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The Economics of Fossil Fuels and Pollution
CHAPTER
THE ECONOMICS OF FOSSIL FUELS AND POLLUTION
4
Ujjayant Chakravorty and Yazhen Gong† Department of Economics, Tufts University, Medford, MA School of Environment and Natural Resources, Renmin University of China, Beijing, China
†
CHAPTER OUTLINE 4.1 Introduction ................................................................................................................................... 67 4.2 The Framework with Nonrenewable Resource and a Ceiling on the Stock of Pollution ........................ 68 4.2.1 Abatement of Pollution ............................................................................................... 70 4.2.2 Nonstationary Demand................................................................................................ 70 4.3 Ceiling with Fossil Fuels with Different Pollution Intensities ............................................................. 71 4.4 Conclusion .................................................................................................................................... 73 Acknowledgments ................................................................................................................................. 74 References ........................................................................................................................................... 74
JEL: Q30; Q48; Q54
4.1 INTRODUCTION Most carbon emissions in the atmosphere come from the burning of fossil fuels, such as coal, oil, and natural gas, which together supply an overwhelming share (more than 80%) of the world’s commercial energy (International Energy Agency, 2013). Thus, stabilizing the climate implies reducing the emissions from fossil fuel combustion and switching to less carbon-intensive fuels, such as a substitution away from coal to natural gas in electricity generation, or a larger share of renewable fuels, such as wind and solar energy in the energy mix. From an economics perspective, it is important to think about policy instruments that may facilitate this transition away from fossil fuels to cleaner energy sources. However, this issue is somewhat complicated because all of the major fossil fuels are nonrenewable in nature. Of course, we can debate as to whether the stocks of oil, coal, and gas can be assumed to be fixed, as in standard economic models of nonrenewable resources, or if the significant rate of new discoveries and
Sustainable Economic Development. © 2015 Elsevier Inc. All rights reserved.
67
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CHAPTER 4 THE ECONOMICS OF FOSSIL FUELS AND POLLUTION
technological change suggests that we will never encounter a situation in which the supply of these resources is physically constrained. From the point of view of economic theory, it is important to think about how the exhaustibility of resources may affect pollution taxes and resource use, as well as the time of transition from a typical fossil fuel, such as oil, to an alternate clean resource, such as solar energy. In this chapter, we consider a specific form of a damage function, which is a ceiling on the stock of carbon emissions. We posit a scenario in which an extension to the Kyoto Protocol or another international agreement imposes a binding target for atmospheric carbon.1 One may think of this as the 2 C limit imposed by the IPCC beyond which scientists suggest that the earth may see catastrophic changes to its ecological balance. From an economic modeling point of view, this assumption is convenient because it imposes a limit on the stock of emissions from the use of a fossil fuel, and we avoid considering an explicit damage function. As previous studies have suggested, the path of taxes and energy prices may be highly sensitive to the derivatives of a damage function (Farzin and Tahvonen, 1996). In Section 4.2, we outline a simple model of environmental regulation with only one fossil fuel. In Section 4.3, we extend the analysis to two resources with different pollution characteristics. Section 4.4 concludes by discussing the limitations of the framework and suggesting possible analytical and empirical applications.
4.2 THE FRAMEWORK WITH NONRENEWABLE RESOURCE AND A CEILING ON THE STOCK OF POLLUTION Here we introduce the basic ideas. Imagine a stock of oil which is fixed, and a social planner extracting it with some discount rate r . 0 and a utility function given by U(q), where q is the rate of extraction of oil in each time period t. Suppose the cost of extraction of oil is constant and given by b . 0. Then this is the well-known Hotelling (1931) problem that is written as ðN
½UðqÞ 2 bqe2rt dt
(4.1)
_ 5 2q; Xð0Þ 5 X . 0 XðtÞ
(4.2)
Max 0
subject to the constraint
where r is the discount rate of the social planner. The solution to this problem is quite familiar— resource prices go up over time, there is a markup between the price of the resource and the extraction cost, and consumption goes down over time. Although we do not do this here, one can 1 Since fossil fuels account for 75% of global emissions (the rest is deforestation) the effect of an international environmental agreement (e.g., the Kyoto Protocol) can be assumed to be a direct restriction on carbon emissions from the production of fuels such as coal. Many empirical studies on the effect of environmental regulation on energy use have concluded that the energy sector that is likely to be most impacted by climate regulation is electricity because it mainly uses coal, the dirtiest of all fuels. Clean substitutes for oil in the transportation sector or natural gas in residential heating (the cleanest of all fossil fuels) are much more expensive than the substitutes available in electricity generation such as hydro and nuclear power. That is, relative to coal, oil and natural gas have strong comparative advantage in their respective uses.
4.2 THE FRAMEWORK WITH NONRENEWABLE RESOURCE
69
reformulate this model by specifying some price, say p; at which some backstop resource (say biofuels or solar) is available in abundant quantities, in which case the terminal price at which there is a complete transition occurs at this price p. Now consider a ceiling on the stock of pollution. For convenience, suppose we assume that one unit of oil used emits one unit of pollution. Then we can define the stock of pollution as z with some initial level of stock at z(0) 5 z0. For the model to make sense, the ceiling has to be above the initial stock of pollution. One can imagine an initial carbon concentration of say 400 ppm and a ceiling imposed by the IPCC of 450 ppm. By imposing the ceiling, we can rewrite the above problem by introducing another constraint, which can be written as z_ðtÞ 5 q 2 αz;
z0 # z
(4.3)
where the parameter α . 0 represents the natural dilution of the carbon in the atmosphere. In such a simple model, note that we do not include an explicit damage function in which utility may be a decreasing function of the stock of carbon emissions. However, implicitly by imposing a constraint on the stock, we have assumed that damages are zero until the stock hits z but infinite afterward. The model will not allow the stock to rise above z. However, utility comes from burning fossil fuels, and there is no benefit to stay below the ceiling, thus the solution will lead the stock to rise and hit the ceiling at some point in time. Because at the ceiling the amount of energy that can be consumed is limited—we must only use what we can dilute—we have the relationship z_ðtÞ 5 0 which implies that x 5 αz, where x is the amount of fossil energy consumed while at the ceiling. The solution is shown in Figure 4.1. The oil consumed rises until the stock hits the ceiling, stays pb
p
Time
z
z0
Time
FIGURE 4.1 With a ceiling, the price of the fossil fuel increases, stays constant for a while, and finally rises to hit the backstop fuel. The stock of pollution rises, stays at the ceiling, then declines to zero.
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CHAPTER 4 THE ECONOMICS OF FOSSIL FUELS AND POLLUTION
there for some time, and finally declines when the price of oil has risen sufficiently that consumption is no longer constrained by the imposed ceiling. In the figure, we have assumed that at a sufficiently high price defined by p, an alternative clean source of energy (say solar) is economical. At the time when the price of energy is equal to the backstop price, the oil is completely exhausted (see top panel of Figure 4.1). Note that compared to the standard Hotelling model without any stock constraint, the price of energy will include a tax that is equal to the multiplier on condition (3). Burning a unit of fossil fuel will create pollution which will bring the stock closer to the ceiling, and hence there will be a higher price for the fossil fuel. The consumption of the fossil fuel will be the converse of what is shown in Figure 4.1. It will go down from the beginning, keep steady at the ceiling, and finally decline further until exhaustion. The bottom panel shows the stock of pollution, which starts at a low level, rises to the mandated ceiling, stays at the ceiling for some time, and finally slides below the ceiling when the endowment of oil is no longer a problem for the regulation, and a new unregulated Hotelling price path starts exactly from the end point of the ceiling. When the renewable takes over completely, there are no more emissions in the atmosphere, and the stock of pollution declines asymptotically to zero because of the natural dilution. It is clear from the above picture that if the price of the backstop was below the price of energy at the ceiling given by p, then at the ceiling there would be joint use of the two resources, until all oil is exhausted and the backstop takes over. This has been shown by Chakravorty et al. (2006). Along the same lines, one could think of more complicated scenarios such as the deployment of the backstop making it more cost effective. For example, if in order to limit greenhouse gas emissions to 450 ppm an economy was to use a large volume of solar panels, then there may be significant learning effects from this process, which will in turn increase solar use and reduce fossil fuel use. In that case, a deployment of solar may be justified even before the ceiling is attained.
4.2.1 ABATEMENT OF POLLUTION The model presented above does not consider the option of reducing pollution through abatement options such as carbon capture and sequestration (CCS). Moreover, the natural dilution parameter α may be small, as some scientists point out, so that abatement may involve costly investment. With carbon capture, the adoption depends on the cost structure of the abatement technology. If the unit cost of CCS technology is assumed constant, then there is no benefit to its early adoption, in which case, as we may expect, the adoption will only happen at the ceiling, where energy use is constrained. Abatement of pollution will then allow for burning more fossil fuels, yet keeping the aggregate net emissions to zero. Adoption is not beneficial before the ceiling is attained or after the ceiling is crossed. Once the ceiling no longer binds, the shadow price of pollution is zero. However, if abatement through technologies (such as CCS) generates benefits in terms of learning by doing and the unit cost declines with use, then there may be use of this technology strictly before the ceiling, so that the benefits of use can accrue.
4.2.2 NONSTATIONARY DEMAND Things get more complicated when we consider nonstationary demand. This may happen if there is an increase in global population or an increase in per capital consumption of energy driven by income growth. With increasing demand, there may not be constant energy consumption at the
4.3 CEILING WITH FOSSIL FUELS WITH DIFFERENT POLLUTION
71
ceiling. Energy consumption may increase even before the ceiling in spite of a growth in resource prices because of rising scarcity rents and pollution taxes. If demand was shifting exogenously, the pattern of resource use could change. For example, if demand was high during the ceiling and the clean substitute (solar energy) was relatively cheap, both resources may be used at the ceiling. However, after the ceiling period is over, we revert back to the exclusive use of coal, and again when the coal is exhausted completely, there is a complete switch to solar energy. So we may have two disjoint periods when the clean substitute is used.
4.3 CEILING WITH FOSSIL FUELS WITH DIFFERENT POLLUTION INTENSITIES An important issue to consider is the issue of substitution of a fossil fuel not only by a clean fuel, as we discuss above, but by other fuels, with potentially different emission characteristics. For example, almost all energy resources have substitutes—coal and natural gas are substitutes in power generation, where gas is much cleaner than coal in terms of carbon emissions. In transportation, biofuels are a substitute for gasoline, the former being somewhat cleaner in terms of life cycle emissions than gasoline, although it is an issue that is actively debated by scientists. The question arises, how would a ceiling on carbon affect resources that are perfect substitutes, yet have different pollution intensities? Chakravorty et al. (2008) study an extension of the above model in which they consider two resources, say coal and natural gas, each with different pollution intensities. In their model, coal is dirty while gas is a clean resource. Both resources come with known reserves, and emissions face an aggregate stock constraint as discussed earlier. Now given two resources, say 1 for gas and 2 for coal, condition (2) becomes X_ i 5 2 qi ;
i 5 1; 2
(4.4)
If each of the resources has pollution emissions per unit given by θi . 0, then we get the stock constraint as z_ 5
X
θi qi 2 αz;
z0 # z
(4.5)
i
with z as the imposed limit on pollution as before. We write z0 as the initial stock to differentiate from resources which are denoted by subscripts. Assuming away any extraction cost for the two fossil fuels, and incorporating a backstop resource such as solar energy whose consumption is given by y and unit costs written as cr, we can write the new optimization problem as ðN "
Max
U 0
X
!
#
qi 1 y 2 cr y e2ρt dt
(4.6)
i
with the same set of constraints (4) and (5). Note that with two resources, the model gets quite complicated, even though we have simplified and assumed away any extraction costs for fossil fuels. The best way to understand the solution is to think of starting from the ceiling and checking how the two resources will be used. If the starting pollution stock is at the ceiling, then note that
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CHAPTER 4 THE ECONOMICS OF FOSSIL FUELS AND POLLUTION
λr0ept
cr
pi
–uθi
λr0 Time
FIGURE 4.2 Resource price with one abundant resource.
the higher the initial stock of a resource, say coal, the lower its initial price (since costs are zero, price equals scarcity rent). Thus if we start from the ceiling, there is a critical stock at which the ceiling does not bind. We can call this XiH for resource i where the superscript H denotes Hotelling, meaning the maximal stock at which Hotelling rules and there is no constraint on extraction. However, beyond this stock, the extraction will be bounded for a time, otherwise the stock of pollution will be exceeded. This is shown in Figure 4.2. If the starting stock of pollution is below the ceiling, the stock of pollution increases until it hits the ceiling, then decreases, as we have discussed before. However, initial stock of resources implies a longer stay at the ceiling. This defines some maximal level of stock of resource XiH ðZ 0 Þ which is the resource stock beyond which Hotelling no longer holds. The higher the initial stock of pollution Z0, the smaller this resource stock XiH . With two resources things get complicated because they are perfect substitutes and all that matters is the aggregate stock of pollution. Thus there may be opportunities to substitute depending on the abundance of the two resources. For example, if natural gas is abundant, then one may burn a lot of gas at the beginning of the time horizon, then move to a joint use of the two resources at the ceiling. The reason the social planner would like to burn a lot of gas initially is because it is cleaner, and hence more energy can be consumed in earlier periods, rather than later, generating profits at an earlier time. On the other hand, if coal was abundant, and gas was scarce, one would burn coal and get to the ceiling where energy consumption is constrained and thus preserve the stock of limited gas to be used when it is needed the most—when the ceiling binds. Figure 4.3 shows the resource prices starting from the stock at the ceiling. When both resources are abundant, the planner consumes the maximum amount of gas first because it is clean and generates the highest current utility. The price is fixed at p1 . Recall that the stock of emissions is at the ceiling and does not change. However, once some gas is used up, we need to transit to a regime with only coal use. Since coal is dirtier, we can use less of coal and hence generate less utility. The transition from gas price p1 to coal price p2 ; shown in Figure 4.3, occurs by using some combination of the two such that we stay at the ceiling, and both prices are equal. The transition is gradual with a small amount of coal substituting for gas at the beginning
4.4 CONCLUSION
73
cr p2
p1 = p2
p1
Time
FIGURE 4.3 Resource prices when both resources are abundant and the stock of pollution starts at the ceiling.
and finally a small amount of gas which gives way to exclusive coal use. Once price p2 is reached all gas is exhausted. Then we use coal until we arrive at a stock that allows for an unconstrained transition to the backstop (e.g., solar energy) at price cr. If the initial stock is lower than the regulated stock of emissions, then we must find a path to the ceiling through the use of the two resources. If there is a lot of coal, then one can show that it may be beneficial to burn more coal initially and “race” to the ceiling from below the ceiling. This is because the “free” dilution of the carbon given by αz increases the stock of carbon z. Because of this proportionality, the planner benefits from rushing to increase the stock, if the current stock lies below the ceiling. In some sense, this is a perverse result: without regulation, the standard Hotelling theory tells us, we will be indifferent between using the two resources since they are perfect substitutes and equally costly (or costless). However, with regulation there may be a preference to burn the dirty resource first in order to benefit from free dilution. The discussion of pollution intensities suggests that the effect of environmental regulation may be difficult to determine ex ante. The profile of resource use is a function of the pollution characteristics of the two resources, the discount rate, and their relative abundance. If one was to remove the assumption of zero cost of the two resources, then the solution may be even more complicated. If natural gas was cheaper to extract, then it would have a double advantage of being both cleaner and cheaper than coal. Since we care about current benefits will push the extraction of gas relative to coal toward the present and move some coal extraction to the future because it is higher cost.
4.4 CONCLUSION In this chapter, we have considered the economics of regulating fossil fuel use by using a very simple framework. The regulation we consider is somewhat specific—we limit a catastrophic buildup of pollution but do not worry about contemporaneous pollution. In the case of global warming and the accumulation of greenhouse gases, our assumption of an imposed ceiling may be quite realistic. Essentially, we propose a marginal damage function that exhibits low damages until we hit some limit and extremely high damages beyond this value. However, if we consider pollution from coal and oil use in terms of sulfur emissions that cause acid rain, this assumption may be unrealistic.
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CHAPTER 4 THE ECONOMICS OF FOSSIL FUELS AND POLLUTION
In that case, the damage from emissions even when we are below some maximum limit of pollution stock may be significant. This may lead to more joint use of resources and less of the sharp transitions we see in our model (for a general equilibrium model with two resources which are imperfect substitutes, see Smulders and van der Werf, 2008). In our model, the taxes on pollution are given by the shadow price of the stock constraint. In the model with one resource, the tax increases over time and finally reaches a maximum when the ceiling is attained. It declines throughout the ceiling period and equals zero exactly when the ceiling no longer binds. This result of an inverted U-shaped tax path is very similar to what has been obtained for more general damage functions, as in Tahvonen (1997). There is a large literature on the Herfindahl (1967) conjecture which suggests that resources with the least cost must be used first. Many authors have found conditions under which this principle is violated.2 The framework we have discussed above can be thought of as an extension to this literature where we use resource abundance as a proxy for costs—the higher the stock of the resource, the lower is its scarcity rent and hence its true marginal cost. The basic idea in this literature is that relative costs matter, and we represent this by looking at relative stocks of resources. Finally, one may wonder how such a framework can be applied to examine resource and energy use under environmental regulation. There is significant work in this area starting with the pioneering contribution of Nordhaus (1973) who developed a calibration model to study the effect of OPEC oil price shocks on the US economy and modified in the context of learning effects and cost reductions in solar photovoltaics (Chakravorty et al., 1997) and land allocation induced by biofuel mandates (Chakravorty et al., 2013). These empirical models take many other factors into account that make the analytical model complicated—for example, they assume exogenous rates of technological change, new resource discoveries, and energy demand shifts driven by population and income growth. One could use this framework to examine contemporary issues in regulation, such as the effect of the Keystone pipeline or the discovery of shale gas reserves in China and the United States.
ACKNOWLEDGMENTS The authors would like to thank David Joseph U. Anabo for a careful read of the paper and helpful comments.
REFERENCES Chakravorty, U., Krulce, D.L., 1994. Heterogeneous demand and order of resource extraction. Econometrica 62 (6), 14451452. Chakravorty, U., Roumasset, J., Tse, K., 1997. Endogenous substitution of energy resources and global warming. J. Polit. Econ. 105 (6), 12011234. Chakravorty, U., Magne, B., Moreaux, M., 2006. A Hotelling model with a ceiling on the stock of pollution. J. Econ. Dyn. Control 30 (12), 28752904. 2 See, for example, Kemp and Van Long (1980), Lewis (1982), Chakravorty and Krulce (1994), and a more recent application of the same idea to landfill sites (Gaudet et al., 2001).
REFERENCES
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Chakravorty, U., Moreaux, M., Tidball, M., 2008. Ordering the extraction of polluting nonrenewable resources. Am. Econ. Rev. 98 (3), 11281144. Chakravorty, U., Hubert, M.-H., Moreaux, M., Nostbakken, L., 2013. The Long-Run Impact of Biofuels on Food Prices. SSRN Working Paper 2104053. Farzin, Y.H., Tahvonen, O., 1996. Global carbon cycle and the optimal time path of a carbon tax. Oxf. Econ. Pap. 48 (4), 518536. Gaudet, G., Moreaux, M., Salant, S.W., 2001. Intertemporal depletion of resource sites by spatially distributed users. Am. Econ. Rev. 91 (4), 11491159. Herfindahl, O.C., 1967. Depletion and economic theory. In: Gaffney, M. (Ed.), Extractive Resources and Taxation. University of Wisconsin Press, Madison, WI, pp. 6390. Hotelling, H., 1931. The economics of exhaustible resources. J. Polit. Econ. 39, 137175. International Energy Agency, 2013. Key world energy statistics. Retrieved from , http://www.iea.org/publications/freepublications/publication/KeyWorld2013.pdf . . Kemp, M.C., Van Long, N., 1980. On two folk theorems concerning the extraction of exhaustible resources. Econometrica 48 (3), 663673. Lewis, T.R., 1982. Sufficient conditions for extracting least cost resource first. Econometrica 50 (4), 10811083. Nordhaus, W.D., 1973. The allocation of energy resources. Brookings Pap. Econ. Act. 4 (3), 529576, Economic Studies Program, The Brookings Institution. Smulders, S., van der Werf, E., 2008. Climate policy and the optimal extraction of high- and low-carbon fossil fuels. Can. J. Econ. 41 (4), 14211444. Tahvonen, O., 1997. Fossil fuels, stock externalities, and backstop technology. Can. J. Econ. 30 (4), 855874.
THE ECONOMICS OF FOSSIL FUELS AND POLLUTION
4
Ujjayant Chakravorty and Yazhen Gong† Department of Economics, Tufts University, Medford, MA School of Environment and Natural Resources, Renmin University of China, Beijing, China
†
CHAPTER OUTLINE 4.1 Introduction ................................................................................................................................... 67 4.2 The Framework with Nonrenewable Resource and a Ceiling on the Stock of Pollution ........................ 68 4.2.1 Abatement of Pollution ............................................................................................... 70 4.2.2 Nonstationary Demand................................................................................................ 70 4.3 Ceiling with Fossil Fuels with Different Pollution Intensities ............................................................. 71 4.4 Conclusion .................................................................................................................................... 73 Acknowledgments ................................................................................................................................. 74 References ........................................................................................................................................... 74
JEL: Q30; Q48; Q54
4.1 INTRODUCTION Most carbon emissions in the atmosphere come from the burning of fossil fuels, such as coal, oil, and natural gas, which together supply an overwhelming share (more than 80%) of the world’s commercial energy (International Energy Agency, 2013). Thus, stabilizing the climate implies reducing the emissions from fossil fuel combustion and switching to less carbon-intensive fuels, such as a substitution away from coal to natural gas in electricity generation, or a larger share of renewable fuels, such as wind and solar energy in the energy mix. From an economics perspective, it is important to think about policy instruments that may facilitate this transition away from fossil fuels to cleaner energy sources. However, this issue is somewhat complicated because all of the major fossil fuels are nonrenewable in nature. Of course, we can debate as to whether the stocks of oil, coal, and gas can be assumed to be fixed, as in standard economic models of nonrenewable resources, or if the significant rate of new discoveries and
Sustainable Economic Development. © 2015 Elsevier Inc. All rights reserved.
67
68
CHAPTER 4 THE ECONOMICS OF FOSSIL FUELS AND POLLUTION
technological change suggests that we will never encounter a situation in which the supply of these resources is physically constrained. From the point of view of economic theory, it is important to think about how the exhaustibility of resources may affect pollution taxes and resource use, as well as the time of transition from a typical fossil fuel, such as oil, to an alternate clean resource, such as solar energy. In this chapter, we consider a specific form of a damage function, which is a ceiling on the stock of carbon emissions. We posit a scenario in which an extension to the Kyoto Protocol or another international agreement imposes a binding target for atmospheric carbon.1 One may think of this as the 2 C limit imposed by the IPCC beyond which scientists suggest that the earth may see catastrophic changes to its ecological balance. From an economic modeling point of view, this assumption is convenient because it imposes a limit on the stock of emissions from the use of a fossil fuel, and we avoid considering an explicit damage function. As previous studies have suggested, the path of taxes and energy prices may be highly sensitive to the derivatives of a damage function (Farzin and Tahvonen, 1996). In Section 4.2, we outline a simple model of environmental regulation with only one fossil fuel. In Section 4.3, we extend the analysis to two resources with different pollution characteristics. Section 4.4 concludes by discussing the limitations of the framework and suggesting possible analytical and empirical applications.
4.2 THE FRAMEWORK WITH NONRENEWABLE RESOURCE AND A CEILING ON THE STOCK OF POLLUTION Here we introduce the basic ideas. Imagine a stock of oil which is fixed, and a social planner extracting it with some discount rate r . 0 and a utility function given by U(q), where q is the rate of extraction of oil in each time period t. Suppose the cost of extraction of oil is constant and given by b . 0. Then this is the well-known Hotelling (1931) problem that is written as ðN
½UðqÞ 2 bqe2rt dt
(4.1)
_ 5 2q; Xð0Þ 5 X . 0 XðtÞ
(4.2)
Max 0
subject to the constraint
where r is the discount rate of the social planner. The solution to this problem is quite familiar— resource prices go up over time, there is a markup between the price of the resource and the extraction cost, and consumption goes down over time. Although we do not do this here, one can 1 Since fossil fuels account for 75% of global emissions (the rest is deforestation) the effect of an international environmental agreement (e.g., the Kyoto Protocol) can be assumed to be a direct restriction on carbon emissions from the production of fuels such as coal. Many empirical studies on the effect of environmental regulation on energy use have concluded that the energy sector that is likely to be most impacted by climate regulation is electricity because it mainly uses coal, the dirtiest of all fuels. Clean substitutes for oil in the transportation sector or natural gas in residential heating (the cleanest of all fossil fuels) are much more expensive than the substitutes available in electricity generation such as hydro and nuclear power. That is, relative to coal, oil and natural gas have strong comparative advantage in their respective uses.
4.2 THE FRAMEWORK WITH NONRENEWABLE RESOURCE
69
reformulate this model by specifying some price, say p; at which some backstop resource (say biofuels or solar) is available in abundant quantities, in which case the terminal price at which there is a complete transition occurs at this price p. Now consider a ceiling on the stock of pollution. For convenience, suppose we assume that one unit of oil used emits one unit of pollution. Then we can define the stock of pollution as z with some initial level of stock at z(0) 5 z0. For the model to make sense, the ceiling has to be above the initial stock of pollution. One can imagine an initial carbon concentration of say 400 ppm and a ceiling imposed by the IPCC of 450 ppm. By imposing the ceiling, we can rewrite the above problem by introducing another constraint, which can be written as z_ðtÞ 5 q 2 αz;
z0 # z
(4.3)
where the parameter α . 0 represents the natural dilution of the carbon in the atmosphere. In such a simple model, note that we do not include an explicit damage function in which utility may be a decreasing function of the stock of carbon emissions. However, implicitly by imposing a constraint on the stock, we have assumed that damages are zero until the stock hits z but infinite afterward. The model will not allow the stock to rise above z. However, utility comes from burning fossil fuels, and there is no benefit to stay below the ceiling, thus the solution will lead the stock to rise and hit the ceiling at some point in time. Because at the ceiling the amount of energy that can be consumed is limited—we must only use what we can dilute—we have the relationship z_ðtÞ 5 0 which implies that x 5 αz, where x is the amount of fossil energy consumed while at the ceiling. The solution is shown in Figure 4.1. The oil consumed rises until the stock hits the ceiling, stays pb
p
Time
z
z0
Time
FIGURE 4.1 With a ceiling, the price of the fossil fuel increases, stays constant for a while, and finally rises to hit the backstop fuel. The stock of pollution rises, stays at the ceiling, then declines to zero.
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CHAPTER 4 THE ECONOMICS OF FOSSIL FUELS AND POLLUTION
there for some time, and finally declines when the price of oil has risen sufficiently that consumption is no longer constrained by the imposed ceiling. In the figure, we have assumed that at a sufficiently high price defined by p, an alternative clean source of energy (say solar) is economical. At the time when the price of energy is equal to the backstop price, the oil is completely exhausted (see top panel of Figure 4.1). Note that compared to the standard Hotelling model without any stock constraint, the price of energy will include a tax that is equal to the multiplier on condition (3). Burning a unit of fossil fuel will create pollution which will bring the stock closer to the ceiling, and hence there will be a higher price for the fossil fuel. The consumption of the fossil fuel will be the converse of what is shown in Figure 4.1. It will go down from the beginning, keep steady at the ceiling, and finally decline further until exhaustion. The bottom panel shows the stock of pollution, which starts at a low level, rises to the mandated ceiling, stays at the ceiling for some time, and finally slides below the ceiling when the endowment of oil is no longer a problem for the regulation, and a new unregulated Hotelling price path starts exactly from the end point of the ceiling. When the renewable takes over completely, there are no more emissions in the atmosphere, and the stock of pollution declines asymptotically to zero because of the natural dilution. It is clear from the above picture that if the price of the backstop was below the price of energy at the ceiling given by p, then at the ceiling there would be joint use of the two resources, until all oil is exhausted and the backstop takes over. This has been shown by Chakravorty et al. (2006). Along the same lines, one could think of more complicated scenarios such as the deployment of the backstop making it more cost effective. For example, if in order to limit greenhouse gas emissions to 450 ppm an economy was to use a large volume of solar panels, then there may be significant learning effects from this process, which will in turn increase solar use and reduce fossil fuel use. In that case, a deployment of solar may be justified even before the ceiling is attained.
4.2.1 ABATEMENT OF POLLUTION The model presented above does not consider the option of reducing pollution through abatement options such as carbon capture and sequestration (CCS). Moreover, the natural dilution parameter α may be small, as some scientists point out, so that abatement may involve costly investment. With carbon capture, the adoption depends on the cost structure of the abatement technology. If the unit cost of CCS technology is assumed constant, then there is no benefit to its early adoption, in which case, as we may expect, the adoption will only happen at the ceiling, where energy use is constrained. Abatement of pollution will then allow for burning more fossil fuels, yet keeping the aggregate net emissions to zero. Adoption is not beneficial before the ceiling is attained or after the ceiling is crossed. Once the ceiling no longer binds, the shadow price of pollution is zero. However, if abatement through technologies (such as CCS) generates benefits in terms of learning by doing and the unit cost declines with use, then there may be use of this technology strictly before the ceiling, so that the benefits of use can accrue.
4.2.2 NONSTATIONARY DEMAND Things get more complicated when we consider nonstationary demand. This may happen if there is an increase in global population or an increase in per capital consumption of energy driven by income growth. With increasing demand, there may not be constant energy consumption at the
4.3 CEILING WITH FOSSIL FUELS WITH DIFFERENT POLLUTION
71
ceiling. Energy consumption may increase even before the ceiling in spite of a growth in resource prices because of rising scarcity rents and pollution taxes. If demand was shifting exogenously, the pattern of resource use could change. For example, if demand was high during the ceiling and the clean substitute (solar energy) was relatively cheap, both resources may be used at the ceiling. However, after the ceiling period is over, we revert back to the exclusive use of coal, and again when the coal is exhausted completely, there is a complete switch to solar energy. So we may have two disjoint periods when the clean substitute is used.
4.3 CEILING WITH FOSSIL FUELS WITH DIFFERENT POLLUTION INTENSITIES An important issue to consider is the issue of substitution of a fossil fuel not only by a clean fuel, as we discuss above, but by other fuels, with potentially different emission characteristics. For example, almost all energy resources have substitutes—coal and natural gas are substitutes in power generation, where gas is much cleaner than coal in terms of carbon emissions. In transportation, biofuels are a substitute for gasoline, the former being somewhat cleaner in terms of life cycle emissions than gasoline, although it is an issue that is actively debated by scientists. The question arises, how would a ceiling on carbon affect resources that are perfect substitutes, yet have different pollution intensities? Chakravorty et al. (2008) study an extension of the above model in which they consider two resources, say coal and natural gas, each with different pollution intensities. In their model, coal is dirty while gas is a clean resource. Both resources come with known reserves, and emissions face an aggregate stock constraint as discussed earlier. Now given two resources, say 1 for gas and 2 for coal, condition (2) becomes X_ i 5 2 qi ;
i 5 1; 2
(4.4)
If each of the resources has pollution emissions per unit given by θi . 0, then we get the stock constraint as z_ 5
X
θi qi 2 αz;
z0 # z
(4.5)
i
with z as the imposed limit on pollution as before. We write z0 as the initial stock to differentiate from resources which are denoted by subscripts. Assuming away any extraction cost for the two fossil fuels, and incorporating a backstop resource such as solar energy whose consumption is given by y and unit costs written as cr, we can write the new optimization problem as ðN "
Max
U 0
X
!
#
qi 1 y 2 cr y e2ρt dt
(4.6)
i
with the same set of constraints (4) and (5). Note that with two resources, the model gets quite complicated, even though we have simplified and assumed away any extraction costs for fossil fuels. The best way to understand the solution is to think of starting from the ceiling and checking how the two resources will be used. If the starting pollution stock is at the ceiling, then note that
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CHAPTER 4 THE ECONOMICS OF FOSSIL FUELS AND POLLUTION
λr0ept
cr
pi
–uθi
λr0 Time
FIGURE 4.2 Resource price with one abundant resource.
the higher the initial stock of a resource, say coal, the lower its initial price (since costs are zero, price equals scarcity rent). Thus if we start from the ceiling, there is a critical stock at which the ceiling does not bind. We can call this XiH for resource i where the superscript H denotes Hotelling, meaning the maximal stock at which Hotelling rules and there is no constraint on extraction. However, beyond this stock, the extraction will be bounded for a time, otherwise the stock of pollution will be exceeded. This is shown in Figure 4.2. If the starting stock of pollution is below the ceiling, the stock of pollution increases until it hits the ceiling, then decreases, as we have discussed before. However, initial stock of resources implies a longer stay at the ceiling. This defines some maximal level of stock of resource XiH ðZ 0 Þ which is the resource stock beyond which Hotelling no longer holds. The higher the initial stock of pollution Z0, the smaller this resource stock XiH . With two resources things get complicated because they are perfect substitutes and all that matters is the aggregate stock of pollution. Thus there may be opportunities to substitute depending on the abundance of the two resources. For example, if natural gas is abundant, then one may burn a lot of gas at the beginning of the time horizon, then move to a joint use of the two resources at the ceiling. The reason the social planner would like to burn a lot of gas initially is because it is cleaner, and hence more energy can be consumed in earlier periods, rather than later, generating profits at an earlier time. On the other hand, if coal was abundant, and gas was scarce, one would burn coal and get to the ceiling where energy consumption is constrained and thus preserve the stock of limited gas to be used when it is needed the most—when the ceiling binds. Figure 4.3 shows the resource prices starting from the stock at the ceiling. When both resources are abundant, the planner consumes the maximum amount of gas first because it is clean and generates the highest current utility. The price is fixed at p1 . Recall that the stock of emissions is at the ceiling and does not change. However, once some gas is used up, we need to transit to a regime with only coal use. Since coal is dirtier, we can use less of coal and hence generate less utility. The transition from gas price p1 to coal price p2 ; shown in Figure 4.3, occurs by using some combination of the two such that we stay at the ceiling, and both prices are equal. The transition is gradual with a small amount of coal substituting for gas at the beginning
4.4 CONCLUSION
73
cr p2
p1 = p2
p1
Time
FIGURE 4.3 Resource prices when both resources are abundant and the stock of pollution starts at the ceiling.
and finally a small amount of gas which gives way to exclusive coal use. Once price p2 is reached all gas is exhausted. Then we use coal until we arrive at a stock that allows for an unconstrained transition to the backstop (e.g., solar energy) at price cr. If the initial stock is lower than the regulated stock of emissions, then we must find a path to the ceiling through the use of the two resources. If there is a lot of coal, then one can show that it may be beneficial to burn more coal initially and “race” to the ceiling from below the ceiling. This is because the “free” dilution of the carbon given by αz increases the stock of carbon z. Because of this proportionality, the planner benefits from rushing to increase the stock, if the current stock lies below the ceiling. In some sense, this is a perverse result: without regulation, the standard Hotelling theory tells us, we will be indifferent between using the two resources since they are perfect substitutes and equally costly (or costless). However, with regulation there may be a preference to burn the dirty resource first in order to benefit from free dilution. The discussion of pollution intensities suggests that the effect of environmental regulation may be difficult to determine ex ante. The profile of resource use is a function of the pollution characteristics of the two resources, the discount rate, and their relative abundance. If one was to remove the assumption of zero cost of the two resources, then the solution may be even more complicated. If natural gas was cheaper to extract, then it would have a double advantage of being both cleaner and cheaper than coal. Since we care about current benefits will push the extraction of gas relative to coal toward the present and move some coal extraction to the future because it is higher cost.
4.4 CONCLUSION In this chapter, we have considered the economics of regulating fossil fuel use by using a very simple framework. The regulation we consider is somewhat specific—we limit a catastrophic buildup of pollution but do not worry about contemporaneous pollution. In the case of global warming and the accumulation of greenhouse gases, our assumption of an imposed ceiling may be quite realistic. Essentially, we propose a marginal damage function that exhibits low damages until we hit some limit and extremely high damages beyond this value. However, if we consider pollution from coal and oil use in terms of sulfur emissions that cause acid rain, this assumption may be unrealistic.
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CHAPTER 4 THE ECONOMICS OF FOSSIL FUELS AND POLLUTION
In that case, the damage from emissions even when we are below some maximum limit of pollution stock may be significant. This may lead to more joint use of resources and less of the sharp transitions we see in our model (for a general equilibrium model with two resources which are imperfect substitutes, see Smulders and van der Werf, 2008). In our model, the taxes on pollution are given by the shadow price of the stock constraint. In the model with one resource, the tax increases over time and finally reaches a maximum when the ceiling is attained. It declines throughout the ceiling period and equals zero exactly when the ceiling no longer binds. This result of an inverted U-shaped tax path is very similar to what has been obtained for more general damage functions, as in Tahvonen (1997). There is a large literature on the Herfindahl (1967) conjecture which suggests that resources with the least cost must be used first. Many authors have found conditions under which this principle is violated.2 The framework we have discussed above can be thought of as an extension to this literature where we use resource abundance as a proxy for costs—the higher the stock of the resource, the lower is its scarcity rent and hence its true marginal cost. The basic idea in this literature is that relative costs matter, and we represent this by looking at relative stocks of resources. Finally, one may wonder how such a framework can be applied to examine resource and energy use under environmental regulation. There is significant work in this area starting with the pioneering contribution of Nordhaus (1973) who developed a calibration model to study the effect of OPEC oil price shocks on the US economy and modified in the context of learning effects and cost reductions in solar photovoltaics (Chakravorty et al., 1997) and land allocation induced by biofuel mandates (Chakravorty et al., 2013). These empirical models take many other factors into account that make the analytical model complicated—for example, they assume exogenous rates of technological change, new resource discoveries, and energy demand shifts driven by population and income growth. One could use this framework to examine contemporary issues in regulation, such as the effect of the Keystone pipeline or the discovery of shale gas reserves in China and the United States.
ACKNOWLEDGMENTS The authors would like to thank David Joseph U. Anabo for a careful read of the paper and helpful comments.
REFERENCES Chakravorty, U., Krulce, D.L., 1994. Heterogeneous demand and order of resource extraction. Econometrica 62 (6), 14451452. Chakravorty, U., Roumasset, J., Tse, K., 1997. Endogenous substitution of energy resources and global warming. J. Polit. Econ. 105 (6), 12011234. Chakravorty, U., Magne, B., Moreaux, M., 2006. A Hotelling model with a ceiling on the stock of pollution. J. Econ. Dyn. Control 30 (12), 28752904. 2 See, for example, Kemp and Van Long (1980), Lewis (1982), Chakravorty and Krulce (1994), and a more recent application of the same idea to landfill sites (Gaudet et al., 2001).
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Chakravorty, U., Moreaux, M., Tidball, M., 2008. Ordering the extraction of polluting nonrenewable resources. Am. Econ. Rev. 98 (3), 11281144. Chakravorty, U., Hubert, M.-H., Moreaux, M., Nostbakken, L., 2013. The Long-Run Impact of Biofuels on Food Prices. SSRN Working Paper 2104053. Farzin, Y.H., Tahvonen, O., 1996. Global carbon cycle and the optimal time path of a carbon tax. Oxf. Econ. Pap. 48 (4), 518536. Gaudet, G., Moreaux, M., Salant, S.W., 2001. Intertemporal depletion of resource sites by spatially distributed users. Am. Econ. Rev. 91 (4), 11491159. Herfindahl, O.C., 1967. Depletion and economic theory. In: Gaffney, M. (Ed.), Extractive Resources and Taxation. University of Wisconsin Press, Madison, WI, pp. 6390. Hotelling, H., 1931. The economics of exhaustible resources. J. Polit. Econ. 39, 137175. International Energy Agency, 2013. Key world energy statistics. Retrieved from , http://www.iea.org/publications/freepublications/publication/KeyWorld2013.pdf . . Kemp, M.C., Van Long, N., 1980. On two folk theorems concerning the extraction of exhaustible resources. Econometrica 48 (3), 663673. Lewis, T.R., 1982. Sufficient conditions for extracting least cost resource first. Econometrica 50 (4), 10811083. Nordhaus, W.D., 1973. The allocation of energy resources. Brookings Pap. Econ. Act. 4 (3), 529576, Economic Studies Program, The Brookings Institution. Smulders, S., van der Werf, E., 2008. Climate policy and the optimal extraction of high- and low-carbon fossil fuels. Can. J. Econ. 41 (4), 14211444. Tahvonen, O., 1997. Fossil fuels, stock externalities, and backstop technology. Can. J. Econ. 30 (4), 855874.