DISCOUNTING NATURAL RESOURCES WITH

MATHEMATICAL MODELS

BY :
M NAUFAL AFANDI
P2F123010

MASTER OF ENVIRONMENTAL SCIENCE

JAMBI UNIVERSITY
Chapter 1: Concepts and Understanding of Natural Resource
Economics

A. Resource Definition Natural resource

economics is the science that studies the allocation of
natural resources such as water, land, forests or what we call
biological and non-biological. This science seeks answers to how
much resources should be extracted so as to produce the greatest
benefits for society.

B. Views on Natural Resources

In understanding natural resources, there are 2 views that
are commonly used, namely:
1. Conservative View or Pessimistic View/perspective.
2. Exploitative View or Ricardiani Perspective.

C. Classification of Natural Resources

In general, we group natural resources into 2, namely:
1. Stock group, this group has limited or non-renewable reserves.
Examples: mineral, metal, oil and natural gas resources.
2. The "flows" group, in this type of resource the physical
quantity of the resource changes over time and can be renewed.

D. Measuring the Availability of Natural Resources

Resource measurement is simplified from the concept of Rees
(1990). For stock resource groups, some of the concepts used
include:
1. Hypothetical resources, deposit measurement concepts that
are not yet known but are expected to be discovered in the
future based on surveys currently being carried out.
2. Speculative resources, this concept is used to measure
deposits that may be found in little or unexplored areas, where
geological conditions allow the discovery of deposits.
 3. Conditional reserves, deposits that are already known but
with current output prices and technology cannot be utilized
economically.
4. Proven reserves, natural resources that are known and
exploited economically.
Measuring the types of resources that can be renewed (flow),
using concepts including:
1. Maximum Potential Resources
2. Sustainable Capacity (Sustainable Capacity/Sustainable
Yield)
3. Absorption Capacity (Absoptive Capacity)
4. Carrying Capacity

E. Measuring the Scarcity of Natural Resources

One crucial aspect is understanding when these resources will
run out. Realizing the weaknesses of physical measurements,
Hanley et al., (1997) suggest using monetary measurements by
calculating the real price, unit cost, and economic rent from
resources.

F. Attraction between Natural Resources and Economics

Natural resources are an input factor in economic activities.
The relationship between natural resources and the economy can
be seen in the picture.
Chapter 2: Public Goods, Externalities, and Property Rights

A. Public Goods
From an economic perspective, goods can be classified
according to the criteria for use or consumption and ownership
rights. Problems with public goods arise because producers
cannot ask consumers to pay for the consumption of these goods
and consumers also know that producers have no control at all
over who consumes them. Based on their characteristics, public
goods have 2 dominant characteristics, namely:
1. Non-rivalry (no competition) or non-divisible (not exhausted).
2. Non-Excludable (no restrictions)

B. Externalities and Market Failure

Consumption of public goods often gives rise to what are
called externalities or external impacts. Externalities are
defined as the impact (positive or negative) or in economics as
net costs or benefits, from the actions of one party on another
party. Friedman (1990) states that externalities and public
goods are two different ways of looking at the same problem.
Market failure is a reflection of the nature of natural
resources which in some cases constitute a public good. So,
public goods, externalities and market failures are one link in
the chain that often arises in natural resource management. To
understand market failure, there are several indications that
can be studied. Ledyard (1987) suggests that market failure can
be understood using the market success concept approach.

C. Rights and Ownership Regime

Failure to clearly determine ownership rights will also give
rise to externalities, especially in relation to the management
of natural resources. Ownership rights (property rights) are
legal claims (secure claims) to resources or services produced
from these resources.
D. Response to Externalities
In general, there are several actions to prevent or reduce
the occurrence of externalities, namely granting ownership
rights (assigning property rights), internalization, and
imposing taxes (pigouvian tax).
Chapter 3: Foundations of Natural Resource Economics

A. Welfare Economics
1.Demand Curve
One fundamental important thing from the economic aspect of
natural resources is how the extraction of natural
resources can provide benefits or welfare to society as a
whole. The measure of welfare that has become the
foundation of neo-classical economics is the measurement of
the surplus that can be obtained from consumption and
production of goods and services produced from natural
resources. Surpluses obtained from natural resources are
basically obtained from the interaction between demand and
supply.
In a neo-classical economic perspective, the demand curve
can be derived from two different sides. First, the demand
curve can be derived from maximizing satisfaction or
utility which will then produce an ordinary demand curve or
often referred to as the Marshall demand curve. Second, the
demand curve can also be derived from minimizing
expenditure which will produce a compensated demand curve
or often called the Hicks demand curve.
Neo-classical consumer theory assumes that individuals act
rationally and, given existing constraints, seek to
maximize satisfaction from the consumption of two goods.
The satisfaction of consuming two goods is not unlimited,
because consumers are also limited by a fixed income. Thus,
the decision that must be taken by consumers is how to
choose these two goods that will produce maximum
satisfaction within the existing budget constraints.

2.The Supply Curve Affects Economic Welfare

Supply curve derivation is theoretically easier to do and
understand than demand curve derivation. The supply curve
for goods and services describes the quantity of goods that
producers can supply at a certain price level. Because the
supply curve is derived from the cost function (especially
short-run costs). Producers will only produce if the price
of output is equal to the marginal cost of producing it.
However, not all price levels will meet the requirements
for producing good

3. Surplus
One of the crucial things in natural resource economics is
how the surplus of natural resources is utilized optimally.
Basically, the concept of surplus places a monetary value
on the welfare of society from extracting and consuming
natural resources. Surplus is also an economic benefit
which is nothing but the difference between gross benefits
and costs incurred by society to extract natural resources.
Using a surplus approach to measure natural resources is an
appropriate measurement because resource utilization is
assessed based on the best alternative use.
The economic surplus in question will be divided into
consumer surplus, producer surplus and natural resource
rents. Consumer surplus equals the benefits society obtains
from consuming natural resources. Producer surplus can also
be considered as the surplus that can be obtained by the
owner of a productive resource or asset when the income
from the resource exceeds its cost of income. The third
component of surplus measurement is resource rent. This
resource rent is a surplus that can be enjoyed by the owner
of the resource (for example: the government) which is the
difference between the amount received from the use of the
resource minus and the costs incurred to extract it.

4. Discounting
As explained above, natural resource extraction is an
intertemporal decision-making process. This is because
natural resources, both renewable and non-renewable, are
assets or capital (natural assets) whose utilization is not
only determined by the productivity of the capital itself,
but also concerns the availability (supply) for future
consumption, as well as the risks and uncertainties of
natural resource extraction. From the producer's side,
intertemporal decisions also concern the opportunity cost
of capital, in this case whether capital invested to
extract natural resources is more valuable than invested in
other economic activities in the future. Likewise, the
opportunity cost of natural capital concerns whether, for
example, the fish we catch now are more valuable than if we
wait to harvest them in the future.
From the consumer's side, the intertemporal aspect concerns
time preferences. Consumers are often characterized by a
positive time preference where they prefer current benefits
to future benefits. In other words, intertemporal choice
concerns comparing the value or economic benefits of
natural resources at different time periods. So how should
this choice be determined? One of the keys to determining
intertemporal decision making is through the discounting
process by determining the appropriate discounting rate.
The discounting process is a reflection of how society
behaves towards the extraction of natural resources and how
society behaves towards the extraction of natural resources
itself. Below we will discuss several definitions regarding
the discount rate and its relation to the extraction of
natural resources.
In natural resource economics, we must be careful in
discussing discount rates because failure to understand
this concept will lead to wrong perceptions. In Neo-
Classical economics, the discount rate is differentiated
between the utility discount rate or social discount rate
and the consumption discount rate. The Utility Discount
Rate is referred to as the pure rate of time preference,
where if this rate is positive, it shows the degree of
desire or preference now rather than later. The utility
discount rate is also defined as the rate at which the
value of the increase in utility changes when consumption
is delayed. This UDR value is related to the concept of
welfare maximization which is based on utilitarian
foundations.


 e U C 
pt
W t t
t 0

Mathematically, community welfare is written where Ut(Ct)

is the utility or satisfaction obtained from consuming Ct.
Consumption discount rate or CDR on the other hand is
defined as the rate at which the value of consumption
increase changes when consumption is delayed. This CDR
value is related to welfare maximization based on
consumption.


 e C
 rt
W t
t 0

As stated above, SDR and CDR are two different discount

rate indicators, both of which can be separated through
splitting. If it is assumed that utility increases in line
with consumption and that this increase experiences a
decreasing rate or diminishing return as indicated by the
second derivative of the utility function, we can define
the elasticity of marginal utility with respect to
consumption.
 2 
C.  U /  U 2 
 
      C.U " (C )  0
U / C U ' (C )

So the relationship between CDR and SDR can be written as

:4

C
   
C

Where is the derivative of consumption over time. Equation

(3.27) clearly illustrates the relationship between CDR and
SDR. From the equation above, it can be seen that the
amount of CDR is determined by three things, namely:
1. Social discount rate (pure time preference) 
2. The elasticity of marginal utility to consumption( ),
 .
3. Consumption growth rate( C / C )

From the equation above it can also be concluded that CDR

will be the same as SDR if and only if / is equal to zero,
which means the consumption growth rate is constant over
time or elasticity = 0, which implies that utility is
linear (hard to find in reality). In general, Hanley and
Spash (1995) state that SDR will be smaller than CDR or < r
for several reasons below:

1. As a whole, society is of the view that investment in

the present will provide benefits in the future so that as
a whole society will collectively save more than
individuals. Consequently, the government as a
representative of the public must provide a lower SDR for
investments in the public interest.

2. Every individual who is also in the role of society will

give and want a discount rate (SDR) that is lower than if
the individual were acting as himself.
3. Determining SDR or p=0 is impossible because the
impatience motive will still exist.

5. Market Discount Rate and Consumption Discount Rate

Market Discount Rate (MDR), identified with interest rate,
is a rate determined by the balance of borrowing rate and
landing rate from the money market, which is a kind of
banking institution. Although the MDR can be used as a
guide for the appropriate rate level for natural resource
extraction, economists to date have not completely agreed
on determining the appropriate rate. This is due to the
complexity of natural resource extraction and the economic
interactions within it. Some economists suggest
implementing a discount rate that is weighted between CDR
and MDR so that a more precise SDR value is obtained. Notes
regarding the Discount rate is about the value being
 measured. Capital investment is closely related to the risk
of uncertainty, causing variations in the discount rate val

Chapter 4: Economic Models of Non-Renewable Resources

Natural resources cannot be renewed or depletable resources

are natural resources that do not have the ability to regenerate
biologically. These resources are formed geologically and
require a very long time to become natural resources that are
ready to be processed or ready to be used, for example oil mines
and gold mines. These natural resources are natural resources
that have a fixed stock. So its nature causes the methods of
extracting non-renewable and renewable natural resources to be
different. Some of the main differences between natural resource
management and conventional economic models include:
In the competitive economic model, profit maximization is
determined when marginal revenue equals marginal cost. In the
non-renewable natural resource model, unextracted stocks have a
value that is reflected in their opportunity costs. Thus,
optimal extraction of natural resources is not only determined
by price and marginal costs but also opportunity costs.
Extraction of natural resources is an investment problem
because the value of the resource rents obtained is related to
time, so that the determination of rents or profits is not only
calculated for the present but throughout time.
Extraction of non-renewable resources faces stock constraints.
Because there is no regeneration process.
The extraction of renewable resources is related to
intertemporal aspects where the role of time is very crucial.