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USING THE CUMULATIVE AVAILABIITY CURVE TO ASSESS
THE THREAT OF MINERAL DEPLETION: THE CASE OF LITHIUM
by
Andrés Yaksic Beckdorf
and
John E. Tilton1
Abstract
The cumulative availability curve shows the quantities of a mineral commodity
that can be recovered under current conditions from existing resources at various prices.
The future availability of a mineral commodity depends on the shape of its cumulative
availability curve (determined by geologic considerations, such as the nature and
incidence of the available mineral deposits), the speed at which society moves up the
curve (determined by future demand and the extent to which this demand is satisfied by
recycling), and shifts in the curve (determined by cost-reducing technological change
and other factors). While the shape of the curve for any given mineral commodity may
or may not be known, it is knowable since the geologic processes responsible for the
curve’s shape took place many years ago. In contrast, the factors governing how fast
society moves up the curve and how the curve shifts over time are not only unknown
but also unknowable.
Using lithium as an example, this article shows that knowledge about the shape
of the cumulative availability curve can by itself provide useful insights for some
mineral commodities regarding the potential future threat of shortages due to depletion.
Despite the inherent uncertainties surrounding the future growth in lithium demand as
well as the uncertainties regarding the future cost-reducing effects of new production
technologies, the shape of the lithium cumulative availability curve indicates that
depletion is not likely to pose a serious problem over the rest of this century and well
beyond.
JEL Classifications: Q32; L72
Keywords: Mineral depletion, mineral availability, nonrenewable resources,
cumulative availability curve, lithium
1
Andrés Yaksic Beckdorf (aiyaksic@puc.cl) was a graduate student in mineral economics at the Mining
Center of the School of Engineering, Pontificia Universidad Católica de Chile at the time this study was
conducted. John E. Tilton (jtilton@ing.puc.cl) is Profesor de la Cátedra de Economía de Minerales at the
Mining Centre of the School of Engineering, Pontificia Universidad Católica de Chile, and Research
Professor in the Division of Economics and Business, Colorado School of Mines. He is also a University
Fellow at Resources for the Future. They are grateful to John H. DeYoung, Jr., and Philip Maxwell for
helpful comments.
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Introduction
Although depletion has not yet caused severe shortages, the rapid growth in
demand for mineral commodities over the past century—coupled with the growth
expected over the next century as the economies of China and other developing
countries expand—have many pondering how long this benevolent situation can
continue. Although scholars and others have debated this issue for some time, they
remain divided. Nevertheless, we have learned a great deal about mineral depletion and
the nature of the threat it poses.
Still needed, however, are reliable indicators for individual mineral commodities
of the potential for depletion to produce serious scarcity in the future—what some have
called a ‘red list’ of depletion-threatened commodities, or what one might think of as an
early warning system. In his book On Borrowed Time, Tilton (2003) proposes such a
measure—the cumulative availability curve.2 Yaksic (2008) in his MS thesis Análisis de
la Disponibilidad de Litio en el Largo Plazo has recently attempted to illustrate the
usefulness of this methodology by applying it to the long-run availability of lithium.
This article describes this analysis and its major findings.3
Before doing so, however, Section 2, which follows this introduction, briefly
highlights the important findings of particular relevance for our purposes flowing from
the on-going debate over mineral depletion. Section 3 then describes the cumulative
availability curve and its usefulness. Sections 4 estimates the cumulative supply curve
for lithium and discusses the insights it provides regarding the future availability of this
mineral commodity. Finally, Section 5 reviews the major findings and explores some of
2
On Borrowed Time uses the term cumulative supply curve. Since this curve is quite different from the
conventional supply curve, to avoid confusion we now refer to this curve as the cumulative availability
curve.
3
The only other application of the cumulative availability curve of which we are aware is Aguilera and
others (2009). This study assesses the threat that depletion poses for petroleum products.
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their implications for assessing the threat of depletion for mineral commodities in
general.
Depletion and the Long-Run Availability of Mineral Commodities
Shortages of mineral commodities can arise for a variety of different reasons—
wars, embargos, cartels and other market manipulations, natural disasters, accidents,
cyclical booms in global demand, inadequate investment in new mines and processing
facilities, and resource depletion.4 This last—resource depletion—it is important to note
differs from all the other causes in at least two important respects. First, shortages due
to depletion are likely to arise slowly and persistently, and to be permanent or at least of
very long duration. Shortages due to business cycle fluctuations, wars, accidents, and so
on are likely to arise suddenly, often without much warning. Despite a few exceptions—
the DeBeers cartel, for example, probably kept diamond prices artificially high for over
a century—such shortages are also temporary, lasting no more than a decade and often
only a couple of years or less.
Second, shortages of mineral commodities arising for reasons other than
resource depletion are quite common. Surging demand for mineral commodities in India
and especially China coupled with insufficient investment in new production capacity
over the past decade or two, for example, have recently created global shortages for
petroleum, copper, iron ore, tin, and a host of other mineral commodities. On the other
hand, to our knowledge there is not yet a documented case of resource depletion causing
significant shortages of mineral commodities.
4
A shortage, as the term is often used, reflects a surplus of the demand for a mineral commodity over its
supply at the prevailing market price. For our purposes, however, this definition is too narrow, since it is
always possible to bring demand and supply into balance by allowing price to rise. As a result, a shortage
is defined here to include situations where rising and substantially higher prices are required to equate
supply and demand. The terms shortage and scarcity are used interchangeably, and both imply a lack of
availability.
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That depletion has not been a problem in the past, of course, does not mean this
favorable situation will continue indefinitely in the future. Indeed, as noted earlier,
many have argued and continue to argue that resource depletion poses a substantial
threat to the long-run availability of mineral commodities. Others have challenged this
view, and a lively debate over this issue continues to this day. We will not review this
debate here, as Tilton (2003, 2006) has done so elsewhere.
Suffice it to say that we have learned much from the exchange of views over the
past 40 years. We know now, for example, that the world will never literally run out of
mineral commodities despite their nonrenewable nature. This is in part because some
mineral commodities, the metals for example, are not destroyed when used and so at
some cost are available for reuse. In the case of petroleum and other energy resources,
the substitution of cheaper alternatives, including solar and other renewable sources,
will occur long before the highest-cost nonrenewable resources are extracted and
consumed.
The debate has also highlighted the serious shortcomings of using physical or
fixed stock measures of mineral resources to assess the threat of depletion, even though
the use of these measures somehow manages to persevere despite their shortcomings.
The fixed-stock approach typically takes estimates of the reserves, resources, or
resource base for a mineral commodity, and assumes they reflect a nonrenewable, fixed
stock of what remains for society to consume.5 Estimates of future consumption are
5
Reserves indicate the amount of a mineral commodity contained in deposits that are both known (that is,
discovered) and economic to exploit under current conditions. Resources encompass reserves plus the
quantity of a mineral commodity contained (a) in deposits that are as yet undiscovered but which would
be economic or potentially economic once discovered, and (b) in known deposits whose exploitation
though not currently economic is potentially economic. The U.S. Geological Survey (2008, Appendix C)
defines a resource as “a concentration of naturally occurring solid, liquid, or gaseous material in or on the
Earth’s crust in such form and amount that economic extraction of a commodity from the concentration is
currently or potentially feasible.” The resource base includes all of a mineral commodity found in the
earth’s crust. It encompasses resources, as well as a great deal of other mineral occurrences not now
considered potentially feasible for future exploitation. The U.S. Geological Survey (2008, Appendix C)
does not use the term resource base. However, the resource base encompasses what the USGS calls
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then typically used to estimate how many years remain before the available stock is
exhausted.
Neither reserves nor resources, however, are really a fixed stock. This
shortcoming is widely recognized in the case of reserves, since new discoveries and new
technologies are constantly adding to mineral reserves.6 Though less appreciated, the
same is true as well for resources. As Tilton and Lagos (2007) have documented, the
U.S. Geological Survey has over the past several decades increased its estimates of
global copper resources from 1.6 to 3.7 billion tonnes. Some of this increase came from
the realization that new technology made seabed nodules a potential source of copper in
the future, but most represents a reassessment in light of changes in technology,
geologic science concepts, and other conditions of what is potentially available from
land-based deposits.
While a stronger case can be made that the resource base does indeed represent a
fixed stock, it is of little use in assessing the long-run availability of mineral
commodities for other reasons. In particular, long before the last barrel of oil or the last
ton of copper were extracted from the earth’s crust, the cost of production would
become prohibitive, causing demand to decline to zero. As a result, while the life
expectancies of reserves and resources are unduly pessimistic, those based on the
resource base are unduly optimistic. In the case of lithium, for example, the resource
resources (which include reserves) and other occurrences. The USGS defines other occurrences as
“materials that are too low grade or for other reasons are not considered potentially economic.” It also
notes that the boundary between other occurrences and resources is “obviously uncertain, but limits may
be specified in terms of grade, quality, thickness, depth, percent extractable, or other economic-feasibility
variables.”
6
Moreover, within the mining industry it is widely recognized that there exists little economic incentive
to identify reserves beyond 20 to 30 years of consumption, given the costs of such efforts and the time
value of money.
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base estimated at 4.8 x 1014 tonnes would at current rates of consumption last for some
23 billion years.7
As a result, it is now widely (though not universally) accepted that economic
measures of mineral scarcity are more useful than physical measures. Economic
measures reflect the opportunity costs, or what society has to give up, to obtain one
more ton of a mineral commodity. Real mineral commodity prices are the most
frequently encountered economic measures.8 A rise over time in the real price of, for
example, iron ore implies growing scarcity, while a decline implies growing
availability.
While generally considered far superior to physical measures of scarcity, trends
in real prices do have their own shortcomings and limitations.9 For example, as noted
earlier, scarcity and shortages can arise for reasons other than resource depletion. As a
result, mineral commodity prices fluctuate considerably, particularly over the short run.
For this reason, price trends over the long run offer the most useful insights regarding
mineral depletion.
In addition, prices reflect only those environmental and other social costs that
producers and ultimately consumers actually pay. This means trends in real prices will
overestimate the rise in scarcity if government policies are forcing producers to
7
The concentration of lithium in the earth’s crust is estimated at between 20 and 65 ppm and the weight
of the earth’s crust at 2.4 x 1019 tonnes. See Erickson (1973). Using 20 ppm produces the resource base
estimate of 4.8 x 1014 tonnes of lithium. In addition, the oceans contain 0.17 ppm of lithium, suggesting
that this resource contains an additional 2.5 x 1011 tonnes of lithium. See Steinberg and Dang (1975).
8
Other economic measures include the real production costs of marginal producers and user costs. User
costs, which are also called Hotelling rents and scarcity rents, reflect the net present value of the lost
future profits associated with producing one more unit of a mineral commodity now rather than in the
future. Under given conditions, user costs reflect the value of the marginal reserves in the ground required
to produce one more unit of a mineral commodity. Data on production costs and user costs are difficult to
obtain. For this and other reasons, the real prices of mineral commodities are by far the most widely used
of the economic measures of mineral scarcity.
9
For a more complete discussion of the shortcomings of the economic measures of resource scarcity, see
Tilton (2003), ch. 3.
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internalize an increasing share of the total social costs and underestimate the rise in
scarcity if the opposite is the case.
Perhaps the greatest shortcoming of trends in real prices as an indicator of the
future threat of depletion is that the prices we have are historical. As a result, they
largely reflect conditions in the past. Of course, where the market anticipates future
scarcities current prices will rise as consumers and others build up their stocks. Still,
given the long-run nature of the threat from mineral depletion, it is far from clear to
what extent and how far into the future current prices anticipate scarcity. What we
would like to know are the long-run trends in real mineral commodity prices far into the
future. Here, as the next section shows, the cumulative availability curve can be of some
help.
The Cumulative Availability Curve
The cumulative availability curve shows the amount of a mineral commodity
that can be recovered profitably at various prices from different types of mineral
deposits under current conditions (that is, current technology, prevailing labor and other
input prices, and so on).10 One would like the cumulative availability curve to reflect
estimates of both known (discovered) and unknown mineral deposits. Some times this is
possible, as Aguilera and others (2009) in their attempt to construct cumulative
availability curves for petroleum resources show. However, normally reliable
10
The cumulative availability curve differs from the common supply curve in economics in two important
respects. First, the conventional supply curve indicates how much of a commodity will be supplied to the
market during a given time period, such as a year or month, while the cumulative availability curve shows
how much could be supplied cumulatively over all time. The former is a flow variable, the latter a stock
variable. The cumulative availability curve only makes sense for commodities produced from
nonrenewable resources. The cumulative availability of corn, television sets, and trucks at prices at or
above production costs is presumably infinite. Second, the conventional supply curve indicates how much
suppliers will actually provide to the market at various prices, which due to market power and other
considerations may deviate from what they could supply profitably at various prices. The first reference,
of which we are aware, to the cumulative availability curve is found in Tilton and Skinner (1987), where
it is called the cumulative supply curve. For more on the cumulative availability curve, also see Tilton
(2003) and Tilton (2006).
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information on unknown deposits is not available, as is the case for lithium. In this
situation, cumulative availability curves can be estimated on the basis of known
deposits, as long as one keeps in mind new discoveries are likely to shift the curve down
and to the right over time.
The slope of the cumulative availability curve is positive, since higher prices
permit the profitable exploitation of poorer quality and so higher cost deposits.
However, as Figure 1 indicates, a positive slope is consistent with a variety of shapes
with very different implications for future resource availability. The gradually rising
curve shown in Figure 1a implies that substantial future increases in output are possible
with only modest increases in production costs and prices. The curves shown in Figures
1b and 1c are far less benign. Both suggest at some point substantial increases in costs
will occur making much higher prices necessary.
The cumulative availability curve is a useful expository device for grouping the
many different factors governing future mineral commodity prices. The first group
determines the shape of the cumulative availability curve. It encompasses the various
geologic factors affecting future costs and prices, such as the nature and incidence of
mineral occurrences. The second group determines how quickly the world moves up the
cumulative availability curve. It includes all the factors that affect current and future
demand for the mineral commodity, including growth in per capita income and
population. It also encompasses the government policies and other factors influencing
recycling and secondary production. The third group determines to what extent the
cumulative availability curve shifts over time. It includes changes in factor costs and the
forces behind such changes, and as well the effects of innovation and technological
change on the costs of finding and producing mineral commodities. In addition, as noted
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above, if the cumulative availability curve is estimated on the basis of identified
resources only, the discovery of new deposits also belongs to this group.
In the past, we know that the cost-reducing effects of new technology have for
most mineral commodities offset, at least over the longer run, any upward pressure on
costs caused by higher factor prices. As a result, the cumulative availability curve has
tended to shift downward over time. For a number of mineral commodities, the costreducing effects of new technology, reflected in the downward shift of the cumulative
availability curve, have more than offset the cost-increasing effects of depletion,
reflected in the movement over time up the curve. In such cases, the trends in real prices
over the past century or more have been downward, suggesting growing rather than
declining availability, mineral depletion notwithstanding. For most mineral
commodities, the two countervailing forces have more or less offset each other, and
their trends in real prices have been relatively flat. Significantly upward sloping, real
price trends are harder to find over the past century, which is why, as noted earlier, there
are few if any documented cases of depletion having caused shortages or scarcity of
mineral commodities in the past.
The future, of course, could be different, and our interest here lies with possible
future scarcities and thus with expected future price trends. To assess the latter, we
would like to know (a) the shape of the cumulative availability curve, (b) the speed at
which society will move up the curve, and (c) extent to which the curve will shift with
time. With a fair amount of certainty (which is rare when talking about the future), we
know there is little hope of reliably predicting either of the last two developments. The
extent to which the cumulative availability curve will shift depends on the introduction
and diffusion of new technologies. Both are notoriously difficult to predict over the near
term let alone over the next century. Similarly, how rapidly society will move up the
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curve hinges on changing consumer preferences for mineral-intensive products,
population growth, per capita income growth, and trends in recycling, all of which are
similarly difficult to anticipate over the longer term.
Fortunately, the shape of the cumulative availability curve—the first
consideration—is more tractable, since it depends on the nature and incidence of
existing mineral occurrences. It is true that our knowledge of subeconomic resources for
many mineral commodities is quite limited, since exploration is largely carried out by
firms focused on finding economic and particularly highly economic deposits.
However, it is clearly possible to obtain more information on subeconomic mineral
occurrences. These resources were created in the past, in many cases hundreds of
millions of years ago, and ignorance about them largely reflects a lack of interest on the
part of exploration firms because such deposits are uneconomic at the present time.
Moreover, as pointed out earlier, the shape of the cumulative availability curve
can provide useful insights about the potential threat of depletion. This is true even
though reliable information regarding how fast society will move up the curve and to
what extent the curve will shift over time is unknown.
The curve shown in Figure 1a implies, as cumulative production proceeds over
time, that the price needed to elicit additional supply increases but at a decreasing rate.
When this is the shape of the curve, new technology should find it increasingly easy to
offset the cost-increasing effects of depletion. However, the cumulative availability
curve, at least for a number of mineral commodities, may be less benevolent than the
one shown in Figure 1a.
For instance, the costs of mineral commodities produced as by-products and coproducts, such as indium, gallium, cobalt, the platinum-group metals, and of particular
importance here lithium, are lower because a substantial share of the total mining and
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processing costs are borne by the associated joint products. Should demand at some
point exceed the supply available from by-product and co-product output, these
commodities would have to be produced as main products. At this point, a substantial
jump in the price may be required, implying a sharp surge or a discrete break in the
cumulative availability curve, as shown in Figures 1b and 1c.
Moreover, according to Skinner (1976) and Gordon and others (1987), even
copper and other major metals currently produced as main products may have
cumulative availability curves similar to those shown in Figures 1b and 1c. This, they
contend, is due to the geochemical processes that created the mineral deposits for these
metals millions of years ago, which they believe are unlikely to have produced a
benevolent unimodal relationship between the grade and quantity of metal. Rather they
suspect this relationship may possess two or more peaks in the available quantity of
metal as grade declines. In this case, once the rich (high-grade) deposits are exploited,
society may have to turn to much lower grade, and thus much more costly, deposits for
additional supplies.
In addition, the processing methods required to liberate the copper and other
metals in very low grade deposits may be quite different from those employed today. In
particular, the use of mechanical and chemical processes for concentrating the ore may
not be feasible. As a result, the energy required could be one or several orders of
magnitude greater, also causing a sharp jump in costs.
As Skinner himself points out, his thesis is largely based on theoretical
considerations. Very little empirical work has been carried out on the costs incurred in
processing very low grade deposits, largely because the latter are of little commercial
interest.
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Lithium11
The Swedish scientist Johan August Arfwedson discovered lithium, a minor
metal, in 1817. Today the world extracts lithium from two types of resources—brines
and minerals—to produce lithium carbonate, lithium hydroxide, lithium chloride,
lithium metal, and the other lithium-containing products shown in Figure 2. The major
end-use industries consuming these lithium products, as Figure 3 shows, produce
batteries, lubricating greases, frits, glass, air conditioners, aluminum, and
pharmaceutical products. The annual output of these products contains about 21,800
tonnes of lithium. Chile, Australia, Argentina, China, and the United States are the
major producing countries accounting for 43, 25, 13, 6, and 4 percent respectively of the
lithium extracted from brines and minerals.12
As Figure 4 shows, the real price of lithium carbonate (the most important
lithium product and the one for which a long-run price series exists) has declined since
1953 (the first year figures are available) due largely to new, low cost sources of lithium
supply and new production technologies. As a result, lithium has over the past half
century become less, not more, scarce, and depletion has not been a problem.
Nevertheless, the expected growth in demand over the coming century for lithium
batteries to power hybrid and fully electric automobiles has raised some concern about
the future availability of lithium (Tahil, 2007; Tahil, 2008; Bradbury, 2008).13
11
This section is based on Yaksic (2008) and the sources cited there. Also, see Ebensperger and others
(2005) for an overview of the lithium industry that examines the industry’s resources, production, end-use
consumption, and prices as well as its future prospects.
12
The figure of 21,800 tonnes for annual lithium production and the country shares cited are estimates
based on Ober (2008), Sernageomin (2006), Roskill (2006), and other sources. The estimate of 21,800
tonnes for total lithium production is slightly below estimates found elsewhere for the reasons noted in
Yaksic (2008, pp. 25-28). The country production figures reflect extraction from natural resources. China
and other countries that import and then further process lithium products have larger market shares when
the total value of lithium production is considered.
13
Others, however, are less concerned. See, for example, Evans (2008a and 2008b). It is also worth
noting that the current concern is not the first time that scientists and others have worried about the longrun availability of lithium. In the 1970s an expected surge in lithium demand for use in nuclear fusion
raised fears that inadequate lithium resources could curtail the development of this new source of energy.
See Hammond (1976).
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In addition to brines and mineral deposits, lithium can be extracted from clays
and seawater. Brines—currently the most important and cheapest sources of lithium—
are largely associated with dry lakes, such as the Salar de Atacama in the altiplano of
northern Chile. Brines are also found with geothermal deposits as well as oil fields.
Hard rock mineral deposits, as noted, constitute the other type of resource from which
lithium is currently extracted. Although lithium is found in some 145 different minerals,
only a few (spodumene, lepidolite, petalite, amblygonite, and eucriptite) are sources of
lithium in deposits that have economic value. Clays (especially hectorite) and seawater
are both potential sources of supply.
Cumulative Availability Curves
With the assistance of various industry and government officials and an
extensive review of the available historical documents and studies, Yaksic (2008) has
compiled a listing of known lithium resources along with estimates of their quantities
and production costs (see Appendix). With this information, one can construct the
cumulative availability curves for lithium shown in Figure 5. Estimating production
costs is challenging, in part because many producing firms consider the costs of their
on-going operations proprietary and in part because one can only approximate the costs
of resources not currently being exploited. For this reason, Figure 5 shows production
costs under two scenarios—a high cost or pessimistic scenario (the top curve) and a low
cost or optimistic scenario (the bottom curve).
The costs, shown on the vertical axis of Figure 5, and hence the prices needed to
cover production costs are in terms of dollars per pound of lithium carbonate, the most
important lithium chemical. The horizontal axis shows the available resources,
measured in tonnes of contained lithium (rather than tonnes of lithium carbonate
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equivalent),14 whose production costs are at or below various prices. For our purposes,
this difference in indicated units is unimportant.
What is important is that the curves shown are incomplete. In particular, only a
small part of the cumulative availability curves associated with lithium production from
seawater (that is, the horizontal segment at 10 dollars for the top curve and at 7 dollars
for the bottom curve) are shown.15 This is because the quantity of lithium recoverable
from seawater is huge—44.8 billion tonnes.16 Including all this tonnage in Figure 5
would increase the length of the cumulative availability curves by more than a thousand
fold.
Implications for Depletion
Having estimated cumulative availability curves for lithium, we can consider
next the future demand for lithium and how rapidly society is likely to move up these
curves. As pointed out earlier, predictions of future mineral demand are rarely accurate
since they depend on technological change, shifting consumer preferences, population
growth, and other variables that are difficult to estimate accurately in the longer run. For
this reason, we consider a high growth scenario, which is likely to overestimate the
growth in demand and so represents a worse-case scenario for lithium depletion. Table 1
identifies the specific assumptions on which this scenario rests. In general, it assumes
that the demand for lithium in automobile batteries surges over the coming decades and
14
5.323 metric tonnes of lithium carbonate (Li2CO3) contain one metric ton of lithium (Li).
The estimated production costs of 7 to 10 dollars per pound of lithium carbonate are based on Steinberg
and Dang (1975). During the 1970s the expected growth in electric power generation from nuclear fusion
was expected to increase greatly the demand for lithium, raising concerns about its long-run availability.
Various researchers conducted laboratory scale studies to estimate the costs of recovering lithium from
geothermal brines, oil field brines, and other potential resources. As part of this effort, Steinberg and
Dang (1975) carried out an economic analysis for the extraction of lithium from seawater, estimating
production costs for the process in the range of 22 to 32 (1974) dollars per kilogram of lithium metal.
This compares with a selling price of lithium metal from conventional mineral sources of about 20 dollars
per kilogram at the time. We then increased the estimated costs of 22 to 32 dollars for subsequent
inflation, and then converted them from lithium metal to lithium carbonate and from kilograms to pounds
to obtain the estimated costs of 7 to 10 dollars per pound of lithium carbonate from seawater. This
approach, it is important to point out, does not take into account any reduction in production costs due to
technological progress since the time of the Steinberg and Dang study.
16
This figure assumes that 20 percent of the lithium in seawater is recoverable.
15
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that the demand for lithium grows briskly in its traditional end uses (other than for
aluminum production where lithium use is expected to be phased out over the next
couple of decades).
Under these conditions, the cumulative output of lithium required from 2008 to
2100 totals 17.5 million tonnes. This figure reflects only the needed primary lithium
production, since recycled lithium or secondary production does not deplete lithium
resources and thus does not move society up the cumulative availability curve.17
Under this worse case scenario, at some point in the 22nd century the world
could find it attractive to extract lithium from seawater.18 The costs of producing
lithium from this source are between 7.00 and 10.00 dollars per pound of lithium
carbonate. Since the current price is around 2.80 dollars per pound (see Figure 4), at
most depletion might drive the price up by 7.20 dollars a pound over the next century.
Moreover, at that price an estimated 44.8 billion tonnes of lithium are available (see
Appendix Table 3), which for all practical purposes is an unlimited source of supply.
An increase of 7.20 dollars would not significantly curtail the use of lithium in
automobile batteries. A 9 kWh lithium battery today requires approximately 15 pounds
(6.75 kilograms) of lithium carbonate equivalent. As result, the lithium used in the
battery today costs approximately 42 dollars.19 This would increase to 150 dollars if the
price were to rise to 10.00 dollars per pound of lithium carbonate. This is but a small
fraction of the total cost of the battery, which can exceed five thousand dollars, and of
the total cost of the car, estimated at 20 to 30 thousand dollars.
17
Under the assumed conditions, annual production in the year 2100 is estimated at 330,000 tonnes of
lithium equivalent or 1.76 million tonnes of lithium carbonate equivalent.
18
Actually, given our likely overestimation of demand and the many known resources of lithium we have
not considered, either because resources estimates or costs estimates are not available, we doubt that
lithium will be produced from seawater in the 22nd century unless costs of extracting lithium from
seawater fall substantially.
19
The figure of 42 dollars is an estimate only, since the lithium products used in lithium batteries are not
just lithium carbonate.
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The cumulative availability curves shown in Figure 5 similarly make it difficult
to argue that depletion is behind the recent jump in lithium carbonate prices from
around 1.50 dollars a pound in 2005 to 3.00 dollars a pound in 2007, as lithium can be
extracted from many, currently available sources at less than 2.00 dollars a pound.
Finally, it is worth highlighting two caveats that tend to reinforce the above
findings. First, the discovery of new lithium deposits and new technologies that reduce
production costs may well shift the cumulative availability curves shown in Figure 5
downward over time. Second, the cumulative availability curves shown in Figure 5 are
based on conservative assumptions and estimates. The assumed recovery rates for
various resources, for example, are quite low. In the case of seawater, for instance, only
20 percent of the 224 billion tonnes of lithium in this source is considered recoverable.
In addition, a number of known but uneconomic sources of lithium are excluded from
the curves due to the lack of reliable estimates for availability or costs.20 Overall, these
caveats strengthen the conclusion that depletion does not pose a significant threat to the
long-run availability of lithium.
Conclusions
Over the long run, as society consumes its high quality, low cost mineral
resources, depletion could cause the real prices of mineral commodities to rise,
threatening the high living standards currently enjoyed in many countries around the
world. Whether this will actually take place, it is now known, depends largely on a race
between the cost-increasing effects of depletion and the cost-reducing effects of new
technology. We also know that in the past new technology has successfully offset the
20
These resources include various dry lakes in Chile, Argentina, and Bolivia that are known to contain
important volumes of lithium but have not been explored in detail (see notes to Appendix Table 2). The
same holds for a number of lithium mineral deposits recently discovered in Australia and Canada.
Marginal geothermal brines in New Zealand, Italy, Japan, Iceland, and France are also not considered, nor
the lithium resources in North Dakota and Utah in the United States associated with oil fields.
16
Version: 90521
tendency for depletion to push prices higher. What we do not know, given the inherent
uncertainties surrounding the future course of technological change and the other
determinants of mineral commodity prices, is whether this favorable situation will
continue in the future.
Despite such uncertainties, lithium shows that in some instances information
about the shape of the cumulative availability curve can provide useful insights into the
likely future threat of mineral depletion. Where the curve rises gradually and eventually
becomes relatively flat (as is the case for lithium, particularly once extraction from
seawater takes place), some assessment of the maximum long-run price is possible
under any plausible scenario of future demand growth. In the case of lithium, for
example, it appears that almost unlimited supplies can be extract from seawater for
between 7.00 and 10.00 dollars per pound of lithium carbonate. As the current price is
about 2.80 per pound, these figures suggest that depletion will not be a serious threat,
even if lithium is widely used over the coming century in hybrid and fully electric
automobiles.
Not all mineral commodities, of course, may have such benevolent cumulative
availability curves. Mineral commodities whose cumulative availability curves rise
steeply or have discrete breaks are more exposed to the threat of depletion.
In this regard, however, there is an important asymmetry between mineral
commodities with gradually rising cumulative availability curves and those with steep
slopes or with discrete breaks in terms of the implications for depletion. In the case of
the former, if the relatively flat portion of the curve occurs at prices close to current
prices, as is the case for lithium, one can confidently conclude that depletion will not be
a serious threat. In the case of the latter, however, one cannot conclude that depletion
will necessarily be a problem. The reason being in such cases we have no way of
17
Version: 90521
knowing how much of the upward pressure on costs likely to arise from depletion will
be offset by the cost-reducing effects of new innovations and technology.
Finally, for some mineral commodities the information needed to construct
cumulative availability curves is not available. This, as we have seen, is the case for
copper. On this issue, however, it is useful to highlight the difference between
information that is unknown and unknowable and information that is unknown but
knowable. Information on technological change, population growth, changes in future
consumer preferences, and the other determinants governing how rapidly society will
move up the cumulative availability curve and to what extent the curve will shift down
over time is not just unknown. It is also essentially unknowable. In contrast, the
geologic information needed to estimate cumulative availability curves, though it may
currently be unknown for many mineral commodities, is knowable. At some cost and
effort, it can be obtained. And, as the case of lithium illustrates, knowledge of the shape
of cumulative availability curves can by itself provide useful insights into the future
threat of depletion for some mineral commodities.
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Unpublished M.S. thesis, Santiago, Pontificia Universidad Católica de Chile, p.
1-150.
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Table 1
Lithium 2008 to 2100 Demand Forecast Assumptions by Major End Use Markets
End Use Market
Automobile Batteries
Secondary Batteries
(rechargeable - portable
devices)
Primary Batteries (nonrechargeable - portable
devices)
Lubricating Greases
Frits and Glass
Air Conditioning
Aluminum
Others
Assumptions
1) World population will grow according UN
estimations from 6.5 billion people in 2008 to
9.0 billion people in 2100.
2) The global ratio of people per automobile will
fall from 8 in 2008 to 3 in 2100.
3) Annual battery production equals the growth in
the world vehicle fleet plus the replacement of
old car batteries (10 year average life assumed).
4) The percentage of hybrid and fully electric
automobiles will increase from its 2008 level of
under 1 to 100 percent by 2050 where it will
remain for the rest of the century.
5) Hybrid and fully electric automobiles on average
will use 9 kWh lithium batteries.
6) Lithium batteries will on average last for 10
years.
7) Lithium batteries will be recycled, recovering
80% of the lithium.
15% growth for ten years; then 10% growth for ten
years more; 3% growth until 2050; 1% growth from
2051 to 2100.
8% growth for ten years; then 5% growth for ten years
more; 3% growth until 2050; 1% growth from 2051 to
2100.
5% growth for next ten years; then 3% growth for the
next twenty years; finally 1% growth until 2100.
3% growth for ten years; then 2% growth for the next
twenty years; finally 0.5% growth until 2100.
5% growth for ten years; 3% growth for the next ten
years; finally 1% growth until 2100.
0% growth for ten years; 5% reduction over the next ten
years; no lithium consumption after 20 years.
4% growth for ten years; 2% growth in the next ten
years, finally 1% growth until 2100.
Notes:
a
These assumptions are likely to produce demand forecasts that exceed the actual
growth in lithium consumption over the 21st century for the following reasons: (1)The
ratio of people per automobile is unlike to reach 3 by the end of the century. (2) The
assumed rate of growth of hybrid and electric vehicles—4.5 million by 2010, 27 million
by 2020, 146 million by 2050, and 308 million by 2100—is optimistic, in part because
all automobiles may not be hybrid or fully electric by 2050. (3) Some hybrid
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automobiles may use smaller batteries than the assumed 9 kWh battery, containing less
lithium. For example, the Toyota Prius HEV uses a battery of 1.3 kWh. (4) New
technologies may reduce the amount of lithium needed per battery. (5) The assumption
that the use of lithium in secondary batteries, which are used in portable devices such as
cell phones, will grow between 10 and 15 percent per year over the next 20 years is
optimistic. (6) The forecasts only consider the recycling of automobile batteries, though
other lithium batteries may be recycled as well. (7) The forecasts assume that demand
for the other lithium applications (excluding aluminum production) will grow for more
than 90 years without leveling off.
Figure 1
Illustrative Cumulative Availability Curves
a.
Slowly rising slope
due to gradual
increase in costs.
Price
and
costs
b.
Price
and
costs
Cumulative output
c.
Discontinuity in slope
due to jump in costs.
Sharply rising slope
due to rapid increase in costs
Price
and
costs
Cumulative output
Source: Tilton and Skinner (1987), and Tilton (2003).
24
Cumulative output
Version: 90521
Figure 2
Types of Lithium Resources, Reserves, Products, and Major End-Use Applications
Lithium
Minerals
Resources
Brines
Clays
Sea Water
Lithium
Reserves
Minerals
Brines
Lithium Chloride
Lithium Chloride
Lithium
Concentrates
Lithium Carbonate
Products
Lithium Metal
Lithium Hydroxide
Butil
Lithium
Glazes and
Frits
Major
Applications
Aluminum,
Continuous Casting
Powder, Secondary
Batteries,
Pharmacuticals,
Glazes and Frits
Greases,
Lubricants,
Batteries and
Inorganic
Derivates
Dehumidifier Systems
25
Synthetic Rubber,
Polymers and
Organic Derivates
Pharmaceuticals
and Primary
Batteries
Version: 90521
Figure 3
Major End Uses of Lithium
Others
22%
Batteries
25%
Chemical
Processing
3%
Continuous
Casting
3%
Lubricating
Greases
12%
Pharmaceuticals
3%
Aluminum
4%
Polymers
4%
Glass
8%
Frits
10%
Air
Conditioning
6%
Source: SQM (2007).
Figure 4
Average Lithium Carbonate Prices, 1953-2008
7
Current Dollars
2008 Dollars
Dollars per pound
6
5
4
3
2
1
0
1953
1958
1963
1968
1973
1978
26
1983
1988
1993
1998
2003
2008
Version: 90521
Sources: Industrial Minerals (1999, 2000), Ober (1994 – 2006), U.S. Bureau of Mines
(1953 – 1993), Yaksic (2008).
Figure 5
Cumulative Availability Curves for Lithium Under High and Low Cost Scenarios
With Predicted Cumulative Demand from 2008 to 2100a
High Cost Scenario
Low Cost Scenario
Predicted Cumulative Lithium Demand 2008 – 2100
2100
Cost (US$/lb. lithium
carbonate)
10
8
6
4
2
0
5
10
15
20
25
30
35
40
Availability (Million tons of Lithium)
Note: aThe reported data take into account losses that occur during processing. See Appendix Table 3.
27
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Appendix
Appendix Table 1
Lithium Resources in Minerals by Country and Deposit
COUNTRY
AUSTRALIA
AUSTRIA
BRAZIL
CANADA
CHINA
FINLAND
MALI
NAMIBIA
PORTUGAL
RUSSIA
USA
ZAIRE
ZIMBABWE
TOTAL
DEPOSIT
/PROVINCE
RESOURCESa (tonnes
of lithium equivalent)
Greenbushes
Mount Cattlin
Mount Marion
Koralpa
Minas Gerais
Bernic Lake
Barraute, Quebec
La Motte
Thompson Brothers
Yellowknife
Separation Rapids
Jaijika
Gajika
Maerkang
Lantta
Various
Various
Barroso - Alvao
Various
Kings Mountain
Cherryville
255,000
64,500
19,800
100,000
85,000
18,600
106,000
22,600
26,000
129,000
72,200
450,000
560,000
220,000
12,800
26,000
11,500
10,000
1,160,000
200,000
335,000
North Carolina
Undeveloped
Manono - Kitololo
Masvingo
2,600,000
2,300,000
56,700
8,800,000
Notes:
a
Lithium mineral resources include reserves. The figures are in-situ resources. As a
result, they reflect the lithium in the ground before processing losses. It is recognized
that there are more lithium mineral resources in other places of the world (e.g., China).
However, there is no information to quantify them.
28
Version: 90521
Sources: Anstett and others (1990), Avalon Ventures (2008), Black Pearl Minerals
(2008a, 2008b), Evans (2008a, 2008b), Galaxy Resources (2008), Garrett (2004),
Geoscience Australia (2008), Norton (1973), Industrial Minerals (2007), Pavlovic
(2002), Roskill (2006), Ober (2000), Vine (1976), Yaksic (2008).
29
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Appendix Table 2
Lithium Resources in Brines by Country and Deposits
COUNTRY
DEPOSIT
/PROVINCE
RESOURCESa (tonnes
of lithium equivalent)
ARGENTINAb
Hombre Muerto
815,000a
Rincon
1,870,000g
Olaroz
325,000h
BOLIVIAc
Uyuni
5,500,000a
CHILEd
Atacama
35,700,000i
Maricunga
220,000a
Zhabuye
1,530,000a
DXC
140,600a
Taijinaier
260,000a
Qaidam Basin, Qinghai
2,020,000j
ISRAEL
Dead Sea
2,000,000
USA
Silver Peak
40,000a
Searles Lake
31,600
Great Salt Lake
526,000
CHINA AND
TIBET
e
1,000,000
f
1,000,000
Salton Sea
Smackover
TOTAL
52,300,000
Notes:
a
Lithium brine resources include reserves. The figures reflect the lithium in the ground
before processing losses. Other resources of lithium brines are known to exist elsewhere
(e.g., northern Chile and Argentina). However, the information needed to quantify them
is not available. Figures for Hombre Muerto, Uyuni, Maricunga, Zhabuye, DXC,
Taijinaier, and Silver Peak only include reserves. As a result, their total resources are
much greater than the reported figures.
b
Only three dry lakes are included. Other lithium containing salars in the Argentinian
altiplano are Pastos Grandes, Ratones, Antofalla, Centenario, Pozuelos, Cauchari,
Salinas Grandes, Jama, and others.
c
Only one dry lake is included. There are other lithium containing salars in the Bolivian
altiplano including Empexa, Coipasa, and Pastos Grandes.
d
Only two dry lakes are included, while there are many lithium containing salars in the
Chilean altiplano.
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Version: 90521
e
Only one geothermal brine is included.
f
Only one oilfield brine is included.
g
1.40 million tonnes after 75% recovery is equivalent to 1.87 million tonnes in-situ.
h
Preliminary estimation.
i
Seven million tonnes are lithium reserves.
j
The Qaidam Basin has about 33 salt lakes, consisting of more than 13.92 million tonnes
of lithium chloride resource. Taijinaier is included in the total figure.
Sources: Admiralty Resources (2008), Ballivián and Risacher (1981), Evans (2008a,
2008b), Garrett (2004), Industrial Minerals (2007), Pavlovic (2002), Orocobre (2008),
SQM (2009), Yaksic (2008).
Appendix Table 3
Total Lithium Resources in Minerals, Brines, Clays, and Oceans
Minerals
Brines
Hectoritesb
Jaderitesc
Total (without
oceans)
Oceans
IN SITU
(million tonnes of
lithium equivalent)
8.8
52.3
2.0
0.9
RECOVERABLEa
(million tonnes of
lithium equivalent)
4.4
23.5
1.0
0.5
64.0
29.4
224,000
44,800
Notes:
a
The figures shown in this column are after processing losses. They assume a 50 percent
recovery rate for hectorites and jaderites, a 50 percent recovery rate for pegmatites, a 45
percent recovery rate for brines, and a 20 percent recovery rate for oceans. An important
portion of the lithium not recovered during processing could be recovered by reprocessing, though production costs would be higher. Such recovery, however, is not
considered in the figures reported in this column.
b
The figures for hectorites may not include all the identified resources in the United
States. See Evans (1986) and Kunasz (1994).
c
Lithium in jaderites is not considered in the cumulative availability curve because cost
data for this resource are not available.
Sources: Evans (2008b), Western Lithium Corporation (2008), Yaksic (2008).
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Appendix Table 4
Lithium Reserves and Resources by Country and Deposits, Ranked by Production
Costs, With Grades, Evaporation Rates, and Magnesium to Lithium Ratios
R
A
N
K
I
N
G
1
2
4
8
11
15
18
19
20
22
23
25
26
DEPOSIT,
PROVINCE OR
COUNTRY
Atacama
DXC
Zhabuye
Taijinaier
Hombre Muerto
Olaroz
Silver Peak
Rincon
Maricunga
Greenbushes
Uyuni
Masvingo
(Bikita)
Bernic Lake
Cherryville
Barroso-Alvao
and Covas de
Barroso
Gajika
Maerkang
Brazil
Separation
Rapids
Quebec
Jaijika
Qaidam Basin
Searles Lake
Kings Mountain
Etykinskoe
Namibia
Salton Sea
Great Salt Lake
COUNTRY
GRADE
(percent
lithium)
Chile
0.15
China (Tibet) 0.04-0.05
China (Tibet) 0.05-0.1
China
0.03
Argentina
0.06
Argentina
0.09
USA
0.023
Argentina
0.04
Chile
0.092
Australia
3.00
Bolivia
0.04
RATIOS
(magnesium
to lithium)
EVAPORATION
RATE
(mm per year)
RANGE OF
COSTS
(dollars per
pound)
6.4
0.22
0.001
34
1.37
2
1.5
8.5
8
n/a
19
3,700
2,300
2,300
3,560
2,600
2,600
1,000
2,600
2,600
n/a
1,500
0.70 – 1.00
1.00 – 1.20
1.00 – 1.20
1.10 – 1.30
1.10 – 1.30
1.10 – 1.30
1.10 – 1.30
1.20 – 1.50
1.20 – 1.50
1.20 – 1.50
1.30 – 1.80
Zimbabwe
1.4
n/a
n/a
1.30 – 1.80
Canada
USA
1.28
0.68
n/a
n/a
n/a
n/a
1.30 – 1.80
1.30 – 1.80
Portugal
0.37-0.77
and 0.72
n/a
n/a
1.40 – 2.00
China
China
Brazil
n/d
n/d
n/d
n/a
n/a
n/a
n/a
n/a
n/a
1.40 – 2.00
1.40 – 2.00
1.50 – 2.00
Canada
0.62
n/a
n/a
1.80 – 2.20
Canada
China
China
USA
USA
Russia
Namibia
USA
USA
0.53
0.59
n/d
0.0065
0.69
0.23-0.79
n/d
0.022
0.004
n/a
n/a
n/d
125
n/a
n/a
n/a
1.3
250
n/a
n/a
n/d
1,000
n/a
n/a
n/a
1,800
1,800
1.90 – 2.30
1.90 – 2.30
1.50 – 2.50
2.00 – 2.50
2.00 – 2.50
2.10 – 2.70
2.20 – 2.80
2.20 – 2.80
2.20 – 2.80
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Israel Jordan
0.002
2,000
n/d
2.40 – 3.00
Zaire
0.58
n/a
n/a
2.40 – 3.00
Mali
Canada
n/a
n/a
n/a
n/a
2.40 – 3.00
2.50 – 3.00
n/a
n/a
3.50 – 4.70
USA
1.4
0.66
0.24 –
0.53
n/d
n/a
n/a
3.50 – 4.70
Russia
n/d
n/a
n/a
3.50 – 4.70
20
n/d
5.00 – 6.40
n/a
n/a
7.00 – 10.00
29
Dead Sea
32
Manono Kitololo
Bougouni Area
Yellowknife
33
McDermitt
USA
North Carolina
Russian
pegmatites
36
Smackover
USA
37
Oceans
n/a
0.0386/
0.0365
0.000017
Notes:
n/d = no data are available.
n/a = not applicable, either because the evaporation rate and ratio of magnesium
to lithium are not relevant for lithium extracted from hard-rock mineral deposits
or for other reasons.
Source: Yaksic (2008) and the sources cited there. Production costs are estimates by
Yaksic (2008) based on a variety of industry sources.
33