ERE6: NonRenewable Resources

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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

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Last week

• A simple optimal depletion model
• Resource substitutability
• Static and dynamic efficiency
• Hotellings rule
• Optimality
• Extraction costs
• Renewable resources
• Complications

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Potential, Resource and Reserves
gas
coal
oil
In Mrd. toe
Source RWE Weltenergiereport 2004
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Resources and Reserves
Increasing degree of economic feasibility
McKelvey classification
Increasing degree of geological assurance
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Potential for oil
Source Bundesamt für Geowissenschaften und
Rohstoffe (BGR)
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Oil production
Source BGR
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Availability
Source BGR
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Mineral Reserves
Million metric tons
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Social optimum Two-periods
Demand function
Net social benefits
Welfare function
Constraint
Langrange
Necessary conditions
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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
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Net price Pt
Graphicalsolution
PT K
Demand
P0
Pt
T
45
R0
R
Time t
Rt
Area total resource stock
T
Time t
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Perfect Competition
Perfect competition
Identical firms
Firms objective function
Equations of motion
Hamiltonian
Necessary conditions
Intertemporal efficiency
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Increase in demand
Net price Pt
K
P0/
D/
P0
D
T
R0
T/
R
R0/
Time t
T/
T
45
Time t
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Increase in interest rate
P
C
A
B
K
P0
Time
T
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Net price Pt
Increase in interest rate (2)
K
Demand
P0
P0/
T
R0
T/
R
R0/
Time t
T/
T
45
Time t
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Net price Pt
Increase in stock size
K
Demand
P0
P0/
T
R0
T/
R
R0/
Time t
T
T/
45
Time t
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Frequent new discoveries
Pt
Net price path with no change in stocks
Net price path with frequent new discoveries
t
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Backstop technology becomes cheaper
Net price Pt
K
Backstop price fall
PB
P0
P0/
D
R
T
R0
T/
R
R0/
Time t
T/
?
T
45
Time t
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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

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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
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Extraction costs (2)
Resource price
Original gross price
K
Original net price
New gross price
New net price
T/
T
Time
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Gross price Pt
A rise in extraction costs
Original gross price path
K
New gross price path
P0/
P0
T
R0
T/
R
R0/
Time t
T
T/
45
Time t
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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

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Monopoly
Firms objective function
Equations of motion
Hamiltonian
Necessary conditions
Marginal profit function
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Monopoly and perfect competition
Net price Pt
Perfect competition
PT PTM K
Demand
Monopoly
P0M
P0
TM
T
R0M
R
R0
Time t
T
Area
TM
45
Time t
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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

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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

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How Real is Hotelling?

• Hotellings 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