Elin Berg, Snorre Kverndokk and Knut Einar Rosendahl

Transcription

1 Dscusson Papers No. 245, January 1999 Statstcs Norway, Research Department Eln Berg, Snorre Kverndokk and Knut Enar Rosendahl ptmal l Exploraton under lmate Treates Abstract: In ths paper we focus on how an nternatonal clmate treaty wll nfluence the exploraton of ol n Non-PE countres. We present a numercal ntertemporal global equlbrum model for the fossl fuel markets. The nternatonal ol market s modelled wth a cartel (PE) and a compettve frnge on the supply sde, followng a Nash-ournot approach. An ntal resource base for ol s gven n the Non-PE regon. However, the resource base changes over tme due to depleton, exploraton and dscovery. When studyng the effects of dfferent clmate treates on ol exploraton, two contrastng ncentves apply. If an nternatonal carbon tax s ntroduced, the producer prce of ol wll drop compared to the reference case. Ths gves an ncentve to reduce ol producton and exploraton. However, the ol prce may ncrease less rapdly over tme, whch gves an ncentve to expedte producton, and exploraton. In fact, n the case of a rsng carbon tax we fnd the last ncentve to be the strongest, whch means that an nternatonal clmate treaty may ncrease ol exploraton n Non- PE countres for the comng decades. Keywords: Internatonal lmate Treates, Exhaustble Resources, ptmal l Exploraton JEL classfcaton: H23, Q30, Q40. Acknowledgement: We are ndebted to Kjell Arne Brekke, Torsten Bye and Jan Øyvnd ftedal for valuable dscusson. Ths work was supported fnancally by the Norwegan Mnstry of Envronment, and was ntated when all authors were at Statstcs Norway. Address: Knut Enar Rosendahl, Statstcs Norway, Research Department. E-mal: knut.enar.rosendahl@ssb.no Eln Berg, Norsk Hydro A/S, P.. Box 200, 1321 Stabekk, Norway. E-mal: eln.berg@nho.hydro.com. Snorre Kverndokk, The rsch entre for Economc Research, Gaustadallèen 21, 0371 slo, Norway. E-mal: snorre.kverndokk@frsch.uo.no.

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3 1. Introducton A clmate treaty lke the Kyoto Protocol, that regulates the emssons of carbon doxde ( 2 ), may have mportant mpacts on the ol market. ombuston of fossl fuels s the man source for anthropogenc 2 emssons, and such a treaty wll nfluence the magntude and composton of fossl fuel consumpton, and therefore also producton pattern and exploraton actvty. The mpacts of carbon restrctons on the ol market have been studed n, e.g., Whalley and Wgle (1991), Wrl (1994,1995), Tahvonen (1996) and Berg et al. (1997a). However, none of these studes have explctly modelled ol exploraton; avalable ol reserves are handled exogenously. Berg et al. (1997b) concluded that the reserve base of Non-PE may be the most mportant parameter nfluencng PE s cartelsaton gans, ndcatng that ol exploraton may be an mportant determnant of the whole market structure. Hence, t should be vtal to nclude exploraton actvty n the analyses of a clmate treaty. ne of the few papers that explctly analyses the effects of envronmental regulatons on ol exploraton s Jn and Grgalunas (1993). They examne the mpacts on frms n the ol and gas ndustry by ncorporatng the envronmental complance costs nto the exploraton and producton stages. By studyng a compettve market, they conclude that the total nvestment n exploraton and ol producton generally wll decrease as a result of rsng complance costs. However, they fnd that wth expectatons of ncreasng complance costs n both exploraton and producton, the optmal exploraton may start at a hgher level than wthout envronmental regulatons. Exploraton actvty related to non-renewable resources has been examned ether as a problem of constraned ntertemporal maxmsaton or as a problem of stochastc optmsaton under uncertanty (see, e.g., Pndyck, 1978; Glbert, 1979; Arrow and hang, 1982; Devarajan and sher, 1982; Lvernos and Uhler, 1987; Swerzbnsk and Mendelsohn, 1989; and arns and Quyen, 1998). 1 The semnal paper of Pndyck (1978) ntroduced exploraton nto a model of optmal extracton of nonrenewable resources, and became a standard for modellng ol exploraton n the years to come. Pndyck recognsed that producers are not «endowed» wth reserves, but nstead must develop them through the process of exploraton. The resource base s treated as the bass for producton, and exploraton actvty as the means of ncreasng or mantanng reserves. Resource producers must 1 An mportant part of the lterature on ol exploraton are econometrc studes. or a survey on econometrc models on ol exploraton, see, e.g., Rodrguez Padlla (1992). 3

4 smultaneously determne ther optmal rates of exploraton actvty and producton. A pvotal assumpton n Pndyck s analyss s that producton costs rse as reserves declne. Hence, the optmal reserve level balances revenues wth exploraton costs, producton cost, and the «user cost» of depleton. Solow and Wan (1976) show that n the absence of new dscoveres, an aggregate extracton cost functon can be defned and ndexed by ether the level of reserves or the amount of cumulatve extracton. However, when new dscoveres occur, the proper specfcaton of the aggregate extracton cost functon depends on the exploraton technology and s n general dfferent from that whch s approprate n the no-dscovery case. Thus, accordng to Swerzbnsk and Mendelsohn (1989) the common practce of ncludng an aggregate extracton cost functon from the no-dscovery case n a model wth exploraton results n a msspecfcaton as long as the qualty of the resource s not homogeneous. Ths s the procedure n Pndyck (1978), where the unt extracton costs of new dscoveres are set equal to the mnmum unt costs of exstng reserves at the tme of dscovery. Ths wll artfcally encourage early exploraton to fnd cheap ol. In our study we analyse the effects of an nternatonal clmate treaty on the exploraton actvty outsde PE. We study the effects of both constant and rsng carbon taxes, globally and regonally. An extended verson of the PETR model (see Berg et al., 1997a,b) s used. Ths s a numercal ntertemporal global equlbrum model for the fossl fuel markets, where producers take nto account that the fuels are nonrenewable. pposed to the orgnal verson of the model, exploraton n Non- PE s explctly modelled based on Swerzbnsk and Mendelsohn (1989). Uncertanty s not consdered as we assume a determnstc relatonshp between exploraton effort and new dscoveres. We consder Non-PE countres as prce takers, so that ther producton actvty and, therefore, ther exploraton actvty depends on the prce path of ol whch s consstent wth Hotellng s theory of exhaustble resources (Hotellng, 1931). In ths paper we fnd that a clmate treaty mplemented by an nternatonal 2 tax wll reduce the producer prce of ol gvng an ncentve to reduce the ol producton and exploraton actvty. However, the prce of ol s ncreasng at a lower rate after the ntroducton of a carbon tax. Ths gves the compettve producers an ncentve to move producton nearer n tme, as the dscounted value of future producton s reduced more than the value of current producton. As ths ncentve shows to be the strongest n the most plausble tax scenaro,.e., wth a rsng carbon tax over tme, Non-PE countres wll actually ncrease ol exploraton somewhat for the comng decades. Ths 4

5 counterntutve result shows the mportance of takng an ntertemporal approach n studes of fossl fuel markets. The paper s organsed as follows. In Secton 2, the model s outlned, whle data are gven n Secton 3. The smulaton results are presented n Secton 4. We provde some senstvty analyses n Secton 5 to test the robustness of the results. In the fnal secton, the paper concludes. 2. The model The PETR-model was frst ntroduced n Berg et al. (1997a,b). In the new verson of the model presented n ths paper, ol exploraton actvty n Non-PE countres has been ncluded. urther, the cost structure for Non-PE producers has been changed to ft n wth the dstncton between dentfed and undentfed resources. The model descrbes the nternatonal markets for fossl fuels n an ntertemporal way, consderng that the fuels are nonrenewable resources. All prces and quanttes at each pont of tme are determned smultaneously n the model. onsumers determne ther demand accordng to current ncome and prces of the fuels, whereas producers determne ther supply and exploraton actvty accordng to the market condtons n all perods assumng perfect foresght. We specfy three fossl fuels (j =,G,K) n the model; ol (), natural gas (G) and coal (K). onsumers are stuated n three regons ( = 1,2,3), ED-Europe (1), Rest-ED (2) and Non- ED (3). Moreover, we defne two groups of producers n the world ol market (k =,), namely PE whch acts as a cartel (), and a compettve frnge (). There are three regonal natural gas markets wth perfect competton, and the coal market s assumed to be a compettve world market. All varables are functons of tme. However, we wll suppress the tme notaton n the followng. The functonal forms are assumed to be constant over tme The demand sde The consumer prce of a specfc fuel n a specfc regon, Q j, s the sum of the producer prce, P j, fxed unt costs due to transportaton, dstrbuton and refnng, z j, exstng fuel taxes (subsdes are 5

6 consdered as negatve taxes), v j, and, eventually, a carbon tax. Thus before a clmate agreement s mposed, we have (1) Q = P + z + v Q = P + z + v K K K Q = P + z + v G G G K G The demand of each fuel, X j, s represented by a log-lnear demand functon, and s a decreasng functon of the consumer prce of that fuel and an ncreasng functon of the consumer prces of the two other fossl fuels. nally, the demand functons change over tme to reflect economc growth. Moreover, we assume that there exsts a sngle carbon-free backstop technology (e.g., solar, wnd or bomass) whch serves as a perfect substtute for fossl fuels. The technology s avalable n copous supply at a fxed consumer prce, P, at each pont of tme n all regons. ver tme, however, the unt cost of the backstop technology s reduced by a constant rate µ to reflect technologcal change. Wth κ as the ntal backstop prce, we have: (2) P = κ e µ t Analytcally, the demand structure s specfed as follows. Let X j be defned by (3) ln X j = lnω + a lnq + b lnq + c lnq + d lny j j j K j G j where ω j s a constant coeffcent, a, b, c, d are prce and ncome elastctes, and Y s the j j j j gross natonal ncome. Then the demand for fuel type j n regon s gven by (4) X j X j, Qj < P = 0, Qj > P X j [ 0, ], Qj = P 6

7 onsder the ol market, and let x k denote the producton of ol by producer k. Then the restrcton of market clearng n the world ol market can be wrtten (5) x + x = X 3 = 1 rom (1)-(5), we can descrbe the producer prce of ol as a unque functon of the other varables: (6) P = P( x + x, z + v, z + v, z + v, QK, QK, QK, QG, QG, QG, P, Y, Y, Y ) In a smlar way, we can descrbe the producer prces of natural gas and coal l producton The supply sde of the nternatonal ol market conssts of a cartel (correspondng to PE) and a compettve frnge. 2 Whle the frnge always consders the ol prce path as gven, the cartel regards the prce as a functon of ts supply. Hence, the margnal revenue for the frnge s equal to the prce, whereas for the cartel, margnal revenue s n general less than the prce. We choose the Nash-ournot model of a domnant frm to calculate the open loop soluton of the game, where both the frnge producers and the cartel take the supply of all other producers as gven when decdng ther own producton profle. 3 Instead of consderng the resources as strctly exhaustble, we assume that the unt extracton costs of both the cartel and the frnge are ncreasng functons of cumulatve producton whch approach nfnty as cumulatve producton approaches nfnty. Hence, wth a fnte backstop prce the economc reserves are fnte (see, e.g., Heal, 1976). However, the compettve frnge has an opportunty to nfluence ts extracton costs by fndng ol of better qualty (meanng lower extracton costs) than the prevously dentfed remanng resources. Ths s done by exploraton actvty. Exploraton costs also approach nfnty as cumulatve exploraton approaches nfnty, so ths s a model of economc exhauston (zero long-term scarcty rent) rather than physcal exhauston. Although there currently s 2 There exsts two versons of the orgnal model, dfferng only wth respect to the treatment of the global ol market; one consstng of a cartel and a frnge, and one descrbng a hypothetcal compettve market. In ths study we only apply the former verson. 3 The term Nash-ournot-model of a domnant frm was used by Salant (1976). It can be shown that ths Nash-equlbrum s tme consstent but not subgame perfect, see, e.g., Hoel (1992). 7

8 some exploraton actvty n PE countres, too, such as Venezuela, Indonesa and Ngera, compared to Non-PE countres, PE as a whole has vast resources that are easly accessble. Thus, ol exploraton n PE countres does not have notceable mpact on the supply from the cartel, at least n the nearest future The optmsaton problem for PE Let j k be the unt cost of producton of fuel j for producer k. To descrbe the cost structure of PE we have chosen the followng exponental functon A t α η τ (7) = e where α s the ntal unt cost, k A j s cumulatve producton and η j s a constant depleton parameter determnng how fast unt costs ncrease as the reserves are depleted. ne of the man reasons behnd the low ol prces the last decade s probably technologcal change. We therefore assume that unt costs are reduced by a constant rate, τ k, each year (t s tme), ndependent of producton. Ths means that over tme unt costs may be reduced or ncreased, dependng on the producton rate. PE seeks to maxmse the present value of the net revenue flow,.e., the ol wealth. It s facng a downward slopng demand schedule at each pont of tme, and takes the extracton path of the frnge as gven. The control varable n the optmsaton problem s the extracton path and the state varable s accumulated producton. Let r be the dscount rate, and P Wth an nfnte plannng horzon, the optmsaton problem s as follows: ( x ;) s the producer prce gven n (6). (8) max [ ( ; ) ] s.t. (9) A = x rt P x x e dt x 0 (10) x 0 (11) = αe η A τ t 8

9 9 The current value Hamltonan, H,sgvenby (12) ( ) ( ) [ ] H P x A t x x = + ;, λ where λ k (t) ( 0) s the shadow cost assocated wth cumulatve extracton up to tme t. The scarcty rent for the cartel s defned as π λ =, and reflects that extractng one more unt today ncreases costs tomorrow. The necessary condtons for an optmal soluton are gven by the Pontryagn s maxmum prncple. rom ths prncple we get the tme path of the shadow cost (13) λ λ r H A A x = =, whch can be rewrtten usng the defnton of the scarcty rent: (14) π π r A x = x maxmses the Hamltonan for all x 0 whch for an nteror soluton requres (15) λ H P P x x x = + + = 0 Ths gves the producer prce of ol when PE produces (16) x x P P + = π where x x P s the cartel rent. The margnal revenue of PE, MR, s defned as

10 (17) MR = P P + x x = + π Dfferentatng (17) and usng (11) and (14) we fnd the tme path of the margnal revenue (18) MR rπ τ In equlbrum, then, as long as the cartel produces, the change n the margnal revenue over tme must equal ts scarcty rent tmes the dscount rate, mnus ts unt cost tmes the technologcal rate of change. The frst part reflects the standard Hotellng rule, whle the second part reflects that the margnal revenue does not have to ncrease that fast n optmum as the costs are fallng due to technologcal change. In each demand regon there s a maxmum producer prce for each fossl fuel, whch s defned as the backstop prce mnus regonal costs due to transportaton, dstrbuton and refnng of the fuel, and regonal fuel and carbon taxes. The cartel wll stop producng at tme T ( ) 0, when the unt cost reaches the maxmum producer prce. Let A be the aggregate producton of PE over the entre tme horzon. The transversalty condton s then (19) max( P z v ) ( A, T ) T = The optmsaton problem for Non-PE The compettve frnge has an opportunty to nfluence ts extracton costs by fndng ol of better qualty than the resources already dscovered. Ths s done by exploraton actvty. Thus, we ntroduce a separaton of resources nto dentfed resources and new dscoveres. The specfcaton of the Non- PE optmsaton problem s based on Swerzbnsk and Mendelsohn (1989). The undscovered ol s located n several deposts wthn dfferent ol felds n the Non-PE regon. New deposts are dscovered va random search n dfferent ol felds. Let D be the aggregated dscovery, ncludng resources that are not economcally recoverable today, and let w be the new dscoveres at a specfc pont of tme. Thus 10

11 (20) D = w where D(0) = D 0 >0denotes the aggregated dscoveres untl the startng pont of our analyss. At each pont of tme, there s a constant exploraton unt cost for each unt dscovered wthn each feld, G, whch s known to the frnge pror to any exploraton. Thus, we assume a determnstc relatonshp between exploraton effort and new dscoveres. However, the unt costs ncrease over tme as more ol s dscovered (cf. the constant depleton parameter γ n equaton (21)), reflectng that the most accessble felds are searched frst. urther, let δ be the rate of technologcal progress n exploraton costs, and β the ntal unt exploraton cost. Then, we can specfy the followng exploraton unt cost functon for Non-PE countres: β γ (21) G = e ( D D 0 ) δt By payng the exploraton unt cost, the frnge wll dscover a unt of ol and learn the qualty of t,.e., ts unt extracton cost. nly unts that have been dentfed may be extracted. The qualty of ol wthn a depost can be descrbed by a depost-cost profle, (c,t), whch at each pont of tme determnes the fracton of ol wthn a depost wth a unt extracton cost less than c. We specfy the depost-cost profle as follows: 1 τ ce (22) ct (,) = e ϕ 1 t mn where mn s the lowest possble unt extracton cost at tme t=0. We see that 1 as c. ϕ s a constant coeffcent descrbng the cost dstrbuton wthn the depost, whle τ s a parameter reflect- mn mn ng the technologcal progress n ol extracton outsde PE. Hence, = e t τ t denotes the lowest possble unt cost at tme t,.e., ( t mn,t)=0, whch decreases over tme. We assume that the depost-cost profle s dentcal n every depost and n all felds n the Non-PE regon, and that ths profle also apples to the prevously dentfed resources, D Thus, we assume that there s no systematc aggregate relaton between the costs of dentfyng and extractng varous deposts. Moreover, ths s a formalzaton of the assumpton that new deposts are dscovered by a random search wthn each feld, where the probablty of encounterng unts wth partcular extracton costs s equal to the relatve abundance of such unts wthn the feld (Swerzbnsk and Mendelsohn, 1989). 11

12 Let (t) denote the unt cost of extracton from prevously dentfed resources. Swerzbnsk and Mendelsohn (1989) show n the case wthout technologcal change that s non-decreasng along any cost-mnmzng path. rst, ths means that from prevously dentfed resources the cheapest unts are extracted frst. Secondly, all resources wthn a newly dscovered depost wth unt costs below are extracted mmedately. In the case wth technologcal change, wll no longer necessarly be non-decreasng. However, based on the proposton above, we can show that wth equal ~ technologcal rate of change n exploraton and extracton, () t () t e τt = wll be non-decreasng. 5 The same s true as long as producton from prevously dentfed resources s postve, even f the rates of technologcal change dffer. Then the two mplcatons stated above stll hold. Hence, assumng one of these condtons holds true, we see that the cumulatve extracton (A) at a specfc pont of tme (ncludng extracton before the startng pont of our analyss) s equal to the fracton of the accumulated dscoveres (D) wth extracton costs less than,.e., (23) A = (, t) D Thus, we get A (24) (, t) = D Equatng (22) and (24) gves after some calculaton, the unt extracton cost for the frnge from prevously dentfed resources,.e., the resources avalable at the startng pont of the analyss: D A (25) = mn ϕ ln D e t τ However, as ndcated above, the frnge wll also extract from newly dscovered resources, and ths extracton rate wll equal w(t)(,t),.e., the share of the resources wth extracton costs lower than.let f ( c t) = ( c, t) / c,. By usng ths and employng (22), the total costs of extractng from newly dscovered deposts are gven by 5 The proof s straghtforward, and s avalable on request to the authors. 12

13 1 τ e t mn ( ) mn τ t ϕ τ t (26) w cf (,) c t dc= w( t + ϕe ) e ( + ϕe ) mn t As w(, t) s the extracton rate from newly dscovered deposts, the unt extracton cost from newly dscovered deposts s: (27) 1 (, t) mn t cf (,) c t dc The total ol producton n Non-PE at a specfc pont of tme s then the sum of the extracton from newly dscovered deposts, w(, t), and extracton from old resources, q. (28) x = w(, t) + q The frnge maxmses ts resource wealth takng the producer prce as gven. The optmsaton problem wth an nfnte tme horzon s then descrbed by equaton (29). As above, all varables are functons of tme. rt max P ( w, t + q) w cf ( c, t) dc q w G e dt qw, mn 0 t (29) ( ) subject to (30) A = w + q (31) D = w gven q 0, w 0, and the functonal forms n (21), (24), (25), and (26). Let λ and µ be the shadow values correspondng to A and D. Then the current value Hamltonan, H, of ths maxmsaton problem s: 13

14 (32) H = P ( w(,) t + q) w cf (,) c t dc q w G + λ ( w(,) t + q) + µ w mn t Hence, the necessary condtons for an optmum are (33) H q = P + λ 0 (=0forq>0) (34) H w = P (, t) cf ( c, t) dc G+ λ (, t) + µ 0 (=0 for w > 0) mn t H (35) λ rλ q H = = wf (, t) A A A q H (36) µ rµ q D D w G D wf t H = = + (, ) D q rom (33) we then see that for q>0 (37) P = λ Thus, as long as the frnge produces from old resources, the prce must equal the unt cost plus the scarcty rent due to extracton from old resources, λ. To fnd the tme path of the prce for q>0, we dfferentate (37), and use (30), (31), (35) and the dfferentaton of equaton (24) wth respect to A and D, respectvely. Thus we fnd: (38) ( τ ) P = rp r + = r( P ) τ Hence, as long as the frnge produces from old resources, the prce follows a Hotellng path adjusted for technologcal change. 14

15 rom (34) we see that for w>0 (39) P = 1 cf c t dc + G t (,) λ 1 µ (, ) mn t (, ) t By dfferentatng (39), and usng (30), (31), (35), (36) and the characterstcs of the extracton cost functon, we fnd the development n prce for w>0: (40) P = rp + ( 1 ( f (, t), t)(1 (, t) mn t τ, t)) 1 cf ( c, t) dc + G ( ( mn t ) (, t) mn t f ( δg, t) ( f ( c, t) c dc t, t) τ, t) ( ) 2 Wthout technologcal change (.e., δ= =τ = =0), we see that all terms except the ones wthn the square brackets, are zero. Moreover, the second term n the square brackets s the unt costs of dentfyng and extractng a unt from new deposts. Thus, wth postve exploraton actvty, the prce follows a Hotellng path adjusted for technologcal growth. The frst (negatve) term after the square brackets denotes the effect of technologcal progress wthn exploraton actvty. Ths gves ncentves to delay exploraton, whch clearly reduces the prce ncrease. The other terms sum up the total cost effect of technologcal progress wthn extracton on a certan fracton of a new dscovery. Hence, ths sum s by defnton also negatve as long as the technologcal progress s postve. Ths gves ncentves to delay exploraton as the extracton costs of undentfed resources wll be lower n the future. Thus, both technologcal factors have a dampenng effect on the prce ncrease. The condton for smultaneous producton from old and new deposts,.e., q>0and w>0, s found by equatng (38) and (40): (41) τ 1 δ ( 1+ ) = cf ( c, t) dc + G1+ r mn r t τ f t f t c f c t 2 (, ) (, )( ) dc t r (, t) ( mn ) 2 1 (,) + 1 τ mn t t 15

16 Thus, the cost of extractng a unt from prevously dentfed resources adjusted for technologcal change, must equal the cost of dentfyng and extractng a unt from a new depost adjusted for technologcal change n both exploraton and extracton. The transversalty condton for the frnge, where T ( ) A 0, s the last perod of producton and and D are aggregate producton and dscovery over the entre tme horzon, s (42) max( P z v ) ( A, D, T ) T = 2.3. Gas producton Snce the ol market s the man focus of our analyses, the gas and coal markets are modelled n a more smplfed way. f course, the connectons between the markets through the demand sde are mportant, as consumer prces of gas and coal are parts of the demand functon for ol. However, wth relatvely low substtuton elastctes between ol and the two other fossl fuels, more smplfed modules should be suffcent for the gas and coal markets. Because of large transportaton costs, natural gas s manly traded n regonal markets. In the model we have somewhat arbtrarly dvded the world nto the three followng regons. ED-Europe s consdered as a sngle regon, whereas the rest of the ED s taken together (.e., despte separate markets, the Pacfc area s techncally ncluded n the North-Amercan market). The thrd regon s Non-ED, where the former Sovet Unon s a domnatng market. We further smplfy and model compettve gas markets. However, gas producers dynamcally optmse, and extracton costs for gas are modelled n the same way as for PE. The costs dffer between the regons. or more nformaton on the optmsaton problems n the gas markets, see Appendx oal producton The coal market s consdered as an nternatonal compettve market. Snce coal resources n the world are huge compared to ol and gas, we smply assume that the producer prce of coal s fxed at each pont of tme. However, the prce s reduced over tme due to technologcal change. or more nformaton on the optmsaton problem n the coal market, see Appendx 1. 16

17 3. Non-PE data The data appled for the demand structure and the supply from PE and producers of gas and coal were dscussed n Berg et al. (1997a). These are gven n Appendx 2, and we wll gve a short descrpton of the sources we have used below. Then we focus on data for Non-PE producers. Prce elastctes have been taken from Golombek and Bråten (1994), whereas ncome elastctes were derved based on consderatons around the Autonomous Energy Effcency Index (AEEI) (see Matsouka et al. (1995)). Estmates of exstng taxes were taken from EN (1995), IEA (1995a) and Gupta and Mahler (1995). osts of refnng, transportaton etc. have been found n EN (1990) and Golombek et al. (1995). The demand functons were calbrated to agree wth prce and consumpton fgures n Intal unt costs for PE are based on Ismal (1994), whereas correspondng cost estmates for gas and coal are based on Golombek et al. (1995), IEA (1995a,b) and EN (1990). Unt costs for PE and for gas producers are assumed to grow exponentally wth respect to accumulated producton. The functons are calbrated so that the unt costs equal $20 per barrel of ol equvalents (boe) when the proved reserves stated n BP (1995) are produced. At the same tme unt costs declne due to a fxed rate of technologcal change (ths also apples to coal). The ntal backstop prce of $108 per boe s taken from Manne et al. (1995). We assume a slghtly more rapd technologcal progress (stll exogenous) for the backstop technology than for the fossl fuels. A market rate of 7 per cent s used as a dscount rate n all markets. Accordng to EIA (1997a) world-wde fndng costs by 24 major energy companes regstered n the US (.e., RS (nancal Reportng System) companes) n the perod were $4.33 per barrel of ol equvalent. EIA defne fndng costs as exploraton and development expendtures, dvded by reserve addtons. However, n our analyses development expendtures are ncluded n the extracton costs. Moreover, EIA s reserve addtons does not nclude currently unproftable dscoveres. Thus, we would suppose that the value of the ntal unt exploraton cost n our model, β, would be lower than the above fgure. n the other hand, EIA s estmate ncludes both ol and gas exploraton, and data reported by agan (1997) for the US ndcate that fndng costs for ol only may be about one thrd hgher. The Norwegan l Drectorate (1997) reports that unt exploraton costs for ol and gas n Norway are about $1.5 per barrel of ol equvalent dscovered. As fndng costs n ED-Europe are close to the average (EIA, 1997a), we choose to use the fgure for Norway, adjusted upwards by 17

18 one-thrd. That s, the ntal (1995) unt exploraton cost, β, ssetequalto$2perbarrelofol dscovered. Ths estmate also compares well wth a lst by Petrocompanes (1998) of fndng costs (here excludng development costs) n varous ol companes. Accordng to EIA (1997b) a low and hgh estmate of undscovered ol n Non-PE s 197 and 685 bllon barrels, respectvely. Ths s based on an assessment prepared by the US Geologcal Survey (USGS). However, EIA ponts out that the USGS s assumng constant technology and economcs, and that the potental may be much hgher f technology contnues to advance or/and f real ol prces ncrease over tme. Thus, somewhat arbtrarly, we choose to calbrate the depleton parameter γ n the exploraton cost functon so that the unt exploraton cost reaches $20 per barrel when the average of the low and hgh estmate above has been dscovered (gnorng technologcal change for the moment). Then, usng 10 bllon boe as metrcs, we arrve at γ = Wth an annual dscovery of e.g. 10 bllon boe (whch s close to actual dscoveres per year n Non-PE - see Petroconsultants (1996)), ths wll of course mply a cost ncrease of 5.2 per cent per year (stll gnorng technologcal change). As ths parameter s hghly uncertan, we present senstvty analyses of ths as well as other parameters at the end of the paper. There has been a remarkable technologcal change n exploraton outsde PE the last decade. or the Unted States, agan (1997) concludes that an acceleratng rate of techncal change reduced average fndng cost 15 per cent (onshore) and 18 per cent (offshore) per year by The technologcal advances have partcularly taken place after the dramatc drop n ol prces n 1986, and t s doubtful that ths wll contnue for a prolonged perod. Thus, takng a somewhat conservatve vew, we set the annual rate of technologcal change n exploraton costs equal to 2 per cent ntally, declnng gradually to 1 per cent over a 30 year perod. To calbrate the depost-cost profle (see equatons (22) and (24)) we must frst of all determne the current values of D and A,.e., accumulated dscoveres and producton up to the year rom EIA (1997b), Table 13, we fnd an estmate of accumulated producton n Non-PE at the end of Addng the producton n 1993 and 1994, we arrve at A 1995 = 446 bllon barrels. urthermore, D 1995 s the sum of A 1995 and remanng dentfed resources outsde PE at the end of rom Table 13 n EIA (1997b) we fnd that remanng dentfed reserves n Non-PE were 397 bllon barrels at the end of Ths ncludes proved, probable, and possble reserves. To also nclude the more uncertan potental addtonal reserves (whch are not economcally recoverable today), we add 10% based on nformaton from the UK (Petroleum Economst, 1998). Moreover, to adjust to the 18

19 end of 1994, we use the percentage change of Non-PE reserves dentfed by Petroconsultants (1996). nally, addng A 1995 we arrve at D 1995 = 872 bllon barrels, whch subsequently mples that 1995 = To further dentfy the depost-cost profle, we use an estmate of unt costs n ol producton outsde PE of $10.9 per barrel (calculated from Ismal, 1994). We assume that takesonthsvaluen 1995, so that (10.9,1995)=0.51. Moreover, accordng to Adams (1991), 6 up to 70 per cent of ol resources outsde PE could be developed at less than $20 per barrel. When combnng ths fracton wth the fgure calculated above on remanng resources, we arrve at 299 bllon barrels, whch s almost halfway between the stated Non-PE reserves n BP (1995) and Petroconsultants (1996), respectvely. Both BP and Petroconsultants defne (proved) reserves as remanng resources whch can be recovered under exstng economc and operatng/techncal condtons, so ths assumpton seems vald. Thus, we have another pont on the depost-cost profle, and are able to determne the values of mn ($5.5 per barrel) and ϕ (7.6). We have generally assumed the rate of technologcal change n ol and gas producton to be 1 per cent per year. Intally, however, as ol producers outsde PE have had mpressve technologcal mprovements lately (see, e.g., Ismal, 1994), we assume a rate of 2 per cent n Non-PE. Ths rate s gradually reduced to 1 per cent after 30 years. 7 In fgure a we llustrate the shape of the depost-cost profle n 1995 and The current value of and (,1995) s marked wth an. 6 Quoted by MacKenze (1996). 7 Then we ensure that the condtons dscussed n front of equaton (23) are fulflled. 19

20 gure A. The calbrated depost-cost profle of Non-PE ol felds n 1995 and (c,t) 0,9 0,8 0,7 0,6 0,5 X 0,51 0,4 0,3 0,2 0,1 0 (c,1995) (c,2010) Unt extracton cost, $ per barrel Results are presented n a Reference scenaro where there are no carbon taxes, and n three tax scenaros where carbon taxes are ntroduced. In the ED carbon tax scenaro I a carbon tax of $10 per boe s ntroduced n the ED regons from 2000, and outsde ED as well from Ths may be one possble tax scenaro based on the Kyoto Protocol agreed upon n December 1997, whch put restrctons on 2 emssons n ED countres (n addton to Russa, Ukrane and Eastern European countres) n As a comparson, n the Global carbon tax scenaro the same carbon tax s ntroduced n all regons from 2000 onwards. However, there are reasons to beleve that restrctons on 2 wll be gradually tougher. Hence, a more plausble tax scenaro may be the one we call the ED carbon tax scenaro II. Here a carbon tax of $5 per boe s ntroduced n the ED regons n the frst perod, ncreasng to $10 n the second perod, and fnally $20 from 2020 onwards. rom 2030 the $20 tax s leved outsde ED, too. Smulatons were carred out for the tme perod wth ten year perods, usng the GAMS/MINS system (see Brooke et al., 1992). Thus the results n each perod are the average over the ten years, e.g., the results for the year 2000 are the average over the perod

21 4. Smulaton results 4.1. The Reference scenaro In 2000 the total ol producton n the world s calculated to 24.9 bllon barrels of ol (boe) per year (.e., 68 mbd - mllon barrels per day). PE produces about 7.0 bllon boe (19 mbd), see fgure b. Thus the PE s share of the total producton s 28 per cent whch s less than the real 1994 share of 41 per cent. Ths may ndcate that PE acts as a more effectve cartel n the model than n realty, or that they are n a more leadng poston n the real market than n our Nash-ournot model, e.g., lke a Stackelberg leader. In the latter case PE must gve credble sgnals to the market that the cartel wll produce more than what s seemngly proftable n the short run n order to prevent developments of new ol felds n Non-PE. We wll come back to ths problem later on n the dscusson of the results. The annual Non-PE producton n 2000 s 18.0 bllon boe (49 mbd). It ncreases slghtly untl 2040, where t reaches the top producton of 21.6 bllon boe. The last perod of producton n Non- PE s PE has a steady ncrease n ts producton as long as Non-PE s n the market. However, when Non-PE stops producng, PE takes over the whole market. The last perod of producton n PE s then the prce of the backstop s so low that further ol producton s not economcally vable. The ol exploraton n Non-PE, or the new dscoveres, start on an annual level of about 8.0 bllon boe n 2000, see fgure b. As a comparson, actual dscoveres n Non-PE n the perod were n average 8.2 bllon boe per year, as reported by Petroconsultants (1996). However, ths fgure only ncludes resources that are recoverable under current economc and techncal condtons, and from fgure a we see that for 1995 about 80 per cent of new dscoveres n the model may be put n ths category. In later perods from 2010 to 2040, exploraton and new dscoveres are qute hgh,.e., on a level between 11 and 18 bllon boe per year. ne reason for the somewhat lower exploraton n the frst perod may be that the ntal resource base s hgh. Moreover, as the dfference between extracton costs from old resources and new dscoveres are ncreasng over tme as the lowest-cost deposts are extracted frst, ths may call for ntensfed exploraton effort n later perods. However, as the costs of makng new dscoveres ncrease, exploraton actvty eventually comes to an end n the mddle of the next century. Non-PE has a smultaneous exploraton and producton from prevously dentfed resources n all perods. In the frst perod around three quarter of the producton 21

22 come from resources dscovered n earler perods, and the rest from new dscoveres. Then, for the next three decades, the dstrbuton s farly even. nally, n 2040 and 2050 about 80 per cent of the producton come from new dscoveres. Total new dscoveres n Non-PE over the tme horzon s about 627 bllon boe, whch s not far from the hgh estmate of undscovered ol n Non-PE stated by EIA (1997b) (see Secton 3). gure B. l producton and new dscoveres, reference scenaro bllon boe/year Producton n Non-PE Producton n PE New dscoveres n Non-PE Year The ol prce starts at $16.3 and ncreases to $32.5 n 2040, before t meets the maxmum producer prce of ol, see gure 3. rom 2050 onwards, the producer prce follows the maxmum producer prce. Due to the smultaneous exploraton and producton from old resources n Non-PE from 2000 to 2050, the prce path satsfes equatons (38) and (40) smultaneously as long as the prce s less than the maxmum producer prce. 22

23 gure. l producer prce, reference scenaro l producer prce Maxmum producer prce 25 $/boe Year Global 2 emssons due to combuston of fossl fuels ncrease from 6.3 bllon tons of carbon n 2000 and reach the top of about 12.5 bllon tons n 2060, see gure 4. Then emssons drop as ol s substtuted by the backstop n Due to ncreasng coal consumpton, the emssons rse thereafter, wth a small drop from 2080 to 2090 when the backstop replaces natural gas globally. oal s consumed and produced over the entre tme horzon. gure D. 2 emssons from fossl fuel combuston, reference scenaro bllon tons of carbon per year Global emssons ED emssons Year 23

24 4.2. Effects of constant carbon taxes The ED carbon tax scenaro I In the ED carbon tax scenaro I, a carbon tax of $10 per boe s leved on ED countres from 2000 onwards, but also on countres outsde ED from As seen from fgure e, the producer prce of ol s reduced by only $0.3 n the frst perod, whch means that the consumer prce ncreases wth $9.7. However, the slope of the prce path s lower, and n 2040 the producer prce s reduced by $3.5. rom 2050 onwards, when both prce paths follow the respectve maxmum producer prce paths, the producer prce s $10 less than n the Reference scenaro. See also equaton (38) to understand the mpacts on the slope by a fall n the prce. gure E. l producer prce, reference scenaro and ED tax scenaros $/boe l producer prce - Reference scenaro l producer prce - ED tax scenaro I l producer prce - ED tax scenaro II Max. producer prce - Reference scenaro Max. producer prce - ED tax scenaro I Max. producer prce - ED tax scenaro II Year The reason for the small ntal change n the ol prce s the PE behavour. As seen from fgure f, PE reduces ts producton qute sgnfcantly n the year 2000, by about 14 per cent, as a response to ths clmate polcy. The cartel knows (at least n the model) that reducng producton gves a hgher prce. In a statc model, the optmal response by a cartel s to reduce ts producton to retan ts margnal revenue,.e., the cartel rent. In a dynamc model, however, PE also takes nto consderaton the exhaustablty aspect, ntroduced by the scarcty rent, and the ol rent now conssts of the cartel rent and the scarcty rent. But the margnal extracton costs n PE are almost constant as long 24

25 as Non-PE s n the market, whch means that the scarcty rent s rather low, and PE behavour s not much nfluenced by the dynamc aspects. Thus for PE t s optmal to reduce the producton to retan ts cartel rent and therefore ts ol rent, see also Berg et al. (1997a). gure. l producton n PE, reference scenaro and ED tax scenaros 40 bllon boe/year Reference scenaro ED tax scenaro I ED tax scenaro II Year Non-PE s a compettve frnge, and vews the ol prce as gven. A lower ol prce level gves an ncentve to reduce producton. However, the slope of the prce path also matters. An ncreasng prce path gves an ncentve to delay producton. As the prce ncreases less under the clmate polcy, ths ncentve s weakened, and Non-PE wants to move the producton profle nearer n tme,.e., to ncrease producton n earler perods and to reduce producton n later perods. rom fgure g we see that ths last effect manly occurs n the later perods of Non-PE producton. In 2030 producton ncreases by 2.4 per cent even though the prce has fallen by $1.9 per boe. The reason s of course that the prce fall n the next perods s much larger, whch reduces Non-PE producton sgnfcantly n these perods. Thus, n 2030 the ncentve to accelerate producton s stronger than the ncentve to reduce producton level due to lower prces. In the three frst perods Non-PE producton decreases somewhat, but never more than 2.3 per cent. ver the tme horzon, the aggregated Non-PE producton s reduced by about 4 per cent to 1,007 bllon boe. 25

26 gure G. l producton n Non-PE, reference scenaro and ED tax scenaros 25 bllon boe/year Reference scenaro ED tax scenaro I ED tax scenaro II Year The mpact of the carbon tax on exploraton actvty follows closely the mpact on Non-PE producton, see fgure h. In the three frst perods new dscoveres decrease by up to 3 per cent. Then, n 2030 exploraton actvty ncreases somewhat,.e. by 2.3 per cent, before t falls below the reference scenaro n the next perods. Thus, n these later perods the ol exploraton path has been moved nearer n tme n a smlar way as the producton profle. Aggregated dscoveres are reduced by 6.5 per cent - before 2040 the reducton s only 0.4 per cent. We therefore conclude that ntroducng a constant carbon tax n the ED area has only neglgble mpacts on Non-PE producton and exploraton before the mddle of the next century. Ths s manly due to PE behavour, but also to the dynamc aspects of non-renewable resources. 26

27 gure H. New dscoveres n Non-PE, reference scenaro and ED tax scenaros 18 bllon boe/year Reference scenaro ED tax scenaro I ED tax scenaro II Year A carbon tax of $10 per boe ntroduced n ED countres wll reduce global emssons by 10 per cent to 5.8 bllon ton carbon n 2000, see fgure. Ths s around the actual level of fossl fuel-related carbon emssons n The emssons wll, however, ncrease slghtly over tme and peak at 9.6 bllon tons n Due to the carbon tax, coal s actually substtuted by the backstop from 2110 onwards, whch gves no carbon emssons. 2 emssons n the ED area are reduced by 20 per cent n 2000 and 2010, and reach a level of 2.9 bllon tons n 2010, whch s about 5 per cent above the actual 1990 level. At frst glmpse ths reducton may seem too small compared to the agreed reducton n the Kyoto Protocol of 5.2 per cent compared to However, as explaned above ths overall commtment apples to countres outsde the ED, too, n whch emssons are expected to decrease between 1990 and 2010, and t apples to an aggregate of 6 greenhouse gases (ncludng 2 ). 27

28 gure I. 2 emssons from fossl fuel combuston, reference scenaro and ED tax scenaros bllon tons of carbon per year Global emssons - Reference scenaro ED emssons - Reference scenaro Global emssons - ED tax scenaro I ED emssons - ED tax scenaro I Global emssons - ED tax scenaro II ED emssons - ED tax scenaro II Year The Global carbon tax scenaro When the carbon tax s ntroduced n all regons from the begnnng, the prce path of ol s more or less dentcal to the prce path n the ED carbon tax scenaro I. Thus, Non-PE producton and exploraton s also almost dentcal. The reason for ths s agan the PE behavour. As the Non- ED regon also meets clmate restrctons, t has a lower demand for fossl fuels than n the ED carbon tax scenaro I. In the same manner as PE reduces ts supply when the tax s leved n the ED area only, t reduces ts supply even more when the tax s leved globally so as to prevent the ol prce from fallng. Moreover, after 2030 the maxmum producer prce s equal n these two tax scenaros. Thus, the result s that the prce paths n the two tax scenaros are almost dentcal. 8 Global 2 emssons n 2000 have been reduced by 21 per cent to 4.9 bllon tons of carbon. Thereafter, the emssons ncrease and follow the path of the ED carbon tax scenaro I from 2030 (when the carbon tax apples globally n both scenaros). As fossl fuel prces are almost dentcal to the ED carbon tax scenaro I, 2 emssons n the ED regons are also almost equal n these two tax scenaros. 8 Snce ths scenaro s almost dentcal to ED carbon tax scenaro I, t s not shown n the fgures. 28

29 Ths scenaro shows that the general mpacts on exploraton n Non-PE countres wll be the same whether or not the carbon tax ntally s ntroduced n all regons or only on ED countres, as long as the tax s leved globally after some decades. Ths s manly due to the PE behavour Effects of rsng carbon taxes The ED carbon tax scenaro II As stated above, the most plausble scenaro s that we wll see a rsng carbon tax, frst ntroduced n ED countres. The reason s that the goal of stablsng emssons wll be ncreasngly tougher to reach as the dstance from the Busness as Usual path gets larger. Moreover, several studes have concluded that the optmal tme path of a carbon tax may be rsng ntally (e.g., Ulph and Ulph (1994) and Hoel and Kverndokk (1996)). In the ED carbon tax scenaro II we analyse the effect of one such scenaro, where the carbon tax n ED s $5 per boe n the frst perod, $10 n the second perod (2010), and $20 thereafter (from 2020). In 2030 the carbon tax of $20 per boe s leved on all countres. rom fgure e we see that the ol prce has fallen even more than n the frst ED carbon tax scenaro. Moreover, the ol prce path ncreases less rapdly over tme, and reaches ts maxmum level n 2030 just above $20 per boe. Note that the ol prce n 2000 s actually lower n ths case when the carbon tax s $5 per boe ntally than when the carbon tax s constant and equal to $10 per boe. Ths s due to the ntertemporal behavour, and the fact that the prce path s barely ncreasng over tme. As explaned above, the producers then have ncentves to accelerate ther producton compared to the stuaton n the ED carbon tax scenaro I wth more rapdly ncrease n the ol prce, and so the ntal prce s suppressed. Ths s confrmed n fgure f whch shows that PE does not reduce ts producton as much n the begnnng as when the constant carbon tax s ntroduced. In 2020 and 2030, however, when the tax s $20 per boe, PE s producton s sgnfcantly reduced. Thus, the reducton n PE supply seems to be tght connected to the sze of the tax n the specfc perod, as long as Non-PE produces. We also see that PE takes over the market one perod earler, but as the cartel also stops producng one perod earler, ts aggregated producton s reduced by 34 per cent compared to the reference scenaro. The Non-PE reacton to ths carbon tax scenaro s nterestng. rom fgure g we see that producton outsde PE has ncreased n each of the frst four perods. Then producton drops to one 29

30 sxth when the prce reaches the maxmum producer prce. The reason s that the ncentve to accelerate producton due to an almost flat prce path s stronger than the ncentve to reduce producton level due lower prces. Hence, Non-PE s response to ths carbon tax scenaro s actually an ncrease n producton for the frst 40 years to come. In fgure h we see that ths concluson also apples to exploraton actvty outsde PE. To ncrease Non-PE producton n early perods, more exploraton seems to be optmal. ompared to the reference scenaro, n 2030 the dscovery rate s ncreased by 18 per cent, and at the end of the fourth perod, aggregated dscoveres n Non-PE are 6 per cent hgher. However, over the entre tme horzon, aggregated dscoveres are reduced by 24 per cent as the lfe of Non-PE ol s shortened by one decade. Stll, t s a startlng result that for the frst 40 years ol exploraton outsde PE s not beng negatvely affected by a clmate agreement. In fact the contrary may occur. Notce that carbon emssons n ED are between 0 and 10 per cent above the actual 1990 level for the frst forty years, and never exceed more than 25 per cent above ths level, see fgure. Global emssons, too, do not exceed more than 25 per cent above ts 1990 level. Hence, despte the counteractve effect n Non-PE actvty, ths tax scenaro s not far from stablsng emssons n the long run. Whether the commtment put forward n the Kyoto Protocol s reached or not, s however unclear (see the end of Secton 4.2). 5. Senstvty analyses and dscusson As exploraton n Non-PE countres s the man topc n ths paper, we concentrate the senstvty analyss around ths actvty. As ponted out n Secton 3 there are several parameters that are qute uncertan. The depost-cost profle were calbrated under the assumpton that 70 per cent of remanng resources could be extracted at a unt cost lower than $20 per boe. If we rather assume that the share s 60 per cent, the depost-cost profle gets more lnearly,.e., the value of ϕ gets hgher (ϕ== 9.9) and the ntal mnmum cost decrease to $3.8 per boe. In ths reference case exploraton s ncreased n the frst perod, as the dfference between extracton cost from old resources and the best qualty deposts n new dscoveres has ncreased. However, ths s compensated n later perods, so that aggregated dscoveres are almost unchanged. If we nstead make the depost-cost profle more non-lnear by assumng that 80 per cent of remanng resources can be extracted at a unt cost less than $20 per boe 30