Effects Upon the Progression of a Society and Its Business Structures Due to Dependency Upon a Nonrenewable Resource: The San Juan Mining Region By Mark Ciotola, [email protected]
Abstract: Businesses and their communities that are substantially dependent upon utilization of a
nonrenewable resource experience a lifecycle progression that transforms the structure of such
businesses and the socio-economic nature of such communities. Understanding the relation
between the progression of a society and its utilization of non-renewable resources can help
communities and businesses develop strategies to become more resilient to the socio-economic
effects of resource depletion.
The San Juans mining region of Colorado (1765-1921) is used as a case study to explore the effect
that utilization of a critical nonrenewable resource has upon the socio-economic progression of
communities and their business structures. The San Juans mining region produced gold and silver
from dozens of mines, around which towns and communities eventually developed. It contained
a fixed amount of exploitable gold and silver (nonrenewable resources), for which there was a
substantial demand, representing an economic potential. Anecdotal sources provide abundant
qualitative information to paint a qualitative picture of life in the San Juans, and enough
quantitative information to provide a few data points for initial model verification.
Economies such as the San Juan mining region and their businesses depend upon the consumption
and utilization of critical resources. There are two types of resources, those that are renewable
and those that are not. Renewable resources represent flows, and are akin to annuities in finance.
Nonrenewable resources represent bubbles, and are akin to a sum in finance.
Geologist M. King Hubbert used a bell-shaped curve to model domestic U.S. petroleum
production over time. This method was in turn based upon that of David Foster Hewett who
modeled regional metal production in Europe. Hubbert’s model is symmetric around the point of
maximum production. However, many instances in society and economics are not symmetric over
time. To overcome this limitation, the Hewett-Hubbert curve has been subsequently derived from
thermodynamic principles that can be generalized to model the utilization of any nonrenewable
resource. This approach is called the efficiency-discounted exponential growth (EDEG) method
and is used to model the San Juans region metal production.
The economic and social progression of a region are derived as a function of its position on a
Hewett-Hubbert curve. Hence, regional economies and their businesses that depend upon
nonrenewable resources can be analyzed as functions of a Hewett-Hubbert curve. Here, mining
activity is a proxy for economic activity, and hence is utilized to trace the region’s economic,
business and social progression. Based upon the business and socio-economic progression of the
San Juan mining region, a generic history of a mining community is presented.
The possibility of the use of such modeling and analysis to create a business and community
sustainability dashboard is discussed. Businesses and communities that wish to become more
resilient can generate a Hewett-Hubbert curve. They could then identify their position on that
curve to develop well-timed strategies to mitigate the harmful effects of resource depletion.
I. INTRODUCTION The economies and societies of mining regions are substantially dependent upon mining activity.
However, the valuable materials being mined in a region comprise nonrenewable resources. The
consumption of such resources over time and the resulting economic development can be
modeled. In turn, the social progression of the region can be modeled as a function of that
economic development. This paper strives to prototype a framework to approach the economic
and social progression of a society, using a case study involving a region dependent upon a nonrenewable resource as a case study. This paper does not attempt to create a definitive,
deterministic model but rather a means for explore and analysis.
II. METHODOLOGY: INTRODUCTION TO HEWETT-­HUBBERT CURVES A. Previous Approaches to Model Mineral Production
There have been previous attempts to model mining and petroleum production. In the 1940s,
geologist M. King Hubbert used a bell-shaped curve to model domestic U.S. petroleum production
over time (Deffeyse, 2001). Hubbert’s approach has been presented essentially utilizing a normal
probability distribution, known as a “bell-shaped” curve. Hubbert developed this petroleum curve
during his involvement with Technocracy, Inc., an early sustainability organization, and then
subsequently refined it. The underlying method originated with the work of David Foster Hewett
who modeled regional metal production in Europe (Hewett, 1929).
The Hewett-Hubbert curve is well known in sustainability circles as “Peak Oil”. The
normal distribution curve is conceptually consistent with observation, since distribution of national
petroleum reserves are widely scattered with a random component. This curve involves a rise,
leveling off then implies a fall in production. Hubbert’s model is symmetric about the point of
maximum production. However, many instances, mineral production is not symmetric over time.
To model such asymmetry, an equation was derived from the Maxwell-Boltzmann distribution
function to model mining output over time for the San Juan mining region in Colorado (Ciotola,
1995). The Maxwell-Boltzmann distribution function is used in physics to describe the
distribution of molecular speeds in a gas. It also provides a rise-fall pattern that is qualitatively
consistent with the rise and fall of mining production in a sufficiently large region. In the case of
a mining region, there is a veritable “cloud” of people. Throngs of grizzly, independent
prospectors scattered widely over a confined region does not seem so unlike a cloud of kinetic,
widely-space particles comprising an ideal gas. Even well financed, corporate mining operations
(in the later stages of the region’s mining life) trying to find mysteriously hidden and placed
pockets of gold and silver among mountains of rock seemed to fit within the gas cloud analogy.
A few data points were utilized to constrain the parameters for this model for the San Juans
region.
B. Hewett-Hubbert Curves
The Maxwell-Boltzmann distribution was originally chosen because it provided an
asymmetric approach. Yet, the Maxwell-Boltzmann distribution function was merely an analog.
To develop a more fundamental approach, the Hewett-Hubbert curve has been subsequently
derived from thermodynamic principles that can be generalized to model the utilization of any
nonrenewable resource. Hubbert’s model has been recast in terms of a collection of heat engines
operating upon a nonrenewable thermodynamic potential. Such an approach reaches deep into the
statistical mechanical roots of systems. This allows Hubbert’s model to be generated directly from
actual energy or resource data.
Untapped mineral or petroleum reserves represent a potential. The miners and their
machinery and infrastructure present a collection of heat engines. According to the proposed eth
Law of Thermodynamics, entropy increase shall follow the Principle of Least Time. Evidence in
support of the eth Law is provided by heat refraction and the parallel conductors example (Anila,
2010; Ciotola 2001). The eth Law of Thermodynamics can be restated for operational purposes as
the Principle of Fast Entropy, that isolated systems shall tend to configure themselves in a
manner that maximizes their rate of entropy production. Everything else being equal, increased
economic activity results in a greater rate of entropy production. Hence it is assumed that if an
economic system can increase production, then it will do so. In that light, the maximum rate of
growth for an isolated economic system is pure exponential growth.
Yet, as in the case of a mining region, a critical resource of limited quantity is being
utilized, and likewise represents a finite thermodynamic potential. Typically, as this potential
becomes consumed, processes utilizing the potential experience decreasing thermodynamic
efficiency. This is analogous to diminishing marginal returns in economics. Consequently, growth
levels off and eventually becomes negative.
This situation can be illustrated by considering a heat engine that can transform potential,
comprising thermal reservoirs of differing temperatures, into work. Initially, the temperature
difference between the reservoirs remains high, so the engine outputs work at high efficiency.
Further, the engine is capable of using its outputted work to reproduce itself. The engine
produces enough work to produce a second engine, which doubles the amount of work produced,
as well as doubles the heat flow between reservoirs and also the rate of entropy production. As
the quantity of heat engines increases, the cumulative heat flow thus increases. Though quite
large, eventually the warmer reservoir becomes slightly cooler and the cooler reservoir becomes
slightly warmer, resulting in declining efficiency. Yet work still gets accomplished and hence
more heat engines are built, and total work may actually increase for awhile. As the temperature
difference continues to decrease, efficiency falls so much that the total work begins to decrease.
Eventually, the temperature difference falls to zero, so that no more work can occur, and the rate
of entropy production falls to zero. This approach is called the efficiency-discounted exponential
growth (EDEG) method and is used to model the San Juans region metal production.
Deriving the Efficiency-Discounted Exponential Growth (EDEG) Equation
Although efficiency-discounted exponential growth simulations can become rather involved, a
first approximation can be created quite simply, as long as reasonable start and finish times can be
assigned. The criteria for start and finish times is when significant production began and ended.
This approach assumes that the system will be large and independent, and that production will be
continuous.
We can express decreasing efficiency using an adaptation of the formula for engine
efficiency. As discussed, efficiency-discounted exponential growth (EDEG) applies to situations
where a nonrenewable resource is consumed. EDEG assumes that societies strive to grow
exponentially. EDEG further assumes that as the resource is consumed, the efficiency of converting
that resource into a productive benefit declines. The combination of these to assumptions produces
a rise and fall in production.
Let us derive an EDEG function. We first take the consumption rate of a nonrenewable
resource with respect to time dC/dt. Then we discount it by efficiency 𝜖 to get the production rate
with respect to time dP/dt for that time period.
𝑑𝑃 𝑑𝐶
=
𝜖
𝑑𝑡
𝑑𝑡
If one sums the production increases for all of the time periods of interest, then one
obtains the total production P for the time range of interest 𝑛.
0
.12
𝑑𝐶
𝑥 𝜖.
𝑑𝑡 .
The ability to consume is typically based upon the build-up of equipment, workers and
other productive infrastructure. For an isolated society, such increases must be financed (or
simply built) out of previous production. So dC/dt is actually a function of P, which in turn is a
function of dP/dt. Yet dP/dt also depends upon efficiency. In many cases, efficiency does not
remain constant over the lifetime of a process. Thermodynamics indicates an intrinsic way to
model efficiency. For a Carnot heat engine, efficiency 𝜖 is a function of the temperature
difference of two thermodynamic reservoirs ∆T:
𝜖 = 1 − 𝑇6
𝑇7
It is possible to relate this quantity to economic expressions, such as gross margins. However, for
the sake of prototyping, we will use a simplified expression for efficiency:
𝜖 = 1 − 𝑃.
𝑃0
where Pi is total production this far and Pn is the total production that can ever occur. Efficiency
represents what percentage of consumption can be turned into production. In the case of metal
ores, placer surface deposits of pure gold can be processed at 100% efficiency (excluding
transportation and overhead). They can simply be picked up and used or sold as is. However,
gold ore removed from underground has varying percentages of gold metal. Some is quite high
while others may contain just a few specs per stone. Here, a rough expression of efficiency
would be the percentage of gold that gold ore contains. Efficiency also includes other intrinsic
physical costs or sources of difficulty. For ore containing the same percentage of gold,
consuming ore that is deep underground is less efficiency than consuming such near the surface.
Digging deeper mine shafts if more expensive. Note that this intrinsic physical efficiency is
independent of the ability to consume. Plugging efficiency back into our earlier expression:
𝑑𝑃 𝑑𝐶
𝑃.
=
1 − 𝑑𝑡
𝑑𝑡
𝑃0
We also need to model consumption. We could simply model consumption C as being
equal to production P. The above is sufficiently self-contained approach to create a first
approximation of a model of production with respect to time. Summing dP/dt up to time n will
always equal Ptotal. The efficiency function will always be sufficient to achieve this effect.
However, the results are likely to be ill-timed.
A better approach is to parameterize consumption by discounting production by the cost
of creating consumptive capacity. Say, for example consumptive capacity is chiefly composed of
mining machinery. Then production itself should be discounted by the cost of such machinery.
Say for example, that a ton of gold will pay for a machine that can itself extract (consume) half a
ton of gold per year. Then production should be discounted by 50% to indicate consumption. So
we modify our formula:
𝑃.
𝑑𝑃 𝑑𝐶 1 − 𝑃0
=
𝑑𝑡
𝑑𝑡
𝑏
where b is the cost per unit of consumptive capacity in terms of a unit of production. This
concept is akin to return on investment (ROI), but different in that the output is not financial
production but the ability to consume. If we were strictly speaking of money, b does not
represent the ability to make profits but rather to gain gross revenues.
III. APPLICATION OF METHODOLOGY TO SAN JUAN MINING REGION The following case study will illustrate how the EDEG approach be applied to a mining region.
A. Brief description and history of the San Juans mining region
The selection of the San Juans for this case study was inspired by Smith’s Song and Hammer
(Smith, 1982), and some of the narrative information is drawn from that source. The San Juan
mining region of Colorado produced gold and silver from dozens of mines, around which towns
and communities eventually developed. Mining began as early as 1765. Its heydays were between
about 1889 and 1900. Currently there is again mining in miscellaneous minerals, but not much in
gold, which was the primary economic driver for the “great days” (Smith, 1982; Twitty, 2010).
Spanish gold mining of placer deposits took place between about 1765-1776. Placer
deposits are native pieces of nearly pure gold found on the surface. Some mining took place in
1860, but it was interrupted by U.S. Civil War. At this point, “only the smaller deposits of highgrade ore could be mined profitably.” Mining slowly started again in 1869. There were 200 miners
by 1870. An Indian Treaty was negotiated in 1873, which removed a major obstacle to an increase
of mining (Smith, 1982; Twitty, 2010).
By 1880 there was nationally a ‘surplus of silver; pressures to lower wages; labor troubles.’
In 1881 a railroad service was established, resulting in a ‘decline in ore shipping rates.’ Around
1889, English investors had come to control the major mines by this time. The 1890 production
total for San Juans was $1,120,000 in gold; $5,176,000 in silver. The region produced saw
$4,325,000 in gold and $5,377,000 in silver in 1899 (Smith, 1982).
By 1900, the region began to take on more of the characteristics of a settled community.
There was a movement for more “God” and less “red lights.” By 1909, “the gilt had eroded”
(dilapidation set in; decreasing population). In 1914, production greatly fell, due to decreased
demand from Europe (because of World War I) and the region lost workers. Farming becomes
more important to local economy than mining. Recreation and tourism revenues become the only
bright spot for many mining towns. Silver and gold mining all but ceased by about 1921. The
region is now used primarily for recreation and some agriculture (Smith, 1982; Twitty 2010).
B. Suitability of the Use of San Juan Region Mining Productions as a Case Study
We can use an EDEG approach to model gold and silver mining production in the San Juan region
of Colorado. Here, mining activity is a proxy for economic activity, which is in turn a proxy for
entropy production. Mining requires energy, and more mining requires more energy. Entropy
production is proportional to energy production, everything else being equal.
The EDEG method works most easily with an entirely closed, isolated system. The San
Juan region was a mountainous frontier region and can be approximated as being isolated. It
contained a fixed amount of exploitable gold and silver, for which there was a substantial demand.
That exploitable gold and silver in light of such substantial demand represents a potential.
However, there are several factors that impact the validity of this approach. First, the region
is not entirely dependent upon its own resources for growth. Miners, equipment and investments
can and did come from outside of the region. Second, the region is not extremely large, so the
opening and closing of individual mines due to poor management or unlucky veins can make the
data somewhat noisy and “lumpy”. Third, external economics and politics played a tremendous
role over the demand for metals and their prices, which impacted the amount of production. Fourth,
this is not a single metal region, but involved at least four major metals (gold, silver, copper and
lead) (Henderson, 1926), each with their own characteristics and economic structure for extraction,
processing and demand.
Nevertheless, the region does meet the chief characteristics. There is only a limited amount of
the metal in the ground, and the region does have reasonably distinct beginning and end points
for substantial mining activities. Through the sources utilized, there is abundant information to
paint a qualitative picture of life in the San Juans, and enough quantitative information to
generate and constrain models.
D. San Juan EDEG model
Although the San Juans regions encompasses several counties, we have chosen the county named
San Juan to model. Annual production data is available for that country for most years of interest
for the five most important metals. We first generate a conceptual model for the county.
The first plot is annual production of silver and gold in unadjusted dollars. An initial
value of total gold under the ground of $10,000,000 was selected. That is below the actual figure,
but it allows easy rough visual calculations of proportions of area under the curve. The total area
under the curve represents cumulative production.
Initially, mining involved finding placer deposits on the surface. Mining continued on a
relatively low level, but gradually increased, including deeper and deeper subsurface mines. As
with any exponential growth curve, production begins slowly, but then turns a corner and really
takes off. We see that in the below model around 1895. Alas, with mining, all good things must
come to an end. As gold is extracted from the ground, there is less remaining to remove.
Production must eventually fall off and cease, as shown by the model for about 1923. Not for
modeling purposes, historical events that will indicate the beginning and end points apparent and
can be used to initiate and terminate the model. Minor amounts of mining before and after these
start points can often be ignored with relatively little loss in accuracy. A cost of capacity ration
of 2.5 is utilized. That is, it costs $2.5 of investment to produce an annual rate of $1 of gold. This
is analogous to a return of investment (ROI) of 40%. That may seem high, but only a small part
of the ROI actually might have gone back to investors. This is speculative.
The second plot shows cumulative production. The height of the second plot is equal to
the area under the first plot. Unless gold is placed back into the ground, the plot must continue to
rise until all the commercially viable gold removal has taken place.
How would the model appear for actual data? Gold from 1873 to 1923 is both modeled
and the actual data plotted below. A treaty with native Americans who owned the land was
signed in 1873, opening the way to increased mining. Large-scale gold mining ceased in 1923.
The total amount of gold extracted was $22,711,113 (Henderson, 1926), so we use this figure for
the total amount under the curve. (It is much easier to model historical figures than to predict
future figures). To get the peak to correspond closely with the actual peak, we find a
consumption capacity cost ratio of 3 works reasonably well. This corresponds to an ROI of 33%.
The fit of the plot to the data is not dreadful, but there is still considerable “noise”. The price
paid for gold is frequently changing. Particular mines rise and fall within the country due to
either gold exhaustion or financial mismanagement. Note that this plot is just for one metal,
albeit it the driver for other mining. The other metals must be considered to obtain a more
accurate picture of the economy, but we will just consider gold for the sake of illustration.
IV. ANALYSIS AND SECONDARY FUNCTIONS A. Modeling Economic and Businesses Progression with a Hewett-Hubbert Curve
Regional economies and their businesses that depend upon nonrenewable resources can be
analyzed as functions of a Hewett-Hubbert curve, going through a lifecycle as the region
progresses through the curve. The structure of the regional economy and the nature and
characteristics of its businesses will change as a function of the curve. Obviously, the size of
economy increases after the initiation of the curve, and then it must level off and taper down as
the underlying resource becomes exhausted. There may be some residual economy even after the
end of the curve, possibly forming a long tail. If a new, long-term primary economic activity is
formed such as tourism, then the tail may be both long and fat.
The quantity of firms will initially increase, then level off, then likely taper down. There
are two chief causes of the increase. First, as the region becomes successful, additional primary
industry ventures will likely be attracted, especially at the early stages where many new small
firms may be supported. There will be individual prospectors and small groups of prospectors
that will extract small amounts of high value minerals from placer deposits or small stakes and
claims. They will bring their own transportation and supplies. They will provide all (or nearly
all) of their own services. With the formation of mines, small towns will appear. These towns
will provide food and other supplies to the miners that directly support their activities. There may
be some lodging and entertainment. The composition of such a town might be a general store, a
livery business and a hotel (with a meal and entertainment venue).
As the mining region develops, its population and wealth will increase. Therefore the
diversity of business types to support the population and its activities will increase. As mines
become larger (and more abundant), more settled types of miners will appear. They will either
start or bring families. Establishments providing basic medical services will appear, along with
competitors for the earlier types of businesses. A blacksmith may appear. There may be a
dedicated building supply firm, and an assayer. As the town gets more established, it may
establish a government. There will be a town clerk, law enforcement and a school. Finally, a few
professionals may appear such as layers. The town may stay at this point if the population
remains stable. Or if the town continues to grow, there may be a department store.
Second, as the magnitude of the economy increases, the diversity of firms will likely
increase due the greater wealth available to afford specialized goods and services. There are
typically two chief causes of the tapering. First, total economic activity may decrease, so that
fewer firms can be supported. Second, even during the peak, extensive industry consolidation
may occur. Individual businesses will tend to become larger, as both the volume of the economy
increases as well as due to mergers and acquisitions. We can thus deduce a hypothetical
economic centralization function. We can assume an arbitrary number of mining companies, then
consolidate that number. Consolidation leads to economies of scale. Yet it also leads to more
separation and disconnect between the workers and higher levels of management, leading to
strikes and other labor problems. We can clearly see this phenomena as the San Juan economy
progresses.
Centralization = = (quantity of ending mines – quantity of beginning mines) quantity of beginning mines
B. Modeling Social Progression with A Hewett-Hubbert Curve
The social progression is also dependent upon the position of the curve. Just the the curve is the
result of an irreversible process, so too is the social evolution of a community. There are several
social functions that correspond with curve position. Related to economic centralization is a
counter function of feelings of individual empowerment. While centralization increases,
individual empowerment for the average person is decreasing. Another function is hope and
optimism for the future. It is high when the curve is increasing rapidly, but lower once the curve
levels off. However, there is typically a time lag. Expectations of growth may remain well after
production begins leveling off, resulting in both economic and social crises due to overshoot.
The decline of the “hope” function may lead to cynicism, depression, increased substance abuse
(relative to income) and domestic violence, similar to what was experienced during the decline
of weavers in England at the dawn of the industrial revolution.
Another function is the formation of infrastructure and gentrification. There are more
stores, libraries, schools and other services as production increases (this is likely also lagging
progression). Another might be the female/male ratio, and likewise the proportion of children in
the population. It tends to increase as the curve progresses, at least until the end. This might also
be a lagging function.
V. CONCLUSION Tracing the quantity of ore removed from the ground as a percentage of total ore can help
determine the effective “age” of that community, that can be then used to develop a sustainability
dashboard to help a mining region schedule and strategize its transition to long-term economic
and social stability.
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