# Efficient Allocation of a Non-renewable Mineral Resource Over Time by D2MK25b

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```									Efficient Allocation of a
Non-renewable Mineral
Resource Over Time
Wednesday, March 2
Number 1
P = 8 – 0.4 q                P = MEC + MUC
P0 = 8 – 0.4(8.004) = 4.80   MUC0 = 4.80 – 2.00 = 2.80
P1 = 8 – 0.4(7.305) = 5.08   MUC1 = 5.08 – 2.00 = 3.08
Etc.                         Etc.

2.80(1.1) = 3.08
MUC increases at the
3.08(1.1) = 3.39
rate of discount (10%)
Etc.
#1 - Graph P, MEC and MUC over time
8.00
7.00
6.00
5.00                                          Price
4.00                                          MEC
\$

3.00                                          MUC
2.00
1.00
0.00
0   1   2   3          4   5   6   7
time
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
   Numbers 4 and 5
   Options for efficiency and sustainability
Number 2
P = 8 – 0.4 q                P = MEC + MUC
P0 = 8 – 0.4(8.798) = 4.48   MUC0 = 4.48 – 2.00 = 2.48
P1 = 8 – 0.4(8.177) = 4.73   MUC1 = 4.73 – 2.00 = 2.73
Etc.                         Etc.

2.48(1.1) = 2.73
MUC increases at the
2.73(1.1) = 3.00
rate of discount (10%)
Etc.
Number 2 (continued)
   MUC does not increase at the rate of discount
between periods 4 and 5. Why?
   What is the maximum price you would expect
for the resource in period 5? Why?

\$6.00 = 8 – 0.4q     If q = 5,
0.4q = 2             q of depletable is 2.863 units
q=5                  q of renewable is 2.137 units
#2 - Graph P, MEC and MUC over time
8.00
7.00
6.00
5.00                                  Price
4.00                                  MEC
3.00                                  MUC
2.00
1.00
0.00
0   1   2    3    4     5
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
Number 3
P = 8 – 0.4 q             MEC = 2 + 0.1q
P0 = 8 – 0.4(7.132) = 5.15 MEC0 = 2 + 0.1(7.132) = 2.71
P1 = 8 – 0.4(6.523) = 5.39 MEC1 = 2 + 0.1(13.66) = 3.37
Etc.                      MEC2 = 2 + 0.1(19.68) = 3.97
Etc.
(In this case, q is the
cumulative amount extracted.)
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
7.00

6.00

5.00
Price
4.00
MEC
3.00
MUC
2.00

1.00

0.00
0   1   2   3   4   5    6
What happens to MUC over time if
MEC is increasing?
\$

= MUC
MEC + MUC = P

MEC

TIME
Impacts on optimal extraction rates
when market conditions change
   When marginal extraction costs are an
increasing function of quantity extracted:
   Opportunity cost is lower
   The resource is used more slowly since cost is
increasing
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 total net benefits          At t=0, NB=\$35.22
from mineral resource                 Keep \$15.22, put 20.00
is \$152.17.                            into fund
   For a perpetuity:                 At t=1, PV NB=\$33.17
                                     Keep \$15.22, put 17.95
payment
PVperpetuity                      into fund
i
   So            x                   In PV terms
\$152.22                           Keep \$13.84, put
.1                        \$16.32 into fund
   Payment = \$15.22                  Etc.
Sustainability efforts – building a
capital stock (Number 5)
   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
   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
(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                  Save and
now
OR         use more
money
later
Why would taxing away rents result in
faster rate of resource extraction?

Q mineral   Q mineral   Q mineral    Q mineral

\$ mineral    \$ mineral   \$ mineral    \$ mineral
Mine and                              Save, mine
use income
now
OR               later, and use
income later
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. start of war 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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