چرخه هایی در قیمت های منابع غیرقابل تجدید با آلودگی و آموزش همراه با کار

We study how environmental regulation in the form of a cap on aggregate emissions from a fossil fuel (e.g., coal) interacts with the arrival of a clean substitute (e.g., solar energy). The cost of the substitute is assumed to decrease with cumulative use because of learning-by-doing. We show that optimal energy prices may initially increase because of pollution regulation, but fall due to learning, and rise again because of scarcity of the resource, finally falling after transition to the clean substitute. Thus nonrenewable resource prices may exhibit cyclical behavior even in a purely deterministic setting.

More than 85% of commercial energy today is supplied by the three major fossil fuels, namely coal, oil and natural gas. Each of these resources, in varying degrees, is a major contributor to environmental problems such as global warming. These resources are also nonrenewable. However, there are many clean substitutes such as solar and wind energy which are currently more expensive in the cost of producing a unit of electricity or usable heat. Empirical evidence suggests that the cost of these clean substitutes fall as they begin to acquire more market share (McDonald and Schattenholzer, 2001). In this paper, we examine the substitution of a clean energy source for a polluting one in energy production. For example, solar or wind energy are clean but expensive substitutes for coal in electricity generation.1 We posit a scenario in which an extension to the Kyoto Protocol or another international agreement imposes a binding target for atmospheric carbon.2 A forward-looking social planner internalizes the intertemporal knowledge spillovers from using the clean technology. We ask: if there is significant learning in the clean substitute, how will that affect optimal energy prices and the process of substitution? Many studies have looked at the problem of nonrenewable resource extraction as well as learning-by-doing in new technologies. However, the focus of our paper is on the role played by environmental regulation in this substitution process. Specifically, we ask how a cap on the stock of pollution or, equivalently, a carbon concentration target may affect the switch to the clean substitute when the latter exhibits learning effects. We characterize this problem by assuming a fairly general cost specification for the nonrenewable resource and the learning technology. Unit extraction costs for coal increase with cumulative depletion. The average cost of solar energy is assumed to decrease with cumulative use but increase with the quantity supplied each period. For example, the unit cost of a solar panel may decline over time, the higher the number of panels built in the past.3 But at any given time, the unit cost is increasing and convex with respect to the number of units supplied. This is quite realistic because as more and more solar units are brought into the market at any moment, they may have to be deployed in regions that are less favorable to solar energy such as those with lower incidence of solar radiation or in dense urban areas with higher installation costs. There are several optimal solutions to this model, which we describe in the paper. But the key result arises when the clean technology is used before regulation becomes binding.4 We show that in the initial period, energy prices rise because of scarcity and impending regulation. As soon as regulation becomes binding and the stock of pollution is at its maximum level, energy prices start falling. Clean energy use increases during this period but emissions cannot increase because of regulatory constraints. However there comes a time when resources are scarce enough that regulation no longer binds, and prices rise again, driven by the scarcity of the fossil fuel until it is no longer economical to mine higher cost deposits. This rise in prices also leads to an increased adoption of clean energy. Finally the polluting fossil fuel becomes too expensive to mine and the clean alternative takes over as the sole supplier of energy and once again, energy prices fall because of learning. In standard models of Hotelling, the price of a nonrenewable resource rises until a clean substitute is used. If the substitute is available in infinite supply and fixed cost, energy prices rise until this transition and then stay constant. When learning in the backstop is included, energy prices rise until the resource is economically exhausted then fall once substitution to the backstop has taken place (e.g., see Oren and Powell, 1985). We show that with both learning and regulation, optimal energy prices may rise and fall successively. This long-run non-monotonic behavior of energy prices is counter-intuitive and occurs because of the interplay of regulation, scarcity of the fossil fuel and learning in the clean technology.5 It occurs when it is optimal to deploy the clean technology before regulation binds or during it, although in the latter case, the rise and fall of energy prices is not as pronounced, as shown later in the paper. A recent review of the empirical significance of the Hotelling (1931) model suggests that “its most important empirical implication is that market price must rise over time in real terms, provided that costs are time-invariant” (Livernois, 2008). Livernois also points out that empirical tests of the model have been generally unsuccessful. Our results suggest that in the long run, resource prices may exhibit significant structural variations driven by regulatory policy and market forces, which may result in alternating phases with secular upward or downward price movements. Although for convenience, the paper is motivated in terms of coal and a clean substitute such as solar energy, it is equally applicable to other settings, such as the monopoly production of oil by a cartel such as OPEC with a competitive clean technology (e.g., a hydrogen car). The solution predicts that oil prices may rise, followed by a decline when emissions constraints become binding. They rise again when regulation ceases to bind, followed by an eventual decline when there is a complete transition to the clean substitute. What is surprising is that energy prices may start decreasing upon attaining the regulated level of emissions. In reality, there may be many short-run factors (e.g., speculation in commodity markets) that are at play in the determination of energy prices, but these results may at least partly explain the fluctuations in the prices of fossil fuels such as crude oil, natural gas and coal in recent years at a time when there is a general expectation that environmental regulation will bind at some time in the near future. The model then predicts that if say, an international treaty imposed a target of 450 ppm (parts per million) of carbon,6 we would expect prices to rise initially but start decreasing as soon as this constraint becomes binding. When the constraint no longer binds and we fall below the 450 ppm level, energy prices will rise again, and finally fall when we make a complete transition to the clean substitute. The textbook Hotelling model, with learning or pollution regulation, does not predict this cyclical behavior. Our paper also contributes to a large literature on the role of environmental regulation in generating endogenous technological change, and the importance of considering these incentives in setting policy. Arrow (1962) introduced the notion of learning-by-doing, where cumulative experience rather than the passage of time or directed investment leads to lower marginal production costs. Newell et al. (2002) demonstrate how policies change the long-run cost structure for the firm and drive innovation. Popp (2006), Gerlagh and van der Zwaan (2003), Nordhaus (2002), and Goulder and Mathai (2000) account for the potential for induced technological change in determining optimal climate change policy. Bramoullé and Olson (2005) show how new abatement technologies may be preferred to existing ones because of the dynamic incentives arising from learning-by-doing. Like these papers, endogenous technological change in response to emissions policy is important in our results, but we examine specifically how technological change interacts with resource scarcity. Endogenous technological change has also been examined in the context of finite resource extraction, but not in conjunction with a binding constraint on emissions. Tahvonen and Salo (2001) characterize the optimal extraction of finite resources when physical capital becomes more productive with use, increasing the marginal productivity of alternative and traditional energy sources over time. Dasgupta et al. (1982) characterize optimal resource extraction rates when probability of the discovery of a substitute technology can be altered through investment.7Tsur and Zemel (2005) have considered scarcity and research and development in a model of economic growth. None of these studies consider the impact of coincident environmental constraints, however. Yet another set of papers have taken the traditional Hotelling framework and examined conditions under which resource taxes may be non-monotonic. For example, Sinclair (1994) shows the possibility of declining resource taxes when interest rates are allowed to vary exogenously. Single-peaked resource price paths have also been shown to occur when stock externalities are produced by use of the polluting resource, as in Ulph and Ulph (1994). Hoel and Kverndokk (1996) obtain an inverted U-shaped path of emissions taxes using an explicit pollution damage function. In a model with a polluting resource but a non-polluting backstop, Tahvonen (1997) shows the possibility of simultaneous use of the two resources and the potential for a single-peaked price path of the nonrenewable. In a Hotelling model with a resource-exporting cartel and a coalition of resource-importing governments, Rubio and Escriche (2001) show that the resource price and Pigouvian tax need not move in the same direction over time. While it is clear that many studies have shown the phenomena of non-monotonic resource prices, none have demonstrated the existence of multiple price peaks as we show in this paper. Section 2 develops the dynamic model of a nonrenewable resource with learning in the clean technology. We discuss the necessary conditions and develop some basic insights. Section 3 characterizes optimal energy price paths and the sequence of resource use. Section 4 concludes the paper by highlighting policy implications and limitations of the framework considered in this paper.