More Gas to Reduce CO 2 Emissions?

Transcription

1 More Gas to Redue CO 2 Emissions? Julien Daubanes & Fanny Henriet & Katheline Shubert ETH Zurih, Paris Shool of Eonomis, CNRS, University Paris January 29, 206, Preliminary and inomplete draft, do not irulate Abstrat Shale gas is hoped to effetively help gas produing regions meet their emission redution ommitments. We examine an open eonomy that produes both shale gas and another, more arbon intensive fuel like oal. We find that imposing a domesti emission ap may in fat ontribute to inrease global emissions. This may happen if the emission ommitment, implemented through a ap and trade system or a arbon tax, leads to inrease domesti gas extration. Indeed, gas releases oal that is exported instead of being onsumed domestially, inreasing emissions in the rest of the world. Our two-resoure setting thus ontradits the standard analysis of emissions leakage with a single resoure. We establish testable onditions under whih governmental emission ommitments warrant the domesti exploitation of gas, and 2 imposing a ap on domesti emissions inreases global emissions. Introdution and Detailed Desription The use of shale gas notoriously releases less arbon emissions than regular fuels. Now more than ever, it is hoped that a large substitution of regular, very arbon intensive fuels by gas an help redue arbon emissions, mitigating a limate problem labeled the ultimate ommons problem of the twenty-first entury Stavins 20. On this basis, an inreasing number of top CO 2 emitting ountries that are endowed with large shale gas deposits plan to meet their emission redution governmental ommitments by promoting the shale gas resoure; among them, the US, Russia and China. For example,

2 shale gas promotion seems at the heart of the urrent US Administration s energy strategy. As President Obama puts it, the US "position as the top natural gas produer... not only an provide... heap power, but it an also help redue [US] arbon emissions." Remarks by the President on Climate Change, June 25, 203. Not so surprisingly, this view is supported by the gas industry. The hope that natural gas an play a major role in national limate and energy poliy strategies has also been substantiated by aademi experts see the MIT report of Jaoby, O Sullivan and Paltsev, 20, on the US, 2 but remains ontroversial see the reent projetions of Chakravorty et al. 205, for China. Figure shows US onsumption of oal and natural gas from eletriity generation from 200 to 204, and Figure 2 shows US energy related CO 2 emissions on the same period. The progressive substitution of oal by gas is learly apparent. It is expeted to ontinue in the near future. The downward trend is also lear: emissions have been redued by 0% between 2007 and 203. However, this redution may be explained by many other fators besides oal to gas substitution. Feng et al. 205 for instane deompose the deline in CO 2 emissions aording to different fators, inluding donsumption volume, energy intensity and fuel mix. They find that the eonomi slowdown has been an important driver of the derease in CO 2 emissions but the fuel mix played a signifiant positive role in this derease. Knittel et al. 205 find that the drop in the prie of natural gas between June 2008 and the end of 202 translates to a large redution in CO 2 emissions from the eletriity setor. Regardless of whether the substitution of regular fuels by natural gas is desirable for an eonomy onerned by its CO 2 emissions, the global effet of this strategy is limited by a leakage phenomenon: substitution by gas releases amounts of tradable fuels like oal; the resulting supply meets the foreign energy demand of regions that do not have emissions target, ontributing to inrease emissions in those regions. For example, empirial evidene shows that the reent US shale gas boom has been aompanied by a severe rise in US exports of oal between 2007 and 202 see Figure 3. Of ourse, this upward trend in US exports may be explained by other fators. However, the standard analysis of CO 2 leakage delivers a relatively optimisti message: domesti efforts to redue CO 2 emissions are ompensated by leakage only partially but not ompletely e.g. Eihner and Pethig 20 and Fisher and Salant 202, to an extent that depends on the elastiities of supply and demand of the CO 2 ontaining ommodity BP, BG Group, Eni, Statoil and Total reently delared: We urge governments to take deisive ation at Deember s UN summit. We are also united in believing suh ation should reognize the vital roles of natural gas and arbon priing in helping to meet the world s demand for energy more sustainably. Letter on the role of gas and arbon priing to media, June, Aording to the report see Jaoby et al. 20, the emergene of shale gas supplies is a boon to the US eonomy and an aid to potential limate poliy." 2

3 Natural Gas Coal Figure : US onsumption of natural gas and oal for eletriity generation MMBtu Figure 2: US energy related CO2 emissions millions of tons 3

4 Figure 3: US oal exports Thousand Short Tons and of the market share of the CO 2 reduing eonomy. Carbon leakage has been extensively studied in various settings, e.g. Ritter and Shopf 203 or Quentin Grafton et al Yet there exists no theoretial study where arbon leakage arises as a result of the substitution of one polluting resoure by another less polluting resoure. We extend the leakage literature to take into aount the multipliity and heterogeneity of resoures that atually ompete for the energy demand, in the spirit, for example, of Chakravorty et al The optimisti message of a less than 00% leakage onveyed by the standard analysis with a single resoure does not arry over to our novel two-resoure setup: an eonomy that relies on domesti natural gas to meet its emission ommitment may in fat ontribute to inrease global emissions. Burniaux and Oliveira Martins 202 study arbon leakage in a general equilibrium framework with multiple fossil fuels, but they group natural gas with arbonfree energy. The paper also relates to the green paradox litterature see for instane, Sinn 2008, van der Ploeg and Withagen 202 as an environmental poliy, here a domesti ap on emissions, ould lead to an adverse effet: the inrease of world emissions. In this projet, we examine an open eonomy that produes both natural gas and another, more arbon intensive fuel thereafter, oal. There are three mains hannels of arbon leakage: 3 i International energy markets; 3 see Dröge et al for a typology, 4

5 ii firm s prodution osts, investments deisons and reloalisation; iii the dynamis of tehnologial innovation and poliy diffusion. In this paper, we only fous on leakage through international energy markets. Optimal resoure extration with various pollution ontents and/or osts has been studied by Herfindahl 967, Heal 976, van der Ploeg and Withagen 202 and Coulomb and Henriet 203, among others. Reently, Henriet and Shubert 205 has studied the optimal exploration and exploitation of shale gas and a renewable bakstop in an eonomy initially produing its eletriity with oal-fired power plants. However, the losed eonomy setup prevents it from studying arbon leakage issues. Natural gas domesti prodution is onsumed domestially. Coal domesti prodution may be exported to the rest of the world. We address the following questions. Faed with an emission redution objetive, should a natural gas produing eonomy inrease its domesti gas prodution? 2 Does this strategy derease global emissions? The analysis involves the minimal elements needed to address those questions. That is, all setors are ompetitive. There is a single poliy, that sets a ap on domesti emissions. This ap is implemented in a ost-effetive manner, for example by use of a tradable permits system. There is no impediment to the perfet substitution of one resoure by another, as should be the ase in a medium to long run perspetive over whih resoure-using tehnologies an be adapted. We establish testable onditions under whih a more stringent governmental emission ommitment warrants more domesti exploitation of gas, and 2 this strategy inreases global emissions. Combining those onditions, we haraterize situations where domesti poliy is strongly ounter-effetive: even when an eonomy finds optimal from a domesti perspetive to rely on its natural gas to meet its own emission ommitments, this strategy may effetively ontribute to inrease global emissions. That is this result that ontradits the standard analysis of less than 00 perent leakage. With several resoures, the novelty is that an emission ap not only penalizes the most polluting resoures, but also enourages the least polluting ones. Thus, despite leakages, less oal is produed in the aggregate, as one should expet from the standard leakage analysis; but this redution an be more than ompensated beause the rise of natural gas makes energy more abundant. The onditions that we establish bring up new insights. They involve measurable eonomi notions suh as the elastiities of gas and oal supply and demand, and the market shares of the emissionreduing eonomy in the two setors respetively. They an easily be used to assess the role that natural gas should play in any ountry: that is, for eah ountry, whether domesti gas promotion is desirable from a domesti perspetive and whether suh poliy helps to meet global efforts to redue CO 2 emissions. Our systemati examination and the formulas 5

6 we obtain are therefore ritial for the design of effetive poliies against the global limate problem that are aeptable at the national level. The first part of the analysis follows Hoel 994 s and Harstad 202 s stati piture of the energy market. In fat, the exploitation of natural gas and other resoures introdues a dynami dimension. Exploitable resoures are developed first and are then exploited over time. Thus in a seond part, we also build on the literature on intertemporal extration of natural resoures see Quyen 99, Arrow and Chang 982, Pindyk 978, Gaudet and Lasserre 988. We show how the analysis aommodates this intertemporal extension. This extension highlights the role of the ultimately exploited resoure quantities. Yet those umulative quantities behave in the same way as their instantaneous flow ounterparts in the stati analysis; that is, the onditions obtained in the first stati setup qualitatively follow through in the long run. Setion 2 presents the model. In setion 3, we derive the effet of a more stringent domesti emission ap on gas extration and world emissions. Extensions are presented in setion 4. 2 Model and Sketh of Analysis We examine an open eonomy in whih a ountry H Home produes natural gas in quantity x H g and another, more arbon intensive fuel thereafter, oal, in quantity x H. Gas is not traded and is produed by ountry H alone. Coal is also produed and onsumed in the rest of the world F. The quantity of oal extrated in the rest of the world is denoted x F. Home onsumes the quantity x H g of gas and a quantity y H of oal, whereas the rest of the world onsumes a quantity y F of oal. The two fossil resoures are perfet substitutes in eletriity generation. Burning one unit of natural gas resp. oal inreases emissions by resp.. Coal supply There is a ompetitive world market where oal an be sold to eletriity produers at prie p. The ost of supplying x units of oal in the Home ountry is given by C H x, where C H. is an inreasing and stritly onvex funtion. The Home oal produers take the world oal market prie p as given and maximize: p x H C H x H. Similarly, the Foreign oal produers fae an inreasing and onvex supply ost funtion denoted C F.. They take the world oal market prie as given and maximize p x F C F x F. At the equilibrium: p = C H x H p = C F x F 2 6

7 Alternatively, we denote the supply of oal x H = S H p C H p, x F p, x H + x F = S p. C F = S F p Gas supply Gas is only produed and onsumed in the Home ountry. It is sold to eletriity utilities by gas produers in a ompetitive market at prie p g. The ost of supplying x H g units of gas is represented by a onvex and inreasing funtion C H g x H g. The Home gas produers take the market prie p g as given and maximize: p g x H g equilibrium: C H g x H g. At the p g = C H g x H g 3 Alternatively, we denote the supply of gas x H g = S g p g Cg H p g. Climate poliy There is a single poliy, in ountry H, that sets a ap on domesti emissions e. This ap is implemented in a ost-effetive manner, for example by use of a tradable permits system or a arbon tax. This tax or the permits prie is denoted τ. The revenues from the tax or the quotas are redistributed lump sum to onsumers. At the equilibrium: e = x H g + y H 4 Market for eletriity in the Home ountry Consumers have a quasi-linear utility funtion. When one onsumes y unit of eletriity, bought at prie q, one gets utility: By qy. Eletriity is produed with a one-for-one tehnology using oal or shale gas, whih are perfet substitutes. Eletriity produers must pay a tax or the permit prie on emissions. At the equilibrium, the final energy prie in the Home ountry is: q = p g + τ = p + τ 5 and demand in the Home ountry is given by: B x H g + y H = q 6 Alternatively, we denote the domesti demand of eletriity x H g + y H = D H q B q. Market learing In the rest of the world, eletriity is produed with a one-for-one tehnology using only oal. There is no limate poliy. Consumers have a quasi-linear utility funtion, whih yields a demand for oal y F = D F p. The equilibrium of the oal market reads: y H + y F = x H + x F 7 7

8 Equilibrium The equilibrium values of p, p g, x H, x F, x H g, y H, y F, τ are given by the system of equations to 7. Eliminating p g, x H, x F, y H, y F yields the following system in p, x H g : θ s B e + θ x H g and τ between these equations C g H x H g + p = 0 8 S H p + S F p D F p = e x H g 9 3 Effets of a more stringent domesti emission ap In this setion, we look at the effet of strenghtening the ap on domesti emissions on natural gas extration. We assume a marginal hange de in the ap e. Proposition. Faed with a lower ap e on its emissions, the Home ountry inreases gas domesti use x H g if and only if: > D H q D F p S p 0 Proof. See Appendix. To understand this proposition, note that, using the definition of domesti eletriity demand D H q = x H g + y H, the market learing ondition 7 an be rewritten as: S g p g = D H q [ S }{{} p D F p ] }{{} domesti eletriity demand residual oal supply It is straightforward that the tax τ has two effets playing in opposite diretions on the gas produer prie p g : On the one hand, the tax dereases the oal produer prie ompared to the natural gas produer prie: p = p g τ. Following an inrease in τ, the residual supply urve of oal for the domesti market S p D F p is shifted to the right in the gas produer prie, quantity spae. If domesti demand D H q was unhanged, the residual demand urve D H q [ S p D F p ] would be shifted to the right and would ross the gas supply urve at a higher gas produer prie, implying that more gas is developed. That would be the only effet were domesti demand totally inelasti. 8

9 The magnitude of this effet is: S gp g d p g = [ S p D F p ] dτ In general, there is another effet playing in the opposite diretion: the tax inreases the domesti energy prie q = p g + τ, and thus shifts the domesti demand D H q to the left in the prie, quantity spae. If the residual supply of oal for the domesti market was unhanged by the tax, the supply urve of gas and the residual demand for gas would ross at a lower gas produer prie, implying a lower gas supply. The magnitude of this effet is: S gp g d 2 p g = D H qdτ To sum up, the effet of the tax on gas extration is ambiguous. On the one hand, the tax dereases the oal produer prie ompared to the gas produer prie, leading to a lower supply of oal on the domesti market, and thus leaving more room for natural gas. On the other hand, the tax redues domesti demand, reduing the demand for gas as well. The overall effet is given by: S gp g dp g = { D H q + [ S p D F p ]} dτ Let us define the elastiities of eletriity demand in Home and Foreign ountries: ɛ H D = DH qq D H q, ɛf D = DF p p D F p and the elastiity of world oal supply: ɛ S = S p p S p Let us look at ondition 0. For a marginal inrease in τ from τ = 0, it an be rewritten as: > ɛh D D H ɛ F D D F + ɛ S ɛ F D S D F This ondition is more likely to be satisfied, i.e. a ap on emissions is more likely to lead the Home ountry to inrease natural gas extration, if the differene in pollution ontents of oal and gas is high; the Home ountry is small in front of the rest of the world D H D F ; 9

10 the prie elastiity of the world oal supply is large; the prie elastiity of eletriity demand is small. In partiular, if demand in the Home ountry is totally inelasti or if the world supply of oal is very elasti, a more stingent ap on emissions in the Home ountry leads to inrease natural gas extration. The intuition is the following: if demand is very inelasti, inreasing the quantity of gas extrated dereases exatly by the same amount the quantity of oal onsumed domestially, thus reduing emissions; if the world oal supply is very elasti, an inrease in gas extration redues oal prodution and redues domesti emissions. Let us alibrate roughly the model to the US ase, to get insights on how likely the inrease of natural gas extration is. EIA 202 gives that the US oal onsumption is 2% of world total oal onsumption. We assume that gas represents half of eletriity onsumption, so that D H /D F 0.24 and S /D F.2. The empirial literature gives prie elastiity of energy demand between 0.05 and see Bentzen and Engsted 993, Masih and Masih 996, Truby and Paulus 202. We make the assumption ɛ H D = ɛf D 0.5. Condition may be written as: i.e., with our alibration: ɛ S > ɛ F D F D S ɛh D D H ɛ F D D F 0.24 ɛ S > The ondition is satisfied for all values of ɛ S as soon as /.24. Most estimates of the CO 2 emissions oeffiient of oal relative to natural gas yield figures around 2 Heath et al. 204, Jenner and Lamadrid 203, Alvarez et al Things are more ontroversial regarding the relative global warming potential of the two fossil fuels, mainly beause of the methane leakage assoiated to shale gas exploitation see Howarth et al. 20. Anyway, /.2 appears as quite plausible. Hene it is very likely that the inrease of shale gas extration will redue emissions in the Home ountry. The question that arises next is whether this leads to inrease or derease world CO 2 emissions. Of ourse, a neessary ondition for an inrease in world emissions is an inrease in natural gas extration. Let us look now at the effet on world emissions E = e+ D F p. We have: de = de + D F p dp 0

11 so that: Proposition 2. If the Home ountry imposes a unilateral ap on its emissions, world emissions are inreased if and only if: > Proof. See Appendix. [ D H q D F p S + θ S θ p θ p g S gp g θ ] D H q A neessary ondition for world emissions to inrease is that the Home ountry inreases gas extration in order to omply with the domesti emission ap. For a marginal derease in domesti emissions ompared to business as usual i.e. a hange from τ = 0 to dτ, the sign of the hange in world emissions is a seond degree equation in reahes its maximum for: = S D F /2 2 see Appendix, whih S D F D H It is straightforward that 0 < <. For = 0 and =, world emissions are dereased thanks to the emission ap in the Home ountry. But for 0 < <, it may well be the ase that emissions are inreased beause of the domesti emission ap. Let us look at the onditions for this to our. The maximum hange in emissions, obtained for a ratio of the emission oeffiients of, has the sign of: D F 2 + 4D H S S S g + S g D F D H Corollary 3. For a marginal derease in domesti emissions ompared to business as usual i.e a hange from τ = 0 to dτ, there exists some values of the ratio of the emission oeffiients suh that world emissions are inreased beause of the domesti ap on emissions, if and only if: ɛ F 2 D 4ɛ H ɛ S S D H S D ɛ ɛ Ss D F S S g D + ɛ F Sg S g D F + ɛf D + ɛ H D D H > 0 D F Elastiity of natural gas supply between 0.76 and.6 Brown and Krupnik 200. There are hardly any estimate of oal and gas supply in the literature, however the order of magnitude are between 0. but issues with the eonometris, see Dahl and Duggan 996 and 7.9 for oal prodution. Between years 970 and 2000, oal prodution has been steadily inreasing while the real prie of oal has delined. Bek et al. 99 found a supply elastiity for Australian mines between 0.4 and.9 but Light 999 and Light et al. 999 find a

12 Inrease in world emissions Zero elas+ity of oal supply 0 θ s / Zero elas+ity of foreign demand supply elastiity of 0.3. Dahl and Duggan 996 found reserve elastiities between 0.4 and 7.9. Labys et al. 979 found supply elastiities of 0.. We take equal elastiities of supply for gas and oal supply and we onsider that half of the domesti demand is met with gas, i.e. D H Sg = 2. We find that the LHS of Eq.?? is negative. As a result, the world emissions are likely to derease thanks to the domesti emission ap, if this is done in a ost effetive manner. We next ompute the leakage rate assoiated with a domesti ap: [ de DF θ de = [ θ D H S g 2 D H S g ] ] S F Considering a marginal domesti ap, this an be rewritten: de de = ɛf D D F ɛ H D D H ɛ F D ɛ H D + ɛh D DH ɛ Sg S g 2 [ ] 2 D F θ ɛ D H + H D DH ɛ Sg S g ɛ SS ɛ F D DF 2 2

13 So that the leakage rate is approximatively equal to: de de 37% In omparison, the leakage rate in our model if gas was a arbon free resoure would be around 30% and with only one polluting resoure, i.e. if gas is as polluting as oal, the leakage rate in our model is approximatively 28%. These estimates are in line with the litterature, see Burniaux and Oliveira Martins 202 for a review. The leakage rate may be underestimated by onsidering an homogenous polluting resoure, or that gas is a arbon free resoure. 4 Extensions 4. Imperfet ompetition Assume now that the Home ountry maximizes its welfare under the onstraint that its own emissions remain below the threshold ē, but takes into aount the effet of its limate poliy on the oal world market prie. Denoting the exports elastiity η exp = DF p S F pp D F p S F p This elastiity is positive as long as the Home ountry is a net exporter. The solution is given by: B y H = p + µ η exp C H x H = p η exp Cg H x H g = p + µ η exp x H g + y H x H g = e x H g + x H y H = D F p S F p The solution an be deentralized with three instruments: A tariff τ = µ p η exp or an export tax µ + p η exp A pigovian prodution tax on gas: µ 3

14 A pigovian prodution tax on oal: µ This result is in line with Hoel 99. Let us ompare the result with a perfet ompetition result, denoting p the ompetitive world oal prie of the previous setion. 4 straightforward that, for all values of the ap e: p < p < p η exp As a result, for a given e the leakage is always less important with imperfet ompetition beause the Home ountry is a net exporter of oal, thus preferring a high prie for oal. A orollary of this result is that, if the objetive of the home ountry is to reah the ap e without inreasing world emissions, this an be done by imposing a tax on CO 2 emissions, together with a arefully hosen export tax. It is 4.2 A ap on oal use As a result of new Environmental Protetion Ageny EPA rules regulating air pollution, many oal-fired power plants will be fored to shut down. Let us look now at what would happen if there was a ap on oal use in the Home ountry, y H. Then, the quantity of natural gas extrated always inreases. When the ap is tightened, we get: dy g dy H = S gp g D H q S gp g So that whenever the ap on oal use dereases, natural gas use inreases. It is straightforward that domesti emissions derease, as dyg <. dy H The effet on world emissions is the following: de dy H S g S = S D θ F g S g D H whih an be rewritten as: de dy H ɛ S ɛ Sg = θ ɛ S + ɛ F g D S D ɛ F Sg + ɛ H D S g D H 4 The FOC of the ompetitive solution are rewritten in appendix B 4

15 World emissions inrease if and only if: The leakage rate an be written: de de = > ɛ S ɛs S D F S g D H ɛ Sg + ɛ H D ɛ Sg ɛ S + ɛ F D S ɛf D + ɛ F D ɛ Sg S g D H D F + ɛ H D ɛ Sg S g D H + ɛ H D A numerial appliation for the US gives a leakage rate around 42%. 4.3 Dynami Extension In this part, we extend the previous model into a dynami model. Exploration and development at date 0 allow to build reserves that will be extrated Gaudet and Lasserre, 988. These extration osts are denoted Cg H X g, where X g is the total amount of natural gas extrated in the Home ountry, C H X H, where X H is the total amount of oal extrated in the Home ountry, and C F X F, where X F is the total amount of oal extrated elsewhere. There is a eiling E on the stok of pollution. We denote pt the oal world prie at date t. As oal produers are in perfet ompetition and extration osts are paid at date 0, this prie rises at the rate of interest. In the rest of the world, the supply of oal is given by: p0 = C F X F and demand at date t : pt = B F y F t We rewrite y F t = Dpt B F pt and Y F t = 0 B F ptdt. As extration is performed at date 0, only the overall demand over time is relevant for equilibrium. The problem amounts to solve: max ˆ 0 [ B H y H t + pt x H g t + x H t y H t ] e rt dt C H g X g C H X H 3 5

16 under the onstraints: ˆ ˆ x H g tdt + y H t x H g tdt E µt ˆ 0 ˆ Let us write the Hamiltonian of the problem: H = [ B H y H t + pt x H g t + x H t y H t ] 0 x H g tdt X H g λ H g t 5 x H tdt X H λ H t 6 µt x H g t + y H t x H g t λ H g tx H g t λ H tx H t The optimality onditions are given by: B H y H t = pt + µe rt 7 pt + µe rt = µe rt + λ H g e rt 8 pt = λ H e rt 9 where λ H g and λ H are the initial values of the sarity rent on natural gas and oal respetively, and µ is the initial arbon value in the Home ountry. The enveloppe theorem yields: C H g C H X H g = λ H g 20 X H = λ H 2 6

17 The solution of the dynami problem is thus given by: p0 = λ H 22 Y H = ˆ 0 B H p0 + µe rt dt 23 µ + λ H g = µ + λ H 24 C H g C H X H g = λ H g 25 X H = λ H 26 E = X H g + Y H X H g 27 C X F = λ H 28 Y F = ˆ 0 B F λ H e rt dt 29 Y F + Y H = X H g + X H + X F 30 The system of equation is the same as in the stati ase, provided that we define for both ountries the umulated demand as Dp = 0 B pe rt dt instead of Dp = B pdt in the stati ase. All the previous results remain unhanged, as far as aggregate variables are onerned. Referenes Alvarez, R. A., Paala, S. W., Winebrake, J. J., Chameides, W. L., and Hamburg, S. P Greater fous needed on methane leakage from natural gas infrastruture. Proeedings of the National Aademy of Sienes, 097: Arrow, K. J. and Chang, S Optimal priing, use, and exploration of unertain natural resoure stoks. Journal of Environmental Eonomis and Management, 9: 0. Bek, T., Jolly, L., and Lonar, T. 99. Supply response in the australian blak oal industry. Working paper, ABARE Tehnial Paper 9.. Australian Government Publishing Servie, Canberra. Bentzen, J. and Engsted, T Energy Eonomis, 5:9 6. Short- and long-run elastiities in energy demand. Brown, S. P. and Krupnik, A Abundant Shale Gas Resoures: Long-Term Impliations for U.S. Natural Gas Markets. Disussion Papers dp-0-4, Resoures For the Future. 7

18 Burniaux, J.-M. and Oliveira Martins, J Carbon leakages: a general equilibrium view. Eonomi Theory, 492: Chakravorty, U., Fisher, C., and Hubert, M. H Will shale gas redue arbon emissions from hina? mimeo. Chakravorty, U., Moreaux, M., and Tidball, M Ordering the extration of polluting nonrenewable resoures. Amerian Eonomi Review, 983: Coulomb, R. and Henriet, F The grey paradox: How oil owners an benefit from arbon regulation. Working papers, Paris Shool of Eonomis. Dahl, C. and Duggan, T. E U.S. energy produt supply elastiities: A survey and appliation to the U.S. oil market. Resoure and Energy Eonomis, 83: Dröge, S., van Asselt, H., Brewer, T., Grubb, M., Ismer, R., Kameyama, Y., Mehling, M., Monjon, S., Neuhoff, K., Quirion, P., et al Takling leakage in a world of unequal arbon pries. Climate strategies, :2 6. Eihner, T. and Pethig, R. 20. Carbon leakage, the green paradox, and perfet future markets*. International Eonomi Review, 523: Feng, K., Davis, S. J., Sun, L., and Hubaek, K Drivers of the us o2 emissions Nat. Commun, 6. Fisher, C. and Salant, S Alternative Climate Poliies and Intertemporal Emissions Leakage: Quantifying the Green Paradox. Disussion Papers dp-2-6, Resoures For the Future. Gaudet, G. and Lasserre, P On omparing monopoly and ompetition in exhaustible resoure exploitation. Journal of Environmental Eonomis and Management, 54: Harstad, B Buy oal! a ase for supply-side environmental poliy. Journal of Politial Eonomy, 20:pp Heal, G The relationship between prie and extration ost for a resoure with a bakstop tehnology. Bell Journal of Eonomis, 72: Heath, G. A., O?Donoughue, P., Arent, D. J., and Bazilian, M Harmonization of initial estimates of shale gas life yle greenhouse gas emissions for eletri power generation. Proeedings of the National Aademy of Sienes, 3:E367 E376. 8

19 Henriet, F. and Shubert, K Should we extrat the European shale gas? The effet of limate and finanial onstraints. Douments de travail du Centre d Eonomie de la Sorbonne ISSN : 955-6X. Herfindahl, O. C "Depletion and Eonomi Theory" In Extrative Resoures and Taxation ed. Mason Gaffney, University of Wisonsin Press. Hoel, M Effiient limate poliy in the presene of free riders. Journal of Environmental Eonomis and Management, 273: Howarth, R., Santoro, R., and Ingraffea, A. 20. Methane and the greenhouse-gas footprint of natural gas from shale formations. Climati Change, 064: Jaoby, H. D., O Sullivan, F. M., and Paltsev, S. 20. The influene of shale gas on us energy and environmental poliy. Tehnial report, MIT Joint Program on the Siene and Poliy of Global Change. Jenner, S. and Lamadrid, A. J Shale gas vs. oal: Poliy impliations from environmental impat omparisons of shale gas, onventional gas, and oal on air, water, and land in the united states. Energy Poliy, 53: Knittel, C. R., Metaxoglou, K., and Trindade, A Natural gas pries and oal displaement: Evidene from eletriity markets. Working Paper 2627, National Bureau of Eonomi Researh. Labys, W. C., Paik, S., and Liebenthal, A. M An eonometri simulation model of the US market for steam oal. Energy Eonomis, :9 26. Light, M., Kolstad, C. D., and Rutherford, T. F protool. Tehnial Report Coal markets and the kyoto Light, M. K Coal subsidies and global arbon emissions. The Energy Journal, 204:pp Masih, R. and Masih, A. M Stok-watson dynami {OLS} dols and error-orretion modelling approahes to estimating long- and short-run elastiities in a demand funtion: new evidene and methodologial impliations from an appliation to the demand for oal in mainland hina. Energy Eonomis, 84: Pindyk, R. S The Optimal Exploration and Prodution of Nonrenewable Resoures. Journal of Politial Eonomy, 865:

20 Quentin Grafton, R., Kompas, T., and Van Long, N Substitution between biofuels and fossil fuels: Is there a green paradox? Journal of Environmental Eonomis and Management, 643: Quyen, N. V. 99. Exhaustible resoures: A theory of exploration. Review of Eonomi Studies, 584: Ritter, H. and Shopf, M Unilateral limate poliy: Harmful or even disastrous? Environmental and Resoure Eonomis, pages 24. Sinn, H.-W Publi poliies against global warming: a supply side approah. International Tax and Publi Finane, 54: Stavins, R. N. 20. The Problem of the Commons: Still Unsettled after 00 Years. Amerian Eonomi Review, 0:8 08. Truby, J. and Paulus, M Market Struture Senarios in International Steam Coal Trade. The Energy Journal, 0Number 3. van der Ploeg, F. and Withagen, C Too muh oal, too little oil. Journal of Publi Eonomis, 96: A Emissions Differentiating system 8-9 yields: θ A g A 2 dx g dp = 2 D H de with A = 2 θ A 2 = S W D F > 0 D H S g < 0 Hene: dx g dp = A A 2 2 A 2 A θ θ 2 D H de 20

21 i.e. dxg de dp de = = A A 2 A A θ 2 A D H 2 θ 2 θ 2 + D H A 2 [ θ ] + D H ] D F S W [ θ D H S g As A A 2 2 < 0, dx g de dp de < 0 D F S W + < 0 D H > 0 Total emissions: de de = + D F dp de = = = A A 2 A A 2 2 A A [ A A 2 [ θ 2 D H S g [ θ 2 + D F θ D ] H S g S W S g 2 + ] D F D H θ S W D θ S W + θ ] D F S W H D H Hene de de < 0 D F S W D H > + θ S W θ S g θ D H or equivalently: de de < 0 S W D H D F 2 + 2S W D F S W DH > 0 S g 2

22 B FOC for the ompetitive ase The FOC were: B y H = p + µ C H x H = p C H g x H g = p + µ x H g + y H x H g = e x H g + x H y H = D F p S F p 22