Economics of nonrenewable and renewable resources

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Economics of non-renewable andrenewable
resources
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Natural Resources
Excludability
Natural Production
Use
consumption
production
non
renewable
with
without
good
good
renewable
(private good)
(public good)
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Types of Reserves
Geologic Uncertainty
Current Reserves
undiscovered,but economicallyviable resources
Economic viability
known, but economically unviable reserves
Reserves, we haven't even started to look for
yet
or will never be found
Reserves that will never be economically viable
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The efficient and optimal use of non-renewable
resources (multi-period)

• The model set-up (very simplified)
• The social utility from consuming a quantity R of
  the resource may be defined as
• Then, the economy's inter-temporal social welfare
  function

First element the objective of society
see nonrenewable.xls
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A resource demand curve
P
Quantity of resources extracted, R
R
0
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The optimisation problem is to make social
welfare maximising choices of

• (a) Rt, for t 0 to t T (that is, we wish to
  choose a quantity of resource to be extracted in
  each period), and
• (b) the optimal value for T (the point in time at
  which depletion of the resource stock ceases),
  subject of the constraint that
• where S is the total initial stock of the
  non-renewable resource, where the remaining stock
  gt
• where , the rate of change of the remaining
  resource stock with respect to time.

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so we get

• The economy's inter-temporal social welfare
  function
• where
• U aggregate utility flow ? social utility
  discount rate and t time periods R resource
  flow (amount extracted and used per period) S
  environmental resource stock.

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Optimality conditions for the multi-period model
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Optimal Depletion Model for non-renewable
Resources
(Net)Price Pt

• Resource Demand function (N)
• Hotelling's Efficiency Condition
• Initial Value of the Resource (P0)
• Final Value of the Resource (PT)

PT K
Demand
Pt
P0
R0
T
Time t
R
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Rt
K is also called 'choke price'. At this price
people change their demand to an alternative
resource, or product
S total resource stock
T
Time t
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Hotelling's Rule non-uniqueness of efficient
time paths of the resource net price
Hotelling Rule (necessary condition but not
sufficient condition)
Royalty Path
Pt
Assumption rp
initial and termination conditions?
t
The optimal path will be that one which satisfies
S gt 0 as t gt 8
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Hotelling's Rule with Backstop Technology
available
P
Choke Price
PK
Net Price
tT
t
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Does a Market Economy Yield an Optimal and
Efficient Allocation of Resources

• Answer yes, but under certain circumstances.
• Intuition on the efficiency of the market
  mechanism
• In a competitive market economy, profit
  maximisation requires that firms take proper
  account of their revenue and cost functions.
• The (aggregate) utility function provides
  appropriate information about the market demand
  curve, and so provides appropriate information
  about firms' revenues.
• Any costs of production and extraction will be
  taken into account by business.

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However, a market economy will probably not
deliver and efficient and optimal allocation

• Monopoly depletion too slow.
• Social costs of resource depletion not considered
  (e.g., pollution externalities).
• Private market interest rate above the social
  discount rate.
• Presence of public goods
• Absence of well-defined and enforceable property
  rights
• Incomplete information
• Agents' functions may depend upon environmental
  quality

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Furthermore

• 1) Optimality and distribution of initial
  endowments we have made social utility depend
  only on the aggregate total of consumption, and
  not on its distribution. But market demand curves
  WILL depend on distribution of endowments, and
  may not correspond to an economy's (social)
  utility function if that latter function is
  defined differently.
• 2) Sustainability optimal outcomes may not be
  sustainable. To achieve sustainability, we may
  need to impose an additional constraint on the
  above optimisation exercise, of the form Ut gt
  Ut-s for all sgt0 or Ct gt Ct-s for all sgt0
  (Of course, sustainability may not even be
  feasible).

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Model Extensions economic system, or incorporate
extraction costs

• National income accounting identity
• where K manufactured capital stock
• The economy's production function
• marginal product of the resource
• marginal product of capital
• and so

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Renewable Resources

• 1) Renewable flow Resources
• Such as solar, wave, wind and geothermal energy.
  These energy flow resources are non-depletable.
• 2) Renewable stock resources
• living organism fish, cattle, and forests, with
  a natural capacity for growth.
• inanimate systems (such as water and atmospheric
  systems) reproduced through time by physical or
  chemical processes
• arable and grazing lands as renewable resources
  (such as the recycling of organic nutrients) and
  physical processes (erosion, nutrient leaching,
  etc.) gt Are capable of being fully exhausted.

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Biological growth processes
Growth of fish stock(tonnes)
natural equilibrium
fish stock (tonnes)
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Biological growth and harvest
when fishing starts then additional growth will
be harvested and will not be available for the
stock in the next period. What if more than
additional growth is harvested?
Growth of fish stock(tonnes)
higher harvest intensity
Sustainable Yields (Y(E0), Y(E1),...,)
Y(E0)
Y(E1)
Fish stock (tonnes)
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Harvest amount and harvest intensity
Relationship between harvest amount and harvest
intensity (growth, and stock size).
Maximum Sustainable Yield (MSY)
Growth offish stock(tonnes)
medium harvest-intensity gt big harvest amount
high harvest intensity gt little harvest amount
low harvest intensity gt little harvest amount
Y(E0)
Y(E1)
Y(E2)
Y(E3)
Y(E4)
fish stock (tonnes)
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Revenue and Cost with respect to harvest intensity
Steady-State1) constant harvest amounts2)
constant regeneration3) constant stock
PP Private Property
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Rent elimination in Open Access Fishing
The Tragedy of the Commons
- Entry continues until all rents are dissipated
(profit per boat gt zero).- Stock size will
tend to be lower, and harvest rates will tend to
be higher (not always) compared with a restricted
access fishery.- Extinction is more likely, but
not necessarily happen
Revenue and Cost of harvest intensity()
Cost
Revenue
harvest intensity
E0
E1
E2
E3
E4
EOA
EPP
PP Private PropertyOA Open Access
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OPEN ACCESS and Species Extinction

• The extinction of renewable resource stocks is a
  possibility in conditions of open access, but
  open access does not necessarily lead to
  extinction of species.
• Open access enhances the likelihood of
  catastrophic outcomes because
• Incentives to conserve stocks for the future are
  very weak.
• Free riding once a bargain has been struck
• Crowding diseconomy effects

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Excessive Harvesting and Species Extinction

• There are many reasons why human behaviour may
  cause population levels to fall dramatically or,
  in extreme cases, cause species extinction. These
  include
• Even under restricted private ownership, it may
  be 'optimal' to the owner to harvest a resource
  to extinction. Clark (1990) demonstrates,
  however, that this is highly improbable.
• Ignorance of or uncertainty about current and/or
  future conditions results in unintended collapse
  or extinction of the population.
• Shocks or disturbances to the system push
  populations below minimum threshold population
  survival levels.

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Renewable Resource Policy

• Command-and-Control
• Quantity restriction on catches (EU Total
  Allowable Catches)
• Fishing season regulations
• Technical restriction on the requirement used -
  for example, restrictions on fishing gear, mesh
  or net size, or boat size.
• Incentive-based-Policies
• Restrictions on open access/property rights
• Fiscal incentives
• Establishment of future markets
• Marketable permits ('individual transferable
  quotas, ITQ)

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Forest as Renewable Resource

• Forests provide multi-functional values (wood
  utilization, recreation, protection against
  natural hazards, etc.).
• Major interest commercial wood production
  (natural forest versus commercially used forest).
• Core Question What is the optimal harvest time
  that maximizes the Net Present Value?
• Differences to Fish Resource
• each tree and each population can be harvested
  separately.
• usually the entire tree will be harvested and not
  additional growth.
• property rights and controlling are usually much
  more clear and secure.
• forest lands have often opportunity cost (land
  use possibilities ltgt ocean).

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Forestry

• in 2000, about 3.9 bil. ha forest world wide (95
  Natural forest, 5 Plantation forest).
• about 9.4 mil ha Forest area is transformed into
  other landuse in the last 10 years.
• http//www.fao.org/forestry/index.jsp

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Forest population growth
S 1.132t 0.0878t2 - 0.0005t3 S Stock (CM)
t 123 years
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Maximum Sustainable Yield (MSY)???
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A single-periodic Forestry Model

• Assumption
• all trees are planted and harvested at the same
  time.
• no reforestation gt one period.
• forest land has no alternative utilization
  possibility gt opportunity cost are zero.
• planting cost (k), and marginal harvesting cost
  (c) and the price for wood (P) are constant over
  time (real).
• the forest population receives a value only
  through its wood utilization, and its existence
  (or harvesting) creates no external effects.
• Question
• What is the optimal time to harvest this forest?

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A single-periodic Forest Model

• We receive the answer, when we determine the
  optimal age that maximises Net Present Value.
• ST available forest stock at time T
• (P - c) net price (p) (price - marginal
  harvesting cost)
• i private discounting rate
• k planting cost
• Net Present Value is maximised, if we receive
  from
• the highest value.

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A single-periodic Forest Model

• using the product rule

setting equation 0 gt
and solve for i
with constant p
or
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A single-periodic Forest Model
means that the discount rate (i) equals the
proportionate growth rate of the forest
population.
NB1
slope i 0.03
NB2
48 years
123 years
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(No Transcript)
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Optimal harvesting programmes
i 0.00
i 0.01
i 0.02
i 0.03
i 0.04
i 0.05
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A multi-period Forestry Model
PV
t
t0
t1
t3
t4
t2
...
What is the optimal planting time for each period?
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multi-period Forestry Model
an infinite geometric series 1/(1 - eiT)
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Multi-periodic Forestry Model
1. derivative for T and setting 0
is the efficiency condition for maximizing Net
Present Value in rotational forestry. It
determines optimal rotation lengths (T) in
infinite time frame, assuming that prices and
cost stay constant.
rhs
lhs
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Multi-period Forestry Model
i 0.05
i 0.04
i 0.03
i 0.02
i 0.01
i 0.00
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The optimal rotation length of the multi-period
Forestry Model is determined by

• the biological growth curve of the forest
  population on particular plot conditions (e.g.,
  Parameter, a1, a2, a3),
• interest or discount rate i,
• cost of planting and reforestation (k) vs. -!!!
  single periodic!!!, and
• net price for wood (p), or its gross price (P)
  and the marginal harvesting cost (c) p (P -
  c).

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Summary

• Usually only harvesting yields determine the
  value of the natural resource.
• Forest protection competes with alternative
  investments.
• The extent of protection is determined by the
  profitability of alternative investments.
• A prerequisite are clearly defined property right
  or the right to use.
• Under strict circumstances is a market allocation
  optimal (multifunctional utilization
  possibilities?)