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Master in Human Development & Food Security
ENVIRONMENTAL AND
NATURAL RESOURCES
ECONOMICS
Luca Salvatici
(Department of Economics –Roma Tre
University
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Renewable, Nonrenewable, and Enviromental
Resources
Economics might be defined as the study of how society allocates scarce
resources.
The field of resource economics would then be the study of how society
allocates scarce natural resources.
QUESTION 1: What is the central subject in the field of resource
economics?
A distinction between resources and environmental
economics is necessary to continuous our analysis.
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RENEWABLE, NONRENEWABLE,
AND ENVIROMENTAL RESOURCES
Environmental Economics is concerned with the conservation of natural
environments and biodiversity.
But our focus is
about
Renewable
resource
Natural
Resources
Nonrenewable
resource
Must display a significant rate of
growth or renewal on a relevant
economic time scale.
An economic time scale is a time
interval for which planning and
management are meaningful.
A critical question in the allocation of natural
resources is “How much of the resource should be
harvest today, and in each period?”
Dynamic
optimization problem
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Question
QUESTION 2: What is the economic distinction between renewable
and non renewable resources?
A renewable resource must display a significant rate of grown or renewal
on a relevant economic time scale. An economic time scale is a time
interval for which planning and management are meaningfuly.
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Natural resources: definitions
Limited availability (stock) at a given time and:
• Nonrenewable resources: given stock on a relevant economic
time scale => Nonrenewable resources are incapable of
significant growth, e.g., fossil fuels, ores, diamonds
• Renewable resources: renewable resources are capable of
growth (on some meaningful timescale), e.g., fish, (young
growth) forests => rate of growth is determined by biological
factors that can be influenced by human activity but the
maximum rate cannot be changed
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Natural resources: basic concepts
• Natural resources are natural assets from which we derive
•
•
•
•
value (utility)
Broad definition includes amenity value, provision of
ecosystem services, etc.
We focus here on natural resources that must be extracted or
harvested
In general, efficient and optimal use of natural resources
involves intertemporal allocation
Distinguish between renewable and non-renewable resources
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Definitions and key features of natural
resources
• Natural resources are “stocks of materials that exist in the
natural environment that are both scarce and economically
useful in production or consumption, either in their raw state or
after a minimal amount of processing”.
• Imperfections in some natural resource markets raise questions
about the efficiency of extraction and optimal extraction rates: the
impact of trade on resource management in these
circumstances is difficult to assess (open access may reverse some of
the predictions of standard trade theory).
• Technical change and capital accumulation can partially offset the
exhaustibility of non-renewable resources. Trade can contribute to
this process.
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RENEWABLE, NONRENEWABLE,
AND ENVIROMENTAL RESOURCES
Maximize some
measure of net
economic
value
The optimal rate
of harvest in a
particular period
may be zero
Dynamic
Optimization
Problem
Example
Solution: schedule
or “time path”
indicating optimal
amount to be
harvested in each
period.
If a fish stock has been historically
mismanaged, and the current stock is below
what is deemed optimal, then zero harvest
may be best until the stock recovers.
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Dynamics
• Finding the best allocation over time is a dynamic
(not static) optimization problem
What makes a problem dynamic?
• The critical variable in a dynamic optimization
problem is a stock or «state» variable that requires
a difference or differential equation to describe its
evolution
• The key feature is that a decision taken today will
change the state variable in the next period
Robinson Crusoe example
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Nonrenewable resources dynamics
R(t): remaining reserves in period t
q(t): rate of extraction
R(t+1) – R(t) = – q(t)
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Renewable resources dynamics
y(t) = harvest in period t
X(t) = stock at the beginning of period t
F(Xt) = net growth function
X t +1 − X t = F ( X t ) − yt
Escapement:
−
≥0
<
⇒
−
>0
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Discounting
• In general, individuals have positive time preferences over
•
•
•
•
•
consumption (money)
This gives the social discount rate or pure social rate of
time preference δ
High discount rates heavily discount future benefits and
costs
The discount rate and the interest rate measure
essentially the same thing
Hence, the discount rate reflects the opportunity cost of
investment (saving)
Market interest rates also reflect risk, inflation, taxation,
etc.
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Discounting
Two explanations for discounting:
•money could be invested for a greater future return (the
opportunity cost of capital), and
•people are impatient (time preference).
If we think in terms of the market for investment funds, the
opportunity cost rationale says what firms are willing to pay
for new funds, while the impatience rationale identifies the
amount that individuals require as compensation for
delaying consumption by investing their funds.
In the economists’ ideal world – fully competitive markets,
no distortionary taxes, perfect information, and complete
rationality – these rates would be identical. In point of fact,
most economists agree that the discount rate suggested by
the impatience explanation – the “social” discount rate – is
substantially lower than the rate indicated by the opportunity
cost of alternative investments.
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Intergenerational equity
• If the weight attached to the
welfare of the next generation
is small, investments to
protect the environment are
unattractive and inventories
of natural resources tend to
be low
• What are we doing for the
next generation?
But… what have they done for
us?
“I do not have to spend time worrying
about my neighbor’s children because
my neighbor can take care of them
just fine, and I apply the same
thinking, absent exceptional
circumstances, to distant future
generations. I am not willing to spend
a lot of money to help very remote
future generations, because I think
they will be just fine without my
concern and resources – indeed, there
is every reason to think that their lives
will be far more pleasant than those of
the current generation.” (John J.
Donohue III, Why We Should Discount
the Views of Those Who Discount
Discounting, 108 Yale L.J. 1901, 1905,
1999.
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What is (or ought ot be) the ‘right’
discount rate?
• The present value of a €10000 payment 10 years from
now would be €7441 if δ =0.03, but if the time horizon is
100 years it drops to €520, and with δ =0.1 to €0.72
• Exponential discount: a human life today would be worth
less than a slice of cake in the Roman period!
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The economic measure of
scarcity
Economia delle risorse naturali (a.a.2006/07)
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Economic valuation
P=C+A
P-C=A
- Resource market price (P)
- Average extraction cost (C):
• constant
• dependent on the flow (control) variable (e.g.,
proportional to the extraction rate)
• dependent on the stock (state) variable (e.g.,
inversely related to the stock level)
- Rental value (A): present value of the benefits to be
obtained postponing the exploitation of one resource
unit (resource rent)
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What is a rent?
In economics, the concept of economic rent is equivalent to that of
(positive) economic profit –
that is a return in excess of normal profit,
where the latter is the return that an entrepreneur should earn to cover the
opportunity cost of undertaking a certain activity rather than its best
alternative. In other words, any revenue exceeding total costs including the
opportunity cost (or normal profit) is economic rent.
Two types of rents:
1.
Differential (Ricardian) rent: The classical notion of differential rent is
related to land. The idea is that greater rent accrues to land of higher
productivity and better quality (e.g. greater fertility), with marginal land
receiving no rent.
2.
Scarcity rent: Scarcity rents arise when there are restrictions on the
supply of a natural resource, so thatdemand exceeds supply. These
restrictions can be natural or legal.
In general, the resource rent is the total of the differential rent and the
scarcity rent.
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Scarcity assessment
Real world: Natural resource commodity prices may rise
or fall over time because:
• Marginal production cost might decrease (technology
improves) or increase (exploit cheapest sources first).
• Demand may grow over time unless a new technology
displaces this demand (e.g., coal replaced firewood,
natural gas replaced coal, alt. energy replaces natural
gas?),
• Future demand and marginal cost cannot be known
with certainty.
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Hotelling rule: intuition
In the absence of extraction costs, the firm is
indifferent between maintaining or extracting the
resource only if the resource price increases at rate
δ:
• for a lower increase rate, it would be convenient
to extract at the most rapid rate;
• for a higher increase rate, it would never be
optimal to extract the resource.
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Two-periods example: assumptions
1. There is a well-functioning competitive market for the
2.
3.
4.
5.
nonrenewable resource in question (no monopolies or
cartels)
Market participants are fully informed of current and future
demand, marginal production cost, market discount rate,
available supplies, and market price
We will look at the most basic dynamic case: two time
periods: today (period 0) and next year (period 1)
Marginal cost is constant
Market demand is “steady state”, meaning that demand in
period 1 is the same as in period 0 (no growing or
shrinking demand)
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Two-periods example: data
Demand: P = 200 – Q
Supply: P = 10
Discount rate “δ” = 10 percent (0.1)
Total resource stock Qtot = 100
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Case 1: Ignore period 1 while in period 0
(“live for today”)
Competitive market equilibrium:
200-Q0 = 10
Q0 = 190
Problem! Qtot = 100 < 190.
Scarcity-constrained market equilibrium
Q0 = 100;
P = 200 – 100 = $100.
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Case 1: Consume All in Period 0
250
Price
200
150
100
50
Demand
Supply
0
0
20
40
60
80
100
Quantity
120
140
160
180
200
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Case 1: Consume All in Period 0
250
Price
200
150
CS = $5000
100
PS = $9000
50
Demand
Supply
0
0
20
40
60
80
100
Quantity
PV of total gains from trade = $14,000
120
140
160
180
200
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Case 2: Consume Half in Period 0 and Half in Period 1
250
200
Price
CS = $1,250
150
100
PS = $7,000
50
Demand
Supply
0
0
20
40
60
80
100
120
140
160
180
Quantity
PV of total gains from trade, period 0, = $8,250
PV of total gains from trade, period 1, = $8,250/(1+0.1)1 = $7,500
200
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Case 2: Divide Qtot equally
over periods 0 and 1:
Sum of the PV of total gains from trade over
periods 0 and 1:
$8,250 + $7500 = $15,750
Note that $15,750 in PV of total gains from trade from
dividing the resource equally over periods 0 and 1
EXCEEDS the $14,000 in total gains from trade when
we consumed all of the resource in period 0. Thus
equal division is closer to being dynamically efficient.
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Master in Human Development & Food Security
Hotelling’s rule
Methods for solving for the dynamically efficient
allocation of the fixed stock of resource over time:
the dynamically efficient allocation occurs
when the PV of marginal profit (also known as
marginal scarcity rent or marginal Hotelling
rent) for the last unit consumed is equal
across the various time periods.
(P0-MC)/(1+δ)0 = (P1–MC)/(1+δ)1
Marginal profit, period 0
Marginal profit, period 1
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Hotelling’s rule: example
Let demand be given by P = a –bqi. The
integral of demand is total benefits, aqi –
bqi2/2. Likewise total cost is cqi (c is constant
MC). If the available resource stock is Qtot,
then the dynamically efficient allocation of a
resource over “n” years is the solution to the
following maximization problem:
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Example: FOCs
∑i (aqi – bqi2/2 – cqi)/(1+δ)t + λ[Qtot - ∑i
qi],
where t = 0, 1, 2, …, n. If Qtot is
constraining, then the dynamically
efficient solution satisfies:
•(a – bqi – c)/(1+r)t - λ = 0, i = 0, 1, …, n.
•[Qtot - ∑i qi] = 0
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2 periods problem: FOCs
Now let’s apply the parameters from our problem
(a = 200, b = 1, c = 10, δ = 0.1, 2 periods).
The dynamically efficient solution satisfies:
(200 – q0 – 10)/(1+0.1)0 = λ
(200 – q1 – 10)/(1+0.1)1 = λ
100 = q0 + q1
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2 periods problem: Hotelling’s rule
(200 – q0 – 10)/(1+0.1)0 = (200 – q1 – 10)/(1+0.1)1
Since q1 = 100 - q0, substitute (100 - q0) for q1 and
simplify:
190 - q0 = (190 - (100 - q0))/(1.1)
190 – 0.9091*90 = q0(1+0.9091) =
q0 = 108.182/1.9091 = 56.667
q1 = 100 – 56.667 = 43.333
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Hotelling’s rule: test
P0 = 200 – 56.667 = 143.333
(P0 – MC)/(1+0.1)0 = $133.33
P1 = 200 – 43.333 = 156.667
(P1 – MC)/(1+0.1)1 = $133.33
Therefore,
satisfied.
Hotelling’s
rule
is
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Dynamically Efficient Market Allocation I
Period 0 gains from trade:
CS = (200 - 143.333)*56.667/2 =
$1,605.55
PS
=
(143.333-10)*56.667
$7,555.56
PV(TS) = $9,161.11
=
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Dynamically Efficient Market Allocation II
Period 1 gains from trade:
CS = (200-156.667)*43.333/2 = $938.87
PS = (156.667-10)*43.333 = $6,355.48
PV(TS) = $7,294.35/1.1 = $6,631.23
Sum of PV of total gains from trade, periods 0
and 1: $9,161.11 + $6,631.23 = $15,792.34.
This is $42.34 larger than a 50/50 split in Case
2.
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Dynamically efficient equilibrium: intuition
• When a resource is abundant then
• The profit created by resource scarcity
consumption today does not involve
an opportunity cost of foregone
marginal profit in the future, since
there is plenty available for both today
and the future. Thus, when resources
traded in a competitive market are
abundant, P = MC and thus marginal
profit is zero.
•
• As the resource becomes increasingly
scarce, however, consumption today
involves an increasingly high
opportunity cost of foregone marginal
profit in the future. Thus as resources
become increasingly scarce relative to
demand, marginal profit (P-MC) grows
in competitive markets is called
Hotelling rent (also known as resource
rent or by the Ricardian term scarcity
rent). Hotelling rent is economic profit
that can be earned in certain natural
resource cases due to the fixed supply
of the resource.
Due to fixed supply, consumption of a
resource unit today has an opportunity
cost equal to the present value of the
marginal profit from selling the resource
in the future.
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Non-competitive markets: Solow
paradox
• Solow, Robert M. 1974. “Intergenerational Equity
and Exhaustible Resources”, Review of Economic
Studies, pp. 29-45.
• The optimal extaction period is longer in the case of
monopoly than in perfect competition
Economia delle risorse naturali a.a.2007/08
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p
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P
pm
pc
0
Tc
Tm
t
x
x*c
x*m
0
Tc
Tm
t
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What is the ‘paradox’ about?
Should we prefer monopoly over
competion?
It could be a «second-best» option,
but we need to show that the perfect
competion extraction path is not
optimal:
• Different δ?
• Externalities?
Economia delle risorse naturali a.a.2007/08
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Why are natural resources prone to
cartelization?
• A producer cartel is about monopolistic
coordination aimed at jointly cutting supply
or raising price, thus leading to increased
revenue for the group.
There are 3 major problems that a cartel
must overcome if it is to be successful.
1. There is the problem of determining the
optimal level of output and the rules
governing the allocation of that output
among cartel members
2. Once output decisions have been taken,
cartel members have an incentive to
renege on the agreement and sell
additional output, thus reaping additional
profits.
3. A cartel has to be able to prevent entry by
new firms.
The case of natural resources:
1. natural resources tend to be concentrated
in few countries, hence few producers
generally account for a large proportion of
world supply.
2. natural resources tend to exhibit high fixed
costs of extraction. These costs reduce the
risk of dissolution of a cartel due to entry by
new firms, as they make it difficult for
outside producers to equip themselves with
the production capacity necessary to enter
the market.
3. natural resources tend to be relatively
homogeneous. This increases the incentive
for firms to defect, as a higher
responsiveness to price changes is
associated with less differentiated goods.
However, deviations from a cartel
agreement are easier to detect when
products are similar than when they are
differentiated
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Sustainability
• Solow shows that constant consumption can be sustained
by a suitable path of capital accumulation, despite declining
resource flows. This is possible only if there is a certain
degree of substitutability between capital and a natural
resource, and if
the latter is a non-essential input.
• This intuition was translated into a policy rule by Hartwick,
who argued that the rent derived from resource extraction
should be invested in building the capital stock (broadly
defined to include infrastructure, physical capital,
education) needed to guarantee constant consumption
over time.
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Renewable resources
Wildlife Populations: groups of animals, all of the same
species, that live together and reproduce
Issues:
• Sustanability
• Access
Biomass: the aggregate mass of the biological material (such
as the total weight of fish of particular age classes or the cubic
metres of standing timber), or in terms of population numbers
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Biological growth processes
• In order to investigate the economics of a renewable resource, it is
first necessary to describe the pattern of biological (or other) growth
of the resource. To fix ideas, we consider the growth function for a
population of some species of fish. This is conventionally called a
fishery. We suppose that the population in this fishery has an
intrinsic (or potential) growth rate denoted by γ. This is the
proportional rate at which the fish stock would grow when its size is
small relative to the carrying capacity of the fishery, and so the fish
face no significant environmental constraints on their reproduction
and survival. The intrinsic growth rate γ may be thought of as the
difference between the population’s birth and natural mortality rate
(again, where the population size is small relative to carrying
capacity).
• Be careful not to confuse a rate of change with a rate of growth. A
rate of change refers to how much extra is produced in some
interval of time. A rate of growth is that rate of change divided by its
current size (to measure the change in proportionate terms).
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Stability
Economia delle risorse naturali (a.a.2006/07)
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Critical depensation: graph
Economia delle risorse naturali (a.a.2006/07)
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Gordon-Schaefer model: graph
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Gordon-Schaefer model: rent
dissipation
Rent: TR - TC
Free access ==> TR - TC = 0
• E > E* ==> TC > TR
• E < E* ==> TC < TR
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When is a fishery overfished?
When stock is at X = K, the fishery is unexploited (and in effect has been for
some considerable span of recent time).
• When stock is below XMSY the fishery could be described as being in a
developmental phase. Specifically, we might say that the fishery is ‘under
exploited’ if stocks are close to XMAX so that the fishery is capable of
producing a great deal more under increased fishing pressure, or as
‘moderately exploited’ if X is closer to XMSY so that the fishery is capable of
producing some more under increased fishing pressure.
• When X is in the (close) neighbourhood of XMSY the fishery is ‘fully exploited’
(and the fishery is producing close to its MSY).
• When X is less than XMSY we might choose to apply one of three labels
depending on how much lower is X than XMSY and in which direction the
fishery is moving:
•
• The fishery is ‘overfished’: stocks at lower level than XMSY; and the catches in recent years
have been showing a downward trend (so current catches less than recent historical high).
• The fishery is ‘depleted’ – a more extreme version of ‘overfished’ in which stocks are very
far below XMSY.
• A ‘recovering’ fishery is one in which stocks are very low relative to historical maximum
levels, but in which harvest levels are trending upwards (the fishery is moving from left to
right towards XMSY.
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Single owner: economic and biological overexploitation
Master in Human
Development & Food
Security
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Maximizing the Present Value of
Resource Rent in a Gordon-Schaefer
Model
• The classical Gordon–Schaefer model presents equilibrium revenue (TR)
and cost (TC), including opportunity costs of labor and capital, in a
fishery where the fish population growth follows a logistic function.
• Unit price of harvest and unit cost of fishing effort are assumed to be
constants.
• In this case, the open access solution without restrictions (OA) is found
when TR=TC and no rent (abnormal profit, P=TR-TC) is obtained.
Abnormal profit (here resource rent) is maximized when TR'(X)=TC'(X)
(maximum economic yield, MEY).
• Discounted future flow of equilibrium rent is maximized when P'(X)/d=p,
where p is the unit rent of harvest and d is the discount rate. This
situation is referred to as the optimal solution (OPT), maximizing the
present value of all future resource rent.
• The open access solution and MEY equilibriums are found to be special
cases of the optimal solution, when the discount rate is infinite or null,
respectively.
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Dynamics
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