Transcript Document 7536472

Dynamic Efficiency and
Mineral Resources
Monday, Feb. 28
Property rights in minerals


Mineral rights generally go with surface
rights.
Mineral rights may be severed from surface
rights



e.g. surface rights are sold but mineral rights
retained.
e.g. mineral rights are sold but surface rights
retained.
Mineral rights include rights of access but also
the responsibility to provide sufficient surface
support
Mineral extraction decisions


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Private property rights
Owner will extract that amount of
resource that maximizes her net returns
over time.
Rent – accrues to owner of resource
because of scarcity
Natural Resource Rent
In our previous example (two-period, social planner
model), rent was viewed as all returns going to
society.
$
Period t0
9
8
Rent
7
6
MB
5
Wages, etc.
3.905
4
MC
3
2
1
0
0
5
10
15
20
Quantity
10.238
Formal definition of rent:

Returns to a resource in excess of what
is required to bring the resource into
production.



e.g. any earning above extraction cost for
minerals
In formal sense, must have a market
and a PRICE to have rent.
P = MEC+MUC
Natural resource rent to resource owner
When a resource is privately owned, the owner earns
rent. The remaining surplus accrues to consumers.
Consumer
surplus
$
Period t0
9
8
7
Rent (producer
surplus)
3.905
6
MB
5
4
MC
3
Wages, etc.
2
1
0
0
5
10
15
20
Quantity
10.238
Dynamic efficiency and
mineral extraction

In a well-functioning market, a mineral
owner’s incentives lead to a rate of extraction
that satisfies:



MNB0 = PVMNB1 = … = PVMNBt
This maximizes the present value of rents to
the owner of the resource.
Rents to owner reflect user costs to society

If owner doesn’t make decision based on earning
rent, then opportunity costs of current use are
ignored.
Marginal rent to resource owner is equal
to marginal user cost to society
MUC = 1.905
Marginal rent = 1.905 $
Period t0
9
8
7
Total rent = 1.905*10.238
= 59.41
6
MB
5
3.905
4
MC
3
2
1
0
0
5
10
15
20
Quantity
10.238
Exercise – how a market allocation of a
depletable resource responds to various
factors

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Illustrate dynamically efficient extraction rate
and marginal user costs
How does the availability of a renewable
substitute affect extraction rate? (A more
sustainable solution?)
How do increasing marginal extraction costs
affect extraction rate?
Can investment of rents also address
sustainability?
In a two-period world:
 MNB0 = PBMNB1
 MB = 8 - .4q
 MEC = $2, r=.1
 Total Q = 20 = q0+ q1

Solve for qs

2 equations, 2 unknowns
In an unlimited time
frame:
 MNB0 = PBMNB1 =…=
PVMNBt
 MB = 8 - .4q
 MEC = $2, r=.1
 Total Q = 20 = q0+
q1+…+ qt

Solve for qs

t equations, t unknowns
Computer algorithms use
iterative process to solve for qs.