Allocation of
Depletable & Renewable Resources
Finite stocks of depletable resources
– when do they get scarce?
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When demand is in excess, Should we allow
the system to collapse?
Price of oil high $147+ in June 2008 - falls in
2008 to a low $32 in Dec 08 - now rises$ 69
on Oct, 05 2009 – still availability reduces –
demand rising – life style
New type of vehicles? – solar/wind/CNG?
What happens if no substitute or renewable
resource is available?
Some like solar or surface water, are at
constant MC
Concepts of stock of depletable resources
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3 concepts to classify:
Current reserves – known resources
Potential reserves – depends on how much people
are ready to pay
Resource endowment – geological
Common mistakes in understanding concept:
- to understand distinctions use data on current reserves Fundamental error – understatement of time
- Assuming that entire resource can be made at a price that
people are ready to pay
We can never determine actual size of endowment.
Other categories:
- depletable, recyclable resources - copper
- recyclable resource
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- Current reserves of depletable, recyclable resource
can be augmented by economic replenishment & by
recycling.
- Their potential reserves can exhaust – depends on
demand & durability and ability to reuse the products
- All depletable resources are not recyclable/reusable –
coal, oil & gas once heated escape in atmosphere –
non-recoverable
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All depletable resources are finite
Reusing & recycling makes them last longer
Renewable resources can be replenished - naturally
For some, continuation & volume of flow depends on
humans – Fishing, soil erosion
For some flow independent of humans – solar
Some can be stored with proper facilities – solar energy
converted to biomass by photosynthesis.
A different service is provided by storage of renewable
resources than storage of depletable resources.
Extends their
economic life
Can serve as means to
smoothen out cyclical
imbalances of SS & DD
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Storage of
Renewable resources - smoothens cyclical
imbalances of demand & supply – can create buffer
stocks
Depletable resources - extends their economic life
Challenge for depletable resources: allocating
dwindling stocks among generations
Once depletable resources’ stocks dwindle we tend to
go to renewable resources – then we must sustain
their flow
Challenge for managing renewable resources:
maintenance of an efficient & sustainable flow
How to respond to these challenges?
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Depletable doesn’t run out suddenly
When there is a substitute renewable resource available
to a depletable resource at constant marginal cost – oil &
solar energy
Transition will happen if its MC < maximum willingness
to pay – MC of Dpl res will not exceed beyond MC of
Renwl res, as society will move to RR when it is cheaper
Maxm willingness to pay (choke price) sets upper limit –
on total marginal cost when no substitute is available
MC of extraction of the substitute sets upper limit on the
price when one is available
Quantity extracted gradually falls as MC rises until
switch is made to the substitute
Switch Point
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If a renewable resource is available, more of
depletable will be extracted - in the future new
resource is available
Depletable resource exhausted sooner
At switch point (transition point) Cn of RR begins
Consumption sequencing: Depletable resource 
switch point  renewable resource
Transition from one constant cost depletable resource
to another depletable resource with a constant but
higher MC
When total MC of 1st resource would  and then
when is = MC of 2nd, at time of transition
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MC rises slowly for 2nd resource, at least initially.
Total MC = MEC + MUC. In both MEC is constant
while MUC increases at rate r. At the time of
transition MEC constitutes much larger proportion of
TMC for 2nd resource than for 1st.
TMC1
TMC2
Price
MECost2
MExtrCt1
T*
O
Transition Point
Time
Increasing marginal extraction cost (MEC)
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Efficient allocation of DRes in longer time +
availability of other DRes that are perfect substitutes
Situation: When MEC of depletable res. rises with
cumulative amount extracted – 1st grade then 2nd gr
Dynamic efficient allocation by maximising PV of
NB using modified cost of extraction function
MUC falls over time & at transition it goes to zero
MUC – opportunity cost reflecting forgone future
marginal net benefits
Under increasing cost every unit extracted increases
the cost of extraction
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As current MC rises over time, sacrifice made by
future generations falls – net benefit received by
them, if a unit of resource is saved for them gets
smaller & smaller, as MEC gets larger & larger
Opportunity cost of current extraction drops to zero &
TMC = MEC at switch point
Under constant cost reserve gets exhausted – under
increasing some is left
History: Cost of depletable resource (oil) has ⇧ over
time
∴ resources are not used efficiently?
Role of exploration & technological progress
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Exploration for new resource? Technological
progress? – these two are significant in determining
actual consumption path
New resource’s search is expensive – MEC 
Solar used in India – costly installation – but if oil
prices ⇧ all the time – solar is future
⇧ MC of known resource larger the potential in net
benefits from exploration
With low MC new resource → ⇧ consumption
With no new resource Cn falls
More extraction with technological progress
Market Allocations
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Actual markets – efficient allocation?
Profit maximisation compatible with dynamic
efficiency?
Resource in the ground has 2 potential sources of value
to owner – use-value: when sold & asset-value: when
in ground
While price rises ‘in-ground’ is getting more valuable –
capital gain when conserved –
A wise producer balances present & future production
to maximise the value of resource
In prescient competitive market P of res = TMC of
extracting & using the resource
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Generally TMC curve shows changes in the prices
over time – expected
All other costs except evn costs are borne by the
producer – e.g. health risks, acids in water from
mines - if no outside attempt to internalise it, will not
be part of extraction decision
If MC is ↑ by cost of env. Damage – P ↑ & DD  Rate of Cn lower - time of transition later
Environmental & natural resource decisions are
intimately linked
To sum up,
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Efficient allocation of depletable & renewable resources
depends on circumstances
When extracted at constant MC, efficient quantity of
DRes extracted over time declines smoothly to zero
If renewable constant-cost substitute is available the
quantity of DRes extracted will  smoothly
In both cases, all available DRes will be used up & MUC
will  over time and will be maximum when last unit is
is extracted
Technological progress (doesn’t allow MC to rise) &
exploration (expands size of current reserves) activity
tend to delay the transition to renewable resources
Market allocation of DRes can be efficient when PR
structures are properly defined