Dynamic Efficiency and
Mineral Resources
Monday, Feb. 27
Mineral extraction decisions



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.
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
MEC + MUC = P
0
0
5
10
15
20
Quantity
10.238
Exercise – how a market allocation of a
depletable resource responds to various
factors




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.