ESSAYS IN RENEWABLE ENERGY AND EMISSIONS TRADING

Transcription

1 ESSAYS IN RENEWABLE ENERGY AND EMISSIONS TRADING By JOSHUA D. KNEIFEL A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTORATE OF PHILOSOPHY UNIVERSITY OF FLORIDA

2 c 2008 Johua D. Knefel 2

3 To My Parent, who have upported me through all of my academc achevement. 3

4 ACKNOWLEDGMENTS I thank my upervory commttee char, Lawrence Kenny, along wth my other commttee member (Sanford Berg, Jonathan Hamlton, and Jane Luzar) for ther comment and adve regardng my dertaton. Specal thank goe to Paul Sotkewcz for h nteret, gudance, and upport n my reearch. I alo thank my parent for ther never-endng upport. 4

5 TABLE OF CONTENTS page ACKNOWLEDGMENTS LIST OF TABLES LIST OF FIGURES ABSTRACT CHAPTER 1 EFFECTS OF STATE GOVERNMENT POLICIES ON ELECTRICITY CAPACITY FROM NON-HYDROPOWER RENEWABLE SOURCES Introducton Lterature Revew Model Varable and Data Economc and Poltcal Varable: W t Regulatory Polcy Varable: R t Stattcal Specfcaton and Emprcal Analy Economc and Poltcal Varable: W t Regulatory Polcy Varable: R t State Fxed-Effect Varable: S t Year Varable: T t Concluon EFFECTS OF COAL CONTRACT CONSTRAINTS ON SO 2 TRADING PROGRAM COMPLIANCE DECISIONS Introducton Polcy Background Ttle IV of the Clean Ar Act Amendment Phae I of Ttle IV Phae II of Ttle IV Clean Ar Intertate Rule Lterature Revew Ttle IV: Phae I Utlty-Level Model of Complance Cot Long-Term Coal Contract Ineffcence Reultng from Coal Contract Contrant Model and Parameter Generatng Unt Level Decon-Makng Proce Generatng Unt Problem Frt-Order Condton

6 2.6.3 Characterzng a Unt Spot Market Fuel Choce and Margnal Cot of Abatement from Fuel Swtchng Neceary condton for ung both hgh ulfur and low ulfur coal Only hgh ulfur coal ue: Neceary condton Only low ulfur coal ue: Neceary condton Coal Ue Under a Hgh Sulfur Coal Contract Contrant Coal Ue under a Low Sulfur Coal Contract Contrant Generatng Unt-Level Complance Cot Generatng Unt Net Allowance Poton: Exce Demand Correpondence Cot avng of fuel wtchng veru allowance purchae when P A > MCA, Effect of hgh ulfur coal contract on exce demand and cot Cot avng of allowance purchae veru fuel wtchng when P A < MCA, Effect of low ulfur coal contract Fuel wtchng veru allowance purchae when P A = MCA, Generatng Unt Scrubber Intallaton Choce When wll a generatng unt ntall a crubber? Dfferent margnal cot of abatement Exce demand correpondence Impact of Coal Contract on Exce Demand Correpondence Impact of a bndng hgh ulfur coal contract Impact of a bndng low ulfur coal contract Poble Implcaton on the Allowance Market and Indutry Complance Cot Concluon THE EFFECT OF FUEL CONTRACTING CONSTRAINTS ON SO 2 TRADING PROGRAM COMPLIANCE: EMPIRICAL EVIDENCE Introducton Revew of Generatng Unt Model Generatng Unt Problem Optmal Complance Choce Allowance Market Equlbrum Comparatve Statc: Effect on the Allowance Market Comparatve Statc: Effect of Relatve Fuel Cot on the Allowance Market Comparatve Statc: Effect of Coal Contract on the Allowance Market Gven the Scrubber Choce Impact of hgh ulfur coal contract on allowance market

7 Impact of low ulfur coal contract on allowance market Comparatve Statc: Effect of Coal Contract on the Allowance Market wth Endogenou Scrubber Choce Hgh ulfur coal contract bnd Low ulfur coal contract bnd Complance Cot Complance Cot wth Coal Contract Relatve to Complance Cot from Prevou Stude Total Indutry Complance Cot Impact of Allowance Allocaton on Complance Cot Gven Scrubber the Choce Impact of Allowance Allocaton wth Endogenou Scrubber Choce Smulaton Model Introducton Data Fuel data Allowance, actual emon, and demand data Techncal generator and crubber data Smulaton Model Degn Smulaton Reult Total ndutry cot and allowance market reult Indutry and generatng unt coal ue Generatng unt crubber ntallaton choce Impact of allowance allocaton on the allowance market and complance cot Summary of mulaton reult Plant Level Decon-Makng Proce Introducton Plant-Level Problem Frt-Order Condton Characterzng a Unt Spot Market Fuel Choce Cae 1: Neceary condton for ung both hgh ulfur and low ulfur pot market coal Cae 2: Neceary condton for only hgh ulfur pot market coal ue Cae 3: Neceary condton for only low ulfur pot market coal ue Exce Demand Correpondence Characterzng a Generatng Unt Contract Fuel Choce Cae 1: Neceary condton for hgh ulfur contract coal ue at Generatng Unt Cae 2: Neceary condton for low ulfur contract coal ue at generatng unt Non-Affected Generatng Unt at an Affected Plant

8 Characterzaton of non-affected generatng unt at an affected plant Non-affected generatng unt and hgh ulfur coal contract Scrubber Intallaton Choce Margnal cot of abatement wth and wthout a crubber A Plant Preferred Order of Scrubber Intallaton At whch generatng unt wll a plant ntall a crubber? At what allowance prce wll a plant ntall a crubber at a gven generatng unt? Scrubber ntallaton and hgh ulfur coal contract Scrubber ntallaton and low ulfur coal contract Scrubber Intallaton Example: Plant wth Two Affected Generatng Unt Cae 1: Intall no crubber Cae 2: Intall one crubber Cae 3: Intall two crubber Scrubber Intallaton Example: Plant wth One Affected and One Non-Affected Generatng Unt Summary of Plant Level Reult CONCLUSIONS A CONTRACT IMPACTS ON COSTS AND SCRUBBER INSTALLATION INDIFFERENCE PRICE A.1 Impact on Total Cot and Complance Cot from a Coal Contract Contrant A.2 Dervaton of Cot-Mnmzng Input Ue to Fnd P S A B MARKET EQUILIBRIUM AND SIMULATION DESIGN B.1 Condton for Extence of an Equlbrum B.2 Techncal Detal of Smulaton Model Degn REFERENCES BIOGRAPHICAL SKETCH

9 Table LIST OF TABLES page 1-1 Dependent and Control Varable Regreon Reult Polcy Varable Varable Effect of Sgnfcant Varable Phae I Complance Cot Etmate Hgh Sulfur Coal Contract: Aumpton Hgh Sulfur Coal Contract: Reult Low Sulfur Coal Contract Example: Aumpton Low Sulfur Coal Contract Example: Reult Example Eplon Magntude: Cae Example Eplon Magntude: Cae Example Eplon Magntude Example: Contract Coal Dtrbuton Sulfur Converon by Fuel Type Smulaton Reult Impact of Contract Contrant on Scrubber Choce Smulaton wth Engneerng Data Impact of a Reducton n the Allowance Allocaton of 10% Math Example: Two Affected Unt

10 Fgure LIST OF FIGURES page 2-1 The SO 2 Allowance Prce Exce Demand Correpondence and Complance Cot Savng from Fuel Swtchng Over Allowance Purchang Hgh Sulfur Contract: Shft n Mnmum Exce Demand No Contract: Complance Cot Hgh Sulfur Contract: Complance and Total Cot Hgh Sulfur Contract: Relatve Savng from Contract Coal Cot Savng from Ung Allowance Over Fuel Swtchng Low Sulfur Contract No Contract: Complance Cot Low Sulfur Coal Contract: MCA,c Low Sulfur Coal Contract: MCA,c Complance Cot: P A = MCA, Hgh Sulfur Coal Contract Low Sulfur Coal Contract Exce Demand Correpondence: MCA, < P S A Exce Demand Correpondence: MCA, P S A Impact of a Hgh Sulfur Coal Contract: MCA, < P S A Impact of a Hgh Sulfur Coal Contract: MCA, > P S A Impact of a Low Sulfur Coal Contract: MCA, > P S A Impact of a low ulfur Coal Contract: MCA NS < P S A Exce Demand Correpondence Impact of Hgh Sulfur Coal Contract Impact of Low Sulfur Coal Contract Exce Demand Correpondence wth Scrubber Choce Impact of Hgh Sulfur Coal Contract

11 3-6 Impact of Low Sulfur Coal Contract Gven Scrubber Choce: Shft from Hgh Sulfur Contract Gven Scrubber Choce: Shft from Low Sulfur Contract Wth Scrubber Choce: Shft from Hgh Sulfur Contract Wth Scrubber Choce: Shft from Low Sulfur Contract B-1 Upper Sem-Contnuou Correpondence B-2 Correpondence wth Scrubber Choce

12 Abtract of Dertaton Preented to the Graduate School of the Unverty of Florda n Partal Fulfllment of the Requrement for the Degree of Doctorate of Phloophy ESSAYS IN RENEWABLE ENERGY AND EMISSIONS TRADING Char: Lawrence Kenny Major: Economc By Johua D. Knefel Augut 2008 Envronmental ue have become a key poltcal ue over the pat forty year and ha reulted n the enactment of many dfferent envronmental polce. The three eay n th dertaton add to the lterature of renewable energy polce and ulfur doxde emon tradng. The frt eay acertan whch tate polce are acceleratng deployment of non-hydropower renewable electrcty generaton capacty nto a tate electrc power ndutry. A would be expected, polce that lead to gnfcant ncreae n actual renewable capacty n that tate ether et a Renewable Portfolo Standard wth a certan level of requred renewable capacty or ue Clean Energy Fund to drectly fund utlty-cale renewable capacty contructon. A urprng reult that Requred Green Power Opton, a polcy that merely requre all utlte n a tate to offer the opton for conumer to purchae renewable energy at a premum rate, ha a zable mpact on non-hydro renewable capacty n that tate. The econd eay tude the theoretcal mpact fuel contract contrant have on a electrcty generatng unt complance cot of meetng the emon complance retrcton et by Phae I of the Ttle IV SO 2 Emon Tradng Program. Fuel contract contrant retrct a utlty degree of freedom n coal purchang opton, whch can lead to the ue of a more expenve complance opton and hgher complance cot. 12

13 The thrd eay analytcally and emprcally how how fuel contract contrant mpact the emon allowance market and total electrc power ndutry complance cot. Th paper ue generatng unt-level mulaton to replcate reult from prevou tude and how that fuel contract appear to explan a large porton (65%) of the prevouly unexplaned complance cot mulaton. Alo, my tudy conder a more approprate plant-level decon for complance choce by analytcally analyzng the plant level decon-makng proce to how how cot-mnmzaton at the more complex plant level may devate from cot-mnmzaton at the generatng unt level. 13

14 CHAPTER 1 EFFECTS OF STATE GOVERNMENT POLICIES ON ELECTRICITY CAPACITY FROM NON-HYDROPOWER RENEWABLE SOURCES 1.1 Introducton Renewable energy ha recently become an mportant apect n the U.S. electrcty generaton mx and a prmary focu of government polcy for envronmental and energy ecurty/prce volatlty reaon. Frt, the publc growng concern for the envronment and progrevely trngent regulaton of emon n the electrc power ndutry ha drven polce to ncreae the amount of renewable energy n the electrcty generaton portfolo. Electrcty producton from renewable reource create lttle, and often zero, emon of the pollutant that reult from tradtonal fol fuel generatng technologe. More renewable energy ue help utlte n ther emon complance oblgaton. Moreover, the propect of complance wth any future carbon emon regulaton would further trengthen the ncentve to hft toward cleaner electrcty generatng technologe. 1 Second, recent uncertanty n the U.S. energy upply due to poltcal concern n the Mddle Eat countre and other foregn ol producng countre a well a volatlty n ol and natural ga prce have led to a puh to ncreae U.S. energy ndependence through a greater dometc energy upply and to decreae the mpact on the economy from any prce hock n the fol fuel market, uch a the natural ga prce pke n and followng the 2004 and 2005 hurrcane eaon. 2 1 Smth et al. (2000) etmate the dplacement of emon from the Maachuett Renewable Portfolo Standard. 2 Brd et al. (2005) explan the market factor behnd wnd power deployment, whch nclude the volatlty of natural ga prce. GDS Aocate (2001) upported th factor a well n the reaonng behnd the enactment of Hawa Renewable Portfolo Standard. The delvered prce of natural ga to electrc utlte ha ren from $2.62/mllon cubc foot (MCF) n 1999 to $8.45/MCF n 2005 (EIA Annual Energy Revew 2005). 14

15 Complementng federal polce uch a the producton tax credt, tate government have taken acton to ncreae renewable energy capacty and generaton, wth 41 of the 50 tate enactng polce to encourage the ue of renewable energy n ther tate. Indvdual tate polce how a great deal of varance. The objectve of th paper to determne whch tate polce have led to ncreaed deployment of aggregate non-hydro renewable energy capacty nto a tate electrc power ndutry. 3 The lterature on tate renewable energy polce cont manly of cae tude on polcy effectvene. Only one prevou paper ue econometrc method to etmate the effect of varou tate polce on renewable capacty. Menz and Vachon (2006) meaure the mpact on wnd capacty n 39 tate for In contrat, my paper ue panel data from all 50 tate for to etmate the effect on total nonhydro renewable capacty deployment, not jut wnd power capacty deployment. It etmate the effect of addtonal polce, and alo control for dfference n the market and poltcal envronment. Three dtnctly dfferent type of polce are found to be effectve at expandng non-hydro renewable capacty deployment: a command-and-control polcy known a a Renewable Portfolo Standard (RPS), a tax-and-ubdy cheme facltated through a Publc Beneft Fund (PBF) or Clean Energy Fund (CEF), and a market-baed polcy where conumer can expre ther preference to buy power from renewable reource at a premum prce. The command-and-control polcy target the utlty by mandatng a pecfed level of capacty that mut come from renewable energy, and generally referred to a a Renewable Portfolo Standard. The tax-and-ubdy cheme collect an addtonal charge per unt of electrcty conumed from all cutomer n a tate and place the proceed nto th Publc Beneft Fund or Clean Energy Fund. Mone from the PBF/CEF are ued to 3 The electrc power ndutry accounted for 60% of renewable energy producton n

16 ubdze renewable capacty deployment through grant, loan, or producton ncentve. The market-baed polcy create a dfferentated demand by mandatng that utlte mut offer ther cutomer the choce to purchae green power, whch allow conumer to expre ther preference through payng an extra, utlty common-approved charge for green power. The econometrc reult upport many of the concluon from varou cae tude wth repect to Renewable Portfolo Standard and Clean Energy Fund polce. Moreover, the reult preented here alo how, unlke prevou tude, that the potental for offerng conumer the opton to purchae renewable electrcty at a hgher prce than conventonally produced electrcty can ncreae renewable capacty n a tate. 1.2 Lterature Revew The bulk of the lterature n th area ue cae tude to determne the pecfc charactertc of effectve tate renewable energy polce. There are two man type of cae tude: (1) analye of a pecfc polcy enacted n a partcular tate; and (2) a ummary of the general mpact of a pecfc polcy mechanm ued acro multple tate, ncludng polcy degn charactertc that are effectve acro multple tate. Langn and Wer (2003) analyze the Texa Renewable Portfolo Standard, ncludng the achevement of the polcy mechanm and the degn charactertc that allowed the polcy to be effectve at ncreang renewable energy capacty. It wa found that the clearly defned capacty requrement have been effectve n ncreang renewable capacty n Texa. Wer et al. (2004) condered all Renewable Portfolo Standard and found the ptfall n the current polcy degn. Some key problem n polcy degn nclude nuffcent duraton and tablty of target, weak enforcement, and narrow applcablty of the polcy. Other condton that may mpact a polcy effectvene are the preence of long-term power purchaer and poltcal and regulatory tablty. 16

17 Peterk (2004) provde a non-econometrc analy of the effectvene of dfferent type of Renewable Portfolo Standard a of 2003 for the Unted State Energy Informaton Aocaton (EIA). He fnd that only Renewable Portfolo Standard that mandate a certan level of capacty (number of megawatt) have had any gnfcant mpact on renewable capacty deployment. Polce wth renewable generaton or ale requrement a well a voluntary polcy program were found to have no gnfcant effect. Chen et al. (2007) compare the reult from 28 polcy mpact projecton for tate or utlty-level Renewable Portfolo Standard and fnd that (1) the mpact on electrcty prce mnmal, (2) wnd power expected to be the prmary renewable ued to meet polcy requrement, and (3) the beneft-cot etmate rely heavly on uncertan aumpton, uch a renewable technology cot, natural ga prce, and poble carbon emon polcy n the future. Bolnger et al. (2001) decrbe n detal 14 dfferent tate Clean Energy Fund, enumeratng the regulatory background, fundng approache, the current tatu of the fund, and the reultng mpact on renewable energy. Program that fund utlty-cale project are found to be the mot effectve at ncreang renewable capacty deployment. 4 Bolnger et al. (2004, 2006) ummarze the ame 14 Clean Energy Fund. They fnd that due to delay and cancelled project actual capacty often much lower than ntally oblgated capacty. Wer and Olon (2004) examne partcpaton n 66 utlty green power program. They fnd local green power program have redental partcpaton rate rangng from 0.02% to 6.45% and averagng 1.39%. However, th tudy doe not look at any tate-level Requred Green Power Opton that requre all utlte n a tate to offer conumer the opton to purchae renewable energy. The paper focue on partcpaton rate of 4 Fundng uually baed on actual producton, but t pad n a lump um once the capacty ha been contructed. 17

18 the utlty-baed program, but doe not analyze the mpact of thee local program on renewable energy generaton or capacty. Brd et al. (2005) ummarze federal renewable energy polce, general market factor, and tate-pecfc factor, uch a tate polce, that are drvng the deployment of wnd power. The key market factor are the volatlty n natural ga prce durng the early 2000 and the lowered wnd energy generaton cot due to larger wnd turbne, whch have combned to make wnd power more compettve wth natural ga-fred generaton. Only one paper ha attempted to econometrcally etmate the effect of tate renewable energy polcy on renewable capacty. Menz and Vachon (2006) ue ordnary leat quare to etmate tate polcy effect on wnd power capacty and generaton wth a panel dataet for 39 tate for whle controllng for wnd power avalablty, retal choce, and polcy dummy varable for Publc Beneft Fund, Renewable Portfolo Standard, Requred Green Power Opton, and fuel mx dcloure. 5 Renewable Portfolo Standard, whch requre a mnmum amount of renewable energy capacty or generaton, and Requred Green Power Opton, whch requre all utlte n a tate to offer renewable-baed electrcty to all conumer for a premum prce, are found to have a tattcally gnfcant effect on wnd capacty deployment. No tattcally gnfcant effect were found for Publc Beneft Fund, whch ad both the fundng of energy effcency, and for Clean Energy Fund, whch fund renewable energy program and project. 1.3 Model Th paper ue an ordnary leat quare approach a dd Menz and Vachon (2006), but dffer n many apect. Th paper nclude tate fxed-effect, a larger ample, 5 Fuel mx dcloure a polcy that requre the fuel mx a power producer ue n t electrcty generaton to be dcloed to the publc. It beleved that conumer wll ue th nformaton to purchae electrcty from power producer that ue cleaner burnng fuel or alternatve energy. 18

19 and addtonal and more detaled polcy varable a well a control varable for a tate electrcty market and poltcal envronment. Wthout controllng for dfference n market ze and poltcal envronment, omtted varable may ba the reult and lead to ncorrect polcy nterpretaton. State fxed-effect are ued to control for renewable avalablty and capacty contructed pror to 1996, whch n large part due to the mplementaton of pror federal polcy at the tate level a well a the effect of envronmental preference not captured by other varable. C t = α 0 + β R t + δ W t + S + ɛ t The model etmate total non-hydropower renewable capacty (Ct) for , where ubcrpt the tate and t the year of the pecfc obervaton. R t the vector of even regulatory polce (Clean Energy Fund, Renewable Portfolo Standard wth Capacty Requrement, Renewable Portfolo Standard wth Generaton/Sale Requrement, Net Meterng, Interconnecton Standard, State Government Green Power Purchang, and Requred Green Power Opton) and W t the vector of eght poltcal and economc varable. Vector S the tate fxed-effect dummy varable and vector Tt are the year varable. The year varable, mot of the control varable, and ome of the polcy varable are nteracted wth each tate electrcty generaton level to control for market ze n each tate. The dependent varable the total non-hydropower renewable nameplate capacty n the electrc power ndutry (Ct), whch nclude all nameplate capacty of utlte, ndependent power producer (IPP), and ndutral or commercal combned heat and power producer that ue olar, wnd, geothermal, or boma a an energy ource. 6 The um of all non-hydropower renewable energy n a tate ued ntead of the capacty 6 Nameplate capacty the amount of capacty the generator produce under deal condton. Non-hydro renewable nameplate capacty derved from EIA Htorcal State Electrcty Databae found on the EIA webte n whch olar, boma, geothermal, and wnd nameplate capacty are combned nto a ngle category labeled Other Renewable. 19

20 of one pecfc type of renewable energy becaue ung only one type would preclude any nteretng cro-tate comparon of polcy effect of tate wth dfferent avalable renewable energy reource. 7 For example, comparng the effect of a polcy on Mane and Texa ung only wnd power capacty exclude the polcy effect on boma capacty, whch a more lkely renewable choce for Mane. Both type of renewable reource mut be ncluded to drectly compare the effectvene of polce acro tate. The effect of tate renewable energy polce are bet etmated ung total tate non-hydro renewable capacty a the dependent varable becaue everal polce mandate or fund a pecfc amount of renewable capacty. Polce that do not et pecfc renewable capacty requrement can be meaured n capacty term by controllng for each tate market ze, whch wll be dcued n more detal n Secton 4. A large amount of renewable capacty created before 1996 orgnated from the Publc Utlte Regulatory Polcy Act (PURPA), a federal polcy paed n 1978 requrng utlte to purchae electrcty from Qualfyng Faclte (QF), whch are IPP that meet pecfc requrement and nclude renewable-baed faclte. For a varety of reaon, the effect of PURPA vared from tate to tate. State dummy varable (S) meaure thee effect and other unchangng tate factor, uch a renewable reource avalablty. 8 7 Hydropower not ncluded n the renewable energy capacty becaue mot hydropower wa created well before the md-1990, wth few change n capacty or cot over the tme perod beng analyzed. Thee apect allow hydropower to be condered a type of current generatng technology, whch nclude team or ga turbne fred by natural ga, coal, petroleum, or nuclear power. For hydropower to be a vable power opton there mut be an avalable rver or tream a well a a gnfcant change n elevaton. Mot of thee te n the U.S. already have hydropower capacty n place. Removng hydropower from the dependent varable allow the focu of the paper to be on the polcy effect on the emergng technologe of wnd, olar, boma, and geothermal power 8 (Morr, 2003). There ome concern that expraton and buyout of PURPA contract durng the 1990 have led to decreae n renewable capacty, epecally n Calforna where deregulaton n the early to md-1990 created competton baed on prce 20

21 1.4 Varable and Data Economc and Poltcal Varable: W t Eght varable account for non-polcy varablty (Wt) n nameplate non-hydropower renewable capacty n the electrc power ndutry of each tate for The economc varable meaure the percentage of capacty from hydropower and nuclear power n a tate, net generaton, retal prce, fuel cot, renewable energy cot, and ugarcane producton, whle the poltcal varable meaure a tate preference for renewable capacty. Thee varable are nteracted wth generaton to control for dfferent market ze acro tate. 9 Table 1-1 ummarze the data for the dependent varable (RENEWABLE CAPACITY) and the control varable. 10 Total generaton (GEN) the total amount of electrcty generated (n terawatthour) n a tate for a gven year. 11 It expected that more renewable capacty wll be found n tate that generate more electrcty to help meet the hgher demand for electrcty found n thoe tate. 12 The other control varable a well a ome of the polcy varable are nteracted wth generaton to account for market ze acro tate. For example, wthout any conderaton of cot or envronmental mpact. Any capacty hut down due to PURPA contract expraton after 1996 wll decreae the potve effect of any enacted polcy. There alo the poblty of a tate changng t nterpretaton and enforcement of PURPA after 1996, whch would not be captured n the model. 9 Electrcty generaton n a tate ha been choen to repreent market ze ntead of electrcty ale n a tate becaue ome electrcty ale orgnate from outde a partcular tate. 10 Data on capacty, generaton, and prce are found n the Htorcal Databae of the Electrc Power Annual urvey on the EIA webte. Electrcty ummary data avalable at the tate level from the EIA. 11 A terawatt-hour (TWh) the ame a 1,000 GWh or 1 bllon kwh. 12 Total generaton wa choen ntead of total ale becaue ome of the electrcty demand for a tate power producer may come from other tate. Generaton not contamnated wth thee ntertate ale, whch may otherwe nflate or deflate the market ze meaure. Generaton and ale are hghly correlated (0.952). 21

22 an ncreae n fuel cot wll have a larger mpact on renewable capacty n Calforna than n Rhode Iland. Larger tate hould have more fundng to pay for project to ncreae renewable capacty. Renewable Portfolo Standard wth Sale Requrement et requrement on the percent of generaton that mut orgnate from renewable ource. State wth more generaton wll have more total generaton that requred to orgnate from renewable reource, whch hould lead to more renewable capacty n thoe tate. The followng three varable are ncluded n the model to control for market tructure. Two of thee varable are hydropower capacty (PCT HYDROPOWER) and nuclear power capacty (PCT NUCLEAR) a a percentage of total capacty excludng non-hydro renewable. Hydropower hould lead to le non-hydro renewable capacty becaue hydropower ha low margnal producton cot, and the capacty typcally wa contructed many year ago. Wth lower margnal cot and unk captal cot aocated wth hydropower, hydropower wll be the frt renewable energy to be mplemented becaue t more economcally compettve than mot non-hydropower renewable avalable to the electrc power ndutry. Conumer and/or polcy drven demand for renewable-baed electrcty may not dfferentate between hydropower and other renewable ource, whch allow hydropower to be a ubttute of non-hydro renewable. Smlar to hydropower, nuclear power ha low margnal cot of producng bae load electrcty, ha unk captal cot, and ha no emon. If non-hydro renewable capacty deployed baed on economc factor, gven mlar emon profle, greater nuclear or hydropower capacty hould decreae the amount of non-hydro renewable capacty. An alternatve poblty that regulator n tate wth large amount of nuclear power encourage power producer to ue other reource type to meet new demand. Renewable energy may be ued by utlte to allevate preure from envronmentalt over nuclear power, thu leadng to greater deployment of renewable energy capacty n tate wth large amount of nuclear capacty. The gn of PCT NUCLEAR wll depend on whch of thee two factor ha the larger effect on power producer. 22

23 A tate annual weghted average real fuel cot (n 2002 dollar) per mllon Btu (FUEL COST) meaure the mpact of both a tate compoton of fol fuel mx and a tate average cot for each fol fuel type: coal, natural ga, and fuel ol. 13 FUEL COST capture the effect of all thee varable, whch may have offettng effect on renewable capacty. FUEL COST ued ntead of creatng eparate varable for the cot and capacty of each fol fuel for everal reaon. Frt, ung one varable ntead of fve varable mplfe the model. Second, data on pecfc fol fuel cot are mng for many tate. 14 Levelzed cot of each renewable ource the etmated real cot of producton per klowatt-hour of electrcty over the lfetme of the equpment, ncludng all federal producton ncentve. 15 It capture the economc compettvene of each renewable 13 Fuel cot data can be found on the EIA webte n the electrcty databae ecton under Monthly Cot and Qualty of Fuel for Electrc Plant Databae (FERC Form-423). The cot per unt, Btu per unt, and number of unt purchaed for every fuel purchae made by all publc utlte are ued to obtan a nomnal average fuel cot meaure. The data are aggregated and deflated ung the Conumer Prce Index for all good from the Federal Reerve Bank of St. Lou to get the tate annual average real fuel cot per mllon Btu n January 2002 dollar. FUEL COST ha 30 mng obervaton for 8 dfferent tate. Idaho the only tate wthout any fol fuel purchae. Etmate of the fuel cot are ued to fll n the mng data. The non-idaho mng obervaton are extrapolated from the extng data for a tate from Idaho obervaton are generated by ung the average fuel cot of the tate borderng Idaho. A mng data dummy varable ncluded n the model to capture any ba created through the extrapolaton and approxmaton. 14 There are mng fuel cot obervaton for coal (69), natural ga (65), and fuel ol (58). Th mght be due to no delvere of a partcular fuel to a tate, or t could be the mng obervaton are due to change n data reportng requrement durng the ample perod. 15 Levelzed cot calculated by a model that account for the ntal captal cot of contructng the capacty, expected lfetme of the equpment, nteret rate on debt, nflaton rate, fuel cot, operatonal and mantenance cot, capacty factor of the equpment, and federal producton ncentve. Read McVegh (1999) for a more detaled decrpton of levelzed cot ued n th paper. 23

24 energy type. Renewable energy a well a nuclear and hydropower have lttle or no fuel cot and very hgh captal cot, whle current generatng technologe baed on fol fuel have large fuel cot but lower captal cot. 16 A renewable energy ha gotten cheaper to produce, t ha become more economcally compettve. Th mple that decreae n the levelzed cot of each type of renewable energy wll lead to more renewable capacty. The levelzed cot alo nclude federal producton ncentve polce that vary over tme. 17 Many reearcher have tred to etmate the levelzed cot of energy for each renewable ource. Makng uch an etmate beyond the cope of th paper, o the data et beng ued for th varable obtaned from McVegh et al. (1999). The etmated levelzed cot of energy n the U.S. for each renewable energy ource n real 2002 dollar and etmated for every fve year, from 1980 to Thee data pont are ued to nterpolate a polynomal curve that had the bet ft (hghet r-quared value). Due to th nterpolaton from etmated data, the cot of energy for each type of renewable energy a reaonable though mprece etmate of the decreang cot of renewable energy over tme n the U.S. The reultng trend lne for each type of renewable energy have a hgh correlaton. So a weghted average of the levelzed cot of wnd, olar, boma, and geothermal for the entre U.S. ued to create the new varable RENEW COST, whch an average natonal trend for renewable energy cot Fol fuel cot are uncertan for current generatng technologe, and techncal effcency of captal equpment uncertan for renewable energy generaton. 17 The Renewable Energy Producton Incentve (REPI) and Producton Tax Credt (PTC) were paed n the Energy Polcy Act (EPACT) of The level of the REPI decded by Congre annually, whle the PTC wa reenacted n 1999 and The data pont for 1985, 1990, and 1995 were etmated baed on actual cot nformaton whle 2000 and 2005 were forecat made n The polynomal curve have an order of two for boma and geothermal and three for olar and wnd. 19 The weghted average for each year baed on the ource hare of total non-hydropower net ummer renewable capacty n the U.S n Net nameplate 24

25 If renewable capacty beng contructed on economc ground, a re n the retal prce of electrcty make renewable energy more proftable and hould have a potve effect on renewable capacty. 20 However, retal prce n a tate may be multaneouly determned wth renewable capacty becaue ung more renewable capacty ncreae the average cot of producton, whch could lead to hgher prce. Ung the tate retal prce could alo lead to multcollnearty problem wth fol fuel cot becaue hgher fuel cot wll lead to hgher electrcty prce. To control for th endogenety and poble multcollnearty, the model mut ue a proxy for a tate retal prce. A proxy mut be correlated to the endogenou varable and have no mpact telf on the dependent varable. The weghted average real retal prce per klowatt-hour of the borderng tate (BORDER PRICE) an deal proxy for retal prce becaue t meet both of thee requrement. 21 capacty data for each type of renewable energy are not avalable from the EIA, makng net ummer capacty the cloet avalable alternatve meaure. Even though there a cot of energy etmate for both olar thermal and olar Photovoltac, the olar capacty data are not egregated nto thee two type. A non-weghted average of olar thermal and PV taken to get the levelzed cot for total olar capacty. Snce all olar power account for le than 2.5% of total non-hydro renewable capacty n the U.S., t unlkely that ung ome weghted average of olar thermal and olar PV would make any gnfcant dfference. Summer capacty refer to the maxmum output generatng equpment expected to upply to a ytem demontrated by tet at the tme of ummer peak demand. Nameplate and ummer capacty have hgh correlaton, but are not dentcal due to dfferent operatng condton acro utlte. Defnton of nameplate n Footnote Average retal prce baed on all ale n the market: redental, commercal, ndutral, and other cutomer. Data are avalable from the EIA Htorcal Databae. Average retal prce data are orgnally n nomnal term for each month. Two tep have to be taken to adjut the data nto real term for each year. Frt, the monthly data are dvded by the CPI for all good to get the monthly data nto real term. Second, monthly electrcty ale are ued to get a weghted average prce for each year. The reultng varable the real average retal prce for each tate and year n January 2002 dollar. 21 Borderng tate are all tate that ether hare a border, uch a Arzona and New Mexco, or meet at a corner, uch a Arzona and Colorado. The prce are weghted by ale n the borderng tate. The correlaton of retal prce to BORDER PRICE

26 Ung BORDER PRICE ntead of the tate retal prce remove the poble collnearty wth FUEL COST a well. Florda, Hawa, Louana, and Texa ue the byproduct of ugar producton from ugarcane a a boma fuel. For example, n Hawa ugarcane one of the prmary ource of boma. Due to market condton mot of the ugarcane farm n Hawa were hut down over the 1990, removng the fuel ource for much of the boma capacty n the tate. Change n ugarcane producton are lkely to have an mpact on the amount of boma capacty n a tate. The change n total ton of ugarcane producton from 1996 level (SUGARCANE PROD CHANGE) ncluded n the model to control for t mpact on renewable capacty. SUGARCANE PROD CHANGE the only control varable not nteracted wth generaton. A poltcal varable ncluded to meaure change n renewable energy preference n a tate. The League of Conervaton Voter (LCV) ratng ued to determne f polcy preference for envronmental protecton ncreae renewable energy capacty ndependent from t polcy effect. The League of Conervaton Voter (LCV) annually publhe the Natonal Envronmental Scorecard, whch rate all congreonal vote on conervatonal ue by each repreentatve. 22 For example, f there are ten total vote n a year on envronmental ue and a congreperon voted n favor of conervaton x tme, h or her LCV ratng would be 60. An average of all the vote by a tate repreentatve taken to get the average Houe of Repreentatve core (LCV SCORE). The core from the Houe of Repreentatve are ued ntead of the Senate becaue repreentatve have a horter term n offce 22 Data from the Natonal Envronmental Scorecard avalable from the League of Conervaton Voter webte, The LCV ratng ha been ued n pror tude, ncludng Baldwn and Magee (2000), Kalt and Zupan (1984), and Nelon (2002). 26

27 than enator, two year veru x year. The horter term create greater preure on repreentatve to act accordng to ther conttuent preference. A hgh LCV ratng for a tate ndcate that the tate conttuent are envronmentally frendly and are more lkely to demand electrcty from renewable energy, all other thng beng equal. Conumer or envronmental group n tate wth hgher LCV ratng may be more lkely to preure utlte to ue greater amount of renewable energy no matter whch, f any, polce have been enacted by the tate. Polce may be endogenou to hgher LCV ratng becaue tate wth congreperon who vote for federal pro-envronmental polce may be more lkely to enact tate pro-envronmental polce. The polcy endogenety ue not addreed n the body of th paper becaue LCV SCORE not a trong enough predctor of tate polce to be a atfactory ntrument. Note alo that removng LCV SCORE from the regreon doe not change the other reult Regulatory Polcy Varable: R t Seven of the ndependent varable are polcy varable capturng the effect of dfferent type of renewable energy regulaton, ether by a tate leglature or Publc Utlty Common (Rt). 23 Mot polce are enacted through tate leglaton, and then enforced by the Publc Utlty Common (PUC). There are a few ntance, however, n whch a PUC adopt gudelne wthout tate leglaton. No leglaton or PUC acton requred for tate governor to ue executve order to create a tate government green power purchang agreement or to et voluntary goal for generaton. 23 Informaton on renewable polce avalable on the Databae of State Incentve for Renewable Energy (DSIRE) webte, whch a project of the Intertate Renewable Energy Councl and funded by the U.S. Department of Energy. The nformaton compled from many dfferent ource, ncludng federal and tate offcal, publc utlty common, and renewable energy organzaton. The ource of the nformaton ncluded wthn each polcy decrpton. Bollnger et al. (2001) nclude addtonal nformaton on the enactment and degn of Publc Beneft Fund. 27

28 Polcy dummy varable value are determned by a polcy enactment date, zero before enactment and one after enactment. The enactment date the year that the polcy paed by the tate leglator, created through an executve order, or announced a a mandate under new PUC gudelne. Some of thee polce allow a grace perod for power producer to meet the new regulaton. The effectve date the year that the polcy requrement mut be met. The average lag from the enactment to effectve date a lttle over one year, but can be longer for Renewable Portfolo Standard. The enactment year a better choce to determne when the polcy begn to mpact the power producer. Once a power producer become aware of a future requrement, t may begn to contruct any neceary renewable capacty. Thee acton could lead to large amount of renewable capacty beng contructed between the enactment date and effectve date. Regulatory polce decrbed below nclude a Renewable Portfolo Standard wth a Capacty Requrement, Renewable Portfolo Standard wth a Generaton/Sale Requrement, Clean Energy Fund, Net Meterng, Interconnecton Standard, State Government Green Power Purchang, and Requred Green Power Opton. Table 3-2 ummarze the data for the polcy varable. The frt polcy that wll be dcued a Renewable Portfolo Standard, whch pecfe an amount of a tate electrcty producton, ale, or capacty that mut be renewable-baed. Renewable Portfolo Standard can be dfferentated nto three man tructural form, polce that et (1) mandatory renewable generaton or ale level, (2) voluntary renewable generaton or ale goal, and (3) mandatory renewable energy capacty requrement. The frt type of Renewable Portfolo Standard et a percentage of total generaton or ale for each power producer/retaler that mut orgnate from renewable ource, uually ncreang every year or every few year. For example, Arzona tered renewable level that have to be met began at 0.2% n 2001 and ncreaed by 0.2% each year, 28

29 reultng n a requrement of one percent n Mot other tate Renewable Portfolo Standard have mlar tructure, but vary n percentage level and enforcement date. 24 Iowa, Mnneota, Texa, and Wconn have mandated utlte to ntall a certan level of megawatt of renewable capacty. 25 A long a the requrement are mplemented effectvely, renewable capacty requrement hould ncreae renewable capacty by the ame number of megawatt requred by the mandate. Thee capacty requrement wll make th type of Renewable Portfolo Standard more effectve n th model becaue they target actual capacty contructon veru generaton or ale baed Renewable Portfolo Standard. The dfference between Renewable Portfolo Standard can be accounted for n the model by two varable: a varable that meaure the ze of the renewable generaton or ale requrement (RPS: SALES REQ) and a varable that meaure the ze of the capacty requrement (RPS: CAP REQ). 26 The capacty requrement ze and date are ued to extrapolate the expected requrement for each year aumng a lnear functon, where the power producer ncreae capacty by the ame amount each year untl they meet the fnal requrement, to form the varable RPS: CAP REQ. 24 In 1998, Wconn ntroduced mandatory capacty level before t enacted a Renewable Portfolo Standard wth mandatory generaton or ale n Two tate (Illno and Hawa) wth Renewable Portfolo Sale Goal (not requrement) are counted a Renewable Portfolo Standard wth a ale requrement. The only reult that change when thee non-mandatory goal are treated a a requrement of zero the coeffcent on RPS: SALES REQ become maller and become le gnfcant for all pecfcaton. All other coeffcent reman relatvely unchanged. 25 Mnneota ha had both type of Renewable Portfolo Standard nce A voluntary generaton goal wa enacted n 2001, whle the capacty requrement wa enacted n Capacty requrement range from 50 to 2000 MW, and generaton/ale requrement range from 0-30%. 29

30 RPS: SALES REQ an even more complex varable. The generaton/ale requrement, whch uually et a target about fve year after enactment, lnearly nterpolated backward to the enactment date of the polcy. For example, a polcy enacted n 1996 wth a ale requrement of 1.0% begnnng n 2000 would be lnearly nterpolated to be 0.2% n 1996 and ncreae by 0.2% each year untl t reache 1.0% n Although the requrement not enforced untl 2000, t would be neceary for power producer to begn contructon at leat everal year before 2000 to get the neceary capacty contructed n tme to meet the ale requrement. Although th polcy doe not drectly requre the contructon of renewable capacty, an ncreae n the requred amount of renewable generaton may lead to a need for more renewable capacty. If current level of renewable capacty cannot meet a future generaton/ale requrement, addtonal capacty wll need to be contructed. 27 A Clean Energy Fund a tate-level program that often, but not alway, created through the retructurng of the electrcty market and ued to fund grant, loan, and producton ncentve for both reearch and development and actual deployment of alternatve energy. Many Clean Energy Fund focu on fundng actual renewable capacty deployment, whch hould lead to more renewable capacty n a tate. Clean Energy Fund are pad for through Sytem Beneft Charge (SBC), whch are addtonal charge pad by all conumer on ther electrcty conumpton. SBC can be 27 Some tate Renewable Portfolo Standard a wth generaton/ale requrement allow the ue of ome hydropower electrcty to meet the requrement. However, there are normally pecfc requrement a to whch faclte wll be elgble, ncludng retrcton on a unt maxmum capacty, type of hydropower, and year of ntallaton. For example, ome tate do not allow generatng unt greater than 30 MW to be elgble. One tate doe not allow any hydropower to orgnate from dammed hydropower plant. Another tate only allow electrcty from new hydropower capacty to be elgble. Thee retrcton wll decreae the effectvene of thee polce to ncreae renewable capacty n a tate. However, the complexte of the retrcton make t dffcult to create an approprate meaure for thee effect. 30

31 condered a conumpton tax on electrcty to fund deployment of renewable capacty n the ndutry. In Mnneota, a ettlement wth the electrc utlty Xcel Energy created a mlar fund that payng for renewable energy reearch and deployment. Mane created a voluntary fund mlar to a Clean Energy Fund for the tate cutomer to donate money. 28 Smlar to Renewable Portfolo Standard, Clean Energy Fund mut be dfferentated to undertand how effectve thee polce are at ncreang renewable deployment n a tate. The varable ued n th model a varable that meaure the amount of capacty that beng funded for utlty-cale project from Clean Energy Fund (CEF: CAP FUNDED). 29 Some cutomer may prefer to buld generatng capacty to provde ther home wth ome of ther own electrcty. Net Meterng (NET METERING) allow cutomer that are able to produce more electrcty than they conume n a gven month to ell any exce to the utlty to offet the charge for electrcty n month the cutomer a net purchaer. The effect of net meterng expected to be negatve becaue f renewable energy demander produce ther own renewable electrcty through a olar PV ytem or mall wnd turbne, they wll demand le renewable capacty from power producer. From a utlty perpectve, f t requred to reach a renewable capacty or ale target, thee cutomer-owned faclte may erve to offet a utlty need to buld renewable 28 Databae of State Incentve for Renewable Energy (DSIRE) doe not nclude New Mexco a havng a Clean Energy Fund, whle Bolnger et al. (2001) verfe that New Mexco doe have a Clean Energy Fund. 29 The capacty oblgaton a of 2003 are nterpolated backward lnearly to the enactment year o that an equal amount of addtonal capacty oblgaton are made each year and total the overall oblgaton a of The data for varable orgnated from the Databae of Utlty-Scale Renewable Energy Project from the Clean Energy State Allance (CESA). 31

32 capacty. NET METERING nteracted wth GEN to control for the polcy effect baed on market ze. Interconnecton tandard (INTERCON STANDARDS) are a et of gudelne ued to afely and effectvely connect ndvdual renewable generatng unt to the electrc utlty power grd. Some have techncal requrement, uch a generator type and ze lmt, mandatory afety and performance tandard, and nurance requrement that mut be met before a net meterng cutomer can connect to the utlty network. Interconnecton tandard mut be met by any commercal, ndutral, redental, or government cutomer that decde to connect to the grd. Wthout thee tate polce, the net meterng connecton could caue major problem for the grd, power producer, and other purchaer. Interconnecton tandard ncreae the cot of hookng up to the grd for net meterng and may offet ome of the negatve effect from net meterng. INTERCON STANDARDS alo nteracted wth GEN to control for market ze. 30 State Government Green Power Purchang polce requre that ome percentage of a tate government electrcty purchae be from renewable ource. Thee purchae agreement range from 5% to 50% of a tate government electrcty purchae. Smlar to Renewable Portfolo Standard wth Sale Requrement, a State Government Green Power Purchang agreement ncreae the need for renewable-baed electrcty generaton. A tate government electrcty ue re, the renewable generaton needed to meet the requrement ncreae. If the new generaton need cannot be met by current renewable capacty, power producer wll need to contruct new renewable energy capacty. The ze of the State Government Green Power Purchang requrement, n term of a percentage of the tate government electrcty purchae, nteracted wth GEN to 30 Snce only four obervaton have nterconnecton tandard and no net meterng, the nteracton term meaure the effect of nterconnecton tandard on tate that already have net meterng polce. Only 86 of the 187 obervaton (46%) wth net meterng alo have nterconnecton tandard, whch remove concern of multcollnearty. 32

33 control for both the tate purchae requrement and the tate market ze (PCT STATE PURCHASING*GEN). A Requred Green Power Opton requre utlte to offer cutomer the opton to purchae renewable power at a premum. There are two veron of how thee opton are mplemented. The mot common type gve conumer the opton to make voluntary contrbuton, called voluntary renewable energy tarff n return for the guarantee that ome of the conumer electrcty conumpton produced from renewable ource. Conumer purchae electrcty at the market prce and then pay a premum for block of green electrcty, uually about $2 per 100 kwh. The econd type allow the producer to charge conumer a hgher rate per klowatt-hour, but only to cover the addtonal cot for electrcty from renewable ource. Both the premum block rate and premum per klowatt-hour rate mut be approved by the tate Publc Utlte Common (PUC). Requred Green Power Opton elct cutomer preference and a crude meaure of wllngne to pay for renewable energy by allowng conumer to voluntarly pay hgher prce for the knowledge that they are upportng renewable-baed electrcty. The creaton of th nche market for renewable energy generaton hould have a potve mpact on renewable capacty. The varable REQ GREEN POWER OPT a dummy varable, whch nteracted wth GEN n the model to meaure the effect of the polcy baed on the tate market ze (REQ GREEN POWER OPT*GEN). 1.5 Stattcal Specfcaton and Emprcal Analy Ordnary Leat Square regreon wth tate fxed-effect and robut tandard error are ued n th paper to etmate total non-hydro renewable capacty. Robut tandard error are ued to account for heterokedatcty, whch wa found to ext n the model by ung a Breuch-Pagan/Cook-Weberg Heterokedatcty Tet. 31 Table 3 report 31 The reult wa a Ch-Sq=448 and P( )>Ch-Sq=0.0000, o there a gnfcant dfference n the varance of the dependent varable, whch create heterokedatcty. 33

34 the regreon reult. Specfcaton 1 nclude only the polcy varable. Specfcaton 2 nclude the economc market and poltcal control varable, and Specfcaton 3 replace RENEW COST wth year dumme nteracted wth GEN. The followng ubecton decrbe the reult ung the coeffcent from Specfcaton Economc and Poltcal Varable: W t The coeffcent for GEN ngnfcant, whch cannot be ealy nterpreted becaue of how many dfferent way that a tate generaton can mpact a tate level of renewable capacty. Although the coeffcent ngnfcant, generaton level do have effect through other varable that are nteracted wth GEN, whch are explaned below. The percentage of other capacty compred of hydropower nteracted wth generaton (PCT HYDRO*GEN) not tattcally gnfcant. However, the coeffcent for the percentage of other capacty compred of nuclear power nteracted wth generaton (PCT NUCLEAR*GEN) potve and tattcally gnfcant. A one tandard devaton (12.46%) ncreae n the percentage of non-renewable capacty compred of nuclear power lead to an ncreae of 2.09 MW per terawatt-hour of generaton n a tate. So th one tandard devaton change n a tate wth a medan generaton level (51.15 TWh) lead to an ncreae of 107 MW. It poble that utlte wth more nuclear power are deployng more renewable capacty becaue the utlte are focued on dverfyng t generaton mx, ether to decreae the utlte ue of fol fuel and lower emon or to allevate preure from envronmentalt who are upet about the ue of nuclear power. The coeffcent on the average LCV core for the Houe of Repreentatve nteracted wth generaton (LCV SCORE*GEN) are potve and gnfcant. A one tandard devaton ncreae (26.51 pont) n a tate LCV core lead to an ncreae of MW per terawatt-hour of generaton. A one tandard devaton ncreae n a tate wth medan 32 Reult from Specfcaton 2 are nearly dentcal to reult from Specfcaton 3 wth the ame nterpretaton. 34

35 generaton lead to an ncreae of 34 MW. Preference for renewable energy capacty do n fact lead to a mall amount of deployment of ome renewable capacty, holdng polce fxed. A expected, renewable energy cot nteracted wth generaton (RENEW COST*GEN) ha a negatve and tattcally gnfcant coeffcent. A one-cent per kwh decreae n renewable energy cot lead to an ncreae of MW per terawatthour of generaton. In a tate wth medan generaton, a one cent decreae n RENEW COST lead to an ncreae of 36 MW. RENEW COST decreaed by 1.79 cent from 1996 to 2003, whch mple an ncreae of 65 MW for a tate wth medan generaton. Th effect doe not jut nclude the technologcal change n renewable energy. A mentoned n Secton 4, all federal producton ncentve are ncluded n the cot of producton for each renewable ource, capturng the federal polcy change a well a the technologcal advance. The year varable coeffcent, whch explan the ame mpact a RENEW COST, are explaned n detal n Secton 5.4. The coeffcent on average border tate retal prce nteracted wth generaton (BORDER PRICE*GEN) negatve and margnally tattcally gnfcant only n Specfcaton 3 of Table 3. Hgher electrcty prce do not appear to reult n more renewable energy capacty contructon. In fact, the negatve coeffcent mple that an ncreae of one cent n the prce of electrcty lead to a mall decreae n renewable capacty by 13 MW n a tate wth medan generaton. A one tandard devaton (2.07 cent) ncreae n prce lead to a decreae of only 27 MW. It poble that conumer n a tate wth hgh electrcty prce have le of an appette for further ncreae n prce through more expenve renewable generaton Hgh electrcty prce may be one of the factor drvng the enactment of tate renewable energy polce. However, hgh prce by themelve do not appear to lead to renewable capacty deployment n a tate. 35

36 The coeffcent for average fuel cot nteracted wth generaton (FUEL COST*GEN) tattcally gnfcant. It dffcult to nterpret the meanng of the coeffcent, nce the component of the varable may lead to oppote effect. Hgher cot hould make renewable energy capacty more compettve. But the varable alo reflect dfference n fuel type ue n a tate. To take one example, nce natural ga more expenve than coal, more natural ga ue would lead to a hgher average fol fuel cot and make renewable energy more compettve n the market. On the other hand, natural ga reult n lower emon than ung coal or ol. All ele equal, a tate wth more natural ga capacty wll have lower emon than f a tate had hgher amount of coal capacty, whch lower the need for non-emttng renewable capacty to meet emon reducton goal. If th hold true, a hgher average fol fuel cot wll be correlated wth le renewable capacty contructon. To allevate any concern about FUEL COST, an addtonal pecfcaton etmated replacng FUEL COST wth fve varable: average cot of coal, average cot of ol, average cot of natural ga, percent of non-renewable capacty compred of coal, and percent of non-renewable capacty compred of natural ga. Natural ga and coal capacty are treated n the ame manner a hydropower and nuclear power capacty n the model. Each varable nteracted wth GEN, jut lke the other control varable. A hgher percentage of total non-renewable capacty compred of coal correlated wth more renewable capacty, whch gve ome upport that tate wth drter conventonal capacty ue more renewable capacty. A the prce of coal ncreae, le renewable capacty contructed. Thee two reult upport the dea that the emon requrement utlte mut meet are a drvng force to renewable deployment, whle economc compettvene n the market doe not have much of an mpact. Cauton neceary n nterpretng the reult wth the addtonal et of fuel varable becaue there are many mng obervaton that mut be extrapolated. The dummy varable that control for mng obervaton for coal and natural ga are both tattcally 36

37 gnfcant, whch brng up concern about the varable coeffcent and any poble bae due to the mng data. The mot mportant reult from th pecfcaton that the addtonal varable have no effect on the polcy varable coeffcent, whch reman relatvely unchanged relatve to the orgnal model. The coeffcent on SUGARCANE PROD CHANGE ngnfcant. The mng fuel cot dummy varable nteracted wth generaton (MISSING FUEL COST*GEN) control for any meaurement error caued by the extrapolaton of the 38 mng data pont and ngnfcant a well Regulatory Polcy Varable: R t Table 4 etmate the tattcally gnfcant effect from both the control varable and the polcy varable baed on a tate wth medan generaton level. Clean Energy Fund, Renewable Portfolo Standard wth Capacty Requrement, and Requred Green Power Opton have tattcally gnfcant effect on renewable capacty n the electrc power ndutry. Renewable Portfolo Standard wth Generaton/Sale Requrement and State Green Power Purchang Program are margnally gnfcant n Specfcaton 1, but loe ther gnfcance once control varable are ntroduced nto the model. CEF: CAP FUNDED, whch meaure the amount of capacty that the fund ha agreed to help fnance, ha a margnally tattcally gnfcant coeffcent. Th nclude capacty that ha been agreed upon, but ha not yet been bult, ether becaue the project ha not been fnhed or the project later canceled. For each megawatt of capacty that the Clean Energy Fund ha funded or agreed to fund n the near future, approxmately MW ha been contructed. Th not gnfcantly dfferent than the fracton of capacty that ha actually been contructed a of 2003, whch wa 0.33 MW per 1 MW. Even though actual renewable capacty probably not contructed lnearly over the lfetme of the polcy, the etmate from the lnear nterpolaton eem to be repreentatve of actual capacty contructon due to the Clean Energy Fund. 37

38 The coeffcent on RPS: CAP REQ potve and gnfcant, and about the ame ze a would be expected. For each megawatt of capacty requred by the Renewable Portfolo Standard, approxmately 1.14 MW contructed. The coeffcent not gnfcantly dfferent than one. Smlar to CEF: CAP FUNDED, the lnear nterpolaton approach taken n degnng RPS: CAP REQ effectve at capturng the polcy effect by allowng varaton n the tmng of capacty contructon. The mot nteretng reult from the model the effect that Requred Green Power Opton have on renewable capacty. The coeffcent for REQ GREEN POWER OPT*GEN ha a potve and tattcally gnfcant coeffcent and ha ome of the larget effect on renewable capacty of any varable, where enactment lead to renewable capacty ncreang by 3.46 MW per terawatt-hour of generaton. A tate wth a medan generaton level (51.15 TWh) that enact a Requred Green Power Opton would have an ncreae of 177 MW. Wahngton ha the larget electrcty market of tate that have enacted a Requred Green Power Opton (100.1 TWh), whch would lead to an ncreae n renewable capacty of 346 MW. To gve ome perpectve on thee reult, the etmated mpact n total renewable capacty can be expreed n term of a percentage of total capacty n a tate. Dependng on the tate, a Requred Green Power Opton lead to an ncreae of about %. 34 The tattcally and economcally gnfcant ncreae mple that Requred Green Power Opton, whch create a nche market for green power by requrng tate to offer renewable-baed electrcty to ther conumer at a premum, are very ueful n ncreang the amount of renewable energy capacty n a tate Thee etmate are made by takng the etmated effect of a Requred Green Power Opton n a tate on total renewable capacty n 2003, and then dvdng that value by total capacty n the tate for The reultng mpact a meaure of the change n renewable capacty n percentage term of total capacty. 35 Th etmaton n the range of the average partcpaton rate for all local green power program of 1.4% (Wer and Olon, 2004). 38

39 The coeffcent for both STATE PURCHASING: PCT REQ*GEN and RPS: SALES REQ*GEN are margnally tattcally gnfcant n Specfcaton 1. However, once control varable are ncluded n the regreon, the coeffcent are no longer tattcally gnfcant. Intal tate government purchae level are mnmal and account for a relatvely mall porton of the electrcty market n a tate. The low demand can tll be met by current renewable generaton n a tate. Gven the ze and tattcal gnfcance of the coeffcent n Specfcaton 3, t unlkely that tate government purchae of renewable energy wll reult n any gnfcant ncreae n renewable capacty n a tate. There are multple reaon for the ngnfcance of RPS: SALES REQ*GEN. Frt, mot Renewable Portfolo Standard wth ale requrement have been enacted farly recently and currently have low requrement. Power uppler may be able to meet ther low ntal requrement by ung current renewable capacty. Second, ome of the tate mplementng thee polce have avalable hydropower capacty already n place that condered elgble to meet a porton of thee currently low mandate, whch decreae the polce effectvene n encouragng new non-hydro renewable capacty deployment n a tate. Thrd, ome tate allow the purchae of Renewable Energy Credt (REC), whch are certfcate that repreent the envronmental rght of renewable electrcty, ntead of actual generaton. Many of thee ame tate allow power producer/retaler to purchae REC from out-of-tate power producer to meet ther n-tate requrement. All three of thee factor wll decreae the polcy mpact on n-tate renewable capacty deployment. A few more year of data hould reult n RPS: SALES REQ*GEN to have tattcally gnfcant mpact on renewable capacty n t tate. Nether net meterng nor nterconnecton tandard appear to have an mpact on renewable capacty. The coeffcent on NET METERING and INTERCON STANDARDS are tattcally ngnfcant. 39

40 1.5.3 State Fxed-Effect Varable: S t Forty-nne tate fxed-effect varable are ncluded n Specfcaton 3 n Table 3 to control for tate nterpretaton of federal polce enacted pror to 1996 a well a any tme-nvarant dfference acro tate. 36 Tme-contant varaton acro tate nclude the avalablty of renewable energy reource and the ntal level of a tate preference for renewable energy ue. The coeffcent hould be hghly correlated to the amount of renewable capacty that exted n The correlaton between a tate ntal renewable capacty and t tate-fxed effect coeffcent The tate fxed-effect eem to effectvely control for the mpact of extng regulaton and the market envronment pror to Year Varable: T t The thrd pecfcaton replace the natonal renewable energy cot trend varable (RENEW COST) wth year varable nteracted wth GEN. The coeffcent are tattcally ngnfcant for all year except for 2003, where the mpact MW per terawatt-hour of generaton n a tate. A tate wth medan generaton ha an ncreae of 27 MW from 1996 to Thee year varable meaure the mpact of renewable energy becomng more economcally vable a well a federal polcy mplemented to encourage renewable energy ue. The federal Renewable Energy Producton Tax Credt (PTC) and federal Renewable Energy Producton Incentve (REPI) were enacted n The federal PTC wa renewed n both 1999 and 2001, whle the fundng for the REPI change from year to year baed on congreonal appropraton. Each year coeffcent control for the mpact of thee polce on each tate a fundng for thee producton ncentve change a well a the mprovement n the technology behnd renewable energy. 36 One tate mut be dropped from the model to remove multcollnearty of the fxed-effect varable. 40

41 1.6 Concluon State have enacted many polce to ncreae the deployment of non-hydro renewable capacty nto the electrc power ndutry n that tate. The lterature evaluatng the effectvene of thee program cont of cae tude and one tattcal tudy, whch explan the ue of wnd power. My tattcal tudy utlze a larger panel, more polce, and more control varable to explan the deployment of total renewable capacty n a tate. Three regulatory polce appear to be effectve at ncreang renewable capacty deployment n a tate. The gnfcant reult from thee regulatory polce confrm many of the fndng from pror cae tude, whch fnd Renewable Portfolo Standard wth Capacty Requrement and Clean Energy Fund have ncreaed renewable capacty. An addtonal polcy, Mandatory Green Power Opton, alo found to ncreae capacty deployment n a tate a well. The prevou emprcal tudy found Publc Beneft Fund, whch nclude any Clean Energy Fund n a tate, to be ngnfcant n ther model. My paper fnd that Clean Energy Fund wth utlty-cale project ncreae the deployment of renewable capacty n a tate. By ung Sytem Beneft Charge (SBC) a tate can effectvely make conumer pay for cleaner energy wthout creatng a dfferent market for renewable energy demand. Smlar to the cae tudy fndng by Bolnger et al. (2001, 2004, 2005), larger utlty-cale project make Clean Energy Fund more effectve at ncreang renewable capacty deployment n a tate. Th paper fnd that dfferent type of Renewable Portfolo Standard have dfferent effect on renewable capacty. Each megawatt of capacty mandated by Renewable Portfolo Standard wth Capacty Requrement reult n the deployment of one megawatt of addtonal renewable capacty n a tate. But recent Renewable Portfolo Standard that mandate generaton or ale level appear not to have tattcally gnfcant effect. Thee reult mrror Peterk cae tudy n that only Renewable 41

42 Portfolo Standard wth Capacty Requrement have ncreaed renewable capacty, but expand on the cae tudy by fndng evdence on the ze of the polcy effect holdng other polce fxed. Statewde Requred Green Power Opton appear to have been a effectve a any other polcy. Forcng utlte to offer cutomer the opton to purchae renewable-baed electrcty at a reaonable premum rate dratcally ncreae renewable capacty n a tate. The polcy ha a greater mpact n larger electrcty market and appear to be effectve regardle of a tate poltcal envronment. There are major renewable polcy mplcaton f thee reult hold when addtonal year are eventually ncluded n the model. Only fve tate have currently mplemented Requred Green Power Opton even though creatng a tatewde green power market appear to be a effectve at ncreang renewable energy capacty n a tate a a command-and-control cheme of a Renewable Portfolo Standard or tax-and-ubdy cheme of a Clean Energy Fund. State government purchang agreement of renewable energy appear to be no more than wndow dreng for poltcan to how ther upport to the envronmental communty, and addtonal fundng to renewable power producer. The remanng polce n the model do not appear to mpact renewable energy capacty contructon n the the electrc power ndutry. State government green power purchang doe not ncreae renewable electrcty demand enough to drve capacty contructon. Net meterng and nterconnecton tandard target redental and commercal capacty and do not mpact electrc power ndutry decon. The mportant polcy mplcaton that are from the reult ndcate polcymaker have a wde array of tool at ther dpoal to promote renewable energy deployment n a tate to meet envronmental and energy ecurty polcy goal. The array of polcy mechanm wll become even more ueful to tate government f the propect of U.S. clmate change/carbon emon polcy become a realty. 42

43 Table 1-1. Dependent and Control Varable Varable Mean. Std. Dev.. Mn. Max. Medan. RENEWABLE CAPACITY (MW) GEN (TWh) PCT HYDROPOWER (Percentage) PCT NUCLEAR (Percentage) BORDER PRICE (2002 cent/kwh) RENEW COST (2002 cent/kwh) FUEL COST (2002 dollar/mmbtu) LCV SCORE (0 to 100) SUGARCANE PROD CHANGE

44 Table 1-2. Regreon Reult Total Non-Hydro Renewable Capacty (1) (2) (3) CEF: CAP FUNDED (MW) (0.107)* (0.145) (0.124)* RPS: CAP REQ (MW) (0.175)*** (0.168)*** (0.168)*** RPS: EFFECTIVE GEN REQ (0.056)*** (0.077) (0.071) PCT STATE GREEN POWER PURCHASING*GEN (0.014)* (0.017) (0.016) REQUIRED GREEN POWER OPT*GEN (0.667)*** (1.207)*** (1.166)*** NET METERING*GEN (0.205) (0.214) (0.227) INTERCON STANDARD*GEN (0.211) (0.195) (0.210) SUGARCANE PRODUCTION CHANGE (Ton) (0.023) (0.023) GEN (1 TWh) (1.150) FUEL COST ($/mmbtu)*gen (0.107) (0.109) FUEL COST MISSING*GEN (0.843) (0.802) BORDER PRICE (Cent/kWh)*GEN (0.207) (0.117)** RENEW COST (Cent/kWh)*GEN (0.211)*** LCV SCORE*GEN (0.011)** (0.011)** PCT HYDRO*GEN (0.028) (0.024) PCT NUCLEAR*GEN (0.043)*** (0.052)*** YR1997*GEN (0.151) YR1998*GEN (0.186) YR1999*GEN (0.182) YR2000*GEN (0.199) YR2001*GEN (0.247) YR2002*GEN (0.199) YR2003*GEN (0.226)** CONSTANT (7.689)*** (55.340)*** (50.741)*** Obervaton State Fxed-Effect R-quared Robut Standard Error n Parenthee;* gnfcant at 10%;** gnfcant at 5%;*** gnfcant at 1% 44

45 Table 1-3. Polcy Varable Varable State wth Polcy Non-Zero Obervaton CEF: CAP FUNDED 8 51 RENEWABLES PORTFOLIO STANDARD RPS: CAP REQ 4 27 RPS: SALES REQ 6 39 NET METERING INTERCON STANDARDS STATE PURCHASING: PCT REQ 6 14 REQ GREEN POWER OPT

46 Table 1-4. Varable Effect of Sgnfcant Varable Varable Mean Std. Dev. Increae Per Unt per TWh Std. Dev. n Medan Gen. State RENEW COST (2002 cent/kwh) MW -36 MW BORDER PRICE (2002 cent/kwh) MW -27 MW PCT NUCLEAR MW 107 MW LCV SCORE (0-100) MW 34 MW Effect of Enactng a Polcy Mean Std. Dev. Per Unt Effect Impact n Medan Gen. State PBF: CAP FUNDED MW per 1.0 MW 20.6% of Funded Capacty RPS: CAP REQ MW per 1.0 MW 114% of Req. Cap. REQ GREEN POWER OPT MW per TWh 177 MW Note 1: Reult are for Spec. 3 excludng RENEW COST, whch from Spec. 2. Note 2: All other varable are tattcally ngnfcant. 46

47 CHAPTER 2 EFFECTS OF COAL CONTRACT CONSTRAINTS ON SO 2 TRADING PROGRAM COMPLIANCE DECISIONS 2.1 Introducton Ttle IV of the 1990 Clean Ar Act Amendment (CAAA) ntroduced the frt ulfur doxde (SO 2 ) emon cap-and-trade program n the Unted State (U.S.). The program wa clamed to be a ucce by the Clnton Admntraton due to a lower than projected allowance prce, and total complance cot well below the etmated cot under an alternatve command-and-control polcy. 1 A growng body of evdence ugget that much of the potental cot avng have not been acheved by the Ttle IV SO 2 Tradng Program. 2 State publc utlty common (PUC) regulaton, adjutment cot, and long-term coal contract have all been cted a leadng to non-cot-mnmzng acton taken by many electrc utlte. 3 There a body of evdence ndcatng tate PUC regulaton ha led to complance cot that are n exce of leat-cot complance n cap-and-trade program a had been prevouly conjectured. However, thee etmate appear not to account for much of the exce complance cot that reulted durng Phae I of Ttle IV. 4 No work ha been done to date to how the effect long-term coal or other fuel contract have on the ablty of cap-and-trade program to acheve the leat-cot complance oluton. Fuel contract contrant decreae the degree of freedom n 1 Burtraw et al. (2005); Sotkewcz and Holt (2005) 2 Carlon et al. (2000); Ellerman et al. (1997); Sotkewcz and Holt (2005) 3 Carlon et al. (2000), Ellerman et al. (1997), Ellerman et al. (2000), Boh (1994); Boh and Burtraw (1997), Fullerton et al. (1997), and Swft (2001) all lted ether tate regulaton or long-term coal contract or both a poble reaon for the apparent or potental ub-optmal behavor. 4 Sotkewcz and Holt (2005) found actual complance cot to be much hgher than ther etmated cot whle controllng for the effect of tate regulaton. 47

48 complance choce on whch polluton market rely to mprove cot-effectvene n utlty decon-makng. It may well be the cae the preence of long-term contract are drvng part, or mot, of the devaton from leat-cot that have been mulated or etmated n the lterature for Phae I. If long term coal contract dd n fact lead to neffcence under Phae I, contract could have mlar effect under the newly enacted Clean Ar Intertate Rule (CAIR) of 2005 that further retrct SO 2 emon. In th paper a model of unt-level SO 2 complance contructed that ncorporate the preence of coal contract to examne how long-term coal contract affect utlty complance choce and a unt complance cot. A expected, the preence of coal contract contrant lead to complance cot n exce of the hypothetcal leat-cot oluton. The preence of bndng hgh ulfur contract contrant that were lkely n Phae I of the Ttle IV SO 2 Program may explan the lower than expected allowance prce n Phae I that accompaned complance cot that were above the leat-cot oluton. It alo found that the preence of bndng low ulfur coal contrant that may ext under CAIR, whch may lead to allowance prce that are hgher than wthout the bndng contrant. The effect of the contract contrant eem counter-ntutve: bndng hgh ulfur coal contrant leadng to lower exce demand for allowance, whch could reduce the allowance market prce. Bndng low ulfur coal contrant leadng to hgher exce demand for allowance, whch could ncreae the allowance market prce. The nteracton between the contract contrant and the dcrete nature of the crubber choce lead to thee unexpected reult. 2.2 Polcy Background Ttle IV of the Clean Ar Act Amendment Under the Ttle IV SO 2 emon tradng program, affected unt are allocated allowance, whch permt the holder to emt one ton of SO 2 n the year n whch the allowance ued or any year thereafter, and that may be traded (bought or old) n the market or banked for future ue. At the end of each year, generatng unt are requred to 48

49 hold at leat enough allowance to cover ther yearly emon to be n complance. The program allow generatng unt everal degree of freedom n choong how to bet meet t complance oblgaton: wtch from hgh ulfur to low ulfur fuel; ntall crubber; and buy or ell allowance; or any combnaton thereof Phae I of Ttle IV Phae I of Ttle IV, whch ran from , capped the ntal level of emon at 8.7 mllon ton of SO 2 per year for the 110 larget pollutng plant, whch ncluded 263 generatng unt. The EPA allocated allowance grat to thee affected unt baed on average heat nput durng multpled by an emon rate of 2.5 lb. SO 2 /mmbtu. An addtonal 168 unt partcpated n Phae I n 1996 baed on the rule etablhed by EPA allowng a plant to opt-n unt (7 unt), degnate ubttuton unt (160 unt), or degnate compenatng unt (1 unt) a part of ther Phae I complance plan. The voluntary partcpaton of thee addtonal unt reulted n a total of 431 affected generatng unt under Phae I. A ubttuton unt a unt that would eventually be affected n Phae II that voluntarly enrolled nto Phae I to meet ome or all of the requred emon reducton for a Phae I unt (Sotkewcz and Holt, 2005). Subttuton unt receve an allowance allocaton baed on t htorcal heat nput. A utlty may decde to reduce t electrcty producton at a Phae I affected unt. To do o, the utlty mut have a compenaton unt from the Phae II unt the utlty operate to cover the neceary addtonal electrcty. Th compenaton unt then brought nto Phae I and gven an allowance allocaton baed on t htorcal heat nput. Indutral ource of SO 2 emon could ue the opt-n provon and voluntarly enroll nto Phae I and receve 5 There are addtonal complance opton, ncludng huttng down the affected unt and hftng dpatch away from the affected unt (Energy Informaton Aocaton, 1997) 49

50 allowance allocaton mlar to ubttuton and compenaton unt. There were even unt that entered the program through th opt-n provon (Ellerman et al., 2000). 6 Allowance prce were low compared to ntal margnal abatement cot etmate, and relatvely table throughout Phae I and the begnnng of Phae II. Intal margnal cot etmate ued by the EPA ranged from $199-$226 (Smth and Ellerman, 1998). The market opened n 1995 at a prce of $150, oon ht a low of $70 n early 1996, and then lowly roe back to around $150. Other than a lght pke n 1999 a utlte potoned themelve for the tart of Phae II, the allowance prce remaned relatvely table around $150 (Burtraw et al., 2005) Phae II of Ttle IV Phae II, whch began n 2000 and wll contnue untl the mplementaton of CAIR n 2010, nclude all unt over 25 MW n generatng capacty. The more than 2,000 affected generatng unt throughout the U.S. were allocated allowance baed on an emon rate of 1.2 lb. SO2/mmBtu of heat nput, multpled by the unt baelne heat nput durng New generatng unt were gven no allowance and were requred to purchae any neceary allowance n the allowance market. Phae II allocaton were capped at 10.0 mllon ton annually n 2000, have decreaed to 9.5 n 2002 where t wll reman untl 2010, when t drop to 8.95 mllon ton. The bankng provon ha allowed utlte to trade ntertemporally wth utlte ung the ubtantal allowance bank accumulated through Phae I for complance n Phae II leadng to annual emon level n exce of 10 mllon ton n each year from 2000 to There wa an ncentve to opt-n generatng unt voluntarly f t benefcal to the utlty. Optng Phae II unt nto Phae I gve utlte addtonal way to decreae emon and ell allowance and, apparently more mportantly, bank allowance for future ue n Phae II. Actual SO 2 emon by Phae I unt were much lower durng Phae I than the total allowance allocaton durng Phae I, whch allowed utlte to bank addtonal allowance for ue durng Phae II (Ellerman et al., 1997). 50

51 The allowance prce remaned farly table through the begnnng of A large pke up to over $700 took place n 2004, whch accordng to Burtraw et al. (2005) ha been aocated wth everal factor: an ncreae n natural ga prce, ncreaed electrcty demand, and the propoal of future emon control leglaton now referred to a the Clean Ar Intertate Rule (CAIR) Clean Ar Intertate Rule In 2005, the EPA ued the Clean Ar Intertate Rule (CAIR) that further retrct the emon of SO 2 n 25 eatern tate and the Dtrct of Columba effectve n The tate under CAIR are the ame tate that had affected unt under Phae I. Generatng unt tll receve ther allowance allocaton a defned under Phae II. Begnnng n 2010, the emon value of the allowance for unt n the CAIR regon cut n half from 1.2 to 0.6 lb. SO 2 /MMBtu of heat nput whch mple a unt mut hold two Ttle IV allowance for each ton of actual emon. Startng n 2015 unt mut hold 2.86 Ttle IV allowance for every ton of emon, whch tranlate to an allocaton of approxmately 0.4 lb. SO 2 /MMBtu. Meanwhle generatng unt outde the CAIR regon wll contnue operate under the Ttle IV, Phae II Program wth trade allowed to take place between CAIR and Phae II unt. Unt under Phae II and CAIR partcpate n the ame allowance market and face the ame market allowance prce. The pke n allowance prce up to over $1,600 n 2006 een n Fgure 2.8 may have been a reult of the propoal and enactment of CAIR. Utlte could have choen to bank allowance ntead of ellng allowance n the market to enure ther ablty to cover requrement at the begnnng of CAIR. It tll uncertan what led to the temporary pke n allowance prce, but t appear lkely that t wa a temporary reacton to the polcy envronment or other market condton a the allowance prce ha quckly decreaed to t current prce of le than $600/ton. 51

52 2.3 Lterature Revew Ttle IV: Phae I There ha been gnfcant reearch done on the Ttle IV SO 2 Cap-and-Trade Program, both for Phae I and Phae II (Ellerman et al. (2000); Burtraw et al. (2005)). From Table 2-1, t can be een that, n general, the complance cot etmate before Phae I took effect were hgher than the etmate made after Phae I became effectve and actual data could be ued n the etmate. The pre-polcy etmate range a hgh a $1.34 bllon/year wth mot etmate at leat $860 mllon/year. The actual cot etmate are toward the lower end of th range between $730-$990 mllon/year. There are everal reaon for the dfference between ntal etmate and actual aggregate ndutry complance cot. The mot mportant factor wa the decreae n delvered low ulfur coal prce. At the unt level, lower low ulfur coal prce decreaed the margnal cot of reducng emon through fuel wtchng, whch wa the complance opton choen by 52% of all affected unt, whle 32% of affected unt choe to purchae allowance, 10% ntalled a crubber, 3% hut down, and 3% choe other method. 7 Several of thee tude have etmated the cot avng reultng from the allowance tradng ytem. Carlon, et. al. (2000) ued an econometrc-baed mulaton model to etmate the potental cot avng from tradng n the program compared to a unform emon rate tandard. The potental avng wa etmated at $250 mllon, 80% of whch a reult of wtchng from hgh to low ulfur coal and 20% from techncal change, uch a mproved crubber technology (Burtraw et al., 2005). Keohane (2002) mulate whch generatng unt would have ntalled crubber under a unform emon-rate tandard and fnd that the total number of crubber would have been one-thrd hgher than the actual number of ntalled crubber under the 7 Energy Informaton Aocaton, The Effect of Ttle IV of the Clean Ar Act Amendment of 1990 on Electrc Utlte: An Update 52

53 cap-and-trade approach. Sotkewcz and Holt (2005) fnd that due to PUC regulaton, not only there a greater number of crubber actually ntalled at the begnnng of Phae I relatve to the leat cot oluton (18 crubber), but only nne of thoe actually ntalled are at unt that ntall crubber under the leat cot oluton. An ncreae n the number and neffcent locaton of crubber ntallaton ncreae the total cot of complance becaue ntallng a crubber the mot expenve complance opton under Phae I. In the ntal year of Phae I, many frm were not actve partcpant n the allowance market, choong to wtch fuel and bank allowance or hft allowance between only ther own unt (Hart (1998); Ellerman et al. (1998)). The frm that dd partcpate manly traded allowance wthn the ame utlty company. Boh and Burtraw (1997) fnd that ntra-utlty tradng account for two-thrd of the allowance tranacton whle the remanng one-thrd were nter-utlty trade. Snce mot trade were made between unt owned by the ame company, tradng between two generatng unt at the ame plant would be a common occurrence. Many tude uggeted tate publc utlty regulaton and other tate law a a reaon for the neffcence reultng from th elf-uffcent behavor (Boh (1994); Boh and Burtraw (1997); Swft (2001)). Armura (2002) ue econometrc approache to tudy the mpact of PUC regulaton on complance choce, and fnd that utlte that face PUC regulaton are more lkely to wtch fuel ntead of purchang allowance for complance. Wnebrake et al. (1995) etmated the cot neffcence from tate government retrcton on a utlty allowance tradng, and etmate the total cot etmate for the frt ten year of Ttle IV ( ). A command-and-control approach wa etmated to reult n complance cot of $4.19 bllon greater than n the unretrcted permt tradng ytem ($5.02 bllon, or an average of $502 mllon/year) and an etmated allowance prce of $143/ton. Wnebrake et al. (1995) mulate the addtonal cot from retrcton on between-tate tradng that were under conderaton by both New York and Wconn. Both tate were 53

54 tryng to mnmze allowance ale to tate whoe emon wll eventually reach New York/Wconn and reult n hotpot, whch are are area wth extreme emon level that reult n greater damage n a partcular area relatve to damage throughout the ret of the regon. Preventng utlte n New York and Wconn from ellng allowance to utlte outde ther tate would have reulted n more than double the complance cot n both tate, and ncreaed natonwde complance cot. Some of the addtonal cot from thee retrcton would have been offet by lower cot for utlte not n New York or Wconn that would have been able to ell more allowance due to the addtonal demand no longer beng met by allowance ale from New York and Wconn utlte. Some tude further explan the neffcence by examnng the actual lot cot avng that are pecfcally a reult of tate PUC regulaton under Phae I. Carlon et al. (2000) fnd that the actual complance cot were $339 mllon (59%) greater n 1996 than the leat-cot oluton. The tudy conclude the dfference between actual complance cot and the leat-cot complance may be attrbutable to adjutment cot aocated wth changng fuel contract and captal expendture a well a regulatory polce. Sotkewcz and Holt (2005) fnd that PUC regulaton reulted n $131 mllon of the addtonal complance cot relatve to the leat cot oluton. However, there a gnfcant amount of complance cot that remaned unexplaned. 8 My tudy conjecture long-term coal contract may be reponble for what appear to be neffcent behavor reultng n addtonal complance cot. 8 Sotkewcz and Holt model the poblty of ex pot prudence, whch aume that there ome cot, uch a future tate PUC cot dallowance, to the generatng unt for choong a le cot-effectve opton. If PUC regulaton allow for total pa-through of cot wthout threat of ex-pot prudence, then a generatng unt ndfferent to cot and may not make the lowet cot complance opton. 54

55 2.3.2 Utlty-Level Model of Complance Cot Prevou tude have etmated the complance cot at the generatng unt or utlty-level, and focu on the mpact of tate regulaton on utlty-level complance choce. Swnton (2002) calculate the hadow prce of emon reducton for even Florda power plant from 1990 to 1998 and compare ther optmal choce to ther actual acton. Several factor were dcued a the reaon for ome utlte makng ub-optmal decon: tate PUC regulaton, program learnng curve, mall magntude of potental gan from trade, and uncertanty over the program longevty. Swnton (2004) follow the ame approach except t expand the tudy to 40 plant wth data from 1994 to 1998, and ntroduce the poblty that long-term coal contract may prohbt utlte from wtchng coal type, although t not modeled. Both tude fnd the actual utlty-level complance cot to be much hgher than the etmated leat-cot oluton. Coggn and Swnton (1996) ue an output dtance functon to etmate the hadow prce of SO 2 emon abatement for electrc power plant n Wconn. The tudy etmated the allowance hadow prce to be greater than the oberved allowance prce at the tme, whch they aert may be partally explaned by Wconn trct tate regulaton on SO 2 emon. Several tude have hown analytcally or through mulaton model that tate PUC regulaton can lead to neffcence at the utlty-level. Boh and Burtraw (1992) develop a model of utlty decon-makng gven two complance opton, purchang allowance or ntallng emon control technology. Boh and Burtraw derve two recommendaton o that tate regulaton doe not reult n neffcent complance choce by a utlty. Frt, f a utlty allowed return le than t cot of captal wth repect to both complance opton, ymmetrcal cot recovery rule are recommended a uneven treatment of cot recovery may create ncentve for a utlty to make uboptmal complance choce. Second, f a utlty allowed to earn more than t cot of captal wth regard to both 55

56 complance opton, Boh and Burtraw recommend the more expenve be treated le favorably. Fullerton et al. (1997) ue a numercal model to determne the mpact tate regulaton wll have on a utlty complance cot by modelng the cot-mnmzng utlty complance choce and a utlty complance choce under t Publc Utlty Common rule. The tudy fnd that aymmetrcal cot recovery rule can lead to utlty complance cot much hgher than the leat-cot oluton, and pobly hgher than a command-and-control approach Long-Term Coal Contract Jokow (1985, 1988) tate that coal contract decreae tranacton cot n coal purchang that reult from uncertanty and complexty n future coal market. A utlty may be wllng to pay more than the current pot market prce for coal to protect telf from unexpected hgher rate n the future. Jokow (1988, 1990) fnd that durng perod n whch the pot market coal prce were lower than the contracted prce, the contract prce faled to adjut downward. Th downward rgdty of coal prce can lead to utlty coal cot beng hgher than optmal n the hort run. Some renegotaton, breach of contract, and ltgaton ha occurred, but nearly all contract appear to have contnued unchanged. The man reaon for the contrant n alterng thee coal contract that le than 15% of coal conumed by utlte uppled by a coal company owned by the ame utlty (Jokow, 1987). Frm have hgh legal or negotaton cot of breakng a coal contract when the agreement made wth a frm that ha no fnancal te to the utlty. Coal contract may alo be a reult of regulaton protectng the local coal ndutry (Armura 2002). Due to the nablty of contracted coal prce to decreae wth pot market prce, large coal prce 56

57 reducton can lead to gnfcant dfference between coal contract prce and pot market coal prce. 9 Ellerman and Montero (1998) found that nvetment and nnovaton n coal producton and delvery a well a greater competton between ralroad due to the Stagger Ral Act of 1980 created lower coal prce durng the frt year of Phae I, epecally for low ulfur coal from the Powder Rver Ban. Thee lower coal prce led to lower margnal cot of abatng SO 2 emon through fuel wtchng, whch reflected n the lower than expected allowance prce n 1995 (Burtraw et al., 2005). Conderng the downward rgdty of contract coal prce, the ame coal prce reducton alo reulted n lower pot market prce for both hgh ulfur and low ulfur coal relatve to the coal prce under contract. 2.4 Ineffcence Reultng from Coal Contract Contrant There are three plauble cenaro where bndng contract contrant reult n ub-optmal complance choce. Frt, durng Phae I a utlty wth hgh ulfur coal contract may be unable to wtch to low ulfur coal for complance when t 9 A utlty cannot ell contracted coal on the pot market becaue of the tranacton cot nvolved n ellng to another utlty from both t contract for coal purchae and t contract for coal tranportaton. A coal contract et a gven type and amount of coal for an agreed upon prce from a partcular coal ource. A tranportaton contract et a gven prce for delvery of coal purchae from a coal ource. The combnaton of thee two contract reult n the delvered cot of a coal purchae. For one utlty to ell coal to another utlty, t would need to ether buy out t contract wth a provon to delver the coal to the other utlty or t would need to pay for the hpment of the coal from t faclty to the other utlty. There are large addtonal cot aocated wth ether of thee acton. A hown n Jokow, few contract were bought out, breached, or renegotated. Alo, there doe not appear to be any ale of coal from one utlty to another. 57

58 cot-effectve to do o. Conequently, the utlty forced to ub-optmally ntall a crubber or purchae allowance. 10 Second, durng Phae I pot coal prce were declnng and often were lower than the prce of contract coal of mlar charactertc (heat and ulfur content). Contract contrant may have prevented utlte from wtchng to lower prced pot market coal alternatve of mlar ulfur and heat content than wa beng utlzed under contract. Thrd, under CAIR ome utlte may be locked nto low ulfur coal contract entered nto for Ttle IV complance and may be unable wtch back to hgh ulfur coal and crub f t cot-effectve to do o. Conequently, the contract contrant puhe a utlty nto ub-optmal complance choce uch a allowance purchae or crubber ntallaton whle ung low ulfur coal. An examnaton of the data for Phae I affected unt ndcate that of the 26 crubber ntalled by the end of 1996 n repone to the paage of the 1990 Clean Ar Act Amendment, 23 of thoe crubber were ntalled at faclte wth 40 percent or more of t coal delvere by contract and wth 20 of them havng a weghted average SO 2 emon rate greater than the Phae I allowed level of 2.5 lb. SO 2 /mmbtu (pound per mllon Btu of heat). 11 Addtonally, the 14 generatng unt wth crubber and greater than 75% of coal under contract all have emon rate over 2.5 lb. SO 2 /mmbtu. Th ndcate the poblty that hgh ulfur coal contract contrant are drvng ome 10 The actual purchang of allowance not what ncreae ndutry-wde complance cot. It the ub-optmalty of the allowance purchae that ncreae the total complance cot n an ndutry. 11 A total of 29 crubber were ntalled between 1990 and Three of the crubber are not condered to have been ntalled for complance of Phae I. Two were ntalled on Port Wahngton unt n Wconn to meet New Source Revew requrement whle a thrd wa ntalled on a Yate unt a reult of a plot program. 58

59 complance decon. 12 The dea that pot market purchae may have been preferred can be ndcated n the fact that many Phae I faclte n 1996 had allowed both long-term hgh and low ulfur coal contract to expre durng the perod and replaced thoe wth pot market coal of an equvalent or lower ulfur content. Th may alo be an ndcaton of potentally bndng low ulfur contract contrant a utlte face future complance decon under CAIR. 13 Contract contrant wll contnue to bnd a generatng unt decon untl the expraton of the contract. The average length of coal upply contract (weghted by tonnage) n 1996 wa 16.5 year wth 53.3% of delvered coal under contract gned for greater than 10 year and 22.1% of greater than 30 year. The mpact of coal contract rgdte wll dpate over tme. However, the mpact of thee contract on complance decon could contnue to lnger for year due to the length of many of thee contract Data ued avalable from the EIA FERC-423 databae and Electrc Power Annual Data from the EIA FERC-423 Databae and Coal Tranportaton Rate Databae how the percentage of coal purchaed through contract agreement. Of the 93 Phae I Affected Unt wth contract expraton between , 62 dd not gn any new contract, 13 replaced hgh ulfur contract wth low ulfur contract, and only 18 replaced old contract wth new contract for the ame ulfur content. Contract were hfted from year (decreae of 48 to 33%) to contract of 5 or fewer year (ncreae from 13 to 24%). Low ulfur contracted coal delvere ncreaed by 389% and hgh ulfur contracted coal delvere decreaed by 50% for Phae I affected unt between 1988 and 1997 whle non-affected unt aw an ncreae of 82% and a decreae of 42%, repectvely. From the avalable FERC-423 data for 133 plant wth at leat one affected unt, 34 reduced the percentage of coal under contract by greater than 25 percent: 12 wtched from hgh contract coal to hgh pot market coal, 12 wtched from low ulfur contract coal to low ulfur pot market coal, 8 wtched from hgh ulfur contract coal to low ulfur pot market coal, and 2 wtched from low ulfur contract coal to hgh ulfur pot market coal. 14 The length of the contract doe not repreent the year remanng on the length of the contract. There wll be varaton n the tme frame under whch thee contract expre. 59

60 2.5 Model and Parameter The model a tatc producton cot model that draw heavly from Sotkewcz (2003) and Fullerton et al. (1997), whch mulate producton cot at the generatng unt level wth contrant on demand for electrcty and emon level, and ntroducng hgh ulfur coal and low ulfur coal contract contrant. It would eem that addng contract contrant to the model would not caue any major drupton. However, the model reult n rather complex nterpretaton due to how the contract contrant nteract wth the non-convexte of a unt crubber choce. Let be the ndex of unt. The parameter n the model are decrbed below. Technology Parameter: z {0, 1} repreent a generatng unt dcrete crubber choce where z = 1 f a unt ntall a crubber and z = 0 f a unt doe not ntall a crubber. P z repreent the levelzed yearly cot of a crubber, whch are the average annual cot from deprecaton and ue of captal plu the operaton and mantenance cot of ntallng and operatng a crubber. 15 r [0, 1] repreent the crubber emon capture rate or emon removal effcency rate, whch the fracton of emon that the crubber remove from the exhaut tream. The removal rate ndependent of the ulfur content of the coal ued by a utlty becaue t remove ome percentage of emon after producton. Dependng on the crubber technology and vntage, t can remove 25-99% of SO 2 emon. 16 Demand Parameter: D repreent electrcty demand, n mllon Btu of heat nput, for a gven generatng unt. Demand derved by takng the total klowatt-hour of electrcty 15 The captal cot are aumed to be $260/kW under Phae I and $141.34/kW under CAIR. Captal cot are dcounted at a 10% rate baed on a 20 year equpment lfepan ( d(1+d) t (1+d) t 1). The operaton and mantenance cot are aumed to be 2.0 mll/kwh under Phae I and 1.23 mll/kwh under CAIR. 16 Table 30: Flue Ga Deulfurzaton (FGD) Capacty n Operaton at U.S. Electrc Utlty Plant a of December 1996 from the 1996 Electrc Power Annual Vol. II 60

61 demand multpled by the heat nput requred to generate one klowatt-hour of electrcty. Demand at the unt level aumed to be fxed. Modelng each generatng unt hourly dpatch and hourly cot n the context of varyng load and dpatch are not ealy modeled, and would requre arbtrary aumpton about how unt would be utlzed. For thee reaon, t aumed n th paper that utlte do not have the opton to hft electrcty producton acro generatng unt to meet demand. Coal Parameter: Ch,C l are the quantte, n ton, of hgh ulfur and low ulfur pot market coal ue for a gven unt, repectvely. Ch c,cc l are the quantte, n ton, of hgh ulfur and low ulfur contract coal ue for a gven unt, repectvely. Ph,P h are the delvered prce, n dollar/ton, of hgh ulfur and low ulfur pot market coal for a gven unt, repectvely. Ph c,p h c are the delvered prce, n dollar/ton, of hgh ulfur and low ulfur contract coal for a gven unt, repectvely. Delvered coal prce wll dffer acro regon of the U.S. due to the locaton of coal mne acro the country. 17 It aumed that generatng unt are prce taker n purchang coal. Hh,H l are the heat content for hgh ulfur and low ulfur pot market coal for a gven unt, repectvely. Heat content the average amount of heat, n mllon Btu, n one ton of coal. The delvered prce the dollar/mmbtu pad for coal. Hh c,hc l are the heat content for hgh ulfur and low ulfur contract coal for a gven unt, repectvely. The heat content wll dffer acro regon of the U.S. due to the heat content of coal from dfferent coal mne acro the country. Sh,S l are the ulfur content for hgh ulfur and low ulfur pot market coal for a gven unt, repectvely. Sulfur content the percentage of a ton of coal compred of ulfur. 17 For example, a generatng unt n Wconn wll have dfferent delvered coal prce for a partcular coal type relatve to a unt n Georga. Wconn cloer to the low ulfur coal mne n the Powder Rver Ban n the Wetern U.S., whch reult n a much lower delvered prce to Wconn than to Georga. 61

62 Sh c,sc l are the ulfur content for hgh ulfur and low ulfur contract coal for a gven unt, repectvely. The ulfur content wll dffer acro regon of the U.S. due to the heat content of coal from dfferent coal mne acro the country. m repreent the rate at whch ulfur tranformed nto SO 2, whch aumed to be a contant (1.9) for mplcty. 18 C c h, C c l repreent the contract contrant for a gven unt, whch requre the ue of a mnmum amount of each coal type. Allowance Parameter: E repreent a generatng unt ton of SO 2 emon. A e repreent a generatng unt ntal allowance allocaton n ton of SO 2 emon. A repreent a generatng unt net allowance poton n ton of SO 2 emon, whch the dfference between the actual allowance ued and a unt ntal allowance allocaton. A unt a net buyer of allowance (potve exce demand) f t ue more allowance than t ntal allocaton (A > 0), a net eller (negatve exce demand) f t ue fewer allowance than t ntal allocaton (A < 0), and nether f t ue exactly the ame amount of allowance a t ntal allocaton (A = 0). P A the allowance prce, whch endogenouly determned n the model by the decon of the utlte. Each allowance that bought (old) wll ncreae (decreae) the utlty producton cot by P A. Each generatng unt take P A a gven. 2.6 Generatng Unt Level Decon-Makng Proce The model a tatc model wth decon made at the generatng unt level where each generatng unt chooe t coal ue, net allowance poton, and crubber choce to 18 Sulfur content the ton of ulfur per ton of coal. In th paper, any coal that reult n emon greater than 2.5 lb. SO 2 /MMBtu condered hgh ulfur coal. Under Phae II of Ttle IV and CAIR, the hgh ulfur-low ulfur cut-off value reduced from 2.5 to 1.2 lb./mmbtu. Under CAIR the new allowance allocaton baed on 0.6 lb./mmbtu, whch cannot be met by fuel wtchng alone becaue low ulfur coal normally range from lb./mmbtu wth few hpment of low ulfur coal reultng n emon of 0.6 lb./mmbtu. m = 1.9 for btumnou and anthracte coal, m = 1.75 for ubbtumnou coal, m = 1.5 for lgnte coal. Thee dffer due to each coal type compoton. 62

63 mnmze t cot baed on t contrant for emon, electrcty demand, and coal ue for both hgh ulfur and low ulfur contract coal Generatng Unt Problem mn z P z + P A A + P z,a hc,ch h + PlC l + PhC c h c + PlC c l c (2 1),C l,cc h,cc l ubject to...a e + A (1 z r )(m)(c hs h + C c hs c h + C ls l + C c ls c l) λ 1 (2 2) (C hh h + C c hh c h + C lh l + C c lh c l) D λ 2 (2 3) C c h = C c h µ h (2 4) C c l = C c l µ l (2 5) C h, C l 0 (2 6) z {0, 1} (2 7) Equaton (3 1) repreent the unt cot functon. Thee cot nclude the cot of crubber ntallaton (z P z ), net cot of allowance purchae (P A A ), and cot of coal purchae (P h C h + P l C l + P c h Cc h + P c l Cc l). The emon contrant hown n (3 2), where the number of allowance held (A e + A ) mut be a large a the amount of total emon by the generatng unt [(1 z r )(m)(ch S h + Cc hsh c + C l S l + Cc lsl c )]. Total emon a functon of the amount of each coal type ued a well a the emon reducton due to a crubber, f one ntalled. The Lagrange multpler on the emon contrant repreented by λ 1. The demand contrant requre that the amount of heat nput to generate electrcty (Ch H h + Cc hhh c + C l H l + Cc lhl c ) mut cover the conumer demand (D ) for electrcty expreed a heat nput, whch een n (3 3). The Lagrange multpler on the demand contrant repreented by λ 2. Coal contract contrant requre the unt to ue a pecfc amount of each contract coal type, C c h for hgh ulfur coal n (3 4) and C c l for low ulfur coal n (3 5). A unt wll ue exactly the contracted amount becaue (1) f the contract coal more expenve than pot market coal, then a 63

64 unt wll not want to ue any more contract coal than neceary and (2) f contract coal cheaper than pot market coal, the coal producer would prefer to ell any addtonal non-contracted coal through the pot market. The Lagrange multpler for each contract contrant on each coal type repreented by µ h for hgh ulfur contract coal and µ l for low ulfur contract coal Frt-Order Condton The partal dervatve wth repect to A yeld the mpact of a one unt change n the net allowance purchaed on the unt total cot. P A λ 1 = 0 (2 8) Snce A can be ether potve or negatve baed on the net allowance poton, (2 8) wll hold wth equalty. The addtonal cot to the frm of emttng one more ton of emon equvalent to the allowance prce, λ 1 = P A. Let f {h, l} repreent the type of coal and g {, c} repreent the type of purchae. Each coal type ha t own ulfur content (S g f ), heat content (Hg f ), and delvered prce (P g f ). The partal dervatve wth repect to Cg f repreent the mpact a one unt change n f type ulfur coal (hgh or low) from a g type purchang agreement (pot market or contract) ha on the unt total cot. P h + λ 1 (1 z r )(m)(s h) λ 2 H h 0, = 0 f C h > 0 (2 9) P l + λ 1 (1 z r )(m)(s l) λ 2 H l 0, = 0 f C l > 0 (2 10) P c h + λ 1 (1 z r )(m)(s c h) λ 2 H c h µ h = 0 (2 11) P c l + λ 1 (1 z r )(m)(s c l) λ 2 H c l µ l = 0 (2 12) The cot of ung one more unt of C g f can be daggregated nto four dfferent cot change: P g f the addtonal cot of purchang one more unt of coal, λ 1(1 z r )(m)(s g f ) the addtonal cot of the extra emon from one more unt of coal, 64

65 λ 2 H f the beneft from meetng the demand remanng from ung the addtonal unt of coal, and µ f repreent the reducton n cot from meetng the contract contrant. If C f > 0, then (3 37) or (2 10) hold wth equalty. Snce the contract contrant hold wth equalty, (2 11) and (2 12) alway hold wth equalty Characterzng a Unt Spot Market Fuel Choce and Margnal Cot of Abatement from Fuel Swtchng A generatng unt choce of fuel type baed on t crubber ntallaton choce a well a t margnal cot of abatement relatve to the allowance prce. In th ecton, the crubber choce taken a gven and the focu olely on comparng the allowance prce to the margnal cot of abatement of wtchng from hgh ulfur coal to low ulfur coal Neceary condton for ung both hgh ulfur and low ulfur coal If a generatng unt ue both hgh ulfur and low ulfur pot market coal (C h > 0, C l > 0), the addtonal cot of ung each coal type are equal and (3 37) and (2 10) hold wth equalty, or P h + λ 1(1 z r )(m)(s h ) H h = P l + λ 1(1 z r )(m)(s l ) H l (2 13) (2 13) can be rearranged to olate the hadow prce of allowance or emon, λ 1, to derve the Margnal Cot of Abatement from Swtchng Fuel from hgh ulfur pot to low ulfur pot market coal (MCA, ) n (2 14). Explotng (2 8), the allowance prce equal MCA, : P A = λ 1 = MCA, = Pl P Hl h Hh (1 z r )(m)( S h S Hh l ) Hl (2 14) The hadow prce equal to the dfference n prce per unt of heat dvded by the dfference n emon per unt of heat Only hgh ulfur coal ue: Neceary condton If a generatng unt ue only hgh ulfur pot market coal (C h > 0), the addtonal cot to the generatng unt of ung hgh ulfur pot market coal weakly le than ung 65

66 low ulfur pot market coal and (3 37) hold wth equalty whle (2 10) hold wth weak nequalty, or P h + λ 1(1 z r )(m)(s h ) H h P l + λ 1(1 z r )(m)(s l ) H l (2 15) (2 15) can be rearranged to how the allowance prce weakly le than MCA, : P A MCA, = Pl P Hl h Hh (1 z r )(m)( S h S Hh l ) Hl (2 16) Only low ulfur coal ue: Neceary condton If a generatng unt chooe to ue only low ulfur pot market coal (C l > 0), the addtonal cot of ung low ulfur pot market coal weakly le than ung hgh ulfur pot market coal and (2 10) hold wth equalty whle (3 37) hold wth weak nequalty, or P h + λ 1(1 z r )(m)(s h ) H h P l + λ 1(1 z r )(m)(s l ) H l (2 17) (2 17) can be rearranged to how that the allowance prce weakly greater than MCA, : P A MCA, = Pl P Hl h Hh (1 z r )(m)( S h S Hh l ) Hl (2 18) Coal Ue Under a Hgh Sulfur Coal Contract Contrant µ h the hadow prce of the hgh ulfur contract contrant, whch nclude both the change n cot due to fuel cot and emon. If contract coal more expenve than pot market coal, then µ h > 0 and t ncreae fuel cot. If contract coal cheaper than pot market coal, then µ h < 0 and t decreae fuel cot. Aume a unt ha a hgh ulfur coal contract and ue only low ulfur pot market coal (no hgh ulfur pot market coal). So (2 10) and (2 11) hold wth equalty. It ha been hown n (2 17) that f a unt ue only low ulfur pot market coal, P A MCA, : P c h + λ 1(1 z r )(m)(s c h ) µ h H c h = P l + λ 1(1 z r )(m)(s l ) H l (2 19) 66

67 By rearrangng (2 19) and explotng (2 8), t can be hown that the allowance prce equal to Margnal Cot of Abatement of wtchng from hgh ulfur contract to low ulfur pot market coal (MCA c, ) plu an addtonal term repreentng the beneft of meetng the contract contrant, whch weakly greater than MCA, : λ 1 = P A = MCA c, + From (2 20), f MCA, MCA c, µ h H c h (1 z r )(m)( Sc h S Hh c l ) MCA, Hl more expenve than pot market hgh ulfur coal. If MCA, (2 20) > 0, then µ h > 0 and hgh ulfur contract coal MCA c, < 0, then µ h can be potve or negatve. If µ h < 0, then contract coal cheaper than pot market coal and the addtonal complance cot due to emon domnate the avng from the lower fuel cot. If µ h > 0, then contract coal cheaper than pot market coal and the avng from the lower fuel cot domnate the ncreaed complance cot due to emon. µ h H c h (1 z r )(m)( Sc h S Hh c l ) MCA, Hl MCA c, (2 21) Now aume a unt ha a hgh ulfur coal contract and ue only hgh ulfur pot market coal (no low ulfur pot market coal). (2 11) and (2 12) hold wth equalty whle (2 10) hold wth weak nequalty. Alo, t ha been hown that when a unt ue only hgh ulfur pot market coal, P A MCA,. Ung the ame approach a n the prevou cae, t can be found that the allowance prce weakly le than MCA c, addtonal term repreentng the beneft of meetng the contract contrant: plu an P A MCA c, + µ h H c h (1 z r )(m)( Sc h S Hh c l ) Hl (2 22) The gn of µ h cannot be determned by comparng MCA, and MCA c,, but the frt-order condton for hgh ulfur contract and pot market coal can be ued to determne t gn. P h + λ 1(1 z r )(m)(s h ) H h = P c h + λ 1(1 z r )(m)(s c h ) µ h H c h 67

68 µ h H c h = P h c + λ 1(1 z r )(m)(sh c ) P h + λ 1(1 z r )(m)(sh ) Hh c Hh If the addtonal cot, both from fuel cot and emon, of ung hgh ulfur (2 23) contract coal more expenve than ung hgh ulfur pot market coal, then µ h > 0. If the addtonal cot, both from fuel cot and emon, of ung hgh ulfur contract coal le than ung hgh ulfur pot market coal, then µ h < 0. If the addtonal cot, both from fuel cot and emon, of ung hgh ulfur contract coal the ame a ung hgh ulfur pot market coal, then µ h = 0. Now aume a unt ha a hgh ulfur coal contract and ue both hgh ulfur and low ulfur pot market coal. So (2 10) and (2 11) hold wth equalty. Alo, t ha been hown n (2 15) that when a unt ue both hgh and low ulfur pot market coal, P A = MCA, : P A = MCA, = MCA c, + µ h H c h (1 z r )(m)( Sc h S Hh c l ) Hl (2 24) By olvng for µ h n (2 24), the gn of µ h can be determned. If MCA, MCA c, = 0, then µ h = 0 and hgh ulfur contract coal ha the ame cot a hgh ulfur pot market coal. If MCA, MCA c, > 0, then µ h > 0 and contract coal more expenve to ue than pot market coal. If MCA, MCA c, < 0, then µ h < 0 and contract coal cheaper to ue than pot market coal. µ h H c h (1 z r )(m)( Sc h S Hh c l ) = MCA, Hl MCA c, (2 25) Coal Ue under a Low Sulfur Coal Contract Contrant µ l the hadow prce of the low ulfur contract contrant, whch nclude both the change n cot due to fuel cot and emon. If contract coal more expenve than pot market coal, then µ l > 0 and t ncreae fuel cot. If contract coal cheaper than pot market coal, then µ l < 0 and t decreae fuel cot. Aume a unt ha a low ulfur coal contract and ue only hgh ulfur pot market coal. It ha already been hown n (2 16) that when a unt ue only hgh ulfur pot 68

69 market coal, P A MCA,. (3 37) and (2 12) hold wth equalty whle (2 10) hold wth a weak nequalty. Ung the ame approach a n the prevou ecton yeld: λ l = P A = MCA,c µ l H c l (1 z r )(m)( S h Sc Hh l ) MCA, Hl c Ung (2 26), the gn of µ l can be determned. If MCA, MCA c, (2 26) > 0, then µ l > 0 and low ulfur contract coal more expenve to ue than low ulfur pot market coal. If MCA, MCA, MCA c, from emon. If MCA, MCA c, < 0, then µ l can ether be negatve or potve. If < 0 and µ l > 0, then the hgher fuel cot domnate the lower cot MCA c, emon domnate hgher fuel cot. µ l H c l < 0 and µ l < 0, then the the lower cot from (1 z r )(m)( S h Sc Hh l ) MCA,c Hl c MCA,c (2 27) Now aume a unt ha a low ulfur coal contract and ue only low ulfur pot market coal. So (2 10) and (2 12) hold wth equalty whle (3 37) hold wth a weak nequalty. It ha already been hown n (2 17) that when a unt ue only low ulfur pot market coal, P A MCA,. P A MCA,c µ l H c l (1 z r )(m)( S h Sc Hh l ) Hl c (2 28) Although the gn of µ l cannot be determned by comparng MCA, and MCA,c. The frt order condton for low ulfur contract and pot market coal can be ued to determne t gn. P l + λ 1(1 z r )(m)(s l ) H l µ l H c l = P c l + λ 1(1 z r )(m)(s c l ) µ l H c l = P l c + λ 1(1 z r )(m)(sl c ) P l + λ 1(1 z r )(m)(sl ) Hl c Hl (2 29) If the addtonal cot, both from fuel cot and emon, of ung low ulfur contract coal more expenve than ung low ulfur pot market coal, then µ l > 0. If the 69

70 addtonal cot, both from fuel cot and emon, of ung low ulfur contract coal le than ung low ulfur pot market coal, then µ l < 0. If the addtonal cot, both from fuel cot and emon, of ung low ulfur contract coal the ame a ung low ulfur pot market coal, then µ l = 0. Now aume a generatng unt ha a low ulfur coal contract and ue both hgh ulfur and low ulfur pot market coal. So (3 37), (2 10), and (2 12) hold wth equalty and P A = MCA, : P A = MCA, = MCA,c µ l H c l (1 z r )(m)( S h Sc Hh l ) Hl c By olvng for µ l, the gn of µ l can be determned. If MCA,c MCA, µ l = 0 and contract coal a cotly to ue a pot market coal. If MCA,c then µ h > 0 and contract coal more expenve to ue than pot market coal. If (2 30) = 0, then MCA, > 0, MCA,c coal. MCA, < 0, then µ h < 0 and contract coal cheaper to ue than pot market MCA, = MCA,c µ l H c l (1 z r )(m)( S h Sc Hh l ) Hl c (2 31) Generatng Unt-Level Complance Cot Total complance cot for a generatng unt are the addtonal cot due to atfyng the emon contrant, ncludng cot from wtchng fuel, the cot from t net allowance poton, and crubber ntallaton cot. Complance cot may be potve or negatve dependng on t complance decon and t ntal allowance allocaton. The crubber ntallaton cot are repreented by P z, and wll only attrbute to a unt complance cot f a crubber ntalled (z = 1). The cot of a unt net allowance poton the dfference between a generatng unt ntal allowance allocaton and t actual emon multpled by the allowance prce (P A A ). The cot of wtchng fuel the larger of two value: (1) total cot of actual coal purchae (P h C h + P l C l + P c h Cc h + P c l Cc l) mnu the cot of purchang only hgh ulfur 70

71 pot market coal gven any contracted coal (P hĉ,max h where: Ĉ,MAX h = D C c hh c h Cc lh c l H h + P c h Cc h + P c l Cc l), or (2) zero The latter wll only occur f t weakly cheaper for the generatng unt to ue low ulfur coal wthout the emon retrcton ( P h H h ued regardle and wll cancel out. (2 32) P l H l ). Notce that the contracted coal wll be z P z + P A A + max{(p lc l + P hc h P h Ĉ,MAX h ), 0} (2 33) Combnng each of the three cot component reult n a unt total net complance cot. Even though the contract coal ha no drect affect, the contract wll ndrectly affect complance cot through a unt allowance poton and crubber choce. Propoton 1 how the uffcent condton under whch a coal contract wll ether ncreae or decreae complance cot. Propoton 1: Gven the crubber choce () () () (v) If P A > MCA, and the ulfur to heat content rato of hgh ulfur contract coal ( Sc h ) greater than the ulfur to heat content rato of hgh ulfur pot market coal Hh c ( S h ), then a hgh ulfur coal contract ncreae complance cot. Hh If P A MCA, and the ulfur to heat content rato of hgh ulfur contract coal ( Sc h ) greater than the ulfur to heat content rato of hgh ulfur pot market coal Hh c ( S h ), then a hgh ulfur coal contract ncreae complance cot. Hh If P A MCA, and the ulfur to heat content rato of low ulfur contract coal ( Sc l H c l ) greater than the ulfur to heat content rato of low ulfur pot market coal ( S l H l ), then a low ulfur coal contract ncreae complance cot. If P A < MCA,, then a low ulfur coal contract decreae complance cot. See the Appendx A for detaled proof of Propoton 1. Propoton 1(v) may eem counter-ntutve, but t how the mportance of beng careful about defnng a unt 71

72 complance cot veru a unt total cot, whch omethng to keep n mnd for the remander of the paper Generatng Unt Net Allowance Poton: Exce Demand Correpondence Aume there are no contract contrant (C c h = 0, Cc l = 0). A generatng unt net allowance poton, or exce demand, the dfference between a unt ntal allowance allocaton and the unt actual allowance ue a governed by (3 2). From (3 2) and (3 3), the mnmum and maxmum exce demand for allowance can be formally derved. If P A < MCA, whch can be derved from (3 3): a unt wll ue the maxmum amount of hgh ulfur pot market coal C,MAX h = D H h (2 34) The ue of all hgh ulfur pot market coal lead to the maxmum emon level: E MAX = (1 z r )(m)(sh)( D ) (2 35) Hh Inertng C,MAX h n for Ch n (3 2) gve an expreon for the maxmum allowance exce demand, whch the dfference between the maxmum emon level (E MAX ) and the ntal allowance allocaton (A e ): A MAX = E MAX A e = (1 z r )(m)(sh)( D ) A e Hh (2 36) If a unt ntal allocaton cannot cover t maxmum poble emon, then t wll have a potve net allowance poton and be a net buyer of allowance. If P A > MCA,, a unt wll ue the maxmum amount of low ulfur pot market coal, whch can be derved from (3 3): C,MAX l = D H l (2 37) The ue of all low ulfur pot market coal lead to the mnmum emon level: E MIN = (1 z r )(m)(sl)( D ) (2 38) Hl 72

73 Inertng C,MAX l n (2 37) for Cl n (3 3) gve an expreon for the mnmum allowance exce demand, whch the dfference between the mnmum emon level (E MIN ) and the ntal allowance allocaton (A e ): A MIN = E MIN A e = (1 z r )(m)(sl)( D ) A e Hl (2 39) If a unt ntal allocaton can cover t mnmum poble emon, then t wll have a negatve net allowance poton and be a net eller of allowance. If P A = MCA,, a unt may ue any combnaton of hgh ulfur pot market coal and low ulfur pot market coal, whch lead to any level of exce demand n the range (E MIN A e, E MAX A e ). The allowance exce demand can be repreented by ( ) A = θe MAX (1 θ)e MIN A e where the contant θ [0, 1]. A unt that ndfferent between fuel wtchng and allowance purchae could be ether a net buyer or a net eller. Combnng the exce demand for each of the three cae create the Exce Demand Correpondence: A = A MAX θa MAX A MIN (1 θ)a MIN f P A > MCA, f P A = MCA, θ [0, 1] f P A < MCA, A generatng unt exce demand correpondence can be een graphcally n Fgure 2.8(). Hgh ulfur pot market coal ue correpond to the rght-hand vertcal lne where P A < MCA,. Low ulfur pot market coal ue correpond to the left-hand vertcal lne where P A > MCA,. The cae where a generatng unt ue ome combnaton of low ulfur pot market coal and hgh ulfur pot market coal repreented by the horzontal lne at whch P A = MCA,. 73

74 Cot avng of fuel wtchng veru allowance purchae when P A > MCA, coal ( P h H h Aumng that hgh ulfur pot market coal cheaper than low ulfur pot market < S l H l ), a generatng unt that doe not have an emon contrant prefer to ue hgh ulfur pot market coal to meet electrcty demand. 19 Allowng generatng unt to have a choce n ther complance opton can lead to cot avng n everal cae. Frt, conder the cae that P A > MCA,. Ung low ulfur pot market coal lead to the mnmum number of allowance ued by the unt (A MIN ). Aumng that the ntal allocaton by the frm larger than the mnmum poble allowance ue, the unt wll ell t remanng allowance after meetng t allowance requrement. The exce demand for uch a unt can be een n (2 39), where the exce demand wll actually be negatve. The unt cot avng from wtchng fuel over purchang allowance (P A MCA, )(A MAX A MIN ), whch the area a+b een n Fgure 2.8(). The dark-haded area (a) the cot avng for the generatng unt from abatng emon through fuel wtchng ntead of purchang addtonal allowance. The lght-haded area (b) the cot avng from abatng more than t ntal allocaton and ellng the extra allowance Effect of hgh ulfur coal contract on exce demand and cot Now conder how a hgh ulfur coal contract wll mpact a generatng unt allowance exce demand correpondence n Fgure 2.8, whch ummarzed n Propoton 2. Propoton 2: Gven the crubber choce, () () For the range of allowance prce P A MCA,, a hgh ulfur coal contract wll weakly ncreae a unt allowance exce demand. For the range of allowance prce P A MCA, weakly decreae exce demand f Sc h H c h S h. Hh, a hgh ulfur coal contract wll 19 The aumpton that hgh ulfur coal cheaper than low ulfur coal upported by actual coal prce. 74

75 () For the range of allowance prce P A MCA, weakly ncreae exce demand f Sc h H c h Proof of Propoton 2(): S h. Hh, a hgh ulfur coal contract wll For allowance prce P A > MCA,, a unt prefer to ue all low ulfur coal, whch lead to the mnmum allowance exce demand (A MIN ). A hgh ulfur coal contract force ome hgh ulfur coal ue and decreae low ulfur coal ue from C,MAX l to Ĉ,MAX l, whch the maxmum amount of low ulfur coal a unt wll ue gven t hgh ulfur coal contract: C,MAX l > Ĉ,MAX l = D C c Hh c Hl h Hl The decreae n low ulfur pot market coal ue ncreae emon from E MIN whch the mnmum emon gven the hgh ulfur coal contract contrant: (2 40) to ÊMIN, E MIN < ÊMIN = (1 z r )(m)(s lĉ,max l + S c hc c h) (2 41) Hgher emon mut be covered by addtonal allowance, whch reult n the mnmum exce demand wth a hgh ulfur coal contract to be greater than the mnmum exce demand wth no hgh ulfur coal contract: A MIN < ÂMIN = ÊMIN A e (2 42) Therefore, a hgh ulfur coal contract wll ncreae exce demand for allowance prce P A > MCA,. Proof of Propoton 2() and 2(): For allowance prce P A < MCA,, a unt prefer to ue all hgh ulfur coal, whch lead to the maxmum allowance exce demand (A MAX ). A hgh ulfur coal contract force a unt to decreae t hgh ulfur pot market coal ue from C,MAX h where: C,MAX h > Ĉ,MAX h = D C c Hh c Hh h Hl to Ĉ,MAX h (2 43) 75

76 If Sc h H c h < S h, the ulfur content per unt of heat content lower for hgh ulfur Hh contract coal than hgh ulfur pot market coal and wll decreae the maxmum emon from E MAX to ÊMAX : E MAX < ÊMAX = (1 z r )(m)(s hĉ,max h + S c hc c h) (2 44) Lower emon reult n a decreae n a unt maxmum exce demand from A MAX to  MAX n Fgure 2.8(): A MAX > ÂMAX = ÊMAX A e (2 45) Therefore, a hgh ulfur coal contract for coal wth a lower ulfur to heat content rato wll decreae exce demand for allowance prce P A < MCA,. If Sc h H c h > S h, the ulfur content per unt of heat content greater for hgh ulfur Hh contract coal than hgh ulfur pot market coal and wll ncreae the maxmum emon from E MAX to ÊMAX : E MAX > ÊMAX = (1 z r )(m)(s hĉ,max h + S c hc c h) (2 46) Greater emon reult n an ncreae n a unt maxmum exce demand from A MAX to  MAX n Fgure 2.8(): A MAX < ÂMAX = ÊMAX A e (2 47) Therefore, a hgh ulfur coal contract for coal wth a hgher ulfur to heat content rato wll ncreae exce demand for allowance prce P A < MCA,. A bndng hgh ulfur coal contract that retrct a unt ablty to wtch to low ulfur coal can force a net eller of allowance to decreae ther allowance ale from A MIN to ÂMIN and abate fewer emon than the generatng unt would prefer a hown n Fgure 2.8(). If the contract contrant large enough t wll hft ÂMIN to the rght of A = 0 and force a unt to be a net buyer. If the contract contrant force the generatng unt to ue all hgh ulfur coal, then the exce demand a vertcal lne where the unt only choce to purchae the maxmum amount of allowance. Th cae may have 76

77 occurred durng Phae I becaue ome generatng unt purchaed 100% hgh ulfur coal through contract n Hgh ulfur coal aumed to be the preferred coal to ue pror to Ttle IV a unt would wh to ue the cheapet coal regardle of ulfur content, whch wa uually hgh ulfur coal. In Fgure 2.8, a unt prefer to ue low ulfur coal becaue P A > MCA,, and the complance cot from wtchng fuel to abate emon can be een n area (a + b). Area (b + c) the revenue ganed (negatve cot) from ellng the remanng allowance that are avalable due to abatng emon below a unt ntal allowance allocaton. The net complance cot for a unt wll be the cot of wtchng fuel mnu the revenue from allowance ale, or (a + b) (b + c) = (a c). If (a c) < 0, then a unt wll have negatve complance cot. Now conder how a hgh ulfur coal contract wll mpact the exce demand correpondence, complance cot, and total cot. A ha already been hown above and can be een n Fgure 2.8, a hgh ulfur coal contract wll ncreae the mnmum exce demand from A MIN to ÂMIN and may ncreae or decreae the maxmum exce demand dependng on the relatve ulfur to heat content rato of contract to pot market coal. Thee hft n a unt exce demand may have three dtnct effect on a unt cot. The frt cot mpact the addtonal complance cot to a unt from lot allowance ale, whch repreented by area (d) n Fgure 2.8. A unt mut ue ome hgh ulfur coal, whch reult n a unt coverng addtonal emon through more expenve allowance ntead of wtchng to low ulfur coal. The econd mpact reult from the dfference n the ulfur to heat content rato between hgh ulfur contract and pot market coal. If Sc h H c h emon a unt can create wll decreae and ÂMAX < S h, then the maxmum Hh < A MAX. Th wll decreae the complance cot by (f) n Fgure 2.8() for reducng emon to the allowance allocaton 20 Avalable from FERC-423 Data. 77

78 emon level. If Sc h H c h and ÂMAX > S h, then the maxmum emon a unt can create wll ncreae Hh > A MAX. Th wll ncreae the complance cot by area (f) n Fgure 2.8() for reducng emon to the allowance allocaton emon level. Conder how thee hft n exce demand wll mpact a unt net complance cot. The ncreae n the mnmum exce demand wll ncreae net complance cot by decreang area (b) and area (c). If maxmum exce demand decreae, net complance cot decreae by area (f) n Fgure 2.8(). Combnng the two mpact reult n net complance cot of (a c) n Fgure 2.8(). If maxmum exce demand ncreae, net complance cot ncreae by area (f) n Fgure 2.8(). Combnng the two mpact reult n net complance cot of (a + f c) n n Fgure 2.8(). The thrd cot mpact reult from dfferent prce for hgh ulfur pot market and contract coal, whch repreented by area (e). Hgher prced contract coal caue a unt to have addtonal fuel cot to meetng electrcty demand, whch an ncreae a unt total cot. The graphcal decrpton of a hgh ulfur coal contract mpact on exce demand and cot can be een n the example defned n Table 3-1. Gven the coal charactertc, demand, allowance allocaton, and allowance prce, and ung a hgh ulfur contract coal prce of $1.50/mmBtu, the mnmum and maxmum allowance ue and MCA, can be computed f a unt face no hgh ulfur coal contract (C c h = 0). For th example, hgh ulfur contract and pot market coal are aumed to have the ame charactertc, whch olate the effect that hgh ulfur coal contract have on exce demand for allowance prce P A > MCA c,. The mnmum allowance ue baed on the low ulfur coal charactertc 11,400 ton whle the maxmum allowance ue baed on the hgh ulfur pot market coal charactertc 38,000 ton. The MCA, $270.68, whch lower than the allowance prce of $ So a unt wll wtch to all low ulfur coal to mnmze t total cot. In dong o, t wll ue ue 11,400 of t allowance allocaton to cover t mnmum emon 78

79 level and ell the remanng 8,600 allowance at $ each. Net complance cot are the addtonal cot from wtchng to low ulfur pot market coal plu the cot of allowance purchae, whch $4.62 mllon. Total cot are the total cot of fuel purchae mnu allowance ale, whch $35.82 mllon. Now conder the ame unt wth a hgh ulfur coal contract for 500,000 ton of coal, whch account for half of the requred heat nput. The maxmum allowance ue reman at 38,000 ton, but the mnmum allowance ue decreae to 24,700 ton becaue of the coal contract. The MCA c, $ and MCA, $90.23, whch much lower than the allowance prce of of $ The coal contract reult n complance cot (cot of wtchng fuel mnu allowance ale) of $5.01 mllon and total cot to meetng electrcty demand (low ulfur pot market coal purchae plu hgh ulfur contract coal purchae plu allowance purchae) of $38.61 mllon. Complance cot ncreaed by $390,000 becaue the unt could not wtch all t coal ue to low ulfur coal. Total cot to the unt ncreaed by $2.79 mllon becaue of the hgher prce for the contract coal. Another poblty that the hgh ulfur contract coal could actually be cheaper, whch reaonable becaue the man reaon for makng a coal contract agreement for protecton agant future coal prce fluctuaton. Th cae can be een n Fgure 2.8, where MCA c, > MCA, and there actually a cot avng to the unt from ung hgh ulfur contract coal over hgh ulfur pot market coal. The net complance cot reman the ame a n the prevou example, area (a c). 21 However, the total cot to the unt wll decreae relatve to not havng coal under the contracted prce. Area (d + e) the addtonal complance cot to the unt for not beng able to wtch to low ulfur coal. Area (e) are the cot avng of ung lower prced hgh ulfur contract coal over hgh ulfur pot market coal. 21 For mplcty, the ulfur to heat content rato aumed to be equal for hgh ulfur contract and pot market coal. 79

80 By ung the ame aumpton a n Example 1 except changng the prce of hgh ulfur contract coal to $1.20/mmBtu, complance cot and total cot to a unt when contract coal cheaper can be computed. MCA c, $ The change n net complance cot reman the ame at $390,000 whle the cot due to the lower prced coal actually decreae by about $1.2 mllon. The unt actually ha beneft by lowerng t total cot by $810,000 through the coal contract even though t mut ncreae t complance cot Cot avng of allowance purchae veru fuel wtchng when P A < MCA, coal ( P h H h Aumng that hgh ulfur pot market coal cheaper than low ulfur pot market < S l H l ), a generatng unt that doe not have an emon contrant prefer to ue hgh ulfur pot market coal to meet electrcty demand. Conder the cae that P A < MCA,. Ung hgh ulfur pot market coal lead to the maxmum number of allowance ued by the unt (A MAX ). Aumng that the ntal allocaton to the unt maller than the maxmum poble allowance ue, the unt wll purchae addtonal allowance to meet t allowance requrement. The exce demand for uch a unt can be een n (2 36), where the exce demand wll be potve. Gven that a unt preferred to ue hgh ulfur coal before SO 2 contrant, the unt cot avng from ung allowance over wtchng fuel (MCA, P A )(A MAX A MIN ), whch the area a+b een n Fgure 2.8. The dark-haded area (a) the cot avng for the generatng unt from purchang addtonal allowance ntead of wtchng fuel. The lght-haded area (b) the cot avng from ung the allocated allowance ntead of abatng emon and ellng the extra allowance Effect of low ulfur coal contract Now conder how a low ulfur coal contract wll mpact a generatng unt allowance exce demand correpondence n Fgure 2.8, whch ummarzed n Propoton 3. Propoton 3: Gve the crubber choce, 80

81 () For the range of allowance prce P A MCA,, a low ulfur coal contract wll weakly decreae a unt allowance exce demand. () For the range of allowance prce P A MCA, decreae exce demand f Sc l H c l S. Hl () For the range of allowance prce P A MCA, ncreae exce demand f Sc l H c l Proof of Propoton 3(): S l. Hl, a low ulfur coal contract wll, a low ulfur coal contract wll For allowance prce P A < MCA,, a unt prefer to ue all hgh ulfur coal, whch lead to the maxmum allowance exce demand (A MAX ). A low ulfur coal contract force ome low ulfur coal ue and decreae hgh ulfur coal ue from C,MAX h to Ĉ,MAX h, whch the maxmum amount of hgh ulfur pot market coal a unt wll ue gven the low ulfur coal contract contrant: C,MAX h > Ĉ,MAX h = D H h C c l Hl c Hh (2 48) The decreae n maxmum hgh ulfur coal ue decreae a unt maxmum emon from E MAX to ÊMAX : E MAX > ÊMAX = (1 z r )(m)(s hĉ,max h + S c lc c l) (2 49) Lower emon decreae the allowance ued, whch reult n the maxmum exce demand wth a low ulfur coal contract to be lower than the maxmum exce demand wth no low ulfur coal contract: A MAX > ÂMAX = ÊMAX A e (2 50) Therefore, a hgh ulfur coal contract wll ncreae exce demand for allowance prce P A < MCA,. Proof of Propoton 3() and 3(): For allowance prce P A > MCA,, a unt prefer to ue all low ulfur coal, whch lead to the mnmum allowance exce demand (A MIN ). A low ulfur coal contract 81

82 decreae the maxmum amount of low ulfur pot market coal ue from C,MAX l Ĉ,MAX l : C,MAX l > Ĉ,MAX l = D H h C c Hl c l Hl to (2 51) If Sc l H c l < S l, the ulfur content per unt of heat content lower for low ulfur contract Hl coal than low ulfur pot market coal and wll decreae the mnmum emon from E MIN to ÊMIN : E MIN > ÊMIN = (1 z r )(m)(s lĉ,max l + S c lc c l) (2 52) Lower emon reult n a decreae n a unt mnmum exce demand from A MAX to  MAX n Fgure 2.8(): A MIN > ÂMIN = ÊMIN A e (2 53) Therefore, a low ulfur coal contract for coal wth a lower ulfur to heat content rato wll decreae exce demand for allowance prce P A > MCA,. If Sc l H c l > S l, the ulfur content per unt of heat content greater for low ulfur Hl contract coal than low ulfur pot market coal and wll ncreae the mnmum emon from E MIN to ÊMIN : E MIN < ÊMIN = (1 z r )(m)(s lĉ,max l + S c lc c l) (2 54) Greater emon reult n an ncreae n a unt mnmum exce demand from A MIN to  MIN n Fgure 2.8(): A MIN > ÂMIN = ÊMIN A e (2 55) Therefore, a hgh ulfur coal contract for coal wth a hgher ulfur to heat content rato wll ncreae exce demand for allowance prce P A > MCA,. A bndng low ulfur coal contract that retrct a unt ablty to ue allowance can force a net buyer of allowance to decreae ther allowance purchae from A MAX to ÂMAX and abate more emon than the generatng unt would prefer a hown n Fgure 2.8. If 82

83 the contract contrant large enough t wll hft ÂMAX to the left of A = 0 and force a unt to be a net eller. If the contract contrant force the generatng unt to ue all low ulfur coal, then the exce demand a vertcal lne where the unt only choce to purchae the mnmum amount of allowance. Th cae may occur durng Phae II f ome generatng unt purchaed 100% low ulfur coal through contract. In Fgure 2.8, the net complance cot can be een n the haded area (a) that repreent the cot of purchang allowance to cover the unt emon above t allowance allocaton. Now conder how a low ulfur coal contract wll mpact the exce demand correpondence, complance cot, and total cot. A ha already been hown above and can be ee n Fgure 2.8, a low ulfur coal contract wll decreae the maxmum exce demand from A MAX to ÂMAX and may ncreae or decreae the mnmum exce demand dependng on the relatve ulfur to heat content rato of contract to pot market coal. Thee hft n a unt exce demand may have two dtnct effect on a unt cot. The frt cot mpact the addtonal complance cot to a unt from wtchng from hgh ulfur pot market to low ulfur contract coal ntead of purchang allowance, whch repreented by area (c) n Fgure 2.8. A unt mut ue ome low ulfur coal, whch reult n a unt abatng addtonal emon ntead of purchang allowance. Area (c) the dfference between the cot of wtchng fuel to decreae emon, area (b + c), and the decreae n cot from allowance purchae, area (b). Net complance cot ncreae from (a + b) to (a + b + c). The econd cot mpact reult from dfferent prce for low ulfur contract and pot market coal, whch repreented by area (d). Hgher prced contract coal caue a unt to have addtonal fuel cot to meetng electrcty demand, whch ncreae a unt total cot. The graphcal decrpton of coal contract mpact on exce demand and cot can be een n the example defned n Table 2-4. Gven the coal charactertc, demand, 83

84 allowance allocaton, and allowance prce, and low ulfur contract coal prce of $1.80/mmBtu, the mnmum and maxmum allowance ue and MCA, can be found f a unt face no low ulfur coal contract (C c h = 0). For th example, low ulfur contract and pot market coal are aumed to have the ame charactertc, whch olate the effect that low ulfur coal contract have on exce demand for allowance prce P A < MCA c,. The mnmum allowance ue baed on the low ulfur coal charactertc 11,400 ton whle the maxmum allowance ue baed on the hgh ulfur pot market coal charactertc 38,000 ton. The MCA, $270.68, whch hgher than the allowance prce of $ So a unt wll purchae allowance to mnmze t total cot. In dong o, t wll ue ue the entre 20,000 ton allowance allocaton and purchae an addtonal 18,000 allowance to cover t maxmum emon level. Net complance cot are the addtonal cot from purchang allowance, whch $3.6 mllon. Total cot are the total cot of fuel purchae plu allowance purchae, whch $34.8 mllon. Now conder the ame unt wth a low ulfur coal contract for 500,000 ton of coal, whch account for half the requred heat nput to meet demand. The mnmum allowance ue reman at 11,400 ton, but the maxmum allowance ue decreae to 24,700 ton becaue of the coal contract. The MCA,c than the allowance prce of $ and MCA, $451.13, whch much hgher of $ The coal contract reult n net complance cot (addtonal cot of allowance purchae and fuel wtchng) of $4.54 mllon and total cot to meetng electrcty demand (hgh ulfur pot market coal purchae plu low ulfur contract coal purchae plu allowance purchae) of $38.14 mllon. Complance cot ncreaed by $940,000 becaue the unt could not ue all hgh ulfur coal. Total cot to the unt ncreaed by $3.34 mllon becaue of the hgher prce for the contract coal. Another poblty that the low ulfur contract coal could actually be cheaper than low ulfur pot market coal, whch reaonable becaue the man reaon for makng a coal contract agreement for protecton agant future coal prce fluctuaton. Th cae can 84

85 be een n Fgure 2.8, where MCA c, < MCA, and there actually a cot avng to the unt from ung low ulfur contract coal over low ulfur pot market coal. The complance cot reman the ame a n the prevou example, area (a + b + c). However, the total cot to the unt wll decreae relatve to not havng coal under the contracted prce. Area (c + d) addtonal cot to the unt for not beng able to wtch to low ulfur coal. Area (d) the cot avng of ung lower prced hgh ulfur contract coal over hgh ulfur pot market coal. By makng the ame aumpton a n Example 1 except changng the prce of low ulfur contract coal to $1.50/mmBtu, we can olve for complance cot and total cot to a unt. MCA,c $ The change n complance cot reman the ame at $940,000 whle the cot due to the lower prced coal actually decreae by $1.2 mllon. 22 unt actually gan by lowerng t total cot by $260,000 through the coal contract even though t mut ncreae t complance cot Fuel wtchng veru allowance purchae when P A = MCA, In the knfe-edge cae a generatng unt ha no trct preference between purchang allowance and abatng emon becaue P A = MCA,. The unt exce demand may be any value n the range [A MIN A e, A MAX The A e ]. The generatng unt ha no preference n complance opton becaue any combnaton of abatement and allowance purchae reult n the ame complance cot of area (a) n Fgure 2.8. A hgh ulfur coal contract wll have the ame mpact on the exce demand correpondence when P A = MCA, a n Secton where P A > MCA,. However, the mpact on complance cot and total cot wll be dfferent. The reaonng for th that the contract doe not force a unt to ue a more expenve complance opton. By comparng Fgure 2.8 to Fgure 2.8, thee dfference can be derved. The hft n a unt 22 For mplcty, the ulfur to heat content rato aumed to be equal for low ulfur contract and pot market coal. 85

86 mnmum exce demand ha no mpact on complance cot. Total cot wll tll ncreae by area (c) f the relatve prce of hgh ulfur contract coal more expenve than hgh ulfur pot market coal. The hft n maxmum exce demand wll tll mpact complance cot by area (f). A low ulfur coal contract wll have the ame mpact on the exce demand correpondence when P A = MCA, a n n Secton where P A < MCA,. However, the mpact on complance cot and total cot wll be dfferent. The reaonng for th that the contract doe not force a unt to ue a more expenve complance opton. By comparng Fgure 2.8 to Fgure 2.8, thee dfference can be derved. The hft n a unt mnmum exce demand ha no mpact on complance cot. Total cot wll tll ncreae by area (c) f the relatve prce of hgh ulfur contract coal more expenve than hgh ulfur pot market coal. The hft n maxmum exce demand wll not mpact complance cot becaue the addtonal cot of abatng emon are offet by the decreae n allowance purchae Generatng Unt Scrubber Intallaton Choce It not poble to completely characterze a generatng unt decon baed on MCA and allowance prce alone becaue of the non-convexte of crubber ntallaton. In th ecton a unt decon wth the opton of ntallng a crubber are examned, the allowance prce at whch a unt wll ntall a crubber derved, the change n the exce demand correpondence hown, and the effect of coal contract on the exce demand examned When wll a generatng unt ntall a crubber? Let ( C h, C l, Ã) and (Ĉ h, Ĉ l, Â) be the cot mnmzng combnaton of pot coal and allowance wth and wthout a crubber ntalled, repectvely. A unt ndfferent to ntallng a crubber f the total cot wth a crubber ntalled are equal to the total cot wthout a crubber ntalled: P z + P S AÃ + P h C h + P l C l = P S AÂ + P hĉ h + P lĉ l (2 56) 86

87 P S A the allowance prce at whch the unt ndfferent between ntallng a crubber or not. The amount of hgh ulfur and low ulfur contract coal wll be the ame both wth and wthout a crubber and wll cancel out, but the contract coal tll affect the allowance poton. 23 A generatng unt decon wll hnge on th allowance prce. (2 56) can be ued to olve for PA S, the mnmum allowance prce at whch a generatng unt wll ntall a crubber: A unt wll prefer to ntall a crubber at P S A P S A P z + P h ( C h Ĉ h ) + P l ( C l Ĉ l ) (Â Ã) a crubber weakly le than the cot of purchang an allowance Dfferent margnal cot of abatement (2 57) f the average cot of abatement from ung The ntallaton of a crubber lead to an ncreae n the unt margnal abatement cot of wtchng from hgh ulfur pot market to low ulfur pot market coal relatve to the margnal abatement cot wthout a crubber ntalled: M CA, = Pl P Hl h Hh (1 r )(m)( S h S Hh l ) Hl MCA, = Pl P Hl h Hh (m)( S h S Hh l ) Hl (2 58) Scrubber ntallaton decreae the ze of the denomnator of M CA, by (r )(m)( S h H h S l H l ), whch due to the fact that only a fracton (baed on the crubber reducton rate) of the emon reducton from wtchng fuel realzed Exce demand correpondence A generatng unt exce demand correpondence become gnfcantly more complcated when a unt crubber ntallaton choce ntroduced nto t decon-makng proce. The exce demand correpondence a combnaton of a unt exce demand 23 See Appendx A for the dervaton of th equaton. 87

88 correpondence wth and wthout a crubber wth a dcontnuty repreentng the dcrete choce eparatng the two pece. A generatng unt exce demand correpondence can be derved from t optmal complance choce a the market allowance prce change. For allowance prce M CA, < P A, a generatng unt ntall a crubber becaue P S A < P A, and wtche fuel from hgh ulfur pot market to low ulfur pot market coal becaue M CA, < P A. So a generatng unt wll have mnmum exce demand when a crubber ntalled (A SMIN ), whch ha already been derved n (2 36) gven that z = 1. For allowance prce P S A < P A < M becaue P S A < P A, and ue hgh ulfur coal becaue P A < M, CA, a generatng unt ntall a crubber, CA. So a generatng unt wll have maxmum exce demand when a crubber ntalled (A SMAX ), whch ha already been derved n (2 39) gven z = 1. For allowance prce MCA, < P A < PA S, a generatng unt doe not ntall a crubber becaue P A < PA S, and wtche fuel from hgh to low ulfur coal becaue MCA, < P A. So a generatng unt wll have mnmum exce demand wthout a crubber ntalled (A MIN ), whch ha already been derved n (2 36) gven z = 0. For allowance prce 0 < P A < MCA,, a generatng unt doe not ntall a crubber becaue P A < PA S, and hgh ulfur coal becaue P A < MCA,. So a generatng unt wll have maxmum exce demand wthout ntallng a crubber (A MAX ), whch ha already been derved n (2 39). A = A MAX θa MAX A MIN A SMAX θa SMAX A SMIN (1 θ)a MIN (1 θ)a SMIN f 0 < P A < MCA, f (MCA, = P A < PA S ) θ [0, 1] f MCA, f P S A P A < M f M f M < P A P S A CA, CA, = P A θ [0, 1] CA, < P A < P S A or 0 < P A < P S A < MCA, 88

89 Ung thee four dfferent exce demand for each allowance prce range and the knfe-edge allowance prce, t poble to mathematcally derve the exce demand correpondence. The exce demand correpondence een n Fgure 2.8() nclude a generatng unt net allowance poton under the four dfferent allowance prce range f ( P h H h ( P h H h < P l H l ). If P l H l ) a generatng unt face negatve margnal abatement cot and wll ue only low ulfur coal, whch wll reult n a pecal cae of only two prce range where the only choce a unt make whether to ntall a crubber n Fgure 2.8(). 24 MCA, P A If a generatng unt never prefer to wtch fuel before ntallng a crubber becaue < P S A PA S, there a pecal cae n whch the allowance prce range MCA, < doe not ext for the exce demand correpondence. The exce demand correpondence under th cae can be een n Fgure Impact of Coal Contract on Exce Demand Correpondence Gven the crubber choce, a coal contract retrct the avalable coal ue opton, whch affect the exce demand correpondence a hown n Secton 6.7. A contract contrant alo change the allowance prce at whch a generatng unt wll optmally ntall a crubber, whch alter the exce demand correpondence a well. Under Phae I, a generatng unt wthout a crubber may prefer to ue low ulfur coal, but when facng a hgh ulfur coal contract contrant t would ntall a crubber and prefer to ue hgh ulfur pot market coal. The oppote may occur under CAIR, where generatng unt may face low ulfur coal contract contrant. A unt may wh to ntall a crubber and ue all hgh ulfur coal, but the low ulfur contract contrant may reult n no crubber beng ntalled and allowance purchae occurrng ntead. The combnaton of thee two effect may change the exce demand correpondence for all allowance prce. P l H l 24 An example where P h Hh generatng unt n the tate of Wconn. n the actual data the delvered prce of coal to 89

90 Frt, t mportant to generalze the ndfference prce at whch a generatng unt wll ntall a crubber (PA S ), whch can be derved by ettng a unt cot when t doe not ntall a crubber, whch nclude net allowance purchae (A ) and fuel cot (Ph C h + P l C l ), to a unt cot when t doe ntall a crubber, whch nclude net allowance purchae (A SMAX ), fuel cot (Ph C,MAX h ), and cot of a crubber (P z ). Aumng that hgh ulfur pot market coal cheaper than low ulfur pot market coal, a unt ue all hgh ulfur pot market coal f t ntall a crubber becaue M CA, > P A. It uncertan f a unt wll ue hgh or low ulfur coal f t doe not ntall a crubber, and wll depend on the relatonhp between P A and MCA,. P z + P S AA SMAX + PhC,MAX h = PAA S + PhC h + PlC l (2 59) A unt that face a coal contract wll face a dfferent ndfference allowance prce of (P S A ɛ) becaue parameter value on both de of the equalty wll change. ɛ could be potve or negatve dependng on everal condton, ncludng the type of coal under contract. The new value that olve th equalty are the contract contraned cot mnmzng parameter value. The fuel cot for the contract coal wll be the ame both wth and wthout a crubber and wll cancel out. P z + (P S A ɛ)âsmax + P hĉ,max = (PA S ɛ)â + P hĉ h + P lĉ (2 60) By olvng for the contant P z n (2 59) and (2 60) and ettng the two expreon equal to each other, the gn and value of ɛ can be derved Impact of a bndng hgh ulfur coal contract The mpact of a hgh ulfur coal contract on the two pece of the exce demand correpondence wll be the ame a n Secton 6.7 where the crubber choce gven except there wll be an addtonal mpact on exce demand from the contract on the allowance prce at whch a unt ndfferent to ntallng a crubber. 90

91 There are two cae for whch the value of ɛ mut be derved to determne the contract mpact on the allowance ndfference prce, the frt of whch wll have two ubcae. A wll be hown for each of the cae, f ( Sc h H c h S h H h ), then ɛ wll be potve and may decreae the allowance prce at whch a unt wll prefer to ntall a crubber. In the frt cae, wthout a hgh ulfur coal contract, a unt prefer to ue low ulfur pot market coal wthout a crubber and hgh ulfur coal wth a crubber. The two ubcae wll be determned by the generatng unt charactertc and the ze of the contract contrant. In the frt ubcae, both wth or wthout a hgh ulfur coal contract, a unt prefer to ue low ulfur pot market coal f t doe not ntall a crubber and hgh ulfur pot market coal t doe ntall a crubber. For th to hold, (MCA, (MCA, < P S A ɛ < P S A ). < P A < M, CA ) and If a unt that ha no hgh ulfur contract coal (C c h = 0), a unt ue the maxmum amount of hgh ulfur coal wth a crubber and the maxmum amount of low ulfur coal wthout a crubber, and ndfferent to ntallng a crubber at allowance prce P S A : P z + P S AA SMAX + PhC,MAX h = PAA S MIN + PlC,MAX l (2 61) (2 61) can be rearranged to fnd an expreon for P z : P z = P S A(A MIN A SMAX ) PhC,MAX h + PlC,MAX l (2 62) A hgh ulfur coal contract wll change the optmal value of the other parameter, whch wll change the ndfference allowance prce by ome value ɛ: P z + (P S A ɛ)âsmax + P hĉ,max + PhC c c h = (PA S ɛ)âmin + P lĉ,max + PhC c c h (2 63) (2 63) can be rearranged to fnd an expreon for P z : P z = (P S A ɛ)(âmin ÂSMAX ) + P lĉ,max P hĉ,max (2 64) 91

92 Snce P z a contant, the two expreon for P z n (2 62) and (2 63) can be et equal to olve for the value of ɛ: ɛ = P A S(ÂMIN A MIN + A SMAX ÂSMAX ) + Pl (Ĉ,MAX l (ÂMIN ÂSMAX ) C,MAX l ) Ph (Ĉ,MAX h C,MAX h ) (2 65) Fllng n for allowance and coal ue parameter, t poble to determne the gn of ɛ. A SMAX A MIN = ( D ) (S Hl l )(m) A e = ( D )(S H h)(m)(1 r h ) A e  MIN = ( C c hsh c + D C c hhh c S H l) (m) A e l [  SMAX = C c hs c h+ ( D C c hh c h H h ) (S h )] (m)(1 r ) A e C,MAX h = D A e Hh Ĉ,MAX h = D C c hh c h H h C,MAX l = D H l Ĉ,MAX l = D C c hh c h H l By fllng thee expreon nto (2 65), the expreon for ɛ can be mplfed to parameter for coal prce, ulfur content, heat content, and crubber capture rate. [ ] ] C c hhh c (PA [(r S)(m) )( Sc h S Hh c h ) + ( S Hh h S Hh l ) ( P Hl l P Hl h ) Hh ɛ = (ÂMIN ÂSMAX ) An nterpretable form derved by eparatng term, multplyng though by (ÂMIN (2 66)  SMAX ), and dvdng through by m( S h S Hh l ). Hl ɛ(âmin ɛ(âmin ÂSMAX ) = C c hhh c ÂSMAX ) = C c hhh c [ P S A r ( Sc h H c h [ P S A r ( Sc h Sh S Hh l Hl H c h Sh S Hh l Hl S h H h ) S h H h ) + PA S ( P l P Hl h ) Hh m( S h S Hh l ) Hl + (P S A MCA, ) From the ntal aumpton that a unt ue low ulfur coal when t doe not ntall a crubber, t known that PA S > MCA,. So f ( Sc h Hh c the ze of the hgh ulfur coal contract (C c h) ncreae. If ( Sc h H c h unknown. ] ] (2 67) S h H h ), then ɛ > 0 and ɛ ncreae a < S h H h ), then the gn of ɛ 92

93 An example reflectve of Phae I data wll help to explan whch gn mot lkely for ɛ. The example n Table 2-6 baed on data from the a unt that ntalled a crubber under Phae I. 25 The frt example wll conder ɛ gven that a unt ue low ulfur coal from the Southern Appalachan Mountan and hgh ulfur coal from the Northern Appalachan Mountan. Southern Appalachan coal ha a low average ulfur content (0.65%). In th example, hgh ulfur pot market coal aumed to have both a lower ulfur content and prce than hgh ulfur contract coal. Gven the aumpton n Table 2-6, a unt wll prefer to ue low ulfur coal f t doe not ntall a crubber becaue MCA, = $ and P A = $250. If a crubber ntalled, a unt prefer to ue hgh ulfur pot market coal becaue the margnal cot of abatement ncreae above the allowance prce to M mllon, whch reult n P S A CA, = $4, The annualzed crubber cot are P z = $ = $1, A hgh ulfur coal contract for 50% of coal ue reult n a decreae n the ndfference allowance prce of ɛ = $1, to (P A ɛ) = $ (a 76% decreae n PA S ). Although a unt complance choce are not altered at P A = $250, the large decreae n ɛ encourage crubbng at much lower allowance prce than wthout the coal contract. Th ubcae wll hold for a contract contrant of le than 73.5% of coal ue. Th example how that for many unt, hgh ulfur coal contract would not have enough of an mpact to reult n crubber ntallaton n Phae I. Only about 10% of unt actually ntalled crubber to comply wth Phae I, but thee unt account for over half of total abatement by affected unt. In the econd ubcae, aume that wthout a hgh ulfur coal contract, a unt prefer to ue low ulfur pot market coal f t doe not ntall a crubber and hgh ulfur pot market coal t doe ntall a crubber becaue (MCA, < P A < M (MCA,, CA ) and < PA S ). However, wth a hgh ulfur coal contract, a unt prefer to ue hgh ulfur pot market coal both wth and wthout a crubber becaue (P S A ɛ < MCA, ). 25 Gen. JM Gavn had 100% coal under contract. 93

94 If a unt that ha no hgh ulfur contract coal (C c h = 0), a unt ue the maxmum amount of low ulfur coal f a crubber not ntalled, but ue the maxmum amount of hgh ulfur coal f a crubber ntalled. The unt ndfferent to ntallng a crubber at allowance prce PA S: P z + P S AA SMAX + PhC,MAX h = PAA S MIN + PlC,MAX l (2 68) (2 68) how that the cot wth and wthout a crubber are equal for a gven PA S, and can be rearranged to fnd an expreon for P z : P z = P S A(A MIN A SMAX ) PhC,MAX h + PlC,MAX l (2 69) Snce a unt ue low ulfur coal wthout a crubber, a hgh ulfur coal contract wll change the coal ue by a unt wthout a crubber and change the ndfference allowance prce by ome value ɛ: P z + (P S A ɛ)âsmax + P hĉ,max + PhC c c h = (PA S ɛ)âmax + P hĉ,max + PhC c c h (2 70) (2 70) can be rearranged to fnd an expreon for P z : P z = (P S A ɛ)(âmax ÂSMAX ) (2 71) The two expreon for P z n (2 69) and (2 71) can be et equal to olve for the value of ɛ: ɛ = P A S(ÂMAX A MIN + A SMAX (ÂMAX ÂSMAX ) Pl C,MAX l + Ph C,MAX h ÂSMAX ) (2 72) By fllng n for allowance and coal ue, t poble to determne the gn of ɛ. A MIN = ( D ) (S Hl l )(m) A e  MAX = ( D C c hhh c S Hh h + C c hsh) c m A e A SMAX = ( D ) (S Hh h )(m)(1 r ) A e  SMAX = ( D C c hhh c S H h+c c hsh) c (m)(1 r ) A e h 94

95 C,MAX h = D Hh C,MAX l = D H l By fllng nto (2 72), the expreon for ɛ can be mplfed to parameter for coal prce, ulfur content, heat content, and crubber capture rate: ɛ(âmax ÂSMAX ) = mpa S [ r C c ( hhh c Sh c S ) ( h S + h D S l Hh c Hh Hh Hl ) ] D ( P l H l The new form n (2 73) eaer to determne the gn of ɛ becaue the gn of the P h H h ) (2 73) left-hand de unchanged whle mplfyng the rght-hand de. Now get the rght-hand de nto a form that nterpretable by eparatng term and dvdng through by m( S h S Hh l ). Hl ɛ(âmin ( Sc ÂSMAX ) = PAr S C c h S hhh c Hh c h ) Hh ( S h S Hh l Hl ) + P S AD D ( Pl P Hl h ) Hh m( S h S Hh l ) Hl (2 74) The lat two term n (2 74) can be combned to get D (P S A MCA, ): ɛ(âmin ÂSMAX ) = PAr S C c hhh c ( S c h Hh c S h H h Sh S Hh l Hl ) + D (P S A MCA, ) (2 75) From our ntal aumpton that a unt ue all low ulfur pot market coal f t doe not ntall a crubber, f t doe not have a hgh ulfur coal contract, then PA S > MCA,. If ( Sc h H c h S h H h ), then the frt term non-negatve, whch make ɛ > 0. A n Cae 1, an ncreae n the ze of the hgh ulfur coal contract (C c h) ncreae the value of ɛ. However, f ( Sc h H c h < S h H h ) then t uncertan whether ɛ potve or negatve. Aumng the data n Table 2-6, th cae wll occur f the contract greater than 73.5% of coal ue. For th cae to occur, a hgh ulfur coal contract mut reult n a unt preferrng to ue hgh ulfur coal wthout a crubber ntalled when, wthout a contract, t ntally prefer to ue low ulfur coal wthout a crubber (P S A > MCA, PA S ɛ < MCA, ). A unt mut alo prefer to ue hgh ulfur coal wth a crubber both wth and wthout a hgh ulfur coal contract (P S A ɛ < P S A and, < M CA ). The allowance 95

96 prce at whch a unt wll ntally ntall a crubber P S A = $1, , whch much hgher than the aumed allowance prce (P A = $250.00). A the ze of a contract coal ncreae from 50% to 75% of coal ue, ɛ ncreae from ɛ = $1, to ɛ = $1, , repectvely. Wth a coal contract of 50%, a unt tll prefer to ue low ulfur coal f t doe not ntall a crubber becaue (P S A ɛ) = $ > MCA, = $ However, a the coal contract ncreae n ze to 75%, a unt now prefer to ue hgh ulfur coal f t doe not ntall a crubber becaue (P S A ɛ) = $ < MCA, = $ Alo, a unt wll now ntall a crubber becaue (P S A ɛ < P A), whch may have a large mpact on complance cot. In the thrd cae, aume that a unt, both wth and wthout a hgh ulfur coal contract, prefer to ue hgh ulfur coal both wth and wthout a crubber becaue (P A < MCA, ) and (PA S ɛ < P A S < MCA, ). Gven that a unt that ha no hgh ulfur contract coal (C c h = 0), a unt ndfferent to ntallng a crubber at allowance prce P S A : P z + P S AA SMAX + PhC,MAX h = PAA S MAX + PhC,MAX h (2 76) (2 76) can be rearranged to fnd an expreon for P z where the only change n cot the change n a unt net allowance poton: P z = P S A(A MAX A SMAX ) (2 77) A hgh ulfur coal contract wll change the ndfference allowance prce by ome value ɛ becaue t alter the cot from net allowance purchae and fuel cot: P z + (P S A ɛ)âsmax + P hĉ,max + PhC c c h = (PA S ɛ)âmax + P hĉ,max + PhC c c h (2 78) (2 78) can be rearranged to fnd an expreon for P z : P z = (P S A ɛ)(âmax ÂSMAX ) (2 79) 96

97 The two expreon for P z n (2 77) and (2 79) can be et equal to olve for the value of ɛ: ɛ = P A S(ÂMAX A MAX (ÂMAX + A SMAX ÂSMAX ) ÂSMAX ) Fllng n for allowance and coal ue, t poble to determne the gn of ɛ. (2 80) A MAX = ( D ) (S Hh h )(m) A e  MAX = ( D C c hhh c S Hh h + C c hsh) c (m) A e A SMAX = ( D ) (S Hh h )(m)(1 r ) A e  SMAX = ( D C c hhh c S H h+c c hsh) c (m)(1 r ) A e h By fllng nto (2 80), the expreon for ɛ can be mplfed to parameter for coal prce, ulfur content, heat content, and crubber capture rate: ɛ(âmax ÂSMAX ) = PAmr S C c hhh( c Sc h S h ) (2 81) Hh c Hh If hgh ulfur contract coal ha a weakly hgher ulfur to heat content rato than hgh ulfur pot market coal ( Sc h H c h (C c h) ncreae, the ze of ɛ ncreae. If ( Sc h H c h Under the ntal aumpton, P S A S h H h ), then ɛ > 0 and a the amount of coal under contract < S h H h ), then ɛ < 0. < MCA,. The example n Table 2-7 ue data repreentatve of a unt that ntalled a crubber under Phae I. 26 A unt facng thee coal charactertc prefer to ue hgh ulfur coal wth or wthout a crubber ntalled becaue MCA, = $1, > P A = and MCA, = $1, > P S A = In th cae, ɛ much maller than n the prevou example at ɛ = $44.66 becaue a unt doe not prefer to ue low ulfur coal wthout a crubber. There are no addtonal complance cot from not beng able to wtch from hgh to low ulfur coal. Although the ze of ɛ maller than n other example, the ntal ze of P S A much maller than n the prevou two cae. So a maller value of ɛ may tll alter a unt complance choce. 26 BL England had 94% of coal under contract. 97

98 Baed on the above two cae, the gn of eplon can be ummarzed n the followng Propoton 4. Propoton 4: Gven a hgh ulfur coal contract, () () ɛ 0 f ( Sc h H c h S h H h ). The gn of ɛ unknown f ( Sc h H c h < S h H h ). Gven the mpact a hgh ulfur coal contract ha on exce demand defned n Propoton 2 and the gn of ɛ defned n Propoton 4, the mpact of a hgh ulfur coal contract derved n Propoton 5(a) and 5(b). Propoton 5(a): Aumng ( Sc h H c h S h H h ) and allowng for the crubber choce () () () For the range of allowance prce P A M weakly ncreae a unt exce demand. For the range of allowance prce PA S P A M wll weakly ncreae exce demand., CA, a hgh ulfur coal contract wll, CA, a hgh ulfur coal contract For the range of allowance prce (PA S ɛ) P A PA S, a hgh ulfur coal contract wll weakly decreae exce demand f A MIN ÂSMAX and weakly ncreae exce demand f A MIN ÂSMAX. (v) CA, For the range of allowance prce M P A (PA S contract wll weakly ncreae a unt exce demand. ɛ), a hgh ulfur coal (v) For the range of allowance prce 0 P A MCA,, a hgh ulfur coal contract wll weakly ncreae a unt exce demand. Proof of Propoton 5(a): () (), When a unt face P A M CA, a unt prefer to ntall a crubber and ue all low ulfur coal. From Propoton 2(), a hgh ulfur coal contract ncreae the mnmum emon level, whch wll weakly ncreae a unt allowance exce demand. CA, When a unt face PA S P A M all hgh ulfur coal. From Propoton 2(), gven ( Sc h Hh c, a unt prefer to ntall a crubber and ue S h ), a hgh ulfur coal Hh contract ncreae the maxmum emon level, whch wll weakly ncreae a unt allowance exce demand. () From Propoton 4(), when a unt face (PA S ɛ) P A PA S, a hgh ulfur coal contract decreae a unt ndfference allowance prce of ntallng a crubber 98

99 below the allowance prce by ɛ > 0, whch lead to a unt ntallng a crubber where t ntally would not and decreae a unt emon and a unt exce demand. From Propoton 2(), gven the crubber choce and ( Sc h S Hh c h ), a hgh Hh ulfur coal contract wll weakly ncreae a unt emon and exce demand. If A MIN ÂSMAX, the combned net effect of the counterng hft weakly negatve and weakly decreae exce demand. If A MIN ÂSMAX, the combned net effect weakly potve and weakly ncreae exce demand. (v) (v) When a unt face ( Sc h H c h S h H h ), a unt doe not ntall a crubber and prefer to ue low ulfur coal. From Propoton 2(), a hgh ulfur coal contract ncreae a unt mnmum emon level and exce demand. When a unt face 0 P A MCA,, a unt doe not ntall a crubber and prefer to ue hgh ulfur coal. From Propoton 2(), gven ( Sc h S Hh c h ), a hgh ulfur coal Hh contract ncreae a unt maxmum emon level and exce demand. Propoton 5(a) hown graphcally n Fgure 2.8(). Propoton 5(b) expree the mpact a hgh ulfur coal contract wll have on a unt exce demand correpondence by aumng that ɛ > 0. Propoton 5(b): Aumng ( Sc h H c h S h H h ), ɛ 0, and allowng for the crubber choce () () () For the range of allowance prce P A M weakly ncreae a unt exce demand. For the range of allowance prce PA S P A M wll weakly decreae exce demand., CA, a hgh ulfur coal contract wll, CA, a hgh ulfur coal contract For the range of allowance prce (PA S ɛ) P A PA S, a hgh ulfur coal contract wll weakly decreae exce demand. (v) CA, For the range of allowance prce M P A (PA S contract wll weakly ncreae a unt exce demand. ɛ), a hgh ulfur coal (v) For the range of allowance prce 0 P A MCA,, a hgh ulfur coal contract wll weakly decreae exce demand. Proof of Propoton 5(b): (), When a unt face P A M CA, a unt prefer to ntall a crubber and ue all low ulfur coal. From Propoton 2(), a hgh ulfur coal contract ncreae the mnmum emon level, whch wll weakly ncreae a unt allowance exce demand. 99

100 () () (v) (v) CA, When a unt face PA S P A M all hgh ulfur coal. From Propoton 2(), gven ( Sc h Hh c, a unt prefer to ntall a crubber and ue S h ), a hgh ulfur coal Hh contract decreae the maxmum emon level, whch wll weakly decreae a unt allowance exce demand. If ɛ > 0, when a unt face (PA S ɛ) P A PA S, a hgh ulfur coal contract decreae a unt ndfference allowance prce of ntallng a crubber below the allowance prce, whch lead to a unt ntallng a crubber where t ntally would not and decreae a unt emon and a unt exce demand. From Propoton 2(), Gven the crubber choce and ( Sc h H c h S h H h ), a hgh ulfur coal contract wll weakly decreae a unt emon and exce demand. The combned net effect weakly negatve and weakly decreae exce demand. CA, From Propoton 2(), when a unt face M P A (PA S ɛ), a unt doe not ntall a crubber and prefer to ue low ulfur coal. A hgh ulfur coal contract ncreae a unt mnmum emon level and exce demand. From Propoton 2(), when a unt face 0 P A MCA,, a unt doe not ntall S h ), a hgh ulfur coal Hh a crubber and prefer to ue hgh ulfur coal. Gven ( Sc h Hh c contract decreae a unt maxmum emon level and exce demand. Propoton 5(b) hown graphcally n Fgure 2.8(). There are condton under whch ome of thee allowance prce range do not ext. For example, P S A < MCA, n the thrd cae decrbed above. So there no prce range (MCA,, PA S ) n Fgure 2.8. However, Propoton 5(a) and 5(b) tll hold for the prce range that do ext. In Cae 2, ɛ large enough to hft the allowance prce from P A > MCA, to (P A ɛ) < MCA, demand correpondence to hft from Fgure 2.8 to Impact of a bndng low ulfur coal contract and caue the vual repreentaton of the exce Propoton 5 can be proven ung the ame approach that wa ued to determne the gn of ɛ wth a hgh ulfur coal contract ued to how that ɛ alway le than or equal to zero, and may ncreae the allowance prce at whch a unt ndfferent to ntallng a crubber. Once agan there wll be three cae under conderaton. In the frt cae, aume that both wth and wthout a low ulfur coal contract, a unt prefer to ue low ulfur pot market coal f t doe not ntall a crubber and hgh ulfur 100

101 pot market coal f t doe ntall a crubber becaue (MCA, (MCA, < P S A ). < P A < M, CA ) and If a unt ha no low ulfur contract coal (C c l = 0), a unt ue the maxmum amount of hgh ulfur coal wth a crubber and the maxmum amount of low ulfur coal wthout a crubber, and ndfferent to ntallng a crubber at allowance prce P S A : P z + P S AA SMAX (2 82) can be rearranged to fnd an expreon for P z : + PhC,MAX h = PAA S MIN + PlC,MAX l (2 82) P z = P S A(A MIN A SMAX ) PhC,MAX h + PlC,MAX l (2 83) A low ulfur coal contract wll change a unt coal ue and allowance purchae, whch change the ndfference allowance prce by ome value ɛ: P z + (P S A ɛ)âsmax + P hĉ,max + PlC c c l = (PA S ɛ)âmin + P lĉ,max + PlC c c l (2 84) (2 84) can be rearranged to fnd an expreon for P z : P z = (P S A ɛ)(âmin ÂSMAX ) + P lĉ,max P hĉ,max (2 85) The two expreon for P z n (2 83) and (2 85) can be et equal to olve for the value of ɛ: ɛ = P A S(ÂMIN A MIN + A SMAX ÂSMAX ) Pl (C,MAX l (ÂMIN ÂSMAX ) Ĉ,MAX l ) + Ph (C,MAX h Ĉ,MAX h ) (2 86) A SMAX Fllng n for allowance and coal ue, t poble to determne the gn of ɛ. A MIN = ( [ ] D ) (S ( Hl l )(m) A e  MIN D C c = lhl c ) (S Hl l ) + C c lsl c (m) A e = ( D ) (S Hh h )(m)(1 r ) A e  SMAX = [ ( D C c lhl c ) (S l )+C c lsl c H l ] (m)(1 r ) A e 101

102 C,MAX h = D Hh Ĉ,MAX h = D C c lh c l H h C,MAX l = D H l Ĉ,MAX l = D C c lh c l H l By fllng thee expreon nto (2 86), the expreon for ɛ can be mplfed to parameter for coal prce, ulfur content, heat content, and crubber capture rate. [ C c lhl c (PA S)(m)[ (r )( Sc l S Hl ɛ = c h ) ( S Hh h S Hh l ) ] ] + ( P Hl l P Hl h ) Hh (ÂMIN ÂSMAX ) (2 87) A more nterpretable expreon derved by multplyng through by ((ÂMIN and dvdng through by m( S h S Hh l ). Hl ɛ(âmin ɛ(âmin ÂSMAX ) = C c lhl c ÂSMAX ) = C c lhl c [ [(r )( S l (PA) S Hl S h H h ) ( S h S Hh l ) Hl [(P SA)(r ) ( S l S Hl h ) Hh ] 1 + ( P l P Hl h ) Hh (m)( S h S Hh l ) Hl ( S h S Hh l ) (P A S MCA, Hl ÂSMAX )) From the ntal aumpton that a unt ue low ulfur coal when t doe not ntall a crubber, t known that (P S A > MCA, ). Snce ( Sc l Hl c ) < S h H h ), then ɛ < 0 and t magntude ncreae a the ze of the low ulfur coal contract (C c l ) ncreae. A bndng low ulfur coal contract more lkely to mpact unt under CAIR. An example ung recent data reflectve of the coal avalablty and delvered prce for a ] ] (2 88) (2 89) unt n Alabama n 2000 wll help to how ɛ < Under the aumpton, a unt wll prefer to wtch fuel to abate emon f t doe not ntall a crubber becaue MCA, = $561.40, whch much lower than the aumed allowance prce P A = $ If a crubber ntalled, a unt prefer to ue hgh ulfur pot market coal becaue the margnal cot of abatement much greater than the allowance prce (M CA, = $11, 228). A unt wll not ntall a crubber becaue the allowance prce at whch a unt ndfferent to ntallng a crubber (P S A = $731.46) hgher than P A. A low ulfur coal contract 27 The data can be found n Table 15.A of the 2000 Electrc Power Annual Volume II. 102

103 for 50% of coal ue reult n ɛ = $42.00, whch ncreae the ndfference prce to (P A ɛ) = $ The example how that ome unt wll not be mpacted by a low ulfur coal contract becaue the ncreae n the ndfference prce doe not alter the crubber choce. In the econd cae, aume that wthout a low ulfur coal contract, a unt prefer to ue hgh ulfur pot market coal both f t doe or doe not ntall a crubber becaue (PA S < MCA, ). However, wth a low ulfur coal contract, a unt prefer to ue low ulfur pot market coal f t doe not ntall a crubber and hgh ulfur pot market coal f t doe ntall a crubber becaue (MCA, < P S A ɛ < MĈA, ). If a unt ha no low ulfur contract coal (C c l = 0), a unt ue the maxmum amount of hgh ulfur coal both wth and wthout a crubber, and the unt ndfferent to ntallng a crubber at allowance prce P S A : P z + P S AA SMAX + PhC,MAX h = PAA S MAX + PhC,MAX h (2 90) (2 90) how that the cot wth and wthout a crubber are equal for a gven PA S, and can be rearranged to fnd an expreon for P z : P z = P S A(A MAX A SMAX ) (2 91) Snce a unt ue hgh ulfur coal both wth and wthout a crubber, a low ulfur coal contract wll change the coal ue by a unt both wth and wthout a crubber and change the ndfference allowance prce by ome value ɛ: P z + (P S A ɛ)âsmax + P hĉ,max + PlC c c l = (PA S ɛ)âmin + P lĉ,max + PhC c c h (2 92) (2 92) can be rearranged to fnd an expreon for P z : P z = (P S A ɛ)(âmin ÂSMAX ) + P lĉ,max + P hĉ h (2 93) 103

104 The two expreon for P z n (2 91) and (2 93) can be et equal to olve for the value of ɛ: ɛ = P A S(ÂMIN A MAX + A SMAX (ÂMIN ÂSMAX ) + P lĉ,max P hĉ,max ÂSMAX ) (2 94) By fllng n for allowance and coal ue, t poble to determne the gn of ɛ. A MAX = ( D ) (S Hh h )(m) A e  MIN = ( D C c hhh c S Hl l + C c lsl) c m A e A SMAX = ( D ) (S Hh h )(m)(1 r ) A e  SMAX = ( D C c hhh c S H h+c c hsh) c (m)(1 r ) A e h Ĉ,MAX l = D C c lh c l H l Ĉ,MAX h = D C c lh c l H h By fllng nto (2 94), the expreon for ɛ can be mplfed to parameter for coal prce, ulfur content, heat content, and crubber capture rate: ɛ(âmin ÂSMAX ) = mpah S lc c l c [ D mpa( S S h S l Hh Hl [ ] ( S h S l ) + r Hh Hl ( Sc l S h ) H Hl c Hh ) ( P l H l P h ] ) Hh An nterpretable form derved by multplyng through by (ÂMIN through by m( S h S Hh l ) and combnng lke term: Hl ɛ(âmin ɛ(âmin ÂSMAX ÂSMAX ( Sc l S ) = PAr S Hl c h ) Hh ( S h S Hh l ) + (D HlC c l) c Hl ( Sc l S ) = PAr S Hl c h ) Hh clc cl( P l H l P h ) Hh (2 95) ÂSMAX ) and dvdng [P A ( P l P Hl h ) Hh m( S h S Hh l ) Hl ( S h S Hh l ) + (D HlC c l)(p c A MCA, Hl ] (2 96) ) (2 97) From our ntal aumpton that a unt ue all hgh ulfur pot market coal f t doe not ntall a crubber f t doe not have a hgh ulfur coal contract, then P S A < MCA,. The total amount of heat content from the contract coal (Hl ccc l ) weakly le than the total heat content needed to meet demand (D ). So the econd term weakly negatve. Meanwhle, the frt term negatve becaue ( Sc l H c l < S h ) and ( S Hh h Hh > S l H l ), whch mean 104

105 ɛ < 0 and an ncreae n the ze of the hgh ulfur coal contract (C c h) ncreae the magntude of ɛ. The econd example n Table 2-8 ue data that reflect th cae. Wthout a coal contract, P S A = $520.35, whch le than MCA, = $ and P A = $700.00, and a unt wll ue hgh ulfur coal both wth and wthout a crubber ntalled. In th cae, a unt wll ntall a crubber becaue P S A < P A = $ Now conder a low ulfur coal contract for 50% of all coal ue, whch reult n ɛ = $ and wll ncreae the ndfference prce above both MCA, and P A to (PA S ɛ) = $ Wth the low ulfur coal contract, a unt wll now not ntall a crubber and prefer to ue low ulfur pot market coal. In the thrd cae, aume that a unt, both wth and wthout a low ulfur coal contract, prefer to ue hgh ulfur coal wth and wthout a crubber becaue P S A < (P S A ɛ) < MCA,. Gven that a unt ha no low ulfur contract coal (C c l = 0), a unt ndfferent to ntallng a crubber at allowance prce P S A : P z + P S AA SMAX + PlC,MAX l = PAA S MAX + PhC,MAX h (2 98) (3 26) can be rearranged to fnd an expreon for P z where the only change n cot are the prce of a crubber and the change n a unt net allowance poton. P S A equal to the average cot of reducng a unt of emon from crubber ntallaton: P z = P S A(A MAX A SMAX ) (2 99) A low ulfur coal contract wll change the ndfference allowance prce by ome value ɛ becaue t alter the cot from net allowance purchae and fuel cot: P z + (P S A ɛ)âsmax + P hĉ,max + PlC c c l = (PA S ɛ)âmax + P hĉ,max + PlC c c l (2 100) (2 100) can be rearranged to fnd an expreon for P z : P z = (P S A ɛ)(âmax ÂSMAX ) (2 101) 105

106 The two expreon for P z n (2 99) and (2 101) can be et equal to olve for the value of ɛ: ɛ = P A S(ÂMAX A MAX (ÂMAX + A SMAX ÂSMAX ) ÂSMAX ) Fllng n for allowance and coal ue, t poble to determne the gn of ɛ. (2 102) A MAX = ( D ) (S Hh h )(m) A e  MAX = ( D C c lhl c S Hh h + C c lsl) c (m) A e A SMAX = ( D ) (S Hh h )(m)(1 r ) A e  SMAX = ( D C c lhl c S H h+c c lsl) c (m)(1 r ) A e h By fllng nto (2 102), the expreon for ɛ can be mplfed to parameter for coal prce, ulfur content, heat content, and crubber capture rate. Snce ( Sc l H c l the magntude of ɛ. ɛ(âmax ÂSMAX ) = PAmr S C c hhh( c Sc l S h ) (2 103) Hl c Hh < S h H h ), ɛ < 0 and an ncreae n the ze of the coal contract (C c l) ncreae The thrd example n Table 2-8 ue data reflectve of delvered cot and coal charactertc for a unt n Florda. A unt ntally prefer to ue hgh ulfur coal both wth and wthout a crubber becaue (P A = $600.00) < (MCA, = $3, ). A unt wll prefer to ntall a crubber n th example becaue the ndfferent prce P S A = $ A low ulfur coal contract for 50% of coal ue wll ncreae the ndfference prce to (P S A ɛ) = $642.42, whch wll reult n a unt not ntallng a crubber. Baed on the above three cae, the gn of eplon can be ummarzed n Propoton 6. Propoton 6: Gven a low ulfur coal contract, ɛ 0. Gven Propoton 3 and Propoton 6, the mpact of a low ulfur coal contract derved n Propoton 7(a) and 7(b). Propoton 7(a): Aumng ( Sc l H c l S l H l ) and allowng for the crubber choce

107 , () For the range of allowance prce P A M CA, a low ulfur coal contract wll weakly ncreae exce demand. () For the range of allowance prce (PA S ɛ) P A M wll weakly decreae exce demand., CA, a low ulfur coal contract () For the range of allowance prce PA S P A (PA S weakly ncreae exce demand. ɛ), a low ulfur coal contract wll (v) For the range of allowance prce M weakly ncreae exce demand. CA, P A PA S, a low ulfur coal contract wll (v) For the range of allowance prce 0 P A MCA,, a low ulfur coal contract wll weakly decreae exce demand. Proof of Propoton 7(a): () () CA, When a unt face P A M, a unt prefer to ntall a crubber and ue all low ulfur coal. From Propoton 3(), gven Sc l S Hl c l, a low ulfur coal contract Hl ncreae the mnmum emon level, whch wll weakly ncreae a unt allowance exce demand. When a unt face (PA S ɛ) P, A M CA, a unt prefer to ntall a crubber and ue all hgh ulfur coal. From Propoton 3(), a low ulfur coal contract decreae the maxmum emon level, whch wll weakly decreae a unt allowance exce demand. () From Propoton 6, when a unt face PA S P A (PA S ɛ), a low ulfur coal contract ncreae a unt ndfference allowance prce of ntallng a crubber above the allowance prce, whch lead a unt to not ntall a crubber where t ntally would have done o and ncreae a unt emon and a unt exce demand. From Propoton 3(), gven the crubber choce and Sc l S Hl c l, a low ulfur coal Hl contract wll weakly ncreae a unt emon and exce demand. The combned net effect weakly potve and weakly ncreae exce demand. (v) (v) CA, When a unt face M P A PA S, a unt doe not ntall a crubber and prefer to ue low ulfur coal. From Propoton 3(), gven Sc l S Hl c l, a low ulfur coal Hl contract ncreae a unt mnmum emon level and exce demand. When a unt face 0 P A MCA,, a unt doe not ntall a crubber and prefer to ue hgh ulfur coal. From Propoton 3(), a low ulfur coal contract decreae a unt maxmum emon level and exce demand. Propoton 7(a) hown graphcally n Fgure 2.8(). Propoton 7(b): Aumng that ( Sc l H c l < S l H l ) and allowng for the crubber choce

108 , () For the range of allowance prce P A M CA, a low ulfur coal contract wll weakly decreae exce demand. () () For the range of allowance prce (PA S ɛ) P A M wll weakly decreae exce demand., CA, a low ulfur coal contract For the range of allowance prce PA S P A (PA S ɛ), a low ulfur coal contract wll ncreae exce demand A SMAX ÂMIN and weakly decreae exce demand f A SMAX ÂMIN. (v) For the range of allowance prce M weakly decreae exce demand. CA, P A PA S, a low ulfur coal contract wll (v) For the range of allowance prce 0 P A MCA,, a low ulfur coal contract wll weakly decreae exce demand. Proof of Propoton 7(b): () () CA, When a unt face P A M, a unt prefer to ntall a crubber and ue all low ulfur coal. From Propoton 3(), gven Sc l < S Hl c l, a low ulfur coal contract Hl decreae the mnmum emon level, whch wll weakly decreae a unt allowance exce demand. When a unt face (PA S ɛ) P, A M CA, a unt prefer to ntall a crubber and ue all hgh ulfur coal. From Propoton 3(), a low ulfur coal contract decreae the maxmum emon level, whch wll weakly decreae a unt allowance exce demand. () From Propoton 6, when a unt face PA S P A (PA S ɛ), a low ulfur coal contract ncreae a unt ndfference allowance prce of ntallng a crubber above the allowance prce, whch lead a unt to not ntall a crubber where t ntally would have done o and ncreae a unt emon and a unt exce demand. From Propoton 3(), gven the crubber choce and Sc l < S Hl c l, a hgh Hl ulfur coal contract wll weakly decreae a unt emon and exce demand. If  MIN A SMAX, the combned net effect of the counterng hft weakly potve and weakly ncreae exce demand. If ÂMIN A SMAX, the combned net effect weakly negatve and weakly decreae exce demand. (v) (v) CA, When a unt face M P A PA S, a unt doe not ntall a crubber and prefer to ue low ulfur coal. From Propoton 3(), gven Sc l < S Hl c l, a low ulfur coal Hl contract decreae a unt mnmum emon level and exce demand. When a unt face 0 P A MCA,, a unt doe not ntall a crubber and prefer to ue hgh ulfur coal. From Propoton 3(), a low ulfur coal contract decreae a unt maxmum emon level and exce demand. 108

109 Propoton 7(b) hown graphcally n Fgure 2.8(). A wth a hgh ulfur contract, ome of the prce range may not ext for a partcular cae. However, the remanng part of the propoton hold. 2.7 Poble Implcaton on the Allowance Market and Indutry Complance Cot Under Phae I of Ttle IV, there were many generatng unt facng hgh ulfur coal contract for at leat a fracton of ther total coal ue. If a bndng hgh ulfur coal contract lead a unt to chooe a uboptmal complance choce, uch a purchang addtonal permt or ntallng a crubber ntead of wtchng fuel, and reult n weakly hgher complance cot. A unt uboptmal choce not only ncreae a unt complance cot, but hould alo ncreae complance cot for the ndutry a a whole. A ha been how n everal example, hgh ulfur coal contract for a large fracton (50-100%) of coal ue can greatly reduce a unt ndfference prce to ntallng a crubber. Some unt under Phae I ntally appear to have ntalled a crubber when t wa not a unt optmal complance opton, ncreang a unt complance cot. Addtonal crubber ntallaton hould have reulted n greater emon reducton, whch hould multaneouly lower demand and ncreae upply of allowance a a unt wtche from a net demander to a net eller. In dong o, the equlbrum allowance market prce hould be drven lower, whch may explan the lower than expected allowance prce realzed durng Phae I. Even though the allowance market prce wa lower than expected, the neffcent unt complance choce reulted n hgher than expected total ndutry complance cot. Under future CAIR regulaton, a unt complance opton may be retrcted by low ulfur coal contract agreed upon durng the 1990 to meet Ttle IV emon requrement. A unt may fnd ntallng a crubber and ung hgh ulfur coal to be t bet complance opton. However, low ulfur coal contract may lead a unt to chooe a uboptmal complance choce, uch a wtchng fuel or ntallng a crubber whle ung 109

110 low ulfur coal. Suboptmal complance decon wll lead to hgher complance cot at the unt-level and may lead to hgher total ndutry complance cot. A ha been how n everal example, low ulfur coal contract for a large fracton (50-100%) of coal ue can greatly ncreae a unt ndfference prce to ntallng a crubber. Some unt under CAIR may not ntall a crubber when t optmal for them to do o, ncreang a unt complance cot. Fewer crubber ntallaton would reult n greater emon, whch hould multaneouly ncreae demand and decreae upply of allowance a a unt would be a net demander ntead of a net eller, and the allowance market prce hould be drven hgher than would be expected. In th cae, a hgher than expected allowance market prce would occur wth hgher than expected total ndutry complance cot. 2.8 Concluon Th paper analytcally derve the mpact that long-term fuel contract contrant may have on a generatng unt complance choce and complance cot n meetng SO 2 emon retrcton. There are fve mportant reult from th analy. Frt, gven the crubber choce, t eay to determne how a coal contract wll mpact a unt exce demand for allowance. A hgh ulfur coal contract wll weakly ncreae a unt exce demand whle a low ulfur coal contract wll weakly decreae a unt exce demand. Second, ome coal contract may actually decreae a unt total cot relatve to ung only pot market coal whle ncreang a unt complance cot f a coal contract allow a unt to lock n a lower prce for a gven type of coal. The coal contract wll retrct complance choce, whch may reult n hgher complance cot. If the fuel cot avng greater than the ncreae n a unt complance cot, then the coal contract lower a unt total cot. Snce a unt only care about t total cot, a unt complance decon do not necearly mnmze a unt complance cot. 110

111 Thrd, under certan condton a unt complance cot wll ncreae when a coal contract reult n a uboptmal combnaton of pot market coal ue, allowance purchae, and crubber ntallaton. A uboptmal combnaton may reult from two tuaton: (1) a coal contract alter a unt complance choce or (2) the complance choce doe not change, but the coal under contract ha a hgher ulfur to heat content rato than the ame type of coal avalable n the pot market, whch ncreae a unt allowance purchae. Fourth, coal contract contrant change the allowance prce at whch a unt wll prefer to ntall a crubber. In the cae of Phae I, a hgh ulfur coal contract may ncreae a unt ndfference prce, whch create a greater ncentve for a unt to crub and ell t extra allowance. Th reult may explan why ome crubber were ntalled at ub-optmal unt whle the allowance market prce wa much lower than expected durng Phae I. The oppote may occur under CAIR, where a low ulfur coal contract may ncreae a unt ndfference prce and lower the ncentve for a unt to ntall a crubber even f t would be the optmal complance choce. In ether cae, a uboptmal complance choce wll be made and a unt complance cot wll weakly ncreae. Ffth, there certanty how a coal contract wll mpact a unt exce demand for allowance even when the crubber choce condered for mot allowance prce range. However, due to the dcrete crubber choce and the change n the ndfference prce due to a coal contract, t uncertan how a coal contract wll alter a unt exce demand f the allowance market prce fall n one partcular prce range. A hgh ulfur coal contract wll hft exce demand a derved n Propoton 2 except f the allowance market prce fall n the prce range (P S A ɛ, P S A ) and Sc h H c h > S h. If the allowance market Hh prce fall n th range, there are two counterng effect on exce demand, the decreae n exce demand reultng from the crubber ntallaton and the ncreae n exce demand from the hgher ulfur content of hgh ulfur contract coal relatve to hgh ulfur pot market coal. A low ulfur coal contract wll hft exce demand a derved n Propoton 111

112 3 except f the allowance market prce fall n the prce range (P S A, P S A ɛ) and Sc l H c l < S l. Hl If the allowance market prce fall n th range, there are two counterng effect on exce demand, the ncreae n exce demand reultng from no crubber ntallaton and the decreae n exce demand from the lower ulfur content of low ulfur contract coal relatve to low ulfur pot market coal. 112

113 Table 2-1. Phae I Complance Cot Etmate Source M CA/ton Pred. Cot Leat-Cot Actual Cot ICF (1989, 1990) $199-$226 $ mllon N/A N/A EPRI (1993, 1995) $879-$1238 $900-1,340 mllon N/A N/A GAO (1994) $299 $1,170 mllon N/A N/A Wnebrake, et al. (1995) $143 $502 mllon N/A N/A Pre-Polcy Etmate $143-$1238 $450-$1340 mllon N/A N/A Ellerman et al. (1997) $ N/A N/A $730 mllon Sotkewcz and Holt (2005) $150-$180 N/A $423-$553 mllon $990 mllon Carlon et al. (2000) $71 N/A $571 mllon $910 mllon Pot-Polcy Etmate $71-$800 N/A $423-$571 mllon $730-$990 mllon Source: Boh and Burtraw (1997); Carlon et al. (2000); Sotkewcz and Holt (2005); Smth and Ellerman (1998) 113

114 Table 2-2. Hgh Sulfur Coal Contract: Aumpton Coal Type Prce/mmBtu H g f Prce/Ton S g f Cl $ $ % Ch $ $ % Ch c (Ex. 1) $ $ % (Ex. 2) $ $ % C c h P A $ A e 20,000 ton 24,000,000 mmbtu D Table 2-3. Hgh Sulfur Coal Contract: Reult Cot Complance Total Cot Complance Total Cot Cot (Ex. 1) (Ex. 1) Cot (Ex. 2) (Ex. 2) Uncontraned $4.62 mllon $35.82 mllon $4.62 mllon $35.82 mllon Contraned $5.01 mllon $38.61 mllon $5.01 mllon $35.01 mllon Change $390,000 $2.79 mllon $390,000 -$810,000 Allowance Ue (Ton) MCA Mnmum 11,400 ton MCA, $ Maxmum 38,000 ton MCA c, (Ex. 1) $90.23 Contraned Mn. 24,700 ton MCA c, (Ex. 2) $ Table 2-4. Low Sulfur Coal Contract Example: Aumpton Coal Type Prce/mmBtu H g f Prce/Ton S g f Cl $ $ % Ch $ $ % Cl c (Ex. 1) $ $ % (Ex. 2) $ $ % C c l P A $ A e 20,000 ton 24,000,000 mmbtu D 114

115 Table 2-5. Low Sulfur Coal Contract Example: Reult Cot Complance Cot (Ex. 1) Total Cot (Ex. 1) Complance Cot (Ex. 2) Total Cot (Ex. 2) Uncontraned $3.6 mllon $34.8 mllon $3.6 mllon $34.8 mllon Contraned $4.54 mllon $38.14 mllon $4.54 mllon $34.54 mllon Change $940,000 $3.34 mllon $940,000 -$260,000 Allowance Ue (Ton) M CA Mnmum 11,400 ton MCA, $ Maxmum 38,000 ton MCA,c (Ex. 1) $ Contraned Max. 24,700 ton MCA,c (Ex. 2) $

116 Table 2-6. Example Eplon Magntude: Cae 1 Scrubber Charactertc Generatng Unt Charactertc Captal Cot $260/kW Capacty MW O and M Cot 2 mll/kwh Heat Rate 10,000 Btu/kWh Pz $15,886,295 Cap. Factor 75% r 95% C c h 50%, 75% of Coal Ue PA $ D 24,000,000 mmbtu Parameter Charactertc Value Reult Low Sulfur Coal Prce $1.50/mmBtu 50% Contract (Spot) Heat Content 24 mmbtu/ton P A S = $1, ɛ = $1, Sulfur Content 0.65% P A S ɛ = $ Pct. P A S = 76% Hgh Sulfur Coal Prce $1.30/mmBtu 75% Contract (Spot) Heat Content 24 mmbtu/ton P A S = $1, ɛ = $1, Sulfur Content 2.5% P A S ɛ = $ Pct. P A S = 85% Hgh Sulfur Coal Prce $1.50/mmBtu (Contract) Heat Content 24 mmbtu/ton Sulfur Content 4.0% 116

117 Table 2-7. Example Eplon Magntude: Cae 2 Scrubber Charactertc Generatng Unt Charactertc Captal Cot $260/kW Capacty MW O and M Cot 2 mll/kwh Heat Rate 10,000 Btu/kWh Pz $15,886,295 Cap. Factor 75% r 95% C c h 50% of Coal Ue PA $ D 24,000,000 mmbtu Parameter Charactertc Value Reult Low Sulfur Coal Prce $2.79/mmBtu BL England (Spot) Heat Content 24 mmbtu/ton 50% Contract Sulfur Content 0.5% P A S = $ ɛ = $44.66 Hgh Sulfur Spot Coal Prce $1.52/mmBtu PA ɛ = $ Pct. P A S = 10% (Spot) Heat Content 24 mmbtu/ton Sulfur Content 1.91% Hgh Sulfur Coal Prce $1.72/mmBtu (Contract) Heat Content 24 mmbtu/ton Sulfur Content 2.32% 117

118 Table 2-8. Example Eplon Magntude Scrubber Charactertc Gen. Unt Charactertc Captal Cot $141.34/kW Capacty MW O and M Cot 1.23 mll/kwh Heat Rate 10,000 Btu/kWh Pz $9,016, Cap. Factor 75% r 95% C c h 50% of Coal Ue PA $700.00, $ D 24,000,000 mmbtu Parameter Charactertc Value Reult Low Sulfur Coal Prce $1.50/mmBtu Cae 1 (Alabama) (Alabama) Heat Content 24 mmbtu/ton P A S = $ ɛ = -$42.00 Sulfur Content 0.7% PA ɛ = $ P ct. P A S = 6% Hgh Sulfur Spot Coal Prce $1.10/mmBtu (Alabama) Heat Content 24 mmbtu/ton Sulfur Content 1.6% Hgh Sulfur Spot Coal Prce $2.00/mmBtu Cae 2 (CAIR) (CAIR Example) Heat Content 25 mmbtu/ton P A S = $ ɛ = -$ Sulfur Content 1.0% PA ɛ = $ Pct. P A S = 68% Low Sulfur Coal Prce $2.20/mmBtu (CAIR Example) Heat Content 25 mmbtu/ton Sulfur Content 0.6% Hgh Sulfur Spot Coal Prce $2.30/mmBtu Cae 3 (Florda) (Florda) Heat Content 24 mmbtu/ton P A S = $ ɛ = -$76.82 Sulfur Content 1.4% PA ɛ = $ P ct. P A S = 14% Low Sulfur Coal Prce $3.50/mmBtu (Florda) Heat Content 25 mmbtu/ton Sulfur Content 0.7% 118

119 Fgure 2-1. The SO 2 Allowance Prce. Data wa gven to me by Dalla Burtraw of Reource for the Future Fgure 2-2. Exce Demand Correpondence and Complance Cot Savng from Fuel Swtchng Over Allowance Purchang 119

120 Fgure 2-3. Hgh Sulfur Contract: Shft n Mnmum Exce Demand Fgure 2-4. No Contract: Complance Cot Fgure 2-5. Hgh Sulfur Contract: Complance and Total Cot 120

121 Fgure 2-6. Hgh Sulfur Contract: Relatve Savng from Contract Coal Fgure 2-7. Cot Savng from Ung Allowance Over Fuel Swtchng Fgure 2-8. Low Sulfur Contract 121

122 Fgure 2-9. No Contract: Complance Cot Fgure Low Sulfur Coal Contract: MCA,c Fgure Low Sulfur Coal Contract: MCA,c 122

123 Fgure Complance Cot: P A = MCA, Fgure Hgh Sulfur Coal Contract Fgure Low Sulfur Coal Contract 123

124 Fgure Exce Demand Correpondence: MCA, < PA S Fgure Exce Demand Correpondence: MCA, P S A 124

125 Fgure Impact of a Hgh Sulfur Coal Contract: MCA, < PA S Fgure Impact of a Hgh Sulfur Coal Contract: MCA, > P S A Fgure Impact of a Low Sulfur Coal Contract: MCA, > P S A 125

126 Fgure Impact of a low ulfur Coal Contract: MCA NS < PA S 126

127 CHAPTER 3 THE EFFECT OF FUEL CONTRACTING CONSTRAINTS ON SO 2 TRADING PROGRAM COMPLIANCE: EMPIRICAL EVIDENCE 3.1 Introducton The U.S. SO 2 Tradng Program created by Ttle IV of the 1990 Clean Ar Act Amendment led to lower complance cot than what would have occurred under a Command-and-Control approach. However, all complance cot avng were not realzed n the early year of the program. There have been everal conjecture a to why the hypothetcal outcome wa not obtaned, ncludng hort-run rgdte from fuel contract. Chapter 2 how how fuel contract could alter a generatng unt complance decon n the U.S. SO 2 Tradng Program, but gnore any aggregate allowance market and ndutry-wde complance cot mpact. Th paper expand on Chapter 2 by lookng at the allowance market equlbrum mpact and total ndutry complance cot from fuel contract through analytc and emprcal modelng. Gven the crubber choce, an allowance market equlbrum wll ext. Allowng for the crubber choce make t mpoble to guarantee an equlbrum, but one tll may ext. Bndng fuel contract may lead to altered unt-level exce demand and, n o dong, the allowance market prce (P A ). Meanwhle, bndng contract can alter complance decon and ncreae total ndutry complance cot. Th paper ue generatng unt-level mulaton to replcate reult from prevou tude and how that hort-run fuel contract appear to explan a large porton of the prevouly unexplaned exce complance cot found n prevou mulaton. Smulatng the leat-cot complance choce wthout ncludng fuel contract contrant reult n mnmum annual ndutry complance cot of $288.3 mllon, whch vare greatly from the actual complance cot of $1.30 bllon found n thee mulaton. Once fuel contract contrant are ntroduced nto the mulaton, the mnmum annual ndutry complance cot become $1.01 bllon. Baed on thee reult, fuel contract contrant explan $651.1 mllon, or 64% of the exce complance cot realzed n the program for

128 Alo, th paper conder a more approprate level for complance decon. The lterature ha only condered complance cot at the generatng unt level. However, actual complance decon would be made at the plant level becaue of the economc relaton and the phycal proxmty between generatng unt. Coal delvered at the plant level, where multple generatng unt may be located. Snce a plant only concerned about mnmzng t total cot at the plant, the mnmzaton at a partcular generatng unt not neceary for a plant to make optmal choce. Th paper analytcally analyze the plant level decon-makng proce to how why t approprate to conder decon a the plant level ntead of the generatng unt level, the nteracton of choce for economcally related generatng unt, and how cot-mnmzaton at the plant level may devate from cot-mnmzaton at the generatng unt level. The paper wll be tructured n the followng manner: Secton 2 wll look at the condton for an allowance market equlbrum whle Secton 3 wll look at the comparatve tatc of the allowance market. Secton 4 wll look at complance cot, both for an ndvdual generatng unt and the entre ndutry. Secton 5 and Secton 6 wll explan the data ued n the generatng unt level mulaton and the reult from the actual mulaton, repectvely. Secton 7 wll analyze the plant level decon makng proce, how t dffer from the generatng unt level model, and what addtonal nformaton the model wll add to the lterature. 3.2 Revew of Generatng Unt Model Generatng Unt Problem mn z P z + P A A z,a,ch + PhC h + PlC l + PhC c h c + PlC c l c (3 1),C l,cc h,cc l ubject to...a e + A (1 z r )(m)(c hs h + C c hs c h + C ls l + C c ls c l) λ 1 (3 2) (C hh h + C c hh c h + C lh l + C c lh c l) D λ 2 (3 3) C c h = C c h µ h (3 4) 128

129 C c l = C c l µ l (3 5) C h, C l 0 (3 6) z {0, 1} (3 7) Equaton (3 1) repreent the unt cot functon. Thee cot nclude the cot of crubber ntallaton (z P z ), net cot of allowance purchae (P A A ), and cot of coal purchae (Ph C h + P l C l + P h c Cc h + P l ccc l ). The emon contrant hown n (3 2), where the number of allowance held (A e + A ) mut be a large a the amount of total emon by the generatng unt [(1 z r )(m)(ch S h + Cc h Sc h + C l S l + Cc l Sc l )]. Total emon a functon of the amount of each coal type ued a well a the emon reducton due to a crubber, f one ntalled. The Lagrange multpler on the emon contrant repreented by λ 1. The demand contrant requre that the amount of heat nput to generate electrcty (Ch H h + Cc h Hc h + C l H l + Cc l Hc l ) mut cover the conumer demand (D ) for electrcty expreed a heat nput, whch een n (3 3). The Lagrange multpler on the demand contrant repreented by λ 2. Coal contract contrant requre the unt to ue a pecfc amount of each contract coal type, C c h for hgh ulfur coal n (3 4) and C c l for low ulfur coal n (3 5). A unt wll ue exactly the contracted amount becaue (1) f the contract coal more expenve than pot market coal, then a unt wll not want to ue any more contract coal than neceary and (2) f contract coal cheaper than pot market coal, the coal producer would prefer to ell any addtonal non-contracted coal through the pot market. The Lagrange multpler for each contract contrant on each coal type repreented by µ h for hgh ulfur contract coal and µ l for low ulfur contract coal Optmal Complance Choce The followng a ummary of a generatng unt complance choce derved n Chapter 2 both wth and wthout fuel contract. 129

130 Gven the crubber choce, a generatng unt that doe not face any coal contract contrant wll make t optmal choce baed on the relatonhp of the allowance prce (P A ) and the margnal cot of abatement from wtchng fuel from hgh ulfur pot market coal to low ulfur pot market coal (MCA, ). If P A > MCA,, then t cheaper to meet the emon contrant by decreang emon by wtchng fuel than purchang allowance. A unt wll ue all low ulfur coal and purchae the mnmum amount of allowance, whch wll reult n the followng complance choce: C h = 0, C l = C,MAX l = D, and A = A MIN. If P A < MCA,, then t cheaper to meet the emon contrant by purchang allowance than decreang emon by wtchng fuel. A unt wll ue all hgh ulfur coal and purchae the maxmum amount of allowance, whch wll reult n the followng complance choce: C h = C,MAX h = D, C l = 0, and A = A MAX. Introducng a hgh ulfur coal contract contrant wll retrct pot market coal ue by C c h and wll alter exce demand (A ). The maxmum amount of hgh ulfur pot market coal ue decreae from D = C,MAX h of low ulfur pot market coal decreae from D If P A to D C c h = Ĉ,MAX h The maxmum amount = C,MAX l to D C c h = Ĉ,MAX l. > MCA,, a unt wll ue t contract contraned maxmum amount of low ulfur pot market coal (Ĉ,MAX l ) and exce demand wll ncreae from A MIN If P A to ÂMIN. < MCA,, a unt wll ue t contract contraned maxmum amount of hgh ulfur pot market coal (Ĉ,MAX h ) and exce demand wll hft from A MAX S h H h Sc h, then A MAX Hh c ÂMAX. If S h Hh Sc h, then A MAX Hh c ÂMAX. to ÂMAX. If Introducng a low ulfur coal contract contrant wll retrct pot market coal ue by C c l and wll alter exce demand (A ). The maxmum amount of hgh ulfur pot market coal ue decreae from D = C,MAX h to D C c l = Ĉ,MAX h of low ulfur pot market coal decreae from D = C,MAX l The maxmum amount to D C c l = Ĉ,MAX l. If P A > MCA,, a unt wll ue t contract contraned maxmum amount of low ulfur pot market coal (Ĉ,MAX h ) and exce demand wll hft from A MIN to ÂMIN. If S l Hl Sc l, Hl c 130

131 then A MIN ÂMIN. If S l Hl Sc l, then A MIN Hl c ÂMIN. If P A < MCA,, a unt wll ue t contract contraned maxmum amount of hgh ulfur coal (Ĉ,MAX h ) and exce demand wll decreae from A MAX to ÂMAX. Allowng the crubber choce to be endogenou reult n more complex mpact of coal contract on complance decon. A generatng unt that doe not face any coal contract contrant wll make t optmal choce baed on two condton: (1) the relatonhp of P A relatve to the allowance prce at whch a unt ndfferent to ntallng a crubber (P S A ) and (2) the relatonhp of P A relatve to MCA, gven the crubber choce. If P S A > P A, a unt wll not ntall a crubber becaue total cot to the generatng unt wll be lower wthout ntallng a crubber. The reultng coal ue and exce demand wll be the ame a decrbed above: C h = D, C l = 0, and A = A MAX and C h = 0, C l = D, and A = A MIN f P A > MCA, where MCA, f P A < MCA, the margnal cot of abatement from wtchng fuel wthout a crubber. If P S A < P A, a unt wll ntall a crubber becaue total cot wll be lower wth a crubber ntalled. A explaned n Chapter 2 the margnal cot of abatement wth a crubber (M, CA ) wll be much hgher than the margnal cot of abatement wthout a crubber (MCA, ). The reultng coal ue and exce demand wll now be C h = D, C l = 0, and A = A SMAX P A > M CA,. f P A < M CA, and C h = 0, C l = D, and A = A SMIN The reult a combnaton of the two exce demand correpondence where at ome allowance prce (PA S ) where a crubber wll be ntalled there a large non-contnuou decreae n a unt exce demand. Introducng a hgh ulfur coal contract contrant wll have the ame drect mpact a when crubber are gven. Coal ue wll be retrcted by C c h. The exce demand correpondence wll be mpacted n the ame manner except there wll be four hft ntead of two. Mnmum exce demand wth a crubber (A SMIN ) and wthout a crubber f 131

132 (A MIN ) wll ncreae to ÂSMIN a crubber (A SMAX and ÂMIN, repectvely. Maxmum exce demand wth ) and wthout a crubber (A MAX ) wll hft n the ame drecton, whch depend on the relatonhp of S h H h to Sc h. A hgh ulfur coal contract create a Hh c greater ncentve to ntall a crubber becaue of the hgher mnmum exce demand, and decreae the allowance prce at whch a unt wll ntall a crubber from PA S to P A S ɛ. For th prce range, a unt wll ntall a crubber where t would not have wthout the hgh ulfur coal contract contrant. Introducng a low ulfur coal contract contrant wll have the ame drect mpact a when crubber are gven. Coal ue wll be retrcted by C c l. The exce demand correpondence wll be mpacted n the ame manner except there wll be four hft ntead of two. Mnmum exce demand wth a crubber (A SMIN ) and wthout a crubber (A MIN ) wll hft n the ame drecton, whch depend on the relatonhp of S l Hl Maxmum exce demand wth a crubber (A SMAX ) and wthout a crubber (A MAX ) to Sc l. Hl c wll decreae to ÂSMAX and ÂMAX, repectvely. A low ulfur coal contract decreae the ncentve to ntall a crubber becaue of the lower maxmum exce demand, and ncreae the allowance prce at whch a unt wll ntall a crubber from PA S to P A S + ɛ. For th prce range, a unt wll no longer ntall a crubber where t would have wthout the low ulfur coal contract contrant. In ummary, coal contract wll retrct a unt coal ue opton, whch may alter a unt complance choce and exce demand for allowance. Le freedom n complance decon may reult n an ncreae n a unt complance cot. 3.3 Allowance Market Equlbrum An allowance market equlbrum wll ext under certan condton. Frt, aume that there perfect nformaton and that all generatng unt are prce taker n the allowance market. The defnton of an equlbrum for the allowance market a follow: Defnton 5.8.1: An equlbrum for the allowance market a prce PA 0, allowance exce demand (A ), pot market coal fuel purchae (C h, C l ), and crubber 132

133 ntallaton choce (z ) uch that: (1) For each {1,..., n}, A, z, Ch, C l olve... mn z P z + P z,a AA + PhC,Ch h + PlC l + PhC c h c + PlC c l c (3 8),C l ubject to...a e + A (1 z r )(m)(c hs h + C c hs c h + C ls l + C c ls c l) (3 9) (C hh h + C c hh c h + C lh l + C c lh c l) D (3 10) C c h C c h (3 11) C c l C c l (3 12) C h, C l 0 (3 13) z {0, 1} (3 14) A Unretrcted (3 15) (2) The allowance market clear. At P A, n A 0 and PA =1 n A = 0 (3 16) =1 Theorem 5.1: Aumng the crubber choce (z ) a gven, an equlbrum ext for the allowance market. From Kakutan Fxed Pont Theorem, a fxed pont ext f the market exce demand correpondence upper em-contnuou, compact-valued, and convex-valued. Each generatng unt exce demand correpondence are upper em-contnuou, compact-valued, and convex-valued, whch mple that the market exce demand alo upper em-contnuou, compact-valued, and convex-valued. Gven thee condton there a fxed pont, and therefore, an equlbrum ext. Note that there may be multple equlbra, but there at leat one equlbrum. The Proof of Theorem 1 n Appendx B. The extence of an allowance market equlbrum no longer guaranteed once the dcrete crubber choce ntroduced nto the model. The non-convex nature of the crubber decon varable make t mpoble to guarantee that an equlbrum ext becaue the exce demand no longer convex for the range (A SMAX, A MIN ). In uch 133

134 a cae, there wll ether be potve or negatve market exce demand. In ether cae, t could be condered a qua-equlbrum becaue t can be aumed that an allowance broker wll ell any exce demand or buy any exce upply of allowance. 3.4 Comparatve Statc: Effect on the Allowance Market Comparatve Statc: Effect of Relatve Fuel Cot on the Allowance Market Snce a generatng unt exce demand for allowance rele on the relatve cot of purchang allowance (P A ) compared to reducng emon through wtchng from hgh ulfur to low ulfur coal (MCA, ). If P A > MCA,, then t cheaper to wtch to low ulfur coal. If P A < MCA,, then t cheaper to purchae allowance. Therefore, changng the parameter of the margnal cot of abatement may alter the exce demand and, n turn, mpact the allowance prce. Propoton 1: Aumng the crubber choce, a hgher fuel prce dfferental for low ulfur pot market coal relatve to hgh ulfur pot market coal wll weakly ncreae P A. Proof of Propoton 1: From Chapter 2, the margnal cot of abatement derved a (3 17). MCA, = Pl P Hl h Hh (1 z r )(m)( S h S Hh l ) Hl Conder the mpact of an ncreae n the prce of low ulfur pot market coal on the MCA,. An ncreae n the prce dfference between fuel per unt of heat from ( P l H l P h ) to ( P Hh l Hl P h ) where P Hh l Hl < P l H l n an ncreae n the margnal cot of abatement from MCA, δ = P l P l H l (3 17) ncreae the numerator of (3 17) and reult to MCA, + δ where. A hgher MCA, (1 z r )(m)( S h H h S l make the relatve cot to the generatng unt H l ) purchang allowance lower, and wll lead to a weak ncreae n a unt exce demand. Exce demand wll ncreae f MCA, < P A and MCA, + δ > P A and not change f MCA, +δ < P A or MCA, > P A. Greater exce demand n the allowance market reult n an ncreae n the total allowance market demand and pobly a decreae n allowance market upply, both of whch wll weakly ncreae P A. 134

135 3.4.2 Comparatve Statc: Effect of Coal Contract on the Allowance Market Gven the Scrubber Choce Aumng the crubber choce a gven, each bndng coal contract wll have an unambguou mpact on the allowance prce. A bndng hgh ulfur coal contract weakly ncreae the allowance prce, ceter parbu. A bndng low ulfur coal contract weakly decreae the allowance prce n the market, ceter parbu Impact of hgh ulfur coal contract on allowance market A generatng unt exce demand for allowance may be altered by a bndng hgh ulfur coal contract contrant. From Chapter 2, a bndng hgh ulfur coal contract wll reult n more hgh ulfur coal ue than would be optmal for a generatng unt and ncreae a generatng unt exce demand. An ncreae n a generatng unt exce demand may ncreae the allowance market prce. Propoton 2: Aumng the crubber choce a gven and ( S h H h contract reult n a weakly hgher allowance prce. = Sc h H c h ), a hgh ulfur Proof of Propoton 2: A ha already been hown n Chapter 2, gven the crubber choce and S h H h generatng unt exce demand. = Sc h, a hgh ulfur contract reult n a weak ncreae n a Hh c If P A < MCA,, a generatng unt prefer to ue hgh ulfur coal, create t maxmum poble emon, and have an exce demand of A MAX. Aumng the ame relatve ulfur content for pot and contract coal, a hgh ulfur coal contract wll not change total emon or exce demand (ÂMAX = A MAX ) and P A reman unchanged. If P A > MCA,, a generatng unt prefer to wtch fuel from hgh to low ulfur coal, create t mnmum poble emon, and have an exce demand of A MIN. However, the hgh ulfur coal contract would force greater than the mnmum amount of emon and weakly ncreae exce demand to ÂMIN. A hgher exce demand wll lead to a decreae n the allowance market upply or both a decreae n allowance market upply and an ncreae n the allowance market demand. In both cae P A weakly ncreae. 135

136 Impact of low ulfur coal contract on allowance market A generatng unt exce demand for allowance may be altered by a bndng low ulfur coal contract contrant. From Chapter 2, a bndng low ulfur coal contract wll reult n more low ulfur coal ue than would be optmal for a generatng unt and decreae a generatng unt exce demand. A decreae n a generatng unt exce demand may decreae the allowance market prce. Propoton 3: Aumng the crubber choce a gven and S l H l contract reult n a weakly lower allowance prce. = Sc l, a low ulfur Hl c Proof of Propoton 3: A ha already been hown n Chapter 2, gven the crubber choce and S l H l generatng unt exce demand. = Sc l, a low ulfur contract reult n a weak decreae n a Hl c If P A > MCA,, a generatng unt prefer to wtch fuel from hgh to low ulfur coal, create t mnmum poble emon, and have an exce demand of A MIN. Aumng the ame relatve ulfur content for pot and contract coal, a low ulfur coal contract wll not change total emon or exce demand (ÂMIN = A MIN ) and P A reman unchanged. If P A < MCA,, a generatng unt prefer to ue hgh ulfur coal, create t maxmum poble emon, and have an exce demand of A MAX. However, the low ulfur coal contract would force le than the maxmum amount of emon and weakly decreae exce demand to ÂMAX. A lower exce demand wll lead to an ncreae n the allowance market upply or both an ncreae n allowance market upply and a decreae n the allowance market demand. In both cae P A weakly decreae Comparatve Statc: Effect of Coal Contract on the Allowance Market wth Endogenou Scrubber Choce Prevouly when the crubber choce wa taken a gven, the mpact of coal contract on the allowance prce wa unambguouly non-negatve or non-potve. Hgh ulfur contract may only lead to an ncreae n the allowance prce whle low ulfur contract 136

137 may lead to only a decreae n the allowance prce. However, takng nto account the crubber choce caue the gn of the mpact on the allowance prce to become ambguou. When you conder the crubber choce n the decon-makng proce, t uncertan how a coal contract wll affect the allowance market becaue the contract may ncreae or decreae exce demand dependng on the allowance prce range derved n Chapter 2. Although t certan that f the coal contract bnd, then there wll be a hft to a ub-optmal exce demand for three dfferent allowance prce range Hgh ulfur coal contract bnd Each of the three prce range derved n Chapter 2 mut be dcued to undertand how a hgh ulfur coal contract wll effect the allowance market, both n term of the allowance market upply, allowance market demand, and the allowance prce. Aume S h H h = Sc h. Hh c If a generatng unt ha a hgh ulfur coal contract, the unt exce demand ncreae for two allowance prce range: (P A > M The ncreae n exce demand wll be from A SMIN The ncreae n exce demand wll be from A MIN CA, ) and (P S A ɛ > P A > MCA, ). to ÂMIN, when (P A > M CA ). to ÂMIN or A MIN to A MAX when (PA S ɛ > P A > MCA, ), dependng on the relatonhp between (PA S ɛ) and MCA,. It wll be the latter n the pecal cae where the generatng unt alway prefer to ue hgh ulfur coal. When the market allowance prce n thee two range that reult n an ncreae n a generatng unt exce demand, there wll be ether an ncreae n the market demand for allowance, or both an ncreae n market demand and a decreae n market upply for allowance. In both tuaton, the allowance prce wll be drven hgher. The thrd prce range that ha a hft n the exce demand (P S A ɛ, P S A ). A generatng unt decreae t exce demand from A MIN to A SMAX, whch a reult of a unt ntallng a crubber for a prce range for whch t ntally would not ntall a crubber. 137

138 When the market allowance prce n th range that reult n a decreae n a generatng unt exce demand, there wll be ether an decreae n the market demand for allowance, or both an decreae n market demand and a ncreae n market upply for allowance. In both tuaton, the allowance prce wll be drven lower Low ulfur coal contract bnd Each of the three prce range derved n Chapter 2 mut be dcued to undertand how a low ulfur coal contract wll effect the allowance market, both n term of the allowance market upply, allowance market demand, and the allowance prce. Aume S l H l = Sc l. Hl c If a generatng unt ha a low ulfur coal contract, the unt exce demand decreae for two allowance prce range: (M CA, P A ). The decreae n exce demand wll be from A SMAX > P A > P S A + ɛ) and (mn{p S A, MCA, } > to ÂMAX when (M CA, > P A > P S A + ɛ). The decreae n exce demand wll be from AMAX to ÂMAX when (mn{p S A, MCA, } > P A ). When the market allowance prce n thee range that reult n a decreae n a generatng unt exce demand, there wll be ether an decreae n the market demand for allowance, or both an decreae n market demand and a ncreae n market upply for allowance. In both tuaton, P A wll be drven lower. The thrd prce range that ha a hft n the exce demand (P S A, P S A + ɛ). A generatng unt ncreae t exce demand from ether A SMAX to A MIN or A SMAX to  MAX dependng on the relatonhp between (P S A + ɛ) and MCA,. Th ncreae a reult of a unt not ntallng a crubber for a prce range for t ntally would have ntalled a crubber. When the market allowance prce n th range that reult n an ncreae n a generatng unt exce demand, there wll be ether an ncreae n the market demand for allowance, or both an ncreae n market demand and a decreae n market upply for allowance. In both tuaton, P A wll be drven hgher. 138

139 3.5 Complance Cot Total complance cot for a generatng unt are the addtonal cot due to the program, ncludng cot from wtchng fuel, the cot from t net allowance poton, and crubber ntallaton cot (een n (3 18)). z P z + P AA + max{(p lc l + P hc h P h Ĉ,MAX h ), 0} (3 18) Complance cot may be potve or negatve dependng on t complance decon and t ntal allowance allocaton. The crubber ntallaton cot are repreented by P z, and wll only attrbute to a unt complance cot f a crubber ntalled n repone to the program (z = 1). The cot of a unt net allowance poton the dfference between a generatng unt ntal allowance allocaton and t actual emon multpled by the allowance prce (P A A ). The cot of wtchng fuel the larger of two value: (1) total cot of actual coal purchae (P h C h + P l C l + P c h Cc h + P c l Cc l) mnu the cot of purchang only hgh ulfur pot market coal gven any contracted coal (P hĉ,max + Ph c Cc h + Pl ccc l), or (2) zero. The latter wll only occur f t weakly cheaper for the generatng unt to ue low ulfur coal wthout the emon retrcton ( P h H h P l H l ). It mportant to conder that the contracted coal wll be ued regardle of the program and wll have no drect mpact on complance cot. However, a contract could have an ndrect mpact by alterng complance decon Complance Cot wth Coal Contract Relatve to Complance Cot from Prevou Stude Prevou tude have aumed no retrcton on coal ue, whch reult n a dfferent etmaton of complance cot. The optmal complance choce n th cae wll not account for any coal ue retrcton. The contant c the mnmum cot for a generatng unt to meet t electrcty demand f emon and coal ue are not retrcted. z P z + PAA + PlC l + PhC h c (3 19) 139

140 A bndng hgh (low) ulfur coal contract contrant lead to two poble cot neffcence, but only one of whch ncreae complance cot. Frt, a contract could lead to a generatng unt ung more than the optmal amount of hgh (low) ulfur coal and le than the optmal low (hgh) ulfur coal. In th cae, actual complance decon are altered and may lead to a ub-optmal coal mx. Second, a contract may force a unt to ue ome hgh (low) ulfur coal that more expenve than the hgh (low) ulfur pot market coal prce, whch ncreae total cot whle leavng complance cot unchanged. In prevou tude, both of thee cot neffcence were dentfed a exce complance cot becaue contract retrcton were gnored n the baelne cot wthout the program (c). (ẑ P z + PAÂ + P lĉ + P hĉ h + PhC c c h + PlC c c l c) (z P z + PAA + PlC l + PhC h c) (3 20) The mnmum complance cot choce wth no contract contrant for prevou tude are denoted by whle the contract contraned mnmum complance cot choce are denoted by n (3 20). The aumed c the total cot of meetng demand aumng no contract contrant or emon contrant. The cot dfference between thee two et of choce wll be the combnaton of change n complance decon and fuel cot. Some of thee exce complance cot may not be complance cot, whch make the derved complance cot too hgh. So t mportant to nclude the contract contraned coal ue n the baelne c to get the approprate complance cot. Aumng that contracted coal at leat a expenve a pot market coal, the complance cot wll be greater for the contract contraned cae a hown n (3 20) and a expreed n (3 21). P z (ẑ z ) + P A(Â A ) + P l(ĉ l C l ) + P h(ĉ h P hc h ) + P c hc c h + P c lc c l 0 (3 21) Conder a mple example where hgh ulfur contract coal more expenve than hgh ulfur pot market coal, low ulfur coal preferred over hgh ulfur coal, and no crubber would be ntalled f a generatng unt had total freedom n t coal ue choce. Now compare a generatng unt complance cot to the complance cot a unt would 140

141 face wth a hgh ulfur coal contract for 100% of t coal ue. The change n complance cot een n (3 22) nclude the addtonal cot from an ncreae n allowance purchae and a decreae n coal cot from ung cheaper, but drter fuel. P A(A MAX A MIN ) PlC,MAX l + PhC c c h > 0 (3 22) Snce the contract coal would have to be ued regardle of enactment of the program, the addtonal cot for hgh ulfur contract coal ue ntead of hgh ulfur pot market coal (Ph c Cc,MAX h P h C,MAX h ) hould not be ncluded n complance cot. However, prevou tude would recognze thee fuel cot a complance cot baed on the aumed cot mnmzaton wthout contract contrant. ẑ P z + P AÂ + P lĉ l + P hĉ h + P c hc c h + P c lc c l ĉ (3 23) The approprate unt-level complance cot wll take the form hown n (3 23) where the baelne total cot wll take the value ĉ, whch repreent the cot of meetng electrcty demand gven the coal contract contrant. Thee cot ĉ wll be dfferent than c becaue the pot market coal ue wll be altered f the contracted coal dffer relatve the pot market coal t replace n producton. P lĉ + P hĉ + PhC c c h + PlC c c l PlC l + PhC h (3 24) Total Indutry Complance Cot The total complance cot to the ndutry are the um of the combned crubber ntallaton cot and fuel wtchng cot for all affected generatng unt. The total ndutry cot from net allowance purchae are zero becaue each allowance old by one generatng unt at PA purchaed by another generatng unt at P A. Aumng that hgh ulfur coal cheaper than low ulfur coal, then the total ndutry complance cot are (3 25). n =1 [ z P z + max{(p lc l + P hc h P hc,max h ), 0} ] (3 25) 141

142 The mnmum uncontraned total ndutry complance cot to the ndutry derved from the followng problem. Each generatng unt chooe t optmal A, C h 0, C l 0, z {0, 1} baed on the market equlbrum allowance prce, P A. The total complance cot a hown n the objectve functon n (3 26) are the um of the complance cot for each generatng unt. Smlar to the generatng unt problem n Chapter 2, there are two contrant that mut be met. Frt, the um of allowance allocaton mut cover the um of emon that are emtted by all affected generatng unt. Second, each generatng unt mut produce enough electrcty to cover t electrcty demand requrement. mn z,a,c h,c l n =1 z P z + max{(p lc l + P hc h P hc,max h ), 0} (3 26).t. n (1 z r )(ClS l + ChS h)(m) =1 n =1 A e (C lh l + C hh h) D {1,..., n} z {0, 1} {1,..., n} If all generatng unt cot-mnmzng decon reult n an equlbrum n the allowance market, then total ndutry complance cot are mnmzed. We can prove th by howng the frt-order condton for the mnmzed total ndutry complance cot match up wth the frt-order condton from the generatng unt problem n Chapter 2, and the optmal choce wll be the ame for both problem. Solve for the frt-order condton gven z. For hgh ulfur coal: P h + λ 1 (1 z r )(m)(s h) λ 2 H h 0, = 0 f C h > 0 (3 27) For low ulfur coal: P l + λ 1 (1 z r )(m)(s l) λ 2 H l 0, = 0 f C l > 0 (3 28) 142

143 The frt-order condton are dentcal to thoe of the ndvdual generatng unt n Chapter 2 when nether coal contract contrant bnd. So a generatng unt cot mnmzng choce of Ch, C l at PA for each generatng unt alo mnmze total ndutry complance cot at P A. Thee frt-order condton can be ued to olve for λ 1, the allowance hadow prce, whch alo the ame a for the generatng unt problem. Snce the complance choce that mnmze the cot for all generatng unt reult n the equlbrum PA, the allowance choce alo mnmze the total ndutry cot. λ 1 = MCA, = Pl P Hl h Hh (1 z r )(m)( S h S Hh l ) Hl (3 29) The ame approach can be ued under the ndutry-wde complance cot problem wth coal contract contrant to how that contract contraned mnmum total ndutry complance cot wll dffer from the uncontraned cot..t. mn z,a,c h,c l n =1 [z P z + max{(p lĉ l + P hĉ h P hĉ,max h ), 0}] (3 30) n (1 z r )(Ĉ lsl + Ĉ hsh + C c lhl c + C c hhh)(m) c =1 (Ĉ lh l + Ĉ hh h + C c lh c l + C c hh c h) D {1,..., n} n =1 A e Ĉ h, Ĉ l 0 {1,..., n} z {0, 1} {1,..., n} The frt-order condton. For hgh ulfur pot market coal... P h + λ 1 (1 z r )(m)(s h) λ 2 H h 0, = 0 f C h > 0 (3 31) For low ulfur pot market coal... P l + λ 1 (1 z r )(m)(s l) λ 2 H l 0, = 0 f C l > 0 (3 32) 143

144 The frt-order condton are dentcal to thoe of the ndvdual generatng unt n Chapter 2. λ 1 = Pl P Hl h Hh (1 z r )(m)( S h S Hh l ) Hl (3 33) Thee frt-order condton can be ued to olve for λ 1, the allowance hadow prce, whch alo the ame a for the ndvdual generatng unt problem. If a generatng unt ue hgh ulfur coal, P A MCA,. If a generatng unt ue low ulfur coal, P A MCA,. If a generatng unt ue both hgh and low ulfur coal, P A = MCA,. So a generatng unt cot mnmzng choce of z, Ch, C l, A for each generatng unt alo mnmze total ndutry complance cot. If the contract contraned complance choce that mnmze the cot for a generatng unt reult n an equlbrum P A, the choce alo mnmze the contract contraned total ndutry cot. Note that the optmal parameter combnaton for the contract contraned cae wll not be the ame a under the uncontraned cae. It ha already been hown that any bndng contract contrant for an ndvdual generatng unt wll reult n a ub-optmal combnaton of coal ue, whch wll weakly ncreae complance cot for the contract contraned generatng unt. Any ub-optmal choce made by one generatng unt wll weakly ncreae the cot for the entre ndutry Impact of Allowance Allocaton on Complance Cot Gven Scrubber the Choce There are everal tude that have condered the mpact of the allowance allocaton dtrbuton on cot effcence of allowance tradng ytem. Montgomery (1972) howed that the allowance allocaton dtrbuton doe not affect complance cot, but t doe not conder the poble effect of contract contrant or PUC regulaton. Stavn (1995) ha hown that tranacton cot n allowance tradng market wth contnuou margnal abatement cot can caue the ntal allowance allocaton dtrbuton to matter for effcency. Montero (1997) extend Stavn (1995) by ntroducng non-contnuou margnal 144

145 abatement cot through dcrete technology choce and ntroducng uncertanty nto the Stavn model. Montero fnd that n an allowance tradng ytem wth tranacton cot, non-contnuou margnal abatement cot reultng from dcrete technology choce can caue the ntal allocaton of allowance to matter for effcency, even wth contant margnal cot of abatement and certanty. The mportance of the allowance allocaton n thee prevou tude rele on the extence of tranacton cot. However, th model ha aumed no allowance tranacton cot, whch allow t to how that even wth coal contract contrant the allowance allocaton dtrbuton wll not mpact a generatng unt complance choce or the total ndutry complance cot. 1 Conder the frt-order condton for both hgh ulfur and low ulfur coal, whch are ndependent of a generatng unt allowance allocaton. The type of coal a unt wll ue wll not depend on A e. P h + λ 1 (1 z r )(m)(s h) λ 2 H h 0 (3 34) P l + λ 1 (1 z r )(m)(sl) λ 2 Hl 0 (3 35) The choce between wtchng fuel or purchang allowance baed olely on a generatng unt relatve margnal cot of purchang the next allowance compared to the effectve margnal cot of abatng the next unt of emon. A can be een, A e ha no mpact on a generatng unt complance decon. A generatng unt wll ue allowance 1 It aumed that generatng unt are unable to break ther contract. Generatng unt could realtcally break ther contract at a very hgh prce and create the addtonal freedom n t complance choce. In uch a cae, contract contrant would reult n very hgh tranacton cot for tradng thoe addtonal allowance. 145

146 when PA < MCA, and wtch fuel when PA > MCA,. P A MCA, = Pl P Hl h Hh (1 z r )(m)( S h S Hh l ) Hl (3 36) Impact of Allowance Allocaton wth Endogenou Scrubber Choce Conder the expreon for the allowance prce at whch a generatng unt ndfferent to ntallng a crubber (PA S ), whch ha already been derved n Chapter 2. P z + P h ( C h Ĉh) + P l ( C l Ĉl) (Â Ã) P S A It poble to fll n for A = (E A e ) nce exce demand the dfference between actual emon and ntal allowance allocaton to ee how A e wll mpact PA S. In the denomnator, A e and A e cancel out, leavng an expreon for P S A that unaffected by A e. So a generatng unt crubber choce wll be made ndependent of A e. P z + P h ( C h Ĉh) + P l ( C l Ĉl) (Ê + A e Ẽ A e ) P S A (3 37) Now conder the complance choce made after the crubber ntallaton decon. It wa hown n Chapter 2 that a generatng unt complance choce are baed on the relatonhp between the P A and MCA, or M, CA, dependng on the unt crubber choce, for a partcular unt of coal. Smlar to what wa hown above, a generatng unt M CA, and MCA, for a gven unt of coal are not affected by A e becaue allowance are not a parameter n the margnal cot of abatement. M CA, = MCA, = P l H l P h H l (1 r )(m)( S h H h S l H l ) P l H l P h H h (m)( S h H h S l H l ) 146

147 3.6 Smulaton Model Introducton It ha been hown analytcally that contract may alter complance choce by alterng coal ue and crubber ntallaton and lead to greater complance cot. Thee reult may be able to explan a large porton of the exce complance cot found n prevou tude. Th ecton wll how how much of thee exce complance cot can be explaned by contract contrant. The frt porton of th ecton wll look at the data ued to parameterze the mulaton model, whch nclude a decrpton of where the data wa obtaned, the technque ued to create the parameter, and ome ue regardng the data. The econd porton wll look at the model degn and approach. The lat porton wll ummarze the mulaton reult n term of the total ndutry, ndvdual tate, and ndvdual generatng unt Data All data ued n the mulaton, wth an excepton for the coal contract data, were obtaned from Dr. Paul Sotkewcz. Ung the ame data allow for drect reult comparon to determne the coal contract mpact. Dr. Sotkewcz orgnally hand-collected the the data from the EIA Cot and Qualty of Fuel 1996, the EIA Electrc Power Annual 1997, and the EPA 1996 Complance Report. Up to th pont all generatng unt are aumed to be coal-fred unt becaue t the prmary fuel opton for electrcty generaton n the U.S. However, there are 24 unt of the 431 unt that ued fuel ol or natural ga for electrcty generaton. The treatment of thee unt decrbed n Secton Fuel data Fuel data on heat content, ulfur content, and delvered prce were obtaned from the EIA Cot and Qualty of Fuel 1996, whch compled nformaton from FERC Form 423. The coal contract data wa gathered drectly from the FERC Form 423 databae for 147

148 1996, whch decrbe the charactertc of all fuel delvered to utlty plant. Informaton on the heat content, ulfur content, purchang agreement, and delvered prce for each hpment are avalable, whch can dffer greatly from utlty to utlty and delvery to delvery for each plant dependng on locaton. The heat content of delvered coal n Btu of heat per ton of coal, barrel of ol, or 1,000 cubc feet of natural ga. All fuel parameter are converted n term of a heat content baelne to allow for comparon acro unt. The purchang agreement labeled a two poble parameter: (1) pot market and (2) contract purchae. An agreement condered a pot market purchae f the agreement for le than 2 year. Purchang agreement of two year or greater are condered to be under contract. The amount of fuel under contract n ton, barrel, or 1,000 cubc feet dependng on the fuel. The data manpulated nto total heat content by multplyng the heat content per unt of fuel by the amount of fuel delvered. Snce coal delvere are made at the plant level, the ze of the contract contrant not ealy derved for each generatng unt. The parameter for the amount of contract coal for each generatng unt wa derved n the followng manner. Frt, any unt at a gven plant that actually ntalled a crubber allocated a much hgh ulfur contract coal a poble whle recevng a lttle low ulfur contract coal a poble. The reaonng for th that a unt wth a crubber wll have a larger margnal cot of abatement from wtchng fuel (MCA, < M, CA ). Second, any remander pread out evenly throughout the remanng generatng unt wthout ntalled crubber. Thrd, f the equal dtrbuton reult n too much coal for a unt to ue n producton, the exce coal wll be hfted to a unt that requre a greater total heat nput. Fourth, f a plant coal contract reult n more heat nput than wa actually requred n producton, coal ue capped at the heat nput needed to meet demand. Any remanng coal condered be reman tored for future ue. 148

149 Conder the followng example for a plant wth three generatng unt each requrng 200,000 mmbtu of heat nput to cover ther electrcty demand and one unt ha a crubber. Contract account for 100% of coal purchang agreement where there are contract for 300,000 mmbtu for both hgh ulfur contract coal and low ulfur contract coal. Baed on the dtrbuton approach decrbed above, Unt 1 wll ue a much of the hgh ulfur coal a poble (200,000 mmbtu) and the remanng hgh ulfur coal wll be dtrbuted equally among the remanng two unt (50,000 mmbtu each for Unt 2 and Unt 3). The low ulfur coal wll be dtrbuted to Unt 2 and Unt 3 equally becaue nether ha a crubber ntalled (150,000 mmbtu each). Snce contract account for 100% of coal ue, there no need to purchae any coal on the pot market. If there had been any exce coal, uch a an extra 10,000 mmbtu of low ulfur contact coal, t would not change the allocaton n Table 3-1 and would be condered coal tored at the plant for ue the followng year. Sulfur content the percentage of each ton of coal, barrel of ol, or 1,000 cubc feet of natural ga that ulfur. The data mut be manpulated to create the dered varable, whch pound of ulfur doxde per mllon Btu of heat. Phae I of Ttle IV dtrbute allowance allocaton baed on 2.5 pound of SO 2 per mllon Btu of heat. So fuel condered hgh ulfur f contan greater then 2.5 lb. of SO 2 per mmbtu and low ulfur f t contan le than 2.5 lb. of SO 2 per mmbtu. Any coal ue that ha a hgher (lower) ulfur content wll ncreae (decreae) emon above (below) t allocaton allow. 2 Gettng the data n term of pound of ulfur doxde per mllon Btu of heat requre an emon factor, whch the amount of ulfur doxde emon that wll reult from a unt of ulfur. Emon factor were found n the EIA Electrc Power Annual By takng the ulfur content multpled by the emon factor dvded by the mllon of 2 Coal ulfur content can vary gnfcantly wthn each category (hgh or low ulfur). 149

150 Btu per unt (ton, 1,000 barrel, or mllon cubc feet), t reult n a parameter n pound of ulfur doxde per mllon Btu (lb. SO 2 /mmbtu). Although nearly all generatng unt affected by Phae I were coal-fred unt, 24 unt ue fuel ol or natural ga for electrcty generaton. For thee unt, fuel ol degnated a hgh ulfur fuel opton whle natural ga degnated a the lower ulfur fuel opton for non-coal fred unt. The delvered prce the cent per ton, barrel, or 1,000 cubc feet pad at the tme of delvery. The prce nclude the purchang of the fuel and the tranportaton cot of hpment. The prce converted to the prce of fuel n cent per mllon Btu. A eparate delvered prce requred for both hgh ulfur and low ulfur fuel, whch a weghted average of all delvere of each category of coal. So the hgh (low) ulfur prce ued n the mulaton the weghted average delvered prce for all hgh (low) ulfur coal delvere. The parameter ued n the mulaton actually dollar per mmbtu, or cent/mmbtu dvded by 100. Another ue that not all generatng unt purchaed both hgh ulfur and low ulfur fuel. Proxe were requred to determne the fuel charactertc facng each unt, and were frt taken from other generatng unt that were owned by the ame company where avalable. If a unt dd not have another unt under the ame company, a proxy wa taken from the geographcally cloet plant becaue hppng cot are an mportant factor n determnng the delvered prce. Regonal varaton n prce wll be much maller varaton n prce acro the U.S Allowance, actual emon, and demand data Data for allowance allocaton, actual emon, and electrcty demand wa found n the EPA 1996 Complance Report. Electrcty demand meaured n term of the heat nput ntead of actual megawatt-hour of electrcty. For a gven unt, there a gven amount of heat nput requred to produce one unt of electrcty. Th lnear nature of electrcty producton per unt of heat nput allow for th mple converon. For 150

151 example, f t requre 1 mmbtu to create 1 MWh of electrcty, a unt facng a demand of 100 MWh would requre 100 mmbtu of heat nput. Allowance allocaton and actual emon can be ued drectly wthout any manpulaton. Actual emon are ued a the ntal allowance allocaton allowance bankng caued the amount of allowance ued durng 1996 be le than the total amount of allocated allowance Techncal generator and crubber data Generator nameplate capacty and heat rate data wa found n the EIA Annual Generator Data The heat rate the amount of heat requred to produce one klowatt-hour of electrcty. Heat rate data unavalable n the 1996 report were gathered from Annual Generator Data Scrubber cot data wa found n the EIA Electrc Power Annual The data wa the htorcal crubber cot data, ncludng tate-by-tate average ntalled cot per klowatt of capacty, average operaton and mantenance cot n term of mll per klowatt-hour, megawatt of capacty for unt wth crubber ntalled, and ulfur removal effcency. 3 The crubber ntallaton choce mult-year decon. However, the mulaton model a one-year model, whch make t neceary to annualze the cot of ntallng and operatng a crubber. Scrubber ntallaton cot wll dffer dependng on the crubber technology and the ze of the generatng unt. Total crubber cot are the dcounted annualzed cot of crubber ntallaton and the operaton and mantenance cot for the 3 Engneerng-baed etmate for crubber ntallaton and operaton cot are an alternatve to htorcal-baed etmate. 151

152 gven electrcty producton. 4 The choen dcount rate of ten percent and a twenty year lfepan for captal equpment are the ame a n Sotkewcz and Holt (2005) Smulaton Model Degn The mulaton requre a mxed nteger lnear program becaue of the dcrete crubber choce. The mulaton model coded n Matlab and the lnear program olved ung the open ource LP Solve mxed nteger lnear programmng olver. If the crubber choce taken a gven, the mulaton become a mple lnear programmng model, whch guarantee an equlbrum. An endogenou crubber choce create a non-convexty that may not reult n an allowance market equlbrum. In uch a cae, there wll be ether a potve or a negatve exce demand for allowance and an allowance prce at whch a generatng unt ndfferent to ntallng a crubber. Th could be condered a qua-equlbrum where the exce demand ether bought from or old to an allowance broker at the qua-equlbrum allowance prce. The techncal explanaton of the becton teratve proce ued to converge to an equlbrum allowance prce decrbed n detal n Appendx B Smulaton Reult Seven dfferent generatng unt level mulaton were run to determne complance cot under everal et of condton dependng on the aumpton on the emon contrant, contract contrant, and crubber choce. Thee mulaton are ued to derve the mpact on not only the ndutry, but alo on ndvdual tate and generatng unt. 4 To annualze captal cot, the followng equaton ued to determne the preent ρ(1+ρ) value of the cot: t where ρ the dcount rate and t the number of year the (1+ρ) t 1 lfetme of the equpment. 5 The ue of htorcal crubber cot data wll reult n dfferent reult than engneerng cot etmate becaue the htorcal cot for crubber n 1996 dollar are cheaper than engneerng etmate for 316 out of 431 unt. 152

153 Total ndutry cot and allowance market reult The mulaton reult are ued to analyze three key ue: (1) replcaton of reult from prevou tude, (2) the mpact contract contrant have on the reult from prevou tude, and (3) the true complance cot reultng from the Ttle IV program. Smulaton 1, 3, and 4 recreate the reult from prevou tude whle Smulaton 2, 5, and 6 ntroduce the contract contrant to the model. Smulaton 7 derve ndutry cot baed on actual complance choce. Frt, conder the ablty of the mulaton model to recreate the reult from prevou tude. Smulaton 1 recreate the uncontraned cot-mnmzaton reult from Sotkewcz (2003) and Sotkewcz and Holt (2005). There were 17 crubber that were ntalled a a reult of the New Source Performance Standard (NSPS) and were unrelated to Ttle IV. Aumng thee crubber a gven, the total cot to the ndutry of meetng electrcty demand were $7.69 bllon. Thee cot wll be ued a the baelne total ndutry cot to determne total ndutry complance cot comparable to prevou tude. Smulaton 3 recreate the emon contraned reult from Sotkewcz and Holt (2005) aumng the 46 crubber that were ntalled n 1996 a gven. The mulaton reult n an allowance prce of $149.64, whch exactly replcate the allowance prce found by Sotkewcz (2003) and Sotkewcz and Holt (2005). Total ndutry cot are $8.23 bllon where 29 crubber were actually ntalled n repone to Ttle IV. The dfference between Smulaton 3 and Smulaton 1 the total ndutry complance cot of meetng the emon contrant, whch $541 mllon and mlar to the reult found n prevou 153

154 tude. 6 Carlon et al. (2000) and Sotkewcz and Holt (2005) found the leat cot outcome to be $571 mllon and $527 mllon, repectvely. 7 Smulaton 4 recreate the emon contraned reult from Sotkewcz (2003) that allow a generatng unt crubber choce to be endogenou. The model aume the 17 crubber ntalled to meet the NSPS, but allow generatng unt to make the crubber ntallaton choce. The mulaton reult n an allowance prce of $ Total ndutry cot are $7.97 bllon, where 27 crubber were ntalled n repone to Ttle IV (42 crubber total). Allowng generatng unt to make ther crubber ntallaton choce reult n two fewer ntalled crubber, whch may explan the lghtly hgher PA becaue fewer crubber wll decreae upply and ncreae demand for allowance. The dfference between Smulaton 4 and Smulaton 1 the total ndutry complance cot of meetng the emon contrant, whch lower than the cot found n Smulaton 3 at $288 mllon. The reult are comparable to the $340 mllon found n Sotkewcz (2003). A expected, freedom n the crubber choce mprove effcency and lower total ndutry complance cot by $252 mllon, or 47% lower than n Smulaton 3. The allowance market doe not clear n Smulaton 4 becaue generatng unt are allowed to make ther crubber choce. The dcrete nature of crubber ntallaton lead to a non-negatve exce demand. However, the exce upply of 53,576 allowance n Smulaton 4 account for le than 1% of the 5+ mllon allowance market and could be aumed to be banked for future ue or old to an allowance broker, whch could be condered a qua-equlbrum. 6 The value lghtly dffer relatve to the reult from Sotkewcz (2003) and Sotkewcz and Holt (2005) becaue the crubber cot etmate n th tudy have hgher etmated varable operatng cot. 7 Burtraw et al. (2005) and Sotkewcz and Holt (2005) 154

155 Second, conder how fuel contract contrant wll mpact the total ndutry complance cot. Smulaton 5 ntroduce fuel contract contrant to the the emon contraned model aumng the 46 crubber ntalled a n Smulaton 3. The mulaton reult n a hgher allowance prce of $206.70, whch could be the reult of a greater demand for allowance due to more hgh ulfur coal ue reultng from hgh ulfur coal contract. Total ndutry cot are $8.76 bllon, where 29 crubber were ntalled n repone to Ttle IV. Aumng thee crubber choce, the mnmum complance cot relatve to the uncontraned model n Smulaton 1 are $1.07 bllon, or $531 mllon (98%) hgher than f contract are not taken nto conderaton. Smulaton 6 ntroduce fuel contract contrant to the the emon contraned model whle allowng generatng unt to make ther crubber choce. The mulaton reult n an allowance prce of $ Total ndutry cot are $8.63 bllon where 44 crubber are ntalled n repone to Ttle IV. The mnmum complance cot when compared to Smulaton 1 are $939 mllon, or $651 mllon hgher than f contract are not taken nto conderaton. The mnmum complance cot are cloe to the actual cot found n Sotkewcz and Holt (2005) at $990 mllon and Carlon et al. (2000) at $910 mllon. Allowng generatng unt to chooe whether to ntall a crubber allow the ndutry to lower t total cot by $132 mllon. A would be expected, ntroducng the contract contrant reult n more crubber ntallaton due to Ttle IV from 27 to 44 becaue hgh-ulfur fuel contract ncreae the ncentve for a contraned generatng unt to ntall a crubber. A n Smulaton 4, the allowance market doe not clear due to the dcrete, endogenou crubber choce. However, the exce demand of 7,797 allowance account for le than 0.2% of the 5+ mllon allowance market, and could be aumed to be bought from an allowance broker. The actual total ndutry complance cot are found n Smulaton 7. By ung the actual emon and electrcty producton for each unt, t poble to determne each unt actual coal mx. Thee actual decon reulted n an allowance prce range 155

156 of $69.33-$95.38 durng 1996, total ndutry cot of $8.98 bllon, and total ndutry complance cot of $1.30 bllon relatve to Smulaton 1. If the contract contrant are excluded from the model and the actual cot are compared to Smulaton 3 and Smulaton 4, the exce complance cot are $757 mllon and $1.01 bllon, repectvely. However, ncludng the contract contrant nto the model reult n exce complance cot of $226 mllon and $358 mllon. Contract contrant explan $531 mllon and $651 mllon of exce complance cot, repectvely. Thrd, the true complance cot wll dffer from thee etmate becaue the approprate baelne wa not ued. A hown analytcally n Secton 4, comparng Smulaton 5 and Smulaton 6 to Smulaton 1 not the mot approprate meaure of complance cot. The contract contrant hould be ncluded n both the baelne mulaton and the polcy-retrcted mulaton. Smulaton 2 run the ame model a n Smulaton 1 except that t nclude contract contrant and reult n total ndutry cot of $8.27 bllon. The dfference between total ndutry cot n Smulaton 1 and Smulaton 2 are the addtonal cot due to contract contrant, whch are $582 mllon. Thee addtonal cot would have reulted wth or wthout the SO 2 Tradng Program and hould not be condered complance cot. Th a key reult becaue thee cot were labeled complance cot by prevou tude even though thee cot are a reult of generatng unt lockng n prce to protect from the uncertanty of hgher coal prce n the future. By comparng reult n Smulaton 5 to Smulaton 2, the mnmum complance cot conderng contract and gven the crubber choce are found to be $490.1 mllon. True mnmum complance cot are much lower ($610 mllon lower) once th addtonal contrant ncluded n the model. In Smulaton 6, the true mnmum complance cot are $357.8 mllon, or $581.6 mllon le than f contract are excluded from the model. Thee are mlar to the leat-cot reult found by Sotkewcz (2003) at $340-$527 mllon, Sotkewcz and Holt (2005) at $423-$553 mllon, and Carlon et al. (2000) at $571 mllon. 156

157 Although actual ndutry complance cot are hgher than the leat-cot reult at $716 mllon, thee complance cot are lower than the complance cot found n Sotkewcz (2003) and Sotkewcz and Holt (2005) at $990 mllon and Carlon et al. (2000) at $910 mllon. Contract contrant appear to explan ome of the exce complance cot found n prevou tude, whch mple that generatng unt decon were more cot-effectve than prevouly tated n the lterature Indutry and generatng unt coal ue By comparng coal ue n Smulaton 5 to that n Smulaton 3, the mpact of contract contrant aumng crubber a gven can be derved. Smulaton 3 ue a total of 2,607,025,040 mmbtu of hgh ulfur coal (40.7%) and 3,794,557,150 mmbtu of low ulfur coal (59.3%). Smulaton 5 ue a total of 2,041,933,640 mmbtu of hgh ulfur coal (31.9%) and 4,359,648,550 mmbtu of low ulfur coal (68.1%). Introducng contract contrant nto the model reult n a 8.8% decreae n hgh ulfur coal relatve to Smulaton 3. Contract contrant reult n le hgh ulfur coal than would have otherwe been preferred. Contract contrant led to 16 unt (3.7% of affected unt) ung a uboptmal coal combnaton. 15 of the 16 unt had 100% of t coal ue altered. Only 2 of thee unt had an ncreae n hgh ulfur coal. Smulaton 4 ue a total of 2,651,410,732 mmbtu of hgh ulfur coal (41.4%) and 3,750,168,009 mmbtu of low ulfur coal (58.6%). Smulaton 6 ue a total of 2,614,773,732 mmbtu of hgh ulfur coal (40.8%) and 3,786,804,109 mmbtu of low ulfur coal (59.2%). Includng contract contrant nto the model reult n a 0.6% decreae n hgh ulfur coal relatve to Smulaton 4. Overall coal ue doe not appear to have been gnfcantly altered. However, th doe not tell the whole tory. Contract contrant led to 27 unt (6.3% of affected unt) ung a uboptmal coal combnaton. 5 of the 27 unt had a change of at leat 98% of coal ue and 15 of the 27 had at leat a 50% change n coal ue. 14 of the 27 unt had an ncreae n hgh ulfur coal ue whle 13 unt had an decreae of hgh ulfur coal ue. The concern wth the contract not necearly that the entre 157

158 ndutry choce are hfted, but that ndvdual generatng unt are not able to make ther cot-mnmzng choce Generatng unt crubber ntallaton choce There are three ue to conder regardng generatng unt crubber choce: (1) mpact from the endogenou crubber choce wthout contract contrant, (2) mpact from the endogenou crubber choce wth contract contrant, and (3) mpact of contract contrant on crubber choce. Frt, comparng crubber ntallaton n Smulaton 4 to Smulaton 3 wll how how crubber decon would be altered f the crubber decon made endogenou and contract contrant are excluded from the model. Allowng the crubber choce to be endogenou reult n 48 generatng unt alterng ther crubber choce, ncludng 25 crubber to be removed and 23 to be added for a total of 2 fewer ntalled crubber. 21 generatng unt mantan the ame crubber choce, but 17 of thoe were ntalled for NSPS. So only 4 crubber choce remaned the ame. Second, comparng crubber ntallaton n Smulaton 6 to Smulaton 5 wll how how crubber decon would be altered f the crubber decon made endogenou and contract contrant are ncluded n the model. Allowng the crubber choce to be endogenou reult n 53 generatng unt alterng ther crubber choce, ncludng 19 crubber to be removed and 34 to be added for a total of 15 more ntalled crubber. 27 generatng unt mantan the ame crubber choce, but 17 of thoe were ntalled for NSPS. So 10 crubber ntallaton remaned the ame. Fnally, t mportant to conder the mpact contract contrant have on a unt endogenou crubber ntallaton decon, whch can be determned by comparng Smulaton 6 to Smulaton crubber choce are altered a a reult of contract contrant, ncludng 25 unt that wll now ntall a crubber and 8 unt that no longer ntall a crubber. Of the 25 unt that choe to ntall a crubber, 20 of them had a hgh ulfur coal contract. Of the 8 unt that choe to not ntall a crubber, all 8 of them had a low ulfur coal contract. So 28 of 33 crubber choce appear to have been drectly 158

159 mpact by contract contrant. A can be een n Table 3-4, contract contrant ncreae crubber ntallaton n Oho, Alabama, Florda, Indana, Mpp, and Mour and decreae crubber ntallaton n Wet Vrgna, New York, Pennylvana, Wconn, Georga, Kentucky, and New Jerey. An unexpected reult n Smulaton 6 that crubber ntallaton actually ncreae relatve to Smulaton 5. Thee are lkely a reult of the aumed crubber cot etmate becaue the htorcal crubber cot data ued n the mulaton lower than the engneerng cot etmate. Scrubber appear cheaper to ntall than the engneerng etmate tate. Of the 404 generatng unt wth at leat a 90% removal rate, 31 htorcal captal cot etmate are hgher, 84 are the ame, and 289 are lower than the etmated engneerng captal cot. 8 The hgher cot etmate are not much hgher than the engneerng cot wth a dfference of $11/kW. However, the htorcal captal cot etmate that are lower than the engneerng captal cot etmate range from $50/kW to $216/kW hgher, whch could have ome gnfcant mpact on crubber ntallaton choce. For example, htorcal captal cot etmate for generatng unt n Mzzour are aumed to be $50/kW whle the engneerng cot etmate are aumed to be $266/kW, or a 432% dfference. A can be een n Table 3-5, there a gnfcant dfference n crubber ntallaton. The ue of engneerng cot etmate for crubber ntallaton reult n a decreae n crubber ntallaton from 44 to 25 n Smulaton 4 and from 61 to 38 n Smulaton 6 becaue of the hgher cot nvolved. Notce that ntroducng contract contrant reult n addtonal crubber ntallaton from 25 to 38, whch cloe to the actual ntallaton of 46 crubber. Complance cot nterpretaton reman mlar to mulaton ung 8 27 of the generatng unt are not drectly comparable becaue htorcal data (50% removal rate) aume a dfferent crubber technology than the engneerng data (90% removal rate). 159

160 htorcal crubber cot etmate data, wth complance cot lghtly hgher for all mulaton Impact of allowance allocaton on the allowance market and complance cot The mpact of alterng the ntal allowance allocaton are a would be expected. Fewer avalable allowance force the ndutry to produce fewer emon, whch wll reult n a hgher allowance prce, more crubber ntallaton, and hgher total ndutry complance cot. A decreae n the ntal allowance allocaton by 10% lead to an ncreae n the number of ntalled crubber by 17 n Smulaton 4 and 12 n Smulaton 6, an ncreae n the equlbrum allowance prce of n Smulaton 4 and $11.48 n Smulaton 6, and an ncreae n the total ndutry complance cot ncreae by $93.6 mllon (32%) n Smulaton 4 and $118.8 mllon (33%) n Smulaton 6. 9 Contract contrant retrct complance opton, whch wll lead to fewer complance choce change, whch lead to le of an mpact on both crubber ntallaton and the allowance market. However, retrctng complance opton alo lead to the hgher complance cot to meet the addtonal emon reducton Summary of mulaton reult Contract contrant appear to explan a large porton of the exce complance cot found n the prevou tude. Much of thee exce cot would have occurred wth or wthout the program due to the contract retrcton, and therefore are not actually complance cot. Thee reult fnd that frm complance choce appear to be more cot-effectve than prevouly thought becaue prevou work ha gnored a key retrcton on a generatng unt freedom n complance opton. 9 The reult are not relant on how the 10% reducton n ntal allowance allocaton occur becaue the dtrbuton of the allocaton wll not alter complance decon. 160

161 The true complance cot to the ndutry appear to be lower relatve to the prevou complance cot etmate. Actual complance decon reulted n total ndutry complance cot that were hgher than the leat cot choce gven the contract contrant ($226 mllon compared to Smulaton 5 and $358 mllon compared to Smulaton 6) Introducton 3.7 Plant Level Decon-Makng Proce The generatng unt model n Chapter 2 doe not account for the fact that two or more generatng unt are often owned and operated by one frm at the ame plant. A plant decon-makng proce may not mnmze cot for each generatng unt becaue a plant concern baed on the combned cot of all generatng unt under t operatonal control. Th model derve the plant level problem, whch allow u to analyze dfference n hgh veru low ulfur coal, pot veru contract coal, allowance exce demand, crubber ntallaton, and the potonng of contract coal ue baed on the dfferent generatng unt charactertc at a partcular plant. A plant level decon-makng model more realtc than a generatng unt level model to determne complance decon becaue coal delvere are made at the plant level where there are often multple generatng unt. All generatng unt at that plant facng the ame coal ue opton, ncludng ulfur content, heat content, and delvered prce for both pot market and contract coal. The contract contrant become more complex n th model where the um of contract coal ue for all generatng unt at a plant mut cover the contract requrement, n =1 Cc f Cc f {1, 2,..., n}. A plant wth multple unt ha greater degree of freedom n t choce a to what fuel type to purchae, n what quantte, and at whch unt to burn the fuel baed on ther emon, demand, and coal contract contrant. The mproved freedom n choce varable hould lead to lower complance cot. 161

162 Some anecdotal evdence of thee cot avng een n a comparon of the 46 generatng unt that had crubber ntalled n Of thoe unt, 37 unt are each located at a plant that dd not operate a generatng unt that dd not have a crubber ntalled. The remanng 9 generatng unt were each located at a plant that operated at leat one other generatng unt that dd not ntall a crubber. By comparng the average exce complance cot (n percentage term), t poble to ee how havng at leat one addtonal generatng unt at a plant mprove t ablte to lower complance cot. For the generatng unt located at a plant wthout an addtonal generatng unt wthout a crubber had average exce complance cot of 6.8% above the unt mnmum complance cot. Generatng unt at a plant wth at leat one addtonal generatng unt that dd not ntall a crubber had average exce complance cot of 2.8% above the unt mnmum complance cot. Three addtonal factor wll be of great mportance at the plant level. Frt, plant are able to trade allowance between generatng unt a needed to cover emon at no addtonal cot. The lterature ha tated that tradng allowance between t unt at the ame plant ha been a common occurrence, whch upport the ue of a model that conder decon at the plant level ntead of the generatng unt level. 10 Second, another apect to conder the choce to ntall a crubber, whch baed on the charactertc of all the unt at a plant, not jut the unt at whch the crubber may be ntalled. Thrd, a plant decon become more complex f t ha one or more unaffected unt. A plant may have one or more generatng unt at t locaton that are not affected by Phae I and doe not have to meet any emon requrement. Ownng a non-affected 10 Montero (1996) 162

163 unt allow greater freedom n coal ue and may greatly alter a plant preferred complance opton. 11 Plant mut conder the total combned cot over all generatng unt, whch may lead to plant level decon that are contrary to a pecfc generatng unt cot-mnmzng choce. A plant may be able to lower total cot by ncreang the cot at one generatng unt to ave money at other unt Plant-Level Problem A plant olve the followng problem. The ubcrpt repreent a pecfc generatng unt for each operatng plant whle n repreent the number of generatng unt owned by the plant. mn z,a,c h,c l,cc h,cc l n =1 z P z + P A A + P hc h + P l C l + P c hc c h + P c l C c l (3 38) ubject to...a e + A (1 z r )(m)[c hs h + C c hs c h + C ls h + C c ls c l ] λ 1 (3 39) (ChH h + ChH c h c + ClH l + ClH c l c ) D λ 2 (3 40) n Ch c C c h µ h (3 41) =1 n Cl c C l µ l (3 42) =1 z {0, 1} (3 43) C h, C l 0 (3 44) {1,..., n} (3 45) The Lagrange multpler on a generatng unt emon contrant repreented by λ 1. The Lagrange multpler on a generatng unt demand contrant repreented by λ 2. Coal contract contrant requre a plant to ue a mnmum amount of each contract coal 11 Due to the degn of the polcy wth compenaton provon, a plant can hft coal ue, but not electrcty producton to a non-affected unt wthout the unt beng ncorporated nto the program. 163

164 type, C c h for hgh ulfur coal and C c l for low ulfur coal. The amount of contract coal at a generatng unt a choce varable becaue a plant able to chooe whch generatng unt to ue t allotted contract coal. The Lagrange multpler of each contract coal type repreented by µ h for hgh ulfur coal and µ l for low ulfur coal Frt-Order Condton The partal dervatve wth repect to A yeld the mpact of a one unt change n t net allowance poton on the unt total cot. P A λ 1 = 0 (3 46) Snce A can be ether potve or negatve baed on the net allowance poton, (3 46) wll hold wth equalty. The addtonal cot to the frm of emttng one more ton of emon equvalent to the allowance prce, λ 1 = P A, whch the ame reult a from the prevou model. The partal dervatve wth repect to C h repreent the mpact a one unt change n hgh ulfur pot market coal ha on the unt total cot. P h + λ 1 (1 z r )(m)(s h) λ 2 H h 0, = 0 f C h > 0 (3 47) If the generatng unt ue ome amount of hgh ulfur pot market coal (C h > 0), then (3 47) hold wth equalty. The partal dervatve wth repect to C l repreent the mpact a one unt change n low ulfur pot market coal ha on the unt total cot. P l + λ 1 (1 z r )(m)(s l ) λ 2 H l 0, = 0 f C l > 0 (3 48) Smlar to hgh ulfur pot market coal, f the generatng unt ue ome low ulfur pot market coal (C l > 0), then (3 48) hold wth equalty. 164

165 The partal dervatve wth repect to Ch c repreent the mpact a one unt change n hgh ulfur contract coal ha on the unt total cot. P c h + λ 1 (1 z r )(m)(s c h) λ 2 H c h µ h 0, = 0 f C c h > 0 (3 49) Unlke wth hgh ulfur pot market coal, hgh ulfur contract coal wll be mpacted by the hgh ulfur coal contract contrant (µ h ). If the generatng unt ue ome amount of hgh ulfur contract coal (Ch c > 0), then (3 49) hold wth equalty. The partal dervatve wth repect to C c l repreent the mpact a one unt change n low ulfur contract coal ha on the unt total cot. P c l + λ 1 (1 z r )(m)(s c l ) λ 2 H c l µ l 0, = 0 f C c l > 0 (3 50) Unlke wth low ulfur pot market coal, low ulfur contract coal wll be mpacted by the low ulfur coal contract contrant (µ l ). Smlar to hgh ulfur contract coal, f the generatng unt ue ome low ulfur contract coal (C c l > 0), then (3 50) hold wth equalty Characterzng a Unt Spot Market Fuel Choce A plant choce of fuel type for a gven generatng unt not only baed on the plant margnal cot of abatement relatve to the allowance prce, but alo the plant crubber ntallaton choce for each ndvdual unt. For th ecton, we aume that the crubber choce gven and focu olely on a generatng unt margnal cot of abatement and the allowance prce, excludng the ue of contract coal. The nteracton of choce for the ue of contract coal, the conderaton of multple generatng unt, and crubber choce wll be dcued later. A n prevou model, three cae mut be condered: a generatng unt ue both hgh and low ulfur pot market coal, only hgh ulfur pot market coal, and only low ulfur pot market coal. 165

166 Cae 1: Neceary condton for ung both hgh ulfur and low ulfur pot market coal Aume that demand for each generatng unt gven and a generatng unt chooe to ue both hgh ulfur and low ulfur pot market coal (C h > 0 and C l > 0), whch mple that both (3 47) and (3 48) hold wth equalty. The addtonal cot to the generatng unt of ung one more unt of low ulfur pot market coal equal to the addtonal cot of ung one more unt of hgh ulfur pot market coal. P h + λ 1 (1 z r )(m)(s h) λ 2 H h = P l + λ 1 (1 z r )(m)(s l ) λ 2 H l (3 51) Snce both (3 47) and (3 48) hold wth equalty, t poble to fnd an expreon for (λ 2 ) n each equaton and et the two expreon equal to each other and derve the allowance hadow prce (λ 1 ) n (3 52). P A = λ 1 = MCA, = P l H l P h H h (1 z r )(m)( S h S Hh l ) Hl (3 52) A dcued earler, the allowance hadow prce (λ 1 ) an expreon for a generatng unt Margnal Cot of Abatement from Swtchng from hgh ulfur pot market to low ulfur pot market coal (MCA, ). From (3 46), we alo know that the actual allowance prce equal the allowance hadow prce (P A = λ 1 ). A can be een n (3 52), the allowance prce (P A ) equal to the margnal cot of abatement (MCA, ), whch the ncreae n coal cot from wtchng from hgh ulfur pot to low ulfur pot market coal per unt of reduced emon. The margnal cot of abatement may or may not dffer acro generatng unt. If a plant doe not ntall any crubber, then MCA, = MCA, j {, j} for all generatng unt and the plant choce wll be dentcal to the generatng unt decon n Secton 5. Th can be een n (3 52) where the only way that the margnal cot of abatement can dffer acro generatng unt through the crubber choce and a crubber emon capture rate. If all generatng unt at a gven plant both ntall a crubber where r = r j, 166

167 then MCA, = MCA, j. Once agan the plant choce wll be dentcal to the generatng unt choce made n Secton 5. Margnal cot of abatement wll only dffer acro generatng unt at a plant f (1) a plant ntall a crubber at ome but not all of t generatng unt, or (2) a plant ntall a crubber at all t generatng unt but the crubber have dfferent capture rate (r r j {, j}). We wll ntroduce the crubber choce, and derve t mpact on a plant choce later Cae 2: Neceary condton for only hgh ulfur pot market coal ue If a generatng unt chooe to ue only hgh ulfur pot market coal (C h > 0), then (3 47) hold wth equalty and (3 48) hold wth weak nequalty reultng n (3 53). P h + λ 1 (1 z r )(m)(s h) λ 2 H h P l + λ 1 (1 z r )(m)(s l ) λ 2 H l (3 53) Equaton (3 53) tate that addtonal cot to the generatng unt of ung one more unt of hgh ulfur pot market coal weakly le than or equal to the addtonal cot of ung one more unt of low ulfur pot market coal ncluve of emon and demand requrement. Followng Secton we can derve the relaton of P A to MCA,. By comparng thee two expreon and olvng for λ 2, you get an nequalty comparng λ 1 = P A and MCA,. Snce the generatng unt ue hgh ulfur pot market coal, the allowance prce weakly le than the margnal cot of abatement (P A MCA, ) a hown n (3 54). P A MCA, = P l H l P h H h (1 z r )(m)( S h S Hh l ) Hl (3 54) Cae 3: Neceary condton for only low ulfur pot market coal ue Smlarly to the above cae, f a generatng unt chooe to ue only low ulfur pot market coal (C l > 0), then (3 47) hold wth equalty and (3 48) hold wth weak nequalty reultng n (3 55). The addtonal cot to the generatng unt of ung one 167

168 more unt of low ulfur pot market coal weakly le than or equal to the addtonal cot of ung one more unt of hgh ulfur pot market coal ncluve of emon and demand requrement. P h + λ 1 (1 z r )(m)(s h) λ 2 H h P l + λ 1 (1 z r )(m)(s l ) λ 2 H l (3 55) Once agan we can derve the relaton of P A to MCA,. By comparng thee two expreon and olvng for λ 2, you get an nequalty comparng λ 1 = P A and MCA,. Snce the generatng unt ue low ulfur pot market coal, the allowance prce weakly greater than the margnal cot of abatement (P A MCA, ) a hown n (3 56). P A MCA, = P l H l P h H h (1 z r )(m)( S h S Hh l ) Hl (3 56) Exce Demand Correpondence When only conderng the ue of pot market coal (no contract contrant), a unt exce demand correpondence wll look nearly dentcal to the correpondence n Chapter 2. The mnmum and maxmum exce demand for allowance can be derved for each of the three cae decrbed above n the ame manner a n Chapter 2. Frt, f a generatng unt face P A < MCA, t wll ue the maxmum amount of hgh ulfur pot market coal. The maxmum amount of hgh ulfur pot market coal expreed n (3 57). Replacng C h C,MAX h = D H h n (3 41) wth the expreon n (3 57) for C,MAX h gve an expreon for the maxmum allowance exce demand n (3 58). A generatng unt maxmum exce demand mut cover the dfference between t ntal allowance allocaton (A e ) and the amount of allowance needed to cover the unt maxmum actual emon (3 57) [E MAX = (1 z r )(m)(s h )( D H h )]. A MAX = E MAX A e (3 58) 168

169 If a generatng unt face P A > MCA,, t wll ue the maxmum amount of low ulfur pot market coal, whch can be found from (3 41). Aumng only low ulfur pot market coal ue to meet demand, the maxmum amount of low ulfur coal expreed n (3 59). C l = D H l (3 59) Replacng C l n (3 41) wth the expreon n (3 59) for C,MAX l gve an expreon for the mnmum allowance exce demand n (3 60). A generatng unt mnmum exce demand mut cover the dfference between t ntal allowance allocaton (A e ) and the amount of allowance needed to cover the unt mnmum actual emon [E MIN = (1 z r )(m)(s l )( D H l )]. If a unt ntal allocaton can cover t mnmum poble emon, then t wll have a negatve net allowance poton and be a net buyer eller of allowance. A MIN = E MIN A e (3 60) If P A = MCA,, a generatng unt may ue any combnaton of hgh ulfur pot market coal and low ulfur pot market coal and lead to any level of exce demand n the range (E MIN A = (ρe MAX A e, E MAX (1 ρ)e MIN A e ). The allowance exce demand can be repreented by A e ) where the contant ρ [0, 1]. A unt that ndfferent between fuel wtchng and allowance purchang could be ether a net buyer or a net eller. Combnng the exce demand for each of the three cae create the exce demand correpondence hown below. A = A MAX ρa MAX A MIN (1 ρ)a MIN f P A > MCA, f P A = MCA, ρ [0, 1] f P A < MCA, A generatng unt exce demand correpondence can be een graphcally n Chapter 2. Hgh ulfur coal ue correpond to the rght-hand vertcal lne where P A < MCA,. Low 169

170 ulfur coal ue correpond to the left-hand vertcal lne where P A > MCA,. The cae where a generatng unt ue ome combnaton of low ulfur coal and hgh ulfur coal repreented by the horzontal lne at whch P A = MCA, Characterzng a Generatng Unt Contract Fuel Choce Unlke n the generatng unt-level model, contracted coal not treated the ame a pot market coal. It not poble to mply requre a certan amount of hgh or low ulfur contract coal ue becaue the ue of contract coal a choce varable at the generatng unt level. The ue of contract coal wll be baed on the relatve margnal cot of ung contract coal at each generatng unt operated by a plant. A plant wll chooe to ue contract coal at the generatng unt that wll reult n the lowet ncreae n the plant total cot. To make thee cot comparon, t neceary to derve the margnal cot of abatement for the gven combnaton of pot and contract coal and compare them acro generatng unt. Intally we wll gnore a plant crubber choce for each generatng unt and a plant make the ame choce for all t generatng unt (z = z j = 0, or z = z j = 1 and r = r j ). Under thee condton, the margnal cot of abatement are dentcal acro all generatng unt, and t doe not matter at whch of thee generatng unt the contract coal ued. Th wll be hown eparately for both a hgh ulfur and low ulfur coal contract becaue the ue of hgh ulfur contract coal ndependent of low ulfur contract coal and va vera Cae 1: Neceary condton for hgh ulfur contract coal ue at Generatng Unt We frt conder a plant wth a hgh ulfur coal contract. We can derve the margnal cot of abatement of wtchng fuel from hgh ulfur contract coal to low ulfur pot market coal n (3 61). The margnal cot of abatement from wtchng from hgh ulfur contract coal to low ulfur pot market coal (MCA c, ) wll be the ame for all generatng unt that make the ame crubber ntallaton choce (z ), ncludng the ame crubber 170

171 technology wth the ame capture rate (r ). P c h + λ 1 (1 z r )(m)(s c h) + λ 2 H c h µ h = P l λ 1 = MCA c, + + λ 1 (1 z r )(m)(s l ) + λ 2 H l µ h H c h (1 z r )(m)( Sc h S Hh c l ) Hl All unt at whch a plant doe not ntall a crubber have the ame margnal cot of abatement of wtchng from hgh ulfur contract coal to low ulfur pot market coal (MCA c, = MCA c, j ). Alo all unt at a plant that ntall a crubber wth the ame capture rate wll have dentcal MCA c, Cae 2: Neceary condton for low ulfur contract coal ue at generatng unt Second, derve the margnal cot of abatement of wtchng fuel from hgh ulfur pot market coal to low ulfur contract coal n (3 62). The MCA,c (3 61) wll be the ame for all generatng unt that make the ame crubber ntallaton choce, ncludng the ame crubber technology wth the ame capture rate. P h + λ 1 (1 z r )(m)(s h) + λ 2 H h = P c l + λ 1 (1 z r )(m)(s c l ) + λ 2 H c l µ l λ 1 = MCA,c µ l H c l (1 z r )(m)( S h Sc Hh l ) Hl c All unt at whch a plant doe not ntall a crubber have the ame margnal cot of abatement of wtchng from hgh ulfur pot market coal to low ulfur contract coal (MCA,c = MCA,c j ). Alo all unt at a plant that ntall a crubber wth the ame capture rate wll have dentcal MCA,c Non-Affected Generatng Unt at an Affected Plant So far t ha been aumed that all generatng unt operated by a plant are all (3 62) affected unt, meanng that all unt face an emon complance contrant a a reult of Phae I. However, there are 27 plant (out of 160 total plant) that have both affected 171

172 and non-affected unt. 12 Now we wll ntroduce generatng unt that are not Phae I affected nto a plant decon-makng proce. The emon contrant doe not bnd (λ 1 = 0) for thee unt, whch mean that non-affected generatng unt wll prefer to ue the coal type wth the lowet delvered prce. For mot plant th wll be hgh ulfur coal, partcularly thoe located n the Eatern U.S Characterzaton of non-affected generatng unt at an affected plant The frt-order condton from Secton 7.3 wll no longer be dependent on the emon for a non-affected unt becaue the emon contrant wll never bnd (λ 1 = 0), a can be een n (3 63) and (3 64). and L C h L C l = P h λ 2 H h 0, = 0 f C h > 0 (3 63) = P l λ 2 H l 0, = 0 f C l > 0 (3 64) Aumng that a generatng unt ue both hgh and low ulfur pot market coal, we ue (3 63) and (3 64) to derve (3 65). If a generatng unt ue both hgh and low ulfur pot market coal, then the prce per unt of heat nput equal for both coal type. A plant wll no longer make t generatng unt level fuel choce baed on t margnal cot of abatement becaue t no longer concerned about abatng emon. Ph Hh = P l Hl (3 65) By ung the frt-order condton, we can determne when a generatng unt wll only ue one type of pot market coal. If a generatng unt ue only hgh ulfur pot market 12 Source: Extng Generatng Unt n the Unted State by State, Company and Plant, 2003 databae. 172

173 coal, then (3 63) hold wth equalty and (3 64) reman weakly greater than zero and low ulfur coal weakly more expenve ( P h H h P l ). If a generatng unt ue only low ulfur Hl pot market coal, then (3 64) hold wth equalty and (3 63) reman weakly greater than zero and hgh ulfur pot market coal more expenve ( P h H h P l ). Hl Non-affected generatng unt and hgh ulfur coal contract Now conder how thee non-affected unt wll mpact a plant coal ue choce for t generatng unt. Th one ue that wll only mpact plant under Phae I becaue only the drtet unt are affected whle under Phae II and CAIR all generatng unt n the U.S. are affected unt. There only a concern wth Phae I where mot unt preferred to wtch from hgh to low ulfur coal. So aume a plant face a hgh ulfur coal contract. Frt, aume that two generatng unt (Unt and Unt j ) are both affected unt. A plant wll be ndfferent to ung hgh ulfur contract coal at ether unt when the frt-order condton for ung hgh ulfur contract coal are equal acro generatng unt. P c h + λ 1 (1 z r )(m)(s c h) λ 2 H c h µ h = P c h + λ j1 (1 z j r j )(m)(s c h) λ j2 H c h µ h λ 1 (1 z r )(m)(sh) c λ 2 Hh c = λ j1 (1 z j r j )(m)(sh) c λ j2 Hh c (3 66) Now aume that Unt an affected unt and t emon contrant bnd (λ 1 > 0) whle Unt j not affected and the emon contrant wll not bnd (λ j1 = 0). Under th condton, the addtonal cot of ung hgh ulfur contract coal at an affected unt greater than at a non-affected unt. P c h + λ 1 (1 z r )(m)(s c h) λ 2 H c h µ h > P c h λ j2 H c h µ h λ 1 (1 z r )(m)(s c h) λ 2 H c h > λ j2 H c h λ 1 (1 z r )(m)(s c h) > 0 (3 67) 173

174 Conder a mple example where a plant operate two generatng unt, one that affected (Unt ) and another that not affected (Unt j ) by Phae I of Ttle IV. Aume P h H h < P l, whch normally the cae under Phae I. 13 Furthermore, the plant Hl prefer to wtch from hgh ulfur coal to low ulfur coal to meet t emon requrement for Unt becaue P A > MCA,. But the plant alo ha a hgh ulfur coal contract for a mall amount of hgh ulfur coal (C c h < D H c h ) that ha dentcal charactertc to hgh ulfur pot market coal. The plant mut chooe at whch generatng unt to ue the hgh ulfur contract coal. Snce plant prefer to ue low ulfur coal to lower t emon at Unt and prefer to ue hgh ulfur coal at Unt j to mnmze t coal cot, then the plant contract wll not bnd and wll not ncreae a plant total cot. Alternatvely, f Unt j wa an affected unt and P A > MCA, j, a hgh ulfur contract would bnd and reult n hgher total cot for the plant. A non-affected unt wll weakly decreae a plant total cot relatve to f the unt WAS affected. Hgh ulfur coal can be hfted to the unaffected unt to relax the emon contrant Scrubber Intallaton Choce Up to th pont, we have aumed a plant crubber choce for a generatng unt a gven. Now conder a plant crubber ntallaton choce for a gven generatng unt. A plant chooe to ue contract coal n dfferent generatng unt dependng on whether t ha ntalled a crubber at the partcular generatng unt. The choce baed on the crubber choce becaue t the only varable that can change the margnal cot of abatement acro a plant generatng unt Margnal cot of abatement wth and wthout a crubber Fndng the allowance prce at whch a generatng unt wll ntall a crubber not a mple a n the generatng unt model becaue a plant mut take nto account the cot of 13 Over 86% of generatng unt had hgher delvered prce for low ulfur coal than hgh ulfur coal on the pot market. 174

175 all unt when choong to ntall a crubber. The margnal cot of abatement for all coal type ha already been derved. Now the MCA for each coal combnaton both wth and wthout a crubber can be derved. The only way the margnal cot of abatement can vary acro generatng unt through the crubber choce (z and r ). Frt, conder the margnal cot of abatement of wtchng from hgh ulfur pot market coal to low ulfur pot market coal (MCA, ) wth a crubber n (3 68), and compare t to the margnal cot of abatement wthout a crubber n (3 69). A n Chapter 2, a crubber decreae the avng from wtchng pot market fuel becaue a crubber caue the emon reducton to be maller than wthout a crubber., λ 1 = M CA = λ 1 = MCA, = P l H l P h H h (1 r )(m)( S h S Hh l ) Hl P l H l P h H h (m)( S h S Hh l ) Hl Second, conder the margnal cot of abatement of wtchng from hgh ulfur (3 68) (3 69) contract coal to low ulfur pot market coal (MCA c, ) wth a crubber n (3 70), and compare t to the margnal cot of abatement wthout a crubber n (3 71). A n the cae of only pot market coal, ntallng a crubber decreae the avng from wtchng fuel. In the cae of a hgh ulfur contract, t le cotly to a plant to ue hgh ulfur coal at a partcular generatng unt f t ha a crubber. c, λ 1 = M CA + µ h H c h (1 r )(m)( Sc h S Hh c l ) Hl (3 70) λ 1 = MCA c, + µ h H c h (m)( Sc h S Hh c l ) Hl Thrd, conder the margnal cot of abatement of wtchng from hgh ulfur pot (3 71) market coal to low ulfur contract coal (MCA,c ) wth a crubber n (3 72), and compare t to the margnal cot of abatement wthout a crubber n (3 73). A n the two cae above, ntallng a crubber decreae the avng from wtchng fuel. In the cae of a low 175

176 ulfur contract, t more cotly to a plant to ue low ulfur coal at a partcular generatng unt f t ha a crubber.,c λ 1 = M CA µ l H c l (1 z r )(m)( S h Sc Hh l ) Hl c (3 72) λ 1 = MCA,c µ l H c l (m)( S h Sc Hh l ) Hl c For each combnaton of coal type, ntallng a crubber decreae the ze of the denomnator, whch ncreae MCA. A n Chapter 2, a crubber greatly decreae the avng from wtchng fuel. A hgher MCA ncreae the range of allowance prce at (3 73) whch a plant wll prefer to purchae allowance ntead of wtchng fuel by lowerng the prce at whch a generatng unt wll be ndfferent between purchang allowance and wtchng from hgh ulfur to low ulfur coal. Any unt operated by a plant that ha a crubber wll have a larger margnal cot of abatement than any unt wthout a crubber (M CA > MCA j ) A Plant Preferred Order of Scrubber Intallaton Gven a plant chooe to ntall a crubber, t wll ntall the crubber at the generatng unt at whch t wll get the greatet bang-for-the-buck, whch wll be the generatng unt wth the lowet average cot of abatement through crubber ntallaton (ACA ). A generatng unt wll have the lowet ACA f the cot of a crubber per ton of emon reducton ( ACA = P z mr (S h C h +Sc h Cc h +S l C l +Sc l Cc l ) ) lower than all other generatng unt operated by a plant. Gve the ame coal ue rato (percent of coal ue for each coal category), the prce per unt of heat or prce per unt of reduced emon only vary baed on total demand (D = C h + Cc h + C l + Cc h ) becaue m and r are contant. In other word, crubber ntallaton wll be baed on the average cot for crubber ntallaton per unt of demand ( ACA = P z D ). The decon baed olely on a unt ACA becaue the margnal cot of abatement are equal acro generatng unt wth no crubber ntalled at the plant. 176

177 Followng along the ame thought proce, f a plant chooe to ntall a crubber at two generatng unt, the crubber wll be ntalled at the generatng unt wth the two lowet ACA. The above condton wll only hold for affected generatng unt. A plant wll not ntall a crubber at a non-affected generatng unt becaue reducng emon at a non-affected unt doe not relax any emon contrant At whch generatng unt wll a plant ntall a crubber? The order a plant wll ntall crubber at t generatng unt and a plant margnal cot of abatement for both wth and wthout a crubber are known. Now t mut be defned when a plant wll ntall a crubber at a gven generatng unt by fndng the allowance prce at whch a plant ndfferent to ntallng a crubber. Th tough to analytcally how becaue a plant ha multple choce to mnmze t total cot through crubber ntallaton. Aume that all generatng unt operated by a plant are affected by Phae I, each unt ue t cot mnmzng combnaton of coal and allowance baed on t crubber choce, and the unt are orted by ACA from mallet to larget (ACA 1 < ACA 2 <... < ACA n 1 < ACA n ). A plant crubber choce wll be baed on the relatve total cot of each poble combnaton of crubber ntallaton. A plant wll not ntall a crubber at any generatng unt f t total cot are lower wth no crubber ntalled than ntallng ( a crubber at the generatng unt wth the lowet ACA C(z1 = 0, z 2 = 0,..., z n = 0) < C(z 1 = 1, z 2 = 0,..., z n = 0) ) where C( ) the total cot for a gven crubber choce and optmal coal and allowance choce. We already know that any other combnaton of crubber ntallaton mut reult n hgher cot. 14 Some plant voluntary enrolled unt nto Phae I, whch are labeled a ubttuton unt or compenaton unt. Although thee unt were not ntally affected, they were enrolled nto the program and face the ame type of requrement a the orgnal unt. For th reaon, they are condered affected unt. 177

178 If total cot are lower wth a crubber ntalled at the generatng unt wth the lowet ACA than wthout a crubber at any unt (C(z 1 = 1, z 2 = 0,..., z n = 0) < C(z 1 = 0, z 2 = 0,..., z n = 0)) and lower than wth a crubber ntalled at the two generatng unt wth the lowet ACA (C(z 1 = 1, z 2 = 0,..., z n = 0) < C(z 1 = 1, z 2 = 1, z 3 = 0,..., z n = 0)), then a crubber ntalled only at the generatng unt wth the lowet ACA. Generalzng th condton, a plant decon to ntall a crubber at generatng unt m. A plant wll ntall m crubber at the m larget generatng unt f ( C(z1 = 1, z 2 = 1,..., z m = 1, z m+1 = 0,..., z n = 0) < C(z 1 = 1, z 2 = 1,..., z m 1 = 1, z m = 0,..., z n = 0) ) and ( C(z 1 = 1, z 2 = 1,..., z m = 1, z m+1 = 0,..., z n = 0) < C(z 1 = 1, z 2 = 1,..., z m+1 = 1, z m+2 = 0,..., z n = 0) ) At what allowance prce wll a plant ntall a crubber at a gven generatng unt? Fndng the allowance prce at whch a plant ndfferent to ntallng a crubber at a gven generatng unt the allowance prce at whch the total cot to the plant are the ame both wth and wthout the crubber (PA S ). Solvng for th value for the plant crubber choce for each generatng unt requre an aumpton on the crubber choce of all other generatng unt. Luckly, the crubber ntallaton choce have already been ordered above. At frt glance, t appear dffcult to derve P S A becaue a plant compare t total cot over all of t generatng unt, and a plant mut chooe whether to ntall a crubber at each unt. However, t ha been hown that a plant wll bae t crubber ntallaton on a ngle factor, relatve ACA. There are everal requrement for a plant to ntall a crubber at a gven affected generatng unt : (1) a plant ntall a crubber at all affected generatng unt wth a lower ACA than unt, (2) t cheaper for a plant to ntall a crubber than to not ntall a crubber at unt. Th requre a mple comparon between the cot of ntallng a crubber veru not ntallng a crubber. Let X repreent the parameter wthout a crubber ntalled, and X repreent the 178

179 parameter wth a crubber ntalled. The cot for all generatng unt j wll not change and wll cancel out, leavng the ame expreon for P S A a derved n Chapter 2. 1 (P jz + P A Ã j + Ph C jh + Pl j=1 C jl + P c h C c jh + P c l +P z + P A Ã + Ph C h + Pl C l + Ph c C h c + Pl c n + (P A Â k + P hĉ kh + Pl Ĉkl + P hĉc c kh + P c j=1 k=+1 1 = (P jz + P A Ã j + Ph C jh + Pl + C jl + P c h C c jh + P c l C c jl) C c l l Ĉ c kl) C c jl) +P A Â + P hĉ h + Pl Ĉl + P hĉc c h + Pl c Ĉl c n (P A Â k + P hĉ kh + Pl Ĉkl + P hĉc c kh + Pl c Ĉkl) c k=+1 P z + P A Ã + P h C h + P l C l + P c h C c h + P c l = P A Â + P hĉ h + P l Ĉ l + P c hĉc h + P c l Ĉ c l (3 74) C c l Aumng no contract coal, we can derve the allowance prce at whch a plant ndfferent to ntallng a crubber for a gven generatng unt n (3 75). P S A = P z + P h ( C h Ĉ h ) + P l ( C l Ĉ l ) (Â Ã) (3 75) A pecal cae ext for (3 75) n whch the generatng unt a non-affected unt, whch reult n P A becaue the unt doe not have to cover t emon wth allowance and gan nothng from ntallng a crubber. An ndfference prce of nfnty mple that a crubber wll never be ntalled at Unt f t an unaffected unt. P S A = P z + P h ( C h Ĉ h ) + P l ( C l Ĉ l ) (Â Ã) = P z + Ph ( C h Ĉ h ) + P l ( C l Ĉ l ) = 0 (3 76) Scrubber ntallaton and hgh ulfur coal contract So far we have gnored any coal contract contrant. We mut determne at whch generatng unt() a plant wll ue contracted coal, whch can be derved from the 179

180 followng three condton: (1) gven a plant ntall no crubber, a plant ndfferent to ung contracted coal at any generatng unt becaue each unt ha the ame MCA, (2) the margnal cot of ung hgh ulfur contract coal at a generatng unt wth a crubber are lower than ung hgh ulfur contract coal a generatng unt wthout a crubber, and (3) any generatng unt wth a crubber wll have a lower ACA than a generatng unt wthout a crubber. We can mplfy a plant contract coal ue choce from thee three condton by ung any hgh ulfur contract coal at the generatng unt wth the lowet ACA, whch alo the generatng unt at whch a plant wll frt ntall a crubber. By dong o, we can determne at whch generatng unt to ue hgh ulfur contract coal before the crubber choce actually made by the plant. If all hgh ulfur contract coal wll not cover the entre heat nput needed to meet demand at the generatng unt wth the lowet ACA (H h C,MAX h > H c h Cc h), then all hgh ulfur coal wll be ued at that unt. If there more hgh ulfur contract coal than can be ued at the generatng unt wth the lowet ACA (H h C,MAX h < H c h Cc h), then the remander wll be ued at the unt wth the econd lowet ACA. The ame proce wll be ued f there reman any addtonal contract coal after meetng the heat nput demand for the generatng unt wth the econd lowet ACA. A plant wth a bndng hgh ulfur coal contract ha a greater ncentve to ntall a crubber at each of t generatng unt becaue t mut ue ome hgh ulfur coal, even f t would prefer to ue low ulfur coal at all generatng unt. A hgh ulfur coal contract decreae the ndfference prce at whch a unt wll ntall a crubber from P A to (P A ɛ) for each generatng unt. The ncentve may not be large enough to reult n a crubber ntallaton at t generatng unt wth the lowet ACA. In uch a cae, a plant ndfferent to ung hgh ulfur contract coal at any of t generatng unt becaue all unt have the ame MCA c,. A bndng hgh ulfur coal contract reult n a decreae n P S A. At P S A where... P z + P A Ã + P h C h + P l C l = P A Â + P hĉ h + P l Ĉ l (3 77) 180

181 If hgh ulfur contract coal at leat a expenve a hgh ulfur pot market coal, we know that... P z + P A Ã + P h C h + P l C l + P c hc c h < P A Â + P hĉ h + P l Ĉ l + P c hc c h (3 78) Th the ame reult a n Chapter 2 where a hgh ulfur coal contract reult n an neffcent coal ue combnaton of hgh and low ulfur coal. The ndfference prce at whch a plant wll ntall a crubber at a gven generatng unt wll weakly decreae when a plant chooe to ue hgh ulfur contract coal at that unt Scrubber ntallaton and low ulfur coal contract It can be determned at whch generatng unt() a plant wll ue low ulfur contracted coal from the followng three condton: (1) gven a plant ntall no crubber, a plant ndfferent to ung contracted coal at any generatng unt becaue each unt ha the ame MCA, (2) the margnal cot of ung low ulfur contract coal at a generatng unt wth a crubber are hgher than ung low ulfur contract coal a generatng unt wthout a crubber, and (3) any generatng unt wth a crubber wll have a lower ACA than a generatng unt wthout a crubber. We can mplfy a plant contract coal ue choce from thee three condton by ung any low ulfur contract coal at the generatng unt wth the hghet ACA, whch alo the generatng unt at whch wll be the lat that a plant wll ntall a crubber. By dong o, we can determne at whch generatng unt to ue low ulfur contract coal before the crubber choce actually made by the plant. If all low ulfur contract coal wll not cover the entre heat nput needed to meet demand at the generatng unt wth the hghet ACA (H l C,MAX l > H c l Cc l), then all low ulfur coal wll be ued at that unt. If there more low ulfur contract coal than can be ued at the generatng unt wth the hghet ACA (H l C,MAX l < H c l Cc l), then the remander wll be ued at the unt wth the econd hghet ACA. The ame proce wll be ued f there reman any addtonal contract coal after meetng the heat nput demand for the generatng unt wth the econd hghet ACA. 181

182 A plant wth a bndng low ulfur coal contract ha a maller ncentve to ntall a crubber at each of t generatng unt becaue t mut ue ome low ulfur coal, even f t would prefer to ue hgh ulfur coal at all generatng unt. A low ulfur coal contract ncreae the ndfference prce at whch a unt wll ntall a crubber from P A to (P A + ɛ) for each generatng unt. A plant ndfferent to ung low ulfur contract coal at any of t generatng unt f no crubber are ntalled becaue all unt have the ame MCA,c. A bndng low ulfur coal contract reult n an ncreae n P S A. At P S A where... P z + P A Ã + P h C h + P l C l = P A Â + P hĉ h + P l Ĉ l (3 79) If low ulfur contract coal at leat a expenve a low ulfur pot market coal, we know that... P z + P A Ã + P h C h + P l C l + P c l C c l > P A Â + P hĉ h + P l Ĉ l + P c l C c l (3 80) Th the ame reult a n Chapter 2. A low ulfur coal contract reult n an neffcent coal ue combnaton of hgh and low ulfur coal. The ndfference prce at whch a plant wll ntall a crubber at a gven generatng unt wll weakly ncreae when a plant chooe to ue low ulfur contract coal at that unt Scrubber Intallaton Example: Plant wth Two Affected Generatng Unt For a mple example, conder the crubber ntallaton choce for a plant wth only two generatng unt. Aume that a plant wll ntall a crubber at Unt 1 before t wll ntall a crubber at Unt 2 becaue (ACA 1 < ACA 2 ). There are three cae that may reult, each of whch decrbed below wth ther own ndfferent prce for ntallng a crubber. 182

183 Cae 1: Intall no crubber In the cae of a plant choong not to ntall any crubber, two condton mut hold. Frt, the total cot of not ntallng any crubber mut be le than ntallng a crubber at the generatng unt wth the lowet ACA 1. P A Â 1 + P hĉ 1h + P l Ĉ 1l + P c hĉc 1h + P c l Ĉ c 1l +P A Â 2 + P hĉ 2h + P l Ĉ 2l + P c hĉc 2h + P c l Ĉ c 2l < P 1z + P A Ã 1 + P h C 1h + P l C 1l + P c h C c 1h + P c l C c 1l +P A Â 2 + P hĉ 2h + P l Ĉ 2l + P c hĉc 2h + P c l Ĉ c 2l From th equaton, we can olve for P S A for th condton to hold n (3 81). The amount of contract coal the ame no matter the crubber choce at each generatng unt made by a plant. P S A < P 1z + P h ( C 1h Ĉ 1h ) + P l ( C 1l Ĉ 1l ) (Â1 Ã1) (3 81) Second, the total cot to the plant of not ntallng any crubber mut be le than the total cot of ntallng crubber at both generatng unt. P A Â 1 + P hĉ 1h + P l Ĉ 1l + P c hĉc 1h + P c l Ĉ c 1l +P A Â 2 + P hĉ 2h + P l Ĉ 2l + P c hĉc 2h + P c l Ĉ c 2l < P 1z + P A Ã 1 + P h C 1h + P l +P A Ã 2 + P h C 2h + P l C 1l + P c h C c 1h + P c l C 2l + P c h C c 2h + P c l C c 1lP 2z C c 2l From th equaton, we can olve for P S A for th condton to hold n (3 82). P S A < P 1z + P h [( C 1h Ĉ 1h ) + ( C 2h Ĉ 2h )] + P 2z + P l [( C 1l Ĉ 1l ) + ( C 2l Ĉ 2l )] (Â1 Ã1) + (Â2 Ã2) (3 82) The mnmum of the two P S A wll be the allowance prce at whch a plant ndfferent to ntallng a crubber and not ntallng any crubber. Notce that the allowance prce 183

184 for ntallng one crubber wll be weakly le than the allowance at whch a plant would ntall crubber at both t generatng unt Cae 2: Intall one crubber We know that a plant wll ntall a crubber at the generatng unt wth the lowet ACA, whch n th cae aumed to be Unt 1. For a plant to ntall one crubber, two condton mut hold. Frt, the total cot of ntallng one generatng unt mut be lower than the total cot of ntallng no crubber. P 1z + P A Ã 1 + P h C 1h + P l C 1l + P c h C c 1h + P c l C c 1l + P A Â 2 + P hĉ 2h + P l Ĉ 2l + P c hĉc 2h + P c l Ĉ c 2l < P A Â 1 + P hĉ 1h + P l Ĉ 1l + P c hĉc 1h + P c l Ĉ c 1l + P A Â 2 + P hĉ 2h + P l Ĉ 2l + P c hĉc 2h + P c l Ĉ c 2l From th equaton, we can olve for P S A for th condton to hold n (3 83). P 1z + P h ( C 1h Ĉ 1h ) + P l ( C 1l Ĉ 1l ) Â 1 Ã1 < P S A (3 83) Second, the total cot of ntallng one generatng unt mut be lower than the total cot of ntallng two crubber. P 1z + P A Ã 1 + P h C 1h + P l C 1l + P c h C c 1h + P c l C c 1l +P A Â 2 + P hĉ 2h + P l Ĉ 2l + P c hĉc 2h + P c l Ĉ c 2l < P 1z + P A Ã 1 + P h C 1h + P l +P A Ã 2 + P h C 2h + P l C 1l + P c h C c 1h + P c l C c 1l + P 2z C 2l + P c h C c 2h + P c l C c 2l From th equaton, we can olve for P S A for th condton to hold n (3 84). P 2z + P h (Ĉ 2h C 2h ) + P l (Ĉ 2l C 2l ) (Â2 Ã2) > P S A (3 84) The allowance prce mut be between thee two ndfference prce, whch reult n P S A < P A for Unt 1 and P S A > P A for Unt

185 Cae 3: Intall two crubber For a plant to ntall a crubber at both generatng unt, two condton mut hold. Frt, the total cot of ntallng two generatng unt mut be lower than the total cot of ntallng one crubber. P 1z + P A Ã 1 + P h C 1h + P l +P A Ã 2 + P h C 2h + P l < P 1z + P A Ã 1 + P h C 1h + P l C 1l + P c h C c 1h + P c l C c 1l + P 2z C 2l + P c h C c 2h + P c l C 1l + P c h C c 1h + P c l C c 2l C c 1l +P A Â 2 + P hĉ 2h + P l Ĉ 2l + P c hĉc 2h + P c l Ĉ c 2l From th equaton, we can olve for P S A for th condton to hold n (3 85). P 2z + P h ( C 2h Ĉ 2h ) + P l ( C 2l Ĉ 2l ) (Â2 Ã2) < P S A (3 85) Second, the total cot of ntallng a crubber at both generatng unt mut be lower than the total cot of ntallng no crubber. P 1z + P A Ã 1 + P h C 1h + P l +P A Ã 2 + P h C 2h + P l C 1l + P c h C c 1h + P c l C c 1l + P 2z C 2l + P c h C c 2h + P c l C c 2l < P A Â 1 + P hĉ 1h + P l Ĉ 1l + P c hĉc 1h + P c l Ĉ c 1l +P A Â 2 + P hĉ 2h + P l Ĉ 2l + P c hĉc 2h + P c l Ĉ c 2l From th equaton, we can olve for P S A for th condton to hold n (3 86). P 1z + P h ( C 1h Ĉ 1h ) + P l ( C 1l Ĉ 1l ) + P 2z + P h ( C 2h Ĉ 2h ) + P l ( C 2l Ĉ 2l ) (Â1 Ã1) + (Â2 Ã2) < P S A(3 86) The allowance prce mut be greater than both of thee two ndfference prce for two crubber to be ntalled. 185

186 We can monotoncally order thee ndfference prce at whch a plant wll be ndfferent to ntallng a crubber n each of the above cae. A mple mathematcal example ung data baed on data from the Colbert generatng unt can be ued to how the monotonc nature of thee ndfference prce n Table 3-7. A plant wth no contract coal wll prefer to ntall no crubber f the allowance prce below $ An allowance prce between $ and $ wll lead a plant to ntall a crubber at Unt 1, but not at Unt 2. A plant wll ntall crubber at both unt f the allowance prce greater than $ Now conder the plant ha a hgh ulfur coal contract for 28.92% of coal ue (13,855,269 mmbtu), whch wll alter the ndfference at whch a plant wll ntall a crubber at Unt 1. We have already hown that hgh ulfur contract coal wll be ued at the generatng unt wth the lowet ACA, whch Unt 1. The requred ue of hgh ulfur coal wll lower the allowance ndfferent prce to ntallng a crubber at Unt 1 to $ There wll be no change n the ndfference prce to ntallng a crubber at Unt 2 becaue the hgh ulfur coal contract doe not bnd for that generatng unt. Now conder the plant ha a hgh ulfur coal contract for all of t coal ue n both generatng unt (47,913,973 mmbtu). The ndfference prce for both generatng unt wll both decreae a a reult. The allowance prce at whch the plant wll ntall a crubber at Unt 1 wll agan be $ The ndfference prce for Unt 2 wll decreae to $ A hgh ulfur coal contract for all of a generatng unt coal requrement reult n large reducton of the allowance prce at whch a plant wll be ndfferent to ntallng a crubber for both Unt 1 ($54 or 28%) and Unt 2 ($77 or 33%) Scrubber Intallaton Example: Plant wth One Affected and One Non-Affected Generatng Unt The P S A for the non-affected unt (Unt 2) wll be nfnty becaue there no prce at whch a plant would want to ntall a crubber at a non-affected unt. The non-affected 186

187 unt wll not buy or ell any allowance ether nce t ha no emon contrant. The only poble choce to ntall a crubber at the affected unt (Unt 1). Cae 1: Intall No Scrubber The total cot of not ntallng a crubber mut be lower than the total cot of ntallng a crubber at the affected unt. P A Â 1 + P hĉ 1h + P l Ĉ 1l + P c hĉc 1h + P c l Ĉ c 1l + P hĉ 2h + P l Ĉ 2l + P c hĉc 2h + P c l Ĉ c 2l < P 1z + P A Ã 1 + P h C 1h + P l C 1l + P c h C c 1h + P c l C c 1l + P hĉ 2h + P l Ĉ 2l + P c hĉc 2h + P c l Ĉ c 2l From th equaton, we can olve for P S A for th condton to hold n (3 87). P S A < P 1z + P h ( C 1h Ĉ 1h ) + P l ( C 1l Ĉ 1l ) (Â1 Ã1) (3 87) Cae 2: Intall One Scrubber The total cot of ntallng a crubber mut be lower than the total cot of not ntallng a crubber at the affected unt. P 1z + P A Ã 1 + P h C 1h + P l C 1l + P c h C c 1h + P c l C c 1l + P hĉ 2h + P l Ĉ 2l + P c hĉc 2h + P c l Ĉ c 2l < P A Â 1 + P hĉ 1h + P l Ĉ 1l + P c hĉc 1h + P c l Ĉ c 1l + P hĉ 2h + P l Ĉ 2l + P c hĉc 2h + P c l Ĉ c 2l From th equaton, we can olve for P S A for th condton to hold n (3 88). P S A > P 1z + P h ( C 1h Ĉ 1h ) + P l ( C 1l Ĉ 1l ) (Â1 Ã1) (3 88) Summary of Plant Level Reult A plant decon-makng proce may not mnmze cot for each generatng unt becaue a plant concern baed on the combned cot of all generatng unt under t operatonal control. The choce to ntall a crubber baed on the charactertc of all the unt at a plant, not jut the unt at whch the crubber may be ntalled. Once the 187

188 order of preferred crubber ntallaton determned baed on the ACA, a plant able to make t cot mnmzng fuel choce. A plant level model more realtc than a generatng unt level model becaue coal delvere are made at the plant level where there are often multple generatng unt. Operatng multple unt allow a plant to relax t contract contrant becaue there are addtonal degree of freedom n fuel ue dependng on each unt emon, demand, and coal contract contrant. Alo, plant are able to trade allowance between generatng unt a needed to cover emon at no addtonal cot. A plant may alo have one or more non-affected generatng unt, whch face no emon contrant. Any hgh ulfur contract coal can be ued at thee non-affect unt wthout any negatve fnancal repercuon due to the polcy. Thee factor can lead to plant-level choce that do not mnmze each generatng unt total cot. 3.8 CONCLUSIONS The U.S. SO 2 Tradng Program led to lower complance cot than what would have occurred under a command-and-control approach. However, all complance cot avng were not realzed n part due to hort-run fuel contract rgdte, partcularly durng the frt year of the program. Th paper conder the allowance market equlbrum mpact and total ndutry complance cot from fuel contract both through analytc and emprcal modelng. An allowance market equlbrum wll ext only f the dcrete crubber choce gven. Allowng for an endogenou crubber choce make t mpoble to guarantee an equlbrum, although one may tll may ext. Bndng fuel contract may alter a unt complance decon and exce demand. Alterng complance decon could lead to both an altered allowance market prce and an ncreae total ndutry complance cot. Generatng unt-level mulaton were able to effectvely replcate the reult from prevou tude and how that fuel contract can explan a porton of the prevouly unexplaned exce complance cot. Smulatng the leat-cot complance choce wthout 188

189 ncludng fuel contract contrant reult n mnmum annual ndutry complance cot of $288.3 mllon, whch vare greatly from the actual complance cot of $1.30 bllon found n thee mulaton. Once fuel contract contrant are ntroduced nto the mulaton, the mnmum annual ndutry complance cot become $939 mllon-$1.07 bllon. Baed on thee reult, fuel contract contrant appear to explan $651.1 mllon, or 65% of the exce complance cot realzed n the program for Thee mpact hould lowly decreae over tme a frm adjut to the polcy envronment and bndng contract expre. However, the mpact on complance cot hould lnger for year due to the long length of coal contract agreement. Alo, contract appear to reman prevalent n coal purchang agreement and could lead to ome ue reultng from further SO 2 emon retrcton. A plant decon-makng proce may not mnmze cot for each generatng unt becaue a plant concern baed on the combned cot of all generatng unt under t operatonal control. The choce to ntall a crubber baed on the charactertc of all the unt at a plant, not jut the unt at whch the crubber may be ntalled. Once the order of preferred crubber ntallaton determned baed on the ACA, a plant able to make t cot mnmzng fuel choce. A plant level model more realtc than a generatng unt level model becaue coal delvere are made at the plant level where there are often multple generatng unt. Operatng multple unt allow a plant to relax t contract contrant becaue there are addtonal degree of freedom n fuel ue dependng on each unt emon, demand, and coal contract contrant. Alo, plant are able to trade allowance between generatng unt a needed to cover emon at no addtonal cot. A plant may alo have one or more non-affected generatng unt, whch face no emon contrant. Any hgh ulfur contract coal can be ued at thee non-affect unt wthout any negatve fnancal repercuon due to the polcy. Thee factor can lead to plant-level choce that do not mnmze each generatng unt total cot. 189

190 Table 3-1. Example: Contract Coal Dtrbuton Plant-Level Contrant Total mmbtu Unt Demand Scrubber Hgh Sulfur Contract 300, ,000 Ye Low Sulfur Contract 300, ,000 No Demand 600, ,000 No Coal Dt n by Unt Hgh Sulfur Coal Low Sulfur Coal Unt 1 200,000 0 Unt 2 50, ,000 Unt 3 50, ,000 Table 3-2. Sulfur Converon by Fuel Type Fuel Emon Converon Factor Baelne Btumnou (38 * Sulfur Content)/(mmBtu per ton) = lb. SO 2 /mmbtu Sub-btumnou (35 * Sulfur Content)/(mmBtu per ton) = lb. SO 2 /mmbtu Anthracte (39 * Sulfur Content)/(mmBtu per ton) = lb. SO 2 /mmbtu Lgnte (30 * Sulfur Content)/(mmBtu per ton) = lb. SO 2 /mmbtu Fuel Ol #2 (144 * Sulfur Content)/(mmBtu per 1,000 bbl.) = lb. SO 2 /mmbtu Fuel Ol #6 (162 * Sulfur Content)/(mmBtu per 1,000 bbl.) = lb. SO 2 /mmbtu Natural Ga (0.60 lb. SO 2 /mmcf)/(mmbtu per mmcf) = lb. SO 2 /mmbtu 190

191 Table 3-3. Smulaton Reult Sm. Emon Contract Scrubber Scrubber PA A Total Cot Compl. Cot Comp. Cot Contrant Contrant Choce Intalled v. (Sm. 1) v. (Sm. 2) (1) NO NO Gven 17 NA NA $7,685,800,000 NA NA (2) NO YES Gven 17 NA NA $8,267,400,000 NA NA (3) YES NO Gven 46 $ $8,226,500,000 $540,700,000 NA (4) YES NO Choen 44 $ ,576 $7,974,100,000 $288,300,000 NA (5) YES YES Gven 46 $ $8,757,500,000 $1,071,700,000 $490,100,000 (6) YES YES Choen 61 $ ,797 $8,625,200,000 $939,400,000 $357,800,000 (7) - - Actual 46 NA NA $8,983,500,000 $1,297,700,000 $716,100,

192 Table 3-4. Impact of Contract Contrant on Scrubber Choce State Decreae State Increae WV -4 MO 2 NY -2 MS 2 PA -2 IN 3 WI -2 FL 4 GA -1 AL 7 KY -1 OH 10 NJ -1 Table 3-5. Smulaton wth Engneerng Data Sm. A P A Scrubber Indutry Cot Comp. Cot Comp. Cot Intalled (v. 1) (v. 2) 1 NA NA 17 $7,685,800,000 NA NA 2 NA NA 17 $8,267,400,000 NA NA 3 0 $ $8,239,000,000 $553,200,000 NA 4 1,972 $ $8,010,200,000 $324,400,000 NA 5 0 $ $8,770,900,000 $1,085,100,000 $503,500, ,611 $ $8,686,300,000 $1,000,500,000 $418,900,000 7 NA NA 46 $8,995,600,000 $1,309,800,000 $728,200,000 Table 3-6. Impact of a Reducton n the Allowance Allocaton of 10% Smulaton 4 Intal Allocaton Allocaton Mnu 10% Increae Indutry Complance Cot $288,300,000 $381,900,000 $93,600,000 Scrubber Intalled Allowance Prce $ $ $33.85 Smulaton 6 Intal Allocaton Allocaton Mnu 10% Increae Indutry Complance Cot $357,800,000 $476,600,000 $118,800,000 Scrubber Intalled Allowance Prce $ $ $11.48 Table 3-7. Math Example: Two Affected Unt Coal Type Prce Sulfur Content Heat Content Low Sulfur Spot $ % 24 mmbtu Hgh Sulfur Spot $ % 24 mmbtu Hgh Sulfur Contract $ % 24 mmbtu Generatng Unt P z r Demand (mmbtu) Unt 1 $2,719,320 90% 13,855,269 Unt 2 $7,298,412 90% 34,058,704 Scrubber Intallaton PA S: No Contract P A S: Unt 1 Demand P A S : Unt 1 and Unt 2 Demand None < $ < $ < $ Unt 1 ($194.48, $230.89) ($140.69, $230.89) ($140.69, $153.61) Unt 2 $ $ $

193 Fgure 3-1. Exce Demand Correpondence Fgure 3-2. Impact of Hgh Sulfur Coal Contract 193

194 Fgure 3-3. Impact of Low Sulfur Coal Contract Fgure 3-4. Exce Demand Correpondence wth Scrubber Choce 194

195 Fgure 3-5. Impact of Hgh Sulfur Coal Contract Fgure 3-6. Impact of Low Sulfur Coal Contract 195

196 Fgure 3-7. Gven Scrubber Choce: Shft from Hgh Sulfur Contract Fgure 3-8. Gven Scrubber Choce: Shft from Low Sulfur Contract 196

197 Fgure 3-9. Wth Scrubber Choce: Shft from Hgh Sulfur Contract 197

198 Fgure Wth Scrubber Choce: Shft from Low Sulfur Contract 198

199 APPENDIX A CONTRACT IMPACTS ON COSTS AND SCRUBBER INSTALLATION INDIFFERENCE PRICE A.1 Impact on Total Cot and Complance Cot from a Coal Contract Contrant Frt, conder a unt total cot wthout a coal contract contrant. Wthout the program retrcton on emon, a unt wll mply mnmze t cot of meetng electrcty demand by ung the coal wth the lowet prce per unt of heat content. PhC h + PlC l (A 1) Wth the emon contrant from the program, a unt wll mnmze t cot of coal ue, net allowance purchae, and crubber ntallaton. z P z + PAA + PhC h + PlC l (A 2) The dfference between (A 1) and (A 2) the total complance cot reultng from the program, whch nclude the change n coal cot, change n the net allowance purchae, and crubber ntallaton cot. z P z + P AA + P h(c h C h) + P l(c l C l ) (A 3) Second, conder a unt total cot wth a coal contract contrant. Wthout the program retrcton on emon, a unt wll mply mnmze t cot of meetng electrcty demand by ung all the the coal under contract, and cover the remander of t coal demand wth the coal wth the lowet prce per unt of heat content. PhC c c h + PlC c c l + P hĉ + P lĉ (A 4) Wth the emon contrant, a unt wll mnmze t cot for coal ue, net allowance purchae, and crubber ntallaton gven t emon and coal contract contrant. ẑ P z + PAA + PhC c c h + PlC c c l + P hĉ + P lĉ (A 5) 199

200 The dfference between (A 4) and (A 5) the total complance cot reultng from the program, whch nclude the change n pot market coal cot, net allowance purchae, and crubber ntallaton. The cot from contract coal cancel out becaue contract coal ue wll be the ame both wth and wthout the program. ẑ P z + PAA + P h(ĉ Ĉ h) + P l(ĉ Ĉ l ) (A 6) The uffcent condton under whch a coal contract contrant wll ncreae or decreae a unt complance cot can be derved from the dfference n complance cot ( ) wth and wthout a coal contract (A 6) mnu (A 3). [ ] ẑ P z + P AÂ + P h(ĉ Ĉ h) + P l(ĉ Ĉ l ) [ ] z P z + PAA + Ph(C h Ch) + Pl(C l Cl ) For mplcty, aume that the crubber choce a a gven and hgh ulfur pot market coal relatvely cheaper than low ulfur pot market coal. So wthout an emon contrant a unt wll prefer to ue the cheaper hgh ulfur coal. Propoton 1 can be proven by conderng the change n complance cot n (A 8) reultng from a coal contract. Frt conder a hgh ulfur coal contract to how Propoton 1() and Propoton 1() hold. Proof of Propoton 1(): If P A > MCA,, a unt prefer to wtch from hgh to low ulfur coal to meet t emon requrement becaue t the leat-cot complance opton. Wthout a hgh ulfur coal contract, a unt wll ue all low ulfur coal (C l = C,MAX l and C h (A 7) = 0) and requre the fewet allowance to cover the mnmum emon level (A MIN ). Wth a hgh ulfur coal contract, a unt wll ue le low ulfur coal (Ĉ,MAX l < C,MAX l ), whch wll 200

201 ncreae the emon level and requre addtonal allowance (ÂMIN [ P AÂMIN +P h(0 Ĉ,MAX ] [ )+P l(ĉ,max 0) The change n complance cot wll be: P AA MIN +Ph(0 C,MAX h > A MIN ). ] )+Pl(C,MAX l 0) (A 8) P A(ÂMIN A MIN ) + Ph(C,MAX h Ĉ,MAX h ) + P l(ĉ,max C,MAX l ) (A 9) The frt term potve becaue ÂMIN C,MAX h A MIN. The econd term alo potve becaue Ĉ,MAX h. The thrd term negatve becaue Ĉ,MAX l C,MAX l. Now fll n for coal ue: C,MAX h = D H h Ĉ,MAX h = D C c h Hc h H h C,MAX l = D H l Ĉ,MAX l = D C c h Hc h H l The change n complance cot reultng from a hgh ulfur coal contract the ncreae n net allowance purchae mnu the cot avng from not wtchng fuel from the hgh ulfur contract coal. P A(ÂMIN A MIN ) + ( P h H h P l )C c H hh c l h (A 10) Now fll n for the net allowance poton: A MIN = D S H lm A e l  MIN = D Ch c Hc h S Hl l + ChS c hm c A e mp A(C c hs c h Cc h Hc h H l S l) + ( P h H h P l )C c H hh c l h Sh By addng and ubtractng mp A, combnng lke term, and dvdng through by Hh m( S h S Hh l ), the expreon can be mplfed to: Hl [ C c hhh c PA( Sh c Hh c Sh S Hh l Hl S h H h ) + P A Pl P Hl h Hh m( S h S Hh l ) Hl ] [ C c hhh c PA( Sh c Hh c Sh S Hh l Hl S h H h ] ) + P A MCA, (A 11) 201

202 For th cae, t aumed the PA > MCA,. So f Sc h Hh c > S h, complance cot wll Hh ncreae, and the ncreae wll be get larger a the coal contract get larger. Proof of Propoton 1(): If P A MCA,, a unt prefer to ue all hgh ulfur coal and purchae allowance to meet t emon requrement becaue t the leat-cot complance opton. Wthout a hgh ulfur coal contract, a unt wll ue all hgh ulfur pot market coal (C h and C l = C,MAX h = 0) and requre the mot allowance ue to cover t maxmum emon level (A MAX ). Wth a hgh ulfur coal contract, a unt wll ue le hgh ulfur pot market coal (Ĉ,MAX h ( Sc h H c h < C,MAX h ). If hgh ulfur contract coal ha a hgher ulfur to heat content rato > S h H h ), a unt wll generate addtonal emon, whch wll requre a unt to purchae more or ell fewer allowance (ÂMAX lke term: P A(ÂMAX > A MAX ). Now fll n for known value and combne A MAX ) = PAC hh c h( c Sc h S h ) (A 12) Hh c Hh All coal ue reman the ame, whch mean the change n complance cot wll be the ncreae n cot from addtonal allowance. If Sc h H c h ncreae. > S h, a unt complance cot wll Hh Proof of Propoton 1(): If P A MCA,, a unt prefer to wtch to all low ulfur ue becaue t the leat-cot complance opton. Wthout a low ulfur coal contract, a unt wll ue all low ulfur pot market coal (C l = C,MAX l and C h = 0) and requre the leat poble allowance to cover t mnmum emon level (A MIN ). Wth a low ulfur coal contract, a unt wll ue le low ulfur pot market coal (Ĉ,MAX l contract coal ha a hgher ulfur to heat content rato ( Sc l H c l < C,MAX l ). If low ulfur > S l H l ), a unt wll generate addtonal emon, whch wll requre a unt to purchae more or ell fewer allowance (ÂMIN > A MIN ). Coal ue wll reman the ame wth and wthout an emon contrant, 202

203 and wll cancel out. Fll n for known value and combne lke term: A MIN = D S H lm A e l  MIN = D Cl chc l S Hl l + ClS c lm c A e P A(ÂMIN A MIN ) = PAC lh c l( c Sc l S l ) (A 13) Hl c Hl The change n complance cot wll be the ncreae n cot from the ncreae n a unt net allowance poton. If Sc l H c l Proof of Propoton 1(v): > S l, a unt complance cot wll ncreae. Hl If P A < MCA,, a unt prefer to ue all hgh ulfur coal and purchae allowance ntead of wtchng fuel to meet t emon requrement becaue t the leat-cot complance opton. Wthout a low ulfur coal contract, a unt wll ue all hgh ulfur coal (C h = C,MAX h and C l = 0) and requre the larget net allowance poton to cover the maxmum emon level (A MAX ). Wth a low ulfur coal contract, a unt wll ue le hgh ulfur coal (Ĉ,MAX h fewer allowance (ÂMAX < C,MAX h ), whch wll decreae the emon level and requre > A MAX ). Snce a unt prefer to ue hgh ulfur coal wth and wthout the emon contrant, coal ue wll reman the ame. Fll n for known value and combne lke term: P A(ÂMIN A MIN )+P h(c,max h Ĉ,MAX h Ĉ,MAX l +C,MAX l ) = P A(ÂMIN A MIN ) (A 14) The change n complance cot the change n cot from the change n net allowance poton. Now fll n for the net allowance poton: Snce Sc l H c l A MAX = D S H hm A e h  MAX < S h, complance cot wll decreae. Hh = D Cl chc l S Hh h + ClS c lm c A e [ C c S lhlp c Am c ] l S h < 0 (A 15) Hl c Hh Another way of lookng at the mpact of coal contract contrant on complance cot to fnd the change n total cot for a unt facng an emon contrant wth 203

204 and wthout a coal contract ((A 5)-(A 2)) and plt t nto two component, the change n complance cot and the change n fuel cot. For mplcty, aume the condton n Propoton 1() hold. z P z + P A(Â A ) + PhC c c h + PlC c c l + P h(ĉ Ch ) + P l(ĉ Cl ) (A 16) Aume that a unt face a hgh ulfur coal contract, and prefer to wtch to low ulfur coal ue to meet t emon requrement ntead of purchang allowance or ntallng a crubber. P A(ÂMIN A MIN ) + PhC c c h + P l(ĉ,max C,MAX l ) (A 17) To be able to nterpret th expreon, t neceary to add and ubtract (P h Cc Hh c h H h ). C c h(ph c Ph Hh c Hh ) + P A(ÂMIN A MIN ) + P hc c Hh c h Hh + P l(ĉ,max C,MAX l ) (A 18) The frt term the change n hgh ulfur coal cot from ung the contract coal ntead of pot market coal. Thee are not change n complance cot becaue they wll occur wth or wthout the program. The remanng term are the change n complance cot reultng from the program. Hh c Hh C c h(ph c Ph ) } {{ } Change n Fuel Cot + P A(ÂMIN A MIN ) + ( P h H h P l )C c H hh c l h } {{ } Change n Complance Cot (A 19) By fllng n for the coal ue, the lat term gve the ame expreon for the change n complance cot a n the proof of Propoton 1(). C c hh c h [ PA( Sh c Hh c Sh S Hh l Hl S h H h ] ) + P A MCA, (A 20) A unt complance cot ncreae f Sc h H c h > S h. Hh 204

205 A.2 Dervaton of Cot-Mnmzng Input Ue to Fnd P S A Aumng no crubber, the cot-mnmzng combnaton of coal and allowance olve the problem below. mnâ,ĉh,ĉl (P AA MAX + P hĉ,max, P A A MIN + P lĉ,max l ) (A 21) Aumng a crubber ntalled, the cot-mnmzng combnaton of nput expreed below. mnã, C h, C l (P A A SMAX + P h,max C h, P A A SMIN + Pl,MAX C l ) (A 22) Notce that contract coal ue and the cot of ntallng a crubber can be gnored becaue all are contant. 205

206 APPENDIX B MARKET EQUILIBRIUM AND SIMULATION DESIGN B.1 Condton for Extence of an Equlbrum Theorem 5.1: Aumng the crubber choce (z ) a gven, a market equlbrum ext. Proof of Theorem 5.1: To prove that a market equlbrum ext, t neceary to apply Kakutan Fxed Pont Theorem. Kakutan Fxed Pont Theorem that tate: If X a non-empty, compact, convex ubet of R m and f f an upper em-contnuou correpondence from X nto telf uch that ( x X) the et f(x) non-empty and convex, then f ha a fxed pont (there an x f(x)). Aumng all other parameter a gven for all generatng unt, a generatng unt exce demand a functon of the allowance prce, A (P A ). Conder a generatng unt exce demand correpondence from Secton 5. A = A MAX ρa MAX A MIN (1 ρ)a MIN f P A > MCA, f P A = MCA, ρ [0, 1] f P A < MCA, To fnd the market exce demand, you mut um all generatng unt exce demand, whch gve you A m = n =1 A. It neceary to how that the market exce demand compact. The market exce demand bounded above by the um of the maxmum allowance exce demand for each generatng unt ( n =1 AMAX of the mnmum allowance exce demand for each generatng unt ( n market exce demand le n a cloed nterval [ n =1 AMIN, n ) and below by the um =1 AMAX =1 AMIN ). So the ] X. X beng a cloed nterval on the real lne non-empty, compact (cloed and bounded), and convex (any pont on the lne connectng any two pont n the et alo n the et). It neceary to how that the et of prce compact (cloed and bounded). Defne the lower bound on prce to be zero becaue t neceary to have a potve prce. Defne the upper bound on prce to be P A = arg mn n =1 A (P A ), or the allowance 206

207 prce that reult n the mallet poble exce demand for a partcular generatng unt multpled by two. Th enure a upper bound that wll be hgher than any poble prce. The cloed nterval for prce [0, P A ], whch non-empty by degn. Snce there an upper bound, a lower bound, and both bound are ncluded n the et (cloed), the et compact. Snce the et of prce and market exce demand are compact and the market exce demand depend on the allowance prce, the market exce demand (A m (P A )) a mappng from [0, P A ] nto X. It neceary to how that exce demand non-empty, convex valued at each P A [0, P A ], and upper em-contnuou. It uffcent to how that each generatng unt exce demand correpondence non-empty, convex, and upper em-contnuou becaue the um of a fnte number of non-empty, convex, upper em-contnuou correpondence alo non-empty, convex, and upper em-contnuou. A generatng unt exce demand (A (P A )) are defned to be mappng from [0, P A ] nto X, whch make them non-empty by contructon. A generatng unt exce demand correpondence cloed and bounded n the nterval [A MIN, A MAX ], whch make t a compact et. The et of exce demand convex becaue the average of any two exce demand value alo n the et. For a correpondence to be upper em-contnuou, the convergence exce demand value of any prce equence mut alo be n the correpondence. Snce every poble prce equence converge to a value that n the exce demand correpondence (ee Fgure B.2), each unt exce demand correpondence upper em-contnuou. Now we mut defne the mappng from X nto the et of prce [0, P A ] a µ(x) where... P A [0, P A ] : P A x = max Q [P µ(x) = A ] Q x f x 0 P A [0, P A ] : P A x = 0 f otherwe Snce [0, P A ] non-empty, µ(x) mut be non-empty a well. The mappng convex valued nce for market exce demand equal to zero (x = 0), µ(x) = [0, P A ]. If there a 207

208 potve exce demand (x > 0), µ(x) = P A. If there a negatve exce demand (x < 0), or exce upply, µ(x) = 0. Snce [0, P A ] compact, the graph of µ(x) cloed, whch mple µ(x) upper em-contnuou. Now defne F (x, P A ) = µ(x) A m (P A ). Snce µ(x) and A m (P A ) atfy all properte needed to apply Kakutan Fxed Pont Theorem, there ext a fxed pont (x, PA ) uch that P A [0, P A ] and x X uch that P A µ(x ) and x A m (PA ). In Englh...There a market exce demand correpondence for whch each exce demand value can only reult from only one allowance prce whle each allowance prce wll reult n at leat one market exce demand value. Once the crubber choce ntroduced nto the decon-makng proce, the correpondence become more complex, a een n Fgure B.2. An equlbrum may n fact ext, but there no way to guarantee an equlbrum becaue the exce demand correpondence no longer a convex et. The average of the two exce demand value (A SMAX and A MIN ) not n the exce demand correpondence. B.2 Techncal Detal of Smulaton Model Degn The equlbrum allowance market prce olved by ung a becton teratve proce. An upper lmt ($1,000) and lower lmt ($0) for the allowance prce are choen. The ntal allowance prce et to the upper lmt and the mulaton olve for each generatng unt cot-mnmzng choce. Then t check f the allowance market n an equlbrum. If market exce demand potve, the allowance prce too low and the allowance prce ncreaed by one-half the dfference between the upper and lower lmt. The old prce now become the new lower lmt whle the upper lmt reman the ame. If the market exce demand negatve, the allowance prce too hgh and the allowance prce decreaed by one-half the dfference between the upper and lower lmt. The old prce become the new upper lmt and the lower lmt reman the ame. In th cae, the upper 208

209 lmt et hgh enough to guarantee the prce too low. So the prce wll decreae by $1,000-($1000-$0)/2=$500 to a new prce of $500. The program then run agan wth the new allowance prce, each teraton decreang the dfference between the upper and lower lmt by half untl the program converge to an allowance prce. Once the program converge, t mut enure a market exce demand of zero. A concern that the program tend to puh a unt choce toward a corner oluton where the market may not clear. Gven the crubber choce, the allowance prce wll converge to a value equal to at leat one generatng unt MCA,, whch allow thoe frm choce to be hfted to an nteror oluton to clear the market wthout alterng the unt total cot or total ndutry cot becaue the unt ndfferent to purchang allowance or wtchng fuel from hgh to low ulfur coal at the equlbrum allowance prce (P A ). Allowng for the crubber choce wll reult n the convergence of P A at an allowance prce where a generatng unt ndfferent to ntallng a crubber. In th cae, there not a true equlbrum and mut conder t a qua-equlbrum a decrbed above. 209

210 Fgure B-1. Upper Sem-Contnuou Correpondence Fgure B-2. Correpondence wth Scrubber Choce 210

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216 BIOGRAPHICAL SKETCH Johua Davd Knefel wa born n 1981 n North Platte, Nebraka. He grew up n North Platte, graduatng alutatoran from Herhey Hgh School n Johua receved h bachelor degree n economc and mathematc n 2003 from Doane College n Crete, Nebraka. He receved h Mater of the Art n economc n 2005 from the Unverty of Florda, where he pecalzed n ndutral organzaton, publc economc, and econometrc. From Fall 2006 through Sprng 2008, Johua ntructed four emeter of a coure n envronmental economc. H clawork and reearch allowed hm to obtan h PhD n economc from the Unverty of Florda. Upon completon of h PhD program, he wll take an economt poton at the Natonal Inttute of Standard and Technology (NIST) n Gatherburg, Maryland. H reponblte at NIST wll nclude reearch on the lfe-cycle cot and envronmental mpact of ndvdual product ued n the contructon ndutry. 216