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

• Author: Partain, Roy Andrew
• Position: V. Economic Models of Exhaustible Resources through VI. Conclusions, with footnotes, p. 103-134 - The California-Quebec Adventure: Linking Cap and Trade as a Path to Global Climate Action

5. ECONOMIC MODELS OF EXHAUSTIBLE RESOURCES

   The level of reliance that so many green paradox models have on either Hotelling or Dasgupta Heal models has been demonstrated by the discussion above in [section] 0. This section of the analysis attempts to determine if that reliance on the Hotelling and Dasgupta Heal models is well founded.

   First, the background to the origin of Hotelling's model is provided to yield insight into the function and purpose of the model. Next, the study will explain the working of the model. The focus will then turn to the assumptions of the model, the caveats that Hotelling provided against those assumptions, and to other concerns related to those assumptions. it will be demonstrated that reliance on a Hotelling model for green paradox studies might not be well founded.

   Second, this section will provide a brief introduction to the origins of the Dasgupta Heal backstop models. The reliance of the Dasgupta Heal models on the original Hotelling models will be demonstrated. similar to the previous discussion, this analysis will demonstrate that reliance on Dasgupta Heal models for green paradox studies might not be well founded. This conclusion will be equally valid for both dirty backstop models and green energy backstop models.

   After Hotelling's model of exhaustible resources, backstop technology models are probably the second most common set of models discussed in green paradox research. The backstop models analyze the optimal production path of an exhaustible resource when there is a substitutable alternative energy technology available, known as a "backstop." There are two basic sets of models: those with green energy technologies, and those with carbon-emitting technologies.

   Partha Dasgupta and Geoffrey Heal created these models in the 1970s; (217) the models were developed in response to concerns that exhaustion of fossil fuels could limit economic growth. (218) One model evaluated then-unconventional fossil fuels as a backstop technology while another model evaluated nuclear energy as a backstop technology choice. (219)

   Both models are generalizations of Hotelling's model of exhaustible resources. (220) Thus, many of the concerns on Hotelling's model apply equally to Dasgupta Heal models. (221) Both models make the same mathematical assumptions as in Hotelling's original model: that forced full depletion will occur within the time of the models. (222) Thus, while the models are well regarded for other applications within resource economics, the following analysis will demonstrate that the use of Dasgupta Heal models within green paradox settings might be less than optimal for resolving critical research questions.

   1. Background of Hotelling's Models

      Harold Hotelling wrote "The Economics of Exhaustible Resources" in 1931 due to calls for the regulation of "minerals, forests, and other exhaustible assets." (223) At that time, there were concerns that some actors were rushing to harvest exhaustible resources and causing a surplus of supply, a collapse of pricing, and great resource waste in many cases. (224) These particular concerns gave cause to the nascent conservation movement and led to calls for the government to protect exhaustible natural resources by limiting the periods and quantities of extraction. (225)

      On the other hand, Hotelling also published his article in response to concerns that other actors were colluding to prevent production and to force high prices onto the public. (226) In previous years this collusion had led to the development of anti-monopoly laws, as famously applied to Standard Oil. In his article, however, Hotelling made reference to a more contemporary case from California wherein several post-break-up Standard Oil affiliates allegedly conspired to limit production and protect prices. (227)

      There was clamor for laws to limit production, to encourage production, to impose taxes and royalties, and to provide legal guidance on mineral ownership. (228) Thus, either the resource owners and operators were overproducing, wasting, and losing welfare through excessively cheap prices, or the resource owners and operators were colluding to prevent extraction and refining to limit supply and ensure higher prices. He referred to these two complaints as the "Scylla and Charybdis between which public policy must be steered." (229)

      Before he could assist in the determination of reasonable policy, he needed to build a theoretical device. Hotelling was particularly concerned with the need to handle infinities and the importance of the "calculus of variations." (230) Thus, much of his model was innovative both in its treatment of exhaustible resources and in its adoption of calculus prior to Samuelson's text. (231) Because of those factors, his model has been seminal and heavily relied upon. (232)

      Given the theoretical challenges Hotelling was working against, (233) he developed a clean, clear, but perhaps very narrow, model of an exhaustible resource. But this was no accident; Hotelling repeatedly qualified the use of his model and advised its careful use: "However, there are in extractive industries discrepancies from our assumed conditions leading to particularly wasteful forms of exploitation which might well be regulated in the public interest." (234) This is an example of Hotelling's caveats: that his model differed from realistic decision processes, and also that his model was designed more as a tool to formulate policy that could change the way industries operated in the real world.

      His models were not intended as scientific demonstrations of how things actually worked at the time; rather, the models were predictions of how industries might behave under ideal conditions. Hotelling was also trying to develop a policy perspective based on public welfare; he assumed that eventually the resource would become fully exhausted. (235) Thus, while Hotelling's model of exhaustible resources is without peer, the user must carefully determine if that vehicle is the correct manner to accommodate theoretical needs. (236)

   2. Hotelling's Model: Optimal Depletion Path ways

      Hotelling begins his model by controlling for the prices of the resource over time by relying upon Bernoulli's model of compound interest and the price of the first mineral extracted, po. (237) Hotelling assumes that minerals will be removed in order of the cheapest first, from a supply of the resource in place, a. (238) From these assumptions, he predicts that the quantity to be produced or extracted at any time t is controlled by the price receivable. (239) If the moment of final, and thus full, depletion can be named T, then the total amount to be depleted can be solved as the sum of depletions from time 0 to time T which he solved with an integral against po, tand the interest rate. (240)

      After extending the model to include social utility and welfare, Hotelling finds that under ideal conditions the pricing structures and interest rates result in similar production schedules for both free competition and optimal-welfare depletion rates. (241) He qualified, however, that the model should not be read to support laissez-faire conservation policies for fossil fuel resources because the overall complexity and uncertainty of fossil fuel markets might result in behaviors contrary to the forecasted results: "there are in extractive industries discrepancies from our assumed conditions." (242) This was the focal point of his research: to identify if conservation policies might be required to attain the socially optimal level of production. Hotelling found that while the model said no regulation would be necessary in free competition scenarios, it was nonetheless necessary to qualify these findings and ultimately argue in favor of regulation. (243)

      Hotelling also provided a monopolistic model that resulted in a finding that monopolies over exhaustible resources would lead to slower depletion of those resources than under the free competition model. This model also resulted in suboptimal welfare since monopolies would over-conserve the exhaustible resource. (244)

      Hotelling's rule on exhaustible resource prices can be presented simply as the idea that the net price of a fossil fuel should increase consistent with the interest rate; the particular assumptions and their consequences are discussed below in the next section. (245) More specifically, Hotelling's rule states that when the market is in equilibrium, the net price of a fossil fuel, i.e. the sales price less marginal costs and marginal taxes, should rise at the same rate as the interest rate; the net price of a fossil fuel should increase in relation to the interest rate, but remain temporally equivalent across all time periods. (246)

      Hotelling assumed that the costs of extracting resources increased as the resources are depleted. (247) He compared the fossil fuel price at time t less the extraction costs at time t, as discounted by the interest rate up to that time t against a similar composite value at time s. (248) If these two values were not the same, then production volumes could, and should, be temporally shifted until net revenue is maximized across all time periods. Once that occurs, that consistent value is the temporally consistent net price for the fossil fuel; that value reflects a full and appropriate time discounting. (249)

      The model is often expanded to reflect both the current level of extraction and the total remaining available reserves of fossil fuel in order to facilitate use in econometric studies. (250) The costs of extraction in such a model are said to depend on both matters. (251) Some theorists have preferred a simpler model, one that reduces complexity by assuming a constant marginal cost of extraction. (252)

      Sinn's original green paradox focused on carbon taxes. (253) Hotelling addressed two forms of taxes on exhaustible resources; (254) if those resources were coal or oil then they would have been carbon taxes.

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