Challenges To Theory And Application Of Optimal Resource Extraction Models

The previous section introduced the basic framework for the determination of optimal resource extraction from non-renewable and (potentially) renewable resources. This section turns to three major issues surrounding the formulation and application of models of optimal resource extraction: discounting, empirical applicability and the limits of partial equilibrium analysis of resource use. The following section then closes with a brief summary and an overview of the role that models of optimal resource extraction may play in the future.


The question is often raised whether society should discount future utility or profits at all. Discounting implies that we value consumption and production in future periods less than present consumption and production. Thus, for decisions with ramifications that extend over long time frames, discounting implies that we value the needs of future generations differently from those of present generations, possibly leading to rapid resource exhaustion. Social discounting is typically justified by the assumption that technological improvement will automatically give rise to increasing economic wealth, and that even though future generations inherit smaller biophysical resource endowments, an enlarged stock of human-made resources will compensate for the reduction in the physical resource base. However, the assumption can be questioned. The possibility that future generations will be better off than the present generation is not a certainty.

There is another problem surrounding the use of a discount rate besides the ethically controversial issue of treating different generations differently. This problem is due to differences in social and individual discount rates. Discount rates applied by individual consumers or producers do not correspond necessarily to discount rates that may be applied by society as a whole to evaluate economic actions, such as the extraction or harvest of natural resources. This issue has caused considerable discussion in the economics literature (Lind et al. 1982; Portney and Weyant 1999). The choice of the discount rate is vital to the evaluation of economic activities. The discount rate determines whether an action has positive present value of profits or utility, whether it is better than others (has higher present value of profits or utility in the set of possible actions) and whether its timing is optimal (for example, whether waiting would resolve uncertainty and, thus, lead to higher present value of profits or utility).

Once a discount rate is chosen for the evaluation of alternative consumption and production plans, the question is whether this rate can be assumed to remain constant over time. Discounting at a constant rate seems appropriate if economic agents assume that the probability of factors affecting the choice among actions remains constant over time (Heal 1986). Since the determination of a social discount rate is already controversial (Lind et al. 1982; Portney and Weyant 1999), assumptions about time dependence of the discount rate are not likely to be accepted easily.

The choice of discount rate reflects time preference and changes in an economy's productivity that result from converting biophysical resources into reproducible, humanmade capital. Not all of the energy and material resources, however, are used to provide goods and services for consumers or to produce new capital equipment. Some resources are used to produce and store the information that describes production processes. One may put a value on such accumulated knowledge in analyzing the economics of materials recycling and energy resource depletion, focusing on ways to preserve economic efficiency while addressing the issue of intergenerational equity (Page 1977; Ruth and Bullard 1993). Page proposed a 'conservation criterion' to ensure an intertemporally egalitarian distribution of exhaustible resources. This conservation criterion states that each generation that irreversibly depletes energy resources or highly concentrated ores has an ethical obligation to leave the next generation enough new technology to produce the same utility from the more dilute resources. He cites the example of improved mining technology or the discovery of new reserves to ensure the next generation's access to the same quantity of low-cost reserves as the present generation inherited. The value of technology, in Page's framework, would be indicated by the level of severance taxes on energy or other resources needed to stimulate the development of such knowledge endowment for the next generation.

Empirical Relevance

Although Hotelling's basic approach is widely accepted among resource economists, empirical evidence for the Hotelling Rule on the basis of a firm's behavior is weak and, with few exceptions (Stollery 1983; Miller and Upton 1985), rather disappointing (Smith 1981; Farrow 1985). The lack of empirical support for the Hotelling Rule is partly due to the fact that the Hotelling's model does not explicitly take into account a firm's production capacities, capital requirements, capital utilization and time adjustments in production technologies.

Traditional models of optimal non-renewable and renewable resource extraction are also simplistic with respect to the behavioral assumptions on which they are built. For instance, short-run and long-run decisions are typically not distinguished (Bradley 1985). Decision makers may not attempt to identify optimal extraction paths over, potentially, many decades to centuries, but rather choose two or more sets of time periods over which decisions are made. As a consequence, one discount rate may be applied over decisions in the immediate future, while different discount rates may be chosen for the medium to long term.

Hotelling-style models on a macroeconomic level are more abundant than their micro-economic counterparts. With these models, time paths of various scarcity measures are investigated on an economy-wide basis. Potential candidates for economic measures of scarcity include resources prices, marginal extraction cost or scarcity rent rates (Brown and Field 1979; Hall and Hall 1984).

One of the most influential studies is that of Barnett and Morse (1963) for mineral resource depletion in the USA during the time from the civil war to 1957. In their analysis,

Barnett and Morse define increasing resource scarcity by increasing real unit cost of extractive products. The hypotheses of an increase in real unit cost of extractive products and an increase of real unit cost of producing non-extractive commodities are rejected. On the basis of these findings, Barnett and Morse (1963) argue that, with the exception of forestry resources, extractive resources in the USA did not become more scarce during the time span considered. Their findings are confirmed by Barnett (1979) but rejected by Smith (1979a) who both update Barnett and Morse's study.

Though these studies are questioned frequently as to their methodological deficiencies, they initiated discussion about both the measurement of resource scarcity and the adequacy of various economic scarcity measures (see Brown and Field 1979; Fisher 1979; Smith 1980; Hall and Hall 1984; Farrow and Krautkraemer 1991; Norgaard 1990) as well as the empirical evidence of non-increasing resource scarcity. General agreement has not been achieved yet and is likely not to occur as long as measures for resource scarcity are tied to economic performance only and do not account for the underlying biophysical reality of economic activities and interactions of economic performance and environmental quality with material cycles and energy flows through the entire ecosystem (Ruth 1993).

Slade (1982, 1985) incorporated exogenous technical progress and endogenous change in ore quality into an optimal control model of resource depletion. A U-shaped trend for resource prices is shown to give a better fit to historic data than linear price trends. Thus she concludes that long-term price movements tend to exhibit upward shifts in resource prices in response to increasing scarcity while technical progress allows for only intermediate price decrease. Slade's analyses redirected the discussion about resource scarcity towards the importance of technical change and exogenous effects on resource depletion (Mueller and Gorin 1985).

Perhaps the most devastating critique of the use of Hotelling-style models for the empirical assessment of resource scarcity has been voiced by Norgaard (1990). He contends that efforts to detect resources scarcity on the basis of optimal resource extraction models fall victim to the following logical fallacy. Optimal extraction models are based on the premises that if (a) resources are scarce, and (b) resource-extracting firms know about the scarcity, then economic indicators reflect scarcity. Empirical studies attempt to track changes in scarcity indicators through time. If, for example, unit cost of extraction, resource prices or scarcity rent rates rise, the conclusion is drawn that resources have indeed become scarce. However, to logically conclude resource scarcity from observed changes in scarcity indicators assumes that premise (b) is fulfilled: that is, that those making the decision about extraction quantities know about the extent of resource's availability. However, if resource-extracting firms already know about the scarcity of the resource, then the exercise of detecting resource scarcity from the empirical record is moot. It would be simpler to ask the decision makers in resource-extracting firms directly.

Models of renewable resource extraction are prone to much of the same critique as models of non-renewable resources. The applicability of a variety of approaches to modeling optimal harvest rates for renewable resources is discussed in considerable detail in Getz and Haight (1989). The models and methods described there do considerably more justice to the biological aspects of growing and harvesting natural resources than the basic model described above. However, common to all those models is the fact that optimal behavior is guided by growth rates and the discount rate. When growth rates are exogenous to the model, the discount rate is the sole determinant of optimal harvest and, as a consequence, the representation of feedbacks between the ecosystem that supports resource growth and economic activity is severely limited.

Partial Equilibrium Approach

By its nature, economic theory is anthropocentric and, thus, selective in the consideration of effects of economic actions on the environment and the role of environmental goods and services for economic activities. It is consumer utility, welfare or profit that is maximized under a set of constraints that are given by the environment and recognized by economic decision makers. Such constraints reflect, for example, the finiteness of an essential resource or the growth rates of plants harvested or animals caught. However, many other important environmental constraints are typically not captured fully in the economic decision process. Rather, these constraints are captured only as far as they impose apparent, immediate restriction on the deployment of the economically valued factors of production. A variety of constraints that are associated with unpriced material and energy flows that may lead to fundamental changes in the physical or biotic environment are frequently not (but can, in principle, be) considered. An obvious example is climate change which is being induced, in part, by the emissions of greenhouse gases from combustion of fossil fuels, methane and carbon emissions resulting from land use changes, and reduced carbon sequestration from biomass harvesting.

Economic actions, such as the extraction or harvest of a resource and the production of goods and services, are accompanied by changes in the state of the economic system and its environment. Production of goods and services in the economy necessitates use of some materials and energy that are typically not valued economically. Additionally, production inevitably leads to waste of materials and energy, thereby affecting the long-term performance of the ecosystem. Models of optimal resource extraction are particularly selective in the consideration of such feedback processes between the economic system and the environment. This is not to say that economics altogether disregards them. All models and theories provide abstractions of real processes. However, neglecting some physical and biological foundations of economic processes may lead to results that neglect vital issues, such as the earth's capacity to support life, which ultimately determine economic welfare. The complex interdependencies between economic decisions and the degradation of the environment due to material and energy use are often neglected or treated as 'externalities'; that is, they are treated as effects that are not a priori part of the decision process but that can be considered a posteriori in economic decisions if there is economic value associated with them. The treatment of important interdependencies of the economic system and the environment as externalities, without restructuring the theory, amounts to making ad hoc corrections introduced as needed to save appearances, like the epicycles of Ptolemaic astronomy (Daly 1987, p.84).

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