MEMORANDUM No 19/26 Clean development mechansm (CDM) vs. nternatonal permt tradng the mpact on technologcal change. Cathrne Hagem ISSN: 89-8786 Department of Economcs Unversty of Oslo
Ths seres s publshed by the Unversty of Oslo Department of Economcs P. O.Box 195 Blndern N-317 OSLO Norway Telephone: + 47 22855127 Fax: + 47 2285535 Internet: http://www.oekonom.uo.no/ e-mal: econdep@econ.uo.no In co-operaton wth The Frsch Centre for Economc Research Gaustadalleén 21 N-371 OSLO Norway Telephone: +47 22 95 88 2 Fax: +47 22 95 88 25 Internet: http://www.frsch.uo.no/ e-mal: frsch@frsch.uo.no No 18 No 17 No 16 No 15 No 14 No 13 No 12 No 11 No 1 No 9 Lst of the last 1 Memoranda: Ger B. Ashem, Tapan Mtra and Bertl Tungodden Sustanable recursve socal welfare functons. 32 pp. Ger B. Ashem, Walter Bossert, Yves Sprumont and Kotaro Suzumura Infnte-horzon choce functons. 24 pp. Erk Hernæs, Fedor Iskhakov and Stenar Strøm Early Retrement and Company Characterstcs. 37 pp. Erk Hernæs, Zhyang Ja and Stenar Strøm Retrement n Non-Cooperatve and Cooperatve Famles. 38 pp. Hlde Bojer Income Capablty and Chld Care. 23 pp. Gunnar Bårdsen and Ragnar Nymoen U.S. natural rate dynamcs reconsdered. 28 pp. Enrco Sorso and Stenar Strøm Innovaton and market dynamcs n the EPO market. 32 pp. Hlde C. Bjørnland, Lef Brubakk and Anne Sofe Jore Forecastng nflaton wth an uncertan output gap. 31 pp. Marna Della Gusta, Mara Laura D Tommaso, Islda Shma and Stenar Strøm What money buys: clents of street sex workers n the US. 31 pp. Cathrne Hagem and Hege Westskog Dstrbutonal constrants and effcency n a tradable permt market. 27 pp. A complete lst of ths memo-seres s avalable n a PDF format at: http://www.oekonom.uo.no/memo/
Clean development mechansm (CDM) vs. nternatonal permt tradng the mpact on technologcal change. by Cathrne Hagem *,** Department of Economcs, Unversty of Oslo, P.O. Box 195 Blndern, N-317 Oslo, Norway Abstract. The clean development mechansm (CDM) under the Kyoto Protocol may nduce a technologcal change n developng countres. As an alternatve to the CDM-regme, developng countres may accept a (generous) cap on ther own emssons, let domestc producers nvest n new effcent technologes, and sell the excess emsson permts on the nternatonal permt market (cap&trade-regme). The purpose of ths paper s to show how the gans from nvestment, and hence the ncentve for nvestment n new technology may devate between the two alternatve regmes. We show that the dfference n gans from nvestment depends on whether the producers face compettve or non-compettve output markets, whether the nvestment affects fxed or varable producton costs and whether the producers can reduce emssons through other means than nvestment n new technology. JEL Classfcaton: L13, Q28 Keywords: Clmate Polcy, Technology Adopton, Emsson Tradng, Clean Development Mechansm, Technologcal Change * Work on ths artcle was conducted durng my partcpaton n the project "Envronmental economcs: polcy nstruments, technology development, and nternatonal cooperaton" sponsored by the Centre for Advanced Study (CAS) at the Norwegan Academy of Scence and Letters n Oslo n 25/26. The fnancal, admnstratve and professonal support of CAS s much apprecated. ** Comments from Ger Ashem and from partcpants at CAS-workshops are hghly apprecated. 1
1 Introducton The purpose of ths paper s to explore the ncentves for nvestment n energy effcent producton technologes under two dfferent clmate strateges n developng countres. Accordng to the Kyoto protocol, developng countres have no quantfed emsson targets for the frst Kyoto perod (28-212). However, ndustralzed countres wth quantfed emsson target are allowed to partly meet ther reducton commtments through nvestments n emsson reducng projects n developng countres (the clean development mechansm (CDM)). The emsson reductons generated from CDMprojects can be used to offset the nvestor s own emsson reducton oblgatons. We compare the ncentves for nvestment under the CDM wth the ncentves for nvestment under an alternatve clmate polcy, namely that the developng country partcpate n nternatonal permt tradng on equal terms as the ndustralzed countres that has ratfed the Kyoto Protocol (see UNFCCC (1998), artcle 17). Accordng to the Kyoto Protocol, the purpose of the CDM mechansm s not only to reduce the complance cost for the ndustralzed countres, but also to assst developng countres n achevng sustanable development (See UNFCCC (1998), artcle 12). The CDM mechansm s a mean to ntroduce more envronmentally frendly technologes n developng countres. Through spn-off effects from technologcal mprovement n some producton unts, the CDM mechansm may promote a generally hgher level of envronmentally frendly technologes n developng countres. However, there are several drawbacks when t comes to the CDM s ablty to promote cost effectve abatement efforts n developng countres. An executve board s desgnated to approve CDM-projects and ssue certfed emsson reducton unts (CERs).A condton for the approval of a CDM-project s that the reducton acheved by the project shall be addtonal to any that would occur n the absence of the project actvty ((see UNFCCC (1998), artcle 12).The addtonally requrement nsures that the CERs are based on real emsson reductons such that the CDM does not lead to hgher global emssons. However, the problem wth ths crteron s that t must be based on a counterfactual baselne for emsson. Once a CDM project s mplemented the emssons that would occur wthout the nvestment s no longer observable. Both the nvestor and 2
the host have ncentves to overstate the baselne emsson n order to make the project more proftable. Furthermore, the potental nvestors effort used n preparng CDM proposals, and the resources used to verfy and certfy emsson reductons may lead to qute hgh transacton costs for acqurng CERs. (See nter ala Mchaelowa (23) for an overvew of estmated transacton cost for varous knds of CDM-projects). Hgh transacton cost of CDM, and the problems connected wth baselne-estmates and verfablty of the emsson reducton acheved by the CDM-project, s an argument for ncludng the developng countres n an envronmental agreement through a cap&traderegme nstead 1. A cap&trade-regme mples that a developng country accepts a bndng cap for ts emssons. The country receves emsson allowances (permts) correspondng to ts caps for emssons and s allowed to partcpate n permt tradng. If the cap for emssons s generous, a developng country gans from partcpatng n ths regme by mplementng low-cost abatement optons and sell permts on the permt market. Due to the hgher transacton costs of CDM, developng countres may become better off under a cap&trade-regme. However, developng countres have been reluctant to accept bndng commtments. One reason for ths s that uncertanty about the busness as usual (BaU) emssons may ncur less beneft than expected. If the BaU emssons turn out to be hgher than expected when acceptng the emsson cap, the cost of the cap&traderegme may become hgher than a CDM-regme, n whch emssons reductons are calculated based on project specfc baselne 2. Another reason for developng countres to prefer a CDM-regme s that they may expect that ths regme lead to hgher transfer of technology than would occur under a cap&trade-regme. One reason for ths s that an nvestor under CDM may have more knowledge about effcent nvestment optons and better fnancng possblty than a manager n the developng country. On the other hand, the host for the nvestment project may have more nformaton about the mpact of an 1 Ths argument s nter ala gven n Bohm (22). 2 Kallbekken and Westskog (25) explore the cost and beneft of takng bndng commtments for developng countres. They fnd that the effcency gan from jonng the emsson tradng regme compared to the CDM-regme mght not be very large compared to the rsk they ncur. 3
nvestment on producton costs and emssons than the nvestors. Such asymmetres may lead to neffcences (ths s nter ala dscussed n Hagem (1996) and Wrl et al. (1998)) In Mllock ((22) t s shown how technologcal transfer as a part of the CDM-contract, can create ncentves for mtgatng the neffcency loss from asymmetrc nformaton. In ths paper, we gnore the mpact of possble asymmetres n nformaton. Furthermore, we assume that emssons and emsson reductons can be correctly calculated, and we assume that frms have equal access to new technology under both regmes. Hence, n ths paper the developng countres technologcal development does not depend on under whch regme an nvestment s mplemented, but whether the country decdes to nvest or not. We focus our analyss on frm facng mperfect competton n the output market, although we also derve the results regardng frms facng a perfectly compettve output market. Due to the hgh transacton cost of ntatng and mplementng a CDMnvestment project, t s probably qute large emtters for whch emssons can be reduced sgnfcantly by an nvestment, whch s attractve for CDM nvestors. These knds of frms have typcally large fxed cost and face an output market wth a lmted number of compettors (e.g. large power plants or large ndustry plants producng e.g. cement). When analyzng the ncentves for nvestment under the CDM-regme s thus relevant to consder the case where the potental hosts for CDM-nvestments may exercse market power n the output market. An nvestment s sad to have a postve (negatve) strategc effect f the other producers response to the acton ncreases (decreases) the proft of the producer takng the acton. (See e.g. Trole (1988), chapter 8.) Wth Cournot competton n the output market, each frm s optmal output and proft are decreasng functons of ts compettor s output. Hence, f nvestment n new more envronmentally frendly technology ncreases the nvestng producer s output, the nvestment has a postve strategc effect. If on the other hand, the nvestment causes the producer to decrease ts producton, the nvestment has a negatve strategc effect. We show that a CDM-contract may gve the frm a strategc dsadvantage n the output market. A CDM-contract gves the host for the project an ncome from emsson reducton. However, as long as emssons are ncreasng n output, 4
a CDM-contract may also lead to larger margnal cost of output producton. The frm s proft maxmzng output falls, whch agan cause ts compettors to ncrease ther output. Ths mples that a frm s ncome from emsson reductons under the CDM-regme may reduce the frm s proft from the output market. 3 The relatonshp between technologcal change and envronmental polcy nstruments has been wdely analyzed n the lterature. (See e.g. Jaffe et al. (22) for an overvew). Incentves for nvestment n new technology when frms are facng an mperfectly compettve output market are nter ala studed n Montero (22) and Requate (1998). However, these studes compare emsson permts and standards, and no studes we are aware of compare the dfferences n nvestment ncentves between a cap&trade-regme and a CDM-regme n the case of mperfectly compettve output markets. In the next secton we defne the developng countres two optons for ts clmate polcy. In secton 3 we derve the dfference n nvestment ncentves under the two optons when the frms n the developng countres face mperfectly compettve output markets. In secton 4 we derve the results for frm n developng countres facng a perfectly compettve output market. Concludng remarks are gven n the last secton. 2 CDM-regme vs. cap&trade-regme We consder a developng country whch s gven the opportunty to choose between two clmate polcy optons. It can ether jon the Kyoto protocol on equal terms as ndustralzed countres, denoted the cap&trade-regme, or the country can let the domestc frms be hosts for CDM-projects, denoted the CDM-regme. The CDM-regme mples that a foregn nvestor fnances (some of) the cost of mplementng the new technology. The host s emsson reductons relatve to BaU emssons generate certfed emsson reducton unts (CERs) whch can be used by the nvestor to offset own emsson reducton oblgatons. The value of each CER thus equals the nternatonal permt prce. 3 Bulow et al. (1985) show how an ncrease n proft from one market may reduce the frm s proft n another (mperfectly compettve) market. 5
If the developng country partcpates n emsson tradng, all domestc frms must hold permts equal to ther emssons and are allowed to trade permts on the nternatonal permt market. In order to smplfy the comparson of the nvestment ncentves under the two dfferent regmes, we assume that emsson reducton requrement of the cap&trade-regme s no strcter than the emsson reducton requrement under the CDM-regme, whch per defnton s zero (the country s not oblged to carry out any emsson reductons). Hence, f a country accepts a cap, the number of permts assgned to the country corresponds to the busness-as-usual emssons. Furthermore, we assume that the country redstrbutes the assgned permts to the emttng frms n accordance wth ther busness-as-usual emssons. The latter assumpton s made for smplfcaton purposes only, and do not affect our result. Achevng an endowment of tradable permts s a pure wndfall gan and does not nfluence the frms nvestment decsons (assumng that pure changes n wealth do not affect the frms nvestment decson) 4. Our assumptons about the cap on emssons and the dstrbuton of free permts mples that f no frms take any actons to reduce emssons, ther ncome are dentcal under both regmes. We consder the ncentves for nvestment n energy effcency mprovng projects. Such projects could typcally lead to lower margnal and/or fxed producton costs n addton to the value of the emsson reducton. In the followng secton, we consder nvestment n a (captal ntensve) ndustry where there are few producers, such that each producer has market power n the output market. A compettve output market s analyzed n secton 4. 3 Imperfectly compettve output market. To show the key dea of the mpact of mperfectly compettve output markets, we consder two symmetrc frms that operate n a developng country and compete à la Cournot n the output market. We assume that the produced good s sold to a foregn country such that we can gnore any welfare effects due to changes n consumer surplus. 4 The property of free tradable permts s nter ala dscussed n Hagem (22). 6
The frms are denoted 1 and 2, but we wll sometmes refer to them by the use of and j. The frms productons are energy ntensve and each frm s nvestment n new technology reduces the use of energy for any gven level of output. In the followng we consder both the case where the nvestment ncreases the productvty of a varable (energy ntensve) producton factor (3.1), and the case where nvestment reduces the energy nsenstvty of a fxed producton factor (3.2). 3.1 Investment ncreases the productvty of a varable nput factor. In ths secton, we consder the case where emssons are caused by the use of a varable nput factor. We gnore other producton costs than the cost of the carbon based energy used n the producton. Throughout the paper we use captal letters to denote physcal varables under the cap&trade-regme, and small letters to denote physcal varables under the CDM-regme. Hence, let E denote the use of energy measured n CO 2 - unts, X the output, and K the technology parameter under the cap&trade-regme, and let e, x and k denote the same varables under the CDM-regme. The producton functon s gven by; E = (1 K ) X = 1, 2 (Cap&trade-regme) and e = (1 k ) x = 1, 2 (CDM-regme) (1) We assume that there s (only) one nvestment opton, K = ( k = ) f the frm does not nvest, and K = K ( k = K)f the frm mplements the nvestment 5. < K < 1. 3.1.1 Frms proft functons Cap&trade-regme: 5 The mplcaton of more than one nvestment opton s dscussed n the concludng remarks 7
For each frm the proft ( Π ) s the sum of net ncome from permt sale plus the net ncome from the output market, less of nvestment cost (f the frm mplements the new technology). Π = t (1 ) E K X + p ( X + X ) q (1 K ) X Q( K ) j = 1,2 j = 1,2 j, (2) where E s the frms BaU emssons (and equal to the allocaton of free permts), q s the prce of energy measured n CO 2 -unts, t s the nternatonal permt prce, px ( + X) j s the output prce (as a functon of total supply) and ( ) QK s the nvestment cost. QK ( ) equals for K =, and equals Q for K decreasng n quanttes ( p < ). = K. The prce of the output s CDM-regme: In the followng, we assume that the CDM-contract s desgned to maxmze the jont total proft of the nvestor and host, that s, proft from output producton plus proft from generatng emsson reductons (CERs). Ths mples that we dsregard any devatng nterest between the nvestor and the host when t comes to the mplementaton of the CDM-project. Furthermore, we assume that all proft goes to the host. The mplcaton of ths latter assumpton s dscussed n the concludng remarks. If the frm enters nto a CDM-contract, the proft (π ) s gven by π = t E (1 K) x + px ( x) q(1 K) + x Q j = 1,2 j= 1,2 j (3) If the frm does not enter nto a CDM-contract, emsson reductons have no value as CERs can only be generated through a CDM-contract whch nvolves some knd of 8
nvestments. If the frm does not enter nto a CDM-contract, t does not mplement the new technology and the proft functon s gven by 6 ; π = px ( x) q x 1,2 j 1,2 j + = = j (4) To fnd the dfferences n the nvestment ncentves under the two dfferent regmes, we consder a two-stage model. At the frst stage, the frms choose whether to nvest or keep the old technology. (Investment under the CDM-regme means that the frm enters nto a CDM-contract). At the second stage, the frms output decsons are made. We solve the model backwards. In the next secton, we derve the Nash equlbrum n the output market (stage 2). In secton 3.1.3 we compare the nvestment decson at stage 1 under the two dfferent regmes, gven that the frms can correctly antcpate the Nash-equlbrum outputs at stage 2 (whch follows from the varous combnatons of nvestment decsons at stage 1). 3.1.2 Second stage Output market Cap&trade-regme: We see from (2) that maxmzng condton: Π wth respect to X gves the followng frst order p X + p ( q+ t) (1 K ) = = 1, 2 (5) From (5) we fnd each frm s optmal output level as a functon of ts own technology parameter and the other frm s output ( X ( K, X )). j From total dfferentatng the frms frst order condtons, and assumng that p + p X < fnd that 7 to nsure the exstence of a unque, pure strategy Nash-equlbrum, we 6 Although the new technology reduces the need for energy per unt producton, we assume throughout the paper that the nvestment s not proftable unless the frm can sell emsson permts/cers. X (, ) 7 K X j p X + p = X p X + 2 p j 9
X ( K, X ) j 1< <. (6) X j (Equaton (6) mples that the reacton functons are downward slopng). Furthermore, we see from the frst order condton (5) that X ( K, X ) > X (, X ) (7) j j For a gven level of output from t compettor, the frm produces more f t has nvested. We see from (6) that a frm s ncreased producton nduces lower output from ts compettor. Hence, the compettor s response to the nvestment ncreases the nvestng frm s proft snce p <. In game theoretcal termnology, the nvestment s sad to have a postve strategc effect. The Nash-equlbrum n the output market s found from solvng the two equatons gven by (5). Let X ( K, K ) and X ( K, K ) denote the Nash-equlbrum outputs n the output 1 1 2 2 1 2 market. From (6) and (7) t follows that X ( K, K ) > X (, K ) (8) j j X ( K, K) < X ( K,) (9) Under the cap&trade-regme, nvestment ncreases the Nash-equlbrum output of the nvestng frm, and decreases the Nash equlbrum output from ts compettor. CDM-regme: If a frm has entered nto a CDM-contract, the frst order condton for proft maxmum s found from maxmzng (3) wth respect to x. The frst order condton of the maxmzaton problem s gven by p x + p ( q+ t) (1 K) = (1) If the frm does not enter nto a CDM-contract, the frst order condton s found from maxmzng (4) wth respect x. In ths case, the frst order condton s gven by; 1
p x + p q=. (11) From (1) and (11) we fnd each frm s optmal output level as a functon of ts nvestment decsons (that s, the decson to enter a CDM-contract) and the output from the other frm. Let x ( K, x ) denote the soluton to (1) and let x (, x ) denote the soluton to (11). j Comparng the two frst order condtons (1) and (11), we see that x ( K, x ) > x (, x ) f ( q+ t) (1 K) < q j j and x ( K, x ) < x (, x ) f ( q+ t) (1 K) > q j j To fnd the Nash-equlbrum n the output market we solve the two equatons for the frms frst order condtons ((1) and (11)). Let x ( k, k ) and x ( k, k ) denote the Nash- 1 1 2 2 1 2 equlbrum outputs under the CDM-regme As dscussed prevously, to ensure an exstence of a unque Nash-equlbrum n the output market, we have assumed downward slopng reacton functons (see (6)). Hence, we fnd that for ( q+ t) (1 k ) < q: j x ( Kk, ) > x(, k) j and x ( Kk, ) < x(, k) j j j j j (12) For ( q+ t) (1 k ) > q, we fnd that: x ( Kk, ) < x(, k) j and x ( Kk, ) > x(, k) j j j j j (13) We see from (12) and (13) that the nvestment has a postve strategc effect f margnal costs decreases ( ( q+ t) (1 k ) < q) and a negatve strategc effect f margnal costs ncreases ( ( q+ t) (1 k ) > q). We refer to the frst case as a stuaton where the 11
nvestment gves the nvestng frm a strategc advantage, and the latter case as a stuaton where nvestment gves the nvestng frm a strategc dsadvantage. By comparng the mpact of nvestment under the cap&trade-regme and the CDMregme, we derve the followng proposton: Proposton 1. Investment n a technology whch ncreases the productvty of a varable nput factor gves the nvestng frm a strategc advantage under the cap&trade-regme, whereas the nvestment may gve the frm a strategc dsadvantage under the CDMregme. In the next secton we explore how ths dfference n the strategc effect of an nvestment nfluences the dfference n the nvestment ncentves under the two regmes. 3.1.3 Frst stage Investment decson. At the frst stage each frm decdes whether to nvest/enter nto a CDM contract. When the frms make ther nvestment decsons at stage 1, t s assumed that they can correctly antcpate the Nash-equlbrum n the output market at stage 2. The Nash-equlbrum at stage 2 s a functon of both frms nvestment decson at stage 1, such that each frm s proft of an nvestment depends on the nvestment decson of the other frm. Let Π ( K, K ) denote frm s proft under the cap&trade-regme and let π ( k, k ) denote j j frm s proft under the CDM-regme. Under each regme, there are four dfferent combnatons of nvestment decsons and hence four dfferent outcomes for the proft for each frm. In table 1 (for the cap&trade-regme) and n table 2 (for the CDM-regme), we summarze that nvestment game at stage 1, and the payoffs followng from the dfferent outcomes at stage 2. (In order to smplfy the dscusson we refer to the dfferent outcomes by a letter and a number (.e Π ( KK, ) s referred to as A1 (see table 1 and 1 table 2))). 12
Table 1. Investment decsons and payoffs under the cap&trade-regme. Frm 1 Invest ( K1 = K ) Don t nvest ( K = ) 1 Frm 2 Invest ( K2 Don t Invest = K ) ( K = ) 2 Π ( KK, ) A1 1 Π ( KK, ) A2 2 Π ( K,) D1 1 Π ( K,) D2 2 Π (, K) B1 1 Π (, K) B2 2 Π (,) C1 1 Π (,) C2 2 Table 2. Investment decsons and payoffs under the CDM-regme. Frm 1 Frm 2 Invest ( k 1 = K) Don t nvest ( k 1 = ) Invest ( k 2 Don t Invest = K) ( k = ) 2 π ( KK, ) a1 1 π ( KK, ) a2 2 π ( K,) d1 1 π ( K,) d2 2 π (, K) b1 1 π (, K) b2 2 π (,) c1 1 π (,) c2 2 13
In the followng, we dscuss how the two dfferent regmes may lead to dfferent Nashequlbrums for the nvestment decsons, although the nvestment opton and the frms producton functons are dentcal under both regmes. Snce both frms have dentcal producton functons, we must have that A1=A2, a1=a2, C1=C2, c1=c2, B1=D2, b1=d2, D1=B2 and d1=b2. Furthermore, we see from the frst order condtons (5) and (1), that f both frms nvest, the Nash-equlbrum n the output market s dentcal under both regme, such that A1=A2=a1=a2. We saw n the prevous secton that nvestment always ncreased the nvestng frm s output ((see (8)) under the cap&trade-regme. Snce hgher output from frm s a dsadvantage for frm j, each frm s better off f the other frm does not nvest. δπ ( = p X < ). Hence, under cap&trade-regme we must have that δ X j D1> A1 ( B2> A2) C1> B1 ( C2> D2) (14) Under the CDM-regme, the rankng of the dfferent outcomes depends on whether the nvestment ncreases or decreases the nvestng frm s output. If nvestment leads to larger output ( ( q+ t) (1 k ) < q), each frm s better off f the other frm does not nvest (as under the cap&trade-regme), and d1> a1 ( b2> a2) c1> b1 ( c2> d2) (15) In the case where nvestment leads to lower output ( ( q+ t) (1 k ) > q), each frm s better of f the other frm nvests, and we must have that d1< a1 ( b2< a2) c1< b1 ( c2> d2) (16) In the followng we consder the case where the nvestment project s such that under both regmes, the frms prefer an outcome where both frm nvest compared to an outcome where none of the frm nvests. 14
Ths mples that A1=A2>C1=C2 and a1=a2>c1=c2, and t follows from (14) that there s only one possble rankng of the outcomes for frm 1 and 2 under the cap&traderegme: Frm 1: D1> A1> C1> B1 Frm 2: B2> A2> C2> D2 (17) For ths rankng, nvest s a domnant strategy for both frms, and the unque Nashequlbrum at stage 1 s that both frms nvest under the cap&trade-regme. Under the CDM-regme, the rankng of the dfferent outcomes depends on whether the strategc effect of an nvestment s postve or negatve. If the strategc effect s postve, we fnd the same rankng of the outcomes as under the cap&trade-regme. Hence, for ( q+ t) (1 k ) < q, the rankng must satsfy (15), and there s only one possble rankng of the outcomes: Frm 1: d1> a1 > c1 > b1 Frm 2: b2> a2> c2> d 2 (18) Hence, f the strategc effect of the nvestment s postve, the Nash equlbrum at stage 1 s that both frms nvest under the CDM-regme Let us now consder the case where nvestment gves a strategc dsadvantage, that s ( q+ t) (1 k ) > q, and the rankng of outcomes fulflls (16). (Note that although c1<a1, ths s not suffcent to ensure that a1>b1 snce b1>c1.) If the strategc dsadvantage of nvestment s suffcently large, each frm prefers to not nvest regardless of what the other frm chooses. Hence, not nvest may become a domnant strategy, and we have the followng rankng of outcomes 8 : Frm1: b1 > a1 > c1 > d1 Frm 2: d2> a2> c2> b2 (19) Ths rankng leads to a unque Nash-equlbrum where none of the frm nvests. We can now derve the followng proposton: 8 Note that the rankng gven by (19) s only one of several possble rankngs. 15
Proposton 2. Consder the case where the outcome where both frms nvest s preferred to the outcome where none of the frms nvests under both regmes. Ths stuaton leads to a unque Nash-equlbrum where both frms nvest under the cap&trade regme, whereas the CDM-regme may lead to a prsoner s dlemma outcome where none of the frms nvests. Proof of proposton 2. A numercal example suffces. Let the demand functon for the commodty produced by the two frms be px ( ) = 3 x. ( x = x + x under the CDM-regme, and x = X + X j j under the cap&trade-regme). Furthermore let q=1 and t=2. For K =4/5 and Q=15, we fnd that D1( 12) > A1( 13) > C1( 1) > B1( 87) and d1( 16) > a1( 13) > c1( 93) > b1( 91) whch makes t a domnant strategy to nvest under both regmes. For K =1/5 and Q=3, we fnd that D1( 15) > A1( 11) > C1( 1) > B1( 97) and b1( 13) > a1( 11) > c1( 93,4) > d1( 92,6) whch makes t a domnant strategy to nvest under the cap&trade-regme, whereas t s s domnant strategy to not nvest under the CDM-regme. The prsoner s dlemma stuaton occurs because of the strategc dsadvantage of nvestment under the CDM-regme. Investment has two devatng effects on the margnal cost of output producton. On one hand, the nvestment ncreases the margnal cost of producton because enterng nto a CDM contract also mples that emssons have become costly. Each unt emsson gves one unt less CDM-credts and hence decreases the beneft of the CDM project by the unt cost of permts. On the other hand, the nvestment ncreases the energy effcency and thus decreases the use of energy per produced output, whch cet. par decrease the margnal cost of producton. If the former effect domnates the latter, the net margnal cost of producton ncreases due to the 16
nvestment. Lower producton from the nvestng frm leads to hgher producton from ts non-nvestng compettor. The compettor s ncrease n producton causes the output prce to fall and hence hurts the nvestng frm. If the nvestment cost plus the fall n ncome from the product market more than offsets the ncrease n ncome followng from the generaton of CDM credts, the frm s better of not nvestng f the other frm abstans from nvestment. The other sde of the con s that a frm becomes better off when ts compettor nvests f the nvestment gves the nvestng frm a strategc dsadvantage. Lower output from ts compettor ncreases the output prce, and the frm that has not nvested gets a larger share of the output market. Ths may make t a domnant strategy not to nvest, although both frms are better off f both nvest compares to the Nash equlbrum where none of the frms nvests. The dfference n gans from nvestment between the two regmes followed from the fact that nvestment n cleaner technology also affected the margnal proft of producton dfferently. In the next secton, we consder an abatement opton that does not affect the frms margnal proft of producton, and we evaluate how ths nvestment opton affects the nvestment decsons. 3.2 Investment affects the emssons from a fxed producton factor. Consder the case where t s the fxed producton factor and not the varable producton factor that generates emssons. Ths s for nstance the case f emsson follows from heatng /coolng of the producton plant. Furthermore, assume that there s a possblty for the frm to reduce emssons through varous knds of abatement efforts. The abatement cost functon, D, s gven by DE K K CE E (, ) = (1 ) ( ) = 1, 2 (cap&trade-regme) and De k = k CE e = (, ) (1 ) ( ) 1,2 (CDM-regme), where E E ( e ) s abatement carred out by frm. Margnal abatement cost s postve for all E E ( e ) >, and s ncreasng n abatement (C >, C > ). 17
Snce output s ndependent of emssons, the proft from the output market s ndependent of any abatement efforts. Let px denote the frm s proft followng from the Nash-equlbrum output at stage 2. Snce each frm s output s ndependent of the nvestment decson, ths correspond to a stuaton where A1(A2)=D1(B2), B1(D2)=C1(C2), a1(a2)=d1(b2) and b1(d2)=c1(c2) n table 1 and table 2. Cap&trade-regme: The frms profts under the cap&trade-regme can be wrtten: Π = ( K ) t (1 ) ( ) E E K C E E QK ( ) + px Maxmzng the frms proft wth respect to E gves the followng frst order condton: t = K C E E (2) (1 ) ( ) Let E ( K ) denote the soluton to (2) for K (2) for K = = K and let () denote the soluton to We defne the gans from nvestment ( Π ) as the ncrease n proft due to nvestment, that s E Π = Π ( K) Π () = t ( E E ( K)) (1 K) C( E E ( K)) Q (21) t E E C E E ( ()) ( ()) The frm nvests under the cap&trade-regme f (21) s postve, that s, f A1(A2)=D1(B2)>B1(D2)=C1(C2). CDM-regme: If the frm enters nto a CDM-contract, the proft functon s gven by 18
π = ( K) t (1 ) ( ) E e K C E e Q+ px Maxmzng the frm s proft functon wth respect to e, gves the followng frst order condton: t K C E e = (1 ) ( ) (22) Let e ( K) denote the soluton to (22). If the frm does not enter nto a contract, there s nothng to gan by reducng emssons and proft arses only from the output market. The gans from nvestment under the CDM-regme, denoted π s gven by π = π ( K) π () = t E e ( K) (1 K) C( E e ( K)) Q (23) The frm nvests under the CDM-regme f (23) s postve, that s, f a1(a2)=d1(b2) > b1(d2)=c1(c2). We see from (2) and (22) that E ( K) = e ( K). Ths mples that the frm s proft f t has nvested s dentcal under both regmes, that s A1(A2)=D1(B2)=a1(a2)=d1(b2). By comparng the gans from nvestment under the two regmes ((21) and (23)), we derve the followng proposton: Proposton 3. If the only abatement possblty s to reduce emssons from a fxed producton factor, the gans from nvestment under the CDM-regme s always hgher than (or equal to) the gans from nvestment under the cap&trade-regme. 19
Proof of proposton 3: If we compare (21) and (23), we see that π = Π for fnd that E () = E. For E () < E, we π > Π snce t ( E E ()) C( E E ()) > f t s proftable for a frm under the cap&trade-regme to mplement any abatement effort f t does not nvest. For the nvestment opton consdered n ths secton, there s no strategc dsadvantage of nvestng. The dfference between the two regmes s only that under the CDM-regme the frm only gets access to the permt market f t nvests, whereas under the cap&traderegme, the frm has an opton to earn money on emsson reducton even wthout nvestment. It can sell excess permts f t mplements some abatement effort under the cap&trade-regme. If the abatement effort (for K=) s proftable, B1(D2)=C1(C2)>b1(d2)=c1(c2), and the gans from nvestment s larger under the CDM-regme than under the cap&trade-regme 9. Hence, an nvestment opton that s not mplemented under the cap&trade-regme may be mplemented under the CDM-regme. If no abatement effort s proftable unless the frm has nvested, that s, B1(D2)=C1(C2)=b1(d2)=c1(c2), the gans from nvestment s dentcal under the two regmes. 4 Compettve output markets. In the secton 3 we consdered a stuaton where the frms faced an mperfectly compettve output market. In the case where nvestment affected the margnal proft from producton (3.1), t also affected the strategc poston n the output market, whch agan changed the compettor s equlbrum output and hence the equlbrum output prce. 9 As ponted out n secton 2, the dfference n the gans from nvestment between the two regmes does not depend on whether the frms receve any permts free of charge under the cap&trade-regme. The net gans from nvestment under a CDM-regme s always larger than (or equal to) the gans from nvestment under a cap&trade-regme, snce (A1-B1) = (D1-C1) (a1-b1) = (d1-c1). Dstrbutng permts free of charge ncrease the proft for frms under the cap & trade regme by t E, whether they nvest or not. 2
If we consder the case where the frms only produce a small share of the world market, the prce of the produced good are ndependent of ther output, and s hence not affected by ther nvestment decson. The nvestment only affects the nvestng frm s output, and does not change the equlbrum output prce. Ths mples that each frm consders ts beneft from nvestment as ndependent of the other frm s acton. Hence, ths corresponds to the stuaton descrbed n secton 3.2, and we must have that A1(A2)=D1(B2), B1(D2)=C1(C2) and a1(a2)=d1(b2), b1(d2)=c1(c2). The dfference between the two regmes s only that under the CDM-regme, the frms get access to the permt market f they nvest, but not f they do not nvest, whereas under the cap&traderegme, the frms have an opton to earn money on permt sale, through the mplementaton of varous abatement efforts, even though they do not nvest (as dscussed n the prevous secton). Hence, the gans from nvestment cannot be lower under the CDM-regme than under the cap&trade-regme.( (A1-B1)= (D1-C1) (a1- b1)=(d1-c1)). Ths dscusson leads to the followng proposton: Proposton 4. If frms face a compettve output market, the net gans from nvestment under a CDM-regme s hgher than (or equal to) the gans from nvestment under the cap&trade-regme. Hence, t s more lkely that nvestment occurs under the CDM-regme than under the cap &trade regme when the frms are facng compettve output markets (and the access to abatement technology s dentcal under both regmes). 21
5 Concludng remarks The purpose of ths paper was to compare the ncentves for nvestment n new technology under two dfferent clmate polces. We showed that f the producers face compettve output markets, or f the nvestment do not nfluence margnal producton cost, the gans from nvestng under a CDM-regme s larger than (or equal to) the gans from nvestng under a cap&trade-regme. When producers face an mperfectly compettve output market, an nvestment may gve the frm a strategc dsadvantage n the output market under a CDM-regme. Ths effect makes t less proftable to nvest under a CDM-regme than under a cap&trade-regme. If frms compete n perfectly compettve markets, or f the nvestment only affects the emssons from a fxed producton factor, there s no strategc effect of the nvestment. In that case, the only dfference between the ncentves for nvestment follows from the dfference n frms opportunty to reduce emsson wthout nvestng, and a CDM-regme may nduce more nvestment than a cap&trade-regme. However, the CDM-regme leads to hgher abatement cost for the producers than a cap&trade-regme as the most effcent abatement opton s not always chosen (f the most effcent abatement does not nclude an nvestment). In the paper, we consdered a stuaton where there was only one nvestment opton. However, there may be a range of dfferent technologes that can reduce emssons and/or ncrease the energy effcency of the frm. Snce nvestment affects the frms strategc poston n the output market dfferently under the two regmes consdered n ths paper, t can also be the case that the frms chooses dfferent level of nvestment under the two regmes. We have also gnored the fact that, n prncple, the calculated emsson reductons from a CDM-project should correct for leakages. We showed that nvestment n new technology n one frm affected the equlbrum output of the other frm, and hence also affected the emssons from the other frm (carbon leakage). Takng ths effect nto account makes t even less proftable to nvest f the nvestment gves the frm a strategc dsadvantage n the output market. Investment then both makes the frm lose market shares and ncrease 22
the compettors output (and hence emssons), whch reduces the calculated emsson reducton acheved by the nvestment. We have also assumed that the hosts for the CDM projects receve the whole net ncome from the project. However, t s lkely that nvestor seeks to acheve more than a zero proft from ts nvestment. In that case, the producers n the developng countres get less ncentve to nvest n new technology under the CDM regme compared to a cap&traderegme (where they do not have to share the proft wth the foregn nvestor). 23
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