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Is a green paradox spectre haunting international climate change laws and conventions?

   A. Models of Exhaustible Resources and Green Policies
   B. Structure of the Study
   A. Sinn's Carbon Tax Green Paradox Models
      1. Anthropogenic Climate Change Created by Market Failures
      2. Rising Carbon Taxes Could Induce Green Paradox Effects
   B. Models of Rising Carbon Taxes
   C. Models of Backstop Technologies
   D. Models of Delayed Implementation After Green Policy
   E. Models of International Carbon Leakage
   F. Michielsen's Integrated Model of Intertemporal and Interspatial
   A. Background of Hotelling's Models
   B. Hotelling's Model: Optimal Depletion Pathways
   C. Hotelling's Models: Caveats and Perspectives
      1. Assumption of Free Market/Monopoly Conditions
      2. Complete Information on Reserves and Depletion Schedules
      3. Conflagration of Full Depletion and Profit Maximization
      4. Hotelling's Rule Part I--Value of Resource
      5. Hotelling's Rule Part II--Flexible Schedule of Extraction
      6. Rising Extraction Costs
      7. Eighth--Secure Property Rights
   D. Dasgupta and Heal's 1974 Green Energy Backstop Model
   E. Heal's 1976 Dirty Energy Backstop Model


Could the United Nations Framework Convention on Climate Change (UNFCCC),), and green laws in general, increase greenhouse gas emissions, and thus worsen the threats and risks of climate change? Many economists examining international responses to climate change fear that green laws may backfire under certain circumstances; a phenomenon known as a "green paradox. (1) In his controversial book, The Green Paradox, German economist Hans-Werner Sinn goes so far as to characterize this backfire as inevitable. (2) Must legal researchers and climate change activists fear that their legal policy efforts will lead to worsening climate conditions? Is there truly no way to avert this green paradox crisis?

Sinn explains the Green Paradox first by referencing human psychology. (3) He claims, "Resource owners aren't stupid ... Arab oil sheikhs, Russian gas oligarchs, and coal barons all have realized that a revolution in the world's energy mix is underway." (4) As a result, he claims that resource owners are selling off more and more fossil fuel resources while legislative efforts to make alternative energy more cost-effective and popular are increasing. (5) This potential green paradox has been echoed by many other economists (6) and surely if there are mechanisms within climate change laws and conventions that give rise to green paradox results, legal researchers, legislators, and climate change policymakers should take caution and consider revamping the existing framework of international climate change conventions and associated domestic policies.

However, most of these authors rely on two economic models originally developed for studying exhaustible resources: the Hotelling and Dasgupta Heal models. (7) If these models are unreliable for green paradox research, then caution should be taken before economists begin to unravel the decades of negotiations that have enabled the existing frameworks.

The research of these circumstances requires the combination of legal requirements and economic models. This present study reviews the concern that certain economic models might be problematic in resolving the first question due to certain assumptions built into those models when they were originally designed for other research purposes. However, the analysis presented is intended for an audience of legal researchers; mathematical materials are minimized in the presentation and the evidence is presented in a format familiar to lawyers. Hopefully this research will better enable other legal researchers to engage in broader research on the potential impacts of green paradox models on future climate change laws and conventions.


The scientific community broadly holds that the cause of global climate change is primarily anthropogenic. (8) To assist in the governance of the dangers posed by global climate change, almost every nation in the world has joined the United Nations Framework Convention on Climate Change ("UNFCCC"); (9) many nations have also agreed to the UNFCCC's Kyoto Protocol. (10) While legislators and policy makers sought to prevent the onset of worsening of climate change by the adoption of this convention and subsequent domestic enactments of similar laws, Sinn raised a concern that these green-intended conventions and laws might in fact give rise to paradoxical results that would worsen and accelerate global climate change. (11) The existence, and potential inevitability, of these green paradoxes is of grave concern to policy makers and legislators concerned with preventing climate change.

Anthropogenic climate change is driven primarily by the emission of greenhouse gases, and consequently, the adopted international conventions and enacted domestic legislations have focused on greenhouse gas emissions. The UNFCCC has a regulatory goal to achieve the "stabilization of greenhouse gas concentrations in the atmosphere at a level that would prevent dangerous anthropogenic interference with the climate system." (12) Nations that have joined under the UNFCCC are required to "formulate, implement, publish, and regularly update ... programs containing measures to mitigate climate change." (13) Those measures are required to focus on reducing emissions and providing for sinks of greenhouse gases. (14) Under the UNFCCC, the regulated greenhouse gases are: (i) carbon dioxide, (ii) methane, (iii) nitrous oxide, (iv) hydrofluorocabons, (v) perfluorocarbons, and (vi) sulphur hexafluoride. (15)

The Kyoto Protocol spelled out specific obligatory mitigation strategies. (16) Parties are directed, inter alia, to: (i) enhance energy efficiency; (17) (ii) provide for greenhouse gas sinks and carbon sequestration; (18) (iii) research, promote, develop and increase the use of new and renewable energy sources; (19) (iv) reduce the various supports and subsidies that enable greenhouse gas emissions; (20) and to (v) limit or reduce greenhouse gas emissions. (21) Further, the Kyoto Protocol mandates that certain emission targets be reached by specific deadlines; a similar element is absent in the UNFCCC. (22)

However, as Sinn and others have demonstrated, (23) in certain circumstances, it appears that such legal policies could backfire and thus increase greenhouse gas emissions. Given the importance to prevent anthropogenic climate change, it thus becomes critical for legislators and policy makers to understand if these green paradox concerns are substantial.

This study attempts to reduce and placate some of those concerns. It attempts to review a large body of theoretical green paradox models to reveal that certain underlying modeling assumptions substantially and materially limit their applicability to the research of green paradox phenomena. As such, this article reveals that most of the existing models that find the existence of green paradox events are unreliable for legal researchers and policy makers.

This paper finds that when certain economic models are relied upon in green paradox research, there are underlying mechanisms that prevent law and policy makers from obtaining clear guidance. As such, increased efforts should be made to promote alternative and more diverse models of green policy impacts on exhaustible resources to better provide the necessary clarity for legislators.


A. Models of Exhaustible Resources and Green Policies

This study takes note that a substantial number of emergent green paradox models are based on a small set of economic models originally developed for studying exhaustible resources. (24) Those models, known as Hotelling and Dasgupta Heal models, contain modeling assumptions that drive certain behaviors within the models. When those models are utilized to research the effects of green laws and conventions, green paradox results have been observed.

Hotelling first developed his early model on depletion rates in between the two world wars; the policy concerns were questionable pricing by resource owners and allegations of over-extraction and wastage of exhaustible resources. (25) He attempted to provide a framework to resolve those and other related policy questions. While his work is seen as seminal today, it was not as commonly cited in its early years. It is worth noting that his models were not exclusively energy resource related, but applicable to any exhaustible resource, such as diamonds or precious metals. (26)

In the 1970s, Dasgupta and Heal expanded on Hotelling's model by focusing on depletable energy resources and adding a choice of an alternative energy source. (27) In this manner, they facilitated the energy policy discussions of replacing one fossil fuel with another or with renewable energy resources. However, despite the focus on energy resources and the potential to adopt an energy alternative, their models remained mathematically similar to Hotelling's model and inherited many of the same assumptions.

The developing awareness of anthropogenic climate change led to the adoption of the United Nations Framework Convention on Climate Change (UNFCCC) and its Kyoto Protocol during the 1990s. (28) In 2008, Sinn took notice that under certain conditions, the legal requirements of green energy policies, when evaluated within a Hotelling-based model, could lead to increased emissions of anthropogenic greenhouse gases. (29) Sinn's forecasted effects, of increased greenhouse gas emissions due to green energy policies, have been labeled as 'green paradox' phenomena. (30) Since his seminal observations, many researchers have developed other economic models of potential green paradox phenomena. (31)

While the potential causes of green paradox phenomena appear diverse, as discussed below at [section] 0, there are only a couple of economic models underlying most of the discussions. They are the Hotelling model of exhaustible resources and the Dasgupta and Heal backstop technology models.

In a survey of twenty articles discussing green paradox phenomena, van der Werf and Di Maria found thirty-two different models of green paradox phenomena. (32) Within those models, twelve were some form of a Hotelling model and eight were some form of a Dasgupta Heal model. (33) For those models discussing carbon prices and taxes and those models discussing the support of alternative energy technologies, only Hotelling models and Dasgupta Heal models were employed. (34) In addressing the delayed introduction of announced climate change policies, two of the three models reviewed were Hotelling models.35 It was not until unilateral policy models were explored that Hotelling and Dasgupta Heal models became minority models, accounting for three of fifteen models, (36) but there were also only eleven articles underlying those fifteen models. Thus, the Hotelling model and its derivative Dasgupta Heal models represent at least nineteen of the thirty-two surveyed models; however, most of the remaining models are slight derivatives of Hotelling's original model. (37) Thus many, if not most, of the green paradox models are predicated on a small class of closely related economic models of exhaustible resources.

Given that the majority of green paradox models rely on Hotelling or Dasgupta Heal models, and that they share many common underlying modeling assumptions, it merits careful consideration if these models are appropriate for research questions related to green paradoxes. In particular, are they open enough to provide proper inspection of the concern, or are they inherently biased in a manner that might prevent their effective use for green paradox research?

The original rhetorical content of Hotelling's model, including certain key assumptions, was largely adopted by Dasgupta and Heal in their models, and has been imported into a variety of green paradox models. (38) Some of those assumptions potentially pose problems of circular results, e.g., if one assumes full depletion then full depletion results in the model make the task of evaluating whether green energy policies cause full depletion difficult to separate from the underlying model's assumption of full depletion. These problems create a situation wherein green energy policy analyses predicated on green paradox models might not be as reliable as they might otherwise appear.

This study attempts to investigate the development of the Hotelling and Dasgupta Heal models and to analyze certain critical elements of those models that might impact analyses of green paradox models. It provides a review of the major green models and establishes their connections to those certain critical elements from the Hotelling and Dasgupta Heal models. The study reveals that those major models do in fact contain those critical elements, and as such, that those models are unable to establish whether certain green paradox phenomena are present or separate from the working assumptions of their underlying economic models. As such, those models might descriptively explain how green paradoxes might occur, but fail to predict whether the green paradox events would actually occur. This paper concludes that while those major green paradox models might describe how green paradox phenomena could occur, they are potentially inappropriate for policy makers to determine if green paradox phenomena would result from certain specific green energy policies. A finding is presented that alternative economic models are needed, including falsifiable economic models, to better evaluate green paradox events and to support the needs of policy makers concerned with the impacts, both expected and unexpected, of their legislative agendas.

B. Structure of the Study

This study investigates the question, are Hotelling and Dasgupta Heal models problematic for the investigation of green paradox models? This study finds that those models might in fact be of concern, especially for legislators and policy makers concerned with the potential effects and side effects of prospective green energy laws.

This study attempts to trace economic models of exhaustible resources from their seminal versions to their application in models of green paradox phenomena. The study explains the central role of key assumptions of those models and how those assumptions affect the resultant analyses into green paradox phenomena. The study will reveal that the original aims and intents of the economic models remain central to their mathematical function yet frustrate efforts to definitively test the potential of green paradox phenomena.

The first part of this article provides a background to the research problem and proposes a means of addressing the issues. The research problem is identified as the practice of green paradox models to rely on a small number of closely related economic models developed for other purposes. Those models are identified as having certain assumptions that might pose problems for the identification of green paradox phenomena. The research question aims to determine whether aims to determine whether the reliance on those few models might pose fundamental problems for the study of green paradox models. The first part also provides a description of the overall study's structure.

The second part of this article provides background on the original development of the green paradox problem and of subsequent classes of green paradox models. First, Sinn's contributions are discussed. His original model of emergent green paradox phenomena is described, and his initial and seminal reliance on Hotelling's model is discussed. Also, his concerns on the inevitability of green paradox problems are reviewed. The subsequent parts provide introductions to the four major classes of green paradox models and to one particular integrated class of green paradox models. Throughout the review of the model classes, the central reliance on Hotelling or Dasgupta Heal models is demonstrated. Even when certain models do not directly derive from those two model classes, they often include assumptions that bring their modeling functions in alignment with those two model classes, thus similar results entail.

The third part of this article provides a detailed review of the underlying Hotelling and Dasgupta Heal model classes. The discussion on Hotelling's model explores the origins and development of his original models. It explains how the models are intended to operate. It provides a detailed listing of Hotelling's central assumptions and demonstrates that Hotelling provided specific caveats on his assumptions and that other evidence can be brought to raise concerns on the applicability of those assumptions to green paradox research. Thereafter, the Dasgupta Heal models are explored with a focus on demonstrating their close affinity with the Hotelling models' assumption, and thus that they would be equally of concern for green paradox modelers. A conclusion is obtained that Hotelling was well aware of the limits of his models, that Dasgupta and Heal extended his models without substantial change to the core assumptions. Thus, the various classes of green paradox models that build on either Hotelling or Dasgupta Heal models also have inherited the same concerns for which Hotelling had previously provided caveats.

This study concludes that models researching green paradox phenomena built upon either Hotelling models or Dasgupta Heal models need to be provided with precautionary adjustments and caveats for legislators and policy makers. Additionally, the conclusion of this study will promote the use of exhaustible resource models that are not substantially based on the assumptions drawn from the Hotelling or Dasgupta Heal models for future research into green paradox phenomena.


This section provides a review of several dominant classes of green paradox models and attempts to demonstrate their common reliance on the Hotelling models of exhaustible resources or on the closely related Dasgupta Heal models of exhaustible resources with back stop energy resources.

This section of the study begins by introducing Sinn's original green paradox concerns and his resultant Hotelling based carbon tax green paradox models. sinn's original presentation of the idea of a green paradox is discussed. The preliminary concerns of sinn are reviewed. Then the original carbon tax green paradox models are described, and his others sources of green paradoxes surveyed. Thereafter, Sinn's concerns on the inevitability of green paradox results are presented.

Following the sinn discussions, reviews are provided of several major classes of green paradox models. Extensive surveys of green paradox models can be found in the literature. (39) A consensus view might be argued to support a four-fold clustering of green paradox models: (i) a class of carbon tax models, (ii) a class of backstop technology subsidy models, (iii) a class of pre-announced policy models, and (iv) a class of international carbon leakage models. (40) Each class of models will be reviewed to demonstrate the extent of their reliance on Hotelling or Dasgupta Heal models.

Finally, a separate model by Michielsen that provides a unifying framework of green paradox discussions is also shown to rely in part on similar economic assumptions to the Hotelling paradigm.

Thus, it will be demonstrated that many, if not most, of the recently published green paradox models rely on the underlying economic assumptions embedded in the earlier models of Hotelling as well as Dasgupta and Heal.

As will be demonstrated below, the green paradox models based on Hotelling models generally found green paradoxes possible, those based on Dasgupta Heal models found them less often, and those based on general equilibrium models were significantly less likely to find green paradoxes. The reasons for this stark and simple result, the dependency on the underlying model form for finding green paradoxes, is reviewed in the following [section][section] 0 through 0.

A. Sinn's Carbon Tax Green Paradox Models

1. Anthropogenic Climate Change Created by Market Failures

Sinn explored the problem of anthropogenic climate change as a result of market failure. To evaluate those green policies designed to control carbon emissions, Sinn began with a Hotelling based model of extraction. (41)

Sinn extended the Hotelling analysis to include a production function that includes land-based capital, such as existing fossil fuels, regular accumulated capital, the carbon-free quality of atmosphere, and time as inputs. (42) The model thus assumes positive and increasing marginal damage to the atmosphere from cumulative fossil fuel use.

Sinn found that there was a singular solution that prevents intertemporal discrimination for this Hotelling model. (43) This unique solution requires a deferral of fossil fuel production; when damage from anthropogenic climate change is taken into account, "a flatter extraction path with less extraction in the present and more in the future is required." (44) The greater the marginal damage to the atmosphere, the greater the reduction in extraction speed is required.

Sinn argued that this deferred production solution is compelling because "it does not involve a value judgment that derives from considerations of inter-generation equity, fairness or sustainability, but follows merely from economic efficiency considerations." (45)

Sinn stated while the world, sans climate change, would operate at one equilibrium, (46) the threat of climate change requires a lower level equilibrium. Nevertheless, Sinn recognized that the world was not following his economic model and its prescribed carbon consumption levels. (47) This was the first problem: the market would continue to over-consume fossil fuels because the costs of climate change were not fully accounted for in market behavior. (48) Climate change could indeed be modeled as a form of market failure.

Sinn identified three major policy issues driving the emergence of the market failures leading to the emergence of global anthropogenic climate change:

i. Intergenerational pricing problems within neoclassical microeconomics,

ii. Equivalent dysfunction of political and economic markets, and

iii. Resource owners' problems of insecure property rights in the resources associated with greenhouse gas emissions.

First, Sinn demonstrated that neoclassical microeconomics failed to provide effective policy recommendations based on the standard model's reliance on modeling multi-generational preferences and utility functions, if known. (49) However, those utility functions and generational preferences are not known in advance of their actual emergence in the future. (50) Thus, the externalities of the carbon emissions could not be appropriately priced and managed by the marketplace due to the lack of complete and accurate information in contemporary time periods.

Second, Sinn posited that policies based on non-market-based ethical considerations would not perform better than the market had already performed; thus, certain political efforts based in 'nirvana ethics' would not be able to cure the market failures. (51) Sinn noted that voters are the same actors as those driving the market; if the actors cannot act clearly in their market transactions, then he asks why should democratic politics result in more clarity regarding the costs of climate change? He answered that similar dysfunction would avail. (52) Thus, Sinn argued, politicians would need to find authority beyond current voters. Could they argue for the needs of future generations, and would politicians be better placed to opine for those future voters than the prospective future ancestors of those future constituents? Again Sinn argued no, that politicians do not have a claim to superior insight into the values of future voters vis-a-vis those future voters' currently voting prospective ancestors. Essentially, those actors currently in the marketplace and currently voting already took into account the effects of their actions on their future descendants. (53)

Sinn detailed the ethical concerns that certain economists have raised that free market solutions cannot be ethically relied upon because interest rates, and thus discount rates, are likely biased against future generations in over-incentivizing current consumption against long run welfare growth. (54) Sinn queried to whom the policy maker should turn to solve that dilemma. He argued that if the 'ethical economists' were correct in their concerns then there could be no solution. Ergo, that the position of 'ethical economists' is either wrong or irrelevant. (55) Moving past 'ethical economists,' Sinn further argued that parents did in fact take their descendants' needs into account as the parents interacted in the market, and thus, government involvement to allow philosophers to advise contrary to those parents would be poor policy. (56)

Sinn proposed that weak assignment of property rights drove part of the market failure. Sinn explored the concern that resource owners often face uncertain property rights to their assets, and the temporal aspect of control led to accelerated depletion of their assets in an attempt to maximize revenues whilst in possession. (57) He focused on the role that states with dictators play in owning fossil fuel resources. Sinn highlighted that their dictators face uncertain terms in office, and that these concerns will imperil otherwise functional markets to overproduce hydrocarbons. (58)

Second, Sinn returned to his property right concerns; policies to deny current fossil fuel resource owners from the benefits of their assets would be defective because the introduction of additional risk of instantaneous expropriation from resource owners would accelerate the production of fossil fuels even more than the free market would have. Thus, climate change policies should be careful to preserve existing property rights, which in turn means that resource owners should not be faced with temporal limits of production nor should they face other bans on production and resultant profits.

Sinn introduced the idea that the market could respond to green energy policies in ways worse than the previous two results. Sinn cautioned that certain green policies could result in increased greenhouse gas emissions instead of their targeted reductions of the same; this type of unexpected policy backfire he called a 'green paradox.'59

2. Rising Carbon Taxes Could Induce Green Paradox Effects

Sinn began his study into green paradoxes by adopting the Hotelling model. (60) Sinn's variant on this model assumed constant marginal costs, but he also assumed that the costs of extraction increased as overall depletion occurred. (61) Sinn also added a tax cost to the extraction costs. Several cases are notable:

i. A constant tax left the production volumes in their original schedule at their original volumes, but with a drop in price. Overall emissions remain unchanged. (62)

ii. A tax that increased in latter periods would require a shift of production from those latter expensive periods into earlier periods due to the arbitrage assumed by Hotelling's rule to equate net revenues from all time periods. (63) However, the initial price of the fossil fuel will be reduced in the earlier periods, in contrast to the equilibrium price without a tax. (64)

Sinn's observation was that Hotelling's rule has perverse effects on green energy policies that attempt to reduce emissions by providing negative incentives via carbon taxes. While constant carbon taxes under Hotelling's rule would not reduce production volumes, rising carbon taxes would shift extraction to earlier time periods. This second result was Sinn's primary green paradox. (65) Because the Hotelling model assumed that the fossil fuels would be fully depleted, (66) an increase in production during one time period will cause a corresponding decrease in another; high costs in a latter period encourage activity to occur earlier. This gave rise to Sinn's central concern:

"However, if firms react to a change in demand today by extracting less, they must extract more tomorrow, and vice versa, and it is by no means obvious that the demand-reducing measures discussed in Sect. 2 will be able to tilt the extracting path in the right direction." (67)

Thus, Sinn demonstrated that Hotelling's model could be leveraged to demonstrate the existence of green paradoxes; (68) however, those demonstrations should come with Hotelling's caveats. Green paradoxes appear to result from the temporal arbitrage built into the model by its reliance on Hotelling's rule. (69)

Sinn considered two different tax models to validate his green paradox concerns:

(i) A cash flow carbon tax, (70) and

(ii) An "ad valorem sales tax on extraction." (71)

He relied on these two carbon tax models to demonstrate that under a Hotelling model, by providing incentives to avoid fossil fuel production in later time periods, the policies also created countervailing incentives to increase production of fossil fuels in earlier time periods. (72) "[T]he resource owners will anticipate extraction ... to compensate for the rising tax rate. Global warming will accelerate." (73) And by 'anticipate,' Sinn clarified that the fossil fuel resource owners "will try to anticipate the price dampening effect by selling more in the present and less in the future...." (74)

Thus, those two green tax policies would result in additional anthropogenic emissions of greenhouse gases: "The green paradox implies that such a policy is likely to backfire and create even more harm for the environment by speeding up global warming." (75)

Sinn stated that the green paradox could result from other causes, not merely from carbon taxes, and included these examples of alternative causes of green paradoxes: (76)

(i) Energy Efficiency:gains in energy efficiency could reduce energy demand from fossil fuels in future time periods; (77)

(ii) Green Energy: increased supplies from green non-fossil fuel energy sources could reduce energy demand from fossil fuels in future time periods; (78)

(iii) Non-Green Energy: increased supplies from non-green non-fossil fuel energy sources could reduce energy demand from fossil fuels in future time periods; (79)

(iv) International Leakage: differing policies between states on abating the causes of climate change. (80)

He stated that the above sources of green paradox could be strengthened by governmental subsidies, by quantity constraints, or by moral persuasion or dissuasion. (81) Additionally, the more the green paradox occurred, and thus the more anthropogenic climate change occurred, the public would increasingly support additional efforts to reinforce those policies, so long as it was contra-factually misunderstood that such policies were reducing emission. (82)

Sinn concluded that "markets unfortunately are unable to find the optimal path" to avoid anthropogenic climate change because they cannot resolve the optimal path between the stocks of carbon pre-combustion and those post-combustion. (83) The problems of incomplete climate change information in fossil fuel pricing and alternative energy pricing, plus the challenges of insecure property rights, leads to the over-extraction and overconsumption of fossil fuels. (84) Sinn expected that political efforts to address climate change will either be fiscally wasteful in not accomplishing emission reductions or worse will create green paradoxes and worsen the trend against no emission policies at all. (85)

In his conclusion, he offered no new solutions that he had not previously ranked from likely to infeasible. (86) He is left stating, "[t]here is a green paradox." (87) Sinn's sense of frustration rings clear, but it remains largely predicated on the internals of Hotelling's models and should be guided by the caveats noted below in [section] 0.

B. Models of Rising Carbon Taxes

The policy concept within this class of models is that authorities would apply some form of a carbon tax or fee upon either the extractors or combustors of fossil fuels to provide the economic incentive to reduce the usage of fossil fuels. (88)

Exemplar models of this form of green paradox include Gerlagh, (89) Hoel, (90) and Habermacher. (91) These models were built on earlier suggestions to have a temporally increasing carbon tax to phase-out the usage of fossil fuels. (92) Van der Werf and Di Maria provided a taxonomy of this model class. (93) They reviewed both Hotelling and Dasgupta Heal versions of the models. (94)

Van der Werf and Di Maria's Hotelling model begins with a roster of assumptions about the depletion decisions of the operator. The model includes an 'extraction path' or depletion function of a stock resource, (95) an exogenously determined price for the fossil fuel per unit, (96) a tax on the carbon emissions set to match a unit usage of fossil fuel, (97) and an increasing cost of production for the fossil fuel: (98)

(i) The interest rate, r, (99) is determined exogenously. (100) This implies that they obtain capital from fully competitive capital markets, and that their internal sources of capital, if existent, are not competitive with r.

(ii) The resource owners are assumed to be price takers. (101)

This assumption is standard for fully competitive markets with competitive vendors of perfectly substitutable goods; the price of the resource is governed by Hotelling's rule.

(iii) The resource owners optimize inter-temporal profits by choosing an extraction path over time; but the model assumes/requires full depletion by the final time period. (102)

(iv) The model assumes that the cost of extracting units of fossil fuel increases over time as more cumulative extraction occurs; (103) i.e., the more that has already been extracted, the more expensive it will be to extract the next unit. (104)

(v) A perfectly substitutable alternative green energy source exists, known as a 'backstop technology.' (105) It has a predetermined price; b. The model assumes that when the price of the fossil fuel exceeds b, the consumers will no longer purchase the fossil fuel at all (106)

(vi) The resource owners and operators will always be able to sell every unit of produced fossil fuel, because the model assumes that the market will continue to completely clear even as the price of the fossil fuel approaches infinity. (107)

As to these assumptions, the model operates by assuming that from time zero until the end time, the whole reservoir of fossil fuel will be depleted. (108) This provides an interesting revelation, in that the model is essentially assuming that the returns to the producer grow at the interest rate, r. (109) This condition is called the Hotelling rule, and its means that the decision maker is temporally indifferent as to when fossil fuels are produced. This is because the profits from all time periods are effectively increased at the same rate as the discount factor of net present value calculations. (110) Van der Ploeg and Withagen refer to the centrality of the Hotelling rule in establishing the green paradox models; they deny that extraction costs are relevant considerations for when crude oil is produced and that the asset value of the reserves is what determines when crude oil is extracted. (111)

Since a Hotelling model requires the complete depletion of the resource, (112) and because the model invokes the Hotelling rule, taxes on later year production and sales will provide an incentive to reschedule those volumes to years without those taxes, i.e. to earlier years. (113) Because the Hotelling model assumes complete depletion, a carbon tax or fee can only reschedule the production and sales of those fossil fuels, it cannot reduce their production. (114) If the carbon tax, [tau], grows at the same rate as r, then no rescheduling is effected because the tax is essentially the same at all time periods. (115) If the growth of the tax rate exceeds the interest rate, then the rescheduling to the earlier time period will occur. (116) While not in van der Werf and Di Maria's model, the equation holds the interesting policy point that if the tax starts high, but then drops, producers can foresee that result then they will increase production of fossil fuels in later time periods. (117)

Van der Werf and Di Maria argued that when the carbon tax is rising, a green paradox will result because the producers will optimize their production volumes to be sold prior to the switch over to alternate green energy sources. They also argued that a green paradox would not occur if the tax grew equal or less than the interest rate. (118) However, this result would hold under any Hotelling model that faces a shortened production time-frame, regardless of causation, due to the requirement of full extraction, above. Thus, whenever the fossil fuel producer reasonably anticipated that the imposition of a carbon tax would suffice to price the fossil fuel higher than the alternative, the producer would be forced by the model to extract the fossil fuel prior to that point in time. Thus, relying on standard Hotelling models will result in green paradoxes, so long as the carbon tax creates an earlier endpoint of the time-frame.

The Dasgupta Heal model is introduced to enable the producer to decide to cease extraction prior to complete depletion by contrasting the cost of extraction against the price of an alternative energy technology. (119) As the model builds upon the Hotelling model, similar concerns as discussed above are inherited, and to that extent their discussion is not repeated hereunder.

For green paradox discussions, the Dasgupta Heal model has two unique effects. First, the model provides a point in time when fossil fuel will no longer be extracted due to its comparatively high costs. Second, the model enables some amount of fossil fuel to remain. These changes could reduce the artificiality of the Hotelling results with a forced temporal shift to earlier periods simply because the model requires complete depletion.

The Dasgupta Heal model assumes a 'backstop' green energy alternative; any introduced carbon tax will effect a reduction in the price that will terminate fossil fuel extraction. (120) The model creates a trigger that the fossil fuel ceases to be extracted when the costs of extraction, after a certain amount of depletion, reaches the same price as the alternative green energy source. (121) If a carbon tax is added to the price of fossil fuel extraction, then the cost of extraction plus the carbon tax needs to remain under the price of the alternative energy source. Equivalently stated, the cost of extraction needs to remain below the price of the alternative reduced by an equivalent value to the carbon tax. (122)

The model provides that the carbon tax effectively reduces the total amount to be extracted; it also affects when that extraction occurs. If the carbon tax rises more slowly than the interest rate, then the carbon tax is more expensive in earlier periods and extraction shifts to later time periods. This also lowers net emissions; thus, no green paradox results. (123) This is also true when the carbon tax rises equally with the interest rate; again, no green paradox. (124) However, when the carbon tax rises quicker than the interest rate, making future extraction more expensive than current, then a green paradox will result. (125) In that case, time-frame fossil fuel extractions remain reduced. (126)

A two-period Dasgupta Heal model with endogenous investment in the alternative green energy source revealed that the behavior of the extraction costs determined if a green paradox resulted or not. (127) If the costs of extraction rose sufficiently fast enough, then a green paradox could result. Otherwise, under flat or decreasing extraction costs there were no resulting green paradox results. (128)

So, the Dasgupta Heal models provide less opportunity for a green paradox than the Hotelling models allowed, above within the current section. This would primarily appear to be due to the modification to the Dasgupta Heal models to allow incomplete depletion whereas their Hotelling models required full depletion of the reserves. Thus, when presented with either economic incentives or shorter time frames, the Hotelling models required time-shifting the production schedules to the earlier time frames and ensured a green paradox for earlier time periods. The Dasgupta Heal models are not as readily green paradox yielding, in that only when certain conditions avail can green paradox results occur, especially so when modified as noted above. A green paradox could occur under a Dasgupta Heal Model only when the cost of extraction increases in later periods, due either to carbon taxes or higher costs of extraction due to depletion.

But much depends on the time value of money as measured in the interest rate versus other changing cost factors. It is perhaps not odd to find that if future costs are too high, then business owners will attempt to make more profit in earlier time periods. If the overall effect of carbon taxes is to make future production of fossil fuels more costly, then perhaps it would be reasonable to expect that fossil fuel producers would attempt to produce more in the earlier periods.

C. Models of Backstop Technologies

The policy concept within this class of models is that authorities would apply some form of a subsidy to stimulate the development and feasibility of alternative green energy sources to provide the economic incentives to reduce the usage of fossil fuels. (129) Exemplar models of this form of green paradox include van de Ploeg and Withagen, (130) Gerlagh, (131) Grafton et al., (132) Hoel, (133) Hoel and Jensen, (134) and Strand. (135) Not everyone agrees that these models are distinct from the previously examined carbon tax models, (136) in that taxes and subsidies can be seen as two means to the same economic policy ends. (137)

The models assume economic support in the form of government provided subsidies to reduce the effective price of alternative green energy sources. (138) Again, the Hotelling and Dasgupta Heal models are the dominant templates for research. (139)

The first major assumption of the subsidy model, under a Hotelling depletion model, is that the final price of depleted units will equal the price of the backstop technology of the alternate energy source. (140) It follows that the lower the effective price of the substitute, the earlier that fossil fuels will be priced out of the market; (141) thus the policy becomes how to lower that price, b. However, under the Hotelling depletion model, the resource owner would need to accelerate the production of the fossil fuel to meet that new alternative energy price. (142) That reaction would lead to both additional volumes of fossil fuels production at each time period and also to reduced prices for those increased volumes of fossil fuels. (143) A green paradox is sure to occur. The stronger the subsidy-effect on the alternative energy source, the stronger the resultant green paradox. (144) A similar model was extended to consider the role of increasing extraction costs and of damages from cumulative carbon emissions. (145) That model found that the marginal cost of the backstop technology was determinative in whether the fossil fuel fields were fully depleted or not due to the green policy of subsidizing the backstop technology. As might be expected, the Hotelling depletion model found that the field would be fully depleted, but the Dasgupta Heal model found that the field would not be fully depleted; thus the Hotelling model provided an assured green paradox but the Dasgupta Heal model was dependent on the marginal costs of the backstop technology in creating a green paradox.

A form of international leakage can be seen within this context, if two countries set subsidies that effectively create different backstop prices, bs, for their domestic consumers. (146) In that case, one country will be delayed in the switch to the backstop and additional fossil fuel will be extracted alongside additional carbon emissions; a green paradox will result. (147)

When the Hotelling model is modified to enable incomplete depletion and competition between the fossil fuel and the backstop technology, (148) there are interesting results. (149) The optimal carbon tax would not be an exponentially rising tax, but a carbon tax growing at a slower rate than the interest rate. (150) This is to encourage the delay of production by making near-term volumes effectively more costly to produce than latter period production volumes. (151)

But that model then analyzes the next best policy if carbon taxes are not feasible; however, the analyses are welfare driven, not emission volumes driven. (152) It discovers that there are two cases: (i) when fossil fuels are cheaper than the backstop; and (ii) when the backstop is cheaper than fossil fuels. (153)

i. When the backstops are more expensive, the model suggests optimal policy would be to increase the price of the backstop by taxing it. (154)

ii. When fossil fuels are more expensive, the model suggests optimal policy would be to decrease the price of the backstop by subsidizing it. (155) The lower the backstop cost, the greater the potential for incomplete depletion of the fossil fuel reserves. (156)

These policy results reflect a green welfare function, (157) not an overall emissions concern, so the findings are not determinative, directly, of the incidence of green paradoxes. The overall result is that initial conditions are critical and complicated, green paradoxes may result under certain conditions. But overall, the Hotelling paradigm of full depletion causing models to suggest green paradoxes remains a concern.

D. Models of Delayed Implementation After Green Policy Announcements

The types of models presented hereunder are models that study the behavior of exhaustible resource producers if the actors, be they producers or consumers, learn of upcoming policies prior to the implementation of those policies.

"In reality, most environmental policies (or even government policies in general) do not come as a surprise. Coming to an agreement (within a government, or between different governments) and administrative procedures cost time." (158)

In those scenarios, the producer has at least one time period without the implementation of the new policy, but with awareness that such policy will be implemented in a later time period; thus, the producer can make strategic use of that knowledge to ensure maximum profits. The first two models are Hotelling models with forced full depletion. The producers are limited in the time periods within which to complete depletion so they accelerate and increase emissions in the term prior to the implementation of the policies. The other model presented demonstrates that the environmental policies have impacts on consumption and cause a reaction to accumulate capital to prevent reduced consumption. This savings strategy in turn accelerates demand for fossil fuels due to their capital efficiency even without the Hotelling assumption of forced full depletion.

Van der Werf and Di Maria found that the dominant model type used in this line of research was the Hotelling model of exhaustible resources. (159) Di Maria et al. relied on a Hotelling 158 159 model (160) and Eichner and Pethig's general equilibrium model was an extension of the Hotelling framework. (161)

Di Maria et al. provided a time before and after the imposition of a carbon tax. In effect, they studied a particular form of a rising carbon tax, one that had a period of zero tax rate. (162) The carbon tax acts as a constraint against production, and making the Hotelling assumption of forced full depletion, the model derives that production will be rescheduled to an unconstrained time period. If the tax rate is rising as in this model, then emissions will be accelerated causing a green paradox. (163)

Eichner and Pethig's general equilibrium model relied on a three-state Hotelling model that included two time periods. (164) This model broke out the regions into a fossil fuel exporting state, a state with enforced green policies, and a state lax in green policy enforcement. (165) Again, the models make the Hotelling assumption of forced full depletion. (166) Also, the green policies are only imposed in the second time period. (167) So, although Eichner and Pethig set their model in a general equilibrium setting, instead of the partial equilibrium setting of Di Maria et al., the overall result is the creation of a policy incentive to produce more carbon emitting fuels in an earlier time period because of de jure limits to production in the later time period. (168)

Smulders et al. took a different approach in avoiding the exhaustible resource model. (169) They explicitly did not assume forced full depletion, what they refer to as the 'scarcity condition.' (170) Instead, they looked to the scarcity of capital and of the decisions leading to its accumulation. (171) By taking this approach they shifted the focus from energy supply to energy demand. (172) Their model demonstrates that when capital accumulation can offset limited energy supplies, and when consumers can react to accumulate capital to prevent loss of future consumption opportunities, a green paradox will result from the increased savings in the near term. (173) It is direct because consumers do not want to experience a decline in energy consumption that fossil fuel consumption will increase in the near term. (174) What appears to be driving this model, deeper than the capital efficiencies of different energy supplies or their intertemporal elasticities of substitution, is that the consumers are facing a shortage of time to accumulate capital, which is derived from the cheaper fossil fuel. (175)

E. Models of Interna tional Carbon Leakage

International carbon leakage can be broadly summed up as the idea that if fossil fuels are not used in one location, then they might be used elsewhere. The concern of an emissions-increasing green paradox as a result of the relocation of that usage is a secondary level of analysis separate from the original leakage analysis. Leakages occur because of economic incentives to relocate the usage of fossil fuels; there are multiple potential incentives discussed in the literature.

Van der Werf and Di Maria identify five basic channels of carbon leakage. (176)

First, the marginal damages channel encompasses the concept that while emissions abatement might be unilaterally undertaken, the benefits of that abatement will accrue to everyone globally since it is the total amount emitted to the whole atmosphere that determines climate change hazards. (177) One country underwrites the benefits of all, thus creating the opportunity for many to free ride those unilaterally-paid costs. Assuming that countries set their marginal costs of abatement equal to their marginal benefits of reduced climate change hazards, Hoel has found that the spill-over benefits from a unilateral reduction in emissions will impact the marginal analysis of other countries. (178) Nevertheless, when countries behave uncooperatively, Hoel found that overall emissions were reduced. Thus, the marginal damages channel was not likely to result in green paradox phenomena. (179)

Second, the energy market channel captures the effect of a unilateral reduction in emissions on the global market for conventional fossil fuels. (180) For example, if one country reduces its purchases of conventional fossil fuels, more quantity will remain on the market for others to purchase. The results depend on price elasticities of demand and cross-price elasticities of demand. (181) Of the four models reviewed, three of the four were Hotelling or Dasgupta Heal models; the remaining model was a static adjusted general equilibria model (AGE). (182) The two Hotelling models found possibilities of green paradox phenomena, which is no surprise. (183) The Dasgupta Heal model introduced a new policy option: states could acquire reserves-in-place and decide to sequester the reserves permanently and prevent the carbon from ever being emitted. (184) Thus, the results of the energy market channel models depended heavily on the underlying models of exhaustive resource utilization; those that found substantial likelihood of green paradoxes were likely to be based on Hotelling models.

Third, the terms of trade effect channel is similar to the previous energy market channel, except that it examines the spillover consequences for products made or transported using fossil fuel inputs. (185) The policy concern is that while a country might ban the use of fossil fuels in its own jurisdiction, its citizens might import products from countries without that policy and defeat the policy's purposes. (186) A key concern is the substitutability of the goods between countries and the incidence of transport costs. (187) Paltsev reported finding it very difficult to identify green paradoxes even with high substitutability, while Burniaux and Oliviera Martins found negative leakage (i.e. net emission reductions) from products with low substitutability. (188) A variety of studies have been undertaken; negative leakage is generally seen as more likely than positive leakage, and much more likely than the possibility of green paradoxes. (189)

Fourth, the international trade in factors of production channel--which perhaps should have been called the international capital channel--examines the movement of capital when some countries constrain the use of fossil fuels and other countries do not. (190) The primary concern, is that capital might move to follow ease of use and flow to those countries with more lax green policies. It is also important to note that the surveyed models are the same models surveyed for the terms of trade effect channel; thus, the lack of a green paradox finding is extended to these models. (191)

Finally, the technology change/technology spillover channel is presented; (192) however, this is a more hopeful topic than the worrisome lines of research explored above. The technology change/technology spillover channel explores the potential for unilateral action on green energy policies to spill over into other countries. In this scenario, technology to reduce emissions becomes distributed across countries that did not invest in the costs of developing it. (193) Practically every surveyed model revealed negative carbon leakage, which one would assume would be the outcome. (194)

Thus, international carbon leakage models provide an interesting result: less evidence of increased emissions from green policies. Furthermore, the relationship between economic model foundations and green paradox research results was substantial: Hotelling models yielded green paradoxes, Dasgupta Heal models could yield green paradoxes, and the other models yielded evidence contrary to the presence of green paradoxes. The importance of the affinity for Hotelling models and the findings of green paradox phenomena appear to hold for this class of international carbon leakage models.

F. Michielsen's Integrated Model of Intertemporal and In terspa tial Leakages

While most articles accommodate various causes of green paradoxes with different mathematical presentations, Michielsen presents a singular model that can accommodate both intertemporal and interspatial concerns, as well as various backstop technologies. (195) Michielsen refers to intertemporal concerns as instances of green paradoxes, but labels the spatial concerns as carbon leakage. (196) He identifies two potential causes of green paradoxes: (i) carbon taxes that increase over time; and (ii) the future development of backstop technologies. (197) He then expands the backstops category in two dimensions for a total of four possibilities; there are cheap and expensive backstops, and there are clean and dirty backstops. (198) He identifies two potential causes of carbon leakages: (i) the relocation of dirty industries from countries with effective green policies to those states lacking effective policies; and (ii) the application of green policies in one set of countries that could cause the price of carbon emitting fuels to fall and increase the demand for them in countries without effective green policies in place. (199)

Michielsen's basic model makes several notable assumptions:

i. the existence of an exhaustible resource, a clean backstop, and a dirty backstop; (200)

ii. the exhaustible resource has zero costs of production, but the backstops have constant marginal costs; (201)

iii. the resource owners will always fully deplete their exhaustible resource; (202)

iv. reliance on Hotelling's rule for inter-temporal valuations; (203) and

v. the energy resources are imperfect substitutes for each other. (204)

He also assumes that the prices of the exhaustible resource will be the same in both countries for his interspatial model. (205)

Michielsen's analysis of rising carbon taxes finds that Sinn's carbon-pricing green paradox occurs if the demand for the dirty backstop is inelastic with regards to the exhaustible resource in both time periods. This inelasticity means that the tax effectively reduces the price of the exhaustible resource in the earlier time period vis-a-vis the latter period. (206) If the exhaustible resource and the dirty backstop are very close substitutes in both time periods, Michielsen finds that the carbon tax raises the price of the exhaustible resource in both time periods, and increases emissions in the earlier period. (207) However, should demand for the dirty backstop be elastic in the latter period, then the effect of the carbon tax is to reduce prices in both time periods and to reduce emissions in the earlier time period. No green paradox results in this situation. (208)

When Michielsen expands his analysis of carbon taxes to an interspatial setting, he reports that the calculations are practically identical to those of the inter-temporal model. (209) As such, carbon leakages result in green paradoxes in the same two cases as in the inter-temporal settings. These carbon leakages are controlled primarily by the degree of product substitutability and demand inelasticity, with the proviso that the time periods are restated as the two locations.

Michielsen's analysis of backstop technology provides for ready reference against the clean backstops of Dasgupta and Heal, and against the dirty backstops of Heal. (210) Michielsen makes the assumption that once a backstop technology is available in one country, the technology would readily become available in all countries. This assumption eliminates the need to develop an interspatial analysis of backstop technologies. (211) In developing his inter-temporal model of backstop technologies, Michielsen renews his assumption of full depletion of the exhaustible resource. (212) He finds the potential for a green paradox more likely under a backstop scenario than under the earlier carbon pricing models. (213) However, the complexities of backstop models are nontrivial. For example, a drop in the price of the exhaustible resource in the earlier period, caused by its increased production, will reduce demand for a close substitute dirty backstop; thus, overall emissions will potentially result in some cross-netting to reduce overall impact.

Michielsen demonstrates that the more perfectly the clean backstop serves as a substitute for the exhaustible resource, the stronger the likelihood that a green paradox will result. (214) He evaluates the scenario when the clean and dirty backstops are perfect substitutes for each other and finds several results: (215) Green paradoxes were obtained:

i. When the clean is cheaper than the dirty backstop in both periods, then the dirty backstop is never used and exhaustible resource owners accelerate production and cause a green paradox.

ii. When the clean is ex ante cheaper than the dirty backstop in the second period, then subsidies will reduce reliance of the dirty backstop in the earlier period and increase depletion speed of the exhaustible resource.

iii. When the dirty backstop and the exhaustible resource are perfect substitutes, as conventional crude oil and shale oil are, a green paradox results when the price of crude oil in the latter period is lower than its dirty backstop. (216)

But green paradoxes did not occur:

iv. When the dirty backstop is cheaper in both periods, and if subsidies fail to alter that condition, then no effective change in emissions would occur.

In summary, Michielsen found a wide variety of scenarios wherein intertemporal and interspatial green paradoxes could occur, especially with the existence of backstop technologies that are the primary hopes of most green energy policies. Those findings are predicated on Michielsen's use of certain Hotelling assumptions, such as full depletion and Hotelling's rule, even though his model does differ from a traditional Hotelling model.
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Title Annotation:I. Introduction through IV. Classes of Green Paradox Models, p. 61-103; The California-Quebec Adventure: Linking Cap and Trade as a Path to Global Climate Action
Author:Partain, Roy Andrew
Publication:UCLA Journal of Environmental Law & Policy
Date:Jun 22, 2015
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