OPEC, Unconventional Oil and Climate Change - On the Importance of the Order of Extraction

We show that OPEC’s market power contributes to climate change by enabling producers of relatively expensive and dirty oil to start producing before OPEC reserves are depleted. We examine the importance of this extraction sequence effect by calibrating and simulating a cartel-fringe model of the global oil market. While welfare net of climate damage under the cartel-fringe equilibrium can be significantly lower than under a first-best outcome, almost the entire welfare loss is due to the sequence effect of OPEC’s market power. In our benchmark calibration, the cost of the sequence effect amounts to 15 trillion US$, which corresponds to 97 percent of the welfare loss. Moreover, we find that an increase in non-OPEC oil reserves decreases global welfare. In a counterfactual world without non-OPEC oil, global welfare would be 13 trillion US$ higher, 10 trillion US$ of which is due to lower climate damages.


Introduction
What is the impact of imperfect competition in the oil market on climate change? This question is relevant given the sizable carbon footprint of oil and the prominent size of OPEC. Oil is responsible for close to a quarter of anthropogenic carbon emissions (IEA, 2016) 1 and, with OPEC producing 40 percent of global oil supply and owning 70 percent of world oil reserves (EIA, 2019b), it is not realistic to assume that OPEC is a price taker in the market of oil.
An old adage says that "the monopolist is the conservationist's best friend" (e.g., Dasgupta and Heal, 1979, p. 329). Indeed, we know from non-renewable resource economics that market power typically leads to higher initial resource prices and slower resource depletion. However, in the case of oil, the consequences of imperfect competition for the Earth's climate are more complex because different types of oil reserves with varying carbon contents are exploited. The reason is that imperfect competition does not only affect the speed, but also the order of extraction of different reserves of oil (cf. Benchekroun et al., 2009Benchekroun et al., , 2010Benchekroun et al., , 2019. Conventional OPEC oil is cheaper and its extraction is less carbon intensive than unconventional oil owned by relatively small oil producers (Malins et al., 2014;Fischer and Salant, 2017;OCI, 2019). Technically recoverable reserves and production of unconventional types of oil by non-OPEC countries have grown significantly over the last decade. The supply of oil sands from Canada has more than doubled, and shale oil production in the US has increased more than tenfold since 2007 (CAPP, 2017b;EIA, 2019b). Current recoverable reserves of Canadian oil sands and of US shale oil amount to 165 and 78.2 billion barrels, respectively (CAPP, 2017a;EIA, 2019c). In this paper, we take into account that when OPEC exercises market power it does not only slow down its rate of extraction-which tends to be good for the climate-but it also opens the door for earlier production by the fringe. As a result, OPEC's relatively cheaper and cleaner oil is extracted later, while the fringe's costlier and dirtier oil is extracted earlier. This 'sequence effect' leads to higher discounted extraction costs and climate damage.
Our paper is related to two strands of literature, the first one studying resource use under imperfect competition. We model the oil market as a situation where supply 1 The other important fossil fuels that contribute to anthropogenic carbon emissions are coal with 28 percent and gas with 12 percent (IEA, 2016). comes from a cartel and a large group of price-taking fringe members. Important contributions to the field of imperfect competition on non-renewable resource markets were made by Stiglitz (1976) on monopoly, Lewis and Schmalensee (1980) on oligopoly, and Gilbert (1978) and Newbery (1981) on dominant firms. Furthermore, Salant (1976), Groot et al. (2003), Benchekroun et al. (2009Benchekroun et al. ( , 2010 and Benchekroun and Withagen (2012) have developed cartel-fringe models of the resource market. See also Withagen (2013) for a survey and the references therein. Our paper is closely related to Benchekroun et al. (2019), who built an oligopoly-fringe model of the oil market, taking into account the presence of a renewable substitute for oil. However, Benchekroun et al. (2019) ignored climate damages, implying that they had to remain silent on the sequence effect of market power for climate change. Furthermore, they did not calibrate their model and left out a welfare analysis. Hence, the current paper complements our earlier work. 2 Second, our article relates to the literature on the sequence of extraction of multiple non-renewable resource deposits with different unit extraction costs. Herfindahl (1967) and Solow and Wan (1976) show that these deposits are optimally extracted in order of increasing marginal extraction costs. The principle of extracting cheap resources before the more expensive ones has become known as the Herfindahl rule.
Over the last decades, several refinements of this rule were proposed. Kemp and Long (1980) show that in general equilibrium, the Herfindahl rule may break down due to a consumption smoothing motive. Other reasons for deviations from the Herfindahl rule are heterogeneous resource demand (Chakravorty and Krulce, 1994), extraction capacity constraints (Amigues et al., 1998;Holland, 2003), upper bounds on pollution stocks (Chakravorty et al., 2008) and supply cost uncertainty (Gaudet and Lasserre, 2011). We contribute to this literature by examining how a violation of the Herfindahl rule due to imperfect competition affects climate change through the timing of carbon emissions.
2 While we follow a large strand of the literature and consider that OPEC acts as a cohesive cartel (see Withagen (2013) for a survey), there is recent empirical evidence for imperfect cartelization of OPEC (cf. Almoguera et al., 2011;Brémond et al., 2012;Kisswani, 2016;Okullo and Reynès, 2016). We have also examined the case where the cartel consists of subgroups that act as Cournot oligopolists (see Benchekroun et al. (2019) for the characterization of the equilibrium). The qualitative nature of the equilibrium and the policy implications remain unchanged, although the sequence effect becomes smaller (e.g., in case of 5 oligopolists 89 percent of the welfare loss of imperfect competition compared to the first-best is attributable to the sequence effect). We have therefore opted to keep the assumption of a cohesive cartel for the ease of exposition and economy of notation.
We quantify the effect of market power on climate damages and welfare. Furthermore, we determine the effects of a resource tax, and perform a sensitivity analysis for reserves, extraction costs, emission factors of the cartel and the fringe, and the specification of the demand function. Our analysis takes into account that conventional oil supplied by OPEC has lower marginal extraction costs and is cleaner than oil from deep-water drilling, oil sands, oil shale, and shale oil supplied by the fringe (Malins et al., 2014;Fischer and Salant, 2017;OCI, 2019). Our main findings are as follows.
First, when decomposing the global welfare loss under the cartel-fringe equilibrium into a 'conservation effect' (slower extraction due to a higher initial oil price) and a 'sequence effect' (front-loading of extraction of the relatively expensive and dirty resource), we find that the sequence effect, which so far has remained unexplored in the literature, is huge in our calibrated model. In the benchmark scenario, imperfect competition causes a social welfare loss of 14.5 percent of first-best welfare, almost all of which (97 percent, corresponding to 15 trillion US$) is imputable to the inefficient order of use of the resources, i.e., to the sequence effect. Furthermore, imperfect competition increases the discounted value of climate damages by 5.3 percent compared to the first-best. Without the sequence effect, imperfect competition would decrease climate damages by 4.8 percent compared to the first-best, due to the conservation effect.
Second, the recent increase in non-OPEC oil reserves and the decrease in their extraction costs have not only increased climate damages, but may also have lowered 'grey welfare' because the relatively expensive non-OPEC oil partially crowds out early extraction of cheap oil by the cartel. We numerically investigate conditions under which the recent boom in nonconventional reserves and the decrease in nonconventional oil extraction costs reduces global welfare. Starting from our benchmark calibration, each additional barrel of non-OPEC oil reserves lowers global welfare by 12 US$. Furthermore, in a counterfactual world without non-OPEC oil, global welfare would be 13 trillion US$ higher, 10 trillion US$ of which is due to lower climate damages.
Our findings are supportive of recent calls for a supply side approach to a climate treaty and for the need for policies that limit investments and extraction of fossil fuels (cf. Harstad, 2012;Erickson et al., 2018;Green and Denniss, 2018;Asheim et al., 2019). A successful supply side treaty has to take into account the heterogeneity of reserves in terms of extraction costs and full-cycle greenhouse gas emissions, as well as the effects of market power on the timing of extraction of the different oil reservoirs.
Our numerical results are obtained within a calibrated stylized model. A caveat is therefore in order. The numbers we obtain are useful only to gain insight into the possible relative magnitudes of the different effects examined. But some remarks on the scope of our study are in order at this point as well. We only consider two types of oil reserves; this clarifies the exposition and the relevant mechanisms at the expense of more realism and more accurate estimates of the effects we measure. We consider linear extraction costs, thus in our model cumulative extraction is exogenous: Climate damage effects merely result from changes in the timing of extraction of different types of oil. Therefore, our analysis mainly applies to the extraction of relatively cheap oil that is available at roughly constant marginal costs and in finite amounts (and not to more expensive oil that is available in larger amounts and at higher, reservedependent extraction costs). Still, the initial aggregate proven oil reserves that we use in our calibrated model contain 839 tonnes of CO 2 (EIA, 2019b), which already is about 84 percent of the remaining carbon budget corresponding to the scenario of keeping the average global temperature rise below 2 degrees Celsius with a 50 percent probability (McGlade and Ekins, 2015). Our results show that even with fixed cumulative emissions, the change in the timing of extraction of the proven oil reserves due to imperfect competition, the shale oil revolution, and the introduction of a resource tax already generate substantial climate damage and welfare effects.
The importance of the inefficient order of use of the different oil reserves is corroborated by the recent findings of Asker et al. (2019). While we use a stylized model with two different types of reserves, they use a rich micro-dataset on production costs and reserves of 11,455 oil fields (constituting 99.9 percent of global reserves). They construct a counterfactual scenario for the period 1970-2100 (when all reserves are assumed depleted) in which these fields are extracted according to the Herfindahl rule, where from 2014 until 2100 it is assumed that oil demand increases at an annual rate of 1.3 percent and actual production satisfies the Herfindahl rule. Asker et al. (2019) find that the total costs of production misallocation between oil fields add up to 744 billion US$ (measured at 2014 prices), which equals 30 percent of the present value of actual extraction costs since 1970. Furthermore, they show that 22 percent of this efficiency loss (i.e., 163 billion US$) can be attributed to OPEC's market power. 3 It is interesting to note that while both Asker et al. (2019) and our paper point to the importance of the inefficiencies due to OPEC's market power, we get to this conclusion from quite different approaches, an indication of the robustness of our results.
In contrast with Asker et al. (2019), in our paper the time path of aggregate oil supply is not exogenous. The extraction paths for the entire time horizon are obtained as equilibrium paths from a theoretical model of resource extraction that incorporates market power, competition by a fringe and the existence of a backstop technology. After fully characterizing the market equilibrium, we calibrate our model on the global oil market and examine different scenarios (e.g., first-best, perfect competition, cartelfringe). Hence, we take into account that market power not only influences the order but also the speed of extraction. Moreover, while Asker et al. (2019) limit their attention to the production cost inefficiency due to OPEC's market power, we examine the repercussions of the order of extraction for climate change, due to differences in both extraction costs as well as carbon emissions factors between oil fields. Furthermore, we use our theoretical model to examine the implications of a resource tax and to perform a welfare analysis.
The remainder of the paper is structured as follows. Section 2 outlines the model. Section 3 characterizes the cartel-fringe equilibrium. Section 4 calibrates the model, quantifies the sequence effect, and discusses the welfare effects of increasing reserves and declining extraction costs of non-OPEC oil, and of a resource tax. Section 5 examines the robustness of our results with respect to non-linear demand functions.

The model
A non-renewable resource is jointly supplied by a price-taking fringe and a cartel with market power. The fringe is endowed with an aggregate initial stock S f 0 and has a constant per unit extraction cost k f . The initial stock of the cartel is denoted by S c 0 . The per unit extraction cost of the cartel is constant and denoted by k c . Extraction rates at time t ≥ 0 by the fringe and the cartel are q f (t) and q c (t), respectively. The time argument will be dropped when possible. A perfect substitute for the resource can be produced, indefinitely, at marginal cost b > 0, by using a backstop technology.
We abstract from technological progress (cf. Fischer and Salant, 2017), as well as from set-up costs. If p ≤ b, inverse demand for the non-renewable resource is given by , with α > 0 and β > 0, where p denotes the price of the resource. 4 If p > b, demand for the non-renewable resource equals zero. Denote the interest rate by r > 0.
The fringe maximizes its discounted profits, taking the price path as given, subject to its resource constrainṫ The cartel is aware of its influence on the equilibrium price and maximizes taking the time path of q f as given, subject to its resource constrainṫ Moreover, the existence of the perfect substitute effectively implies an upper limit on the price the cartel can ask, yielding the additional constraint since b is the price at which consumers are indifferent between the non-renewable resource and the substitute. We assume that k c < k f < b < α.

Cartel-fringe equilibrium
In this section, we first introduce the equilibrium concept. Subsequently, we discuss the different sequences of extraction phases that can occur in the equilibrium of the game.

Equilibrium concept
The cartel chooses an extraction path, taking the extraction path of the fringe as given while the fringe takes the price path as given and chooses its extraction path.

Definition 1 A vector of functions
for allq c satisfying the resource constraint, and , for allq f satisfying the resource constraint.
A full characterization of the cartel-fringe equilibrium is provided in Benchekroun et al. (2019). 5 Hence, we restrict ourselves to explaining its main properties. In a CFE, different phases of resource extraction may exist. By F , C, S and L we denote phases with only the fringe supplying, only the cartel supplying at a price strictly below b, simultaneous supply at a price strictly below b, and supply by the cartel at price b (i.e., limit pricing), respectively. We use the symbol '→' to indicate the sequence of phases, e.g., S → F means that a phase with simultaneous use is preceding a phase with only the fringe supplying at a price strictly below b. We use the notation t ∈ Φ to refer to a moment where the phase of resource extraction is Φ with Φ ∈ {F, C, S, L}.
The sequence of different extraction phases crucially depends on the initial resource stocks and on the cartel's marginal profit at the prices k f (i.e., when the resource price equals marginal extraction cost of the fringe) and b (i.e., when the resource price equals the price of renewables). We denote the cartel's marginal profit as Let us define demand at price k f asq ≡ (α − k f )/β and demand at the limit price b aŝ q ≡ (α − b) /β. Marginal profit of the cartel at these prices reads, respectively, Since k f < b < α, we haveΠ >Π. Figure  It is clear from Figure 1 that the equilibrium always features a regime with simultaneous use. This is an important result, as it drives the 'sequence effect': The existence of a simultaneous use phase implies that in the CFE extraction of the relatively expensive and dirty resources is front-loaded in time, compared to the first-best and the perfectly competitive equilibrium, which both are characterized by the equilibrium sequence C → F , as shown in Appendix A. However, in the cartel-fringe equilibrium a transition from C to F would imply a downward jump in the cartel's extraction level and hence an upward jump in its marginal profits. It would then be better for the cartel to gradually lower its market share during a phase with simultaneous use.
Furthermore, for low and intermediate marginal profit levels (i.e., 0 >Π as in panels (a) and (b) of Figure 1), a CFE always starts with a simultaneous use phase.
The intuition behind this outcome is that, in these cases, marginal profit of the cartel is negative as long as the market price is lower than the marginal extraction cost of the fringe. Hence, if the cartel would initially be sole supplier it would choose an extraction rate such that the price would be higher than the fringe's marginal extraction cost. But then the net price of the fringe would grow at a rate lower than the rate of interest if the cartel would be sole supplier. Hence, the fringe prefers extraction over conservation: It will enter the market and a phase with simultaneous supply will result. Similarly, if the fringe would be the sole supplier initially, marginal profits of the cartel would be positive and growing at a rate lower than the rate of interest. Therefore, the cartel will start supplying immediately. So, as long as both the cartel and the fringe have a positive stock, there will be simultaneous supply.
In the remainder of this section, we will discuss the extraction sequences in the CFE for the different marginal profit scenarios shown in the three panels of Figure 1.

Low marginal profit.
If marginal profit is negative for p ≤ b (the case depicted in panel (a)), the cartel will perform a limit-pricing strategy as soon as the fringe's stock is depleted. Hence, if the relative initial stock of the cartel is large enough the equilibrium sequence reads S → L. However, if the relative initial stock of the cartel is small, the stock of the cartel will be depleted before the stock of the fringe and the equilibrium Moving further to the right in the figure, the initial stock of the fringe becomes large enough to end up with a positive remaining stock when the cartel's stock is depleted.
Hence, there will be a final F -phase and the equilibrium reads C → S → F . The potentially non-monotonic l 1 (S f 0 ) and strictly increasing l 2 (S 0 f ) loci give combinations of S f 0 and S c 0 for which the initial C-phase exactly vanishes. Below these loci, the extraction sequence either reads S → L (to the left of the g(S f 0 ) locus), or S → F (to the right of it).

Welfare implications of the CFE
We now exploit our analysis above to examine the quantitative importance of imperfect competition and the order of extraction of different oil reserves and the repercussions for climate change and welfare. In our framework, the fact that the fringe may start extracting before the low cost resource is exhausted is a source of inefficiency. This inefficiency is further amplified when we consider the emissions of pollution generated by oil and their impact on climate change. In this section we calibrate our model to examine the relative importance, in terms of global welfare, of the inefficient order of use of oil reserves. Our calibrated model also allows us to examine the effect of increases in the fringe's reserves and decreases in its extraction costs on global welfare. Furthermore, we have checked that in all cases that we investigate numerically, the CFE is subgame perfect. 6 We define 'grey' welfare, W G , as the discounted sum of consumer surplus and producer surplus: where T denotes the moment at which the last resource stock is depleted. 7 The atmospheric stock of carbon, E, evolves according tȯ where ω c and ω f denote the emission factor of the cartel and the fringe, respectively.
We follow Hoel (2011), Golosov et al. (2014) and Van der Ploeg (2016) by assuming that climate damages are linear in the stock of atmospheric carbon. 8 The discounted value of climate damage is given by: where ζ > 0 denotes the instantaneous and constant marginal damage of carbon.
Hence, the social cost of carbon (SCC), i.e., the discounted value of current and future marginal damages, is equal to 6 To be precise, we have found that in all cases that we examine numerically, the open loop CFE coincides with the closed loop CFE (which is subgame perfect in Markov strategies, cf. Salo and Tahvonen (2001)) if the fringe is modeled as described by Benchekroun and Withagen (2012, p. 356): "Each fringe firm takes the price path as given and determines its extraction strategy which is allowed to depend on its own stock only; the cartel takes each fringe firm's strategy as given and determines a pricing strategy (or alternatively a production strategy) that depends on its own stock and all fringe's stocks." 7 Alternatively, we could define a the quasi-linear utility function which gives rise to our linear demand function), where x denotes renewables consumption and M expenditure on a numeraire good. This results in the same expression for W G . 8 Golosov et al. (2014) actually assume that marginal damages are proportional to output. However, with the logarithmic utility function and constant savings rate that they impose, this is equivalent to our assumption of constant marginal damages in the utility function.
Social welfare, W , is defined as the difference between grey welfare and climate dam- In determining supply, both the cartel and the fringe ignore the damage caused by their activity. Thus in our framework we have two sources of market failure: Imperfect competition and a negative climate externality. The evaluation of the impact of market failure cannot entirely be captured by the level of the industry's output alone; it should also take into account the composition of aggregate extraction. Indeed, for a given path of aggregate extraction, the equilibrium involves an S-phase during which extraction of the high cost source occurs before the low cost reserve is exhausted. We seek to determine the relative importance of this failure due to the inefficient order of use of resources. For this purpose we compare the CFE characterized above, with the outcomes of three scenarios: The socially optimal extraction of reserves also referred to as the first-best (FB), the perfectly competitive (PC) scenario where the cartelthe owner of the low cost reserves-is assumed to be price taker, and the 'Herfindahl scenario'. In this latter scenario, total extraction at each instant of time is the same as in the CFE, but we impose the order of resource use of the first-best; first extraction by the cartel until its stock is depleted and then extraction by the fringe until depletion. This allows us to decompose the deviation of the CFE from the first-best into a 'conservation effect' (i.e., the deviation of the Herfindahl scenario from the first-best) and a 'sequence effect' (i.e., the deviation of the CFE from the Herfindahl scenario).

Calibration
We calibrate our model by using data on proven oil reserves, global oil consumption, extraction costs, the oil price, the price elasticity of oil demand, and carbon emission factors for different types of oil. Proven reserves owned by OPEC are 1212 billion barrels (EIA, 2019b). In the rest of the world, proven reserves excluding shale oil equal 438 billion barrels (EIA, 2019b). Furthermore, according to the EIA (2013) the "increase in total resources due to inclusion of shale oil" is equal to 11 percent, which implies another 181.5 barrels of oil for the rest of the world. For the parameters of the demand function, we use α = 225.5 US$/bbl and β = 4.3 US$/bbl to get an initial oil demand of 34 billion barrels and an initial price of 80 dollars per barrel (roughly equal to the average crude oil consumption and crude oil price over the last decade (EIA, 2019b)) and an initial price elasticity of demand of 0.55, which is within the range of long-run price elasticities reported by Hamilton (2009). 9   For the renewables unit cost parameter we use b = 102.5 US$/BOE ('barrels of oil equivalent') to indeed get an initial oil use equal to 34 billion barrels in equilibrium.
9 By using the price elasticity of demand ε ≡ − dq/q dp/p = α−βq βq together with the demand function, we obtain α = ε+1 ε p and β = p εq , yielding values for α and β in terms of the observed initial p, q, and ε. 10 Fischer and Salant (2017) use estimates for the ultimately recoverable resources reported by the IEA (2013), instead of the proven oil reserves. 11 Fischer and Salant (2017) include conventional oil, enhanced oil recovery (EOR) and deep-water drilling, heavy oil, oil sands, and oil shale in their analysis.
Our renewables unit cost corresponds to the unit costs of biofuels after 30 years in Fischer and Salant (2017). 12 For the social cost of carbon, we take 250 US$/tC (or 68 US$/tCO 2 ), which is within the Nordhaus-Stern range of about 31 to 85 US$/tCO 2 (Stern, 2007;Nordhaus, 2017). 13 For the interest rate, we take the average of the US long-term composite rate on government bonds over the period 2017-2019, which equals 2.8 percent (U.S. Department of the Treasury, 2019). 14 An overview of our benchmark calibration and the implied equilibrium values is provided in Table 1. 15 Because we have expressed prices and costs in billion US$, welfare and climate damages are expressed in billion US$ as well. The equilibrium of the calibrated model is characterized byΠ < 0 and the sequence S → L: The cartel follows a limit-pricing strategy as soon as the fringe's stock is depleted.

The effects of imperfect competition
In this section, we discuss the effects of imperfect competition by comparing the CFE with the outcome under perfect competition, the first-best, and the Herfindahl scenario (i.e., the CFE without the sequence effect). The perfectly competitive equilibrium and the first-best are characterized in Appendix A. the CFE is entirely located above the perfectly competitive one, and even above the one corresponding to the first-best. Still, panel (b) shows that initially cumulative carbon emissions grow more rapidly in the CFE than under perfect competition and the firstbest. The reason is that although extraction is initially lower in the CFE due to the higher oil price (conservation effect), extraction of relatively dirty oil by the fringe 12 In their benchmark scenario, Fischer and Salant (2017) assume that the backstop cost initially equals 115 US$/BOE and gradually falls over time, due to technological change. 13 We have SCC = ζ r . Hence, in the benchmark scenario we set ζ = 250 · 0.028 = 7 US$/tC. 14 The long-term composite rate is the "unweighted average of bid yields on all outstanding fixedcoupon bonds neither due nor callable in less than 10 years" (U.S. Department of the Treasury, 2019). 15 We use tC to denote 'metric tonnes of carbon', GtC for 'gigatonnes of carbon', bbl for 'barrels of oil' (one barrel contains about 159 litres) and BOE for 'barrels of oil equivalent'.  Table 1. is front-loaded in time in the CFE (sequence effect). The dotted curve shows that if we would eliminate the sequence effect, the CFE would generate a cumulative carbon emissions time profile below the one generated by each of the other cases.  the first-best, in percentage terms. When the relative emission factor equals unity, the CFE coincides with the Herfindahl scenario, as the sequence effect becomes immaterial to climate change. Due to the conservation effect, climate damage is lower than under perfect competition, and even lower than in the first-best. However, by increasing the relative emission factor above 1.2, climate damage becomes higher than in the firstbest, and eventually (above 1.45) higher than under perfect competition.  with r = 0.028, the grey welfare loss in the CFE, compared to the first-best (as depicted in panel (a)), is 10.3 percent, of which only 1.3 percentage points remain in the Herfindahl scenario: 87.4 percent of the grey welfare loss is driven by the sequence effect. Furthermore, at r = 0.028 climate damage (panel (b)) is 5.3 percent higher in the CFE equilibrium than in the first-best, while the Herfindahl scenario would give a 4.8 percent lower climate damage than in the first-best. Panel (c) shows that social welfare at r = 0.028 is 14.5 percent lower in the CFE than in the first-best, of which only 0.4 percentage points remain in the Herfindahl scenario: 97 percent of the loss in social welfare is due to the sequence effect. In absolute terms, the social welfare loss due to the sequence effect corresponds to 15 trillion US$ in our benchmark calibration.
Panel (c) also shows that the difference between the CFE and the Herfindahl curve is increasing in the rate of interest. Intuitively, the higher the rate of interest, the more important timing becomes, and the larger will be the loss in welfare due to the violation of the Herfindahl rule in the CFE.      The main conclusion of our welfare analysis so far is that almost all (97 percent) of the loss in social welfare under the cartel-fringe framework relative to the first-best is due to the inefficient order of use of the resources. Moreover, although the pure conservation effect of imperfect competition would imply 4.8 percent lower climate damages in the CFE than in the first-best, by taking this sequence effect into account, climate damages are actually 5.3 percent larger than in the first-best. A lot of attention in the literature and the policy debate on how to address climate change evolves around ways to reduce the use of polluting resources. The merit of policy options should be 18 The actual emission factor of shale oil depends heavily on flaring. Brandt et al. (2016) report that emissions from shale oil wells in the Bakken Formation in the US in 2013 varied from 2 to 28 gCO 2 eq/MJ over the different wells, compared to a US conventional crude oil mean of 8 gCO 2 eq/MJ. If flaring would be completely controlled, production-weighted mean greenhouse gas emissions from the Bakken Formation would only be 3.5 gCO 2 eq/MJ.  Table 1. For clarity reasons, the scale of the horizontal axis differs between the two panels. evaluated while having this important feature of the climate change problem in mind.
Below, we discuss the introduction of a resource tax while taking into account its impact on the order of use of the polluting resources.

Resource tax
In this section, we analyze the welfare and climate effects of a resource tax at a specific rate τ within our benchmark calibrated framework. 19 Mathematically, introducing the tax in our model boils down to replacing α by α − τ and b by b − τ at all occurrences in Sections 2 and 3. Figure 8 shows the effect of a resource tax on the percentage deviation of social welfare (panel (a)) and on the percentage deviation of climate damage (panel (b)) from the first-best. An important implication of our analysis is that a resource tax can be detrimental to welfare, as shown in panel (a). While a resource tax contributes, 19 The constancy of the tax can be motivated by constant marginal damages of emissions. Note that the perfectly competitive equilibrium only coincides with the first-best if emission factors of the cartel/fringe and the fringe are the same and the resource tax rate equals the SCC multiplied by the common emission factor. With differing emission factors, the first-best cannot be reached by imposing a resource tax. In the calibrated model, the second-best resource tax rate (i.e., the top of the dashed curve in panel (a) of Figure 8) lies between 27 and 38 US$/bbl, the SCC of a unit of extraction by the cartel and fringe, respectively.  Table 1. as intended, to a reduction in climate damages (see panel (b)) it impacts the speed of extraction of oil reserves as well as the composition of the oil extracted.
From panel (b) of Figure 2 we see that pollution accumulates faster in the CF equilibrium than under the first best. A tempting policy response is to impose a resource tax to slow down production and the accumulation of pollution. However from Figure 8 panel (a) we get that social welfare is a decreasing function of the tax. The explanation lies in the fact that the 'fast' accumulation of pollution in the CF equilibrium, observed in Figure 2 panel (b), is due to the 'sequence effect', whereby the dirty reserves are exploited before the 'cleaner' reserves, rather than overproduction of the resource.
Indeed from Figure 2 panel (a), in the benchmark scenario, the price path in the CF equilibrium is above the price path under the first-best indicating that total oil production in the CF equilibrium is below that of the first best. As a result, a resource tax is detrimental to welfare in our benchmark scenario.

Non-linear demand
In this section, we examine the robustness of our results to the specification of the demand function we have used. We consider different demands generated by the general class of (HARA) utility functions where q ≡ q c + q f + x denotes energy demand, with x being the use of renewables. The corresponding energy demand function reads 20 We numerically examine three special cases of the HARA class demand functions: (i) quadratic utility (yielding linear demand, as in the benchmark model), requiring ϕ = 2, χ > 0 and p < χψ; (ii) Cobb-Douglas utility (yielding CES demand), requiring χ = 0 and ϕ < 1; and (iii) power utility (yielding 'shifted CES demand'), requiring ϕ < 1, χ > 0 and ψ = 1 − ϕ (cf. Kagan et al., 2015, p. 506). 21 In each case, the remaining two free parameters of the HARA utility function are chosen such that the demand function runs through (p, q) = (80, 34) as in the benchmark model, and the price elasticity of demand equals 0.55 in this point. Figure 9 shows the percentage welfare loss (compared to the first-best) due to the sequence effect for interest rates varying from 0.01 to 0.05. The benchmark interest rate of 0.028 is indicated by the dashed-dotted vertical line. Panel 20 Note that HARA utility functions are characterized by a non-negative super-elasticity of demand dε dq q ε , which implies that in the CFE the growth rate of p − k c is smaller than r. Hence, the growth rate of the oil price does not exceed the rate of interest. This prevents arbitrators from purchasing oil, hoarding it, and making capital gains (cf. Dasgupta and Heal, 1979, pp. 327-331). 21 We use Euler's method together with time inversion and iteration over the duration of the limit pricing phase (in case the equilibrium reads S → L) or the fringe's stock at the end of the S-phase (in case the equilibrium reads S → F ) to solve the system of differential equations derived from the necessary conditions. Details are available from the authors upon request.  (a)) and the grey welfare loss (panel (b)) of the CFE (compared to the first-best) that can be attributed to the sequence effect. The solid line corresponds to linear demand (ϕ = 2, χ > 0, p < χψ), the dashed line to CES demand (χ = 0, ϕ < 1), and the dotted line to shifted CES demand (ϕ < 1, χ > 0, ψ = 1 − ϕ). The remaining parameters are set at their benchmark values, as shown in Table 1.

Conclusion
OPEC's market power has been shown to result in an inefficient order of use of the different oil reserves. A calibrated version of our model reveals that this source of inefficiency is responsible for almost the entire welfare loss of the cartel-fringe equilibrium compared to the first-best. It is also strong enough to make the recent shale oil revolution detrimental to global welfare. These distortions, which are rarely explicitly discussed during climate negotiations, could play a role in a solution to the climate change problem. Our results are established within a model where energy needs are met by oil (owned by a cartel and a fringe) and by renewables that are perfect substitutes for oil and that can be produced in unlimited amounts by using backstop technologies.
By decomposing the welfare and climate change consequences of imperfect competition into a conservation and a sequence effect, we have demonstrated that although the monopolist may be the conservationist's friend, they will certainly not become best friends. On the one hand, the conservation effect indeed slows down climate change by increasing the initial oil price. On the other hand, imperfect competition causes front-loading in time of relatively dirty unconventional oil, which aggravates climate change. In our calibrated model, imperfect competition reduces social welfare by 14.5 percent compared to the first-best, 97 percent of which is due to the sequence effect.
Furthermore, although the conservation effect lowers climate damages by 4.8 percent, by taking the sequence effect into account we have found that imperfect competition on balance increases climate damages by 5.3 percent.
Our results also have shown that the recent shale oil revolution not only increases climate damage, but also can lower grey welfare as it crowds out relatively cheap OPEC oil. If the interest rate and the social cost of carbon are large enough, the shale oil revolution causes a reduction in social welfare. Furthermore, without non-OPEC oil, global welfare in the CFE would be 13 trillion US$ higher, 10 trillion US$ of which is due to lower climate damages.
Our findings corroborate calls for a supply side approach to a climate treaty and for the need for policies that limit investments and extraction of fossil fuels (cf. Harstad, 2012;Erickson et al., 2018;Green and Denniss, 2018;Asheim et al., 2019). A successful supply side treaty will have to take the heterogeneity of fossil fuel suppliers into account, in particular market power and its repercussions on the timing of extraction of the different reserves.
This paper is a first to attempt to examine the importance of the sequence effect on climate change. Admittedly, our results were derived within a stylized model and under a number of assumptions made for tractability or ease of exposition. Two different streams of future research appear to be promising. The first is to examine the robustness of our conclusion under alternative scenarios. One relevant scenario would consider more sophisticated climate policies that recognize the cartel's market power and that are conditioned on the state of the climate and its evolution over time. Other natural extensions would be to introduce multiple pools with different extraction costs (cf. Fischer and Salant, 2017), stock-dependent unit extraction costs, extraction costs that are strictly convex in the quantity extracted, and unit cost of renewables that decline over time due to technical progress. The combination of stock-dependent extraction costs of the fringe and declining renewables costs is of particular interest. Our conjecture is that the conservation effect of market power will then lead to a reduction in cumulative extraction, because-compared to the perfectly competitive case-it takes more time to deplete the cartel's stock, leading to lower renewables unit cost at the time of depletion of the cartel's stock. However, the sequence effect of market power potentially mitigates or even reverses this fall in cumulative extraction, as part of the fringe's stock will have been used already when the cartel's stock is depleted.
The second stream of future research relates to the policy implications of the sequence effect and the conflicting interests of the different owners of oil reserves, in particular during the negotiation and the design of climate change mitigation options in a global context. While there is a successful and growing literature on strategic interactions between resource users on one-hand and resource owners on the other (e.g., Liski and Tahvonen, 2004;Harstad, 2012;Kagan et al., 2015), there is none that tackles the interactions between two (or several) groups of resource owners and resource users. Such triangular (or multilateral) interactions may well turn out to be key in reaching a sustainable solution to curbing carbon emissions. For example, a possible solution for the problem of inefficient order of use of resources is to allow for the possibility that resource users and owners of the 'cleaner' resource buy out the 'dirtier' reserves or compensate their owners to induce them to halt their extraction (cf. Harstad, 2012;Eichner and Pethig, 2017a,b). This is obviously not a simple task; nevertheless it is definitely worth further investigation. [k c + λ c e rt − α + β(q c (t) + q c (t))]q c (t) =0, For t ∈ C we have Throughout a phase of simultaneous use, (A.2a) and (A.5a) must hold with equality, which is not possible because k f > k c . Hence, simultaneous use cannot occur in a perfectly competitive equilibrium. A limit-pricing phase requires a constant price, which contradicts (A.5b). Furthermore, the equilibrium sequence F → C can be excluded, because, according to (A.2b), during the initial phase the net price p − k f grows at the rate of intrest, implying that the net price p − k c would grow at a rate lower than the rate of interest (because k f > k c ). Hence, the cartel prefers current extraction over future extraction and will undercut the fringe's price. Therefore, the unique equilibrium sequence under perfect competition reads C → F . Thus, by integrating (A.3c) and (A.6c) over time, denoting the transition time by T 1 and the depletion time by T 2 , using the terminal condition λ f = (b − k f )e −rT 2 , the price continuity condition k c + λ c e rT 1 = k f + λ f e rT 1 , and the resource constraints of the cartel and the fringe, we find that the perfectly competitive equilibrium is described by In the perfectly competitive equilibrium described by (A.7a)-(A.7b) the only remaining market failure is the climate externality. Hence, the competitive equilibrium coincides with the first-best if carbon is priced at a rate equal to the SCC. This requires a per unit tax on oil equal to τ = ω c ζ r during C and τ = ω f ζ r during F . By imposing these optimal tax rates, by integrating (A.3c) and (A.6c) over time, denoting the first-best transition time by T * 1 and the first-best depletion time by T * 2 , using the terminal condition λ f = (b− ω f ζ r −k f )e −rT 2 , the social cost continuity condition k c +λ c e rT * 1 + ω c ζ r = k f +λ f e rT * 1 + ω f ζ r , and the resource constraints of the cartel and the fringe, we find that the first-best is described by   social welfare (panels (e) and (f)) from the first best, for various values of the fringe's initial resource stock and marginal extraction costs. The solid line corresponds to linear demand (ϕ = 2, χ > 0, p < χψ), the dashed line to CES demand (χ = 0, ϕ < 1), and the dotted line to shifted CES demand (ϕ < 1, χ > 0, ψ = 1 − ϕ). The remaining parameters are set at their benchmark values, as shown in Table 1. (below the curve) or detrimental to welfare (above the curve). Panel (a) shows the results for an increase in S f 0 from 438 to 619.5. Panel (b) depicts the outcomes for a decrease of k f from 84.5 to 62.5. The solid, dashed and dotted curves correspond to linear, CES and shifted CES demand, respectively. Parameters are set at their benchmark values, as shown in Table 1. For clarity reasons, the scale of the horizontal axis differs between the two panels.