Non-renewable (exhaustible) natural resources

4.5.1 Stocks of non-renewable (exhaustible) natural resources

With exhaustible resources such as coal, mineral oil or ores, the question aris-es whether they should be used now, or they should be raris-eserved for future use. More specifi cally, the question is whether a particular exhaustible natural resource should be put to economic use at all, and if so, at what rate.

Figure 4-2. A categorization of resources

(U.S. Bureau of Mines, 1976, Wolfbauer, 1977, Tietenberg, 1992, p. 127)

As shown in Figure 4-2., not all mineral resources have been identifi ed, and even the identifi ed part comprises reserves only to the extent that they can be recovered and processed economically at a given level of development. In practice, this means that the volume of mineral resources may be estimated roughly from the frequency of specifi c elements on Earth, i.e., that scientists can determine the types of rock in which, for example, mineral oil, mineral coal, iron ore or other economically important mineral resources may have been formed during the history of the Earth, and where such resources may be found today. However, whether a particular mineral resource is actually part of pre-existing reserves depends on the level of technological development, transport conditions, and in some cases even international diplomacy.

For example, at the level of technological development at the turn of the twentieth century, copper ore needed to contain about 6% copper in order to be suitable for use. Today, fl oatation technology enables the economical processing of ores with a copper content of less than 0.5%.

If prices on the world market are high, reserves will increase. With aluminium, for example, at above a certain price level thermal processes may also become economically viable, in addition to electrolytic reduction, making even bauxites with relatively low aluminium content economically suitable for processing (i.e., making them part of reserves).

Occasionally, armed confl ict and political tension also infl uence the acces-sibility of raw materials, and therefore the size of the reserve. The reserve is the part of mineral resources which, given prevailing technological and economic conditions, is of positive in-situ value, i.e., the gains from its use are also suf-fi cient to cover mining royalties, as discussed earlier. With all the foregoing taken into account, it becomes clearer why forecasts are so inaccurate at pre-dicting the scarcity of exhaustible natural resources.

In 1949, the geologist Dr. Marion King Hubbert produced an estimate for US min-eral oil production (Fig. 4-3). The bell curve initially rises sharply to reach a distinct maximum, referred to as the Hubbert peak, with production subsequently declining.

Figure 4-3. Hubbert’s Curves Describing World Oil Production under Two Assumptions about total world oil reserves (Hubbert, 1956)

The initial sharp rise is due to the fact that fi elds are discovered rapidly, and initially production is concentrated in those areas where extraction is sim-ple. When approximately one-half of the total reserve has been extracted, a progressively lower number of new fi elds will be discovered, and extraction will become increasingly diffi cult. Production declines and its cost increases.

Older wells will become depleted. The cycle that captures this initial exponen-tial rise – the peak and the subsequent decline – is referred to as the Hubbert cycle. The size of the world’s mineral oil reserve was initially estimated at 1.35

trillion barrels. According to a more recent estimate, the size of the reserve is now about 2.1 trillion barrels. However, even with such a signifi cant difference, the Hubbert peak has been postponed by a mere 10 years from 1990 to 2000.

Since the mineral oil reserve is represented as the area under the curve, a rela-tively minor change in the time axis near the peak will understandably lead to a major change in production. Based on the Hubbert curve, with reasonable approximation the oil era is defi nitely expected to end around 2050.

As shown in Figure 4-4., production readings are closely aligned with the calculated Hubbert curve. Although as a result of the fi rst oil price shock in 1973 production dropped temporarily, after some years it returned to a course that is still considered to fi t the curve.

Figure 4-4. Hubbert’s Curves for World liquids production (Clark, 2003)

Due to rising prices resulting from the enormous demand for mineral oil, in addition to conventional mineral oil the products of secondary extraction tech-nologies and other products (shale oil, heavy oils, etc.) have also entered the market. However, not even the appearance of these non-conventional prod-ucts will bring about a meaningful change in the situation, and in around 2050 we will witness the end of the era of mineral oil.

4.5.2 The optimal use of exhaustible natural resources

Exhaustible natural resources are different from ordinary assets in that they are available in limited quantities, and they cannot be reproduced. As a result, the production and use of a unit of a non-renewable resource is associated with an opportunity cost, which is equivalent to the value that could be obtained should the resource not be used now (only at a later point in time).

In determining the rate of use of an exhaustible natural resource, this oppor-tunity cost must also be taken into account; that is, in order for the use of the exhaustible natural resource to be considered optimal, its price should cover both the marginal cost of production and the opportunity cost.

As seen in Figure 4-5., the conventional effi ciency criterion that price = mar-ginal cost of production will, for exhaustible natural resources, become price = marginal cost of production + opportunity cost. Figure 4-5. also shows that the use of an exhaustible resource is considered optimal if its current rate of produc-tion is lower compared to what would be optimal for its reproducible equivalent.

In order to ensure that the resource is optimally distributed in time, rather than producing a volume of y**, the entrepreneur must incorporate a positive difference of AB between price and production costs, and limit the volume of production to y*. AB is commonly referred to as rent, marginal profi t, roy-alty, etc. In order to ensure that the use of an exhaustible resource is indeed optimal, the level of AB (royalty) must be constant over time. In practice, this means that the royalty must increase by some percentage corresponding to the interest on capital over time; i.e., it is the discounted royalty value that should remain constant.

Figure 4-5. Use of exhaustible natural resources (Fisher, 1981, p. 13)

The change in an exhaustible natural resource over time can also be written as a formula. As stated above, the royalty will increase in alignment with the inter-est rate if the marginal cost of production is assumed to be constant. In such a case, the royalty for the next period may be described as:

(P₁ – MC) = (P₀ – MC) * (1 + r) from which the price for the next period is

P₁ = MC + (P₀ – MC) * (1 + r) or generally for period t

P_t = MC + (P₀ – MC) * (1 + r)^t

The formula might suggest that the price of a unit of an exhaustible resource will increase steadily over time. In fact, this is not so; fi rst, as shown in Figure 4-5., at a certain price demand is reduced to zero, and second, substitutes (other resources or technologies) often exist which are suitable for the same purpose, and may even be cheaper. In the case of mineral oil or natural gas, possible substitutes include coal, nuclear energy, and solar energy. That is, at a certain price level the economy will revert to a substitute (backstop) resource or technology.

Of course, in reality the situation is more complex, since each natural re-source tends to be used for multiple purposes. As a result, a number of options for substitution may exist, each with their corresponding price. For example, apart from being used in energy production, mineral oil is also used in the chemical industry, and in the fi eld of energy the substitution options are dif-ferent than those for transport and for industrial heating. Obviously, its use in the chemical industry may come at a higher price than its use for energy purposes, etc.

The foregoing material has involved a relatively simplifi ed discussion of the problem. The interested reader will fi nd full details in the literature.