Divestiture of Generation Assets in the Electricity Pool of England and Wales A Computational App
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JournalofRegulatoryEconomics;19:2123±141,2001indeedbeenexertingexcessivemarketpower,theU.K.of®ceofelectricityregulationpreviouslyattemptedtomitigatesuchabusesbyrequiringplantdivestments(OFFER1994).Inaccordancewiththisdirective,17%ofthecapacityownedbythetwomajorprice-settinggenerators(NationalPowerandPowerGen)wasdivestedin1996.Atthattime,anof®cialreportonthemarketpowerofNationalPowerandPowerGenconcludedthatwiththisamountofdivestitureandtheprospectoffurthernewentry,theirability``toaffectthelevelofPoolprices,whethertokeepthemhighorcausethemto¯uctuate,willbesmall''(MMC1996).However,thispredictionwaswrong,andby1998,thosetwogeneratorswereagainaccusedofmaintaininghighprices(DTI1998),Somuchso,infact,thattheregulatoryof®cewasagainsayingthatthe``mosteffectiveroutetoincreasedcompetitionintheshorttermwouldseemtobetotransfermoreofNationalPower'sandPowerGen'scoal-®redplantintothehandsofcompetitors''(OFFER1988).Justhowtodecideupontheappropriatelevelofplantdivestitureisaformidableandunenviableregulatorytask.Clearly,OFFERgotitwrongthe®rsttimein1996,butusedverylittleformalanalysisotherthanindicesofmarketshareandpricesetting.Forexample,Littlechild(1996)referredtoareductionintheHHIindexofmarketconcentrationfromabout3600in1991toabout1600in1996asameasureofsuccessinmakingtheindustrymorecompetitive.Green(1996)addressedthedivestitureissuebyapplyingtheapproachofsupplyfunctionequilibrium(KlempererandMeyer1989),asanextensionofpreviousanalysesfortheEnglandandWalespool(GreenandNewbery1992;Green1996),andsimilarlytowhathadbeendoneelsewhere(e.g.,AnderssonandBergman1995).InthatstudyGreen(1996)broadlyendorsedthelevelofdivestmentbeingundertakenatthetime.However,thederivationofsuchsupplyfunctionequilibriumisanalyticallydif®cult,andthepublishedstudieshavetendedtomakeverystrongassumptionstofacilitatesolutions.Thebasicframeworkistoassumethatgeneratingcompaniesbidsupplyfunctionsintothepool,representingthepriceatwhichtheywillmakeavailablearangeofgenerationcapacity,ashappensintheCaliforniaPowerExchangeandthepoolsofEnglandandWales,Spain,Colombiaandelsewhere.Demandbeingrevealedlater,asaforecast,orviademand-sidebiddingorinactuality(forexpostmarketslikeVictoria)thenclearsthemarket.Analyticalevaluationoftheequilibriumsolutioneitherassumesthatthesesupplyfunctionsarecontinuous(Green1996),whereasthenatureofgeneratingunitsmakesthesefunctionsincreasewithquitedistinctstepsinpractice,orrestrictstheprospectiveanalysisofvariousindustryownershipstructurestosymmetric,equallysized®rms(Rudkevitchetal.1998),orboth(GreenandNewbery1992).Inthispaperwepresentamethodfordeterminingimperfectlycompetitiveoutcomesinelectricitymarketsbaseduponcomputationalmodelingandsimulation.Ratherthandirectlycalculatingtheequilibriumsolution,weformulateacomputationalmodelofpro®tmaximizingbehaviorforeachgeneratingcompanyandthensimulatetheinteractionofthecompanies,observingtheadaptationofsupplyfunctionsduringtherepeatedplayofthedailygame.Inprinciple,thisapproachcantakeactualmarginalcostdataanddealwithbothdiscontinuoussupplyfunctionsandasymmetricmarketconcentrations.Thisrestofthispaperproceedsasfollows.First,wedescribethecomputationalframeworkwehavedevelopedformodelingsupplyfunctioncompetitionanddiscussthepropertiesofthedynamicbehaviorresultingfromsimulatingthestrategicinteraction.Thenafterspecifyingthedemandandmarginalcostassumptionsofthemodel,weseehow
124CHRISTOPHERJ.DAYANDDEREKW.BUNNtheresultsofthisapproachcomparewiththoseobtainedbycalculatingacontinuoussupplyfunctionequilibrium,forthosesimpli®edcircumstancestowhichthelattercanbeapplied.Thisprovidesacalibrationandvalidationoftheapproach.Thenweapplytheapproachtoanalyzingthesecond(1999)roundofplantdivestment,thusdemonstratingtheapplicabilityofthisnewapproachtomodelingcompetitionbetweenasymmetricgeneratingcompanieswithdiscontinuoussupplyfunctions.
2.FormulationoftheComputationalModelWedevelopacomputationalapproachtomodelingtheinteractionofgeneratingcompanieswhocompeteusingsupplyfunctionsinanelectricitypoolwithrulessimilartothosefoundintheEnglandandWalesmarket.Generatingcompaniesaremodeledholdingtheconjecturethattheircompetitorswillsubmitthesamesupplyfunctionsastheydidinthepreviousday.Giventhisconjecture,eachcompanyismodeledasadailypro®tmaximizer,optimizingthesupplyfunctionitsubmitstothemarket.1Usingdataon
observeddemandandestimatesofshort-runmarginalcosts,wesimulatetheinteractionsbetweenthegeneratingcompaniesandanalyzetheresultingsupplyfunctions.Wemodelthesupplyfunctionsashavingbothdiscretecapacityandpriceranges.Inthismarketitisnaturaltohaveadiscretecapacityrangeasagenerator'scapacitycomprisesofindividualgeneratingplants.Hencecumulativeavailablecapacityincreasesinadiscretemanner.Employingadiscretepricerangeisnotsuchanobvioustransformationinthetheoreticalliterature,asthevalueatwhichageneratorpricesitsplantscanvaryalmostcontinuously.Wethisdiscretepricerangeasamodelingsimpli®cationtoallowthesubsequentapplicationofanoptimizationroutinetothesupplyfunctions.Wemodelthesupplyfunctionsashavingbothdiscretecapacityandpriceranges.Inthismarketitisnaturaltohaveadiscretecapacityrangeasagenerator'scapacitycomprisesofindividualgeneratingplants.Hencecumulativeavailablecapacityincreasesinadiscretemanner.Discretizingthepricerangeisnotsuchanobvioustransformationinthetheoreticalliterature,asthevalueatwhichageneratorpricesitsplantscanvaryalmostcontinuously.Weperformthisdiscretizationasamodelingsimpli®cationtoallowthesubsequentapplicationofanoptimizationroutinetothesupplyfunctions.Formally,forallKgeneratingcompanies,leteachgeneratingplantbeastandardsizeequaltoPSandletthepricerangebedividedintoNequalsizedpricerangesindexedfrom1toN,whichwewillrefertoaspricebins.IfthepricerangeofeachbinisalsoastandardsizeandequaltoBS,thenthepricerangeofbiniisiÀ1ÃBStoiÃBS.Thus,wecande®ne