Efficient Allocation of a Non-renewable Mineral Resource Over Time Monday, March 13
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Efficient Allocation of a Non-renewable Mineral Resource Over Time
Monday, March 13
Number 1
P = 8 – 0.4 q
P0 = 8 – 0.4(8.004) = 4.80
P1 = 8 – 0.4(7.305) = 5.08
Etc.
P = MEC + MUC
MUC0 = 4.80 – 2.00 = 2.80
MUC1 = 5.08 – 2.00 = 3.08
Etc.
2.80(1.1) = 3.08
3.08(1.1) = 3.39
Etc.
MUC increases at the rate of discount (10%)
#1 - Graph P, MEC and MUC over time
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
0 1 2 3 4 5 6 7
time
$
Price
MEC
MUC
Impacts on optimal extraction rates when market conditions change Number 2
When a renewable substitute is added Number 3
When marginal extraction costs are an increasing function of quantity extracted
Number 4 Option for efficiency and sustainability
Number 2
What is the maximum price you would expect for the resource in period 5? Why?
P = 8 – 0.4 q
P0 = 8 – 0.4(8.798) = 4.48
P1 = 8 – 0.4(8.177) = 4.73
Etc.
$6.00 = 8 – 0.4q
0.4q = 2
q = 5
If q=5,
of depletable is 2.863 units
q of renewable is 2.137 units
P = MEC + MUC
MUC0 = 4.48 – 2.00 = 2.48
MUC1 = 4.73 – 2.00 = 2.73
…
MUC5 = 6 – 2.00 = 4.00
2.48(1.1) = 2.73
2.73(1.1) = 3.00
…
3.63(1.1) = 4.00
MUC increases at the rate of discount (10%)
Number 2 (continued)
#2 - Graph P, MEC and MUC over time
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
2.48 2.73 3.00 3.30 3.63 4.00
time
$
Price
MEC
MUC
Impacts on optimal extraction rates when market conditions change When a renewable substitute is added:
Opportunity cost of use is lower The resource is used more quickly
P = 8 – 0.4 q
P0 = 8 – 0.4(7.132) = 5.15
P1 = 8 – 0.4(6.523) = 5.39
Etc.
MEC = 2 + 0.1q
MEC0 = 2 + 0.1(7.132) = 2.71
MEC1 = 2 + 0.1(13.66) = 3.37
MEC2 = 2 + 0.1(19.68) = 3.97
Etc.
(In this case, q is the cumulative amount extracted.)
Number 3
Number 3 (continued)
P = MEC + MUC
MUC0 = 5.15 – 2.71 = 2.44
MUC1 = 5.39 – 3.37 = 2.03
MUC2 = 5.59 – 3.97 = 1.63
MUC is not increasing at the rate of discount. Why?
#3 - Graph P, MEC and MUC over time
-1.00
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
0 1 2 3 4 5 6
time
$
Price
MEC
MUC
What happens to MUC over time if MEC is increasing?
TIME
$
MEC
MEC + MUC = P== MUC MUC
Impacts on optimal extraction rates when market conditions change When marginal extraction costs are an
increasing function of quantity extracted: The resource is used more slowly since cost is
increasing However, increasing extraction cost means net
value declines over time. Opportunity cost of use declines over time.
Value of foregone resource is less as extraction cost rises
Increases in demand Increases in population, income, etc. Expect higher prices for any level of extraction This means opportunity cost of current extraction is
higher So MUC is higher for every time period than if
demand were constant. What does this mean for the rate of extraction?
Sustainability efforts – building a capital stock (Number 4) PV of net benefits is $152.17 In period 0, $35.22 is used So, period 0 needs to deposit into capital fund
enough to insure there is $35.22 at the start of year 8 (first year after mineral is depleted)
x(1.1)8 = 35.22 2.144x = 35.22 X=16.43 – to be paid into fund at time 0 16.43(1.1)8 = 35.22 – will be in fund at time 8
PV of net benefits is $152.17 In period 1, $30.15 is used (in PV terms) So, period 1 needs to deposit into capital fund
enough to insure there is $30.15 at the start of year 8 (first year after mineral is depleted)
x(1.1)7 = 30.15 1.949x = 30.15 X=15.47 – to be paid into fund at time 0 15.47(1.1)7 = 30.15 – will be in fund at time 8
Alaska Permanent Fund www.apfc.org What is the purpose of the Permanent Fund?
According to language in the state law which established the Permanent Fund (AS 37.13), the Permanent Fund was created with three purposes:(1) to provide a means of conserving a portion of the state's revenue from mineral resources to benefit all generations of Alaskans(2) to maintain safety of principal while maximizing total return(3) to be a savings device managed to allow maximum use of disposable income for purposes designated by law
Policy Question When Price exceeds MEC, does that mean
that the mine owner is earning excess profits and they should be taxed away?
What happens to extraction rate if rents are taxed away?
$ $ $ $
Use money now
Save and use more money later
OR
Your Savings Account
Why would taxing away rents result in faster rate of resource extraction?
$ mineral $ mineral $ mineral $ mineral
Mine and use income now
Save, mine later, and use income later
OR
Q mineral Q mineral Q mineral Q mineral
Why would taxing away rents result in faster rate of resource extraction? If mine owner does not get to keep rent, the
incentive is to extract the resource quickly and invest the returns in some alternative income-earning venture e.g. Extract the mineral, sell it, and invest the
money at some positive rate of growth
Pt = MECt + MUCt
Can predict changes in price by predicting changes in MEC or MUC
E.G. incident in Middle East Oil prices rise Price gouging? Or increase in MUC? Once more certainty in availability is established,
MUC goes back down
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