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

VIEWS: 5 PAGES: 23

									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
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?
        Your Savings Account



  $         $      $           $

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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