The Role of Capital, Mineral Resources and
Environmental Resources in Sustainable Development
Dina Franceschi
Department of Economics
Fairfield University
Fairfield, CT 06430‑5195
(203)254-4000x2850
dfranceschi@fair1.fairfield.edu
James R. Kahn
Environmental Studies Program
and Department of Economics
Washington and Lee University
Lexington, VA 24450
(540)463-8063
kahnj@wlu.edu
August
6, 2000
Abstract
Since the Brundtland Commission’s delineation
of the term sustainable development in 1987, virtually every country has
incorporated the terms sustainability and sustainable development into their
planning vocabulary and criterion for decision-making. However, many issues
remain unresolved. Broad and sweeping
references to sustainability and sustainable development do not necessarily
translate into implementable policies to achieve these goals. In particular,
unresolved issues include developing an understanding of how one sector of the
economy can contribute to the sustainable development of the economy as a whole
and the role of ecological resources in sustainable development. Our paper
provides an initial conceptual examination of these questions by examining the
interaction between mining, ecological quality and sustainable development,
with specific application to the sustainable development of the Brazilian Amazon.
1.0 Introduction
The term and concept of sustainable
development has received much attention since the late 1980's, when it became
the global theme for a long-term perspective on economic growth. The definition of the terms has been molded
to fit different situations since then[1],
but has mostly retained the original thrust behind which sustainable
development is driven. Generally, the
interpretation relates “improving the prospects of the current generation
without reducing the prospects of future generations” (Brundtland Commission
1987).
The general thrust of the definition of
sustainability in the neoclassical economics literature (which incidently,
predates the term sustainability and dates back to the early 19th
century with the work of Ricardo, Malthus, and John Stuart Mill) is that
certain indicators of economic welfare (or development or standard of living)
are non-declining over time. If economic welfare (or an alternative indicator
of development or standard of living) is a monotonic function of consumption,
then sustainability can be defined as a non-declining intertemporal consumption
path. Sustainable development can then be viewed as a process of change within
the economy which does not violate one of these sustainability criteria (Stern
1997), or more narrowly, can be regarded as an increase in the consumption
levels of the current generation which does not result in future declines in
consumption levels. Alternative
definitions of sustainability focus on the pursuit of economic efficiency, with
some sort of sustainability constraint. For example, Pezzey suggests an
operational definition of sustainability which calls for maximizing net present
value (of the whole intertemporal stream of welfare (or consumption)), subject
to a constraint on non-declining average welfare (or consumption).
The neoclassical economics perspective on
sustainability has essentially become a treatise on the role of capital stocks
in economic growth (Stern 1997). The models generally define two types of
capital, conventional (also called artificial, physical, manufactured or
human-made capital) and natural capital. Natural capital is generally viewed as
an extractive resource, usually non-renewable such as coal, iron or oil.
Natural capital and human-made capital are most often regarded as perfect
substitutes (the elasticity of substitution is equal to one). Under these
conditions, sustainability is possible if sufficient investment takes place in
human-made capital to offset the loss of natural capital. Since artificial
capital and natural capital are completely substitutable, one needs only be
concerned with the accumulation of the aggregate stock of capital.[2]
This has become known as the weak sustainability criterion. In contrast, the strong sustainability
criterion suggests that there are limited opportunities for sustainability, and
one must maintain non-declining stocks of both artificial and natural capital
in order to ensure a non-declining intertemporal welfare path.
Stern notes that there has been little
empirical work on the substitutability of artificial capital at a scale which
is relevant to the sustainability issue. A set of authors[3]
focus on the scale issue and provide conceptual arguments as to why artificial
capital is not likely to be completely substitutable with natural capital.
These arguments are best understood by dividing natural capital into two
categories, extractive resources and environmental resources.
This definition implies a particular path for
society’s stock of capital assets, where assets can be broadly defined to
include the stocks of human-made capital, human capital, extractable resources
and environmental resources. In order to allow for an increasing standard of
living, the aggregate stock of capital assets must be increasing as well,
especially in the face of increasing population. Specific treatments of
sustainability generally have not
looked at all four types of capital stocks mentioned above, and have made
restrictive assumptions about substitutability among different types of
capital.
We attempt to broaden the discussion of
sustainable development by simultaneously examining the role of all types of
capital assets. We then discuss the implications of this reconsideration for
sustainable development of the Brazilian Amazon, a region rich in environmental
and extractable resources, but with a relatively small stock of human-made
capital.
A particularly important aspect of our
approach will be to differentiate between extractable resources (such as
minerals and fossil fuels) and environmental resources (such as ecosystems).
Environmental resources provide a broad range of ecological services such as
nutrient cycling, habitat protection, carbon sequestration and watershed
protection. The importance of this distinction between extractable resources
and environmental resources, as discussed later in the paper, is that
artificial (human-made) and human
capital are likely to be good substitutes for extractable resources, but none
of these types of capital are likely to be close substitutes for environmental
resources.
2.0 Traditional Approaches
2.1 Neoclassical Growth and Development Models
Neoclassical growth and development models
tend to focus solely on problems of artificial (human-made) capital
accumulation. These models developed rules for allocating current output
between consumption and investment in artificial capital. For example, the classic Harrod-Domar model
of development sets up a system of economic growth equations based on the full
employment of capital and labor where the steady-state rates of growth of
capital, labor and output are equal.
The conclusions of the model, given exogenous factors, are that the
warranted rate of growth is equal to the ratio of the propensity to save to the
capital-output ratio. Variations on the
paradigm include, Solow’s factor substitution model which resolves the same
question but with added flexibility in inputs (K and L), and Kaldor’s saving
rate adjustment model which allows flexibility in the saving mechanism to
compensate for disproportional labor force growth. Recall however, that the majority of the classic growth models
examined savings and investment from purely the capital-profit or labor-wage
standpoint.
The policy implications of these models are
that development can be viewed as a process of artificial capital accumulation
and of removal of obstacles to the artificial capital accumulation
process. Poverty of nations was viewed
as a self-perpetuating process, a vicious cycle of poverty which is depicted in
Figure 1. In this view of economic development processes, low income and high
current consumption needs lead to low savings, low investment in artificial
capital and a lack of artificial capital formation. The low stock of artificial
capital implies a continually low marginal product of labor, with a
correspondingly low level of income. In fact, since human-made capital
depreciates, capital stocks may fall over time due to insufficient investment
to counter depreciation, and as a result, income may be falling over time. In
this perspective on development the solution to the problem is simple: inject
capital and break the cycle of poverty. This was essentially the basis of the
international development programs of the 1960s and 1970s. Unfortunately, in
many places such as Sub-Saharan Africa, this development program was largely
unsuccessful, with the current standard of living generally lower than it was
three of four decades in the past. While rapid population growth, tribal
conflict, civil war, AIDS and government corruption may have been important
factors in the lack of economic development in some countries, another important
factor is that development policy may have focused too much on the accumulation
of human-made capital, to the exclusion of consideration of other types of
capital, particularly environmental capital.
Figure 2 illustrates the shortcomings of
these traditional models by showing how environmental degradation can effect
the cycle of poverty. Low income and high current consumption needs lead to
environmental degradation from over-exploitation of renewable resource systems,
causing their (often irreversible) collapse. Also, inefficient production
technologies lead to high emissions of waste products, causing urban
environmental problems and contamination of aquifers.
This environmental degradation lowers the
marginal product of labor. This is particularly important in the rural areas of
developing countries, where desertification, deforestation, fishery collapses
and soil erosion/fertility loss lead to losses in agricultural productivity. In
addition, the human health consequences of air pollution and drinking water
contamination make labor less
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productive and generate costs such as those associated with the
treatment of health problems. Finally, the environmental resources provide
ecological services such as maintenance of climate, biodiversity, nutrient
cycling, waste assimilation, primary productivity, maintenance of atmospheric
chemistry, soil formation, protection of water resources and flood protection,
all of which are important to basic life processes, quality of life and
economic productivity.
2.2 Sustainability and Exhaustible Resources
The conventional treatment of exhaustible
resources in terms of sustainability dates back to the early works of Thomas
Malthus and David Ricardo, where resource scarcity and diminishing returns
dominated the analysis. These models
focused on finite resource supply and whether continued economic growth was
possible as resources became more scarce.
Work by Barnett and Morse (1963) built on these ideas by emphasizing the
inevitable development of, and switching to good substitutes for the resources
that become characterized by increasing scarcity. Utilizing a model based on the free substitution of inputs
(labor, artificial capital and exhaustible resources), Barnett and Morse found
that technological innovation in discovery, extraction and production techniques
lowered the costs of extractable resources, greatly outweighing the cost
increasing effects of depletion. These
influential findings largely refuted the previously held notion that Malthusian
limits to growth existed and would constrain or collapse current consumption
and development rates. Barnett and
Morse’s conclusions have served as the point of embarkation for further
exploration of the relationship between sustainability and exhaustible resource
use, including works by John Hartwick (1977,1993, 1994), Raymond Mikesell
(1994), John Pezzey (1989), John Tilton (1996) and Vincent, Panayotou and
Hartwick (1997).
The assumption of substitutability between
inputs is not an inconsequential one.
The fundamental premise underlying the work of Barnett and Morse is the
interchangeability between labor (human capital), artificial capital, and
extractable natural resources as inputs to the production process. Two issues regarding substitution to achieve
sustainability in these models are of concern.
The most important issue is that the models
do not incorporate the environmental or ecological resources as inputs to the
production process. As discussed earlier, ecological resources provide an array
of important services to a variety of different production processes, day to
day living and other ecological systems.
However, the inclusion of environmental resources or ecological services
into the production function is not in itself sufficient to rectify the
shortcomings of these economic models of sustainability. In addition, one must
consider the notion of complete substitutability among the different types of
capital.[4]
Kahn and O’Neill (1999) argue that at the
large scales defined by the current level of economic activity, artificial
capital can not provide an adequate substitute for environmental resources, as
it is completely infeasible for human
activity to provide the ecological services at the level of natural activity.
For example, although artificial capital can be used to process point source
wastes in a sewage treatment plant, it would be completely infeasible for all
the non-point sources of nutrients (both natural and anthropogenic) to be
processed by treatments plants. Perhaps the best example of the inability of
human-made capital to substitute for natural capital can be found in flood
protection in the Mississippi River flood plain. Flood protection was provided
by environmental resources in terms of wetlands which acted as giant sponges,
absorbed sudden large influxes of rainwater, storing them, and gradually
releasing them to be carried downstream over a prolonged period of time. As
wetlands were converted to farmland and other economic purposes, systems of
dikes and levees were developed to try to control the flooding problem, however
they were not capable of doing so. In fact the “one hundred year flood” which
occurred in 1993 was generated by a “20 year” rainfall, indicating a vast
reduction in flood control protection, despite the provision of the artificial
capital devoted to the production of flood control. It should be noted that
scale is not the only source of concern. Ecological complexity argues against
complete substitutability between environmental capital and other types of
capital (see Kahn and O’Neill 1999).
Further, the traditional neoclassical
approach (which suggests the mitigation of scarcity associated with exhaustible
resources) is based on the premise that the market can allocate supply and
demand and create appropriate incentives through the pricing system. In the classic literature of resource
scarcity, including the work by Barnett and Morse, as an exhaustible resource
or mineral resource base becomes depleted, prices rise. The rise in price is primarily the response
of increased costs of extraction of the relatively less abundant source
(relative in the sense of the deposit being less rich than deposits of the
past). As price of one product rises,
either firms find better extraction technology to control costs or buyers
switch to another product that can satisfy their needs at a lower price. In the case of environmental or ecological
resources, no comparable market mechanism exists to send appropriate signals or
create incentives to mitigate scarcity.
Most often ecological systems do not have prices associated with their
services, because they are external to markets. The public goods (and often open-access) nature of ecosystems
often precludes sustainable long term usage.
Again, the fact that these systems are exceptions to the classic market
mechanisms heightens the need for their explicit inclusion in the formula for
sustainability.
3.0 A Theoretical Treatment of Sustainability
Much time and effort in the recent past has
been devoted to finding the optimal rate of exhaustible resource extraction for
intergenerational sustainability.
Solow, Hartwick, Stiglitz, Pezzey, and others have contributed to this
literature. Hartwick in particular has
derived a saving and investment rule for economies utilizing exhaustible
resources. The Hartwick model and its
results focus on the generation of sustainability through a replacement
mechanism. That is, the rule defines
the level of investment and savings which must be generated by the current
generation to replace the natural capital (exhaustible resource stock) they
have consumed, in order to maintain a constant level of consumption for future
generations (Hartwick 1977 and 1994).
Traditionally, sustainability was approached
using the steady state notion of constant consumption over time, where utility
is defined as a function of consumption.
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The Hartwick model seeks to examine the possibilities of maintaining at least a constant level of consumption over time, which can be expressed as
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Hartwick’s capital theory of investment model begins with a stock of exhaustible resources, S(t), where the continuous extraction of the stock is the flow of the resource, R(t).
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Production is defined as needing two inputs, R and K, exhaustible resource
flow and artificial capital stocks, respectively.
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If Equation (4) is differentiated with respect to time, this gives the
time derivative of production, as in equation (5)
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Hartwick then defines the reinvestment rule as a level of investment
set equal to a chosen proportion (α) of the rents associated with the
production of exhaustible resources. With extraction costs assumed to equal
zero, rents would be equal to the product of resource extraction (R) and the
marginal product of resource flows (FR). The reinvestment rule would
then be given by equation (6).
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Consumption can be measured as a residual or the difference between
production and investment:
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The model then employs Hotelling’s efficiency rule for exhaustible
resources and some clever mathematical manipulation, to find [5]
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This equation merits further discussion. If
the marginal product of resources is positive, and since 0 £ α £ 1,
the sign of will depend on the sign of FR. FR, the
marginal product of resource flows, will be positive. Therefore the sign of will depend on the sign of . If the stock of resources
is finite (and technology is assumed constant as in the Hartwick model) then must eventually
become negative. Therefore, the greatest possible value of is zero, which will
occur when α = 1, or when all the
rents are reinvested in artificial capital. Intuitively, this simply means that
as long as the current generation is reinvesting exactly the rents derived from
the extraction of the exhaustible resource, consumption can be maintained at a
constant level over the time horizon chosen.
In Hartwick’s model, can not be increasing. However, if one allowed the stock of
resources to increase (through technological innovation) then could be increasing
and the reinvestment rule would change, as
α = 0 would maximize . Of course, if technological innovation required investment
in artificial capital, then the optimal proportion of reinvestment or rents
would be somewhere between zero and one, exclusive of the extreme values.
Obviously, these models do not
incorporate environmental resources or ecological services, which, as discussed
earlier, have important implications for sustainability. Environmental
resources can be added to the Hartwickian approach, and this will add
considerable insight to the understanding of the necessary and sufficient
conditions for sustainability.
Environmental resources can be
incorporated by taking the same initial mathematical construct with the
addition of a term that relates the extraction of the exhaustible resource to
the depletion of ecological services.
We will follow Hartwick’s model,
rather than developing a new model, in order to facilitate a comparison
of results. We start with the definition of the ecological resource stock as
being proportional to the exhaustible resource stock. As the mineral resource stock (S) is extracted, it gets smaller
and more land is used and greater degradation is generated, thus causing the
ecological resource stock (E) to get smaller as well. Also, ecological services are some function of the ecological
resource stock. If ecological services
are modeled as enhancing utility or consumption directly, consumption can now
be defined as production plus ecological services minus the change in capital.
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Similar mathematical analysis using the state equation for
exhaustible resource extraction (1), the same reinvestment rule (2) and
Hotelling’s efficiency rule results in a potentially non-sustained rate
of consumption over time.
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If 0 £ α < 1 and both the time derivatives of R and E are
negative, then the time derivative of consumption must be negative. Utilizing
the Hartwick rule of total reinvestment of resource rents, where α=1, the
change in consumption moves with a change in the ecological stock.
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Consumption can actually be enhanced by a growth in
ecological services (e.g., allowing the Everglades Agricultural Area to revert
to wetlands and increasing water flows to heavily populated South Florida) or
conversely diminished by a negligence in ecological protection (e.g. continued
drainage and wetland conversion which reduces water flows to South
Florida). The results become ambiguous
however, when the reinvestment of rents rule is relaxed. Depending on the relative magnitudes of the
two terms, the change in consumption could be negative or positive.
The interpretation of equation
(12) places the sustainability debate in context. At one extreme would be the
“Technological Optimists” who would argue that is positive, that both and FR are
large, and that this would compensate for a negative At the other extreme
would be the “Environmental Pessimists” who would argue that is negative, that can’t be positive due
to the finiteness of crustal mineral deposits, and that must be negative.
A less extreme approach would
recognize the sign of as a policy choice. can be positively
influenced by investment in research and development, artificial capital and human
capital. However, care must be taken so that the process of accumulating these
stocks of capital do not negatively impact environmental capital stocks, and
their ability to produce ecological services such as as maintenance of climate,
biodiversity, nutrient cycling, waste assimilation, primary productivity,
maintenance of human capital, and the protection of environmental capital. The
development of policies to influence technology towards a smaller ecological
footprint is an important part of this process. In addition, policy can invest
directly in environmental capital by remediating existing problems,
reforestation, creation of wetlands, carbon sequestration, and so forth. If the
above conditions are met, then it is theoretically possible for to be positive and sustainable development can be an
achievable goal. However, if the sign of is a policy choice, then
sustainability must be pursued with an active policy agenda and not simply left
to market forces, as the market forces which alleviate scarcity of mineral
resources are not applicable to environment resources.
A similar result with similar
implications occurs when the representation of ecological services enters the
model through the production function as opposed to entering into consumption
directly. Production in this case is a
function of the capital flow, exhaustible resource flow and exhaustible
resource stock.
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Relying on the same relationship between exhaustible
resource stock and ecological resource stock, the change in consumption
relationship after mathematical manipulation again shows reduced consumption
over time with the addition of ecological services depletion.
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The possibility of declining
consumption again occurs, the result being determined by the magnitudes of the
terms. In any case, however, the change
in consumption over time is either improved or diminished by the marginal
contribution to production of the change in ecological services over time. Assuming that the marginal product of the
environmental asset is positive, when α=1, the change in consumption again
moves with the change in the environmental stock.
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One can gather considerable
insights to the areas in which policy can contribute to sustainability by
looking at Equations (12) and (16).
Policy must strive to make the sum of both
terms of this equation positive. This may not seem possible
given the initial assumptions of the model, but the assumptions can be relaxed
to allow for technological change. First, technological innovation can change
the sign of the time derivative of R. Although the crustal abundance of mineral
resources can not be increased, technological innovation can increase the
availability of the resource stock S over time, implying that R need not be
declining over time. R can also be increasing over time due to the judicious
use of renewable resources, including the sun’s energy. Secondly, the time
derivative of the environmental resource is actually equal to -B*R, where B
measures how much extractive resource depletion/usage depletes the stock of
environmental resources. The more that technological innovation can reduce the
environmental impact of extractive resource use (B), the smaller the second
term of the equations (12) and (16) and the less it would offset a potentially
positive first term. It is important not to lose sight of the substitutability
arguments that were made above. If artificial capital and extractive
resources are poor substitutes for ecological services, then as environmental
resources decline, FE will become very large, and consumption will
inevitably have to decline.
The role of the magnitude of FE
merits further discussion to discover the full implications of FE
for determining the sign of . Figure 3 shows the total product function for ecological
services, where the slope of the function is equal to FE. As with
other inputs, diminishing marginal productivity is expected, and is reflected
in the slope of the function in Figure 3. Note that if ecological services are
a monotonic function of environmental resources, E could represent either
ecological services or environmental capital in this graph.
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Two aspects of this total product
function merit further discussion. First, at high levels of ecological
services, the losses associated with a small diminution of ecological services
are also
likely to be small. In fact, if increases in ecological
services become redundant at high levels of ecological services, the slope of
the total product function may equal zero. Second, there may be
a threshold below which production falls dramatically with
further reduction in ecological services. This threshold is likely to exist
because of the complexity and nonlinearity of ecological behavioral functions.[6]
Both characteristics have
important implications for equation (12). If is negative, the product of FE and will be small in the vicinity of E2 and large in the vicinity
of E1. This illustrates the underlying cause of the assertion that a
non-negative is more likely when the level of ecological services is high
than when the level of ecological services is low.
4.0 Implications for Sustainable Development of Amazonia
Policy, the Case of Amazonia
The theory in the preceding
sections can be used as a guide to develop sustainable development policies.
Even without an empirical analysis, it is possible to construct guidelines for
development based on an assessment of capital stocks in comparison to capital
needs. We choose the Amazon region of Brazil as our case study, due to the
threats to ecological resources associated with the development process. In
this region, there is a strong need for
a sustainable development process to protect the global environmental resources
associated with the rainforest.
Given the central role of all
types of capital in the process of sustainable development, the first step in
analyzing this question is to assess capital stocks in the region. Although the
Amazon region is large and heterogeneous, characteristics of the capital stocks
are shared throughout the region. In general, the region is characterized by
low levels of artificial capital, low levels of human capital, abundant
extractive resources and abundant (but threatened) environmental capital. In
the following analysis, we will show how capital augmentation plans should be
developed, and how they may need to differ throughout the region.
The first question is how to
create the surplus to increase artificial capital and human capital. Since this
paper has focused on extractive resources, these will be discussed first.
Currently, mineral production in the Brazilian Amazon is a significant source
of regional and national GDP. The worlds largest tin mine is in Pitinga,
Amazonas, and the world’s largest iron mine is in Carajas, Pará. Primary mineral production currently
accounts for 3% of GDP, total secondary production accounts for 33% of GDP, and
there is significant potential to increase the amount of production.
Furthermore, 25% of all exports come from the mining industry. In light of the previous discussion of the
Hartwick Rule and our modification of the Hartwick Rule, an expansion of mining
can lead to sustainable development if two conditions are fulfilled. First, the rents from the mining must be
reinvested in other forms of capital. Second, the mining activity must not
result in significant damage to the rainforest or river systems. In other words, the expansion of mining
could result in a movement towards sustainable development as long as these two
conditions of reinvestment and environmental protection are met.
For other types of extractive
activities, it is more difficult to obtain a surplus, and environmental impacts
can be even more devastating (Franceschi 1999). For example, the clearing of
rainforest for agricultural field crops leads to permanent loss of rainforest,
but is also unsustainable in another dimension. Poor soils, and the breakage of
the nutrient cycle associated with removing the forest cover implies unproductive
agriculture, with crop production often limited to 2-4 years. Under these
conditions, it is not possible for large scale agriculture to generate a
surplus with which to generate funds for investment, and in fact leads to much
more loss of forest per dollar of current GDP or per job generated in
comparison to mining. Of course, sustainable development
does not require that the surplus used for capital investment be generated from
within the region. These funds for investment can come from other parts of
Brazil or from abroad. In fact, the policies which have been developed to
create and sustain the Manaus Free Trade Zone[7]
represent a transfer from southern Brazil to the Amazon region that results in
an increase in the stock of artificial capital in Manaus. Although
environmental protection was not the original motivation for the policies, they
have resulted in a slowing of deforestation in the area (Rivas 1998), and
Amazonas remains at 97% of its original forest cover, in comparison to other
Amazonian states which have lost over 20% of their original forest cover.
Our discussion of sustainable development
in the Amazon region would not be complete without discussion of subsistence
level activities. For example, small farmers in Rondonia are primarily
responsible for deforestation in that state (Caviglia, 1999). These farmers are
migrants from south Brazil and utilize traditional field crop methods instead
of the sustainable agroforestry techniques employed by Indians and Caboclos[8]. Caviglia shows that the income that can be
generated from sustainable agroforestry exceeds that from traditional field
crop methods, but these migrant farmers continue to use the unsustainable
techniques. Here, an investment in human capital would contribute to
sustainable development through the transmittal of knowledge of the
Indian/caboclo sustainable techniques to the migrant farmers who only know the
unsustainable temperate agricultural techniques of southern Brazil.
5.0 Conclusions
Although the evolution of
sustainable development policies must consider a spectrum of micro-economic,
macro-economic, ecological, cultural, institutional, and social issues, our
paper suggests that a central focus of sustainable development should be the
accumulation of human capital, artificial capital, and natural capital, while
protecting the stock of environmental capital. Mining activity can make an
important contribution to sustainable development by generating a surplus for
other investment activities, but care must be taken so that the mining activity
does not result in too large a reduction in the stock of environmental capital. Above all, our results show that the
inclusion of the strong sustainability criterion requires greater care be taken
in the sustainable development planning process. In particular, simple reinvestment of rents from productive
activities into artificial capital is not enough in most cases to support
development for the long term.
Reinvestment or preservation in the environmental capital stock can be
as important for productivity as human or artificial capital.
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Appendix (to be listed on a website, not
included in paper)
I
The
replication of Hartwick’s results begins with his definitions of consumption
and saving.
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where Q
= F (K(t), R(t)) and “K dot” denotes the change in capital over time or
investment. The change in consumption
over time then, can be defined as,
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This is
subject to the same equation of motion of exhaustible resource flow, equation
(1) in the text,
|
and the
same capital reinvestment rule as equation (2) in the text,
|
|
Substituting
into equation (i), we have
|
Using
Hotelling’s rule for efficiency in the extraction of exhaustible resources,
|
and
simplifying Hartwick finds,
|
|
II
Now
define the ecological stock to be proportional to the exhaustible resource
stock, as mineral resources are extracted from the ground forest is cut down.
|
In this
case, the ecological resource stock impacts consumption directly. The consumption equation, a revision of (i),
will be,
|
(The
representation of time is suppressed for simplicity.)
Taking
the time derivative gives,
|
After
substitution of the reinvestment rule (ii), our equation of motion (iii),
Hotelling’s efficiency rule (iv), and simplification the resulting change in
consumption equation is equation (3) in the text,
|
This can
be interpreted as the change in consumption over time being supported or
reduced by the rate of enhancement or depletion of the ecological stock.
III
The
third case incorporates the condition of the ecological stock being
proportional to the exhaustible stock into the production function. Where production is now defined as,
|
Using
(i) and (iii) we have,
|
Taking
the time derivative gives,
|
Substituting
(iii) and (iv) and simplifying gives a somewhat similar equation for the change
in consumption over time as the second case.
|
Or, by
substituting (ii) we have the text equation (4),
|
This
essentially means that the change in consumption over time moves with the
change in the flow of the marginal productivity of ecological services over
time. Again, depending on relative
magnitudes, the change in consumption over time could potentially be negative,
indicating a decrease in utility for society or an unsustainable path.
[1] See Pezzey’s (1989) compilation of 35
definitions of sustainable development.
[2] Of course, the quantity and quality of human
capital will be important as well, but human capital is generally not discussed
in these neoclassical examinations of necessary and sufficient criteria for
sustainability.
[3] Daly, Kahn and O’Neill, Franceschi and Kahn,
among others.
[4] See Pearce and Warford for a comprehensive
discussion of substitutability among inputs. An important aspect of their
discussion is their focus on environmental capital and its lack of
substitutability with other forms of capital.
[5] The Hotelling efficiency rule says that in a
competitive market environment, the rate of return to capital and the rate of
return to mineral resources are equal. An appendix which details all the
derivations can be found at http://....... (Note: the appendix follows this submitted
version of the paper for the benefit of the reviewers)
[6] See Kahn and O’Neill (1999) for further
discussion
[7] The Federal Government lifts tariffs on
imported components and provides other financial incentives to encourage
assembly and manufacturing activity in Manaus.
[8] Caboclos are people of mixed Indian and
Portuguese descent who have been rainforest inhabitants for many generations,
and whose families have been in the rainforest for as long as three or four
hundred years.