Download Day15 (actually 16)

Efficient Allocation of a
Non-renewable Mineral
Resource Over Time
Monday, March 13
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
rate of discount (10%)
3.08(1.1) = 3.39
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
time
5
6
7
Impacts on optimal extraction rates
when market conditions change

Number 2


Number 3


When a renewable substitute is added
When marginal extraction costs are an increasing
function of quantity extracted
Number 4

Option for efficiency and sustainability
Number 2
P = 8 – 0.4 q
$6.00 = 8 – 0.4q
P0 = 8 – 0.4(8.798) = 4.48
0.4q = 2
P1 = 8 – 0.4(8.177) = 4.73
q=5
Etc.

What is the maximum
price you would expect
for the resource in
period 5? Why?
If q=5,
of depletable is 2.863
units
q of renewable is 2.137
units
Number 2 (continued)
P = MEC + MUC
MUC0 = 4.48 – 2.00 = 2.48
MUC increases at the
rate of discount (10%)
MUC1 = 4.73 – 2.00 = 2.73
…
2.48(1.1) = 2.73
MUC5 = 6 – 2.00 = 4.00
2.73(1.1) = 3.00
…
3.63(1.1) = 4.00
#2 - 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
2.48
2.73
3.00
3.30
time
3.63
4.00
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
4.00
Price
3.00
MEC
2.00
MUC
1.00
0.00
-1.00 0
1
2
3
time
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:



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?
Your Savings Account
$
Use money
now
$
$
OR
$
Save and
use more
money
later
Why would taxing away rents result in
faster rate of resource extraction?
Q mineral
$ mineral
Mine and
use income
now
Q mineral
Q mineral
Q mineral
$ mineral
$ mineral
$ mineral
OR
Save, mine
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. incident in Middle East



Oil prices rise
Price gouging? Or increase in MUC?
Once more certainty in availability is established,
MUC goes back down