跨期排放权交易模型、银行和贷款【外文翻译】.doc

1、原文一AMODELOFINTERTEMPORALEMISSIONTRADING,BANKING,ANDBORROWINGTHISPAPERPROVIDESAGENERALTREATMENTOFEMISSIONTRADING,BANKING,ANDBORROWINGINANINTERTEMPORAL,CONTINUOUSTIMEMODELUSINGOPTIMALCONTROLTHEORY,THEDECENTRALIZEDBEHAVIOROFFIRMSISSHOWNTOLEADTOTHELEASTCOSTSOLUTIONATTAINABLEUNDERJOINTCOSTMINIMIZATIONEXP

2、LICITSOLUTIONSFORTHETIMEPATHSOFEMISSIONSANDPERMITPRICESAREDERIVEDWHENFIRMSAREALLOWEDTOBOTHBANKANDBORROWANDWHENFIRMSAREONLYALLOWEDTOBANKEMISSIONPERMITSTHEPOLICYIMPLICATIONSOFEMISSIONBANKINGANDBORROWINGAREDISCUSSED1INTRODUCTIONMARKETABLEEMISSIONPERMITSAREANECONOMICINSTRUMENTUSEDTOATTAINAPREDETERMINEDL

3、EVELOFENVIRONMENTALQUALITYTHEBASICCONCEPTBEHINDEMISSIONTRADING,ORIGINATEDBYDALES5,ISASIMPLEONEINITIALLY,AREGULATORYAGENCYLIMITSTHEOVERALLLEVELOFEMISSIONS,EITHERBYSETTINGASTANDARDORALLOCATINGEMISSIONS,ANDTHENITALLOWSFIRMSTOTRADETHEIREMISSIONALLOCATIONSORSURPLUSPERMITSITISNOWWIDELYAGREEDAMONGECONOMIST

4、STHATMARKETABLEEMISSIONPERMITSCANBEACOSTEFFECTIVESTRATEGYFORCONTROLLINGENVIRONMENTALPOLLUTANTS,ANDANEXTENSIVELITERATUREONTHEIRPROPERTIESHASDEVELOPEDSEETIETENBERG12ANDCROPPERANDOATES4FORTHOROUGHREVIEWSTHISWORKHASIDENTIFIEDTHREESOURCESOFPOTENTIALCOSTSAVINGSEMISSIONTRADINGBETWEENFIRMS,EMISSIONAVERAGING

5、BETWEENSOURCESWITHINAFIRM,ANDEMISSIONTRADINGTHROUGHTIMEDESPITECOMMONREFERENCETOTHESETHREECOMPONENTS,PREVIOUSTHEORETICALANDEMPIRICALRESEARCHHASFOCUSEDALMOSTEXCLUSIVELYONTHEFIRSTTWOITEMS,TRADINGANDAVERAGINGTHESMALLAMOUNTOFRESEARCHINTOEMISSIONBANKINGANDBORROWINGISREGRETTABLESINCEPUBLICPOLICYMAKERSHAVEA

6、LREADYBEGUNTOINCORPORATEBANKINGANDBORROWINGRULESINTOLAWFOREXAMPLE,THEBANKING（ANDTRADING）OFSULFURDIOXIDEISNOWAUTHORIZEDBYTHECLEANAIRACTAMENDMENTSOF1990,ANDCALIFORNIAALLOWSMANUFACTURERSOFPASSENGERCARSTOBANK（ANDTRADE）HYDROCARBONEMISSIONSINTHECONTEXTOFFUELEFFICIENCY,RATHERTHANEMISSIONS,THEBORROWINGANDBA

7、NKINGOFCAFE（CORPORATEAVERAGEFUELECONOMY）CREDITSFORUPTOTHREEYEARSHASBEENALLOWEDSINCE1980HOWEVER,THECONCEPTOFMARKETABLEPERMITS,ANDINTERTEMPORALTRADINGINPARTICULAR,GOESFARBEYONDTHEREALMOFENVIRONMENTALCLEANUPORFUELECONOMYSTANDARDSITAPPLIESTOTHETRADEOFGOODSWHOSEEXISTENCEISSTATUTORILYGENERATEDBUTPRIVATELY

8、TRANSFERABLEFOREXAMPLE,THECONCEPTAPPLIESTOTHEALLOCATIONOFRESIDENTIALORCOMMERCIALPROPERTYDEVELOPMENTRIGHTSORTOTHEBUYINGANDSELLINGOFFEDERALFUNDSBETWEENBANKSWHOMUSTMEETRESERVEREQUIREMENTSINTHELATTERCASE,CONSERVATIVEBANKSWHOCHOOSETOCARRYSURPLUSRESERVEREQUIREMENTSACTASSELLERSOFOVERNIGHTLOANS（EG,TRADING）A

9、ND,INADDITION,MAYCHOOSETOHOLDADDITIONALEXCESSRESERVESSPECULATIVELYOVERSEVERALTIMEPERIODS（EG,BANKING）INTHEHOPETHATALUCRATIVELOANOPPORTUNITYARISESTHROUGHOUTTHISPAPER,HOWEVER,THEDISCUSSIONOFBANKINGWILLBECOUCHEDINTERMSOFSTANDARDUSAGEWITHINTHEENVIRONMENTALFIELD,WHICHREFERSTOEMISSIONOFPOLLUTANTSBYFIRMSWIT

10、HINTHEENVIRONMENTALLITERATURETHISPAPERFILLSTHETHEORETICALGAPBYPROVIDINGACOMPREHENSIVETREATMENTOFINTERTEMPORALEMISSIONTRADING2INPARTICULAR,ITEXPLORESTHEPROBLEMOFMINIMIZINGTHECOSTOFINTERTEMPORALEMISSIONCONTROLBYNHETEROGENEOUSFIRMSINTHEPRESENCEOFPOLLUTIONSTANDARDSANDEMISSIONPERMITSTHATARETRADABLEACROSS

11、FIRMSANDTHROUGHTIMEINSUCHASETTING,FIRMSMAYDIRECTLYREDUCEEMISSIONS,ANDTHEYMAYPURCHASE,SELL,BANKANDBORROWEMISSIONPERMITSINORDERTOMEETAPPLICABLESTANDARDSORTOTAKEADVANTAGEOFANYSPECULATIVEOPPORTUNITIESTHATMAYARISETOGENERATEPERMITS,AFIRMMAYCHOOSETOPOLLUTELESSTHANTHECURRENTSTANDARDTHESEGENERATEDPERMITSMAYB

12、ESOLDTOADIFFERENTFIRMORDEPOSITEDINANEMISSIONBANKTOBEUSEDLATERBYTHEFIRMORSOLDATALATERTIMETOANOTHERFIRMTHEBORROWINGOFPERMITSOCCURSWHENAFIRMPOLLUTESMORETHANITSCURRENTSTANDARD,BUTTHECUMULATIVEDEFICITMUSTBEREPAIDBYTHEENDOFTHEPLANNINGHORIZONBANKINGANDBORROWINGLOWERTHECOSTOFCOMPLIANCEWITHEMISSIONSTANDARDSB

13、YALLOWINGFIRMSTOADJUSTTHEIREMISSIONSTREAMMOREFLEXIBLYTHROUGHTIMETHEMODELUSEDHEREBUILDSONTHESEMINALSTATICPAPERBYMONTGOMERY（7）ONMARKETABLEPERMITSANDEXTENDSTHEWORKOFTIETENBERG（12）ANDCRONSHAWANDKRUSE（3）,WHOEXAMINESOMEASPECTSOFPERMITMARKETSWITHBANKINGINDISCRETETIMETIETENBERGCHARACTERIZESTHEJOINTLEASTCOST

14、ALLOCATIONOFPOLLUTIONFORACUMULATIVEPOLLUTANTGIVENACONSTRAINTONTHETOTALAMOUNTOFPOLLUTIONOVERTIMEINTHISCUMULATIVEEMISSIONPERMITSYSTEMITAPPEARSTHATALLPERMITSAREISSUEDATTHEBEGINNINGOFTHETIMEHORIZONSOMEPERMITSARETHEREFOREALWAYSBANKEDUNTILUSEDUPBEFORETHEPERMITSAREUSEDUPTHEIRPRICEMUSTRISEATTHERATEOFINTERES

15、TCRONSHAWANDKRUSEEXAMINEAPERMITSYSTEMWITHBANKINGWHEREPERMITSAREALLOCATEDTOFIRMSINEACHOFTPERIODSTHEYSHOWTHATINAMARKETFORTRANSFERABLEANDBANKABLEPERMITS,ACOMPETITIVEEQUILIBRIUMEXISTSANDACHIEVESAGGREGATEEMISSIONTARGETSATLEASTSYSTEMCOSTCRONSHAWANDKRUSEALSOSHOWTHATIFFIRMSDONOTDESIRETOBANK,PERMITPRICESWILL

16、RISEBYLESSTHANTHERATEOFINTERESTTHISPAPEREXTENDSTHEWORKOFTIETENBERGANDCRONSHAWANDKRUSEBYPROVIDINGAMOREGENERALTREATMENTOFPERMITTRADINGINCONTINUOUSTIMETHROUGHTHEUSEOFOPTIMALCONTROLTHEORYINSTEADOFLIMITINGINTERTEMPORALTRADINGTOBANKING,THISPAPERSTARTSFROMTHECONTEXTOFALLOWINGBOTHBORROWINGANDBANKINGWITHREST

17、RICTIONSONBORROWINGASASPECIALCASETHEFORMULATIONALLOWSTHEDERIVATIONANDEXTENSIONOFTHERESULTSOFTIETENBERGANDCRONSHAWANDKRUSE,BUTINTERPRETATIONSARENECESSARILYSOMEWHATDIFFERENTIMPORTANTLY,THECONTINUOUSTIMEFRAMEWORKALLOWSFORTHEEXPLICITSOLUTIONFORTHETIMEPATHOFEMISSIONS,WHICH,COSTSAVINGSNOTWITHSTANDING,MAYB

18、EINTERTEMPORALEMISSIONTRADINGSMOSTSIGNIFICANTASPECTNEITHERTIETENBERGSNORCRONSHAWANDKRUSESPAPEREXAMINESTHISISSUEINDETAIL3INADDITION,THISANALYSISEXTENDSTHEMODELOFCRONSHAWANDKRUSEBYCONSIDERINGTHEQUALITATIVEIMPACTSOFEMISSIONBORROWINGONPERMITPRICES,THEEMISSIONSTREAM,ANDTOTALSOCIALDAMAGES5EQUILIBRIUMCONDI

19、TIONSASDISCUSSEDABOVE,THEREGULATORSGOALISTOMINIMIZETHEJOINTTOTALCOSTSOFPOLLUTIONABATEMENTOFNHETEROGENEOUSFIRMSSUBJECTTOREACHINGAREGIONALEMISSIONSTANDARD,S,OVERTHETPERIODHORIZONSOTHATBT0ITISNECESSARYTOSHOWTHATANEQUILIBRIUMINAMARKETFORPERMITSEXISTSANDISEFFICIENTINTHESENSETHATITISEQUALTOTHESYSTEMCOSTMI

20、NIMIZATIONBYREGULATORSWHOKNOWTHECOSTFUNCTIONSOFALLTHEFIRMSMONTGOMERYSW7XDEFINITIONOFAMARKETEQUILIBRIUMFORPOLLUTIONPERMITSISUSED,BUTMODIFIEDTOACCOUNTFORTHEDYNAMICPROBLEMATHANDESPECIALLY,BUTNOTEXCLUSIVELY,INPROBLEMSWITHLINEARCONTROLVARIABLES,THEOPTIMALPATHOFTHELINEARCONTROLCANBEDISCONTINUOUSINTTHEREFO

21、REINILEMMA1,WHICHAPPEARSINTHEAPPENDIX,ITISNECESSARYTOASSUMETHATTHEOPTIMALCONTROLISCONTINUOUSINTHEPRICEOFPERMITS,P,EVENATPARTICULARIINSTANCES,WHEREISDISCONTINUOUSINTTHISASSUMPTIONISNOTTOOIRESTRICTIVEITSECONOMICCONTENTISSIMPLYTHATATACERTAINPOINTINTIMEIFAFIRMSUDDENLY（EG,DISCONTINUOUSLY）DECIDESTOBUYORSE

22、LLADIFFERENTQUANTITYOFPERMITS,THEDECISIONISBASEDONACONTINUOUSFUNCTIONOFTHEPERMITPRICEANINTERTEMPORALEQUILIBRIUMINTHEPERMITMARKETALSOREQUIRESTHATFIRMSHAVEANINTERNALSOLUTIONDEFINITIONANINTERTEMPORALMARKETEQUILIBRIUMINEMISSIONPERMITSOVERATPERIODHORIZONCONSISTSOFTHEVECTORSANDMINIMIZEEACHFIRMSCOSTSGIVENS

23、UBJECTTOEACHFIRMSCONSTRAINTS（12）（15）FOREACH,ANDTHEMARKETCLEARINGCONDITIONONPERMITSTHEMARKETCLEARINGCONDITIONISAFLOWCONDITIONTHATSIMPLYREQUIRESTHATATANYPOINTINTIMEAPERMITPURCHASEDBYONEFIRMBESOLDBYSOMEOTHERFIRMINADDITION,COSTMINIMIZATIONWILLALSOIMPOSETHEFOLLOWINGTERMINALSTOCKCONDITIONCOSTMINIMIZATIONR

24、EQUIRESTHATTHEPRICEOFAUNITOFPOLLUTIONINTHEBANKBEZEROATTHETERMINALPERIODORTHATTHESTOCKOFPERMITSFROMALLFIRMSBEZERO6CHARACTERIZINGTHEPATHOFEMISSIONSFROMANENVIRONMENTALPERSPECTIVE,PERHAPSTHEMOSTIMPORTANTRESULTOFALLOWINGFIRMSTOINTERTEMPORALLYMOVEPERMITS,ASOPPOSEDTOSIMPLYTRADINGTHEMINSTANTANEOUSLYAMONGTHE

25、MSELVESTOATTAINTHELEASTCOSTALLOCATION,ISTHEEFFECTTHATBANKINGANDBORROWINGCANHAVEONTHESTREAMOFEMISSIONSTHROUGHTIMEANDTHERESULTINGHEALTHANDENVIRONMENTALIMPACTSIFFIRMSUSEBANKINGTOSMOOTHDECREASINGEMISSIONSTANDARDSOVERTIMEANDIFMARGINALDAMAGESFROMPOLLUTIONAREINCREASING,THENBANKINGGENERATESLOWERTOTALPOLLUTI

26、ONDAMAGESWHENCONSIDERINGTHEINTEGRALOVERTHEWHOLETIMEHORIZONOFEACHPERIODSDAMAGEFROMTHEFORMALMODELWECANDERIVESOMEINSIGHTINTOHOWFIRMSADJUSTTHEIREMISSIONSTREAMSWHENTHEYCANTAKEADVANTAGEOFTHEABILITYTOBANKANDBORROWIFDAMAGESFROMEMISSIONSAREACONVEXFUNCTIONANDSTANDARDSARETIGHTENINGTHROUGHTIME,THENALLOWINGFIRMS

27、TOBANKLOWERSSOCIALDAMAGESBANKINGALLOWSFIRMSTOSMOOTHTHEIREMISSIONSTREAMTHROUGHTIMEFORACONVEXDAMAGEFUNCTION,WHERECUMULATIVEDAMAGEISTHEINTEGRALOFDAMAGESINALLTIMEPERIODS,TOTALDAMAGESAREREDUCEDIFTHELEVELOFEMISSIONSISMORECONSTANTTHROUGHTIMETHISRESULTISONEOFTHEQUALITATIVEDIFFERENCESBETWEENASTATICANDADYNAMI

28、CMARKETABLEPERMITSYSTEMBYGIVINGFIRMSANINCENTIVE（COSTSAVINGS）TOMORETHANMEETCURRENTSTANDARDS,FIRMSWILLINTERTEMPORALLYMOVEEMISSIONSTOLOWERSOCIALDAMAGESTHISOCCURSWHENFIRMSAREALLOWEDTOBANKEMISSIONSANDWHENSTANDARDSAREBECOMINGSTRICTERTHROUGHTIMEEMISSIONSTANDARDSBECOMINGSTRICTERTHROUGHTIMEIS,HOWEVER,OFTENTH

29、ENORMIFPOLLUTIONDAMAGESARECONVEX,THENALLOWINGFIRMSTOSHIFTEMISSIONSINTOTHEPRESENTWILLINCREASEENVIRONMENTALDAMAGESWHETHERORNOTFIRMSSHOULDBEALLOWEDTOBORROW,ATTHEEXPENSEOFINCREASINGENVIRONMENTALDAMAGES,DEPENDSONBALANCINGTHECOSTSAVINGSTOFIRMSWITHTHEADDITIONALHARMCAUSEDBYBORROWING7FINALREMARKSTHISPAPERCHA

30、RACTERIZESTHEOPTIMALBEHAVIOROFFIRMSTHATFACEEMISSIONSTANDARDSSETBYREGULATORS,BUTAREALLOWEDTOPURCHASE,SELL,BANK,ANDBORROWEMISSIONPERMITSGIVENAFINITEPLANNINGHORIZONOFLENGTHTITWASSHOWNTHATANEQUILIBRIUMSOLUTIONTOTHEFIRMSPROBLEMSEXISTSANDISEFFICIENTINTHESENSEOFACHIEVINGTHELEASTCOSTSOLUTION（THESOLUTIONATTA

31、INEDBYASOCIALPLANNERWHOKNOWSTHECOSTFUNCTIONSOFALLFIRMS）THEEQUILIBRIUMPERMITPRICEPATHWASSHOWNTOBECONSTANTORDECREASINGDEPENDINGONWHETHERFIRMSDESIREDTOBANKORWEREALLOWEDTOBORROWPERMITSANDWHETHERFIRMSFACEDABINDINGCONSTRAINTONBORROWINGEXISTENCEOFANEQUILIBRIUMPERMITPRICEPATHALSOREQUIRESTHATFIRMSNOTBUYANDSE

32、LLPERMITSATTHEIRMAXIMUMINSTANTANEOUSRATESTRATEGICBEHAVIORANDPRICEANDCOSTUNCERTAINTYWERENOTTAKENINTOCONSIDERATIONASARGUEDINTHEBODYOFTHEPAPER,PERHAPSTHEMOSTIMPORTANTCONSEQUENCEOFEMISSIONBANKINGANDBORROWINGISTHEABILITYOFFIRMSTOSHIFTTHEIREMISSIONSTREAMTHROUGHTIMEINPARTICULAR,WHENSOCIALDAMAGESAREANINCREA

33、SINGFUNCTIONOFTHELEVELOFPOLLUTIONEMITTEDATANYONETIME,THENITISGOODPUBLICPOLICYTOALLOWFIRMSTOBANKEMISSIONSWHENSTANDARDSAREBECOMINGSTRICTERTHROUGHTIMEATLEASTFORNOWOURSOCIETYISBECOMINGINCREASINGLYCONCERNEDWITHENVIRONMENTALQUALITY,ANDEMISSIONSTANDARDSAREBECOMINGMORESTRINGENTTHISPAPERHASSHOWNTHATINTHESECI

34、RCUMSTANCES,BANKINGOFEMISSIONPERMITSCANLOWERSOCIALDAMAGESBANKINGALSOPROVIDESCOSTSAVINGSTOFIRMSBYALLOWINGTHEMTOADJUSTTHEIROWNINTERNALRATESOFEMISSIONREDUCTIONSTOANEXTERNALLYSETSTANDARDALONGWITHAVERAGINGANDTRADING,THEN,BANKINGCANALSOLOWERTHEMONETARYCOSTSOFCOMPLIANCEBANKING,THEREFORE,ALONGWITHAVERAGINGA

35、NDTRADING,SHOULDBECONSIDEREDBYPUBLICPOLICYMAKERSINCHARGEOFENSURINGTHESAFETYOFOURENVIRONMENT出处JOURNALOFENVIRONMENTALECONOMICSANDMANAGEMENT外文题目AMODELOFINTERTEMPORALEMISSIONTRADING,BANKING,ANDBORROWING出处JOURNALOFENVIRONMENTALECONOMICSANDMANAGEMENT作者JONATHANDRUBIN跨期排放权交易模型、银行和贷款本文提供了排放权交易综合解决方案，银行和借贷以及连

36、续时间模型。采用最优控制理论，证明了联合下达到最小化成本分散了企业的行为是企业成本最低的解决方案。排放量的时间、路径及许可证的价格是根据企业在银行的贷款额和银行发放的排放许可证，参照发放行的贷款政策进行讨论而定的。一、简介排污许可证是利用适销对路的经济手段来达到环境质量的一个预定的水平。排污权交易的基本概念起源于DALES5，较简单。起初，监管机构通过设置或分配排放标准来限制排放的整体水平，然后根据公司的营业额分配排污许可证。现在经济学家普遍认为，适销对路的排放许可证可以作为环境污染物控制成本效益的战略，这一点在许多文献上都有阐述。这项工作已经确定了三个来源的潜在成本节约企业间的排放权交易、公

37、司内部排放源之间的平均、以及排放权交易的时间，尽管共同参考由这三部分组成，但以前的理论和实证研究重点几乎完全局限于前两个项目，交易和平均。少量的借贷排放的研究将是令人遗憾的，因为银行的公共决策者已经开始将借贷的银行和规则定为法律。例如，二氧化硫的贷款和交易的授权是根据1990年修订的清洁空气法，允许汽车制造商和加利福尼亚州的客运贷款和交易，碳氢化合物的排放的贷款和交易在1980年获准。然而，许可证适销对路的概念，特别是跨交易，远远超出了环境清理或领域的燃油经济性的标准，它适用于货物贸易的存在是法定的产生但私下转让，例如，这一概念适用的权利分配住宅或商业地产开发或购买和基金销售的联邦银行必须满足

38、准备金要求，在后一种情况下，保守的银行准备金要求进行选择谁作为交易的卖方过剩隔夜贷款。此外，可以选择几个时期银行持有超额准备金的额外时间投机了。在希望出现一个利润丰厚的贷款机会。然而，在本文中，银行将讨论在环境领域使用条款的措辞标准，是指企业排放的污染物。环境文学为本文研究排污权交易提供了一个全面的理论依据，特别是，它探讨了减少排放的成本问题时际在污染控制标准由N异质的存在和企业排污许可证是通过时间在不同企业间流通。在这样的环境，企业可以直接减少排放，而他们可能购买，出售，银行和借款排放许可，以符合适用的标准或采取任何优势投机的机会，可能出现。要生成许可证，企业可以选择污染比现行标准少。这些生

39、成的许可证可能被出售给不同的公司，借用的许可时，会出现企业污染比现行标准多，但累积赤字必须偿还通过规划地平线结束。银行和借贷成本的降低符合排放标准，允许企业通过灵活的时间以调整其排放流。该模型采用的由蒙哥马利在MONTGOMERY7静态文件的基础上销售许可证和扩展了TIETENBERG12和CRONSHAW工作克鲁斯3，审查银行的分立市场的某些方面的许可证时间。TIETENBERG共同的特点，污染最少的费用为分配标准，听取了关于污染物累积的污染总量的时间限制。在此累积排放许可证制度，证该时间范围似乎是所有发行许可证的开始。因此，一些许可证，直到永远库存用完。许可证之前所用的价格必须在上升的利率

40、。CRONSHAW和克鲁斯检查许可证制度与银行在许可证分配给每个时期的T公司。他们表明，在有利可图的转让许证可的市场，一个竞争均衡的存在和实现总排放指标至少系统成本。CRONSHAW和克鲁斯还表明，企业不希望银行允许价格上涨超过了利息率。本文将通过提供TIETENBERG和CRONSHAW和克鲁斯工作一个更普遍的许可交易在连续时间的方案，通过使用最优控制理论。而不是限制贸易跨银行，这本文从允许借款和银行都与上下文限制作为一种特殊情况借款。可以推导的制定和扩建TIETENBERG和CRONSHAW和克鲁斯的结果，但诠释必然有所不同。重要的是，连续时间框架允许的排放量，时间路径明确的解决办法，尽管

41、节省成本，可能是跨期排放权交易的最重要的方面。无论TIETENBERG的NORCRONSHAW和克鲁斯的论文探讨这一细节问题，这种分析扩展了CRONSHAW和克鲁斯模型考虑对许可证的价格，借款的排放影响的定性排放流，社会总损失。二、平衡条件如上所述，监管的目标是尽量减少总成本的联合受污染的N异质公司治理，以达成区域排放标准，S的T型时期的视野，使BT0。这是必要的表明，在市场均衡存在的许可证，并在有效意义上讲，它等于系统成本最小化的监管谁知道所有的厂商成本函数。蒙哥马利的市场均衡定义污染许可证被使用，但修改了动态问题的帐户。特别是，与线性控制变量的问题，最优路径的线性控制可连续在T因此，在引理

42、1的附录中，它是必要的假设最优控制在许可证，磷价格连续的，即使在特别情况下，其中是不连续的在T这个假设不是太限制，其经济内容很简单，即在某一个时间点上，如果一个公司不连续的。决定购买或出售不同数量的许可证，这项决定是基于对许可证价格的连续函数。一个允许市场在跨期均衡还要求企业有一内部解决方案。定义，在跨市场均衡排放许可证在一个T期间地平线包括向量和标量，减少每个企业的成本考虑。每家公司受到的约束，与市场清拆许可条件市场出清条件是一个流动的条件，只需要在任何在时间点一公司购买许可证出售给其他一些公司。在此外，成本最小化还将依据以下终端库存状况成本最小化要求，一个污染单位在银行的价格是零或者说在终

43、端内，允许所有企业库存为零。三、排放路径从环保的角度看，也许最重要的结果是允许企业交易许可证，因为他们彼此之间不是简单地买卖瞬间达到最低的成本分配，是影响该银行和借款可以透过时间和对排放流由此产生的对健康和环境的影响。如果企业使用银行顺利随着时间的推移，如果降低边际损害污染排放标准在增加，那么银行会在产生较低的总污染损害时考虑过了各个时期的损害和整个时间跨度积分。从正式的模型中，我们可以推导出到公司如何调整其排放一些见解，他们可以利用的能力和优势以及银行借贷。这一分析框架已在世界上的确定性。实际上，边际减排成本和边际损失是不确定的。特别是，公司可能利用库存，许可证涵盖的排放水平特别高，因为业务

44、基金期间对产出的需求突然增加。如果边际损失正在增加，这超出的排放大爆发可能会导致不可接受的损害。因此，不妨把总容许上限履行在任何一个特定时期的排放量。四、结束语本文刻画了企业的最佳行为涌出由监管机构设定的标准，但不得收购，销售排污许可证,一平衡解决企业的问题存在，并且是在这个意义上有效实现成本最低的解决方案。平衡许可证的价格路径被证明保持不变或减少取决于企业是否需要到银行或进行允许借用许可证和企业面临是否具有约束力的约束下借款。中均衡许可证的价格路径的存在也要求企业不要购买和出售他们的最大瞬时速度许可证。战略行为价格和成本的不确定性。至于说在论文的正文部分，也许最重要的问题是企业能否转移其排放流通过时间。特别是，当社会的损害是不断增加的功能在任何时候污染排放水平，那么它是良好的公众政策，让排放标准时，银行通过时间限制采取更严格的政策。至少现在我们的社会日益关注环境质量和排放标准越来越严格。本文表明，在这种情况下，银行可以降低排放许可证的社会损害。银行还规定，允许企业调整自己的减排率标准以节省成本。随着平均和交易，那么，银行还可以降低货币成本。因此，随着平均和交易，公众决策者应考虑确保环境安全。