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Environmental and Resource Economics 17: 395–408, 2000. © 2000 Kluwer Academic Publishers. Printed in the Netherlands.

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Resource Characteristics, Extraction Costs, and Optimal Exploitation of Mineral Resources ? A. MARVASTI College of Business Administration, University of Houston-Downtown, One Main Street, Houston, TX 77002, USA (E-mail: [email protected]) Accepted 28 Feburary 2000 Abstract. This paper modifies the traditional theories of non-renewable resource exploitation where reserve size is assumed to be the major determinant of extraction costs. In a competitive model of resource exploitation, characteristics of aggregate reserves are considered as a determinant of extraction cost. Then dynamic solutions for the price and exploratory efforts are developed. Various price paths are feasible under different assumptions with regard to the changes in the reserve characteristics over time. Past empirical research shows that there is no consistent price path for all materials. In fact, it is the quality of newly discovered reserves as well as their size that has affected material prices. To demonstrate the complexity of a firm’s decision to recover mineral from new deposits, potentials for substantial high quality marine mineral resources are evaluated as a substitute for landbased resources. However, several factors including the decreasing trend in marine mining R & D expenditures and the potential impact of large-scale marine mining on price of minerals indicate that mining of most non-hydrocarbon marine minerals will not take place in the near future. Key words: cost function, marine resources, resource quality JEL Classifications: Q3

I. Introduction Some of the recent economic literature on the exploitation of non-renewable resources includes discussions of ore quality. Although in some models changes of quality of reserves have been considered through its impact on extraction cost, the quality of aggregate reserves has not been introduced directly into the traditional models of resource extraction and exploration efforts. In this paper, it is argued that other characteristics of a reserve, besides its size, could determine the extraction cost. A familiar model of intertemporal resource extraction is modified to demonstrate the importance of introducing the quality of reserves in the extraction cost function. The conventional wisdom established by Ricardo in the economic literature is that high grade, low cost, mineral deposits are mined first. Since ore qual? I am grateful to John Livernois, and Carol Dahl for their helpful comments. Any errors are mine

alone.

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ity is assumed to be consistently decreasing over time, non-renewable resource extraction models traditionally have focused on the size of reserves. The common assumption has been a negative correlation between reserve size and per-unit extraction costs. This view, however, has recently come under scrutiny on both theoretical and empirical grounds. For example, Livernois and Uhler (1987) agree with this assumption when reserves of a single deposit is being depleted. They refer to this situation as a change of reserves at the “intensive margin.” However, they argue that when the size of reserves is changing at the aggregate level, i.e. at the “extensive margin”, reserve size and extraction costs are not necessarily negatively correlated. Taurand and Manh Hung (1987) prove that theoretically the Ricardian notion that best reserves are used first does not have general validity. This argument is also supported in the models developed by Kemp and Long (1980) and Amigues et al. (1998) where the decision to extract an exhaustible resource is being made in the presence of an inexhaustible perfect substitute. Davis and Moore (1998), on the other hand, consider capacity constraint in extraction of heterogeneous reserves to show that strict sequencing in the order of cost is not a necessary condition for optimality- a conclusion that is more consistent with reality. Slade (1988) also shows that, under an increasing marginal cost assumption, grade-selection rules become more complicated in a competitive market such that it may be optimal to extract the least-cost deposit last. Finally, Krautkraemer (1989), in his ore quality selection model, points out the significance of technological feasibility, particularly for underground mining in the firm’s choice of deposits. However, the possibility of technological change is not considered in his model. Among empirical studies of non-renewable resources, Martin and Jen’s (1988) analysis of ore quality trends for seven major mineral resources in Canada finds no consistent decline in the grade of most metals mined during the period 1939 to 1989. The lack of consistent evidence on the declining ore quality in time is due to the fact that a firm’s ranking of the mines is subject to change as new reserves are discovered or extraction and processing technologies change. In fact, the results of a study of oil reserves in Alberta, Canada, by Livernois (1987) suggest a positive correlation between size of the aggregate reserves and their extraction costs. While, in a more recent study, a cross-sectional analysis of 159 phosphate mines in the world by Marvasti (1996) finds a negative correlation between size of reserves at each mine and its extraction costs.1 In this paper, the argument made by Livernois and Uhler with regard to the ambiguity of the sign between the size of aggregate reserves and extraction cost is extended. In Section II, a perfectly competitive model of nonrenewable resource exploitation is modified where extraction cost is determined by the aggregate reserves quality – not their size. Quality in this paper is defined as geological characteristics such as grade, mineral composition, depth, and thickness. The equilibrium paths for price and exploratory efforts include the changes in reserve quality which allows a better understanding of the price path. In section III, marine

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mineral resources are discussed as an example of expansion of aggregate reserves which may play an increasing role in supplying minerals to the world in the next century. However, the potential of some marine minerals to satisfy world demand is dimmed by several complexities which includes the concern over severe reductions in the price of some materials as a result of introduction of large scale marine mining. Conclusions are drawn in section IV. II. The Model Following Pindyck (1978), an aggregate extraction and exploration model under perfectly competitive conditions is considered here. A typical firm chooses an optimum extraction rate q, given the market price p. The aggregate extraction cost function C1 (q, θ) is subject to the rate of extraction q and the quality or the characteristics of the aggregate reserves θ. We assume that the marginal cost of extraction is positive, i.e. C1q > 0. But, improvements in the quality of the aggregate reserves reduces extraction cost, meaning that C1θ < 0. However, quality does not necessarily improve with the increase in the size of reserves. Thus, while quality of the reserves could vary with the change in the size of reserves (R), i.e. θ = h(R), the direction of the impact is ambiguous. For a single deposit, exhaustion of reserves is associated with the deterioration of the overall quality measures such that θR > 0, and as a result C1θ < 0. This is consistent with the changes of reserves at the intensive margin in Livernois and Uhler (1987) and the general cost reserve relationship in Pindyck’s (1978) where CR < 0. Increase in the size of aggregate reserves due to explorations, however, could increase extraction cost because the new reserves may have lower overall quality so that θR < 0, C1θ < 0, and CR > 0. However, it is also likely, as Livernois and Uhler have argued (1987), that the addition of reserves at the extensive margin improves the overall quality of the reserves such that θR > 0, C1θ < 0, and CR < 0. Exploration efforts ω are to increase the reserves at the extensive margin and they are justifiable even if θR < 0. This is because without the new reserves, deterioration of reserve quality at the intensive margin will increase the extraction cost even more. While reserve quality affects per unit extraction cost, no clear pattern is assumed between reserve quality and discovery cost. Thus, standard assumptions in regard to the exploration cost C2 (ω) and the rate of change in the remaining reserves x˙ are maintained, i.e. C2ω > 0, fω > 0, and fx > 0. Here, x is the cumulative reserves discovered and f(ω, x) is the rate of increase in reserves. Then, the firm’s objective function and its constraints will be: Z ∞ [p · q − C1 (q, θ) − C2 (ω)]e−δt dt (1) 0

subject to

x˙ = f(ω, x)

(2)

and

˙ = x˙ − q. R

(3)

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Figure 1. Alternative price paths.

The Hamiltonian for the optimization is: Max.H = [p · q − C1 (q, θ) − C2 (ω)]e−δt + λ1 [f(ω, x) − q] + λ2 f(ω, x) (4) In this model, q and ω are treated as control variables and θ and x as state variables. Appendix A includes the first-order conditions and derivation of the price path as following: p˙ = δp − δC1q + C1θ f(ω, x)θR

(5)

Given the consistency of the sign of other components of the price path with the existing models in the literature, the trend in price explicitly depends upon the sign of θR which deals with the disputed interaction between reserve size and quality. If we maintain the assumption that the best quality reserves are found first, then, the quality of aggregate reserves deteriorates in time as new reserves are added at the extensive margin because of new discoveries, i.e. θR < 0. As a result, the price will be rising in time regardless of the size of initial reserves (Figure 1 – line a). However, if the lowest quality reserves are found earlier in time, the dynamic price path would be reflected by Figure 1 – line b.2 Regardless of the rising or the falling of prices in time, at some time period in the future, when the extraction cost is prohibitive, the nonrenewable resources will be economically depleted and the price trend will either asymptotically approach infinity or will approach the choke price. Optimal rate of exploration efforts is derived in Appendix B with following results:     1 1 ˙ θR C2ω ffωx R · f − f + δ + C f · f − C f x ω ω θ qθ ω ω˙ = (6) C2ωω − C2ω ffωω ω

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Figure 2. Trend in exploratory efforts.

This equation is similar to the equation (13) in Pindyck (1978) except for the second term in the numerator. According to Pindyck, the first term in the numerator and the denominator are both positive. In this paper, the second term in the numerator of equation (6) explains the interaction between the rate of discoveries and the quality of reserves. Since C1θ < 0, f > 0, fω < 0, and C1qθ < 0 then the pace ˙ and θR . of the exploration efforts depends upon the sign of R ˙ > 0, i.e. the newly discovered reserves are larger than the size of the If R ˙ will be positive and θR extracted reserves in each period, (C1θ f · fω − C1qθ fω R) determines the trend for the exploratory efforts in time. If θR > 0 the improvement in the quality of the reserves because of the new discoveries increases the ˙ < 0 and θR > 0 incentive for exploratory efforts (Figure 2 – line a). However, if R ˙ remains positive, but smaller than before, as long as then (C1θ f · fω − C1qθ fω R) C1θ · f > C1qθ . In this case, ω˙ will still follow a path similar to line b in Figure 2. This assumes that the first term in the numerator is larger than the second term. ˙ < 0 then the level of exploratory Maintaining this assumption, if θR < 0 and R effort will increase at the lowest rate (Figure 2 – line c). Empirical studies of price paths in the past have not provided a unique trajectory for all mineral resources. Several complex factors typically influence the price path which are mostly left out of formal models of natural resource extraction. For example, while price path is affected by investment decisions over time, investment decisions are in turn determined by various factors including the expected postentry price of minerals. Marine mineral resources are used in the next section as an example of non-traditional behavior of price path and complex decision making processes involved in mineral exploration and extraction.3

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III. Marine Mining Potentially exploitable marine minerals are vast in numbers and in variety. There are approximately 90 different mineral commodities in the marine environment including oil and gas; heavy mineral placers containing gold, chromium, platinumgroup minerals, tin, and titanium; phosphorite; manganese nodules and crusts containing cobalt, nickel, copper, and manganese; polymetallic sulfides; and sand and gravel. In this section of the paper, discussions focus on some non-hydrocarbon marine minerals. Perceptions of increasing scarcity of most land-based resources in the U.S., both in terms of depletion and deepening of reserves, and the lack of reliability in some of the developing country suppliers of minerals have encouraged interest in the mineral resources from the oceans. In some industries such as phosphate mining, there have been other contributing factors including competition from low-cost foreign producers, increasing environmental pressures, and rising interest in alternative uses for land in the mining areas (Marvasti and Riggs 1989). Scientific ocean explorations have proven the existence of significant amount of many minerals (McKelvey et al. 1983; Clark and Clark 1986; Rowland 1985; Manheim 1986; Dubs 1986; Office of Technology Assessment 1987; Thiel and Schriever 1993). A comprehensive review of the potential world ocean mineral resources by Broadus (1987) identifies cobalt, nickel, manganese, copper, zinc, hafnium, zirconium, and ilmenite among seabed material commodities constituting from 25 to as high as 220 percent of the total land-based resources in their group. Anderson (1991) maintains that the average grade for cobalt and manganese in manganese nodules is higher than in the land-based deposits which are currently mined. Technologically, various mining methods are available for the recovery of marine mineral resources. For example, mechanical mining systems such as drag line, clam shell, and bucket-ladder dredges have been commercially used to recover sand and gravel, and gold placers. The mining of seabed minerals is also currently feasible with the hydraulic slurry technology. Although, this technology has been commercially used for sulphur mining recently, it is yet to be tested on a large-scale commercial basis to recover manganese nodules. In the 1970’s, there was an increasing interest by large companies and governmental organizations from various industrialized countries in the commercial exploitation of seabed minerals, particularly manganese nodules. This was indicated by millions of dollars spent on exploration activities and technological development, and the high number of patents granted during this period (Broadus 1987). Figure 3 depicts seabed mining R & D expenditures and patent activities for the period 1969 to 1984. The rising trend in marine mining R & D expenditures for the 1969–1978 period was a reflection of increasing demand for minerals and declining land-based reserve size and quality. This trend is consistent with the analysis of equation (6) when θR < 0 and R˙ > 0. This situation is also depicted

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Figure 3. Estimated seabed mining expenditures and patent activity from 1969 to 1984. (Source: Broadus, 1987)

in Figure 2 – line a. However, the downward trend in the marine mining R & D expenditures in the 1980’s has been caused by the reevaluation of θR and reductions in the price of minerals due to weak demand. Since the level of demand for minerals is absent in the exploration model, the impact of price fluctuations on the level of exploratory effort cannot be analyzed in equation (6).4 Many experts believe that commercial production of most marine minerals will not occur in the near future because of unfavorable economic conditions (Dubs 1986; Office of Technology Assessment 1987; Broadus 1987). This could be true in spite of a higher grade of some seabed resources in comparison with the landbased minerals which are currently mined. For example, a geological review of phosphate resources within the U.S. continental shelf concludes that the off-shore phosphate resources of North Carolina have a high quality which makes them potentially competitive with the existing land-based resources (Marvasti and Riggs 1987). Significant quantity of highly concentrated phosphate is also found in the surficial glauconitic sands on the Chatham Rise, off the east coast of New Zealand (Kudrass 1984). Another example of valuable seabed resources is manganese nodules. The metal content of these nodules is reported to be high, however, their estimated extraction cost is currently higher than the cost of land-based mining. Nevertheless, since the metal content of land-based ores is generally declining, mining of manganese nodules is believed to be economically feasible in the first quarter of the new century (Dubs 1986). The extraction of marine minerals is likely to become an increasingly attractive choice. However, the cost of initiating commercial mining is an obstacle. In the economic literature, it is commonly assumed that firms invest incrementally and continuously. But, capacity choice and investment decisions of the firms are more complex. Pindyck (1988, 1991) argues that most investments are lumpy and largely irreversible. Therefore, most of the investment expenditures are sunk costs. According to Pindyck, firms may also delay irreversible investments in order to wait for new information about prices, costs, or market conditions. The existence

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Figure 4. Introduction of seabed mining.

of sunk costs and uncertain future diminish the optimum investment expenditures. Pindyck maintains that, under these conditions, a much higher internal rate of return is required to stimulate the expansion in an industry. Irreversibility of investment and sunk costs in extractive industries are theoretically analyzed (Cairns and Lasserre 1986) and empirically documented (Lasserre 1985). Investment decisions of the firm to extract ocean minerals are subject to similar consideration. In addition, there are unique problems associated with ocean mining. The following is a list of some of the factors which influence the investment decisions of firms to exploit ocean mineral resources: (1) Exploitation of ocean minerals requires high R & D costs to complete the development of new technology. Some variations of this technology are developed but they are not commercially tested. (2) Costs of exploration and identification of resources are high. (3) There are economies of scale due to the high capital costs and large size of plants which would justify new investments only when growth in demand for the minerals is substantial. For example, one mine site for manganese nodule mining could produce up to 6 percent of world production and 75 percent of the U.S. demand for cobalt (Manheim 1986). (4) Sunk costs exist if current land-based mines are abandoned. (5) There is a time lag of at least 5 to 10 years between discovery of a minable deposit and development of technology and the start of commercial production. Therefore, firms will have to endure a negative cash flow for many years. (6) Existence of excess production capacity in the world. Due to these economic factors, the mining of ocean minerals will not be profitable unless it takes place on a large scale. Also, ocean mining will be justifiable

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Figure 5. Price path.

only if the price of minerals is much higher than the current price because if ocean mining occurs, the price of some minerals such as cobalt will be severely reduced (Adams 1975, 1980; Marvasti 1988). Therefore, the quality of the existing land-based minerals must drop much further before ocean mining takes place on a commercial basis. Figures 4 and 5 show the possibility of a major price reduction for certain minerals such as cobalt if large scale ocean mining is introduced. The impact of marine mining in the market for a mineral that is severely affected by ocean mining is depicted in Figure 4 by the downward shift of the supply curve (from S to S0 ) and subsequently the decrease in price (from P1 to P2 ). Such a price reduction is also depicted in Figure 5 at the time t1 . The mining companies consider the post-entry price of the minerals in their decision to enter large scale exploitation of ocean minerals. Consequently, a large gap between the pre-entry and the expected post-entry price of minerals can become an effective entry barrier to ocean mining for some time. In addition to these economic factors, there are contractual problems especially in the exploitation of minerals from the international waters (Marvasti and Canterbury 1992) which may not be eliminated without a strong economic incentive.5 IV. Concluding Remarks This paper argues that, at the aggregate level, reserve characteristics (e.g., grade and overburden), instead of reserve size, are important in the determination of extraction costs. Introduction of reserve characteristics is especially important following the papers by Livernois and Uhler (1987) and Livernois (1987) where it was proven that CR is not necessarily positive at the aggregate level, or the

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extensive margin. Reduction of reserves for a single deposit, or at the intensive margin, is usually associated with a decline in the quality of the reserves and an increase in extraction costs. The firm, in reaction to the declining quality and size of the reserves at the intensive margin, makes exploratory efforts which lead to new reserves. However, the quality of the new reserves is unpredictable and a consistent pattern of deterioration of the quality of aggregate reserve in time may not be valid for all minerals. In addition, ranking of the mines is subject to technological development, which has not been considered explicitly in this paper. Marine minerals are used in this paper as an example of a major potential expansion in the aggregate reserves of minerals in the future and of the complexity of investment decisions by mining firms. In spite of the indications of their high quality (with respect to grade), the trend in marine mining R & D expenditures and in the price of minerals indicate that significant mining of marine minerals is unlikely to occur until 2020. Meanwhile, further explorations are needed to improve the knowledge of the size and the characteristics of marine minerals before they are recognized as reserves. Possible extensions of nonrenewable resource extraction and exploration models could help us in understanding the behavior of firms in the mining industry. There are various elements of uncertainty in this industry. Pindyck (1980) and Slade (1988) have introduced price uncertainty into the models of nonrenewable resource extraction. However, uncertainties also exist with regard to the size and the quality of reserves. Geologic studies of samples taken from deposits and modern techniques such as computer processed satellite images could reduce these uncertainties before commercial mining begins. Nevertheless, analysis of resource extraction and exploration behavior which considers uncertainties with respect to the size and the quality of reserves would be a valuable task.6

Notes 1. Reserve quality has been addressed in other economic studies. The impact of reserve heterogeneity on extraction cost is implicitly considered by Heal (1976), Weitzman (1976), Pindyck (1978), Eswaran, Lewis and Heaps (1983) and Swierzbinski and Mendelshon (1989). The role of reserve quality is more explicit in the studies conducted by Solow and Wan (1976), Conrad and Hool (1981) and Livernois (1987). The first two assume the decreasing ore quality case. Livernois (1987), on the other hand, studies the interaction between reserve quality and characteristics of extractive technologies in a cross-section analysis of oil reservoirs in Canada. He demonstrates that declining ore quality and some key geological factors affect extraction cost. Marvasti (1996) also finds qualitative characteristics of reserves as well as locational factors to be significant determinants of average extraction costs among phosphate mines around the world. 2. Of course, price path could take other shapes such as ∩ depending upon the trend in the quality of the reserves. Empirical studies of price trajectories for various minerals have demonstrated that several alternative trends are possible (Slade 1982; Broadus 1987). 3. For a complete discussion of the evaluation of mineral projects see Torries (1998).

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4. A positive correlation between level of exploratory effort and recent mineral prices is documented by Eggert (1988). 5. Efforts are under way to modify some of the controversial deep-mining provisions of the Law of the Sea (Joyner 1996; Marvasti 1998). Of course, potential environmental consequences of large scale marine mining are yet to be determined. 6. Torries (1998) has produced an excellent source, which contains analysis of risk, for practitioners to evaluate mineral investment projects.

Appendix A The followings are the first-order conditions with respect to the control and state variables: Hq = pe−δt − C1q e−δt − λl = 0

(A1)

Hθ = C1θ θR e−δt + λ˙ 1 = 0

(A2)

Hω = C2ω e−δt + λ1 fω + λ2 fω = 0

(A3)

Hx = λl fx + λ2 fx + λ˙2 = 0

(A4)

Dynamic equations for λ˙1 and λ˙2 are derived from Hq and Hx as: λ˙1 = C1θ θR e−δt

(A5)

λ˙2 = −(λ1 + λ2 )fx

(A6)

where λ˙1 reflects the path of the change in the present value of profits made in the future as a result of the change in one unit of aggregate reserves in time. Since reserve quality could improve, deteriorate, or remain constant with a change in reserve at the aggregate level, i.e., θR R 0, λ˙1 could also take any sign. To find the price path, a total differentiation of equation (A1) with respect to time and substituting for λ˙1 and R˙ gives equation (5).

Appendix B To obtain the optimal rate of exploration efforts, λ1 from equation (A1) is substituted in equation (A3) so that: −C2ω e−δt + Pfω e−δt − C1q fω e−δt + λ2 fω = 0.

(B1)

Dividing this equation by fω and solving for λ2 gives: λ2 =

C2ω −δt e − Pe−δt + C1q eδt . fω

(B2)

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Replacing λ2 and λ1 from equations (B2) and (A1) in equation (A6) and simplifying the equation gives: λ˙2 =

fx 2 −δt C e fω ω

(B3)

˙ R, ˙ and x˙ from Differentiation of equation (A6) with respect to time, and substituting P, equations (5), (3), and (2) results in: fω C2ωω − C2ω fωω −δt C2ω −δt C2ω fωx f −δt ωe ˙ −δ e − 2 e −C1θ fθR eδt +C1qθ qθR eδt . (B4) λ˙2 = f2ω fω fω Equating equations (B3) and (B4) and solving for ω˙ we obtain:     1 ff − C1 f q θ · f − f + δ + C C2ω ffωx x ω ω R θ qθ ω . ω˙ = f C2ωω − C2ω fωω ω

(B5)

Factoring out −C1qθ fω and replacing R˙ for (f – q), we will have equation (6).

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