Energy Economics and Policy
Spring 2012
Instructors: Chu Xiaodong , Zhang Wen
Email：[email protected],
[email protected]
Office Tel.: 81696127
Energy Supply
• Economics of energy supply study the manner in
which energy resources are allocated through time
and space
• Energy resources can be classified as either
depletable or non-depletable
– Depletable: The stock of the resources is not replaceable
over a limiting time horizon, e.g., fossil fuels
– Non-depletable: The stock of the resources can be
replenished within a reasonable timeframe
• The emphasis is on the allocation of depletable
energy resources
Characteristics of Depletable Resources
• Stock declines over time
– Costly process of discovery
– Costly process of extraction
– Technical change decreases costs of exploration and
extraction over time
• Key results
– Physical Stocks Decline over time
– Price eventually increases with time
– Technical change may cause prices to decrease initially
Example 3.1: Decision to Sell Oil
• Because of limited supply, depletable resources
command a scarcity value
• If you own a barrel of oil which can sell today for 30,
should you sell today, or wait for next year?
(assuming rate of interest r = 0.05)
Example 3.1: Decision to Sell Oil
•
What is a reasonable decision?
–
–
–
If p1 > 31.5, wait
If p1 < 31.5, sell today
In equilibrium: p1 = p0(1+r)
Model of Extraction of a Depletable
Resource
• Starting from the framework by Hotelling, the
models aim to maximize the present value of profits
from extraction of a depletable resource
• The basic model: A perfectly competitive market
T
max   t  pt qt  c(qt ) 
q
t 0
s.t. Rt 1  Rt  qt , c, q, R  0, t
–
–
–
–
–
qt: quantity supplied
pt: price
c(qt): cost of supplying
Rt: resource remaining at the beginning of each period
βt: rate at which future profits are discounted
Model of Extraction of a Depletable
Resource
• With the basic model, assume there is a finite stock
of resource at the beginning, Q , and the time period
in account is T, then
RT 1  0
and
T
Q   qt  0
t 0
i.e., the constraint can be replaced by the above
equation, so
max    p q  c (q ) 
T
t
q
t t
t 0
T
t
s.t. Q   qt  0, c, q  0, t
t 0
Model of Extraction of a Depletable
Resource
• Using the Lagrange multiplier method, the former
problem can be solved as
T


max V    t  pt qt  c(qt )    Q   qt 
q ,
t 0
t 0


T
where λ is the Lagrange multiplier
• The first-order condition for a maximum is given as
V
  t  pt  cq ,t     0
q
which is true for all time periods
Model of Extraction of a Depletable
Resource
• The term λ can be interpreted as the shadow price
of the resource, i.e., the incremental value to the
resource owner of adding an additional unit of
resource
• From the first-order condition of the maxima that
 0  p0  cq ,0   ...   t  pt  cq ,t    t 1  pt 1  cq ,t 1   ...
one can deduce that
p
t 1
 cq ,t 1   1  r   pt  cq ,t 
– Extraction will occur so that the present value of the
marginal profit is the same in all periods
*Writing Skill
• The paragraph of “The intuition behind the result is
rather elegant…” below equation (3.3) on page 53 of
[Evans & Hunt, 2009]) is a good example of
interpreting the logic of a mathematic expression
Model of Extraction of a Depletable
Resource
• From the first-order condition, the price can be
expressed as
t
pt  1  r    cq ,t
– The first term on the right-hand side is the marginal user
cost (MUC), which reflects the opportunity cost of
extraction
– The second term is the marginal extraction cost (MEC),
which is the cost of incremental production
Model of Extraction of a Depletable
Resource
The optimal price path of a depletable resource with constant MEC
Model of Extraction of a Depletable
Resource
• Backstop technology
– A perfect substitute for depletable resource that can be
produced in any amount at constant (usually high) price
– When price of the depletable resource is equal to price of
backstop, we should switch to the backstop
Model of Extraction of a Depletable
Resource
Price
Price path with
backstop
Time
Model of Extraction of a Depletable
Resource
• The resource is no longer used when its price
reaches that of the backstop
– A new resource will be extracted instead of the older one
since it is much more economical
– Backstop establishes the long-run price at which demand
for the depletable resource goes to zero
– If the backstop price is lowered, then the price in all
periods falls
• The nature of MEC is vital in characterizing resource
depletion
– The MUC falls if MEC is rising through time
Model of Extraction of a Depletable
Resource
Price path with
high backstop price
Price path with
low backstop price
Time
Monopoly of Energy Supply
• In a market characterized by imperfect competition,
the resource owner’s extraction decision influence
price, e.g., the production decisions of OPEC
influence the global crude oil price
• The resource owner will raise price in the current
period by constraining the level of production
provided that demand elasticity is not constant
– If demand elasticity is constant, the optimal price and
extraction paths are the same with the competitive case
Monopoly of Energy Supply
Price
Quantity
Time
Monopoly
Time
Generalization of the Basic Model
US domestic first purchase crude oil price and that from the basic model
Generalization of the Basic Model
• In many cases, the basic model fails to adequately
explain reality since many assumptions for the model
is not realistic
–
–
–
–
Extraction costs are function only of current extraction
The total initial quantity of resource is known
There is no uncertainty
Extraction, marketing, and exploration investment occur in
an incremental manner
Generalization of the Basic Model
• Extraction costs
– Factors such as reserve dependency and technological
change should be included
• Costs increase as the resource is depleted
• Costs reduce as the technological innovation is applied
Generalization of the Basic Model
• Exploration
– Reserves can be expanded through exploration of new
resources
• Extraction costs fall with reserves expanded
• Exploration itself becomes increasingly costly as depletion occurs
Generalization of the Basic Model
• Uncertainty
– Considering various sources of uncertainty (e.g., future
demand, price, the cost of exploration, the backstop price,
and technological innovations), the resource owner’s
decision must be based on expected conditions, and the
problem becomes one of investment under uncertainty
Generalization of the Basic Model
• Capital investment
– The production and exploration process is very capital
intensive, and the capital investments generally occur in
large discrete lumps
• The investments are typically not reversible, which results in a
short-run supply curve relatively inelastic
• Short-run supply is constrained by current productive capacity,
and short-run current productive capacity is constrained by the
level of investment
Generalization of the Basic Model
Optimal price paths under different model assumptions
Firm Behavior
• What does a firm actually do when determining
whether or not to explore, develop and market a
depletable resource deposit?
– The exploration and development phase is typically the
most capital-intensive phase of a project
• The firm has multiple such investment opportunities at any given
time
• The firm must decide how to allocate a limited amount of capital
to a suite of potential projects to which it has access
Peak in Production
• Rising prices do not necessarily mean that the world
is running out of crude oil, which may be caused by
that demand is currently accelerating faster than
supply
• The Hubbert curve is widely used in the analysis of
peaking production of petroleum and other fuels on
a nation scale or on a global scale
Peak in Production
The Hubbert curve and peak oil
Peak in Production
• The Hubbert curve is a physical description of the
production life of a depletable resource
Qt 
Q
1  aebt
– Q : recoverable resource
– Qt: cumulative production to date
– a, b: fitted parameters
Peak in Production
• The implication of the Hubbert curve is that once
half of the resource is consumed, a peak in
production will occur and decline will commence
– Diminishing production capacity and well productivity
– Constraints on equipment and personnel for exploration
and development, which comes about from having to drill
an increased number of wells to sustain a given level of
production
– Declining exploration success
Next Lecture
• The main topic will be Models of Competitive
Markets
• Chapters 8 and 9 of [McConnell, Brue & Flynn, 2012]
are within the scope