Certainty and Uncertainty in Cap and Trade System or in Carbon Tax. to Decrease Greenhouse gas Emissions. Haradhan Kumar Mohajan ABSTRACT

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1 Indus Jounal of Managmnt & Socal Scncs ():8- (Fall ) das.pc.og/s/h/ounl.html Ctanty and Unctanty n Cap and ad Systm o n Cabon ax fo Gn Accountng to Dcas Gnhous gas mssons Haadhan Kuma Mohaan ABSRAC hs pap analyzs th pc o quantty contols of gnhous gass n th psnc of unctan costs. h gnhous gass a a stock pollutant n th nvonmnt. Hnc th magnal bnft cuv must b latvly flat whch ndcats to stablsh th pfnc of a pc contol ov a quantty contol. In th cas of pmannt shocks th tadtonal compason of magnal bnfts vsus magnal costs cannot b masud accuatly. h choc btwn quantty and pc contols bcoms ambguous and dpnds upon a mo dffcult masumnt of magnal costs and bnfts. h am of th pap s to mpos taxs to duc gnhous gas mssons. JL. Classfcaton: F; K; L; L; L5 Kywods: Cap and ad Systm Cabon ax Clmat Chang.. INRODUCION Fnland fst nactd cabon tax n 99 on fuls and thn Noway Swdn and Dnmak mplmntd cabon taxs n 99 and 99 (Andson Skou Dngs and Pdson ). Gmany mplmntd an cologcal tax on hatng ful gasoln natual gas and lctcty n 999 (IA 7a). Japan nactd a tax on havy pollutng vhcls n but ducd th tax on low-polluton vhcls to ncouag th dvlopmnt and puchas of gn vhcls (IA 7b). In th UK mplmntd a clmat chang lvy whch adds about 5% to th cost of lctcty (IA 7c). Hungay ntoducd a Nw nvonmntal Budn aff n whch taxs polluton of th sol a and wat (IA 7d). Rcntly USA has stablshd socal cost of cabon (SCC) fo analyss of fdal gulatons (IWGSCC ). At psnt th a two classc altnatvs fo gulatng gnhous gas (GHG) mssons whch a a cap and tad polcy and a cabon tax polcy. Cap and tad s a quantty contol polcy and cabon tax s a pc contol polcy. h cap and tad systm povds a pc whch s a sconday sult of gulatng th quantty of GHG mssons. On th oth hand th cabon tax h matal psntd by th autho dos not ncssaly psnt th vwpont of dtos and th managmnt of th Indus Unvsty as wll as th autho nsttut Pm Unvsty Chttagong Bangladsh. mal: haadhan_km@yahoo.com Acknowldgmnt: Pap was psntd n nd Intnatonal Confnc on Global Dvlopmnt wth Innovatv Solutons- ( nd ICGDIS-) on 5 th & th Dcmb. Autho would lk to thank th dtos and anonymous fs fo th commnts and nsght n mpovng th daft copy of ths atcl. Authos futhu would lk to dcla that ths manuscpt s ognal and has nth pvously bn publshd no cuntly on off to anoth publsh; and wllngly tansfs ts copy ghts to th publsh of ths ounal. Rcvd: 9--; Rvsd : --; Accptd: --; Publshd: -- Ctanty and Unctanty n Cap and ad Systm o n Cabon ax. 8 Haadhan Kuma Mohaan

2 Indus Jounal of Managmnt & Socal Scncs ():8- (Fall ) das.pc.og/s/h/ounl.html ffctvly ducs th quantty of GHG mssons whch s a sconday sult of sttng a pc. o duc GHG mssons both mthods contbut and n dalzd ccumstancs thy sm quvalnt. If w thnk th polcs n th conomc vw w obsv that quantty contol (n cap and tad polcy) s pfabl whn th magnal bnfts fom pc contol (n cabon tax polcy) a shaply slopng as compad aganst th magnal costs but pc contol s pfabl whn magnal bnfts a latvly flat and magnal costs a shaply slopng (Nwll and Pz ). Hnc w obsv that th magnal bnft functon s flat but th magnal cost functon slops shaply (Nodhaus 99). h sx gass; Cabon doxd (CO ) mthan (CH ) ntous oxd (N O) sulphuhxafluoud (SF ) hydofluouocabon (HFC) and pfluouocabon (PFC) togth consttuts sx GHG mssons. hs sx gass bfly calld cabon doxd quvalnts (CO ). h Kyoto Potocol 997 has catd an ntnatonal makt fo allowancs to mt sx gnhous gass but mphass on cabon doxd (CO ) (Mohaan b). At psnt th wold cabon tad ncluds fulfllmnt makts n th U th USA and Nw Zaland psntng ov bllon US dollas n tadd valu and as much as 5 ggatons of mssons p ya (Lnac Kossoy and Ambos ). o nlag th wold cabon tad wth poposd makts n Austala and Japan th ntnatonal makt s poctd to ach magntuds of $- tllon by (Lazaowcz 9; Call )). In post-kyoto ntnatonal famwok th ntnatonal cabon makts man a ky componnt of many counts cabon polcy (U ). h a polluton s th cognton that any manngful clmat chang polcy has to put a pc on CO to dcas GHG mssons. Baumol and Oats (988) poposd that pcng GHG mssons s a fundamntal lsson fom nvonmntal conomcs and th thoy of xtnalts. Mohaan (a) shows that th optmal nvonmntal tax should b lss than th magnal nvonmntal damags. nvonmntal conomsts suggst that th absnc of a pc chag fo scac nvonmntal soucs such as clan a lads to a polluton (Chsny aschn and Wang ). h ffcts of GHG mssons a dscbd n dtal by Mohaan (b).. CRAINY MPORARY UNCRAINY AND PRMANN UNCRAINY ON CARBON A W dvd a tm hozon mssons nto pods ndxd by. mssons n ach pod s dnotd by. h Cost C s an xponntal functon of mssons and a cost paamt and can b xpssd fo pod as follows (Pasonsa and aschn ): C ( ). () h patal dvatvs of () a magnal costs and can b wttn as; C ( ). () h ngatv magnal cost ndcats that th hgh mssons yld low cost. If w dcas mssons thn abatmnt ncass cost. h ncas of th paamt changs th cost upwad whch also stps th cost cuv. As a sult both th cost of abatmnt and th magnal cost of abatmnt ncas. In ths cas w fac unctanty n th cost. Now w ty to fnd two contastng spcfcatons of cost unctanty as follows: Ctanty and Unctanty n Cap and ad Systm o n Cabon ax. 9 Haadhan Kuma Mohaan

3 Indus Jounal of Managmnt & Socal Scncs ():8- (Fall ) das.pc.og/s/h/ounl.html In fst cas th shocks to th cost paamt a compltly tmpoay o tanstoy. A shock affcts th cost paamt n cunt pod but t has no laton on th cost paamt n any futu pod. In th scond cas shocks to th cost hav a pmannt affcts. A shock affcts th cost paamt n cunt pod and th xpctd cost n all futu pods s also ncmntd by th sam amount. h fst spcfcaton of th cost paamt s gvn by: () wh s th statng cost paamt s th constant xpctd gowth at n th man cost paamt s volatlty paamt and a th shocks to th cost paamt whch a ndpndnt standad nomal andom vaabls. h scond spcfcaton of th cost paamt s gvn by:. () Now w assum that a fxd agggat mssons constant s. Hnc fo pods w can wt;. (5) A dynamc mssons polcy can b obtan by sttng mssons n ach pod on som functon of past agggat mssons and on th cunt valu of th cost paamt. Lt th manng allowd mssons n pod s dnotd by. Hnc w can wt fo - as follows: () wh ( ). Now w assum that th valu functon n pod s. In th fnal pod th total cost of manng mssons to abat can b wttn as; (7) ( ) C( ( ) ). h valu fo th cost mnmzng mssons lvl ( ) bcoms Ctanty and Unctanty n Cap and ad Systm o n Cabon ax. Haadhan Kuma Mohaan

4 Indus Jounal of Managmnt & Socal Scncs ():8- (Fall ) das.pc.og/s/h/ounl.html ( ) subct to (5). h soluton of th cost functon taks th fom; mn (8) ( ). (9) Lt th optmz valu at th fnal pod b whch s a functon of th manng allowd mssons comng nto th pod and th alzd cost paamt n th pod can b wttn as; ( ) ( ( ) ) C( ( ) ) C( ) h magnal cost of mssons und th polluton polcy () bcoms; () p wh p ( ). () ( ) C( ( ) ) C( ( ) ) psnts th pc at th pod whch s th ngatv of magnal cost. h logathm of magnal cost fo pod s dfnd by; ln p. () Now fo al pods < th valu functon s th total cost of cunt pod mssons plus th dscountd xpctaton of th valu functon ( ) n th subsqunt pod as follows: () ( ) C( ( ) ) ( ( ) ) h cost mnmzng mssons ( ) In ths stuaton th optmal valu functon s gvn by;. bcoms as follows: ( ) mn. () Ctanty and Unctanty n Cap and ad Systm o n Cabon ax. Haadhan Kuma Mohaan

5 Indus Jounal of Managmnt & Socal Scncs ():8- (Fall ) das.pc.og/s/h/ounl.html and th magnal cost of mssons s gvn by; ( ) ( ( ) ) (5) () p ( ) C( ( ) ) C( ( ) ). W now analyz th abov solutons fo dffnt cass as follows:. Rsults n th Ctanty Cas Fo convnnt w us th backwad pogammng statng fom th nd pod that s w us ndx. In th ctanty cas w us thn th cost paamt follows th dynamcs as blow (Pasonsa and aschn ): ( ) (7) wh. Now n th last pod fo fom (9) w gt; ( ). (8) Hnc fom () and () th valu functon s gvn by; Fo w can wt; ( ) C( ). (9) ( ) C( ) ( ( ) ) [ ] ( ) ( ) ( ) ( ) ( ) ( ) { }. () Fo th fst od condton n th cost mnmzng mssons w gt; ( ) { ( )} Ctanty and Unctanty n Cap and ad Systm o n Cabon ax. Haadhan Kuma Mohaan

6 Indus Jounal of Managmnt & Socal Scncs ():8- (Fall ) das.pc.og/s/h/ounl.html. () hn th optmzd valu functon can b wttn as;. () Fo w can wt; [ ] C. () Fo th fst od condton n th cost mnmzng mssons w gt; Ctanty and Unctanty n Cap and ad Systm o n Cabon ax. Haadhan Kuma Mohaan

7 Indus Jounal of Managmnt & Socal Scncs ():8- (Fall ) das.pc.og/s/h/ounl.html. () hn th optmzd valu functon can b wttn as;. Fo w can wt; [ ] C. (5) Fo th fst od condton n th cost mnmzng mssons w gt;. () Ctanty and Unctanty n Cap and ad Systm o n Cabon ax. Haadhan Kuma Mohaan

8 Indus Jounal of Managmnt & Socal Scncs ():8- (Fall ) das.pc.og/s/h/ounl.html hn th optmzd valu functon can b wttn as; ( ) ( ). (7) Pocdng such a way w can wt th gnal fom of th optmal polcy as follows: In calnda tm fo (8) can b wttn as; ( ) ( ) ( ) ( ) h gnal fom of th optmzd fom can b wttn as follows:. (8). (9) () ( )( ). ( ) In calnda tm fo w can wt () as; ( ) ( ) ( ) ( ). () Fom () th logathm of magnal cost functon bcoms; ln p ( ) ( ). () In th ctanty cas w can tanslat back to an quaton that dscbs mssons n dffnt pods... whch s a functon of th total allowd mssons th total numb of pods th at of gowth n th cost paamt and th dscount at. Hnc w can wt such an quaton by (9) as follows: ( ) ( ) ( ) By usng () quaton () can b xpssd as follows: ln p ( ) ( ). (). () Ctanty and Unctanty n Cap and ad Systm o n Cabon ax. 5 Haadhan Kuma Mohaan

9 Indus Jounal of Managmnt & Socal Scncs ():8- (Fall ) das.pc.og/s/h/ounl.html h mssons ncas lnaly though tm at th at whch s shown n (). So that th magnal cost of abatmnt gows at th dscount at whch s shown n quaton (). If and th latd cost paamt s gowng at a at gat than th dscount at thn ths adustmnt lads to ducng th at of mssons n cunt pod. hs ndcats that ncasng th alzd magnal cost at psnt to psv allowd mssons fo th lat pods whn th cost paamt s hgh. As a sult w hav to duc th gowth at n th alzd magnal cost to qual th dscount at.. Rsults n th mpoay Shock Cas If th p pod shock s tmpoay th cost paamt follows th dynamcs as (Pasonsa and aschn ); wh. (5) In th backwad pogammng fo w hav th sam sult of (8) and (9). Fo w gt fom ();. () Fo th fst od condton n th cost mnmzng mssons w gt;. (7) hn th optmzd valu functon can b wttn as; Ctanty and Unctanty n Cap and ad Systm o n Cabon ax. Haadhan Kuma Mohaan

10 Indus Jounal of Managmnt & Socal Scncs ():8- (Fall ) das.pc.og/s/h/ounl.html. (8) Fo fom () w hav [ ] C. (9) Fo th fst od condton n th cost mnmzng mssons w gt;. () hn th optmzd valu functon can b wttn as;. () Ctanty and Unctanty n Cap and ad Systm o n Cabon ax. Haadhan Kuma Mohaan 7

11 Indus Jounal of Managmnt & Socal Scncs ():8- (Fall ) das.pc.og/s/h/ounl.html Fo fom () w hav [ ] C. () Fo th fst od condton n th cost mnmzng mssons w gt; 8. () hn th optmzd valu functon can b wttn as; 8. () Pocdng such a way w can wt th gnal fom of th optmal polcy as follows: Ctanty and Unctanty n Cap and ad Systm o n Cabon ax. Haadhan Kuma Mohaan 8

12 Indus Jounal of Managmnt & Socal Scncs ():8- (Fall ) das.pc.og/s/h/ounl.html (5) wh fo... and. () In calnda pod fo (5) and () can b wttn as; and (7) fo...- and. (8) h gnalzd fom of th optmzd valu functon can b wttn as;. (9) In calnda pod fo (9) can b wttn as;. (5) Opatng logathm on (5) w gt; p ln (5). (5) W obsv that th optmal mssons polcy n (7) s smla to th ctanty cas n favo of at sha of th manng allowancs and th lna gowth facto. Also th s a dducton n th cunt mssons lvl whch s td to th ovall volatlty of mssons. Agan th s th componnt of mssons that fluctuats wth th cunt alzaton of costs. If th manng numb of pods s lag thn th coffcnt s clos to Ctanty and Unctanty n Cap and ad Systm o n Cabon ax. Haadhan Kuma Mohaan 9

13 Indus Jounal of Managmnt & Socal Scncs ():8- (Fall ) das.pc.og/s/h/ounl.html. hs ndcats that all of th volatlty n th cost paamt s absobd n adustmnt to th cunt lvl of mssons whch kps th cunt lvl of magnal cost appoxmatly constant. Snc th manng numb of pods dcln th coffcnt on th quantty adustmnt dcln. Hnc only a poton of th volatlty n th cost paamt s absobd n adustmnt to th cunt lvl of mssons bcaus th agggat mssons a constant. If th a fw manng pods to sha th manng costs a lag facton must b absobd n th cunt pod. As a sult th fnal pod shows th pc bgns to flct a poton of th volatlty of th cost paamt.. Rsults n th Pmannt Unctanty Cas If th p pod s shock s pmannt th gnal foms a th sam as unctan cas and w obtan h th latons a th sam as quatons (8) to (). h optmal mssons polcy n (9) s dntcal to th ctanty cas. But h mssons a compltly unsponsv to shocks to th cost paamt. Snc non of th cost unctanty s absobd by th quantty of mssons all of th cost unctanty must b absobd by th pc of (). It s th bst polcy snc th GHGs a a stock pollutant thfo th optmal polcy must b a pc contol. Wtzman s (Wtzman 97) ognal pap was about a polcy mak whch was unnfomd about cost but th poduc was nfomd. Pasonsa and aschn () show that th volatlty of mssons and of th logathm pc on pod n tmpoay unctanty a as follows: (5) a ( ) and a ln ( ). But thy show th cospondng sults n pmannt unctanty cas a as follows: (5) a ( ) and a ( ). ln h two cass (5) and (5) gvs th dffnc btwn unctants n cost should hav upon th cost mnmzng mssons path dpndng upon whth t s a tmpoay unctanty o a pmannt unctanty. In th tmpoay cas unctanty s th quantty of mssons whch absobs shocks to th cost paamt but th pc of mssons s latvly constant. In th cas of pmannt unctanty th quantty s constant and t s pc that absobs shocks to th cost paamt (Pasonsa and aschn ). Gnhous gass a a stock pollutant so that th optmal polcy must b a pc contol whch only cosponds wth th tmpoay unctanty cas. In th cas of pmannt unctanty a pc contol wll claly not b optmal as t s th pc that ought to absob all of th shocks to cost. conomsts always tll casually of a cap and tad systm as bng a quantty contol and a cabon tax a pc contol. In al lf a cap and tad systm allows bankng and boowng of allowancs acoss pods can mmc th bnfts of a pc contol. If th cap and tad systm facs tmpoay unctanty n costs thn t wll b th pod by pod quantty of mssons whch wll fluctuat und th cap and tad systm and th pc wll b latvly constant. If th cap and tad systm facs pmannt unctanty n costs thn t wll b th pod by pod pc whch wll fluctuat und th cap and tad systm and th quantty of mssons n ach pod wll not Ctanty and Unctanty n Cap and ad Systm o n Cabon ax. Haadhan Kuma Mohaan

14 Indus Jounal of Managmnt & Socal Scncs ():8- (Fall ) das.pc.og/s/h/ounl.html b stochastc but s dtmnstcally at th at of gowth n costs lss th ntst at.. CONCLUDING RMARKS In ths pap w hav shown stocks and shocks fo GHG ov pc and quantty contols. W hav dscussd both th ctanty and unctanty n cabon tax o cap and tad systm. Rcntly th global clmat chang has bcom th hadach of th nvonmnt analysts th conomsts and th govnmnts of th all natons. Hnc th a no altnatvs of ductons of gnhous gass whch caus th global wamng. houghout th pap th mathmatcal calculatons a gvn n som dtals. RFRNCS Andson R. M. Skou N. Dngs and A.B. Pdson.. An valuaton of th Impact of Gn axs n th Nodc Counts. manod. Baumol W.J. and W.. Oats h hoy of nvonmntal Polcy. Cambdg: Cambdg Unvsty Pss. Call R.. Clmat Chang and Cabon Makts: a Panoamc Hstoy. Cnt fo Clmat Chang conomcs and Polcy Wokng Pap No.. Chsny M. L. aschn and M. Wang.. Rgulatd and Non-gulatd Compans chnology Adopton n xpmntal Makts fo msson Pmts and Optons Contacts. Cnt fo Clmat Chang conomcs and Polcy Wokng Pap No.5. U.. A Roadmap fo Movng to a Compttv Low Cabon conomy n 5. chncal Rpot COM () uopan Unon. IA. 7a. IA Databas on CO mssons fom Ful Combuston Intnatonal ngy Agncy. IA. 7b. lctcty ax. Addssng Clmat Chang Polcs and Masus. Intnatonal ngy Agncy. IA. 7c. Clmat Chang Lvy. Addssng Clmat Chang Polcs and Masus. Intnatonal ngy Agncy. IA. 7d. Nw nvonmntal aff. Addssng Clmat Chang Polcs and Masus. Intnatonal ngy Agncy IWGSCC.. Socal Cost of Cabon fo Rgulatoy Impact Analyss und xcutv Od 8. Fnal Rul chncal Suppot Documnt (SD): ngy ffcncy Pogam fo Commcal and Industal qupmnt: Washngton DC: Small lctc Motos. Dpatmnt of ngy Intagncy Wokng Goup on Socal Cost of Cabon Lazaowcz M. 9. Global Cabon adng: A Famwok fo Rducng mssons. chncal Rpot UK Govnmnt. Lnac N. A. Kossoy and P. Ambos.. Stat and nds of th Cabon Makt. chncal pot Wold Bank. Mohaan H.K. a Optmal nvonmntal axs Du to Halth ffct KASBI Busnss Jounal (): -9. Mohaan H.K. b. Gnhous Gas mssons Incas Global Wamng: Intnatonal Jounal of conomc and Poltcal Intgaton (): -. Nwll R.G. and W.A. Pz.. Indxd Rgulaton. RFF Dscusson Pap - Rsoucs fo th Futu. Nodhaus W.D. 99. Managng th Global Commons. Cambdg. MI Pss. Ctanty and Unctanty n Cap and ad Systm o n Cabon ax. Haadhan Kuma Mohaan

15 Indus Jounal of Managmnt & Socal Scncs ():8- (Fall ) das.pc.og/s/h/ounl.html Pasonsa J.. and L. aschn.. Stocks & Shocks: A Clafcaton n th Dbat Ov Pc vs. Quantty Contols fo Gnhous Gass. Cnt fo Clmat Chang conomcs and Polcy Wokng Pap No. 5. Wtzman M.L. 97. Pcs vs. Quantts. Rvw of conomc Studs (): 8 9. Ctanty and Unctanty n Cap and ad Systm o n Cabon ax. Haadhan Kuma Mohaan