Download Economics of Natural Resources

Economics of Natural Resources
Economics of Natural Resources
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Resources are broadly classified under two
categories:
Renewable and Non- Renewable (depletable)
Resources.
Non-renewable resources are those which remain on
the earth in different form after use and can not be
reconstituted in to their original form after use.
These resources, after use if not recycled properly
become a waste material.
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• On the other hand, resources are renewable when
they can be replenished after use and can be
sustained if natural flow of the resources is
maintained.
• Discussion of resources and their use is important
because in the pursuit of development available
resources are nearly over exploited.
• Therefore their efficient use and allocation is highly
significant for attaining sustainable development.
Economics of Natural Resources
However, understanding the conditions of
efficient allocation of both the types of resources
requires understanding of resource taxonomy
and the distinction between categories of
resources - depletable and renewable and
issues emerging from these distinction.
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Resource Taxonomy:
Three separate concepts are used to classify the
stock of depletable resources:
(1) current reserves,
(2) potential reserves and
(3) resource endowment.
The US Geological Survey (USGS) has developed a
classification system of resources illustrated in figure1, which has two dimensions - economic and
ecological.
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Resource Taxonomy
• A movement, in the figure 1 from top to bottom
represents movement from cheaply extractable
resources to those extracted at substantially
higher prices.
• By contrast, a movement from left to right
represents increasing geological uncertainty
about the size of the resource base.
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Resource Taxonomy
• Current reserves: (shaded area in the figure -1)
are defined as known resources that can
profitably be extracted at current prices and can
be expressed as a number.
• Potential reserves: are resources that can be
extracted at the prices people are willing to pay
for these resources – the higher the price higher
is the potential reserves.
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Economics of Natural Resources
A Categorization of Resource
Total Resources
Identified
Undiscovered
Demonstrated
Measured
Indicated
Reserves
Sub-Marginal
ParaMarginal
Sub - economic
Economic
Measured
Figure 1
Hypothetical
Speculative
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Resource endowment:
This represents the natural occurrence of resources in
the earth’s crust and independent of prices.
This concept is more geological rather than the
economic.
This concept is important because it places an upper
limit on the availability of terrestrial resources.
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Meaning the terms used in the Figure-1:
Identified resources:
specific bodies of mineral –bearing material
whose location, quality and quantity are known
from geological evidence and supported by
engineering measurements.
Measured resources:
material for which quantity and quality estimated
are within a margin of error less than 20 percent,
from geologically well known sample sites
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Meaning the terms used in the Figure-1:
Indicated resources:
material of which quantity and quality have been
estimated partly from sample analyses and
partly from reasonable geological projections.
Undiscovered resources:
unspecified bodies of mineral bearing material
surmised to exist on the basis of broad
geological knowledge and theory
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Meaning the terms used in the Figure-1:
Hypothetical resources:
undiscovered materials reasonably expected to
exist in a known mining district under known
geological conditions.
Speculative resources:
undiscovered materials that may occur in either
known types of deposits in favorable geological
settings where no discoveries have been made
or in yet unknown types of deposits that remain
to be recognized.
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Distinction between two categories of resources:
The first category of resources includes all
depletable, recyclable resources, such as copper.
A depletable resource is one for which the natural
replenishment feedback loop can be safely ignored.
The rate of replenishment of these resources is so
low that it does not offer a potential for augmenting
the stock in any reasonable time frame.
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Distinction between two categories of resources:
• A recyclable resource is one which although
currently being used for some particular purpose,
exists in a form allowing its mass to be recovered
once that purpose is no longer necessary or
desirable.
• The current reserves of depletable resource,
recyclable resource can be augmented by
economic replenishment as well as by recycling.
Stimulant of Economic replenishment includes:
price and technological progress.
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Distinction between two categories of resources:
• Another side of the depletable resources is that
their potential reserves can be exhausted owing
to demand for and durability of the products built
with the resource.
• In most of the cases the size of potential
reserves of depletable resources depend
explicitly on our ability to store the resource. e.g.
helium.
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Not all depletable resources permit recycling or
reuse such as coal, oil and gas which once
combusted turns in to heat energy.
The heat dissipated in to the atmosphere and
becomes non-recoverable.
Even if most of them are recyclable (e.g. copper) the
theoretical upper limit on recycling is less than 100
percent.
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• Renewable Resources:
are differentiated from depletable resources
primarily
by
the
fact
that
natural
replenishment
augments
the
flow
of
renewable resources at a non-negligible
rate.
Examples include:
solar energy, water, cereal grains, forest,
fish, animals etc.
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• For some renewable resources, the continuation
and volume of their flow depend crucially on
humans.
• For examples: soil erosion and nutrient depletion
reduce the flow of food.
• Excessive fishing reduces the stock of fish which in
turn reduces the rate of natural increase of the fish
population.
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Some renewable resources can be stored and
hence provides a valuable way to manage the
allocation the resource over time. Storage of
depletable resources presents a different service
from storage of depletable resources. Storing
depletable resources improves their economic life,
on the other hand storing renewable resources can
serve as a means of smoothing out the cyclical
imbalances of supply and demand.
Economics of Natural Resources
The challenge for management
resources is different from the
managing depletable resources .
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of renewable
challenge for
The challenge for depletable resources involves
allocation dwindling stock among generations
while meeting the ultimate transition to
renewable resources. In contrast, the challenge
for managing renewable resources involves the
maintenance of an efficient sustainable flow.
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Efficient Intertemporal Allocation:
Since we are dealing with the allocation of depletable
and renewable resources over time, the concept of
efficiency can be termed as dynamic efficiency.
Dynamic efficiency of resource allocation assumes that
society’s objective is to maximize the present value of
net benefits derived from the use of the resource. For a
depletable, non-recyclable resource, this requires
balancing of current and subsequent uses of the
resources.
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Economics of Natural Resources
Let’s derive the condition of dynamic efficiency with the help of simple
mathematics.
Let’s assume that the demand curve for a depletable resource is linear and
stable over time.
Thus the inverse demand curve in year t can be written as
(1)
The total benefits extracting an amount qt in year t are then the integral of this
function,
(Total Benefits)t =
=
(2)
Assume that the MC of extracting the resource is constant C and therefore the
total cost of extracting any amount qt in year t can be given by,
(3)
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Economics of Natural Resources
Let’s derive the condition of dynamic efficiency with the help of simple
mathematics.
Let’s assume that the demand curve for a depletable resource is linear and
stable over time.
Thus the inverse demand curve in year t can be written as
(1)
The total benefits extracting an amount qt in year t are then the integral of this
function,
(Total Benefits)t =
=
(2)
Assume that the MC of extracting the resource is constant C and therefore the
total cost of extracting any amount qt in year t can be given by,
(3)
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Economics of Natural Resources
If the total available amount of this resource is , then the dynamic allocation
of a resource over n years is the one which satisfies the maximization
problem.
(4)
Assuming that
is less than would normally be demanded, the dynamic
efficient allocation must satisfy,
(5)
(6)
An implication of the condition is that (p – MC) increases over time at r.
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In order to explain how dynamic efficiency criterion
defines this balance let’s consider the Two Period
Model and N-Period Constant Cost Model in the
subsequent part.
Two Period Model:
This model involves a situation of allocation of finite
resource over two periods.
It is assumed that the resource can be extracted at a
constant marginal costs but the current value of the
marginal costs rises over time.
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Given the stable demand curve for the resource, an
efficient allocation implies that more than half of the
resource was allocated to the first period and less
than half to the second period. This allocation was
affected both by the marginal cost of extraction and by
the marginal user cost.
As supplies of depletable resources are fixed and
finite, production of one unit today precludes future
production of the unit. Therefore, production decision
today must take forgone future net benefits in to
account.
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Assume that we have a fixed supply of a depletable
resource to allocate between two periods and a
constant demand curve in the two periods with the
marginal willingness to pay p = 8 – 0.4 q. The
marginal extraction cost is given as $2.
If the supply were 30 or greater and we were
concerned only with these two period, an efficient
allocation would produce 15 units in each period
regardless of the discount rate.
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Consider a situation of static efficiency where
production in period 1 does not reduce the production
in period 2.
Now assume that available supply is less than 30 but
20 and allocation is 15 units in the period 1 and 5 units
in period 2.
With this new allocation, present value (pv) in period 1
is $ 45, and present value in period 2 is $ 22.73 given
the discount rate (r) is 0.10. (∑ pv = $ 67. 73)
Now our job is to find out the allocation that maximizes
present value. And the one yielding the maximum
present value of net benefit can be selected.
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Economics of Natural Resources
Let’s consider that the marginal willingness to pay is given by the constant
formula P = 8 – 0.4q and marginal cost is constant at $2.
Now assume following parameters values;
a= 8, c = $2, b = 0.4, Q = 20 and r = 0.10
Using these we obtain:
8 – 0.4 q1 – 2 – λ = 0
(8- 0.4q1 – 2 – λ)/1.10 = 0
(1)
(2)
q1 + q2 = 20
The solution of the equations give the results:
q1 = 10.238, q2= 9.762, λ = $1.905.
Two proposition revealed from the Equations:
1. Equation (1) states that in a dynamic efficient allocation the present value
of the marginal net benefit in period 1 (8 – 0.4q1 – 2) has to equal λ.
Equation (2) states that the present value of the marginal net benefit is
period 2 should also equal λ. Therefore they must equal each other.
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Two Period Model:
2. The present value of marginal user cost is
represented by λ.
The equation (1) states that price in the first period (8 –
0.4q1) should be equal to the sum of marginal
extraction cost ($2) and marginal user cost ($1.905).
Multiplying (2) by (1+r), it becomes clear that price in
the second period (8 - 0.4q2) is equal to the marginal
extraction cost ($2) plus the higher marginal user cost
[λ(1+r) = (1.905) (1.110) = $2.905)
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Two Period Model:
Thus it is revealed from this exercise that when the
demand curve is stable over time and the marginal
cost of extraction is constant, the rate of increase I
the current value of the marginal cost is equal to r the
discount rate. Thus in period 2, the marginal user cost
would be 1 + r times as large as it was in period 1.
In essence, two period model suggests that, an
efficient allocation of a finite resource with a constant
marginal cost of extraction involves rising marginal
user cost and falling quantities consumed.
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Summary of Two-Period Model:
More than half the resource in period 1 and less than
half in period
Affected both by marginal cost of extraction and
marginal user cost
Current value of marginal user cost rises over time and
rate of increase equals the discount rate.
An efficient allocation of a finite resource with a
constant marginal cost of extraction involves rising
marginal user cost and falling quantities consumed.
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The N-Period Model:
The two period model can be generalized to cover an
unlimited time period while retaining the demand and
marginal cost curves of the two period model.
Alike two period model, in this model too, the efficient
marginal user cost rises steadily in spite of the fact that
the marginal cost of extraction remains constant. This
rise in the efficient marginal user cost reflects
increasing scarcity and the accompanying rise in the
opportunity cost of current consumption.
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Economics of Natural Resources
Let’s make a mathematical formulation of N-Period Model:
The equation describing the allocation which maximizes the
present value of net benefits are:
(1)
(2)
If the values of the parameters , amount of resource availability
and the rate of discount are known then the quantities which
will maximize the present value of net benefits in different time
period can be obtained.
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• For example, if a = $8, b = 0.4, c = $2, = 40 and r
= 0.10
• Then the allocation which satisfies the conditions
given in equation (1) and (2) is as given below:
• q1= 8.004, q2 = 7.305, q3 = 6.535, q4 = 5.689, q5
= 4.758, q6 = 3.733, q7=2.607, q8= 1.368 and q9 =
0.000, i= 9 and λ = 2.7983
The system of these equations can be solved by
developing a computer algorithm which converges
on the correct answer.
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Transition to a Renewable Substitute:
Let’s now consider a non-renewable/depletable
resource which has a perfect substitute and is
available at constant marginal cost. For e.g. solar
energy which is a substitute for gas or oil, surface
water for groundwater.
The transition from the depletable resource to
renewable resource would take place when the
marginal cost of extraction of renewable resource is
less than the marginal willingness to pay for it.
Economics of Natural Resources
Transition to a Renewable Substitute:
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In the absence of perfect substitute, marginal willingness to pay
(choke price) sets the upper limit on total marginal cost. But
when perfectly substitute renewable resource is available, the
marginal cost of extraction of the substitute sets the upper limit
at a marginal cost lower than the choke price.
In the presence of substitute renewable resource, the
depletable resource is extracted more and transition to the
substitute takes place after certain periods only. The point at
which the transition takes place for the first time is called switch
point.
At the switch point only consumption of renewable resource
begins.
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At the switch point, the marginal cost of the depletable
resource (including marginal user cost) rises to meet
the marginal cost of the substitute, and the transition
occurs.
Let’s now examine how an efficient allocation would
be defined when the transition from one constant
marginal –cost depletable resource to another
depletable resource with a constant but higher
marginal cost takes place.
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Consider figure 2.
The total marginal cost of the first resource would rise
until it equaled that of the second resource at the time
of transition.
In the period of time prior to transition (T*) only the
cheapest resource would be consumed.
Two salient observations:
(1)The transition is smooth; total marginal cost never
jumps to a higher level.
(2)The rate of increase in total marginal cost slows
down after the time of transition.
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Economics of Natural Resources
Price or
Cost
(dollars
per unit)
Total Marginal Cost1
Total Marginal Cost2
Marginal Extraction Cost2
Marginal Extraction Cost1
0
T*
Figure:2
Time
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(1)The total marginal cost of the two resources have to
be equal at the time of transition, otherwise net
benefits could be increased by switching over to
lower-cost resource. In period before transition, the
first resource is cheaper. After transition it is
exhausted.
(2)The components of the TMC that is growing (the
marginal user cost) represents a smaller portion of
the TMC of the second resource than of the first
resource. in both cases the marginal user cost is
increasing at rate r, and the marginal cost of
extraction is constant.
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Economics of Natural Resources
Increasing Marginal Extraction Cost:
Here Marginal Extraction Cost
cumulative amount extracted.
rises
with
the
Its a common case with mineral where higher grades
are extracted first.
Difference in behaviour of marginal user cost
As current marginal cost rises over time, sacrifice
made by future generation diminishes.
By the last period, MC of extraction will be too high
and TMC = MEC at the switch point. Here the
depletable resource is not exhausted fully.
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Exploration of Technical Progress:
The search for new resource is expensive
Bottom of ocean deep within earth
Marginal cost of exploration should be expected to
rise over time
TMC increases when exploitation increases
Smaller and slower decline in consumption
Technical Progress: advances in the state of
knowledge
Period of transition can last depending on situation.
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Economics of Natural Resources
What determines the rate of resource extraction:
An equation where the producer is inefficient between selling the
last unit of the resources (oil) in current period or in the next
period.
Present value of a barrel of oil world be same in both periods :
P1 = o2/(1+r) (!)
⇒91j+r)p1 = p2
⇒ p2 – p1/p1 = r the proportional price rise equals the discount
rate (r).
Hotellin’s Rule predicts price rise through time.
Basic condition determining price and quality in each period
Not enough to determine life cycle of non-renewable resource
Additionally information on initial stock of reserve and price at
which demand falls to zero.
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Property Rights:
The manner in which producers and consumers use
environmental resources depends upon the property
rights governing the resources.
Property rights refer to a bundle of entitlements
defining the owner’s rights, privileges and limitation for
the use of the resources.
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Efficient Property Right Structure:
Following three are the main characteristics that define
the structure of property rights that could produce
efficient allocation in a well performing market economy.
Exclusivity: All benefits and costs accrued as a result of
owning and using the resources should accrue to the
owner and only to the owner either directly or indirectly
by sale to others.
Transferability: All property rights should be transferrable
from one owner to another in a voluntary exchange
Enforceability: Property rights should be secure form
involuntary seizure or encroachment by others.
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When property rights are well-defined:
The owner of the resource enjoys a powerful incentive
to use that resource efficiently because a decline in
the value of that resource represents loss. For
example, farmers who own the land have an incentive
to fertilize and irrigate it because the resulting
increased production raises income level.
Exchange of the property rights facilitates efficiency.
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When property rights are well-defined:
We can illustrated point two by examining the incentives
consumers and producers face when a well-defined system of
property rights is in place. The essence is that the seller has the
right to prevent the consumers from consuming the product in
the absence of payment.
Given a market price, consumers chooses that amount of goods
which maximizes nets benefit. In terms of figure 3, for a given
price p*, consumer’s net benefit is maximized by choosing to
purchase Qd units. Area A is the net benefit received know as
consumer surplus.
Similarly, sellers also face a similar choice (figure 4). Given the
price p* the seller maximizes his or her own net benefit by
choosing to sell Qs units. The net benefit received (Area A) by
the seller is called producer surplus.
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Economics of Natural Resources
Price
(dollars
per unit)
A=
Consumer
Surplus
P*
D
Quantity (units)
Qd
Figure - 3
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Economics of Natural Resources
Price
(dollars
per unit)
S
P*
B=
Producer
surplus
Quantity (units)
Qs
Figure - 4
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Economics of Natural Resources
The price level (in our example P*) which producers and consumers face will
adjust until supply equals demand as depicted in figure 5. Given the price,
consumers maximize their surplus, producers maximize their surplus and the
market clears.
Price
(dollars
per unit)
S
P*
D
Q*
Figure 5
Quantity (units)
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Now, is this allocation efficient? – the answer is
yes. Adopting the defining of static efficiency
(discussed above) it can be inferred that the net
benefit is maximized by market allocation and as
seen in Figure -5, it is equal to the sum of consumer
and producer surplus.
In a system with well defined property rights and
competitive markets in which to sell those rights,
producers try to maximize their surplus and
consumers try to maximize their surplus. The price
system, then induces those self-interested parties to
make choices which are efficient from the point of
view of society as a whole.
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Producer’s Surplus, Scarcity Rent and Long Run
Equilibrium:
Producer surplus is related to profit, which in the short
rum equals profits plus fixed cost. In the long rum,
producer’s surplus equals the profits plus venture to
scarce inputs owned by producers.
As long as new firms can enter into an industry where
profits are earned without raising the profits of
purchased inputs, long run profits will equal to zero
and producer surplus will equal rent. Scarcity Rent:
It’s the producer’s surplus which persists in the longrun competitive equilibrium is called scarcity rent.
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Property Rights:
So far we have discussed that market leads to efficient
allocation when property rights are well defined. What
are the forms that a well property rights system can
take?
In the continuum of property rights regime, distinction is
made among four alternative forms of property rights
regime.
(a)Private Property Regime
(b)State Property
(c) Common Property
(d)Open Access Property
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Private property regime, as has been taken in most
our former discussion, refers to a situation when
entitlements to resources use is given to the private
individual.
State Property Regime: is one where the government
owns and control the property
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Economics of Natural Resources
Property Rights Regime/Institution
PRIVATE
PROPERTY
COMMON
PROPERTY
Group
Limitation
One
Person
Members
Only
Extraction
Limitation
Extraction
Limited by
Individual
Decision
Extraction
Limited by
Rules
OPEN ACCESS
Limited User
Unlimited User
Members
Only
Open to
Anyone
Extraction
Unlimited
Extraction
Limited
Figure – 6: A Trichotomy of Resource Use Regime
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Common Property Regime: This refers to a property right regime
where the property is jointly owned and managed by a specific
group of co- owners. The non-members are excluded from use of
the property and the members use the property based on the
rules agreed upon among the members. The rules for controlling
common property may be imposed from outside too.
Entitlements to use common property resources may be formal
protected by specific legal rules or they may be informal
protected by tradition or custom.
Common property regime exhibit varying degrees of efficiency
and sustainability depending on the rules which emerge from
collective decision making. Successful common property regimes
are: the grazing rights in Switzerland, Fishing in Mawelle in Sri
lanka.
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Open Access (Res Nullius): a property right regime in
which no one owns or exercise control over the
resource.
Resource extraction is based on the principle of first
come first served basis.
Every individual tries to capture as many benefits as
possible before other captures it. This behaviour of
individual results in over exploitation which is known as
the “tragedy of commons”.
In order to explain open access regime, we can refer to
the fate of American Bison.
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Bison are an example of common pool resources
characterized by non-exclusivity and divisibility.
In the early history of US, Bison were plentiful:
unrestricted hunting access was not a problem. i.e. in
the absence of scarcity, efficiency was not threatened
by open access.
As the years passed by, however the demand for Bison
increased and scarcity became a factor.
The social benefits and costs of Bison hunting has
been depicted in figure-7.
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Economics of Natural Resources
Benefits
and Costs
(dollars)
TC
TB
A
B
0
Q1
Figure-7
Q2
Quantity of
Harvesting Effort
(units)
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The Marginal Benefit Curve (not shown) is downward
slopping population sized of the bison decreases with
the corresponding increase in the hunting effort.
Smaller population supports smaller harvests per unit
of effort expended.
The efficient level of hunting activity in this model is
Q1, where net benefit is maximized. This allocation
also yield society a scarcity rent equal to vertical
distance AB.
Exploitation would continue until Q2 where, TB = TC.
Excessive exploitation of the herd occurs because
individual hunters can not appropriated the scarcity
rent.
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Two characteristics of this open access formulation:
(1)In the presence of sufficient demand unrestricted access will
cause resources to be overexploited.
(2)The scarcity rent is dissipated; no one appropriates the rent,
so it is lost.
The reason can be summed up as:
Unrestricted access destroys the incentive to conserve. Further
a hunter exploiting an open access resource would not have
any incentive to conserve because the benefits derived form
restraint would to some extent be captured by other hunters. As
a result of excessive harvest and loss of habitat as land was
converted to farm and pasture, the Great Plains bison herds
nearly became extinct (Lueck 2002)
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110
Renewable Common Property Resources: the Case of
Fisheries
Renewable Resources are those resources for which stock can
be continually replenished.
The stock, however not perpetual. Most of them (especially the
living populations such as plants, animals) are exhaustible if not
efficiently managed.
The growth or decline of these resources depends upon the size
of population. If through human activities the population is
withdrawn beyond a critical threshold the species can become
extinct.
These resources can also be termed as interactive resources,
wherein the size of the resource stock is determined jointly by
biological forces and by actions taken by the society.
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111
When the size of the population determines the availability of the
resources for the future, human actions on it determines the flow
of these resources over time.
The significant question, therefore, is the determination of
optimum rate of use across time and across generation.
The whole gamut of efficient allocation of renewable resources
will be discussed considering fisheries as an example.
The goals of this section are to find out,
a.What is an efficient allocation of the catch from a fishery?
b.How does market allocate this CPR?
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112
Efficient Allocation: Biological Dimension
The biological model, originally proposed by Schafer (1957)
posits that there is an average relationship between the growth
of fish population and the size of the fish population. (consider
Figure 8)
The size of the population is represented on the horizontal axis
and the growth of the population on the vertical axis.
The graph suggests that there is a range of population sizes (S1
to S*) where population growth increases as the population
increases and a range (S* to S2 ) where initial increases in
population leas to eventual declines in growth.
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113
Efficient Allocation: Biological Dimension
S2 is known as the natural equilibrium. At this point,
reduction in stock due to mortality or outmigration
would be exactly offset by increases in the stock due to
births, growth of the fish in the remaining stock and inmigration. In a situation below S2, stock is smaller and
growth would be positive and the size of the stock
would increase until it reaches S2. On the contrary, if
population exceeds S2, it would be exceeding the
capacity of its habitats (called carrying capacity), as
result mortality rates or out migration would increase
until the stock once again restores at S2.
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Figure 8: Relationship between Fish Population and Growth
Growth in
Fish Stock
(tons)
G(S*)
G(S0)
S1
S*
S0
S2
Fish Stock (tons)
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115
S1 is the minimum viable population and represents a
level of population below which growth in population is
negative (i.e. deaths and out migration exceed births
and in-migration). The equilibrium is unstable at this
point. Any movement on the curve towards S2 leads
population to a positive growth and when population
moves to the left of S1, the population declines until it
becomes extinct.
A catch level is said to give sustainable yield whenever
it equals the growth rate of population since it can be
maintained.
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116
S* is known as the maximum sustainable yield
population which yields maximum growth. If catch is
equal to the growth the sustainable yield for any
population size, between S1 and S2 can be
determined by drawing a vertical line from the stock
size of interest on the horizontal axis to the point
where it intersects the function and drawing a
horizontal line over to the vertical axis.
In figure 8, G(S0) is the sustainable yield for population
size S0. G(S*) is the maximum sustainable yield.
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117
Static Efficient Sustainable Yield:
Static Efficient sustainable yield (which does not
incorporate discount rate) is the catch level which, if
maintained perpetually, would produce the largest
annual net benefit .
Let’s illustrate the static efficient sustainable yield with
an help of a diagram.
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118
The assumptions are:
(1)The price of fish is constant and does not depend on
the amount sold,
(2)the marginal cost of a unit of fishing effort is constant
and
(3)the amount of fish caught per unit of effort expended
is proportional to the size of fish population (the
smaller the population, the fewer fish caught per unit
of effort).
Under static efficiency analysis in any sustainable yield,
catches, population, effort levels and net benefits
remain constant. The static efficient sustainable yield
maximizes the constant net benefit.
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Economics of Natural Resources
Figure 9: Efficient Sustainable Yield for a Fishery
Benefits
and Costs
of Fishing
Effort
(dollars)
R(Ee)
C(Ee)
0
Ee
Em
Ec
Quantity of Fishing
Effort (units)
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120
In figure 9, the benefits and costs are portrayed as a
function of fishing effort and can measured in vessel
years, hours of fishing etc.
The shape of the revenue function is given by the
shape of the function in figure 8.
An increase in fishing effort is recorded as movement
from left to right.
Em is the maximum sustainable yield level
corresponding to the sustained levels of efforts. Every
effort level portrayed in figure 9 corresponds to a
population level in figure 8.
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121
The net benefit is presented in the diagram as the
difference (vertical distance) between benefits (prices
times the quantity caught) and costs (the constant
marginal cost of effort times the units of effort
expended). The efficient level of effort is Ee, where the
vertical distance between the benefits and costs is
maximized.
Ee is the efficient level of effort because it is where
marginal benefits (which graphically is the slope of the
total benefit curve) is equal to marginal cost (the
constant slope of the total cost curve). Levels of effort
higher than Ee are inefficient because the additional
cost associated with them exceeds the value of the fish
obtained.
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122
Is maximum sustainable yield efficient?
This answer is no. The maximum sustainable yield
would be efficient only if the marginal cost of
additional effort are zero.
Therefore, this follows that the efficient level of effort
is less than that necessary to harvest the maximum
sustainable yield. The static efficient level of effort
leads to a larger fish population than the maximum
sustainable yield level of effort.
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123
Dynamic Efficient Sustainable Yield:
The static efficient sustainable yield becomes a special
case of the dynamic efficient sustained yield where the
discount rate is zero because the static efficient
sustained yield is the allocation which maximizes the
constant net benefit in every period.
But any higher efforts level than this would yield
temporally larger catches (and net benefit), but this
would be more than offset by a reduced net benefit in
the future as the stock will be low. Thus the
undiscounted net benefits would be reduced.
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124
Dynamic Efficient Sustainable Yield:
Effects of positive discount rate:
(a)the higher the discount rate, the higher the cost (in
terms of forgone current income) of maintaining any
given resource stock, and
(b)positive discount rate increases efficient level of
effort beyond that suggested by the static efficient
sustained yield with a corresponding decrease in the
equilibrium population level.
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125
Increase in effort beyond the efficient sustained yield
level initially results in an increased benefit as amount
of fish caught per unit of effort is proportional to the size
of the population.
However, since this catch exceeds the sustained yield
for that size of population, the population of fish would
be reduced and future population and catch levels
would be lower. Efforts would be increased until that
level of effort is reached where the size the catch
equals the growth of population.
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126
Colin Clark (1976) has shown that in terms of figure 2,
as the discount rate is increased, the dynamic efficient
level of effort is increased until, with an infinite discount
rate, it becomes equal to Ec, the point at which net
benefits become zero.
Why?
With an infinite discount rate, allocation over time gives
rise to Marginal User Cost (MUC) which measures
opportunity cost. This implies that,
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127
For efficient allocation:
(1) Marginal Willingness to Pay (MWP) = Marginal Extraction
Cost (MEC) which equals constant price.
(2) Total Benefits = Total Costs.
Let’s prove the implication two,
Assume,
y = qxe,
where, y = yield, q = proportion of population
harvested with one unit of effort, x = size of
population and e = level of effort.
One of the condition of dynamic efficient allocation has to satisfy with infinite
discount rate is ,
p = c/qx,
where, p = constant price, c = constant marginal cost
per unit of effort and qx = no of fish harvested per unit
of effort.
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128
=> py = ce
where, py is total benefits and ce is total cost implying
net benefits are zero.
We have found that static efficient sustained yield implies a larger fish
population
that
the
maximum
sustained
yield.
But with the positive discount rate, dynamic efficient sustained yield would
imply a smaller fish population.
The likelihood of population being reduced below the level supplying the
maximum sustainable yield depends on discount rate.
In general the Lower the extraction cost and the higher the discount rate, the
more likely it is that the dynamic efficient level of effort will exceed the level of
effort associated with the maximum sustainable yield.
When MEC = 0, Static efficient sustainable yield = maximum sustainable yield.
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129
Would a dynamically efficient management scheme lead to
extinction of fishery?
This is not possible under the circumstances considered here
because Ec is the highest dynamically efficient level possible.
For extinction the benefit from extracting the very last unit would
have to exceed the cost of extracting that unit (including the
costs on future generation).
If population growth rate exceeds the discount rate, extinction
may not occur.
If, however, the growth rate is lower than the discount rate,
extinction can occur in an efficient management scheme is the
costs of extracting the last unit are sufficient low.
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130
Would a dynamically efficient management scheme lead to
extinction of fishery?
This is not possible under the circumstances considered here
because Ec is the highest dynamically efficient level possible.
For extinction the benefit from extracting the very last unit would
have to exceed the cost of extracting that unit (including the
costs on future generation).
If population growth rate exceeds the discount rate, extinction
may not occur.
If, however, the growth rate is lower than the discount rate,
extinction can occur in an efficient management scheme is the
costs of extracting the last unit are sufficient low.
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131
Appropriability and Market Solutions:
Consider the case of allocation resulting from a fishery managed
by a competitive sole owner who has a well-defined property
rights to the fish.
The behavior of the sole owner has been illustrated in figure 10.
in both the panel, horizontal axes represents fishing efforts.
The basic aim of the sole owner is the maximize profits. Given
zero discount rate, the owner can increase profits by increasing
fishing effort until marginal revenue equals the marginal cost.
Clearly this is effort level Ec, the static efficient sustainable yield.
This yields profits which equals the difference between R(Ee) and
C(Ec).
132
Economics of Natural Resources
Total Revenue
and
Costs(dollars)
Figure 10: Efficient Sustainable Yield for a Fishery
R(Ee)
C(Ee)
Price or
Cost
(dollars
per unit)
Fishing Effort (units)
Average
Revenue
Marginal
Revenue
Average Cost =
Marginal Cost
Ee
Em
Ec
Fishing Effort (units)
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133
Consider the situation when property rights to the fish are not
well defined. For example the case of ocean fishery where
access to fishery is completely unrestricted. This is a situation of
open access.
Open access resource beset with two kinds of externalities: a
contemporaneous externality and intergenerational externality.
Contemporaneous externality involves the over commitment of
resources to fishing such as too many boats, too many
fishermen, too much effort which altogether lowers rate of return
of the current fishermen on their efforts.
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134
Intergenerational
externality
occurs
because
overfishing reduces stock which lowers future profits
from fishing.
In the figure 10, we can see how can these externalities
arise.
Under open access, at the efficient level each boat
would receive a profit equal of its share of the scarcity
rent. The individual fisherman has an incentive to
expend further effort until profits are zero. In the figure
3, that point is at effort level Ec where, average benefit
and average cost are equal.
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135
The situation of contemporaneous externality will arise
at this point because too much effort is being expended
to catch too few fish and the cost is substantially higher
than it would be an efficient allocation.
The sole owner will also not choose to expend beyond
Ee, otherwise he will face reduction of profits.
The allocation that results from allowing unrestricted
access to the fishery is identical to that resulting from a
dynamic efficient sustainable yield when an infinite
discount rate is used.
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136
Open-access resources do not automatically lead to a
stock lower than that maximizing the sustained yield.
However, it is not unusual for mature open-access
fisheries to be exploited well beyond the point of
maximum sustainable yield.
Open-access resources may pose threat of species
extinction when harvesting takes below the minimum
viable population.