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Hotelling v. Hubbert:
How (if at all) can economics and peak oil be reconciled?
Economics 331b
1
Hubbert concerns the QHotelling concerns the P
Can they be married into a happy P-Q couple?
2
Hubbert theory
The Hubbert peak-oil theory posits that for any given geographical area, from an individual oil-producing region to the planet as a whole, the rate of petroleum production tends to follow a bell-shaped (normal) curve.
There is no explicit economics in this approach.
3
Hubbert curve for US
0
400
800
1,200
1,600
2,000
2,400
2,800
3,200
3,600
00 10 20 30 40 50 60 70 80 90 00 10
US crude oil productionHubbert curve
(peak 1976; total = 222; cum to date = 197)
Pro
duct
ion (ba
rrel
s/ye
ar)
Data source: Oil production for EIA. Hubbert curve fit by Nordhaus.4
Hotelling theory
• Let rt = net price of oil in ground = pt – et
= price of oilt – extraction costt
• Oil is developed and produced to meet the arbitrage condition for assets:
rt* = market rate of return on assets = ri,j,t = return on oil in the ground for grade i, location j, time t.
• Note that arbitrage condition holds only when production is positive (price-quantity duality condition)
5
Data source: Oil price data from EIA and BLS. Price deflation by CPI from BLS.
200
100
80
6050
40
30
20
1050 55 60 65 70 75 80 85 90 95 00 05 10
Real crude oil prices (2010 $ per barrel)
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200
100
80
6050
40
30
20
101975 1980 1985 1990 1995 2000 2005 2010
Hotelling line Real oil price
Hotelling growth at r = 3% per year
Real oil price
7
Arranged marriage of Hotelling and Hubbert
Let’s construct a little Hotelling-style oil model and see whether the properties look Hubbertian.
Technological assumptions:– Four regions: US, other non-OPEC, OPEC Middle East, and
other OPEC– Ultimate oil resources (OIP) in place shown on next page.– Recoverable resources are OIP x RF – Cumulative
extraction– Constant marginal production costs for each region– Fields have exponential decline rate of 10 % per year
Economic assumptions– Oil is produced under perfect competition costs are
minimized to meet demand– Oil demand is perfectly price-inelastic– There is a backstop technology at $100 per barrel
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How to calculate equilibrium
1. We can do it by bruit force by constructing many supply and demand curves. Not fun.
2. Modern approach is to use the “correspondence principle.” This holds that any competitive equilibrium can be found as a maximization of a particular system.
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Outcome of efficientcompetitive market(however complex
but finite time)
Maximization of weighted utility function:
Economic Theory Behind Modeling
1
and subject to resource and other constraints.
for utility functions U; individuals i=1,...,n;
locations k, uncertain states of world s,
time periods t; welfare weights
ni i i
k,s,ti
i;
W [U (c )]=
1. Basic theorem of “markets as maximization” (Samuelson, Negishi)
2. This allows us (in principle) to calculate the outcome of a marketsystem by a constrained non-linear maximization.
Specific Tools for Finding Solution
1. Some kind of Newton’s method.- Start with system z = g(x). Use trial values until
converges (if you are lucky and live long enough).
2. EXCEL “Solver,” which is convenient but has relatively low power.- I will use this for the Hotelling model.
3. GAMS software. Has own language, proprietary software, but very powerful- This is used in many economic integrated
assessment models of climate change.
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Department of Energy, Energy Information Agency, Report #:DOE/EIA-0484(2008)
Estimates of Petroleum in Place
12
Petroleum supply data
Sources: Resource data and extraction from EIA and BP; costs from WN
Source USOther non-
OPECOther OPEC
OPEC Middle
EastInitial volume (billion barrels) 1,100 3,300 2,900 2,900 Recovery factor 60% 50% 50% 50%Recoverable (billion barrels) 660 1,650 1,450 1,450 Cumulative producion (billion barrels) 206 434 207 324 Remaining volume 454 1,216 1,243 1,126 Marginal extraction cost ($ per barrel) 80 50 20 10 Decline rate (per year) 10% 10% 10% 10%
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Demand assumptions
Historical data from 1970 to 2008Then assumes that demand function for oil grows at
2 percent for year (3 percent output growth, income elasticity of 0.67).
Price elasticity of demand = 0Backstop price = $100 per barrel of oil equivalent.Conventional oil and backstop are perfect
substitutes.
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Solution technique
2200
, , , ,2010
2200
, , ,2010
, ,,
, ,
min [ ](1 )
subject to
, resource constraints, all regions and grades
, must meet demand for all time periods
= oil productio
ti j t i j t B t
t
i j t i jt
i j t t ti j
i j t
c x c B r
x R
x B D
x
, ,
,
n of grade i and j and time t
= cost per barrel oil production
= recoverable oil of grade i and j
= production of backstop technology
= demand for oil
i j t
i j
t
t
c
R
B
D
15
Picture of spreadsheet
16
0
20
40
60
80
100
120
2005 2015 2025 2035 2045 2055 2065 2075 2085
Price of oil
Supply price US
Supply price non OPEC
Supply price non-ME OPEC
Supply price OPEC Middle East
Results: Price trajectory
17
Results: Price trajectory and actual
0
20
40
60
80
100
120
1970 1980 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 2110
Pric
e of
oil
(200
8 pr
ices
)
Efficiency price of oil
Supply price US
Supply price non OPEC
Supply price non-ME OPEC
Supply price OPEC Middle East
History
18
Results: Output trajectory
0
50
100
150
200
250
300
350
400
450
500
1970 1980 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
Oil
Prod
ucti
on (b
illio
n ba
rrel
s per
5 y
ears
) Conventional oil
Oil and backstop
History
How differs from Hubbert theory: 1. Much later peak 2. Not a bell curve; slower rise and steeper decline 19
-15.0%
-10.0%
-5.0%
0.0%
5.0%
10.0%
15.0%
20.0%
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
2055
2060
2065
2070
2075
2080
2085
2090
Rate of increase in real oil prices
History
Efficiency
20
Further questions
Why are actual prices above model calculations?Why is there so much short-run volatility of oil
prices?Since backstop does not now exist, will market
forces induce efficient R&D on backstop technology?
21