1. Dynamic Efficiency and Mineral Resources
Monday, Feb. 28

2. 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

3. 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

4. Natural Resource Rent Rent Wages, etc.
In our previous example (two-period, social planner model), rent was viewed as all returns going to society.
Period t0 $
Rent MB
3.905
Wages, etc. MC
Quantity
10.238

5. 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

6. 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 $
Rent (producer surplus) MB
3.905 MC
Wages, etc.
Quantity
10.238

7. 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.

8. Marginal rent to resource owner is equal to marginal user cost to society
MUC = 1.905
Marginal rent = 1.905
Period t0 $
Total rent = 1.905*10.238 MB
= 59.41
3.905 MC
Quantity
10.238

9. 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?

10. In an unlimited time frame: MNB0 = PBMNB1 =…= PVMNBt MB = 8 - .4q
In a two-period world:
MNB0 = PBMNB1
MB = q
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 = q
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.