated,tListhetaxrateforlargeelectricityusersandhisthehourlynetwork

tariffpaidbylargeelectricityusers.Hence,weimplicitlyassumethatthetaxrateandnetworktariffsdonotchangeover

timey.

Theretailpriceisequaltothewholesalemarketprice(pcyh),plusaretailmargin(r),taxes(orlevies)tRandthedynamic

networktariffsh.Hence,thedemandfunctionforconsumersandprosumerscanbespeciﬁedasfollowing,

p_cyh₊tR₊_r₊

h=aRh−bRhqRcyh, (5)

whereaR

handbRhareparameterstobecalculated.Theaggregationofthedemandfromlargeusersandretailersinducesthe

totaldemandfunctionfacedbyproducers,

qcyh=qLcyh+qRcyh=ah−bhpcyh, (6)

whereahandbharecalculatedfromEqs.(4)and(5)and,

a_h₌ a L h−t L₋ h bL_h + aR h−t R₋_r₋ h bR_h , bh= 1 bL h + 1 bR h .

Notethatbyintroducingadynamicnetworktariffh,wemovetheaggregatedemandfunctionupwardordownwardona

hourlybasis,buttheslopeoftheaggregatedemandfunctiondoesnotchange.Therefore,theaggregatedemandfunction

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3.3. Marketequilibrium

Thewholesaleelectricitymarketis modeledasanimperfectmarket.Facinga certaindemandcurve,theproducers

competeintermsofquantities.Themarketreachesequilibriumwheneachproducer’sstrategyisthebestresponseto

thestrategiesactuallyemployedbyitscompetitors.Domesticelectricitydemandismetbycentralizedproducersandthe

aggregatedecentralizedproduction,hence

qcyh=

i

qi_cyh+qD_cyh. (7)

Andtheresidualdemandfacedbyiisgivenby,

qi

cyh=ah−bhpcyh−q−i_cyh−˛cyh−ˇpcyh, (8)

whereq−i_cyhdenotesthesumoftheothercentralizedproducers’productionamountexcepti.Notethatintheaboveequation,

wehavereplacedqD

cyhbyEq.(3).RearrangingEq.(8),weobtain,

pcyh=

ah−˛cyh−qicyh−q−icyh

bh+ˇ

, (9)

Inpractice,forwardcontractsplayanimportantroleinelectricitywholesalemarkets.Electricityproducerssellapart

oftheirgenerationinforwardmarkets.AllazandVila(1993)haveshownthatﬁrmshaveanincentivetodosoasthismay

reducethemarketpowerofcompetitorsinthespotmarket.Asaresultofthesaleofelectricityinforwardmarkets,the

competitioninthespotmarketsismoreﬁercewhichhasapricereducingeffect,whiletheactualproductionishigher(see

alsoMulderetal.,2015).Becauseofthisrelationshipbetweenforwardandspotmarketcompetition,weexplicitlycontrolfor

theimpactofforwardmarketssalesontheactualproductionlevelofthestrategicplayers.Hence,weassumethatcentralized

powerproducersareactiveintheforwardmarket.Letqif_cyhbetheforwardtradingquantitybyﬁrmiandpf_cyhbetheforward

price.FollowingAllazandVila(1993),“underperfectforesight,equilibriumrequirestheforwardmarkettobeefﬁcient.

Thismeansthattheforwardpriceasafunctionoftheforwardpositionsmustbeequaltothepricethatwillresultfrom

theCournotcompetitiononthespotmarketgiventhesepositions.Therefore,noarbitrageispossible.”Giventheforward

positionsbyeachﬁrm,ﬁrmscompeteovertheproductionquantityinthespotmarket.Hence,theproductionquantityhas

tobesolvedasafunctionoftheforwardpositions.Thenﬁrmsoptimizetheirforwardpositionsgiventhequantitysolved

fromtheproductionperiod,seeAllazandVila(1993).Notethatinourmodelpartoftheproductionismetbywindenergy.

AllthederivationsfortheoptimalproductionandforwardpositionsareincludedinAppendixC.Wehavethefollowing

resultsforthemarketequilibrium,

Proposition4. Underthefollowingconditions,

1.ThedecentralizedpowerproductionisgivenbyEq.(3);

2.TheaggregatedemandfunctionisgivenbyEq.(6);

3.Thedemandissatisﬁedbycentralizedpowerproducersanddecentralizedpowerproduction;

4.Theexpostproductionfromwindenergyiscalculatedbasedonactualcapacityfactorj_handgenerationcapacity(Eq.(2));

5.Centralizedpowerproducersusebothfossilfuelsandwindenergy(Eq.(1));

Wehavethefollowingresult:theoptimalproductionamountusingfossilfuelsbyﬁrmiathourhandtimeyisgivenby,

qiF_cyh=nc

ah−˛cyh−mc(bh+ˇ)

−qiW_cyh−nc(qiW_cyh+q−iW_cyh )

n2

c+1

;. (10)

FromEq.(10),wecaneasilyseethatanyproductionbywindturbineswillreplacetheelectricitygenerationbyfossil-fuel

plantsforproduceri.Foreachvalueofthecapacityfactorforwindturbinesj_h,wewouldhaveacorrespondingmarket

equilibriumregardingfossil-fuelsproduction(10)andwholesaleprices(9).2

3.4. Internationaltradeandlawofoneprice

Inthissection,wefurtherinvestigatehowimportandexportinﬂuencethedomesticprice,whichisdeterminedby(9).

Iftherearepricedifferencesbetweenthetwocountries,weassumethattraderswillproﬁtfromexportfromalowerprice

2 _In_the_model_calibration_and_policy_analysis,_we_also_put_an_additional_constraint_that_the_hourly_changes_within_the_fossil-fuel_electricity_production

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countrytoahigherpricecountry.3_For_country_c,_let_IE

cyhbethenetexportamountinhourhyeary,i.e.,exportminusimport.

Letpu

cyhbetheuniformpricesbetweenthesetwocountriestogetherwithtradingamountIEcyh,hencewehavethefollowing

pu_cyh= ah−˛cyh−

iq i cyh+IEcyh bh+ˇ . (11) Notethatqi

cyharesolvedfromEq.(10)togetherwiththeexanteexpectedwindenergyproduction.4Inaddition,wehave

pu_S,yh=pu_L,yh, (12)

and

IES,yh+IEL,yh=0. (13)

CombiningEqs.(11)–(13),wesolvefor thecorrespondingpu

cyh andIEcyh.Inthesecondstep,wecheckforthecapacity

constraintIUbetweenthesetwocountries.IfIES,yh>IU,thenthe(absolute)sizeoftheimportandexportisequaltothe

capacityconstraintwhilethedifferentpricespd_cyhinbothcountryareasfollows:

pd S,yh= ah−˛S,yh−

iqiS,yh+IU bh+ˇ , pd L,yh= ah−˛L,yh−

iqiL,yh−IU bh+ˇ .

IfIES,yh<−IU,thenthecross-borderﬂowsareintheoppositedirectionwhilethepricesinbothcountriesareasfollows:

pd S,yh= ah−˛S,yh−

iqiS,yh−IU bh+ˇ , pd L,yh= ah−˛L,yh−

iqiL,yh+IU bh+ˇ .

3.5. Carbonmarketandtheinteractionwiththeelectricitymarket

Finally,weaddaninternationalcarbonpermitmarkettothesetofnationalelectricitymarkets.Theelectricityindustryis

assumedtobetheonlyparticipantinthismarket.LetcapybethecarbonemissioncapandPCO2ybetheaverageCO2price.

Foreachfossil-fuelproductiontechnique,thecarbonemissioncoefﬁcientisdenotedasec.Insuchasetting,theadjusted

constantmarginalcostsaccyforcountrycinyearyareasfollows:

accy=mc+PCO2y×ec. (14)

Giventheconstantmarginalcostsaccy,wecalculatethefossil-fuelproductionaccordingtoEq.(10).Thenwecomparethe

actualaggregatedcarbonemissionsoveraperiodwiththeemissioncapforthatperiod.Ifthecarbonemissionsareabove

thecap,wekeepincreasingthecarbonpricesuntiltheemissionsareequaltoorbelowthecap.Hence,thecarbonpriceis

determinedbythecapandtheaggregateddemandforcarbonpermits.

3.6. Bankingofpermits

IntheEUETS,allowancescannotonlybefreelyusedwithinaphase(thecurrentphasebeing2013–2020),butalsosaved

untilthenextphase.Thissavingofpermitsiscalledbanking.Intheaboveanalysiswedidnotcontrolforthisbankingoption.

Inordertoanalysetheimpactofbankingonthemodelresults,wealsorunasensitivityanalysiswhereﬁrmscanfreely

transferanypermitwhichisnotusedtothenextperiod.

Thisismodelledasfollows:iftheaggregatedlevelofemissionsduringaperiodisbelowthecapforthatperiod,then

weassumethatallunusedpermits(whichisequaltothedifferencebetweencapandemissions)istransferredtothenext

period,raisingtheactualcapinthatperiod.

3_We_do_not_make_any_assumption_on_the_type_of_connection_between_markets_and_how_traders_can_make_use_of_cross-border_capacity,_but_we_do_take

intoaccounttheexistenceofacross-borderconstraint.Notethatintheﬁrststepofthecalculation,weallowtraderstoequalizethepricesbetweenthese

twocountriesnothinderedbyacross-bordertransmissionconstraint.Inthesecondstep,wecontrolforthisconstraint.

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Table1

Parameterschosenforthesmallandlargecountries.

Smallcountry Largecountry

Numberofcentralizedproducers 5 8

Constantvariablegenerationcosts(Euro/MWh) 35 30

Windpowergenerationcapacity(GW) 2.9 57.5

Solarpowergenerationcapacity(GW) 1.1 22.5

4. Numericalanalysis

4.1. Parameters,scenariosandpolicyvariants

Inordertoanalysetheinteractioneffectsbetweenclimate-policymeasures,weconductanumericalanalysiswithour model.Werefertoatwointerconnectedregioncasewherewehavealargeandsmallcountry.Differencesinscaleofcountries areimportantinordertobetterassessinternationalspillovereffectsfrompoliciesimplementedinthelargercountrytothe smallercountry.TheparametersforbothcountriesarederivedfromthecharacteristicsofGermany(large)andNetherlands (small),respectively,justtohaveabenchmarkforthecalibrationbutwithouttheobjectiveoffullyrepresentingthese countriesormakingaspeciﬁcpolicyanalysisforthesecountries.Table1listsabriefsummaryofrelevantparameterswe

haveusedinthispaper.

AccordingtotheStatlinedatabaseofStatisticsNetherlands,theinstalledcapacityforwindenergyincludingonshore

andoffshorewindparksisroughly2.9GWin2014.5_Most_wind_energy_production_in_the_Netherlands_is_run_by_centralized

powerproducers.Thecapacityfactorperhourtoemploythewindpowergenerationcapacityiscalculatedbasedonthedata

fromtheDutchRoyalMeteorologicalInstitute.6_The_installed_capacities_for_wind_power_generation_in_Germany_are_taken

tobeabout57.5GW.Becauseofthegeographicalproximity,thecapacityfactorofwindenergyproductioninGermanyis

assumedtohavethesamediscretedistributionperhourasintheNetherlands.

DecentralizedpowerproductionmainlyreferstoCHPandsolarenergy. Theminimumruncapacity forCHPinthe

NetherlandsandGermanyisestimatedtobe5GWh.Weroughlyestimatethat˛D=5000andˇD=30.Theinstalledsolar

generationcapacityin2014arearound1.1GWintheNetherlandsand22.5GWinGermany.7_We_could_calculate_the_solar

cellshourlycapacityfactoruhbasedonthehistoricaldatafrom2006to2014.

DetailsofhowwecalculatethehourlyaggregatedemandfunctionarereportedinAppendixD.Theelectricity

consump-tionamountandwholesalepricesarebasedonaloadproﬁle.Priceelasticitiesarebasedontheresultsintheliterature

fortheelectricitymarket,seeLijesen(2007).Wehavetakenhourlypriceelasticitiesandingeneral,ahigherelasticityfor

off-peakhoursandalowerelasticityforpeakhours(9–20h).Allhourlyelasticitiesareintherangeof−0.3and−0.2.

Inordertokeepthemodelsimulationsassimpleaspossible,weapproacheachyearbysimulatingonly24consecutive

hours.8_Hence,_we_ignore_weekly_and_seasonal_{ﬂuctuations}_in_demand_and_supply_and_treat_the_outcome_of_a_{24-simulation}

asrepresentativeforallhoursinayear.Forthesimulationoftheemissiontradingscheme,forinstance,thismeansthatthe

modelworkswithadailycapanddailyprice,butthiscapandthispricemustbeseenastheannualcapandtheaverage

annualprice.

Asthesupplyanddemandconditionsmayvarystronglyoveryeartoyear,weworkwithscenariosregardingwindspeed

anddemandlevels.9_For_each_wind_speed_level,_we_use_a_probability,_based_on_empirical_evidence_for_the_Netherlands._In

ordertodeﬁnethehourlyprobabilitydistributionweuseactualhourlydataonwindspeed.Werankthehourlydatafrom

lowesttohighestlevelandthendeterminetheaveragevalueinthreeclasses:thelowest31%,thenext38%andthehighest

31%ofallobservations.Table3givestheresultsforthewindspeed.Forthedemandlevel,wescaleupordowntheintercept

ahoftheinversedemandfunction.Foreachscalingfactor,weassignacorrespondingprobabilityandthisholdsforeach

hour.Table2reportstheresultfordemandlevelineachhour.

Notethatforeachhour,wehave3possiblerealizationsofthewindenergycapacityfactorand3scalingsofthedemand.

Therefore,weendupwith9scenariosforeachhour.Runningthemodelforeachhourforeachscenario,weobtainforeach

houraprobabilitydistributionofallresults.ThisMonto-Carlotypeofanalysisenablesustodealwiththeimpactofextreme

circumstances,inparticularregardingtheimpactofrenewablesontheelectricitymarketandtheemissions-tradingscheme.

5 _{http://statline.cbs.nl/Statweb/selection/?DM=SLEN&PA=83109ENG&LA=EN&VW=T}_accessed_on_November_5,_2015. 6 _{http://www.knmi.nl/home}_.

7 _Data_source:_{https://en.wikipedia.org/wiki/Solar}_power_in_the_Netherlands_.

8 _Otherwise_we_would_need_to_simulate₈₇₆₀_h_per_year,_which_would_cost_a_lot_of_computation_time_for_a_model_with_imperfect_competition_with

stochasticdistributionsofexternalfactors,whileaddingsuchcomplexityisnotneededforthepurposeofouranalysis.

9 _The_intermittent_character_of_renewables_as_well_as_the_{stochasticity}_of_demand_is_dealt_with_by_scenarios_where_we_have_{distributions}_for_both._The

modelisrunforanumberofscenarios.Ineachscenarioaspeciﬁc(joint)distributionofwindanddemandoccurs.Implicitlyweassumethattheﬁrms

havefullcertaintyaboutwhichscenariotheyarein.Inotherwords,weimplicitlyassumethatthereisnodeviationbetweentheexpectationsfortheshort

runandtherealisation.Hence,onecanalsosaythatweignoretheproblemsofbalancingandprogrammeresponsibility.Webelievewecanignorethese

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Table2

Inversedemandinterceptscalingfactors.

ahScalingfactor Probability

0.8 0.31

1 0.38

1.2 0.31

Table3

Windpowercapacityfactorwithprobabilitiesineachhour.

Hour Lowcapacitywithprob0.31 Mediumcapacitywithprob0.38 Highcapacitywithprob0.31

1 0.005 0.056 0.397 2 0.005 0.056 0.397 3 0.005 0.056 0.397 4 0.005 0.056 0.423 5 0.005 0.056 0.397 6 0.007 0.063 0.423 7 0.008 0.071 0.451 8 0.011 0.089 0.479 9 0.013 0.110 0.541 10 0.016 0.121 0.573 11 0.023 0.146 0.607 12 0.027 0.160 0.642 13 0.032 0.171 0.678 14 0.032 0.174 0.678 15 0.032 0.160 0.642 16 0.027 0.146 0.607 17 0.020 0.121 0.541 18 0.016 0.099 0.479 19 0.011 0.080 0.451 20 0.008 0.071 0.418 21 0.007 0.063 0.423 22 0.007 0.063 0.423 23 0.005 0.056 0.397 24 0.005 0.056 0.397 Table4

Matrixrepresentationof8policyvariants.

Emissioncaplevel

BaseCap LowCap HighCap

CarbonTax

No Baseline BaselineLowCap BaselineHighCap

Largecountry CarbonTaxL CarbonTaxLLowCap CarbonTaxLHighCap Smallcountry CarbonTaxS

CarbonTaxorSubsidyRES No BaselinenoRES

Usingtheabovedataforthedeterminationofthestartingvaluesofthemodelaswellastheprobabilitydistributions fortheexogenouscircumstances,wesimulatetheelectricitymarketforaperiodof15periods,coveringtheperiod2016 -2030.Now,weconsider8policyvariantsasdescribedinTable4.

Inthe“Baseline”variantitisassumedthatbothcountriesannuallyincreasetherenewable-energycapacitywhilealsoa

internationalcap-and-tradeemissionstradesystemexists.TheannualincreaseinREScapacityisbasedontheassumption

that10%ofelectricitytaxrevenuesisusedtoﬁnancethesubsidiesfortheseinvestments.Theinitialcarbonemissioncap

levelischosentobe1.04Mtonsperday,whichisaboutequaltotheaggregateddailyemissionsbythepowerindustryin

GermanyandtheNetherlands.Inthe“Baseline”,weassumethatthecapisreducedby0.5%annually.Inthepolicyvariants

“LowCap”and“HighCap”thecapisannuallyreducedby1%and0.25%respectively.Weareinparticularinterestedinthe

effectsofintroducingacarbontaxinrelationtothetightnessoftheemissionstradingschemewhichisrepresentedby

theinitiallevelofthecap.Inthevariantswithacarbontaxitisassumedthatthelargercountryimposesacarbontaxof

11.25euro/MWhonfossil-fuelgenerationplants.10_In_order_to_compare_the_results_of_the_carbon_tax,_we_compare_three_pairs

ofvariants:BaselinevsCarbonTaxL,BaselineLowCapvsCarbonTaxLLowCap,BaselineHighCapvsCarbonTaxLHighCap.

Thisallowsustoexaminetheeffectsofafossil-fueltaxgivendifferentlevelsofthecaponcarbonemissionandgivenamore

orlessexogenousautonomousgrowthinrenewable-energycapacity.WealsocomparethevariantsBaseline,CarbonTaxL

10_According_to_the_CO

2emissionscoefficientstonsperMWh,wehavetaken0.3forgas-firedplantsand0.6forcoal-firedplantsinthesimulation.For

aportofolioof50%coal-ﬁredand50%gas-ﬁredfossil-fuelplantswithacarbonpriceof25europerton,wechoosealevelof11.25europerMWhforthe

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Fig.2. DurationcurvesofhourlyRESproduction,Baseline,2016and2030.

andCarbonTax Stoassesstheimpactofaproducertaxinthesmallcountrycomparedtoaproducertaxinthelargercountry.

Finally,inordertoanalysetheinteractionbetweentheemissionstradingschemeandsubsidiesforrenewableenergy,wealso

comparetheresultsofthevariantsBaselinevsBaselinenoRES.Intheformerpolicyvariants,emissionstradingiscombined

withsubsidiesforrenewableenergy,whileinthelattertheonlyclimatepolicyimplementedistheemissiontradingscheme.

4.2. Results

Weﬁrstpresentthenumericalresultsforthe“Baseline”,whichisthescenariowherebothcountriesstimulateRESby

givingsubsidiesforinvestments,whilealsoaninternationalcap-and-tradesystemexists.Weareinterestedinthefollowing

metrics:thewholesaleelectricityprices,thehourlyRESproduction,theutilisationoffossil-fuelplants(deﬁnedasaverage

hourlyproductioninpercentageofinstalledcapacity),theCO2pricesand,ﬁnally,theCO2emissions.Then,wecomparethis

BaselinewiththeBaselinenoRESwherenosubsidiesforRESareincluded.Next,weconsiderthevariantof“Prodtax”which

imposesafossil-fueltaxinthelargecountryontopofthe“Baseline”.Finally,weconductasensitivityanalysisbychanging

theemissioncaplevel.11

4.2.1. Baseline

Asaresultofanexogenousstimulationofinvestmentsinrenewableenergycapacityin the“Baseline”variant,this

capacityincreasesstrongly.Asaconsequence,thevolatilityinthesupplybyrenewablesincreasesstronglyaswell(Fig.2).

Thisisrelatedtothefactthatthehourlyproductionlevelbyrenewablesissometimesclosetozeroincaseofunfavourable

weathercircumstancesindependentofthesizeofinstalledcapacity.Hence,thelowestlevelofproductionbyrenewable

energycapacityishardlyaffectedbythesizeofthiscapacity,whilethemaximumlevelisstronglyrelatedtothis(Fig.2).

Onaverage,thehourlyrenewableenergyproductionismuchhigherin2030comparedwiththelevelin2016.Thisstrong

increaseinREScapacityfairlywellresemblestheactualdevelopmentsinmanyEuropeancountries.Theutilisationof

fossil-fuelplantsinbothcountriesgoesdownasaresultoftheincreaseinRES,seeFig.13.Inaddition,theannualreductioninthe

carbonemissioncapraisesthescarcityofcarbonpermitsand,hence,thecarbonprice,seeFigs.4and5.Duetothedifferent

sizeoftheinitialinstalledgenerationcapacities,themarginalproductionismoreoftenrunbytheRESinthelargecountry

andlessofteninthesmallcountry.Inthelattercountry,theupwardpriceeffectoftheincreasingcarbonpricesdominates

theprice-reducingeffectoftheincreasingshareofRES.Asaresult,thestrongincreaseofRESsigniﬁcantlyreducestheprice

ofelectricity(asinthelargecountry),butthisappearsnottobethecaseinthesmallcountry(seeFig.3).Asthecross-border

capacityhasalimitedsize,tradersarenotabletofullybeneﬁtfromthesepricedifferences.Theremainingpricedifferences

indicatethatthiscapacityisfullyutilized.

4.2.2. Subsidiesrenewableenergy

Beforeanalyzingtheinteractionbetweencarbontaxes,emissionstradingandsubsidiesforrenewables,weﬁrstanalyze

theinteractionbetweenthelattertwoclimatepolicyinstruments.Thecarbonpriceissigniﬁcantlyhigherinthelatter

variant,asisshownbyFig.8.Thishigherpriceisneededaswithoutsubsidiesforrenewableenergythecarbonpriceneeds

todotheworktokeeptheemissionsbelowthecap.Becauseofthevolatilityinthecarbonpricesduetotheﬂuctuations

inexternalcircumstances(windanddemand),thecarbonpricemaybecome(closeto)zeronowandthenasisshownby

11 _Note_for_Figs.₃_–₆_:_the_thickest_lines_denote_the_variants_with_the_default_cap_{(“Baseline”}_and_{“Prodtax”),}_the_thinnest_lines_denote_the_variants

withthehighercap(“BaselineHighCap”and“ProdtaxHighCap”)andthelineswithintermediatethicknessdenotethevariantswiththelowercap

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Fig.3. Averagedailywholesaleprice,largeandsmallcountry,pervariant,2016–2030.

Fig.4.AverageCO2price,pervariant2016–2030.

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Fig.6. DurationcurveofaveragedailyCO2price,pervariant,2030.

Fig.7. CO2emissions,largeandsmallcountry,pervariant,2016–2030.

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Fig.9.DurationcurveCO2priceinBaselineandBaselinenoRES,2016–2030.

Fig.10.CO2emissionsinBaselineandBaselinenoRES,2016–2030.

Fig.9.Fig.10showstheemissionsintheBaselinevariant,withbothemissionstradingandrenewableenergyinvestments,

andtheemissionsintheBaselinenoRESvariantwhereemissionstradingistheonlypolicyinstrument.Itappearsthatin

thelattervarianttheemissionlevelsarehigher,whichindicatesthatthesubsidiesforinvestmentsinrenewabledohavean

additionaleffectonemissions,whichiscausedbythefactthatthewaterbedeffectdoesnotoccurwhenthecarbonpriceis

zero.

4.2.3. Carbontax

Now,thequestioniswhathappensifthelargecountryintroducesacarbontaxontopofthemeasuresstimulatingthe

REScapacityandtheinternationalemissionstradingsystem.Thedirecteffectisthatthegenerationcostsofthefossil-fuel

powerplantsinthiscountryincrease.Asbothcountriesareconnected,theincreaseingenerationcostsinthelargecountry

impliesthatthiscountrywantstoimportfromthesmallercountryinthosehourswhenREScapacityisnotsettingtheprice.

Asaresult,productionshiftstothesmallercountry.Theintroductionofacarbontaxinthelargecountryraisestheutilisation

offossil-fuelcapacityinthesmallcountry(seeFig.13).Hence,theintroductionofacarbontaxinonecountryresultsina

carbonleakage.Thiseffectisrelativelylargewhenthetaxisimplementedinthelargecountry(Fig.7)Thisinternational

spillovereffectofnationalclimatepoliciesalsoraisestheelectricitypriceintheothercountry,asweobserveapriceincrease

inbothcountriescomparedwiththe“Baseline”(Fig.3).

Ifthecarbontaxisintroducedinthesmallcountryinsteadofthelargecountry,thesimilartypeofeffectsoccuralbeit

smaller.TheimpactontheCO2pricesintheregionismuchsmaller,whilealsotheimpactontheoverallemissionsofCO2

issmaller(Fig.11).Whenthesmallcountryintroducesthecarbontax,theshareofrenewablesinthedomesticproduction

increasesrelativelystrongly,whiletheshareinthelargecountryishardlyaffected(Fig.12).

Theshiftinthelocationoftheproductionbyfossil-fuelplantsdoes,however,notmeanthatthereisnoeffectonthe

priceofcarbon(Fig.4).Theintroductionofacarbontaxinonecountryresultsinalower(average)CO2pricewhichimplies

thattheoveralldemandforpermitshasbeenreduced.Thenegativeimpactofthecarbontaxonthecarbonpriceshowsthe

existenceofthewaterbedeffect:theemissionstradingsystembecomeslesseffectiveifacarbontaxisintroduced.However,

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Fig.11.CO2priceandemissions,inBaselineandvariantswithcarbontax,2016–2030.

Fig.12.ShareofRESindomesticgeneration,largeandsmallcountry,pervariant,2016–2030.

effectdoesnotfullyneutralizetheeffectofthecarbontax.ThisresultisrelatedtothefactthatthepriceofCO2maybezero

fromtimetotime(Fig.6).IfthepriceofCO2iszeroanyotherreductioninthedemandforcarbonpermitscannothaveany

effectonthepriceanymore.Hence,weﬁndthatthecombinationofdifferentpolicymeasurestoreducecarbonemissions

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Fig.13.Utilisationoffossil-fuelcapacity,Baselineandvariantwithcarbontaxinlargecountry,largeandsmallcountry,2016–2030.

4.2.4. Welfareeffectsofcarbontax

Imposingacarbontaxraisesthemarginalcostsofelectricityproductionwhichincreasestheelectricityprice.Asaresult

consumershavetopaymore,whichreducestheirconsumersurplus.Astheimpactofthecarbontaxonelectricityprices

isthebiggestinthedomesticmarket,becauseofcross-bordercapacityconstraints,theconsumerwelfareismoststrongly

affectedbythedomesticcarbontax(Fig.14).

Remarkablytheproducersurplusincreasesasaresultofthecarbontax.Althoughthecarbontaxraisesthecostsofthe

conventionalproducers,theproducersofRESdonothavetopaythistax,buttheydobeneﬁtfromtheresultingelectricity

prices.Hence,bothconsumersandRESproducersbeneﬁtfromtheintroductionofacarbontax,whiletheproducersof

conventionalpowerfacesalossintermsoflowerproductionlevelsandlowerproﬁtsperunit.

4.2.5. Sensitivityanalysis

Whenwelowertheemissioncap,subsequentlyweobservealowercarbonemissionlevelandahighercarbonprice

(Fig.4).Becauseofthehighercarbonprice,weﬁndhigherelectricitywholesalepricesinthesmallcountry:the

price-reducingeffectoftheincreaseinREScapacityiscompletelyneutralizedbytheprice-increasingeffectofthetightercarbon

market(seeFig.3).Wealsoobserveastrongerspillovereffectofacarbontaxonfossil-fuelproduction:theutilisationofthe

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Fig.15. Utilisationoffossil-fuelcapacityintheBaselineLowCapandCarbonTaxLowCap,2016–2030.

fossil-fuelplantsincreasesmorestronglyduetotheintroductionofthecarbontaxinonecountry(seeFig.15).Thisimplies

thatincaseoftighteremissions-tradingsystem,theinternationalspillovereffectofnationalpolicies,likeacarbontax,are

larger.Moreimportantly,becauseofthestrongereffectontheCO2prices,thereislesseffectonCO2emissions(seeFig.5).

Thisisrelatedtothefactthatincaseofalowercapthecarbonpricesarelessoftenzerowhichmakesitpossibletostronger

obtainthewaterbedeffectwhichneutralizesemissionreductionsresultingfromthecarbontax.

Whenweaddthepossibilityofbankingpermitsandusingtheminthenextperiod,theresultsremainbasicallythesame

(Fig.16).Incaseofbanking,theCO2priceappearstobezeroinboththeBaselineandthepolicyvariantwithacarbontax.This

resultfollowsfromthefactthatbankingcanresultinahighersupplyinthenextperiodwhenthereisanoversupplyinthe

previousone.Hence,bankingcanmaketheredundancyoftheemissiontradingschemeevenstronger.Asaconsequence,

introducingacarbontaxwhentheemissionstradingmarketisloose,forinstancebecauseofthepossibilityofbanking,

thiscombinationofclimate-policymeasuresmayresultinareductionofcarbonemissions.Thegenerallessonhereisthat

regulatorymeasureswhichmakethecapintheemissionstradingschemelessbinding,mayreducethewaterbedeffect.

5. Concludingremarks

Inthispaperwehaveexploredtheconditionsunderwhichinteractioneffectsoccurbetweendifferenttypesof

climate-policymeasures.Governmentsarecombiningdifferenttypesofpolicymeasuresinordertorealisetheirambitiousobjectives

regardingthereductionofcarbonemissions.Itiswellestablishedintheliteraturethatthecombinedeffectmaybelower

thanthesumoftheindividualeffects.Combiningsubsidiesforrenewableenergyortaxesonfossilfuelstogetherwitha

cap-and-tradesystemsuffersfromthewaterbedeffect.Moreover,nationalpoliciestoreducedomesticemissionsmaybe

offsetbyinternationalspillovereffects.Thequestionwehaveexplorediswhetherthisoffsettingeffectalwaysoccursor

whetheritmaybesubjecttospeciﬁcconditions.ThistopicisrelevantbecauseintheEU,eachcountryhasthefreedomto

chooseitsownnationalenergypolicydespiteofEuropeanclimate-policyobjectives.Europeancountriesapplyamixture

ofdifferenttypesofpolicymeasureswhichmakeithighlyrelevanttoanalyzethenatureofandtheconditionsforthe

interactioneffects.

Usinganumericalpartialtwo-countryequilibriummodelofthepowermarketwhichalsoincludesacap-and-trade

carbonsystem,weﬁndspillovereffectsduetotheintegrationofthetwomarkets.Imposingafossil-fueltaxinonecountry

leadstoahighercostforfossil-fuelproducers.Hence,thiscountryimportsmorefromtheneighboringcountry.Asaresult

ofthis,weobserveahigherutilizationoffossil-fuelcapacityintheneighboringcountry.Thespillovereffectsaresmaller

whenthecarbontaxisintroducedinthesmallcountryinsteadofinthelargecountry.BoththeCO2priceandtheoverall

CO2 emissionsintheregionarelessaffectedthenwhenthelargecountryimplementsacarbontax.Thelowerthecap

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Fig.16.CO2priceandemissionswiththeoptionofbankingpermits,BaselineandCarbonTaxL,2016–2030.

reducecarbonemissionsmaybeoffsetbyinternationalspillovereffects.Coordinationofsuchpoliciesmayimprovethe

effectivenessofsuchpolicies.

However,weﬁndthatthewaterbedeffectdoesnotalwayshold.Itappearsthataddingotherclimate-policymeasuresto

anemissions-tradingsystemmayhaveaneteffectonthelevelofcarbonemissions.Thisresultcomesfromthefactthatthe

carbonpriceinthetradingschemehasaﬂoor,i.e.itcanneverbelowerthanzero.Ifsubsidiesforrenewableenergyresult

inalargeamountofrenewable-energycapacitythismayinsomeperiodsresultinanoveralldemandforcarbonpermits

beingbelowthesupplyofpermitswhichbringsthecarbonpricetozero.Insuchcircumstances,givingmoresubsidiesfor

renewablesorimposingataxoffossilfuelreducetheemissionsbyfossil-fuelplantswithoutbeingneutralizedbyawaterbed

effect.Hence,weﬁndthatthewaterbedeffectonlyholdsifthecap-and-tradesystemisconstantlybinding,whichmeans

thatthereisalwaysapositivepriceforthecarbonpermits.Theprobabilityofalwaysbindingemissions-tradingsystem,

however,reducesifcountrieskeepincreasingthesizeofinstalledREScapacityasiscurrentlythecaseinmanyEuropean

countries.Moreover,asimilareffectmayoccurifregulatorymeasuresaretakenwhichmaketheemissions-tradingscheme

lesstight,suchasbankingwhichincreasesthetimeﬂexibilityofparticipantswithinthescheme.Thepolicyconsequenceof

thisﬁndingisthatnationalclimatepoliciessuchassubsidyschemesforrenewablesmayhaveapositiveeffectonreduction

ofcarbonemissions,althoughthegeneralliteraturesaysthatsuchcannotbethecasewhenanemissions-tradingscheme

exists.

Theseﬁndingsarebasedonanumericalanalysisofaconcisemodeloftheelectricitymarket.Thenumericalsimulations

donotenableustodrawgeneralconclusions,astheﬁndingsmaybesensitivetothechosenparametervalues.Nevertheless,

anumericalapplicationofamodeldoesgiveinsightsintheinterrelationshipsofanumberoffactorsaffectingthemarket.

Becauseofitstheoreticalandstylizednature,thismodelanalysisdoesnotgivepreciseestimatesofthesizeofthe

rela-tionshipsandtheprobabilityofthesituationsinwhichtheinteractioneffectdonotoccur.Althoughthemodelhasarather

detailedrepresentationoftheelectricitysector,itlargelyignoresthesector’sinteractionswiththerestoftheeconomy,

suchasfossilfuelproduction,aggregateinvestmentandemployment.Suchinteractionsarealsoimportantforevaluating

theeffectivenessofclimatepolicies.Empiricalresearchisneededtoobtainpreciseestimatesforthemagnitudeofactual

interactioneffectsbetweencurrentclimate-changepolicies.

Asweonlyfocusedontheoccurrenceandabsenceofinteractioneffectsofdifferenttypeofclimatepolicies,wedidnot

discusstheefﬁciencyoftheseinteractioneffects.Althoughaddingacarbontaxontopofanemissionstradingschememay

resultinmoreemissionsreductionsasthewaterbedeffectdoesnotalwayswork,thisdoesnotmeanthatsuchapolicyis

efﬁcient.Inordertoanalysetheefﬁciencyeffectsofclimatepolicies,amoregeneralequilibriumapproachisneededtaking

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AppendixA. Fossilfuelplantsinvestment

WhentheexpectedproductionbyRenewableEnergySupply(RES)isloworzero,theneedforfossilfuelproduction

mightexceedthecurrentgenerationcapacity.Asaresultofthis,electricityscarcitypricesoccur,seealsotenCateand

Lijesen(2004).Inthefossil-fuelinvestmentdecisions,wealsotakeimportandexportintoaccount.Electricityimporting

companiesaremodelledasprice-takers.LetqI

yhbethetotalelectricityimport.FollowingMulderetal.(2015),thesupplyof

theimportersisapproximatedbyalinearsupplyfunction,

qI_cyh=ıpcyh, (15)

andtheexportamountbyﬁrmiisqiE

cyh.Wehavethefollowingequationforscarcityprices,

QF cy+ıpcyh+

˛cyh+ˇpcyh

−

i qiE cyh=ah−bhpcyh. (16)

NotethattheﬁrsttermQF

cydenotesthefossil-fuelgenerationcapacity,thesecondterm

ıpcyh

ontheleft-handsideofEq.

(16)denotestheimportamount,12_the_third_term

_˛

cyh+ˇpcyh

denotestheproductionamountbyfringesuppliersand

thefourthterm

_iqiE

cyh

denotestheelectricityexportamountwhichismodelledexogenously.Theright-handsideofEq.

(16)denotestheaggregatedemandatacertainelectricitypricelevel.

Thefossil-fuelplantsinvestmentsQF

cyareconsideredinacompetitivesettinginwhichﬁrmscannotbehavestrategically

andexercisemarketpower.Assumingperfectforesight,expectedlong-runmarginalrevenuesshouldbeequaltolong-run

marginalcosts.FollowingtenCateandLijesen(2004),wehavethefollowing:thepriceperMWhwhichisrequiredtokeep

demanddowntocapacity(Eq.(16)),minusmarginalrunningcostsperMWh,accumulatedoverthehoursduringwhich

capacityisabindingconstraint,equalstheincrementalannualizedcostofbuildinganextraMW.Supposetheannualized

fossilfuelinvestmentcostsarecFandalinearfunctionalformofinvestmentcosts,

E

⎡

⎢

⎣

⎛

⎜

⎝

h∈{qF cyh=Q F cy+QcyF}

pcyh−mc

⎞

⎟

⎠

|wh

⎤

⎥

⎦

=cF, (17)

wheremcdenotestheconstantfossilfuelproductioncosts.Theexpression{qF_cyh=QcyF +QcyF}denotesthesetofhourswhen

thecapacityconstraintisbinding.Hence,theinvestmentinfossil-fuelplantsQF

cyshouldbesetatalevelthatequalizes

expectedmarginalbeneﬁts(LHSofEq.(17))andmarginalcosts(RHSofEq.(17)).

AppendixB. RESinvestment

WeassumethattheinvestmentsinRESdependongovernmentsubsidies.SupposetheRESsubsidybudgetforwind

parksisBW

cyandthebudgetforsolarcellsisBScy.Moreover,weassumethatthebudgetisﬁnancedbyataxonelectricity

consumption.TheinvestmentcostsforwindparksandsolarcellsaredenotedbycW

y andcSy,respectively.Thenewlyinstalled

capacitiesforcentralizedpowerproducers(QW

cy)arecalculatedasfollows:

Q_cyW= B W cy cW y .

Similarly,thenewlyinstalledcapacitiesfordecentralizedpowerproducers(QS

cy)arecalculatedasfollows:

QS cy= BS cy cyS .

AppendixC. Optimalproductionamountbycentralizedpowerproducers

Theelectricitymarketismodelledasamarketwithimperfectcompetitionwherethesupplyisdeterminedbyalimited

numberofstrategicsuppliersandafringesupplyconsistingofweatherdependentwindandsolarproductionaswellasCHP

productionwhichactsasapricetaker.Thestrategicsuppliers,whicharesupposedtohavebothfossil-fuelplantsandwind

turbines,competeinquantities(Cournotcompetition).Thesuppliersselltheirproductioninbothforwardandspotmarkets.

Eachﬁrmhasanincentivetomaximizerevenuesinforwardmarketsasthisreducesthemarketpowerofotherﬁrmsinthe

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spotmarket(AllazandVila,1993).Inordertodeterminetheoptimalproductionquantitybythestrategicplayersusingtheir

fossil-fuelplants,weneedtoestimatetheamountsoldintheforwardmarkets.Firstwedeterminetheoptimalproduction

giventhestrategicgameinthespotmarketandthendeterminehowthisdependsontheforwardsales.Afterdetermining

themarginalimpactofforwardsalesontheoptimumproductionamount,weareabletodeterminetheoptimalproduction

level.

Theproductiongameforﬁrmi∈Ncinthespotmarketisgivenby,13

max qiF cyh pcyh(qicyh−q if cyh)−mcq iF cyh, s.t. qi

cyh=qiFcyh+qiWcyh.

wheremcistheconstantvariablecostsforﬁrmiincountryctousetheconventionalresourcestogenerateelectricityand

p_cyh₌ah−˛cyh−q

i cyh−q

−i cyh

bh+ˇ .Theﬁrstorderconditionsforﬁrmiread,

ah−˛cyh−

q−iF_cyh+q−iW_cyh

−2

qiF cyh+qiWcyh

bh+ˇ + qif_cyh bh+ˇ− mc=0, (18)

Eq.(18)holdsforeveryﬁrmiandwecanwritethesystemofequationsfortheﬁrstorderconditionsofeachproducerinto

matrixformasfollows:

⎡

⎢

⎣

2 1 ··· 1 1 2 ··· 1 1 1 ··· 1 ··· ··· ··· ··· 1 1 ··· 2

⎤

⎥

⎦

⎡

⎢

⎣

q1F cyh q2F cyh ··· ··· qncF cyh

⎤

⎥

⎦

=

⎡

⎢

⎣

ah−˛cyh+q1f_cyh−q_cyh−1W−2q1W_cyh+mc(bh+ˇ)

ah−˛cyh+q2fcyh−q−2Wcyh −2q

2W

cyh−mc(bh+ˇ)

···

ah−˛cyh+qncyhcf−qcyh−ncW−2qncyhcW−mc(bh+ˇ)

⎤

⎥

⎦

.

TheabovematrixsolveqiF

cyh,i∈Ncasafunctionofq 1f cyh,q 2f cyh,...,q ncf

cyh.Notethatwealsohaveq iW cyh=q

jW

cyh,i,j∈Nc,i.e.,the

windpowergenerationisalsosymmetricamongallproducers.Wesolvetheabovematrixandobtainthefollowingsolution

fortheoptimalgenerationbyfossil-fuelplantsofi,i∈Nc,

qiF_cyh=

ah−˛cyh+qif_cyh−q−iW_cyh −2qiW_cyh−

j∈Nc,j=/i

qjf_cyh−qif_cyh

−mc(bh+ˇ) n+1 , i,j∈Nc. (19)

Hence,themarginalimpactofforwardsalesontheproductionquantityisdeterminedby:

∂

qiF cyh

∂

qif_cyh = n n+1, (20)

∂

qjF_cyh

∂

qif_cyh =− 1 n+1, (21) wherei,j∈Ncandj=/ i.

Nowwemovetothestageofﬁrmschoosingtheoptimalforwardpositions.AccordingtoAllazandVila(1993),wehave

thefollowingmaximizationproblem,

max

qif_cyh

pf_cyhqif_cyh+pcyh(qicyh−q

if cyh)−mcq iF cyh, s.t. qi cyh=q iF cyh+q iW cyh.

Accordingtothearbitragecondition,itshouldholdthatpf_cyh₌p_cyh.Hence,theabovemaximizationproblemcanbesimpliﬁed

as, max qif_cyh pcyhqicyh−mcq iF cyh, s.t. qi

cyh=qiFcyh+qiWcyh.

13_For_notational_convenience,_we_suppress_the_expectation_sign_for_qiW

(21)

wherepcyh=

ah−q−icyh−q i cyh−˛cyh

bh+ˇ .Takingﬁrstorderconditionswithrespecttoq

if

cyh,weobtainthefollowingequationforﬁrmi,

ah−˛cyh−mc

bh+ˇ

−qiF

cyh−q−iFcyh−q iW cyh−q−iWcyh

∂

qiF cyh

∂

qif_cyh −

qiF_cyh+qiW_cyh

⎛

⎝

qiFcyh qif_cyh+

j∈Nc,j= i/

∂

qjF_cyh

∂

qif_cyh

⎞

⎠

₌0, (22) where ∂q iF cyh ∂qif_cyh and ∂qjF_cyh

∂qif_cyh aregivenby(20)and(21),respectively.Duetothefactthatﬁrmsaresymmetricintermsoftheir

constantvariablecosts,theirﬁnalproductionamountsintheequilibriumshouldbethesameaswell.PluggingEqs.(19)–(21)

into(22),weobtainthefollowingresultfortheoptimumproductionlevelperﬁrm,

qiF_cyh=nc

ah−˛yh−mc(bh+ˇ)

−qiW

cyh−nc(qiWcyh+q−iWcyh )

n2

c+1

, (23)

AppendixD. Calculationoftheaggregatedemandfunction

Supposewewanttocalculatetheaggregatehourlydependentdemandfunction,

qcyh=ah−bhpcyh,

andtheobjectiveistocalculateparametersahandbh.Giventhepriceelasticitiesεhintheliteratureandobservedquantity

˜pcyhandoutput ˜Qcyhinaloadproﬁle,weusethefollowingformulatocalculateahandbh,

εh=− dQ/Q dP/P =− dQ dP × P Q ⇒bh=εh ˜ Qcyh ˜pcyh , ah= ˜Qcyh+bh˜pcyh.

Notethattheaboveformulaisimplementedtocalculatetheaggregatedemandfunctioninthesmallcountryandthe

aggregatedemandfunctionforthelargecountryisobtainedbyscalingupthedemandfunctionofthesmallcountry.

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Exploring Interaction Effects of Climate Policies: a Model Analysis of the Power Market

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