Economics of energy corporations
Depletable resources
V. Hajko
2015
V. Hajko (FSS MU) Introduction to Economics 1 / 33
1 Depletable/Non-renewable resources
Definitions
Basic concepts associated with non-renewable fuel use
2 Peak oil debate
Definitions
Production limitations
V. Hajko (FSS MU) Introduction to Economics 2 / 33
Depletable/Non-renewable resources Definitions
Outline
1 Depletable/Non-renewable resources
Definitions
Basic concepts associated with non-renewable fuel use
2 Peak oil debate
Definitions
Production limitations
V. Hajko (FSS MU) Introduction to Economics 3 / 33
Depletable/Non-renewable resources Definitions
Depletable resources and scarcity
A term in Environmental economics / Natural resources economics in
general applicable to anything valuable (anything with a price recall
the basic terms)
Scarcity of resources vs. unlimited human needs (recall the
non-decreasing property of utility functions)
Strictly speaking, every resource is somehow limited (e.g. consider
"renewability" of sun?)
E.g. Dyson sphere: hypothetical megastructure encompassing a star
and capturing most or all of its power output
Often confused with conventional and unconventional energy sources
(though conventional energy sources are often non-renewable)
Conventional sources: typically being used since a long time, used
frequently
Non-conventional sources: not really widespread
V. Hajko (FSS MU) Introduction to Economics 4 / 33
Depletable/Non-renewable resources Definitions
Non-renewable and renewable resources, definitions
(Non-)Renewable resources: most often discussed in relation with
energy resources
Resources classified as “Depletable” (or Non-Renewable): the sum
over time of all possible production is finite, or the stock of the
resources is not replaceable in a reasonable timeframe
Fossil fuels (Crude oil, natural gas, coal) are typical examples
(optional classification: Recyclable non-renewable resources: can be
partially recovered from their prior use)
Non-depletable resources: their stock can replenish in time
Geothermal, water, wind, solar, biomass(?)
V. Hajko (FSS MU) Introduction to Economics 5 / 33
Depletable/Non-renewable resources Definitions
Energy vs. exergy
The First Law of Thermodynamics: energy can be neither created nor
destroyed; but energy can be converted between various forms (energy
is not scarce!)
The Second Law of Thermodynamics: It is impossible to extract all
heat from a hot reservoir and use it all to do work (a change of state is
associated with an increase in entropy - i.e. exergy is ‘consumed’ in conversion processes,
it is mostly lost in the form of low temperature heat)
no perpetuum mobile is possible.
There is a limit on the maximum efficiency of heat engines: η = useful energy output
energy input or Carnot’s efficiency:
ε =
TS −T0
TS
, where the TS is the temperature of energy source and T0 is the temperature of the sink (the
ambient temperature of the heat system).
Why do people care? Using energy for (thermodynamic) work
Work performed by a system is the energy transferred by the system to another
system → a generalization of the concept of mechanical work in physics
In summary: people do not care about the energy, but about exergy (energy that is
available to be used)
V. Hajko (FSS MU) Introduction to Economics 6 / 33
Depletable/Non-renewable resources Definitions
Exergy relation to fuels
The quality of energy type: how easily can it be converted to another
type (e.g. electricity: easily converted to mechanical work, heat etc.;
vs. heat: difficult to convert to electricity)
Higher quality is associated with more exergy
Energy ladder: Typical progression to increased use of higher quality
energy (often associated with higher costs and lower (or internalized)
externalities)
V. Hajko (FSS MU) Introduction to Economics 7 / 33
Depletable/Non-renewable resources Definitions
Table : Exergy quality indexes of
different forms of energy
Form of energy Quality index (Percentage of exergy)
Potential energy 100
Kinetic e. 100
Electrical e. 100
Chemical e. about 100
Nuclear e. 95
Sunlight 93
Hot steam 60
District heating 30
Waste heat 5
Heat radiation from Earth 0
Source: Wall (1977), adapted from
Davidsson (2011)
V. Hajko (FSS MU) Introduction to Economics 7 / 33
Figure : Energy ladder: End uses and fuels used by households at different income
levels
Source: World Energy Outlook (2002)
Depletable/Non-renewable resources Definitions
Sustainability
World Commission on Environment and Development (1987) states:
“Sustainable development is development that meets the needs of the
present without compromising the ability of future generations to
meet their own needs”.
Life Cycle Exergy Analysis can be used to describe direct and indirect
exergy use and generation during the source life cycle
Sustainability: matching exergy inputs and exergy outputs in the
long-run
a persistent supply of exergy (e.g. energy from the sun) offsets or compensates for
the “exergy” drawn from the finite pool of fuels
If exergy resources are consumed faster than they are renewed: not
sustainable "depletion of resources"
The use of fossil fuels is often considered not sustainable
Because the direct exergy input (e.g. wind) of renewable sources is disregarded - if
not used, natural exergy flows will be wasted and lost
On the other hand, the direct exergy input of fossil fuels is calculated (because it is
decreasing the fossil fuel stocks)
V. Hajko (FSS MU) Introduction to Economics 9 / 33
Depletable/Non-renewable resources Basic concepts associated with non-renewable fuel use
Outline
1 Depletable/Non-renewable resources
Definitions
Basic concepts associated with non-renewable fuel use
2 Peak oil debate
Definitions
Production limitations
V. Hajko (FSS MU) Introduction to Economics 10 / 33
Depletable/Non-renewable resources Basic concepts associated with non-renewable fuel use
Optimal allocation
In analogy with consumer’s optimization problem, the basic question
is: what is the optimal allocation of quantity for consumption, if we
gain utility from the consumption and we consume in more than one
time period?
"How much of the asset should we consume now and how much should
we store for the future?"
Hotelling (1931): one of the most influential theoretical studies of
optimal depletion rates and associated pricing rules
V. Hajko (FSS MU) Introduction to Economics 11 / 33
Depletable/Non-renewable resources Basic concepts associated with non-renewable fuel use
Hotelling’s pricing rule
Formally: max ∑T
t=0 βt
(ptqt − c (qt )),
subject to: Rt+1 − Rt = −qt, c, q, R ≥ 0, ∀t
βt = 1
1+r is the discount factor (with r being risk-adjusted interest
rate), p is price, q is production, c (q) are extraction costs, R is the
remaining supply of a resource
Non-renewable, exhaustible resource with completely known stock, no
discoveries possible, no alternatives, no recycling, private ownership
and constant costs of extraction:
the price of the resource will increase at the interest rate over time
(Hotelling’s ‘r-percent’ rule: pt+1 = pt (1 + r))
it can be shown the price at any given point in time, price must equal
total marginal cost of extraction (the opportunity cost plus the cost of
incremental production)
V. Hajko (FSS MU) Introduction to Economics 12 / 33
Depletable/Non-renewable resources Basic concepts associated with non-renewable fuel use
Hotelling’s pricing rule
Application of Hotelling’s rule in the late 1970s and early 1980s
contributed to (incorrect) predictions of increasing fuel (and non-fuel)
commodity prices
Side result of Hotelling’s pricing: the sustainability (welfare levels
non-decreasing over time) is only possible for one growth path: zero
consumption forever (for any other feasible path consumption and
therefore also utility must fall)
If extraction costs are increasing with time, the opportunity cost of
extraction is diminishing. Then the transition to a new source of
energy arises due to prohibitive costs rather than physically running
out.
V. Hajko (FSS MU) Introduction to Economics 13 / 33
Figure : Optimal price path of a depletable resource with constant extraction costs
Figure : Oil price development
0
20
40
60
80
100
120
140
70 80 90 00 10 20 30 40 50 60 70 80 90 00 10
r=3%
r=4%
r=2%
OIL_N
OIL_R
Depletable/Non-renewable resources Basic concepts associated with non-renewable fuel use
Historical links, "The dismal science of economics"
Thomas Malthus and the "Iron Law of Population" (An Essay on the
Principle of Population, 1796): continued population growth would
lead to poverty:
Conclusion: the population should be held within resource limits: by
positive checks (raising the death rate) and preventive checks (lowering
the birth rate)
William S. Jevons: The Coal Question (1865): coal essential to
production, supply limited: "rate of growth will before long render our
consumption of coal comparable with the total supply. In the increasing depth and
difficulty of coal mining we shall meet that vague, but inevitable boundary that will stop
our progress."
Coal mined in other areas + partial coal phase-out (by oil and gas)
The Club of Rome and The Limits to Growth (1972): simulation of exponential economic
and population growth with finite resource supplies
"Exponential index" of consumption: leading to a prediction of the number of years
until the world would "run out" of various resources
V. Hajko (FSS MU) Introduction to Economics 16 / 33
Depletable/Non-renewable resources Basic concepts associated with non-renewable fuel use
Historical links
Environmentalist Paul R. Ehrlich: The Population Bomb (1968):
inevitable ecological collapse due to overpopulation
"In the 1970s hundreds of millions of people will starve to death in
spite of any crash programs embarked upon now"
Governments must curb population growth to mitigate (otherwise
inevitable) ecological and social disasters.
Simon–Ehrlich wager: 1980, betting on a mutually agreed-upon price
measure of 5 commodities: Simon: prices would decrease,
Ehrlich: prices would increase (depletion + scarcity would lead to
higher price (shift of market supply to the left and demand to the right)
V. Hajko (FSS MU) Introduction to Economics 17 / 33
Figure : Exergy allocation in the past century
Source: Ayres et al. (2003)
Figure : Energy consumption by types, MTOE
0
4,000
8,000
12,000
16,000
1970 1980 1990 2000 2010
Total World
0
1,000
2,000
3,000
4,000
5,000
6,000
1970 1980 1990 2000 2010
OECD
0
2,000
4,000
6,000
8,000
1970 1980 1990 2000 2010
NON-OECD
0
400
800
1,200
1,600
2,000
1970 1980 1990 2000 2010
EU
0
250
500
750
1,000
1,250
1,500
1970 1980 1990 2000 2010
RES_TOTAL
NUCLEAR
COAL
GAS
OIL
Former Soviet Union
Peak oil debate Definitions
Outline
1 Depletable/Non-renewable resources
Definitions
Basic concepts associated with non-renewable fuel use
2 Peak oil debate
Definitions
Production limitations
V. Hajko (FSS MU) Introduction to Economics 20 / 33
Peak oil debate Definitions
Reserves vs. resources
Oil resources:
Contingent resources: quantity of petroleum to be potentially
recoverable from known accumulations (but not interesting enough for
commercial development - e.g. technical, economical, political or social
events
Prospective resources: quantity estimated to be potentially recoverable
from undiscovered accumulations in future development
Oil reserves: quantity of technically and economically recoverable
petroleum
Proven reserves (P90): recoverable under existing technology and
economic and political conditions; recovarable with at least 90%
confidence
Unproven reserves: estimates (typically) based on geological data
Probable reserves (P50): usually in known accumulations 50%
probability of recovery
Possible reserves (P10): at least a 10% probability of recovery
V. Hajko (FSS MU) Introduction to Economics 21 / 33
Figure : Reserves vs. resources
Source: EIA
Figure : OPEC proven (?) reserves, 1986 jump (after introducin quota system
allocation)
Peak oil debate Definitions
What is Peak oil?
Describes a point in time when the rate of crude oil extraction is at
its maximum (following the peak oil is a continuous decline in the
extraction rates)
Not the same as oil depletion (decreasing reserves, as in Hotelling’s
rule)
Rising prices = running out of crude oil
Rising prices if demand is increasing faster than supply
It is difficult to assess the rates of both future demand and even more
difficult to assess future extraction
Note that in reality, Reserves-to-production ratio (R/P ratio, or inverse
of depletion rate, in other words years the reserves will last at given
rate of extraction) is changing in time as the production continues (for
individual wells) - the reserves are always estimated (not known with
certainity)
Nevertheless, given the estimation technique, the timing of Peak Oil
does not change radically (within span of decades) with different
V. Hajko (FSS MU) Introduction to Economics 24 / 33
Peak oil debate Production limitations
Outline
1 Depletable/Non-renewable resources
Definitions
Basic concepts associated with non-renewable fuel use
2 Peak oil debate
Definitions
Production limitations
V. Hajko (FSS MU) Introduction to Economics 25 / 33
Peak oil debate Production limitations
Hubbert peak theory
In 1956 M. King Hubbert (geologist at Shell Oil Company) formulated
a prediction: US oil peak production will peak roughly around 1970.
The world’s oil peak expected to happen in 1995
Qt =
¯Q
1 + aebt
NOT an economic theory, but physical description of the production
life (note what variables are entering the calculations)
To calculate the peak, collect annual production (P) and cumulative
production (Q)
Fit linear regression (i.e. P
Q = a + b.Q), and compute Q∗, such that
P
Q = 0), Q∗ thus indicates maximum cumulative production that will
ever be achieved
Essentially Hubbert curve (showing P over time) is a derivative of
logistic oil accumulation function
Assumes the rate of change of annual oil production is known,the
equation of the oil production curve is the derivative of the logistic
equationV. Hajko (FSS MU) Introduction to Economics 26 / 33
Peak oil debate Production limitations
Hubbert peak theory - calculation
To determine the curve, collect annual production (P) and cumulative
production (Q) and fit linear regression (i.e. P
Q = a + b.Q), then
compute Q∗, such that P
Q = 0)
Q∗ thus indicates maximum cumulative production that will ever be
achieved
If we rewrite the linear relationship asP = a.Q + b.Q2, and if
P = 0→Q = QT , then b.Q2
T = −aQT or b.QT = −a, thus
QT = −a
b or b = − a
QT
we can substitute to original equation: P = a.Q − a
QT
.Q2 →
P = aQ 1 − Q
QT
term 1 − Q
QT
represents the fraction of oil that is remaining to be
produced
V. Hajko (FSS MU) Introduction to Economics 27 / 33
Peak oil debate Production limitations
Hubbert peak theory, empirical evidence
The empirical results are controversial
historically, the oil was supposed to already reach the peak several times
not all peak theory studies follow the simple curve fitting method
originally suggested by Hubbert
Estimates of depletion (point of falling reserves): even more difficult
there is no way for precise measurement (especially for unconventional
oil reserves)
In 2004, Shell had to adjust its balance sheet by 20% (which could not
be classified as proven reserves at the time)
In 2012, SandRidge Energy Inc. adjusted reserve forecasts from from
456 000 barrels per well to 422 000 barrels per well; In 5 months, it
readjusted to 369 000 barrels
volumes typically announced by producer / owner of the oil field - an
incentive to overestimate (e.g. to draw additional investors and/or
"satisfy" the stakeholders) - see the OPEC reserves jump
V. Hajko (FSS MU) Introduction to Economics 28 / 33
Figure : Oil peak estimates
Source: Caruso (2005)
Figure : World ultimate recovery estimates
Published Estimates of World Ultimate Recovery
0 0.5 1 1.5 2 2.5 3 3.5 4
Trillions of Barrels
USGS 5% 2000
USGS Mean 2000
USGS 95% 2000
Campbell 1995
Masters 1994
Campbell 1992
Bookout 1989
Masters 1987
Martin 1984
Nehring 1982
Halbouty 1981
Meyerhoff 1979
Nehring 1978
Nelson 1977
Folinsbee 1976
Adams & Kirby 1975
Linden 1973
Moody 1972
Moody 1970
Shell 1968
Weeks 1959
MacNaughton 1953
Weeks 1948
Pratt 1942
Source: Caruso (2005)
Figure : Peak estimate, EIA, source: Caruso (2005)
0
20
40
60
80
100
120
1900 1925 1950 1975 2000 2025 2050 2075 2100 2125
BillionBarrelsperYear
History
Mean
Low (95 %)
High (5 %)
Peak Range 37 yrs
2031 2068
USGS Based Estimates of Ultimate Recovery
Ultimate Recovery
Probability BBls
-------------------- ---------
Low (95 %) 2,793
Mean (expected value) 3,338
High (5 %) 3,947
Conventional Oil Resources, All Nine Scenarios
(>10o API and <10000 cP Viscosity)
Peak Year of
Mean Estimate
2044
1 Percent Growth per Year
2 Percent Growth per Year
3 Percent Growth per Year
Source: Caruso (2005)
Figure : Oil production
0
40,000
80,000
120,000
160,000
200,000
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
PRODUCTION_EU
production_Former Soviet Union
production_NON-OECD
production_NON-OPEC
PRODUCTION_OECD
PRODUCTION_OPEC
Thousand barrels daily
Figure : Oil proved reserves
0
500
1,000
1,500
2,000
2,500
3,000
3,500
1980 1985 1990 1995 2000 2005 2010
RESERVES_EU
reserves_Former Soviet Union
reserves_NON-OECD
reserves_NON-OPEC
RESERVES_OECD
Billion barrels