Transcript Economics 1100

Ch.7 Allocation of Depletable
and Renewable Resources

Resource Taxonomy
– 3 categories
– 1) Current reserves: known resources,
profitably extracted at current prices
– 2) Potential Reserves: function, not a number;
depends upon price people are willing to pay
– 3) Resource endowment: resources in
earth’s crust
Resource Taxonomy: cont.

Common mistakes
– 1) data on current reserves as max. reserves
» see Ex.7.1 pitfalls in using reserve data. We should
have run out of copper in 1974, based on 1934
forecast using static index
– 2) total resource endowment can be made
available as potential reserves.
Table 7.1 Estimates of Ultimately
Recoverable Oil w/ 10% ROR
Price per barrel
(1976 dollars)
 $11.62
 $13.75
 $22.00
 $30.00+


Ultimate Recovery
(109 barrels)
21.2
29.4
41.6
51.1
Source: U.S. Congress, Office of Technology Assessment, Enhanced Oil
Recovery Potential in the United States (Washington, D.C.: OTA, 1978):7.
Resource taxonomy: cont.

Other ways of categorizing resources
–
–
–
–
1) depletable: no recharge
2) recyclable: can be reused/ different form
3) renewable: replenishes itself
e.g. Oil, gas, coal are depletable and non
recyclable. Copper is depletable and
recyclable. Whales are renewable, but can be
depleted if over harvested.
Efficient Intertemporal
Allocations

Several alternative models
–
–
–
–
1) two period model revisited
2) n-period constant cost case
3) transition to renewable substitute
4) transition from one constant cost depletable
resource to another
– 5) increasing marginal extraction cost
– 6) environmental costs
Two period model revisited
assumptions: demand is constant over time;
marginal cost of extraction is constant over
time.
 Optimal use requires:PVMNB1= PVMNB2
 PVMNB2=MNB2/(1+r)
 marginal user cost: present value of
foregone future net benefits; rises at rate of
interest, r.
 now we will generalize this model to n
periods.

N-period constant MEC: “The Mine”
assumptions: MEC is constant. Demand
curves constant across time.
 major findings:

– efficient price= total marginal cost
– total marginal cost =(marginal extraction cost +
marginal user cost) rises until hits choke price
– marginal user cost rises at rate of interest
– quantity gradually falls to zero in year 9
– does not “suddenly” run out
Transition to a Renewable
Substitute
assume depletable resource is available at
constant MEC of $2
 assume renewable substitute available at
constant MEC of $6; infinitely available

Fossil Fuel
Windpower
Fig. 7.2a Efficient Quantity: Constant MEC, No Substitute
9.00
8.00
7.00
6.00
5.00
Quantity
4.00
3.00
2.00
1.00
0.00
0
5
10
Time
Quantity
Fig. 7.2b Efficient Price Path: Constant MEC, No Substitute
10
Price
8
6
4
2
0
0
1
2
3
4
5
6
7
Tim e
Total Marginal cost
MEC
8
9
10
11
Transition to renewable substitute:
e.g. groundH20 to lake H20

Findings:
– Smooth transition
– quantity gradually reduced as MUC rises at rate
of interest until switch to substitute
– depletable resource is exhausted earlier
– only depletable resource used before switch
– only renewable used after switch
– price only rises to $6 in year 6; remains $6.
Fig. 7.3a Efficient Quantity: Renewable Substitute
Quantity
10
Quantity
8
6
4
2
0
0
1
2
3
4
5
6
Time
7
8
9
10
11
Marginal Cost
Fig. 7.3b Efficient Price: Renewable Substitute
9
8
7
6
5
4
3
2
1
0
Total
Marginal
cost
Marginal Extraction cost
0
2
4
Price
6
8
MEC
10
12
Tim e
Transition from one depletable to
another depletable substitute

assume 2nd depletable resource is available
at higher & constant MEC
Fossil Fuel
Nuclear
Transition: One Constant Cost
Depletable Resource to Another

Findings
–
–
–
–
–
cheapest resource is used first until exhausted
expensive resource used thereafter
transition is smooth
MUC rises at rate of interest
TMC rises slower after transition due to smaller
MUC, which still rises at rate of interest
Fig. 7.4 One Constant Cost Depletable to Another
Price
TMC1
TMC2
Price path
MEC2
MEC1
Time
0
T*
Increasing Marginal Extraction
Cost

Findings:
– biggest difference: MUC declines. Why?
– Why? opportunity cost is smaller as resource
gets harder to pump. almost no scarcity cost at
end. If it costs $5.99 to pump oil and solar is
available for $6.00, there is almost no future
sacrifice if I consume the oil now.
– resource is not exhausted. Some is too
expensive to pump/extract. We don’t
run out, we “run” to the substitute!
Fig. 7.5a Efficient Quantity: Increasing MEC
8
7
Quantity
6
5
4
3
2
1
0
0
1
2
3
4
5
Quantity
6
7
8
9
10
11
Tim e
Fig. 7.5b Efficient Price: Increasing MEC
7
6
Price
5
4
3
2
1
0
0
1
2
3
4
TMC
5
6
MEC
7
8
9
10
11
Tim e
Exploration & Tech. Progress
Our models have not considered
technological progress
 As marginal cost of extraction increases, we
have incentive to search more and develop
cheaper sources.
 If we are successful, MEC may actually
decline over time, but eventually it must
rise.

Market Allocations
Can private market ever give dynamically
efficient allocation?
 Appropriate Property Right Structures:

– common misconception: private producers want
to sell resource as fast as possible
– but if property rights are clearly established,
then prudent producer will act efficiently
– Value of the resource now must be compared to
its potential value next year.
Environmental Costs
What effect does environmental damage
cost have on efficient allocation?
 Two opposing effects on optimal switch
time:

– (Assume rising MEC and that solar is available
at $6 per unit.)
– Demand side: higher prices cause lower
consumption, should stretch out use over time
– Supply side: producers will extract less in total,
thus may hasten time until switch point
Fig. 7.6a Efficient Quantity: Environmental Costs
8
7
Quantity
6
5
4
Quantity w/ environmental costs
3
2
1
0
0
1
2
3
4
5
Quantity
6
7
8
9
10
11
Tim e
Fig. 7.6b Efficient Price: Environmental Costs
7
TMC w/ environmental costs
6
Price
5
4
3
MEC w/ environmental costs
2
1
0
0
1
2
3
4
TMC
5
6
MEC
7
8
9
10
11
Tim e