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The concept of carbon securities and how they differ from carbon taxes and cap and trade systems in terms of equilibrium price, investment level, and variance of the carbon price. It also explores the advantages and disadvantages of each policy instrument and provides a comparison between them.
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The dissertation of Sarah E. Polborn was reviewed and approved* by the following:
Barry Ickes Professor of Economics Acting Head of Department of Economics Dissertation Adviser Chair of Committee
Vijay Krishna Professor of Economics Director of Graduate Studies, Department of Economics
Mark Roberts Professor of Economics
Michael Berkman Professor of Political Science
*Signatures are on Öle in the Graduate School.
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List of Figures............................. vi List of Tables.............................. vii Acknowledgements........................... viii
1 Introduction 1
2 Backstop Technology Research and the Depletion of Fossil Fuels 3 2.1 Introduction............................ 3 2.2 The Model............................ 5 2.3 Analysis.............................. 10 2.3.1 The Extraction Path................... 10 2.4 Expected Carbon Dioxide Emissions and the Cost of Global Warming............................. 13 2.5 Policy and Extensions...................... 18 2.5.1 Correcting the Extraction Path by Setting an Appro- priate Tax Rate...................... 18 2.5.2 Carbon Capture Technology Research......... 19 2.5.3 Backstop Technology with a Per Unit Price b..... 20 2.6 Numerical Example........................ 22 2.7 Conclusion............................ 34
3 The Political Economy of Carbon Securities and Environ- mental Policy 35 3.1 Introduction............................ 35 3.2 The Model and Discussion.................... 40 3.2.1 The Model........................ 40 3.2.2 Discussion of the Model................. 45 3.3 The Tax Game.......................... 50 3.3.1 The Equilibrium..................... 50 3.3.2 E§ect of Uncertainty................... 54 3.3.3 A Comparison to a Traditional Permit System.... 56
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1 Energy cost savings if quantity does not change........ 32 2 Energy cost savings if quantity changes............ 32
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This dissertation was ináuenced and improved by the advice, knowledge, and assistance of several people. I would like to thank my thesis advisor, Barry Ickes, and my committee members Vijay Krishna, Mark Roberts and Michael Berkman for their helpful comments and their support during my time at Penn State. I would also like to thank my brother, Mattias Polborn, for his support and encouragement, especially during my time on the job market. This thesis greatly beneÖted from his insightful comments. Financial support from the National Science Foundation under Grant SES- 0624354 is gratefully acknowledged.
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tles its owner to a Öxed proportion of ex ante unknown future emissions. The total level of carbon emissions is set by the political process after the carbon securities have been sold. In contrast to a traditional permit sys- tem, in which a governmentís choice of emissions quota is ináuenced by one lobby which represents industries that consume signiÖcant amounts of carbon-based energy, a system based on carbon securities creates an addi- tional group of stakeholders with a strong incentive to organize and ináuence the governmentís choice of an emission level. The advantages over existing systems include stronger commitment to abatement policy, an equilibrium carbon price closer to the social optimum, a more predictable environmental policy in the presence of either climate or political uncertainty, and higher investment in abatement technology. The fourth, Öfth and sixth chapter consider extensions of the carbon securities model. The fourth chapter addresses the questions what e§ect the quantity of carbon securities that are bought by carbon-using Örms has on the equilibrium. The Öfth chapter studies what happens if the lobbying game is described as a Tullock game and then provides a number of reasons why a common agency lobbying model is a better choice than a Tullock model. The sixth chapter considers the practical implementation of carbon securities or more generally pollutant securities. It looks at the question how the current SO 2 allowance system in the United States could be changed into a SO 2 securities system.
Among the suggestions what to do about global warming one idea seems par- ticular promising: developing an alternative, climate-friendly energy source, a backstop technology, in order to make fossil fuels obsolete. Such a tech- nology would allow uncut energy consumption while not having a negative impact on the climate. This paper studies the e§ect of backstop technology research on the de- pletion of fossil fuels. The key insight is that backstop technology research encourages fossil fuel owners to supply more of their resource in the near fu- ture because they anticipate that their resource will become obsolete before it is depleted. Thus, while backstop technology research o§ers the promise of an eventual decrease in carbon dioxide emissions, it creates a cost in the form of higher present day greenhouse gas emissions. I apply methods of the theory of optimal extraction of exhaustible re- sources to study the e§ect of backstop technology research on the problem of global warming. The moment of development of the backstop technology is assumed to be an uncertain function of research e§ort. I show that an increase in backstop technology research e§ort leads to more planned near future fossil fuel extraction and thus higher near future carbon dioxide emis- sions. This change in the distribution of carbon dioxide emissions over time a§ects the cost of global warming for two reasons: First, planned extractions of the resource may never happen if a backstop technology has already been developed by that time. Second, a more gradual global warming is likely to be associated with lower cost since it makes adaptation easier. I show that the research intensity which minimizes the expected cost of global warming decreases with the discount rate used for global warming related costs. The Önal section of this paper illustrates the implications of the model by means of a numerical example. For this I use data published by the International Energy Agency (IEA, 2007).
I consider a continuous time model of an economy with n identical suppliers of fossil fuels. The amount of fossil fuel resources owned by Örm j at time 0 is Sj (0) where Sj (0) is an aggregate of di§erent types of fossil fuels, summed with respect to their carbon content. So if the entire stock is consumed, the amount of carbon dioxide released is Sj (0). Given the resource stock, a Örm j chooses for each point in time t an amount of resource Rj (t) to be extracted and sold. The proÖt of the Örm at time t is Rj (t) [P (R(t)) c(Sj (t))] where P denotes the price of the fossil fuel, S the stock of the resource, c() is a cost function, and R = Pn j=1 Rj^ the sum of the extractions of the^ n^ Örms. The Örmís decision problem is to Önd a sequence of extractions that maximizes proÖts. In the following Rj is used as short notation for Rj (t), similarly S and P are to be understood as variables that may take di§erent values at di§erent points in time. While the economy depends at the present time on fossil fuels for its energy needs, there is ongoing research to develop an alternative, climate- friendly energy source, henceforth referred to as backstop technology.
DeÖnition 2.1 A backstop technology is a technical process that can satisfy all energy needs of the economy at a cost lower than or equal to the cost of fossil fuels and that does not produce any greenhouse gas emissions. This implies that once the backstop technology has been developed there is no demand anymore for fossil fuels.
I make the following assumption about the research process that leads eventually to the development of a backstop technology:
Assumption 2.1 The probability that no backstop technology has been de- veloped until time t is e t, where is the instantaneous probability of the development of a backstop technology which may change with time t.
The probability can also be understood as research intensity. The society can a§ect the choice of via providing public funds for research on backstop technology or by giving subsidies to private companies active in
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the alternative energy Öeld. The choice of , which is given exogenously, and the cost of research function will not be explicitly considered in this paper. The question of interest is how fossil fuel owners react to a given research intensity. All Örms know the instantaneous probability that a backstop technology is developed, . They are also aware of the strategies of all of their rivals which implies that they know the price path. At each point in time the Örms play a Cournot game in the sense that they compete in quantities and Örm j optimizes under the assumption that the other (n 1) Örms do not change their strategies if Örm j changes its strategy. I make the following assumptions about the demand for fossil fuels and the extraction cost:
Assumption 2.2 Demand for fossil fuels can be described by an inverse isoelastic demand function P (R) with P 0 (R) < 0 and an absolute price elas- ticity > (^1) n. Additionally, 2 P 0 (R) + P 00 (R)Rj < 0. This is equivalent to requiring that the Örmís revenue function is strictly concave.
Assumption 2.3 Unit extraction cost, c(Sj ), depend on the stock of the resource that Örm j has at its disposal. The cost function is di§ erentiable with c^0 (Sj ) < 0 and bounded from above.
The resource owner j maximizes the discounted sum of proÖts subject to some feasibility constraints:
max fRj g
0
(P [R] c[S])Rj e ite tdt (2.1)
subject to S^ _j = Rj Sj (0) > 0 Rj ; Sj 0 :
The Örst constraint is the equation of motion for the stock of the re- source. The second constraint requires that the initial stock of Örm j is
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such a setup. The solution to (2.1) also has to satisfy
@Hj @Sj (t) =^ c
(^0) (Sj (t))Rj = ( + i)j _j : (2.6)
Plugging (2.5) in (2.6) yields
( + i) =
P (R) (^) RR Rj c(Sj )
proving the Örst condition of the proposition. The Rj , R = nRj , and Sj in Proposition 1 are sequences of planned equilibrium quantities. They are planned in the sense that if no backstop technology has been developed at time t, then extraction will be the R(t) described by equations (2.2) and (2.3). If a backstop technology has been developed when time t is reached then the amount extracted from time t onwards will be 0. In the following this paper will focus on these equilibrium sequences. If there are no extraction cost and no backstop technology research, equa- tion (2.2) reduces to Hotellingís (1931) condition that the percentage rate of price increase equals the rate of interest. Backstop technology research with its implicit threat that the resource becomes worthless encourages a resource owner to discount with + i rather than i. Note that with positive extraction cost the market structure a§ects the optimal extraction condition. If the market is competitive, n is large, then Rj is small compared to R. This implies that for a competitive market equation (2.2) simpliÖes to
( + i) =
P (R) c(Sj )
while for a monopoly, n = 1, it is
( + i) =
P (R) (^) 1 c(Sj ) :
Note that there are two key assumptions in the model outlined above: the supply of fossil fuel is Öxed and backstop technology research is exogenous. While actual supply is Öxed - there is only so much fossil fuel currently available on earth and the natural production of new fossil fuels takes several hundred millenia - one could also think of supply as the currently known fossil fuel stock, which may increase over time as new stocks are discovered. Backstop technology research is thought of as being independent of fossil fuel extraction and therefore also of the price of fossil fuel. This is a simplifying assumption that makes the model mathematically more tractable. However, one might also think that research e§ort towards developing a backstop technology increases if fossil fuel prices increase: an alternative to fossil fuels is potentially more proÖtable if fossil fuel prices increases. The nature of this relationship between fossil fuel prices and proÖtability of research critically depends on whether the developer of the backstop technology is able to act as monopolistic owner of the backstop technology or not. If research intensity of the privat sector increases with the price of fossil fuels, there are some interesting dynamics. Suppose the government in- creases its spending for backstop technology research and thereby increases . An increase of encourages fossil fuel owners to extract more of their resource today. As a consequence, the price of fossil fuels falls. If private sector backstop technology research responds to fossil fuel prices, then this fall of the price of fossil fuel may decrease research intensity.
and consider how for a Öxed level of S the slope changes in response to a change in . Figure 1 illustrates extraction paths for di§erent research intensities. Note that the market structure a§ects the slope of the extraction path. The slope of the extraction path for a competitive market is
dR dS =^ (^ +^ i)
c(S) P (R)
while it is dR dS = ( + i)
1 c(S) P (R)
n n 1
for a monopolist. So an increase in has a smaller e§ect on the slope of the extraction path of a monopolist than on the extraction path of a large number of competitive Örms. This is in line with the familiar result that a monopolists depletes the resource more slowly if faced with an isoelastic demand curve (Stiglitz, 1976).^3 Figure 1 sketches the extraction paths for three di§erent research inten- sities under the assumption that the number of Örms n is large and that extraction cost are negligible. First, consider a baseline case with no research towards a backstop tech- nology, = 0. The extraction path passes through the origin and its slope is dR dS =^ i The economy starts at time t = 0 at the right-hand side of Figure 1 with a stock S 0 =
Pn j=1 Sj^ (0). The larger the extraction^ R^ the faster the economy moves along the curve towards the origin. Second, suppose that there is a positive probability that a backstop technology will be developed. Equation (2.7) shows that an increase in research e§ort makes the extraction path steeper.^4 The intuition for this (^3) Note that this statement hinges on the assumption of iso-elastic demand. Lewis et al (1979) show that if the demand elasticity increases with quantity consumed a monopolist depletes the resource more quickly than a group of competitive Örms. 4 While the constant probability case has initially a higher extraction than the baseline case with no research, the economy moves faster along the extraction path in the Örst
Figure 1: Planned near future extractions increase when there is backstop technology research.
results is that resource owners prefer to sell their resource earlier rather than later when they face the risk that their resource becomes worthless at some future point in time. The higher the probability that a backstop technology is developed, the steeper is the extraction path. Third, suppose that the instantaneous probability that a backstop tech- nology is developed starts at the same level as in the constant probability scenario and then continuously increases over time, e (t)t^ with ^0 (t) > 0. Then the slope of the extraction path is
dR dS =^ ((t)t^ +^
(^0) (t) + i)
Near future extraction is larger and the extraction path is steeper than in the previous scenario.
case. This implies that at some point in time extraction has to be higher in the baseline case.
