1. ERE6: Non-Renewable Resources
Resources and Reserves
Social optimum and a model for a perfectly competitive market
Sensitivity analysis
Increase in interest rate and resource stock
Change in demand and extraction costs
Market failure
Monopoly
Taxes and subsidies
Reality

2. Last week A simple optimal depletion model Extraction costs
Resource substitutability
Static and dynamic efficiency
Hotelling‘s rule
Optimality
Extraction costs
Renewable resources
Complications

3. Potential, Resources and Reserves
Gesamtpotential (Mrd. toe)
5.537
687
1.507
3.343 Öl
Gas
Kohle
Bis Ende 2000 gefördert
Verbleibendes Potenzial
125
552
316
236 57
1.450
287
1.163
100
3.243
Reserven
Ressourcen
219
152/66
334
84/250
123
122/1
1.327
165/1.162
469
2.774
Source: RWE Weltenergiereport 2004

4. Resources and Reserves
Increasing degree of economic feasibility
McKelvey classification
Increasing degree of geological assurance

5. Potential for oil
Source: Bundesamt für Geowissenschaften und Rohstoffe (BGR)

6. Oil production
Source: BGR

7. Availability
Source: BGR

8. Mineral Reserves Mineral Prod. Cons. Econ. Res. Exp. Res. Tech. Res.
Life
Aluminium
112 19
23000
28000
222
Iron
930
960
150000
230000
161
Manganese 25 22
800
5000
42000 32
Chromium 13
419
1950
3260
Zinc
7.1
7.0
140
330
3400 20
Nickel
.92
.88 47
111
2590 51
Copper
9.3
10.2
310
590
2120 33
Lead
3.4
5.3 63
130
550 18
Tin
.18
.22 8 10 68 45
Tungsten
.041
.044
3.5 ? 80
Mercury
.003
.005
0.13
0.24 43
Million metric tons

9. Social optimum: Two-periods
Demand function:
Net social benefits:
Welfare function:
Constraint:
Langrange:
Necessary conditions:

10. Social Optimum: Multi-periods
Social welfare function:
Equations of motion:
Hamiltonian:
Necessary conditions:
Demand function:
Demand goes to zero if price exceeds the choke price (K):
Optimality has that the stock is zero too:

11. Graphical solution Net price Pt PT =K P0 Pt 45° T R R0 Time t Rt
Demand P0 Pt
45° T R R0
Time t Rt
Area =
= total resource stock T
Time t

12. Perfect Competition Perfect competition: Identical firms:
Firms objective function:
Equations of motion:
Hamiltonian:
Necessary conditions:
Intertemporal efficiency:

13. Increase in demand Net price Pt K P0/ P0 R R0/ R0 T/ T Time t T/ T 45°

14. Increase in interest rateP A C B K P0
Time T

15. Increase in interest rate (2)
Net price Pt
Increase in interest rate (2) K
Demand P0
P0/ R
R0/ R0 T/ T
Time t T/ T
45°
Time t

16. Increase in stock size Net price Pt K P0 P0/ R R0/ R0 T T/ Time t T T/
Demand P0
P0/ R
R0/ R0 T T/
Time t T T/
45°
Time t

17. Frequent new discoveriesPt
Net price path with no change in stocks
Net price path with frequent new discoveries t

18. Backstop technology becomes cheaper
Net price Pt K
Backstop
price fall PB P0
P0/ D R* R
R0/ R0 T/ T
Time t T/  T
45°
Time t

19. Results of the sensitivity analysis so far
Higher demand: Higher initial price, higher initial extraction; price increase unaffected, so choke price reached earlier
Higher interest rate: Initial price will be lower, but price increase faster, and choke price reached earlier; overall higher extraction
Greater resource stock: Initial price goes down, initial extraction goes up; growth unaffected; exhaustion postponed
Lower choke price: Final price lower, but price increase unaffected, so initial price must be lower; overall higher extraction

20. Extraction costs Gross price: Hoteling rule required: Resource price
Original gross price
New gross price
Original net price
New net price cL cH
Time T

21. Extraction costs (2) K T T/ Resource price Original gross price
Original net price
New gross price
New net price T T/
Time

22. A rise in extraction costs
Gross price Pt
Original gross price path K
New gross
price path
P0/ P0 R R0
R0/ T T/
Time t T T/
45°
Time t

23. Sum up: Extraction costs
Gross price increases slower
Final gross price is choke price
If the new gross price starts lower, it never picks up with the old; resource extraction must be greater during the entire period; this cannot be optimal
Therefore, new gross price starts higher, extraction is lower, and exhaustion is reached later

24. Monopoly Firms objective function: Equations of motion: Hamiltonian:
Necessary conditions:
Marginal profit function:

26. Monopoly and perfect competition
Net price Pt
Monopoly and perfect competition
Perfect competition
PT = PTM = K
Demand
P0M
Monopoly P0 R R0
R0M T TM
Time t T
Area = TM
45°
Time t

27. Royalty and Revenue Taxes
A royalty tax does not change extraction
A royalty tax does redistribute revenue from firms to the government
Subsidies are negative taxes
A revenue tax is equivalent to increasing the extraction cost, that is, higher initial gross price, slower growth, exhaustion postponed

28. Further issues Private and social extraction costs might differ
Private and social discount rates might differ
Absence of forward markets and expectations
Differences in risk perception
Uncertainty

29. How Real is Hotelling?
Hotelling‘s rule has been derived for very simple economies
So, either the analysis has to be made more complicated, or the data have to be manipulated before we can subject Hotelling to an empirical test
Studies that have done either or both are inconclusive; some say, Hotelling is real, others say not so
It may be that markets assume that resource stocks are infinite, until they are almost depleted