CursusProost

Energy Economics 2011-2012 – prof Stef Proost 1

Chapter 2 Economics of non renewable resources

1. Objectives and outline

Oil, gas and coal are considered as non renewable resources. There stock is limited and it

is increasingly costly to produce them. In this chapter we explain briefly what the theory

of non-renewable resources can offer as insights. The detailed application to the three

primary resources is left for later chapters.

This chapter also prepares for chapters 3 and 4 where we discuss the climate change

problem, environmental externalities and sustainability in the presence of exhaustible

energy resources and long term environmental problems.

The key questions we want to address in this chapter are:

1. What makes a given resource exhaustible?

2. How to use optimally exhaustible resources? : save them for later or use them now?

3. How is the switch between exhaustible and non-exhaustible resources operated?

4. Would profit maximizing resource owners take the right decisions?

5. How would new information about the resource stock or future demand affect price

levels and production profile over time?

6. This is to a large extend knowledge derived from theoretical propositions, has this

theory been verified for particular resources?

Section 2 classifies resources into exhaustible and non exhaustible resources. Section 3

gives some data on energy reserves. Sections 4, 5 and 6 analyze the optimal allocation of

exhaustible resources over time. Section 7 studies how markets allocate resources over

time. Section 8 concludes with a brief review of empirical tests of the theory.


2. Classifying resources The exhaustibility of a resource can be determined using the simple decision criteria of

Table 2.1

Natural Replenishment?

No

(= non-renewable resource)

Yes

(= renewable resource)

Recyclable? Depends on human activity?

Yes

(copper, gold)

No

(oil, gas, coal)

Yes

(water, biomass)

No

(sun, wind)

Table 2.1: Definition of non renewable resources

Within the category of non renewable resources, two dimensions matter for the

classification of resources: the cost of producing them (vertical axis in Table 2.2) and the

geological probability that they exist (horizontal axis in Table 2.2).

Table 2.2: Classification of resources into reserves1

1 Taken from Tietenberg T., “Environmental and resource economics”, Addison Wesley, 2000, 5the edition, page 127


The vertical “economic” dimension has two categories:,

economic: current price is larger than the marginal production cost,

subeconomic: current price is below the marginal production cost,

The horizontal “geological certainty” dimension has many subdivisions:

identified: geological location, quality, quantity is known and supported by

engineering measurements

measured: known from samples with margin of error of 20%,

indicated: known partly from samples and partly from geological

undiscovered: unspecified bodies of mineral bearing material surmised to exist

on the basis of broad geological knowledge and theory,

hypothetical: supposed to exist in a well specified mining district,

speculative: undiscovered resources that may exist in favorable geological

settings where no discoveries have been made

Often one encounters notions as “current reserves”: resources that are known and cost

effective to produce, resource endowment: estimation of the stock in the earth’s crust that

could be mined without considering the cost.

One also uses the static reserve index or R/P ratio = current reserves divided by current

consumption, which gives the number of years that the current consumption could be

sustained with the current reserves. But this only holds if the current consumption is

constant and the current reserves do not change.

3. Some data on energy resources

Estimates on the available resources of oil, gas and coal vary a lot. Some of the resources

are controlled by governments and they do not update regularly their resource data. Take

Saoudi-Arabia as example: the resource stock of oil is unchanged since 1989 although

they have been producing a lot (see BP statistical review). We give her first orders of

magnitude relying on mainly 2 sources: the BP statistical review and the IEA Energy


Outlook 2008. For oil and gas we will discuss the estimation of reserves more in detail

later.

Oil For oil the BP statistical review gives 1237.9 Billion barrels or Reserves/ production ratio

of 41.6 years. These are “proved reserves” defined as reserves that are known and can

with reasonable certainty be recovered profitably at current prices.

The recent IEA world energy outlook shows a graph that integrates the cost side and the

resource side :

:

Figure 2.1 Ultimately recoverable resources of oil (source: IEA 2008)

We see that the BP estimate of reserves is only a small subset of the ultimate recoverable

reserves and that the conversion of gas and coal to liquid fuels can be considered as a

backstop technology. A backstop technology is a technology that produces a substitute at

a more or less constant cost. We also notice that OPEC holds the cheap reserves.


Gas

According to the BP statistical review there are 177.36 Trillion m³ of gas or an R/P ratio

of 60.3 years. The current reserves of gas are more or less equivalent to those of oil 2but

because consumption is lower, the R/P ratio is larger.

Table 2.2 Proven reserves and ultimately recoverable reserves (source IEA, 2008)

Table 2 relates the 177 Trillion m³ proved reserves to the total resource base “ultimately

recoverable conventional resources” of 443.3 Trillion m³. As in the case of oil one

notices a large difference between proved reserves and the ultimate recoverable

resources. Table 2 does not contain the non-conventional gas (coalbed methane, tight gas

sands, gas shales) that could total 900 Tcm³, with 25% in Canada and US and 15% each

in China, India and Russia (IEA, 2008).

Coal For coal, the BP statistical review mentions 847 billion ton of coal current reserves and

an R/P ratio of 133 years. This quantity corresponds to 3.3 times the quantity of oil3. The

2 Using the BP statistical review of World Energy (approx conversion factor table), one can convert 1 billion of m³ of Natural gas into 6.29 million barrels of oil equivalent.


reserves data for coal have since long not been updated because most producing countries

had plenty of coal. So reserves are much larger than reported here (IEA, 2008).

4. Optimal Allocation of resources – basic concepts In order to compare alternative uses of a non renewable resource over time, we need a

clear definition of economic optimality. The simplest notion one can use is the sum of the

discounted economic surplus. There are many caveats in using this concept, we return to

this problem later. First we explain economic surplus in one period and the discounting

and summation over time.

Economic surplus We take a world view here and consider one period (say one year). A world view means

that we do not care who in the world has the resource, obviously a strong asumption to

which we return later. A resource can be used for many purposes, some uses are easily

substitutable, and others are not. Take gasoline for cars as example, I can use a car for 10

000 km/year but also for 20 000 km/ year, the 10 000 km/ year are uses that I could do

without. I can also invest in a more fuel efficient but more expensive car etc.

For a given state of technology, given income distribution and given prices of other

goods (say cars), one can rank the uses of a given resource from very valuable, difficult

to substitute and for which people would be prepared to pay a very high price to uses that

could be easily substituted. In Figure 3 the Willingness to Pay (WTP (Q) curve reports

for every unit of the resource, the highest willingness to pay. In a world where one is not

concerned about income distribution, this is also the best use of that resource. The users

of te resource can be consumers or firms. The other curve reported in Figure 3 is the

marginal production cost function (MC(Q)). This is the cost of producing (extracting) an

extra unit of the resource. The first quantity of the resource produced, if allocated to the

user with the highest WTP, has a “value” or “benefit” A because there is a user prepared

3 Using BP op;cit. one finds that 1 million of coal is equivalent to 1/1.5 million ton of oil equivalent and to 7.33/1.5 million barrels of oil.


to pay A. This user is prepared to pay A because it either gives him direct benefits

(heating the room, driving a km) or allows to avoid more expensive solutions for the

same purpose (taking the train, using electric home heating). This first quantity costs at

the economy only C, so the net benefit of this first unit is the difference A-C. Continuing

the reasoning for larger and larger quantities one maximizes the net benefit or “economic

surplus” by producing a quantity Q*. This quantity maximizes the economic surplus (area

ABC, the difference between the value to users and the production cost). Pushing the

production level further to a level Q** would reduce the economic surplus as the extra

quantity has uses with lower and lower value but costs more to produce.

How can one guarantee that this economic surplus is created by producing a quantity Q*

Two conditions need to be fulfilled. First the quantity produced has to go to those with

the highest WTP. This is guaranteed if one uses the price mechanism to distribute Q*: an

auction (selling the good to the highest bidders, where last unit is sold at price D) could

do the job. If the price mechanism is not used it is hard to generate the same economic

surplus. To see why imagine that the good is given to all users that show an interest. Then

all users that have a positive WTP are candidate, but the quantity available is only Q*,

this means some rationing and if goods are rationed at random, the average WTP of the

receivers of the good is more like E and total economic surplus equals only EFBC,

clearly lower than ABC.

Second, the good has to be produced by the producers with the lowest costs. If this is not

the case, economic surplus is clearly lower.

In a market economy with perfect competition (consumers and consumers take the prices

as given) the economic surplus would be maximized and the price level would be D. The

total economic surplus (here ABC) is then divided between consumers (“consumer

surplus” ADB) and producers (“producers surplus” DBC).


Willingness to Pay function (WTP (Q) ranking all potential uses

Marginal production costFunction MC(Q)

Q quantity

WTPPriceMarginalcost

Q* Q°°

A

B

C

Economic

surplus

DE

F

Figure 2.3 Economic surplus

We will use the notion of economic surplus many times in this course. It is useful

because it allows us to discuss economic efficiency at the level of one market without

having to consider the rest of the economy. This is only valid under rather strict

assumptions4. Important is first that there are no distortions (important taxes that create

wedge between price (or WTP of consumers) and the marginal cost. Second condition is

that we are indifferent about the distribution of income. Or equivalently, that there exist

perfect redistribution instruments that can be used once the economic surplus has been

realized.

Interest rate, discounted sum When one needs to decide on the allocation of a given resource stock over different years,

can we use the simple sum of the economic surpluses used in different years? In principle

no. In our analysis we will assume that there is any year always the opportunity to invest

money in the capital market and realize a certain return at interest rate r.

4 Mass Colell, Whinston, Green J., “Micro-economic theory”, Oxford Univ Press, p325-345


In most of the text that follows, we will always work with a real interest rate r, this is

equal to the nominal interest rate nr corrected by the expected inflation rate i, so

r nr / 1 i

We also assume that this is a risk free interest rate. In principle the capital market will

reward more risky investments with a higher return.

The existence of a capital market where a real return of r can be obtained per year has far

reaching implications for the allocation of resources over time. Whenever one can

generate an economic surplus of 1 Euro this year rather than next year, one will prefer to

realize it this year as it allows lending the Euro to the capital market and getting 1+ r

Euro next year. The latter option is clearly superior to realizing an economic surplus of 1

Euro next year.

The interest rate (and alternative investment and lending opportunities at fixed rate r)

allow us to define the discounted sum of economic surpluses in years 1,2,…,T ES(1),

…ES(T) as:

T

1

( )discounted sum =

(1 )t

ES t

r

Those interested in business economics will recognize the similarity with the discounted

cash flow method for selecting investment projects. The three main differences are that, a

firm makes an analysis using nominal values (depreciation is in nominal terms), a firm

will use its own (nominal) cost of capital and that economic surplus is replaced by net

cash flow of the project.

We have developed up to now criteria for optimal efficiency from a static point of view

(maximize economic surplus within one period) and from a dynamic point of view

(allocation of resources over time). We can now start to use these concepts to study the

allocation of non renewable resources over time, first in a 2 period model and then in an n

period model.


5. Optimal allocation of non renewable resources in a 2 period model

Introduction In this section we will use a simple model with a linear demand function and illustrate the

results with a numerical example5 that everybody can check. We start with an example

without scarcity and tackle then the case with a scarcity constraint.

Model assumptions We use the following definitions and assumptions:

p = f(q) , the WTP function and its inverse function q = f(p) that is called the demand

function, identical for all the periods we consider

q p or (WTP:) a b p q

p = price

MC = MEC = constant marginal extraction cost,

Q = fixed quantity of the non renewable resource,

r = real interest rate,

all decisions are made by a central authority that maximizes the discounted sum of

economic surpluses.

For the numerical illustrations, we use the following values:

p= 8 - 0.4 q

MEC = 2 $

r = 0.10

Q > 30

5 We borrow the simple model and numerical example from Tietenberg (2000)


No scarcity case Consider first the problem of allocating the resource when there is no scarcity. For our

numerical example, this means maximizing the discounted sum of the economic

surpluses realized in the two years: as there is no active resource constraint, it is sufficient

to push exploration and production up to the point where WTP=MC in each period. In

Figure 4 we see that this implies a consumption of 15 units in each period. The scarcity

constraint does not play any role as Q>30.

Figure 2.4: the 2 period model without scarcity constraint

With scarcity We now introduce the scarcity constraint. The objective function is to maximize the

discounted sum of economic surplus in each period: by choosing quantities of production

in each period q1 en q2 such that the total quantity of the resource used is lower than the

available quantity Q:

1 2

1 21 2

,0 0

1- -

1

q q

q qMax a bq dq cq a bq dq cq

r

1 2 1 2 0q q Q or Q q q

It is convenient to use Lagrange’s method6 for this optimization problem under

constraints.

6 In fact we use here rather the Kuhn-Tucker theorem for optimisation with inequality constraints


The Langrangian is defined as:

1 2

1 2

0 0

1- -

1

q q

L a bq dq cq a bq dq cq Q q qr

1 2

In which λ is the Lagrange multiplicator. A maximum of the Lagrangian L(q1, q2, λ)

with respect to the decision variables and the lagrange multiplicator will be a constrained

optimum (where the weak inequalities allow for non binding constraints) and satisfy the

following (necessary) first order conditions:

1 11 1

2 22 2

1 2

0 0

10 0

1

0 0

L La bq c q

q q

L La bq c q

q r

L LQ q q

0

0

0

q

If there is no scarcity constraint active, q1 and q2 can be chosen freely and the lagrange

multiplier is zero:

1 2 0q q Q and

And optimal price and quantities are given by:

* *1 2

a cp c q q

b

The interest rate plays no role in the solution. The best one can do is to choose the best

quantity in each period, there is no opportunity cost associated to the use of more

resources in one period.

When the scarcity constraint is active the solution equals:

* *1 2 2

a c r Qq q

b r r

2 1Q q

And we can solve for the Lagrange multiplicator:


1 11 1

1 1

0 0L L

a bq c qq q

a bq c p c

0

This is the normal procedure to look for an optimum. The Lagrange method is not the

most operational method to find an optimum but economists like to use it because it

allows interesting economic interpretations. It allows to structure the economic intuition.

The Lagrange multiplier can be shown to equal the shadow cost of relaxing the resource

constraint by one unit at the optimum (d L

d Q

): what is the extra economic value that

can be generated when there is one more unit of the resource available, given that one

uses all existing resources optimally.

In our 2 period problem, using the first order conditions, we have:

1 1

2 2 (1 )

p a bq c

p a bq c r

So, if there is a scarce resource, the optimal price in each period equals the marginal

production cost c plus the opportunity cost of using the resource this period: λ. In the first

period this is simply λ, but in the second period, the value generated by the last unit made

available (a-bq2-c) only counts for 1/(1+r) because of discounting. So the opportunity

cost of using one more unit of the resource in period 2 is actually higher: λ(1+r).

This opportunity cost is given different names in the literature. One uses “marginal user

cost”= opportunity cost. Hotelling proposed this rule in the 1930 ties and it became

known as Hotelling’s rule: when a scarce resource is optimally used, the margin (p-c) has

to increase over time at the rate of interest (1+r)t .

We return to our numerical example in the next figure. For an available quantity of 20

and a real discount rate of 10% we have that λ=1.905. We see that the price in the first

period equals 3.905= marginal cost of 2 + opportunity cost of using the resource in this

period (λ=1.905). In the second period, the price equals 4.095 = 2 + 1.905 (1+0.10).


Figure 2.5 Optimal allocation of a scarce resource over 2 periods(Q=20, r=10%)

If the available quantity is lower, one can look for the optimum solution by progressively

increasing λ until the total demand obtained by using Hotellings’ rule (letting margins

increase by interest rate) satisfies exactly the resource constraint. One will then notice

that prices in both periods increase.

6. Optimal allocation of a non-renewable resource over time – the N period case

We can generalize the problem in different directions and using different techniques. One

can choose between continuous optimal control techniques and discrete optimization

techniques. We will use discrete techniques and graphs as these are better to convey

intuition. Only in the last section will we use continuous techniques to discuss

comparative statics over time. Those who are more interested in a mathematical proof of

some of the results can consult the basic articles or an advanced book on natural

resources7.

Basic N-period model Generalising to N periods we have:

7 Pindyck has several interesting papers. Another source is Heal


11,..,

1 0

1

1

i

N

qN N

i iiq qi i

Max a bq dq cq q Qr

Forming the lagrangian:

1

1 0

1

1

iqN N

i iii

L a bq dq cq Q qr

i

One obtains the first order conditions:

1

2

10 0

1

0 0

i

ii i

N

ii

L La bq c q

q r

L LQ q

0

0

q

Solving this optimisation problem requires to check in what periods it is optimal to make

the resource available and once this is known, to know what quantities are optimal in

every period. We know that if periods i and i+1 are part of the optimal extraction period,

we have:

1 1i ip c r p c

If all periods i=1 to T are part of the optimal extraction period, we have:

1(1 ) for i=1,...,Tiip c r

If demand is constant over time and the extracting cost is constant, we have for the

optimal extraction period (i=1…T):

1. The use of the resource decreases continuously over time and stops at T; the intuition

for this result is that, given identical demand functions, starting with an identical

allocation of resources over time, one can gain by advancing slightly the use of the

resource because of the discount rate

2. The whole resource is used; not using the resource would be economically inefficient

because using the resource in one of the T periods would generate an economic surplus –

if one wants to keep some of the resources for later, it is important to include the potential

uses in the objective function


3. The price of the resource increases over time where the margin increases with the

interest rate (not the price but the margin!) – this is the Hotelling rule that also holds for

any path of demand functions (also for growing demand functions)

4. The price in the last period equals the choke price a (the maximum value of the

resource in a future year) ; if the price in T would be smaller than a, one could extract for

one more period and obtain a price higher than the previous period, and this would be

beneficial etc. until one reaches the choke price

Returning to the simple numerical example, using the same demand function (WTP in $

= 8-0.4q ), extraction cost = 2 $ , discount rate 10% and a total quantity of the resource=

40 units. One obtains that λ=2.798 and the optimal extraction period T=9 periods.

Graphically, prices and quantities have the following properties:

Figure 2.6 : Numerical example of the optimal price and quantity of a non renewable

scarce resource

On the left hand panel one sees the decline of the extraction and use, on the right hand

pane, we see the margin between price and marginal cost increasing with the interest rate.

Basic N period model with backstop


A variant that has received a lot of interest is to add a “backstop technology”. A backstop

technology is a technology that can at a fixed (high) cost produce a perfect substitute for

the resource in unlimited quantities. Examples for oil would be an oil substitute produced

on the basis of coal (Fisher-Tropf process used by Germany during the war and by South

Africa during the oil embargo during the Apartheid period) or simply shale oil of which

massive quantities are available.

Using our discrete periods optimization model and adding the possibility of a backstop

production at a fixed production cost of k and using as upper index for the scarce resource

t and for the backstop production st we need to solve the following problem:

11 0

1

1

t sti i

t sti i

q qNt sti ii

q q i

Max a bq dq cq kqr

1

Nti

i

q Q

Using the first order necessary conditions we find the following characteristics (when the

non renewable resource is used for M periods):

1. The maximal price for the resource is limited to the production cost k of the substitute

2. The non renewable is fully used and is exhausted in period M

3. One uses the substitute only when the non renewable resource is full exhausted; the

intuition is that, by using the scarce resource first one saves production costs (it costs

only c < k to produce the exhaustible resource) and saving production costs in period

i<M is important as these savings can be re-invested with a return r.

4. So adding a substitute speeds up the exhaustion of resources

When we return to our numerical example and add a substitute that can be produced at a

cost of 6$ per unit, we have the following profiles for quantity and prices:


Figure 2.7 : Price and quantity of the non renewable resource in the presence of a

renewable substitute

Increasing marginal cost of extraction Often the resource base consists of different basins that have different extraction costs. The general rule is that it is always optimal to use the cheaper resource first. In the next figure one finds an example with a resource base consisting of only 2 parts with a different marginal extraction cost.

Figure 2.8 A non renewable resource base with a cheap and an expensive part


We see that the cheap resource is first fully used and that the margin (p-mec1) increases

with the factor (1+r) every period. When it is fully used, the second resource takes over.

The total marginal cost is here the mec+opportunity cost. One sees that the price-mec2

follows also the Hotelling rule also but only from T* onwards.

The cheapest resource is used first because this allows to save production costs in the first

periods and these savings have a higher weight because of the discount rate.

Reserve dependent costs

The extraction cost in any given year can be made an increasing function of the

production in a given year and a decreasing function of the remaining reserves R. Making

the extraction cost dependent of the remaining reserves could stand for the production

costs of an existing well where the pressure in the reservoir drops with each barrel

extracted. More production requires increasing the pressure by injecting water or steam

etc. and this is more and more costly. When one includes discoveries of always smaller

and smaller fields, costs of exploration go up too.

The end result will be a continuous version of Figure 2.7 and the price can be seen as the

extraction cost plus the opportunity cost of taking the resource out of the ground and this

implies increasing the extraction costs for the rest of the reserves.

, ,1

1( ) where

(1 )

T t

t q t R t n R t nt nn

p c c cr

, 0

So the price should start above marginal extraction cost and equal the marginal extraction

cost in the last period.

Comparative statics of the basic N period case We now use a model with a more general formulation that allows to study the properties

of the optimal solution using a graphical construction.


We will use a continuous time model with a different demand function but still a constant

demand function over time and a constant extraction cost8:

0

0

0

( )

( ) ( )

( )

Tr t

T

t t

R

a R

M a x W U R e d t

Ss u b j t o R a n d R d t S

t

w h e r e U R P R d R c R

a n d P R K e

This problem has an exact solution that allows studying the comparative statics and

obtaining unambiguous results. When it the optimal solution is to use the resource (WTP

is large enough), one obtains the following analytical solutions:

20

2

( )

raS

aST

r

P c Ke

rR T t

a

This solution can be presented graphically:

8 I use here the version of the model as presented by Perman,Ma,McGilvray, Common, , “Natural resource and environmental economics”, Pearson, 1999, 2nd edition, Ch7+8


KATHOLIEKEUNIVERSITEIT

LEUVEN

CENTER FOR ECONOMIC STUDIES

The N-period Model

timeq

q

Pricemec

mec

price

Total use of theresource

Demandfunction

45°

Figure 2.9 Optimal use of a scarce resource

This figure is constructed as follows. The left upper quadrant represents the demand

function that determines quantity for given price in each period. The left lower quadrant

is a 1 to 1 mapping from the left horizontal axis to the negative part of the vertical axis.

Take now one period, on the positive horizontal axis, going upwards, one finds the

(optimal) price in that period; going left one uses the demand function to find the

corresponding quantity, using the lower left quadrant one finds the quantity for that

period. The total use of the resource is the integral over time and thus the area in the

lower right quadrant.

We see the properties we know:

- resource is fully used

- price in last period = maximum price or choke price (K)

- price increases over time where margin increases with factor (1+r) every period

- use of resource decreases over time

We discuss the following parameters one by one: a higher discount rate, an increase in

the known resource stock, higher demand growth due to say higher population growth, a


fall in the price of the backstop technology due to a scientific discovery, changes in the

extraction costs.

Higher discount rate


LEUVEN


The N-period Model – higher discount rate

timeq

q

Pricemec

mec

price


Demandfunction

45°

Figure 2.10 Effect of a higher discount rate

The above figure presents what happens when the discount rate increases. The intuitive

reasoning goes as follows. When the discount rate increases, we know that the margin

(and the price) must increase more strongly over the extraction period. So one must start

at a lower initial price and one will reach the choke price more quickly. Total resource is

again fully exhausted.

A higher discount rate means that it is better to generate benefits in the near future and so

it is logical to advance the extraction of the resource.

A decrease in the size of the resource stock



LEUVEN


The N-period Model – effect of lower resource base

timeq

q

Pricemec

mec

price


Demandfunction

45°

Figure 2.11 Effect of a lower estimate of the resource base

We know that the resource is scarcer, so keeping the initial price path would lead to

exhaustion of the resource before T and this at a price smaller than the choke price. This

can not be an optimum, so the initial price has to be increased and also the total extraction

period will be shortened. To see the latter, imagine one started from the initial T, then

going to period T-1, T-2 ..decreasing the margin every year by a factor (1+r) would lead

to exhaustion of the resource before the period 0. But then one can as well start the

extraction of the resource earlier at a slightly higher price and stop before moment T.

Effect of a lower marginal extraction cost

This can be due to technological progress. The reverse could happen if there is much

more attention to environmental problems that went unnoticed.



LEUVEN


The N-period Model-effect of lower mec

timeq

q

Pricemec

mec

price


Demandfunction

45°

Figure 2.12 Effect of a lower marginal extraction cost

Using the original price path is not optimum because the margin (p-mec) is now larger.

So in order to restore the Hotelling rule, one needs to start from a lower initial price. This

increases the demand in the early periods and this shortens the extraction period.

Increase in the expected demand



LEUVEN


The N-period Model - increase in demand

timeq

q

Pricemec

mec

price


Demandfunction

45°

Figure 2.12 Increase in demand function

An increase in demand can have different meanings. One can increase the number of

identical households are economies that all use the same unit demand function: then we

have an expansion of the demand function rotating at the same choke price as is shown in

this figure. A parallel movement outwards of the demand function means that also the

choke price increases and this would produce a different result.

Imagine that one kept the old price scheme. Then one would exhaust the resource before

T because demand is now higher for every price. Exhausting the resource before reaching

T can however not be optimal. So one needs to increase the initial price and this will also

lead to a shorter extraction period.

A fall in the cost of the backstop technology



LEUVEN


The N-period Model – fall in cost backstop

timeq

q

Pricemec

mec

price


Demandfunction

45°

Because the backstop cost falls, the initial price path is no longer optimal: it would imply

that one leaves some of the resource in the ground. This implies lowering the price in the

final period, in the initial period and using the resource more quickly.

Interpretation of the comparative statics exercise We have interpreted the previous exercises as follows: given that one has an initial stock

of resources, how would the optimal price and quantity profile change if one of the

parameters changes. One can also give another more general interpretation to our

exercise: imagine one is on one of the optimal profiles and suddenly one of the

parameters changes because of extra information that was not anticipated. Then we can

see the comparative statics exercise as a new optimization exercice starting at moment

t<T. If nothing would have changed in the parameters, one would have continued the old

price path. When one changes a parameter, one can by comparing carefully the new and

the old price path have a feeling for the change in the price levels. This is a good exercise

to check your understanding of the different comparative statics cases.


7. The allocation of non renewable resources in a market economy

Perfect competition case The theory of non-renewable resources that we surveyed in the previous sections was

mainly dealing with the optimal use of a scarce non renewable resource over time.

Although we used market prices (auction prices) to make sure the right consumers had

access to the resource we assumed that there was an omniscient planner that optimized

the extraction over time. In reality, it are firms and governments who decide on extraction

and they look for a maximum profit or revenues solution.

We start by examining the perfect competition case. This means that all owners of the

resource take the market prices as given and choose the quantities to extract that

maximize their profits. As each supplier has to decide when and how much to produce,

he considers a path of future prices. It is not necessary that the total resource is

subdivided among a very large group of owners (say students taking this course). It is

sufficient that one has a limited number of suppliers who do not form a cartel and that

have each a reasonable share of the market. In this case they will tend to take the prices

as given as none of them has an interest to restrict his supply to raise prices because the

major beneficiaries will be his competitors who will expand output..

It can be shown that the equilibrium price path has the same properties as the optimal

price path we developed in the previous section: the margin (price-mec) must rise every

period with a factor (1+r). An equilibrium price path is a path of prices at which none of

the suppliers has an interest to supply more, all consumers are at their demand functions

(WTP= price) and demand equals supply in all periods.

Why does the perfect competition case satisfy the Hotelling rule? Assume it would not be

true: then the price in a future year t’>t would be such that

- either p(t’)-c > p(t)-c(1+r) (t’-t)

- or p(t’)-c < p(t)-c(1+r) (t’-t)

In the first case every supplier has an interest to sell less in period t and keep that

production volume for period t’, so this can not be an equilibrium because supply will be

less than demand in period t etc.. until equilibrium is restored.


In the second case, the reverse will happen, instead of selling in period t’, a supply will

prefer to sell more in period t etc.

Important assumptions are here that all suppliers use the same discount rate so that they

have all access to the same conditions on the capital market. A second important

condition is the existence of a full set of futures markets for the commodity.

The monopoly case

For oil we have known several periods where OPEC acted as a monopolist, controlling

the quantity in order to increase their revenues. What does this imply for the rate of

extraction? The next figure shows that this means higher initial prices and a longer

extraction period. Why is this the case? A monopolist knows that by influencing the

quantity supplied he can manipulate prices. In any period he will restrict supply until the

marginal profit ( marginal revenue –marginal cost) increases with a factor (1+r).


LEUVEN


The N-period Model – monopoly instead of competition

timeq

q

Pricemec

mec

price


Demandfunction

45°

Figure 2.13 Comparing the monopoly solution to the perfect competition case

The marginal profit in one period equals the marginal revenue minus the marginal

extraction cost:


pp q m

q qec

This is the well known condition for one period, giving rise to a price>mec. Now we also

need to take into account that selling one unit this period rather than in a future period has

an opportunity cost λ. So the optimal rule is now to have marginal profit increasing at the

discount rate.

In order to understand the intuition of the result that monopolists sell less and extend the

period of extraction, start at the perfectly competitive solution in the first period. For that

price, the monopolist has still an interest to lower the quantity and increase the price

because the marginal revenue is higher than the marginal cost plus the opportunity cost.

The result is that the price is higher and that he saves one unit for use in future periods.

There is a period where both price paths cross as total resource available is identical.

In our case there is an exact solution: the total extraction period with a monopoly is more

or less 2.5 as long as the extraction period with perfect competition.

In the next Figure we illustrate what happens if one has a change in market regime from

monopoly (period T1) into perfect competition. This could be the case when a cartel

breaks down. We know that the suppliers then lower their prices and want to sell more:

prices jump downwards but increase more strongly. If in period T2, the cartel is restored,

one returns to a monopoly path with an upward jump. The oil market has seen these

jumps but whether the theory of non renewable resources is a good explanation is a

different matter.


T2 T1 Time

ME

Choke price

Price

Figure 2.14 Regime switches between monopoly and perfect competition

Some more issues that arise in a market context

Royalty and revenue tax

Most countries charge a royalty tax on their oil and gas production. If the royalty tax is a

fixed % of the net margin, this tax does not affect the depletion period and path as the

Hotelling condition is unchanged by a tax t:

1(1 )( ) (1 )( )(1 )t tt p c t p c r

A tax on (gross) revenues will discourage production and has the same effect as an

increase in the resource extraction cost.

Forward markets and expectations

In the perfect competition case, the Hotelling rule is the result of arbitrage possibilities of

suppliers on forward markets. Forward markets are markets where one can buy the

resource in a given future year. Forward markets exist but only for a limited number of

years (say 5), so there is no “market” price for the years 6 and later.


Extraction under uncertainty

to be completed later

8. How does the model perform in reality? The Hotelling rule is an exact result that holds if reality confirms to the theoretical set-up.

The world is much more complex. An important factor that is still missing in the model

is technological progress that lowers extraction costs and tend to increase the resource

base. Simple empirical tests of the Hotelling theory are rejected in most cases. In the case

of oil this would require that the price path (neglecting the marginal extraction cost)

would increase with a factor (1+r). As can be seen in Figure 2.15, this is clearly not the

case.1

Figure 2.15 Price of oil and r=5% growth paths (source IEA and Medlock (2009))

This is however insufficient to reject the Hotelling theory. In fact over the years,

expectations on future demand, total available reserves, backstop costs and also the


market regimes have changed. Each of these 4 elements changes the current price level

and the fluctuations in the price of oil do therefore not necessarily contradict Hotelling.

9. Conclusions

We have surveyed the theory of non renewable resources. Important questions remain:

Is the model useful to understand reality, a point to which we return in our oil and gas chapters

Is it acceptable that we use all exhaustible resources now and leave none for the future generations? Is this sustainable development? – an issue to which we return in chapter 3

What is the role of environmental considerations in the extraction of exhaustible resources?

10. References Dasgupta, P., G.Heal, (1979), Economic theory and exhaustible resources, Cambridge

University Press

Medlock K.B. III, The economics of energy supply, Ch3 in Evans J., Hunt L., (eds.)

(2009) International Handbook of the Economics of Energy, Edward Elgar

Perman, Ma, McGilvray, Common, , “Natural resource and environmental economics”,

Pearson, 1999, 2nd edition, Ch7+8

Tietenberg (2000)

11. Questions for students 1. Take BP statistical review. Can you explain what happened with Oil reserves in Canada, UK and Saudi-Arabia? 2. Compute ratio present consumption over reserves for oil in 1990, 2000 and 2009, can you explain the evolution? 3. Do you understand what happened to Gas reserves in Canada and the US? 4. Imagine that after the events in Libya, we have a more Western oriented regime that does no longer follow OPEC strategy. What could this imply for the oil prices?


5. Assume there are two suppliers. One has a marginal cost function = 2x, the other has a marginal cost function 4x. Find graphically and algebraically the aggregate marginal cost function. 6. Imagine that scientists found out that from 2025 onwards, it will be possible to have cars running on water at a relatively low cost. What will happen to oil prices now, in 2025 and in 2040? 7. What do the last 400 years of energy supply teach us on resource availability in the future?


Chapter 3 Environment

1. Objectives and outline

Fossil energy use generates different types of negative side effects for society: traditional air

pollution but also global warming. As this issue concerns almost all energy use and is the

main justification for subsidies to “green” energy we need to understand this issue in more

depth.

We do this in three steps. In the first section we survey the the basics of environmental

economics with a simple model. This model is used to discuss the use of different types of

policy instruments. In the second section we discuss the sustainability concept in abstract

terms drawing on a paper by Arrow et al. (2004). In the next chapter we focus on climate

change as this is considered at present as the environmental issue with the highest impact

on the energy sector.

2. Basic environmental economics

Problem setting

When there is a large number of polluters and victims, every victim and every polluter will

take the aggregated pollution level as given. This is the crucial assumption we need to make

for our simplified framework to make sense in the real world1.

We use a simplified framework with only 2 polluters a, b and 2 victims 1 and 2 to which we

add the assumption that they take the actions of the others as given. Our model can be given

many different interpretations. The polluters and victims can be different firms, different

countries, different generations etc.

Initial emission levels are Ea and Eb. The polluters can reduce emissions by quantities Za

and Zb at a total cost Ca(Za) and Cb(Zb). This total emission reduction or abatement cost can

be interpreted most easily as efforts (equipment, level of care) by the firm (or the household)

1 If we would not make this assumption, all problems between our two agents can be solved by bargaining between the two parties. We know that this can produce efficient solutions.


to reduce emissions. But in most cases the cost of emission reduction consists also of the lost

consumers’ and producer surplus due to the price increases for goods produced with dirty

inputs. We will come back to the measurement of emission abatement costs in later lectures.

There are 2 victims I=1,2 with a total environmental damage D1(P) and D2(P). The level of

pollution P (has dimension effects rather than emissions) is defined as:

( ) (a a a b b bP T E Z T E Z )

Where the pollution or damage effects are a weighted sum of emissions by the two polluters.

The weights T can be interpreted as transfer or transport coefficients translating distance,

wind direction, toxicity etc..This is the simplest transfer function one can imagine. In some

pollution problems one defines “a blame matrix” that tells you what share of the pollution of

a country or region ends up in all the other regions. This is an important element in EU

policies on conventional air pollution. Figure 1 illustrates one of the source receptor

relationships used in Gains, a model used to prepare decisions on European policies. Figure 2

illustrates the damage relation, showing the effect of changes in emissions on life expectancy.

Source-receptor relationships for PM2.5derived from the EMEP Eulerian model for primary and secondary PM

PM2.5j Annual mean concentration of PM2.5 at receptor point jI Set of emission sources (countries)J Set of receptors (grid cells)pi Primary emissions of PM2.5 in country isi SO2 emissions in country ini NOx emissions in country iai NH3 emissions in country iαS,W

ij, νS,W,Aij, σW,A

ij, πAij Linear transfer matrices for reduced and oxidized nitrogen,

sulfur and primary PM2.5, for winter, summer and annual

)2**2),1**32

14*1**1,0min(max(*5.0

)**(*5.0

**5.2

jiIi

Wijji

Ii

Wiji

Ii

Wij

iIi

Siji

Ii

Sij

iIi

Aij

Iii

Aijj

knckscac

na

spPM

Figure 3.1 European air pollution dispersion model (Gains)


Loss in life expectancy attributable to fine particles [months]

Loss in average statistical life expectancy due to identified anthropogenic PM2.5Calculations for 1997 meteorology

2000 2020 2020 CAFE baseline Maximum technical

Current legislation emission reductions

Figure 3.1 Illustration of effect of a policy on damage of emissions (source GAINS model)

For the pollution problem we proposed we will analyze three types of solutions: an ideal solution, a centralised solution, and a non-cooperative solution.

Ideal solution Look for solution that maximizes the total welfare assuming that there is perfect control of all variables

Non cooperative solution All polluters are only interested in their own damage and take the actions of the others as given (Nash-Cournot equilibrium)

centralised government solution Assume that there is a central government that has all the information but has to use given policy instruments (taxes, permits etc.) to control the behaviour of polluters

Centralised government solutions with imperfect information

Table 3.1 The different institutional settings considered


The ideal (or theoretical optimum) solution

If we use a quasi linear utility function and we have perfect income distribution instruments,

we can formulate the optimal pollution problem in a very simple way:

PROBLEM 1

1,2

1,2 1,2

,

( ( ))

( ) ( )

( ) ( )

a b i

i i

i a a b b

a a a b b b

choose Z Z and m such as to

Maximise m D P

subject to m C Z C Z R

where P T E Z T E Z

i

If we use all available resources R and substitute m by the resource (or production

constraint) of this economy, this problem comes down to minimize overall damage and

overall costs (PROBLEM 2-often called the “efficiency problem”). Implicitly we assume

1) that we are either indifferent about the distribution of costs and benefits to the different

individuals or that we have other income distribution instruments operating in the

background.

2) The damage of pollution does not depend on the income levels

3) We use a linear production technology except for the production of abatement

PROBLEM 2

1 2( ) ( ) ( ) ( )

( ) ( )a a b b

a a a b b b

Minimize D P D P C Z C Z

where P T E Z T E Z

By selecting appropriate abatement efforts Z by the two polluters.

An interior solution to this optimisation problem is given by the first order conditions:


1 2

1 2

a

a

a

b

b

b

C

ZD D

P P T

C

ZD D

P P T

We see 2 properties here:

1) The optimal level of pollution P* is reached when the marginal cost of reducing pollution

(δCa/ δZa) / Ta equals the total environmental damage (δD1/ δP) + (δD2/ δP) – this

expression holds for every polluter

2) Pollution is reduced in a cost minimal way when the marginal cost of pollution reduction is

equal between the two sources of emissions: (δCa/ δZa) / Ta = δCb/ δZb) / Tb where we see

that the transfer coefficients correct the marginal cost of emission reduction to express it in

terms of pollution reduction costs this will determine the optimal distribution of emission

reductions over the two polluters

We can show these properties also in 3 steps and that is what is usely done in the graphical

procedure.

The first step is then cost efficiency in the reduction of pollution so as to achieve a given level

P°:

PROBLEM 3:

( ) ( )

( ) ( )a a b b

a a a b b b

Minimize C Z C Z

such that T E Z T E Z P

An interior solution to this problem will satisfy

b a

b a

b a

C C

Z Z

T T

This first step allows the construction of a new aggregated total cost function C(P) where, by

construction, pollution levels P are achieved at the lowest cost by combining the efforts of the

two polluters.


Imagine that one does not systematically combine the abatement efforts of the two polluters

in a cost –effective way. Then another aggregated cost function CO(P) has to be used that

reaches pollution levels at always higher costs. Figure 3 illustrates the marginal cost of

reducing emissions of SO2 in a particular zone.

An example cost curve for SO2

L o w s u l f u r c o a l

1 % S h e a v y f u e l o i l

F G D - b a s e lo a d

p o w e r p la n t s

F G Do i l f i r e d

p o w e r p la n ts

0 . 2 % S d ie s e l o i l

F G D la r g e in d u s t r ia l

b o i le r s

0 . 6 % S h e a v y fu e l o i l

F G D s m a l l in d u s t r ia l

b o i le r s

0 . 0 1 % Sd ie s e l o i l

R e m a in in g m e a s u r e s

P r e s e n t le g is la t io n

0

5 0 0

1 0 0 0

1 5 0 0

2 0 0 0

2 5 0 0

3 0 0 0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0

R e m a i n i n g e m i s s i o n s ( k t S O 2 )

Ma

rgin

al

co

sts

(E

UR

O/t

on

SO

2 re

mo

ve

d)

Figure 3.3 Illustration of a marginal cost function for the reduction of emissions in a given

zone

The second step is to construct an aggregated environmental damage function D(P). This is

easy:

Problem 4:

1 2( ) ( ) ( )D P D P D P

The third step is to choose the correct level of emission reduction given the aggregated

damage and abatement cost functions:

Problem 5

( ) ( )Minimize D P C P

Where an optimum interior solution satisfies the traditional marginal damage and marginal

pollution abatement cost.


A graphical illustration is particularly easy when the transfer functions are equal for both

pollutants. In this case we can use the dimension “emissions” for all cost and damage

functions instead of having to use emissions and pollution.

The aggregated damage function is constructed by adding “vertically” the marginal damage

functions of the 2 victims (Fig II and Fig III give rise to MD in Figure I). We use here the

“public good” property of pollution: the pollution generates damages to the two victims so we

have to add the marginal damages to obtain total pollution damage.

The second aggregated curve, the abatement cost function is constructed combining Fig IV

and Fig V into Fig I. Fig IV ranks all emission reduction possibilities for the first polluter in

the order of increasing costs (this generates the marginal cost function). We are interested in

the reduction of pollution at the lowest cost. The construction of the aggregated marginal cost

function uses a given maximum emission reduction cost MAC°. Then the total quantity that

can be reduced for a marginal cost level lower than the target marginal cost level MAC° at

the two emission sources is computed. This generates one point on the aggregated marginal

cost function. Varying the MAC° level allows to construct the complete aggregated marginal

abatement cost function. By the way, we use precisely the same procedure to construct an

aggregated marginal cost function for the supply of a private good.


pollution pollutionpollution

MD

MACMAC A MAC B

MD1

MD2

pollution

pollution

I

III

II

VIV

Optimal abatement for B

Optimal abatement for A

Figure 3.4 Synthesis figure for simplified environmental problem


Non cooperative solution There are situations where there is no central government that can control the polluters.

This is typically the case for international pollution problems where there more than a few

nations are involved. A typical example is climate change: the emission of each nation will

damage all other nations of the world. Here we can not rely upon a central government

because there is no world government. Obviously there are international agreements but

things are not as simple. Indeed it is dificult to make international agreements that can be

enforced. If a country signs an agreement but finds that it is in its interest not to comply

with the agreement, there is no international court that can enforce the agreement.

We can study this problem with our small model. We assume that there are two countries 1

and 2 and we assume that every country can reduce its emissions. Instead of two firms

polluting we have the two countries polluting.

Every country solves the following problem:

Problem 6

1 1 1

1 1 1 2 2 2

( ) ( )

( ) (

Minimize D P C Z

where P T E Z T E Z

)

where we see that every country minimizes its abatement costs and its own damage, taking

the actions of the other countries as given (Z2 °).

The optimal solution for every country is (for an interior solution):

2

1

1 1

1Z

CD Z

P T

This is an equation that expresses the abatement efforts of country 1 as a function of the

efforts of country 2:

1 1 2( )Z R Z

This is called a reaction function. When both reaction functions exist and satisfy certain

properties (continuity) one can guarantee the existence of a Nash equilibrium :


1 2

1 1 2

2 2 1

,

( )

( )

N N

N N

N N

Nash equilibrium Z Z satisfies

Z R Z

Z R Z

How does this non cooperative solution compare to the ideal (and the centralised solution)?

The non-cooperative solution will be less efficient because of two reasons:

a) the emission reduction is not produced in the most cost-effective way

b) the overall emission reduction effort will be too low as every country takes only into

account its own damage and not the damage in the other countries

That there are large differences between the non-cooperative solution and the efficient

solution can be illustrated for Climate Change. Eyckmans, Proost, Schokkaert (1993) show

that for climate change, the non-cooperative solution would produce some 2% of reduction of

emissions while the cooperative solution would generate some 16% of emission reductions.

Centralised government solution Assume the policy maker is interested to achieve the ideal solution that we described earlier.

He can however not necessarily control all the actions of the polluters. He is restricted in the

type of constraints and incentives he can give to the polluters. These restrictions are

sometimes called “constitutional” in the sense that they are part of a more fundamental

contract between citizens that try to preclude the misuse of power by policy makers.

We will discuss three types of centralised solutions that are presented in the next table:

pollution taxes, standards and tradeable permits:

Pollution taxes Tax on all emissions corrected for its effect on

pollution - the revenue of the tax is returned to

all the citizens as a subsidy per head

Standards Emission limit set for every polluter

Tradeable permits Every polluter receives emission rights that he

can trade freely with other polluters

Table 3.2 : main policy instruments discussed


The policy maker has now to solve a problem where his control is more indirect:

Problem 6

( ) ( ( )) ( ( ))

( ) ( )a a b b

a a a b b b

Minimize D P C Z control C Z control

where P T E Z T E Z

Before analysing the problem faced by the government we need to examine how the polluters

react to different types of policy controls by the government.

A tax on emissions Assume that the polluters are producers that minimize their total production costs. When

they are faced with a tax on emissions, corrected for the transfer coefficient (also called

“ambiant pollution taxes”) the polluter faces the following problem: minimize the sum of

abatement costs and emission taxes he has to pay.

Problem 7

( ) ( )a a a a aMinimize C Z t T E Z

If we assume that every polluter minimizes indeed this expression, we can derive his

reaction function to a change in controls from the first order conditions for an interior

minimum solution:

a

a

a

C

Zt

T

this is an implicit equation that gives Za in function of the control t .

An interesting property of the ambiant emission taxes is that they always generate emission

reductions in a cost-minimizing way. Because all polluters are subject to the same pollution

tax t we have indeed (for an interior solution):

b a

b a

b a

C C

Z Zt

T T


This is indeed an interesting property: the policy maker does not need to know the

abatement cost functions to achieve a cost minimizing solution , all he needs to do is set the

same ambiant pollution tax rate for all polluters.

An emission standard In the case of an emission standard, the policy maker fixes one emission limit EL for each

polluter. The polluter then minimizes total costs subject to this limit on emissions:

Problem 8

( )a a

a a

Minimize C Z

subject to E Z EL a

If the constraint is binding we have that Z is directly controlled by the emission limit.

The government has full control but this will only lead to a solution that is cost-efficient if

the policy maker has full knowledge of all the abatement cost functions. This is paradoxical:

decentralising decisions by using indirect controls as there is an emission tax may improve a

solution where the policy maker has full control but not all the information. This is the

fundamental reason why economists like to rely on markets to organize production and

consumption decisions.

A tradeable emission scheme The idea in this scheme is that the policy maker allocates emission rights ER to every

polluter. Next the polluters can trade emission rights, in the final step every polluter has to

limit his ambiant emissions in function of the total number of ambiant emission rights he

possesses.

We represent the net purchase of ambiant emission rights by ERP and we assume that there

is a perfectly competitive market for emission rights where the equilibrium market price is

“per”.

A perfectly competitive emission rights market means that all players take the price on that

market as given. This will typically be the case if there are a large number of traders on the

market and that none of the traders has a dominant position.

An equilibrium price per is a price where the sum of the net trades


a bERP (per) + ERP (per) = 0

The problem of every polluter is now:

Problem 9

( ) .

( )a a

a a a a

Minimize C Z per ERP

subject to T E Z ER ERP

And his behaviour (choosing Z and ERP) will be characterised (for an interior solution) by:

a

a

a

C

Zper

T

This equation holds for all polluters, so we achieve again the property that all pollution

reduction costs are minimised because all polluters react to the same price signal “per”:

b a

b a

b a

C C

Z Zper

T T

The control variables of the government are now: ER a and b but one can show only the

weighted (by transfer coefficients) sum of emission rights matters.

This is again an interesting property: the policy maker controls in fact total pollution rights

and that is all he needs to achieve a cost effective solution.

We can now return to the problem of our policy maker that controls pollution via indirect

policy instruments. We can now solve problem 6 with as constraints the behaviour of

polluters (problems 7, 8 or 9). We summarize some of the properties of the different

instruments in the following table.


Ambiant Pollution taxes Cost efficiency of pollution reduction is

guaranteed

reaching the optimal pollution level requires

that the ambiant tax is set equal to the

Marginal Damage and this requires knowledge

of aggregate MC and MD curve

Standards Cost efficiency of pollution reduction is not

guaranteed


that the total quantity of ambiant pollution

allowed corresponds to the level where aggreg

Marginal Damage = aggreg Marginal cost

Tradeable permits Cost efficiency of pollution reduction is

guaranteed


that the total quantity of ambiant pollution

allowed corresponds to the level where aggreg

Marginal Damage = aggreg Marginal cost

Table 3.3 Properties of some environmental policy instruments

Experience with Emission trading in the energy field: the SO2 trading scheme in the US

See Schmalenzee et al (1998) and ppt. “Tradeable emission permitsSO2 in US” in

TOLEDO


3. Sustainability

Issue and outline There are many definitions of “sustainability” around .We follow a recent paper by

Arrow et al (2004) that is a result of a dialogue between economists and ecologists.

Ecologists are worried about the future of this planet when you put together some trends.

Over the last 100 years, population increased with a factor 4 , industrial output by a facot

35, energy use by a factor 16, fishing output by a factor 35. They consider this as

“unsustainable”.

Economists and ecologists tend to use two different views on sustainability. In the most

simple economic approach one would define a policy as sustainable when it maximizes

the discounted future utility over the rest of the horizon. In the second approach

originating from the ecologist tradition and translated into economist’s language is more

policies are sustainable when they guarantee the utility of future generations. We will

show that both views are not that different.

The sustainability discussion is important for many long term issues and will turn out

crucial for the climate change debate.

Sustainability as a maximum of discounted utility

The simplest “naive” approach is to look for policies that maximize the present value of

discounted utility for the rest of the horizon. In its simplest form this comes down to:

1

1Max ( ( ))

(1 )tt

U C t

There are three important assumptions embedded in this formulation. The first is the

structure and functional form of the utility function. We have simplified the utility

function so that it has only one argument “ aggregate consumption” which is not a strong

assumption as long as one can easily produce all goods from a common input (say

labour). The utility function is also the same for all individuals and represents an ethical


judgment on what is the relative value of giving 1€ of consumption to one poor

individual and one rich individual. In principle one accepts that this function is concave

so that 1 € taken from the rich and given to the poor increases aggregate utility. The

neration but doing this over several

sumption implicit in this formulation is that it is possible to transfer resources

ncavity of the utility

nction and where g is the growth rate of consumption over time:

degree of concavity of the utility function will tell us by how much.

The second assumption embedded in this formulation is the role of the discount rate. One

accepts to weight the utility of consumption now and in the future with one common

interest rate. This is acceptable within one ge

generations in the very long term is another issue.

The third as

over time.

To continue our reasoning it is actually easier to transform the sustainability objective

into an objective that is only a function of consumption over time. We can do this by

using a different discount rate r where η is a measure of the co

fu

r g

And use as objective function :

t

This results from the following steps:

0

Trt

tW C e d

0

( ) ' 0 '' 0

e la s t ic i ty o f m a rg in a l u t i li ty w r t c o n s u m p tio n (c o n c a v i ty o f u t i li ty fu n c t io n )

C U ''= -

U 'c o n s u m p tio n ra te o f d is c o u n t o f c o n s u m p t io n = ra te a t w h ic h th e v a lu e o f d e lt

Tt

tW U C e d t w i th U a n d U

a in

c o n s u m p tio n c h a n g e s w h e n w e m o v e o v e r t im e :

M a rg in a l u t i li ty o f c o n s u m p tio n = '

'' 'T h e d i f fe re n t ia t io n w r t t im e =

'''

t a k in g n e g a t iv e o f th is'

t

t t

t

U e

U e U e

U eU

CU

Cr

C

The intuition behind the transformed discount rate r is simple:


δ is the social rate of pure time preference = how one should trade off utility of

somebody now and the utility of somebody in the future, a reasonable ethical choice

persons

ving at two different moments in time

lasticity of marginal social utility (1 to 4 derived from individual trade offs

nder uncertainty) and is a measure of how fast marginal utility decreases when income

is the

te 1+rr units of consumption the next period.

ore € one would

be larger than 1, so

ere is an interest to reduce consumption now and increase investment

social

count rate r is the assumption that future generations will be richer (g>0). As future

nerations get richer it is rather normal that we should not save extra for them.

would be to take a value 0 as there is no reason to value differently the utility of

li

g is rate of growth of aggregate consumption (1 to 2% in long term)

η is e

u

increases

So r, the social rate of discount is of the order of 2% or more

We can now see whether current consumption is excessive according to this first

sustainability criterion. We need to compare the criterion with the possibilities to carry

over resources from one period to another via investments. Assume that any saving of 1 €

in a given period generates a consumption return of (1+rr) € in the next period. “rr”

real rate of return on invested capital. In other terms, if one would give up one unit of

consumption now, this would genera

In order to maximize our objective under our constraint to carry over consumption over

time, we need to compare r with rr.

If r < rr this means that by reducing consumption now and investing 1 m

generate 1+rr and this would after social discounting (1+rr)/(1+r)

th

If r> rr , it is better to decrease investments and consume more now

Because it is difficult to claim that rr is much bigger than r, it is difficult to claim that

present consumption is excessive. One of the main elements behind a large

dis

ge


Sustainability as guarantee for utility of future generations

It has become more common to see sustainability asa guarantee that future generations

have the production possibilities to have the same consumption level as we have. Now

the main question is what determines future production possibilities? This issue was

ia a production function that is function of

We can now express the evolution of utility over time as a function of net production

over time V(t) that is a function of man made capital Km and natural capital Kn:

assumed away in the previous simpler approach where resources could be easily

transferred from year to year via a real rate of return rr.

We can define future production possibilities v

three inputs: labour (kept constant), man made capital (buildings, technology) and natural

capital (depletable resources, biodiversity,...).

( ) ( ) , ( )

( ( ) , ( ) ) . .

1 ( ) ( ) (( ( ) , ( ) ) . .

( ) ( ) ( ) ( ) ( ) ( ) ( )

1 1 ( ) ( )( ( ) , ( ) ) .

( ) ( ) ( ) ( )

V t V K m t K n t

V K m V K nd V K m t K n t

K m t K n t) 1p m t K m p n t K n t K n

d V K m t K n tp m t K m t p m t K m t t p m t K m t K n t t

K m p n t K n td V K m t K n t

p m t K m t K m t t p m t K m

1.

( ) ( )

( ) ( )w h e r e e la s t i c i t y o f K n w i th r e s p e c t t o K m a lo n g a n i s o q u a n t

( ) ( )

K n

t K n t t

p n t K n t

p m t K m t

o r h o w m a n y u n i t s o f K n o n e n e e d s t o s u b s t i t u t e o n e u n i t o f K m

p n a n d p m a r e p r i c e s o f n a tu r

evolution of production possibilities over time by

with substitution possibilities.

Figure 4.6 gives an idea of the evolution of capital stocks for a given country (here UK)

a l a n d m a n m a d e c a p i t a l

This implies that we can check

checking the availability of man made and natural capital over time and confronting this


Man madeCapitalstock

CURRENT TREND of NATURAL AND MAN MADE CAPITAL OVER TIME – measured with current prices

Natural capitalstock

1750

2000

2100

Example: UK (%of GDP)Physical Investment : +3.7Education: +5.6CO2: -0.3Energy: -2.0NET: +8.9

Source: Arrow et al.

Figure 4.6 Evolution of capital stocks over time in the UK

But in order to know what a given evolution of capital stocks means for production

possibilities one needs to make assumptions about substitutability of the two capital

stocks. In the optimistic view there is easy substitution in the example of Figure 4.7 ,

there is a decrease of natural capital but overall production possibilities still increase

because one ends up on a higher isoquant. In the pessimistic view there is no easy

substitution of natural capital. There is a minimum of natural capital required and once

this limit is reached, the increase of man made capital is useless. See the example of

Figure 4.8.

Man madecapital

OVER TIME

Natural capital

Production level curvesIf substitution perfect

Figure 4.7 Optimistic view on substitutability


Man madecapital

OVER TIME

Natural capital

A

B

Production level curvesIf no substitution possible

Figure 4.8 Pessimistic view on substitutability

There is historical evidence on how mankind has dealt with natural resources and how the

economy has grown in a sustainable or non sustainable way. According to Diamond

(2005) there have been disasters on Easter Island (island 4h by plane west of Chile)

where deforestation has led to internal wars and disappearance of the population. Another

case are the Anasazi indians in south west US where population growth and drought has

led to mere extinction of certain groups. Another example or the Maya indians. Recent

cases of interest or Rwanda and Haiti (very poor but sharing the same island with

Dominican republic that is much richer).

The next table gives some data on the evolution of capital stocks. Some regions (sub

saharan Africa, Middle east decrease their overall capital stock while in most regions the

nman made capaital (mainly education) continue to increase. Whether this is sufficient

for “sustainable development” remains an open empirical question.


Table

4. References

K. Arrow, P. Dasgupta, L. Goulder, G.Daily, P. Ehrlich, G.Heal, S.Levin, K-G Ma¨ler,

S. Schneider, D.Starrett, B.Walker, 2004, “Are We Consuming Too Much?”, Journal of

Economic Perspectives,Volume 18, Number 3,Pages 147–172

Diamond J., 2005, Collapse – how societies choose to fail or to succeed, Penguin books

Schmalensee R., Joskow,P., Ellerman D., Montero J-P, Bailey E., 1998, An interim

evaluation of sulfur dioxide emission trading, JEP, vol 12, n°3, p53-68


Chapter 4 Economics of Climate Change

1. Objectives

Climate change is considered as one of the major environmental concerns of fossil fuel

energy use. Very ambitious emission reduction objectives have been announced for

Greenhouse Gas emissions and these will affect strongly the energy markets.

In this chapter we study the economics of Climate Change in 4 sections. We start with a

problem description at world level. Next we discuss briefly the economics of

international negotiations because this is necessary to understand the EU policy and the

international negotiation process. In the last section we analyze the implementation of the

European climate policy in more detail.

2. Climate change as a problem for the world

We rely heavily on the Stern report (2006, 2008) as this is accessible for non experts. The

Stern report has been critically reviewed by several economists. We will mainly integrate

comments by Weitzman (2007), Nordhaus (2007) and Heal (2009).

In order to understand the climate change problem we work in 5 steps. We first describe

briefly the climate change phenomenon, its drivers and its consequences in mostly

physical terms. The second step is to look for an objective function by which we can rank

different strategies to limit emissions of greenhouse gasses. The third step briefly

presents the types of models that are used for an analysis of the climate strategies at

world level. In the fourth step we give some idea about the cost of abatement and the

damages associated to climate change. In the last step we discuss briefly the policy

proposals advanced in the Stern report.

Physics of global warming


For “dummies” climate change is based on the following reasoning:

1. Human behaviour is at origin of extra GHG emissions, mainly under form of CO2

(75% of problem) but also methane, NO and HFC’s count.

2. GHG accumulate in the atmosphere and stay active for 100 to 200 years (decay

0.5% / year)

3. The increased concentration of GHG traps heat and generates global warming of

the planet

4. Global warming generates climate change – this happens with a delay of 30-50

years because of the thermal inertia of the oceans

5. Climate change has several effects, some positive but on average negative

Each of these relations are uncertain: what will be the economic growth in the future and

to what extent economic growth will be carbon intensive (and emissions will grow

rapidly) is not clear but also the effect of the GHG emissions on the climate (“the physics

of the warming”) and the precise effects associated to climate change (the “nature of the

damage”) are uncertain.

The global warming effects are often summarized under the form of the expected change

in average world temperature compared to the pre-industrial era. At present the

concentration of GHG gasses is 430 ppm CO2equivalent and this is rising between 2.5 to

4 ppm per year. Figure 4.1 gives the average global warming associated to different

levels of GHG concentrations in the atmosphere. If no policy action is undertaken, one

expects that one reaches a Business As Usual concentration in 2050 of the order of 750

ppm CO2eq.. The 90% confidence interval would imply global warming in the range of 2

to more than 6°C.

In order to illustrate what such a change in temperature implies one needs to put this

change in historical perspective. Over the last 3 million years the world has experienced

an increase of 2 to 3° C. Humans experienced 10000 years ago 5°C cooling (ice sheets up

to London – ice melted and England became an island). At 5°C, most ice and snow

would disappear, swampy forests appear everywhere and one could find alligators at the


North Pole. There are also major dislocations of population expected in 100 to 200 years

as large parts of the world become difficult to live in. Given these expectations it looks

reasonable to avoid risks of going beyond 550 ppm and so limit global warming to 3°C

with still risk of 24% reaching 4°C and 9% reaching 5% or 6%

Figure 4.1 Temperature change associated to different concentrations of GHG (source:

Stern (2008).

The GHG emissions come principally from fossil energy use in different sectors and to a

lesser extent from non energy emissions: see Figure 4.2:


Figure 4.2 Sources of world GHG emissions in 2000 (source Stern (2008)).

Avoiding climate change effects requires addressing a stock pollution problem and this is

more difficult than a flow pollution problem. Figure 4.3 gives an idea what temporal

profile of emissions is necessary to reach a given concentration of GHG in 2050.

Figure 4.3 Emissions profile necessary to reach a given concentration in 2050.


As can be seen from this figure even a decrease in emissions from now onwards will lead

to a strong increase of concentration of GHG’s in 2050 because every ton emitted will

contribute to the accumulation of the stock in the future.

How to select a climate change strategy for the world?

If there would be one benevolent world government, what emission profile would be

optimal when one considers all costs and benefits of abating GHG emissions? This is a

central question that has been the source of many discussions among economists and

policy makers. As we know from our sustainability chapter this is an ethical discussion in

which one needs to trade off the well being of different generations: emissions now will

generate damage for the coming generations, the well being of different parts of the

world (some will gain with climate change but others may lose heavily. In addition most

elements are uncertain.

Usually one starts with the following objective function for the world now and in the

future:

0

( ) ttW U C e d

t

t

To make this expression operational one prefers to work with a discounted sum of

consumption rather than utility and this requires assumptions on the concavity of the

utility function and on the growth rate of consumption. This means one works with:

0

Trt

tW C e d

And the discount rate is then: r g

δ is the social rate of pure time preference = how one should trade off utility of

somebody now and the utility of somebody in the future, a reasonable ethical choice

would be to take a value 0 as there is no reason to value differently the utility of persons

living at two different moments in time

g is rate of growth of aggregate consumption (1 to 2% in long term) – this is partly

endogeneous as this can be affected by climate change – if climate change destroys


ecoservices that are a strongly complementary input into production, the production and

consumption will be lower (cfr. Ch3)

η is elasticity of marginal social utility (1 to 4 derived from individual trade offs

under uncertainty) and is a measure of how fast marginal utility decreases when income

increases – the latter measure is used in two types of analysis: in redistribution of income

issues and in behaviour under uncertainty – those who want to avoid risks, tend to have a

very high η as high gains become less important than avoiding losses

Most discussions center on the choice of these parameters. For a 2% expected growth,

one arrives quickly at discount rates r between 1.5 and 5%. This range of discount rates

tends to discourage large abatement efforts now. But a full analysis should also take into

account the distribution of gains and losses over the world and the risks of extreme

events. In the following formulation of the objective function we sum over r=1...R

regions in the world and over s=1,...S possible states of the world with probability p(s,t)

due to uncertainty in the climate developments. This gives for the welfare in period t:

1

1 1

( )( ) ( , )

1

R S

r s

C tW t p s t

When it are particularly the poorest regions in the world (Africa, Bangla-Desh etc.) that

would suffer the damages, the concavity of the utility function would give these damages

a larger weight. Similarly, when the climate effects tend to be rather extreme, the

associated damages generate strong losses of utility (and consumption), risk aversion then

calls for a lot of preventive actions and a stronger abatement policy. This holds certainly

when some of the effects are irreversible: melting of ice caps, extinction of species...

Integrated assessment models

In order to determine the best emission reduction profile, one needs a long term growth

model that tracks the effect of climate change damage and the costs of emission

reduction. Such models need a climate module and an economic module that are both

reduced forms as shown in Figure 4.4.


E C O N O M I CM O D E L ( r e g io n a l g ro w t h m o d e l )( 5 0 t o 2 0 0 y e a rs )

C L IM A T E M O D E LL a g + S t o c k a c c u m u la t io nT r a n s la t e d in to ( re g io n a l ) e f fe c t s

E M IS S I O N S

E F F E C T S

A b a te m e n tc o s ts

d a m a g e s

Figure 4.4 Structure of an Integrated assessment model

One of the best known integrated assessment models is the Nordhaus & Zhang (1996)

“Rice” model. Whose structure is reproduced in Figure 4.5.

The most important parameters driving these models are the discount rate (in Fig 4.5 this

is ρ) , the technological progress (A parameter) , the carbon intensity of the future energy

use (σ) , the abatement cost (b parameter in Ω) and the damage of climate change (θ).

Integrated assessment models are necessary to have the argumentation right but given the

many uncertainties one should not count on precise results.


SWF

Production function

Net output (after damage and abatement)

Net consumption

Capital accumulation

Net emissions (after abatement% μ)

Stock of GHG

T atmospherictemperature

T* deep oceant°

F radiativeforcing

Economic loss factor thataccounts forAbatement and damage

For Mini climate model see: http://chooseclimate.org/jcm/jcm8jul03/index.html

Figure 4.5 Structure of the Rice model (Nordhaus & Zhang, 1996)


Damage of climate change

Estimation of climate change damage is difficult for two reasons. First there is large

uncertainty on the precise physical effects of climate change because the translation into

a new weather pattern: rainfall, storms, change in sea level and its biological effects are

uncertain. Second, the changes that are anticipated are of another magnitude than the

ones we experienced in the recent past.

A good example of how to measure damages to agriculture is the study by Mendelsohn et

al. (1994)). They related the agricultural product in different counties of the USA as a

function of average temperature, rainfall, sunshine and soil quality. The effects of a

global change in temperature can then be analysed by using the differences observed

between counties of the US. They conclude that global warming does not have a negative

impact on the agricultural output of the US. Of course this conclusion only holds for the

US.

There is a large uncertainty on the damages of climate change as can be seen in Figure

4.6 that summarizes several damage estimates:

Figure 4.6 Damage estimates of different sources (Stern (2008))

The damage is primarily a function of the elasticity of marginal utility (risk aversion or

aversion to inequality) and a damage parameter that tells us how strongly damages


increase for an increase in global temperature. The next table gives the loss in

“permanent consumption possibilities’ associated to a BAU development (without

climate policy). The result depends on the choice of the concavity parameter of the utility

function (η) (higher concavity tends to lower the importance of distant damages but also

attaches more weight to catastrophes) and on the choice of the damage function exponent.

For instance for η=1 and γ = 2, the uncertainty in the physical effects implies a loss in

permanent consumption possibilities in the range 2.2 to 22.8% of permanent

consumption.

Table 4.1 Uncertainty on damage costs in the BAU scenario.

Costs of emission abatement

Emissions can be reduced by calling upon two types of actions: by reducing the volume

of the polluting activity (smaller annual mileage for cars) and by reducing the emission

intensity per unit of activity (production or consumption). A typical ranking of different

options to reduce the emission intensity activities is given by the cost curve produced by

McKinsey (Figure 4.6). We will later argue that this cost curve contains several errors.

One of the errors is the computation of the cost of emission reduction by making cars

more fuel efficient. In that computation the high taxes on motorfuels are considered as a

real cost, while one should have taken only the production cost of these fuels.


Figure 4.7 Bottom up approach to abatement costs by McKinsey (source, Stern (2008)).

One of the important parameters for the cost of GHG emission reduction is the degree of

technological progress. Figure 4.8 gives an idea of the cost reductions realized for

different electricity generation technologies. These cost reductions are often a function of

learning by doing and so a function of cumulative output (cfr. later chapter on renewable

energy) .


Figure 4.8 Average cost of electricity for different technologies as a function of

cumulative production

Barrett (2009) made a review of alternative long term options to address climate change

in the long term: one can invest in avoiding the damage by geo-engineering (addressing

the weather on a global scale – think about the hail cannon used by the fruit industry in

Limburg) but one can also invest in adaptation (lower the damage of the physical effects

by building better dikes etc). The other strategy is prevention by either capturing more

CO2 or by avoiding the emissions all together.

Table 4.2 gives an overview of carbon capture technologies, Table 4.3 gives an idea of

the energy supply options without CO2 emissions


What strategy for emission reduction?

Climate change is a problem of decision under uncertainty. Important questions are the

extend of emission reduction as well as the timing of the reductions. One of the ideas is to

postpone abatement efforts so that one has a more precise idea about the level of damages

and could possibly count on cheaper abatement options. On the basis of decision theory it

is not possible to decide in favour or against the postponement strategy. Stern (2008)

defends a preventive strategy that would bring down concentration of GHG to 550 ppm

and limit global warming to an expected 3°C. According to Stern this would cost 1% of

GDP in permanence. Delaying action for 30 years would be much more costly.

He counts on a global deal between the rich countries that are responsible for a large part

of the historic emissions and the developing countries. Figure 4.9 gives the emissions of

CO2 per capita for different countries. As can be seen the richer countries emit up to 10

times more GHG per capita than the developing countries. According to Figure 4.3, one

needs to reduce overall emissions by 30% compared to current levels. As the economy in

2050 may be three times as large as now, emissions per unit of output would have to

decrease by 80 to 85%. Furthermore, in order to allow for a growth in emissions of the

developing countries a very strong abatement effort would be necessary in the rich

countries. The costs of emission reduction in 2030 would be of the order of 30 €/ton of

CO2.

Table 4.2Overview of carbon capture technologies (source Barrett 2009)

Energy Economics 2010-2011 – prof Stef Proost 14Energy Economics 2010-2011 – prof Stef Proost 14


3. Economics of international climate agreements

The international climate negotiations started in Rio de Janeiro (1992) and led to a first

agreement in Kyoto (1997). These negotiations are an ongoing process and the last

rounds of negotiations took place in Copenhagen in December 2010 and Cancun in dec

2010 and was based on reports like the Stern report. For an outsider, an international

agreement is a logical step in an efficient approach to climate change. Up to now the

success of the climate negotiations has been rather limited. The Kyoto agreement was not

ratified by some of the key emitters (USA) and left out some of the important emitters

(China, India). In addition many of the signatories did not comply with their promises. In

Copenhagen and Cancun it also proved impossible to have a full agreement on a climate

agreement that would more or less limit the expected concentration of GHG to 550 ppm.

According to the economic theory reaching a wide agreement on an environmental issue

at world scale is very difficult. Contrary to environmental problems at the scale of a

country, there is no world authority that can enforce international environmental

agreements. One country can take trade sanctions or send fighter jets but this also this

enforcement action is costly and will not be easily undertaken.

Figure 4.9 Emissions of CO2 per capita


Barrett (1994) uses a model with identical countries and finds that the equilibrium

number of signatories in an international environmental game that is played only once

equals 3 whatever the number of countries in the world. We can illustrate the issue using

a simple graph. Figure 4.10 presents a problem where 10 identical problems face an

environmental problem that is caused by the sum of the emissions of the 10 countries.

Each of them faces a marginal damage function (MB) that is horizontal. Every country

can also reduce emissions but at increasing marginal cost: this is the MAC curve.

10 MB

MB

3MB

MAC

abatement

$/ton

1 3 10

nash

Int agreement

Total abatement effortNash: 1x10 = 10Int Agreem 3x3 + 7= 16Full cooperation (FB)= 10x10=100

1

Figure 4.10 Illustration of an international environmental negotiation problem.

Consider first what would be the ideal solution for the world. This comes down to

reducing emissions in every country up to the point where MC equals the sum of the

marginal damages of all the victims, so MC=10 MB and this implies a total abatement

effort of 100 units. This can also be called a fully cooperative or first best solution: what

could be reached if one could make a binding international agreement where every

country would make an effort of 10 units of abatement. Consider now the other extreme

where there is no cooperation at all. In that case every country compares its Marginal

Cost with the Marginal Damage it avoids in its own country. This is called the Nash

“non-cooperative” solution and the total abatement effort equals 10 times 1=10 (cfr.Ch 3

for an example with only 2 countries). The other solution is an international agreement


that satisfies the following stability requirement: a country is as well off when it is

signing the agreement as when it is not signing the agreement. The group that signs the

agreement maximizes its group welfare so it considers the damage of its members. The

equilibrium for this game is 3 signatories and the total abatement effort is here 3

countries that make an effort (MC=3MC so 3x3) plus 7 others that work non

cooperatively (MC=MB so 3x1) or in total 16 units of abatement. As can be seen the

“self-enforcing” requirement for international agreements is a serious handicap and limits

what can be achieved by an international agreement.

This is the solution of a “one shot game”, this is a game that is played over and over

again for a few years where players do not take into account past or future behavior. One

could argue that this is the right concept given that the political majorities in countries

can change and that a new government is not responsible for what the previous

government did (think about Obama and Bush). One could also think about behavior of

countries as more consistent with more continuity and then one could see the game as a

repeated game where each country can start by cooperating and punish those that stop

making efforts by also stopping its efforts and doing this forever . When the discount rate

is sufficiently low, the sanction consisting of stopping cooperation forever is important

and Barrett proves that more performing international agreements become possible. At

present the EU plays such a cooperative strategy in the hope that the others will follow.

4. European Climate change policy

The European climate policy has an international and an internal European dimension.

We discuss first the international dimension.

International negotiation strategy of the EU

The EU has promised to reduce its emissions of GHG by at least 20% in 2020 compared

to the baseline level of 1990. Moreover if there is a comprehensive international climate

change agreement, it promises a 30% reduction by 2020. It also promised to increase the


share of renewables to 20% and have energy savings of 20% by 2020 but these targets

have also other objectives than climate change.

What are the costs of this strategy and how will the EU achieve the 20 and 30 %

objectives? This issue has been studied using the GEM-E3 general equilibrium model.

This model studies the economic development in the world by considering 10 or so

regions and modelling their emissions of GHG as well as the costs of reducing these

emissions.

Table 4.4 Simulation of costs of different EU strategies (source GEM-E3)

Table 4.4 presents the economic effects of the “cooperative” scenario where the rest of

the world also agrees to make efforts and the “unilateral” scenario where only the EU

commits to emission reductions. In the cooperative scenario, the assumption is that the

USA commits to an identical reduction as the EU (-30% in 2020 and progressively more

in 2030)) and that the new industrializing countries commit to monitor their emission/

output ratio‘s so that they cannot sell emission reduction efforts by first increasing their

emission levels. A second important assumption is that there is full trade of carbon

permits in the world. This means that the emission reduction in the EU and the US are

partly bought in China and Brazil. The overall reduction in the world will be 26% and the

gross economic cost (before accounting for climate damage) will be 1.2% of GDP in

2020. The price of a permit of CO2 emission will be of the order of 45 $/ton of CO2. The


cost for the US is lower than for the EU because the US starts from a higher level of

emissions per capita and can therefore more easily reduce emissions than the EU.

It is also interesting to see what strategy could be followed to realize the 20% if the rest

of the world does not sign any agreement. In that case, it would pay for the EU to set up a

monitoring system in a country with cheap emission reductions (China) and start trading

emission reduction efforts even if this country does not sign an agreement. Important to

note is that the demand for permits will be lower and the price of permits will drop to a

lower level.

Of course there is still some hope that other countries will follow the EU in implementing

a strong climate policy but as shown in the previous paragraph good international

agreements are very difficult to reach.

European climate policy

It is important to define a climate policy at EU level for three reasons. First, as we know

from international negotiation economics, it is better to have transfrontier environmental

pollution problems solved at the broadest policy level. Compare the EU 27 with a set of

27 individual countries, the sum of the individual efforts would be much lower. Second,

as costs of emission reduction are very different across countries, it makes sense to

exchange efforts so that overall costs of reductions can be reduced. Finally, the EU is in

fact a common market with a minimum of trade barriers and this is beneficial for the EU

as a whole. Individual climate policy initiatives risk to disturb normal trade patterns.

Take as example two identical steel factories, one in country A and one in country B that

have the same constant variable costs. In country A there is a high carbon tax and in

country B, there is a lax emission regulation. Country B will start exporting to country A

although this does not make any sense from an economic point of view as they have the

same technology and costs.

The EU reaches its overall emission reduction objective by using different policy

instruments for the big industrial emitters (the “Emission Trading System”) and for the

other polluters (home heating, transport, service sector). In fact the EU has two

objectives: the 20% reduction of GHG emissions but also a 20% share for renewables in


energy supply (mainly electricity production). For the big emitters every country receives

emission permits more or less proportional to an average emission rate and the type of

industrial sectors it has. The firms can then trade permits nationally and internationally.

Initially most permits were grandfathered (distributed for free) but there is a tendency to

oblige member states to auction a greater share of the permits. The member states are in

favor of this policy because it generates extra tax revenues without having to vote

(unanimously) on a carbon tax at EU level which would be virtually impossible.

The total emission reduction in the non-ETS sector has been set such that, overall, the

marginal costs of emission reduction in the ETS and non-ETS sector are not too different

(cfr. Table 4.3). As regards the distribution of efforts over EU countries for the non-ETS

sector, the countries with the cheapest options to emission reduction had to promise

larger emission reductions. But when this was a poorer and strongly growing country, the

effort required from the non-ETS sector in this country was reduced.

The instruments used for the non-ETS sector are left to the discretion of the member

states but policies that affect the intra EU trade are mostly taken in common. Important

policies in the non-ETS sector are fuel efficiency standards for cars, insulation standards

for buildings, subsidies for investment in low carbon equipment etc.


Table 4. 5 Results of EU carbon policy.

5. A closer look at the experience with the ETS in the EU

The ETS experience in EU is the first experience with a pollutant at a multi-sectoral scale

(the US has experience with sulfur trading in the electricity sector).

To start the ETS system one needs first a good record of past emissions. This was taken

from a database with all thermal plants large than 20Mw and preferably for 1990, a year

in which there was no interest yet in GHG emissions so that it was impossible to increase


emissions in order to receive more permits. The EC checked that not too many permits

were distributed as this would generate a very low price level for emission certificates.

Although the member states could auction 5 to 10% of the permits they received, only a

few states did this. New entrants received often free emission permits. Those who closed

their plant lost their permits. Those not complying (emission in firm > amount of permits

it had) had to pay a fine of 40 €/ ton CO2 in 2005-2007 and 100 €/ ton CO2 in 2008-

2012. This penaly sets a maximum price for the permits. Firms could “bank (save) or

borrow” emission rights that can be used in later years.

Overall the system worked well but there were large fluctuations in the prices (5 to 30

€/ton of CO2). The fluctuations were the result of different factors: learning by the

market players, changes in the total rights attributed by the Commission, expectations on

future economic activity etc..

What was the impact of the ETS system on industry profits? Several sectors had an

increase in profits, how can this be explained? A system of tradable permits always

increases the marginal cost of production even if the firm receives more permits than it

needs. The marginal cost increases because every unit produced requires some permits,

and every permit used for its own production reduces the amount of permits that can be

sold on the international permit market.

The effect of an ETS system on the price and profits of a sector can be analyzed using

Figures 4.10 and 4.11. Figure 4.10 represents the possibilities of emission reduction per

unit of output. The price of a permit implies that the sector will reduce emissions per unit

of output as long as the marginal cost of emission reduction is lower than the price of a

permit.


Initial emissionPer unit produced

Price ETSEuro/ton CO2

Marginal cost of emission reduction per unit of emission reduction)

Reduction of emissionsPer unit produced

Cost increase due to measures to reduceemissions per unit of product(= abatement cost)

Cost increase due to the purchaseOf emission rights

Figure 4.11 Two sources of abatement costs per unit of output produced

Output

Price

Demand

S=Marg Cost

S+Abatementcost

Spermit system

A2

A3

A1

D

Price of Emission permit

G

C

F

J

E

O1O3O2

Cost of permits bought or

Value of permits received

PriceIncrease

H

Figure 4.12 Effect on profits and prices of an ETS sector.


Figure 4.11 helps to define the upward shift of the marginal cost of production in figure

4.12. The first shift (D to F) from curve S to S+abatement cost represents the extra

abatement cost per unit of product (the triangle in Figure 4.11 corresponds to a cost

increase per unit of output). The second shift upwards (F to A2) corresponds to the need

for permits per unit of output (the rectangle in Fig 4.11 corresponds to an increase in cost

per unit of output).

The new equilibrium in Fig 4.12 is now A2 and this is the result of the cost increase and

the price elasticity of demand. The initial gross profit was H A1 C. The new profit level

after imposition of the ETS system is now J A2 F G when all necessary permits J A2 F E

have been grandfathered. When no permits are received, the gross profit is reduced to E F

H. So whenever the sector receives an important share (40 to 50%) of its previous

emissions as emission permits, the profits of the sector will increase. This will also

depend on the price-elasticity of demand, if this is low, it is easy to increase prices and

maintain profits. This is the case for the electricity sector.

The main challenges for the European ETS system are the price formation in an uncertain

world environment (cfr. Table 4.2) . The objectives for the EU depend on the cooperation

or not of other continents and on the integration or not of the other continents in the ETS

system. Indeed, if one opens to other countries with low emission abatement costs, this

reduces the equilibrium price of permits. On the other hand, if other continents have also

ambitious emission reduction goals, the demand for permits will increase and so may do

the price.

6. References

Barrett S.(1994), Self-enforcing environmental agreements, Oxford Economic Papers,

46, p 878-894

Barrett S. (2009), The coming global climate technology revolution, Journal of Economic

Perspectives, 23, n°2, p53-75

Delbeke J., Klaassen G., van Ierland T., Zpafel P., (2010), The role of environmental

poliy making at the European Commission, Review of environmental economics and

policy, vol4, 1, p 24-43


Mendelsohn R. , W. D. Nordhaus , D Shaw, (1994) The impact of global warming on

agriculture: a ricardian analysis. Amer. Econom. Rev. 84 , pp. 753–771

Stern R. (2008), The economics of Climate Change, American Economic Review, Papers

and Proceedings, 98, p2-37

Weyman-Jones Thomas, 2006, Current issues in the design of energy policy, Ch 33 in

Evans J., Hunt L., (eds.) International Handbook of the Economics of Energy, Edward

Elgar


Chapter 5 Coal

1. Outline

This chapter deals with coal. Coal covers 29% of the world energy needs and is the main fuel for power generation in the world. Its future is uncertain: there are abundant reserves but its use generates more air pollution and more GHG emissions than the other fuels.

We start the chapter with a small introductory section, dealing with conventions and definitions1. In the third section we survey the main uses, the main consumers and producers as well as the main trade flows. As coal is a scarce resource, it is important to know the total available quantity of coal. This is the topic of section 4. Section 5 presents some basic economic principles of the coal market. Section 6 discusses the history of the natural gas market. Section 7 presents a small model of demand and supply of the coal market.

2. Some conventions and definitions

Different types of coal For coal one distinguishes traditionally between peat, lignite and coal. Peat and lignite are precursors of coal that have lower energy density. Within the coal category there are many variants. Some coal types are better suited to make metallurgical coal, other types that are ideal for household use (anthracite), all coal can be used as fuel in power stations.

The heating capacity of coal varies from less than 28000 kj/kg for lignite to 35000 kj/kg for anthracite.

Units The heating capacity of 1 tonne of oil is more or less equivalent to the heating capacity of 1.5 tonne of coal.

Sources of data and forecasts

In this chapter we will use often data of IEA outlook 2008. This is not necessarily the outlook we prefer but it helps to put historic trends in perspective. The IEA outlook is based on many

1 For a good review of mainly technical issues in the gas industry see W.Van Herterijck “Aardgas , technische, economische en politieke aspecten”, ACCO, 2007


assumptions. The price of coal is expected to stabilize in real terms at 110$ per tonne or the equivalent of 22.5 $ / bbl2.

3. Main uses, consumers, producers and trade flows

Main uses

Coal has long been the dominant fuel replacing wood in the past. Coal is noawadays primarily used for power generation, for industrial heat production and home heating.

Use of gas Main substitutes

Home heating & cooking Gasoil, natural gas, firewood

Industrial heat generation

Fuel oil, natural gas

Power generation gas, nuclear, heavy fuel oil

The next graph shows that the consumption of coal is growing strongly in Asia (China, India) over the last years and is more or less stable in the rest of the world.

Main producers

2 Remember that in terms of heating capacity, 1 ton of oil = 7.33 barrels = 1.5 ton of coal


Production is also more or less stable in most continents but growing strongly in China and India.

The main producers are China, the US, India, Australia, South Africa, Russia, Germany..

Trade flows The major trade flows are from the exporters, Australia, Russia, South Africa,North America and Colombia to the main importers Japan, South Korea, India etc.


4. How much coal is there?

We know that for any resource, the reserves depend on two factors: the market price and the degree of confidence one has in the estimates.

There are ample reserves of coal and these are in addition distributed more equally than oil and gas.

conventional coal The proved reserves are of the order of 850 billion ton of coal or 565 billion TOE or 3.3 times the proved reserves of oil.

In addition, as no one seems worried about the extent of the reserves, much less efforts have been done to estimate the ultimate recoverable reserves.

non conventional coal There are two types considered. The first is in situ or underground coal gasification. A technique useful for the coal at large depth. Idea is to apply the technique to layers below 1000 m and to coal layers lying offshore. Estimates are 146 Trillion cubic metres. There is one successful plant in Uzbekistan where the gas produced is used to run a 400 MW power plant.

Coal mine methane is the second type of non conventional coal resource (one also calls it a gas resource as it produces methane).


5. Economics of the coal market

Opening the coal sector to foreign trade

The following two figures illustrate the effects on welfare of an opening of a sector to trade.

The first figure shows the situation without trade. The price is high in the potential importing country and low in the potential exporting country.

POTENTIAL EXPORTERPOTENTIAL IMPORTER

Q importing country Q exporting country

Marginal cost

Marginal costdemand demand

Equilibrium without free trade

P°imp

P°exp

How does one protect a sector from too much foreign competition? There are different ways of doing this: outlawing imports, put very excise duties, give very high subsidies to local production, impose regulations on imports that are very costly etc. Obviously, for a given degree of protection, some instruments are more efficient for a country than others: those that generate revenue for the government are better than those that impose extra costs on imports.

In the next Figure we allow free trade. There is a small transport cost. In equilibrium, the price in the importing country will equal the price in the exporting country + the transport cost per unit of the product.


POTENTIAL EXPORTERPOTENTIAL IMPORTER

Q importing country Q exporting country

Marginal cost

Marginal costdemand demand

import

export

P*impP*exp

P°imp

P°exp

Transport cost

A

BC

D E

F

Total gains from trade=ABC+DEF = - loss for producers in importing country+gain for consumers in importing country+ gain for producers in exporting country – loss for consumers in exporting country

The quantity of imports and exports are equal because there are only 2 countries trading. Both countries gain from free trade but in every country there will be losers and winners. In the importing country, the net gain equals CAB. This is the result of a gain for consumers, who have access to lower prices and have a gain in consumer surplus equal to P° A B P*. But there is also a loss for the producers who face lower prices, have to reduce production and see the price for the remaining production decreased. They lose P° A CP*.

Similarly in the exporting country: there is a net gain of DEF but a loss for consumers P*DFP° and a gain for producers equal to P*EFP°.

Coal has high transport costs Coal is costly to transport as it has low energy density. For this reason one prefers to generate electricity near the mine. When one has to export coal, one combines inland waterways, and sea transport.

Transport costs are an important determinant of coal trade and will be integrated in the modelling approach that will be presented later.

6. History of the coal market in Western Europe

Second World war - 1970 In this period there is a progressive opening of the European national coal markets to imports of coal. There were very large differences in production costs of coal: some countries had surface coal and thick layers, other countries had very deep mines (1000 m) and thin layers. As the coal industry occupied a large work force in many countries, it was difficult to open the coal sector to competition. This started with the European Union for Coal and Steel.


In Belgium as in most of Europe, the local coal production was threatened by cheap coal from abroad but also by cheap HFO and natural gas. This lead the government to protect the coal industry using a combination of techniques: subsidies for production, import quotas etc..

Even inside Belgium some regions were protected against the competition of other regions. The older mines in the Walloon region had higher costs than the Limburg region where production started after world war. The Belgian government restricted the output of Limburg coal in order to let the Walloon mines survive longer.

From 1974-2004 In this period there was a renewed interest in the use of coal. Prices of oil and later gas increased strongly and this gave rise to a much higher demand for coal. Power stations initially designed to burn coal, were transformed to use HFO in the 60 ties, switched to cheaper natural gas and were retransformed into coal powered stations.

The increased demand for coal was not planned, it was the result of the first and second oil price shock, so there were problems of capacity to meet demand and this led to strong price increases for international coal. There was a strong increase in coal exports (Figure 1). Prices increased strongly in the 70 ties but once capacity of production and transport (train, harbours) were adapted prices dropped (Figure 2).

Production expanded mainly in Australia because the South African apartheid regime was still facing a trade embargo. But also the large domestic US market became a net exporter when prices were high enough (Figure 3).



In Europe, the domestic coal industry was an important sector in terms of employment and managed to lobby for protection. Main arguments used were employment and security of energy supplies. One had to wait for the late 80 ties to find a political compromise to stop the production of coal in Limburg. In the 80 ties the real value added (measured at world prices without subsidies) of a person employed in the mine was only 20 to 30% of the added value in the rest of the industry. This means that whenever one can transfer a miner to a job in industry and he produces more than 30% of the average worker in industry there is an efficiency gain for the country as a whole.

Why did this transfer not happen earlier? The main reasons were first that the miner had a good wage (paid by subsidies) and the prospect to find another job is uncertain. Second there was the idea that the number of jobs is fixed: there is something like a stock of workplaces and it is very difficult that another industrial activity could be developed in that region.

The final agreement was based on the following idea: the expected subsidies for the next 10 to 20 years were given to a fund for local development. The fund was used to subsidize the employment of ex miners in other industries. The faster one closed the mines the more funds were available for development. This operation was a success and overall employment in Limburg increased.

From 2004 onwards We see that coal prices on the international market converge more and more.


Coal prices1987-2007

0,00

10,00

20,00

30,00

40,00

50,00

60,00

70,00

80,00

90,00

100,00

y e a r s

Nort hwest Europe marker pr ice †

US cent ral Appallachian

Japan coking coal cif

japan st eam coal cif

Important developments in this period are the high oil (and gas) prices in 2005-2008 and the interest for a limitation of the GHG emissions.

In the EU there is a strict limit on GHG emissions implemented via tradable permits. With high gas prices, the use of coal becomes more attractive but users of coal need much more CO2 permits. The GHG emission limit will be the binding constraint on the expansion of coal use in Europe.

In the rest of the world, there is not yet a binding GHG emission limit so that coal use will continue to expand in the US, China, India.

Also nuclear power can be considered as a strong competitor for coal powered stations but there is a long delay in having new power stations accepted. The competition of nuclear power will also be stronger when there is binding GHG constraint.


7. Modelling the world coal market

Perfect competition model We propose to model the coal market using a simple optimisation technique initially proposed by Samuelson (1952) and Takayama & Judge (1964)3. This can be used to simulate World trade flows if one assumes perfect competition on the world coal market.

Take i=1,...,N producers of coal with a convex continuous total cost function TKi(Xi) where Xi is tota production by I

There are j= 1,...,M consumers of coal with a Willingness to Pay function P(Xj)

The quantity deliverd by producer i to consumer j is called Xij and there are constant transport costs per unit Tij.

Besides perfect competition, we also assume that consumers are not interested in diversifying their supply.

The competitive equilibrium can be modelled by maximizing the sum of total consumer surpluses minus the production and transport costs:

0

M ax ( ) ( )

first o rder cond itions w ith respect to , , , , g ive you :

( ) 0 if 0

0 if 0

0 if 0

subst

jX

ij ijj j i i ij ij i i j i j

j j ijj i

i j ij i j

j j j

i i i

ij i j ij

T XP X d X TK X X X

X X

X X X

P X X

M K X

T X

' ' '

itu ting and in last equation one ob tains (at op tim um )

( ) fo r all i w here 0

and com bin ing 2 of the latter cond itions one has (a t op tim um ):

( ) ( ) fo r all , 0

i j

j i ij ij

j ij j ij ij ij

P X M K T X

P X T P X T X X

In the optimum, we find

a) that the price for each import line that is used by an importer should be identical.

3 Samuelson P., (1952) “Spatial price equilibrium and linear programming”, American Economic Review, Vol 42, n°3 p 283-303 and Takayma T., Judge G.G., (1964), “Equilibrium among spatially separated markets: a reformulation”, Econometrica, vol 32, n°4 , p 510-524


b) for each producer, the net revenue from all destinations that are used should be equal.

Non competitive models

Several non-competitive models have been proposed. One could use a Cournot model where the main exporters (Australia, south Africa, ..) control each their production and there is a competitive fringe. There is some evidence that exporters in Australia and South Africa control their exports via government regulations or private cartels. One of the problems of such a model is that the competitive fringe is very important: the US and China do not export a lot of coal but they have a large national market so their net export and import can react strongly to price fluctuations.


Chapter 6 Oil market

1. Introduction

This chapter deals with the most important energy vector: oil. It is still the type of primary energy that has the largest market share. In addition, it is the fuel that can be used for almost any energy need and, given its low transport cost, balances many energy markets in the world.

We start the chapter with a small introductory section, dealing with conventions and definitions. In the second section we survey the main uses, the main consumers and producers as well as the main trade flows. As oil is a scarce resource, it is important to survey what we know about the total available quantity of oil and what are the determining parameters for this estimate. This is done in section 3. Section 4 presents a few simple models that can be useful to understand the oil market. In section 5 we try to use different economic models to understand the history of the oil market over the last 50 years. Section 6 deals with policy questions on the oil market: what future can we expect? What can consumers do to keep prices low?

An appendix deals with the price formation of oil products.


The different types of oil We deal in this chapter with crude oil, the raw material that is, after a refinery process transformed into final products like gasoline, diesel, fuel oil, heavy fuel oil, bitumen etc. In a separate chapter we deal briefly with the refining and the price formation for the separate products.

For crude oil we distinguish between different types of products because they have a different cost structure and different properties:

Concentional Crude Oil: oil produced from conventional wells on land or on sea, at different depth, can have different gravities and sulphur contents. One uses often the API gravity (141.5/specific gravity)-131.5 where the


specific gravity of water is 1 and so the API of water is 10. The higher the API the “lighter” is the crude and the more light products (gasoline) one can extract out of a ton of crude. Light crudes are Algeria Sahara (44 API), Brent .., heavy crudes are coming from Venezuela, Alaska, etc..

The sulphur content of crude varies from more than 2.5% to less than 0.1%. Sulphur content matters because consumers prefer end products with a low sulphur content for environmental or other reasons.

Non conventional oil

This represents different types of oil that have lower quality (API<15) but could represent a resource stock larger than that of conventional oil.

“heavy oil” is a dense and viscous oil that requires usually the injection of steam and diluents in the reservoir to produce it.

“oil sands” (tar sand, natural bitumen) are mixtures of sand, clay and crude bitumen, - API is on average 8°

“oil shales” is a hard rock that contains oil

Natural Gas Liquids

Liquid hydrocarbons produced as a by-product in the production of gas. They represent a small source of oil distillates and are therefore often treated together with oil.

Units The oil industry uses mostly barrels and million barrels a day. We use the BP statistical yearbook conversion factors:

1 barrel is approx. 1/ 7.33 ton and this allows conversion to Ton oil Equivalent

1 million barrel per day = (1/7.33) (365) = 49.8 million tonnes per year

Sources of data and forecasts


In this chapter we will use often data of IEA outlook 2008. This is not necessarily the outlook we prefer but it helps to put historic trends in perspective. The IEA outlook is based on many assumptions. Important assumptions are a real oil price of 100 $/bbl in 2010 and 122$/bbl in 2030 as well as an economic growth in the world of 3.3% per year until 2030.


Main uses Oil has non energy uses (lubricant, feedstock for chemicals, bitumen for roads) as well as energy uses. Main energy uses are industrial heat, power generation, home heating and motorfuel.

It is relatively easy to substitute in most energy uses except as motorfuel.

Main producers The next figure gives the production of oil by region. Most important producers are Saudi-Arabia, Russia, US , Iran, Canada, Venezuela , ... The middle east producers together with Venezuela, Nigeria, Indonesia, o and the North African producers form the OPEC group that controls some 44% of total oil supply. So in the next figure OPEC is somewhat larger than Middle East + Africa. OPEC acts often as swing producer, sometimes acting as the dominant supplier that controls prices


Figure 6.1 Production of oil by region (source: BP statistical review 2008)

Some of the main producers are also large consumers. This is the case of the US and Russia. In the next Figure one sees the consumption by region. Important trends are the smaller consumption in Europe and the strongly increasing demand in Asia. The US consumption continues to increase.

Figure 6.2 Consumption of oil by region (source: BP statistical review 2008)


Trade flows The cost of oil transport is relatively small because large tankers can be used and the product is easy to ship. Any oil source can in principle be substituted by another oil source but there can be adaptation costs at the refinery.

Figure 6.3 Major Trade flows (source IEA, energy outlook 2006)

One sees that some regions are strongly dependent on imported oil. For many OECD regions it is 60% or higher.

4. How much oil resources are there?

We know that the quantity of oil depends on two factors: the market price and the degree of confidence one has in the estimates. We present here briefly three estimates: the IEA (OECD) energy outlook 2008, the EIA (Department of energy of US ) and finally a recent paper by Aguilera et al (2009). We will use million or trillion barrels of oil for estimates of oil resources. These can be compared with a present consumption of some 30 million barrels per year.


The IEA (OECD) energy outlook 2008 Best is to summarize their view in the following long term cost curve.

Figure 6.4 Long term oil supply curve (IEA, 2008)

In this figure the first block represents oil already produced. The next block is cheap oil from Middle East and Northern Africa followed by other conventional sources of oil. Then we have several blocks representing different techniques of enhanced oil recovery and oil produced in very different conditions. The oil recovery factor is very important as a doubling of the oil rovery factor from 30% to 60% doubles the quantity of oil that can be extracted from a given reservoir.

For the non conventional oil, the cheapest to develop is the heavy oil (mainly Venezuela), followed by bitumen or oil sands (mainly Canada). The extraction of oil from such resources is difficult and may requires a lot of energy and water as these processes require steam. The next resource category are the oil shales that require even more water and energy if the resources are not near the surface. So the extraction of non-conventional oil has an important CO2 emission drawback.

If one really needs liquid fuels one can also transform natural gas and coal into liquid fuels. As there is an extra conversion loss, this will only make sense if the energy need can not be satisfied by coal or gas directly.


This is a long term cost function and for the production to be available at these marginal costs, several conditions need to be satisfied.

First, some of the production needs first exploration (resources are there but “statistically”). Second, any production needs production capacity and this requires long deadlines if it involves difficult production techniques like in the case of production in deep sea. Investment in production capacity will only happen if the producer believes that future prices are high enough to guarantee a sufficient margin. The higher the risk, the higher the return required. Third some technologies are still under development and will only be available after 2030.

The Energy Information Agency view The EIA (US department of Energy) is responsible for a regular outlook on the world energy situation. Interesting feature is that they are bound by law to make all the information (and models) publicly available (http://www.eia.doe.gov/oiaf/ieo/index.html).

The EIA produces estimates of the total resource in place that contains past production (> 1 trillion barrels) and the total resource stock in the reservoirs. Production will be limited by the recovery rate.

http://www.eia.doe.gov/oiaf/ieo/index.html


Paper of Aguilera et al.1 These authors produce an estimate on the basis of USGS estimates of 2000 to which they add three new elements. First they estimate the potential of regions previously not assessed. Second they add future reserve growth . Third they add unconventional resources.

Details can be found in Aguilera et al. .The methodology is mainly statistical but is well documented in the paper. Unfortunately no confidence intervals are given. Here we concentrate our attention on the long run cumulative availability curve. The long run curve shows a much larger potential of conventional oil than IEA (some 50% more) and this at cost levels less than 50% of the ones mentioned in the IEA study. It is not clear why the cost levels are so different. One possibility is that the IEA adds a large risk premium to the capital costs before certain production potentials are made operational.

Also for unconventional oil does one find much more optimistic estimates in the Aguileras study than in IEA.

Overall if one believes the Aguileras study, oil would no longer be a very scarce resource as even with a demand growth of 5% per year, oil resources could supply demand for the next 70 years.

1 Aguilera R., Eggert R., Lagos R.,Tilton J. , « Depletion and the future availability of petroleum resources”, The Energy Journal (2000), Vol 30, N°1,


Figure 6.5 Cumulative supply curve oil resources

5. Three simple models for the world oil market

In the next sections we will discuss the history and possible futures of the oil market. We will rely on three simple economic models that we review in this section. The first model is a simple demand and supply model for one period with an exogenous OPEC production level. It will mainly serve to illustrate the difference between short and long run responses. The second model is a one period model where a cartel acts as dominant supplier. The third model is a multiperiod model where OPEC sets the prices and quantities to optimize its long term profits.

A simple oil market model with exogenous OPEC supply

The simplest model one can use is a model with linear demand and linear non OPEC supply function that is calibrated to long term equilibrium of the oil market. The data one needs to calibrate the model are limited to the


equilibrium price and quantity on the world oil market (say for a year), the exogenous supply by OPEC in that equilibrium as well as the short run and long run demand and supply elasticities. The starting point needs to be long term equilibrium.

In the first step one calibrates the long run model. The procedure is illustrated graphically in Figure X. One starts with the observation of a long run equilibrium P°,Q°, substracting the exogenous OPEC production gives the initial equilibrium non-Opec supply (point A). This initial non-OPEC supply, the price P° and the elasticity of non-Opec supply allows to find the long run (LR) non Opec supply that passes through point A. The LR demand function can be found by using the observed P°,Q° and the LR demand elasticity. It is important to use the elasticities in the observed P°,Q° as the price elasticities of a linear function are not constant.

LR demand

LR non OPEC supply

ExogenousOPEC supply

MarketPrice P°

Quantity

Price

Q°

OBSERVED P°,Q°

ADD Assumption onLR elasticity of Supply to have slope

ADD AssumptionOn LR elasticity ofDemand to have slope

A

Figure 6.6 calibration of the long term model

We can proceed the same way to find the short run (SR) supply and demand functions. These also have the point P°,Q° as an equilibrium but the demand and supply functions have a much stronger slope. This time we use the SR elasticities of demand and supply to calibrate the demand and supply functions. These are much smaller as it is much more difficult to react in the


short term than in the long term because one needs to adapt installations, train personel etc.2 The calibration is illustrated in Figure XX.

We use linear demand and supply functions. There are other functions one could calibrate to a long run equilibrium P°,Q°. An alternative is a constant elasticity function Q=aPb .

SR demand

SR non OPEC supply

ExogenousOPEC supply

MarketPrice P°

Quantity

Price

Q°

OBSERVED P°,Q°

ADD Assumption onSR elasticity of Supply to have slope

ADD AssumptionOn SR elasticity ofDemand to have slope

LR demand

LR non OPEC supply

Figure 6.7 Calibration of the short run demand and supply functions.

Once one has calibrated the short and long run model for the world oil market, one can use the model for comparative statics. An interesting exercise is to analyze the effect of a sudden reduction in the exogenous Opec supply. This is illustrated in Figure 6.8

2 Demand elasticities for durable goods (cars) can be larger in the short run because there is a stock of goods one can use for a longer time.


SR demand

SR non OPEC supply

ExogenousOPEC supplyINTERRUPTION

MarketPrice P°

Quantity

Price

Q°

INITIAL EQUILIBRIUMOBSERVED P°,Q°

LR demand

LR non OPEC supply

New short run equilibrium

New long runequilibrium

Figure 6.8 Effect in short and long run of a sudden interruption in the Opec supply.

The sudden reduction of OPEC production shifts the short run supply curve to the left, the intersection with the SR demand function gives a new SR equilibrium with a much higher price and quantity that is only reduced slightly. In Figure 6.8 we can also see that the new long run equilibrium involves much smaller price increase and a larger quantity decrease.

Pindyck and Rubinfeld3 started from the following data for 1997 : World price (18$/bbl), total demand and supply (23 billion bbl/year) and Opec supply of 10 billion bbl/year.

Using the following data on price elasticities:

PRICE ELASTICITIES Short run Long run

Demand -0.05 -0.40

Non Opec supply +0.10 +0.40

3 Pindyck R., D.Rubinfeld, (2001), “Micro-economics”, 5the ed., Prentice Hall , p50


As one can see, demand elasticities are always negative 4 and supply elasticities are always positive. The short run elasticities are much smaller than the long run elasticities.

Using this data, one can calibrate the following demand and supply functions:

(1) Short run demand D=24.08-0.06P

(2) Short run non Opec supply S=11.74+0.07P

(3) Total SR supply TS=21.74+0.07P

And the long run functions:

(4) Long run demand D=32.18-0.51P

(5) Long run non Opec supply S=7.78+0.29P

(6) Total LR supply TS=17.78+0.29P

We can now compute the possible effects of an interruption of 3 million bbl of OPEC oil using these two systems of equations.

For the short run equilibrium we need to solve the system of equations (1) + a new total supply function TS=(21.74-3)+0.07P and this gives a new short run equilibrium where P=41.08 $/bbl and Q=21.62.

For the long run equilibrium we need to solve system (4) + new total supply function TS=14.78+0.29P and this gives a new equilibrium price of only 21.75 $/bbl and a quantity of only 21.66 $/bbl.

This very simple model already shows an important characteristic of the oil market that is often forgotten: unexpected supply interruptions generate very strong price increases in the short run but after a few years the supply and demand response to a price increase is much larger and the remaining price increase is much smaller. One could also analyse the effect of unforeseen shifts in demand. These could be generated by problems in the supply of a substitute to oil (natural gas). Once one knows the amplitude of the shift one

4 This holds for the oil market but does not need to hold at the level of one private consumer where we only know that the sign of the compensated price effect is negative.


can, using the same procedure, analyse what is the effect of this shift on prices and quantities in the short and long run.

OPEC as dominant firm in a one period model OPEC can be considered as a cartel where producers agree on the total quantity produced and on the allocation of production among their members such as to minimize costs of production. If this is the case, OPEC can be considered as a dominant supplier because it can supply more than 50% of the market and the other suppliers (called “competitive fringe”) are all smaller producers that take the market price as given. This is also called Stackelberg equilibrium.

The implications for the equilibrium on the oil market can be derived in two steps:

Step 1: construct the residual Demand function for OPEC oil by subtracting for each possible price level the competitive supply from the world oil demand

Step 2: Derive OPEC’s optimal production by considering it as a Monopolist confronted with the residual demand function for OPEC oil and a cost function that is the aggregate cost function of the OPEC members.

Using linear demand and supply functions, one can derive an algebraic expression for the dominant supplier model.

Demand for OPEC oil equals (for any price) the difference between world oil demand and competitive supply:

0opec m csD D S

Using a linear competitive supply function:

tt

pq

d

As well as a linear world demand function:

tt

p aq

b


One obtains the residual OPEC oil demand function (for the prices where the competitive supplier is also active):

( ) ( )* topec

da bc b d pD

bd

Figure 6.9 Demand function for dominant supplier

In the second step we derive the optimal production of OPEC. We use for this a constant marginal cost z and look for the optimal price p*:

*

( *( ))( * )

p

da p b dMax p z

bd

*

2 2( )

z adp

b d

and * ( )

2

ad z b dq

bd

We see that the price of the supplier is increasing in his own marginal cost (z) and in the choke price (a) . A monopolist will “absorb” half of the increase in

the marginal cost and this is what we observe here (* 1

2

p

z

).

We see that the price p* is also increasing in the slope (d) of the supply function of the competitive fringe supply: a high slope means that the competitive supply has strongly rising marginal cost so that a price increase


does not generate a strong increase in competitive supplies. This helps the dominant supply to set high prices. In general, the smaller (in absolute value) the price elasticity of world oil demand and the smaller the price-elasticity of the competitive supply, the less elastic will be the residual supply for OPEC oil and the higher will be the price charged by the dominant supplier.

The next figure shows the optimum for the dominant supplier. As in the case of a monopolist, the equality MR (MO in Figure 6.10) = MC (MK in figure) determines the optimum quantity and price.

Figure 6.10 Optimal production for a dominant supplier

OPEC as dominant firm in multi-period model We can elaborate the previous model by adding a reserve constraint for the dominant supplier so that OPEC has to distribute its production over time using the Hotelling rule for a monopolist. We will also add the supply of a backstop technology.

De Keyzer5 constructed a spreadsheet model to test the effects of different parameters on the OPEC strategy if it would follow a Stackelberg (or

5 T. De Keyzer, “Modellering van de oliemarkt met backstoptechnologieën”, Verhandeling Master Economie, 2008


dominant supplier) strategy that maximizes discounted profits over time. The parameters used are (initial equilibrium in 2005):

World demand price elasticity = -0.5

Exogeneous growth in demand for oil: 1.76% per year

World elasticity competitive supply conventional oil = +0.35

Price elasticity backstop supply = + 0.35

Average price in initial year = 42.3 $/bbl

Initial quantity world market = 82 Mio bbd

Initial competitive supply of conventional oil = 48 Mio bbd

Initial Backstop oil supply = 3 Mio bbd

Technological progress in backstop = cost reduction of 3% /year

Marginal cost of OPEC oil increases with 0.0167 $ per Billion bbl

Discount rate = 2.55%

Reserves OPEC: 915 billion bbl

The model is solved using periods of 5 year. The model is simplified: one looks only at stable long term strategies and no total resource constraint was taken into account for the conventional non-OPEC oil and for backstop oil.

The results of this type of model are summarized in the following 2 tables:

Price in $/bbl

Production of OPEC million

bbl/day

2005-2010 40 44.8 2011-2015 45 50.2 2016-2020 50 56.1 2020-2025 55 62.7 2026-2030 61 70.0


According to this optimisation, it is in the interest of the long term profits of

OPEC to increase its supply of oil gradually, increase its market share and

have a price that is gradually increasing. This results in backstop oil supply

that remains rather low. Apparently it is not in the interest of OPEC to use

all its oil. This could be due to three factors: the limited horizon (25 year), the

low elasticity for OPEC oil approx -0.675 = -0.5 – (0.5)(0.35) that makes

price increases less interesting and the increasing marginal cost of OPEC oil.

Market share OPECMarket share

competitive supply Market share

backstop 2005-2010 47 50 3,42 2011-2015 49 48 3,63 2016-2020 50 46 3,84 2020-2025 52 44 4,05 2026-2030 53 42 4,27 Some comparative statics:

The growth rate of demand is an important parameter. It increases the market share of OPEC and this allows it to increase its price. Prices increase from the first period onwards because the opportunity cost is higher in the next periods. The resources of OPEC are fully exhausted (they are taken as fixed here and this is an irrealistic simplification).


different growth rates of demand

0

20

40

60

80

100

120

140

160

180

Periode 1 Periode 2 Periode 3 Periode 4 Periode 5

p

Ref. Scen.

5% groei wereldvraag

0% groei wereldvraag

Figure 6.11 price of oil that max profits of OPEC for different growth rates

6. Understanding the history of the world oil market

Before 1970

History of oil prices is a history of cartels and monopolies even before OPEC became the dominant supplier. As early as 1870 did Rockefeller acquire a monopoly for oil supply in the US with the “Standard Oil Company” and controlled 90% of total supply. After the breaking up of the monopoly in 1911, Rockefeller was followed by the 7 sisters (Esso, Gulf, Texaco, Mobil, Socal, BP, Shell). Some of the 7 sisters originated from the breaking up of the Standard Oil Company. The origin of the “Royal Dutch Shell” is the production of oil in Indonesia, for BP, it was the discovery of oil in the Middle East. Both regions are former colonies of the Netherlands and the UK.

After the 2nd world war, the 7 sisters controlled total oil output as a cartel. One of the big problems of any cartel is to control each other’s output. This was done by a system of co-ownership in each other’s production facilities.


The 7 sisters controlled also sea transport, the refineries and the distribution so that the cartel was very effective.

OPEC was created in 1960 in a response to a fall in tax revenues that originated from a recession and the control of prices by the 7 sisters. OPEC nationalised most of the production. But OPEC was not really capable to increase prices as the 7 sisters also controlled the downstream operations.

Figure 6.12 Real oil prices over time (Source: Hamilton (2008))

1973

This is the “first oil shock”. This was not a deliberate action by OPEC but rather the result of a response by Arab countries to the Yom Kippur war where Israel tried successfully to conquer some strategically important neighbouring land. The Arab coalition denied oil deliveries to “the friends of Israel”. This is not really possible as oil, once on a tanker, can be sold to the highest bidder. The result was a restriction of supply and a strong increase in prices. OPEC realised (almost by accident) that it had market power and there was a belief that prices will stay high forever. In this period the economy was growing very quickly, oil was taking over from coal and all this resulted in a strong growth rate for oil (8 to 10% per year before 1973).


Initially there was a belief that oil demand will simply not react to a higher price. This is correct in the short term but not in the long term. Demand response was to switch to natural gas, coal and nuclear. Converting coal power stations to oil and back to coal or converting oil powered stations to gas does not take much time. Building new nuclear power stations or building new oil platforms in the North Sea takes 5 to 10 years. So the full response to the oil price increase takes time and was hidden by an economy that kept growing.

Gately (1995)6 presents the history of the oil market using two diagrams:

Figure 4.13 Gately’s (1995) interpretation of oil market developments

6 Gately D.,”Strategies for OPEC’s Pricing and Output Decisions” , The Energy Journal, Vol 16, n°3


In the first diagram the real oil price is related to the output of OPEC and level curves for OPEC revenue (price times OPEC output = level of revenues for OPEC) show what happened to OPEC gross revenues over time. The second diagram shows the OPEC output and the non-OPEC output so that rays from the origin show the market share of OPEC.

We know that a dominant producer can only control prices if his market share is large enough: 50% or more. If his market share is too small, any attempt to increase prices by reducing output generates an expansion of the output of the non cartel members so that price increases are costly for the cartel. In the period 1968 to 1973, one sees a strong expansion of demand for oil (at constant price) and it is mainly OPEC that satisfies the increase in demand. This meant its share came close to 2/3 of the market. In these market conditions, the oil production decrease of 1973 worked and allowed to more than double oil revenues of OPEC in the period 1973 to 1979.

1979-1980

With the Iranian revolution at the end of 1978, oil production of Iran decreased and none of the OPEC countries wanted to increase production. This generated the “second oil shock”, prices doubled again and so did the revenues of OPEC

1980-1985

It is now more than 5 to 10 years after the first oil shock so that demand substitution and non-OPEC production can really react. Moreover the Western economies are in a recession. So total demand for oil and for OPEC oil decreased. In addition Iran and Iraq fought a war and needed oil revenues to finance it. OPEC has to decrease its output in order to maintain the price. OPEC tried to defend the price until 1985-1986. Saudi-Arabia as largest producer cut back its production from 10.3 million bbl/day in 1980 to 3.6 million bbl/day in 1985. But prices decreased strongly and the largest OPEC members decided to regain market share by increasing their production (Saudi-Arabia increased its production in 1986 to 5.2 million bbl/day).


Figure 4.14 Production of Iran and Iraq (source: Hamilton)

With hindsight, OPEC could have done much better by using more prudent price increases. There are different explanations for the cartel behaviour that tried to defend the irrealistic price increase in 1980. A first is that OPEC was not aware of the stronger longer term demand and supply response. One can indeed find official statements that go along that line. A second is that the different cartel members had different interest: some want to maximize revenue in the long term because they have ample reserves and do not want to push the development of substitutes too much but others go for the high revenues in the short term (members with small oil reserve base and large population like Algeria). There was often disagreement between the different groups within OPEC because it is difficult to share the costs of output restriction.

1986 – 2004

This is a period with strong price fluctuations and different attempts by OPEC to regain control. At a certain moment prices decreased below the 10$/bbl and the expensive oil producers (North Sea) were fearing bankrupty.

OPEC tried to control output much better but this was often difficult as the smaller members had an interest to sell oil unofficially (via barter trade etc.). OPEC also tried to made agreements with Russia and Norway (expanded output from 0.8 Million bb/d in 1985 to 3.3 Million bb/d. There was also the


invasion of Kuwait by Iraq in 1991 but this had only a small effect on the oil price.

2004 – 2008

There was again a strong price increase. There are several factors. First demand in newly industrialised countries was growing more strongly than expected. Second the last 20 years was a period without any real high and stable prices, so there were less investments in oil supply. In the case of non-OPEC oil, the strong fluctuations in the prices were not very encouraging for investors. In the case of OPEC oil, most production was nationalised and extension of supply was the priority. Third, some sources suspected speculation by the financial markets.

Hamilton’s statistical analysis of the fundamentals of oil prices

Up to now we used an ad hoc explanation using simple demand and supply basics. One can also try to test statistically the real factors driving the oil prices. Hamilton7 (2008) has tried to explain oil prices over the period 1970-2008.

1. A first model is a pure random walk model without any fundamental factors, prices are a function of the changes in the past with an error term. This model could not be rejected and the result is that “oil prices are not predictable in the short term”.

Using the estimates, and starting with a price of 115$/bbl, the uncertainty is such that one may end up, after 4 years , with a price as low as 34$/bbl or as high as391 $/bbl.

2. In the following models Hamilton brings in some economic theory. A first bound on price fluctuations comes from the possibility to store oil Denoting the cost of storing oil by C and using an indterest rate I, the expected price of oil should be larger than todays ‘ price + storage cost (rental cost of

7 Hamilton, (2008) “Understanding crude oil prices”, discussion Paper UCEI, Energy Policy and Economics n°23


facility+interest on cost of oil).If this does not hold all investors would buy oil now and increase their sales net year:

This theory is unable to predict large changes in oil prices.

The same holds for the futures markets: arbitrage between spot and future markets guarantees that the current spot price is a good indicator for the foreseeable changes at a horizon of a few years.

3. The next model is a model testing the hotelling scarcity rent. This implies that the margin (Price-Marginal cost) should rise at the rate of interest:

Different empirical tests do not confirm this hypothesis for the period 1970-2000. In more recent years, there are several statements by OPEC countries that point to a limitation of production to safeguard oil for their descendants. So it is only recently that the scarcity rent may explain price movements.

4. In principle there is a cartel controlling the total output and the price. It is clear that sudden supply interruptions have strongly influenced prices at certain moments (1973, 1979, 2000). But in order to control prices continuously, OPEC needs a system of production quota that is observed by its members. The following figure (Hamilton,2008) shows that the production quota are regularly exceeded by some of the members.


Figure 4.15 Quotas and actual production levels for 5 most important OPEC members

7. And the future?

If we would know the future oil prices and are ready to take a gamble, we

would become very rich. The oil market is probably like the stock market: all

available information is included in the present price.

But there are a few elements that help to explain what is more likely to

happen:

a) demand and supply take time to react to uncertain events


b) OPEC’s market share is likely to increase as they have cheap oil and can

extend their production capacity when they want to

c) at low prices, oil demand is growing in the world as long as there is no

cheap substitute available

Putting fundamentals of demand and supply together, most sources expect

prices in the 50-70 $/ bbl range – according to the IEA, real prices of the order

of 125 $ in 2010-2030 could be an equilibrium.

8. Policies to stabilise or decrease oil prices

The Western consuming countries have experienced large fluctuations in oil

prices and this has generated large oil rents in the Middle East and in other

producing countries. Four types of strategies have been followed to address

this problem: emergency and strategic stockpiles, import taxes, lower oil

dependency and a strong climate action.. We discuss them one by one.

Emergency and strategic stockpiles

Most consuming countries have a stock of oil for at least 3 months. This can

serve for emergency situations. Some countries have a larger stock and can

use this stock when they fear that prices are “manipulated” and are too high.

The use of stockpiles is not so easy. There are two problems. First the simple

fact that one country uses its stockpiles can be interpreted by all other

consumers that there is a very severe shortage and this may increase the

demand and drive up prices. Second, every country that uses its stockpiles

increases supply on world market and this benefits all consumers on the oil


market. When that country is rather small, the action may not have a large

effect.

Import taxes

In a competitive market it pays for the consuming countries to coordinate

their actions and to impose an import tax. This type of action can positively

influence the terms of trade (here the import price would decrease). Again all

consuming countries can gain by this action but there is a benefit for each

country to encourage the other countries to do this but not to do it yourself.

The EU has traditionally a higher tax on oil products than the US (think

about gasoline). An optimal coordinated import tax for oil would be much

higher. Another weakness of this approach is that it assumes non strategic

supply behaviour from the side of OPEC. This is somewhat unrealistic as

OPEC can, as dominant supplier, also act strategically.

Decreasing the oil dependency of the economy

This policy has been taken by most consuming countries. They encouraged

the switch to nuclear, coal and gas and encouraged a lower oil demand for the

transport sector.

Climate Change policy and the world oil market

One of the possible developments is a strong climate action in the world. This

could be implemented by a set of tradable permits or a set of carbon taxes.

Some politicians count on a double benefit from a carbon tax as this tax

would decrease oil demand and decrease the import price of oil.


According to Johannson et al (2009) a strong world wide climate change

policy would actually increase the oil rents of Opec if it acts as dominant

supplier. The main reason is that the oil substitutes (based on coal or

unconventional oil) are also Carbon intensive so that a carbon policy would

reduce the threat of cheap substitutes for oil. A world wide carbon policy

would reduce the oil rent if one implements a policy based on renewables and

on energy efficiency.

9. References

Aguilera R., Eggert R., Lagos R.,Tilton J. , « Depletion and the future availability of petroleum resources”, The Energy Journal (2009), Vol 30, N°1 De Keyzer, T. “Modellering van de oliemarkt met backstoptechnologieën”, Verhandeling Master Economie, 2008 Gately D.,”Strategies for OPEC’s Pricing and Output Decisions” , The Energy Journal, Vol 16, n°3 Johansson D., Azar C. Lindgren K., Persson T., 2009, OPEC Strategies and Oil Rent in a Climate Conscious World, The Energy Journal, Vol. 30, No. 3 Hamilton, (2008) “Understanding crude oil prices”, discussion Paper UCEI, Energy Policy and Economics n°23 IEA, Energy Outlook 2006, IEA, Energy Outlook 2008


Chapter 7 Natural Gas

1. Outline

This chapter deals with natural gas. As it covers 21% of world energy demand and has been growing strongly over the last 30 years, it merits our attention.

We start the chapter with a small introductory section, dealing with conventions and definitions1. In the third section we survey the main uses, the main consumers and producers as well as the main trade flows. As gas is a scarce resource, it is important to know the total available quantity of gas.. This is the topic of section 4. Section 5 presents some basic economic principles of the gas market. Section 6 discusses the history of the natural gas market. Section 7 analyses in more detail a model for the European gas market that focuses on the impact of the liberalisation. Section 8 discusses the reliability of Russian gas supply in Europe, one of the main policy concerns in the EU.


Different types of gas Gas is usually a mix of different types of gasses. Most important for us is the heating capacity of the gas. In European cities one started by using gas manufactured on the basis of coal, so called “town gas”. This was a gas with a much lower heating capacity (24 Mj/m³) than the gas we use nowadays: 36,9 Mj/m³ for Slochteren (NL), 40,7 Mj/m³ for North Sea gas and 42,9 Mj/m³ for Algerian gas.

As long as this heating capacity of the gas is not too different, they are considered substitutes in terms of Mj delivered. In Belgium, the Northern part received the Dutch gas (lower heating value), the rest receives Norwegian and other richer gas.

1 For a good review of mainly technical issues in the gas industry see W.Van Herterijck “Aardgas , technische, economische en politieke aspecten”, ACCO, 2007


Units The gas industry has its own units. Volumes are important for transmission so one uses m³ and cubic feet, for customers it is the heating capacity that counts.We use as much as possible the conventions used by BP statistical review of World energy. Useful for us:

1 billion m³ natural gas = 0.9 MTOE = 36 Trillion Btu = 38 Trillion kJ

Sources of data and forecasts In this chapter we will use often data of IEA outlook 2008 and 2009. This is not necessarily the outlook we prefer but it helps to put historic trends in perspective. The IEA outlook is based on many assumptions. Important assumptions are a real oil price of 100 $/bbl in 2010 and 122$/bbl in 2030 as well as an economic growth in the world of 3.3% per year until 2030. The relative price of gas compared to oil products is kept constant in the IEA outlook 2008. This is a working assumption and not a market equilibrium.

We will also use the BP statistical review and outlook 2010.


Main uses

Manufactured gas (on the basis of coal) was initially mainly used for lighting and cooking in cities and in some industrial processes. Gas has not really a captive market. With the arrival of natural gas in the EU (much earlier in the US), gas is used for cooking, home heating, industrial heat, chemical feedstock and power generation. In these different applications, the substitutes differ as shown in table 1. At present natural gas is only rarely used as energy source for transport. In some countries (Italy) there is a small fleet of natural gas cars and in some cities, busses and special purpose vehicles are adapted to use natural gas mainly because of environmental reasons. Gas can be used in gasoline and diesel engines when an appropriate tank for compressed natural gas is build into the vehicle (cfr. LPG vehicles) and when there is a distribution network. In a few countries like Italy there is significant share of vehicles running on natural gas. In several cities


busses run on natural gas as this reduces the emission of small particles. Natural gas will probably first enter the transport market via use for busses and trucks. An other option is the conversion to methanol that can be used by gasoline engines (MIT,2010).

In Belgium, residential and tertiary use (cooking, home heating) accounts for 1/3 of natural gas consumption, industrial use and power generation each account also for 1/3 of total use.

Use of gas Main substitutes

Cooking Electricity

Home heating Gasoil, previously coal furnaces

Chemical feedstock Naphtha

Industrial heat generation

Fuel oil, coal in the past

Power generation Coal, nuclear, heavy fuel oil

Transport Oil products

Table 1 Main substitutes for natural gas

Figure 1 shows that the consumption of natural gas has been growing continuously in almost the whole world. The transport of gas requires a specific distribution network and is therefore more costly than the transport of oil and coal. For this reason, natural gas consumption is stronger in regions that had early and cheap access to natural gas (US). Most growth is expected in the Middle East and in Asia. In the Middle East producers avoid the costs of gas transportation by producing chemicals at home and using the gas for energy purposes so that more oil can be exported. In Asia, the natural gas is a clean substitute for coal in cities and industries.


Figure 1

Main producers Figure 2 shows that the US production is relying more and more on unconventional gas. Europe is more and more dependent on pipeline imports (Russia) and LNG imports from North Africa and Middle East. China will rely more and more on unconventional gas (shale gas, Coal Bed Methane) and also syngas produced from coal.


Figure 2

The production of unconventional gas has become interesting by the higher prices and the development of better techniques.

Trade flows Gas can be transported by pipeline and by LNG tanker. By pipeline for distances of up to 5000km in pipes of up to 1.5 m diameter and at pressure of 70 bar. This means an average speed of 30km/h. Since the 70 ties LNG transport is developing and is becoming more interesting for longer distances. LNG also offers more flexibility to the exporter and to the importer. The exporter can more easily chose other customers and vice versa for the customer who is less dependent on his pipeline2.

Intercontinental transport requires in general LNG transport (except Algeria to EU). The next Figure gives possible intercontinental trade flows for 2015 and 2030 compared to 2007. As can be seen, most flows increase. The EU is importing much more from Russia and the Middle East (Qatar). Imports by

2 See Van Herterijck (2007) for a more technical description of gas transport and handling.


North America are expected to decrease because of the increased (unconventional) gas production in the US and Canada

Figure 3 Intercontinental flows of natural gas (source IEA outlook 2009)

The main exporters of natural gas via LNG are Qatar, Algeria and Indonesia. Where Indonesia is mainly delivering to the Asian market. Algeria is mainly delivering to Europe and where Qatar delivers to Europe and Asia. Russia exports most of its gas via pipelines but is also entering the LNG market.

The next two figures report on LNG terminal extensions.


OX

FO

RD

INS

TIT

UTE

FO

R E

NE

RG

Y S

TU

DIE

S

22

European LNG TerminalsEuropean LNG TerminalsEuropean LNG Terminals

Source: J.Stern (OIES)

OX

FO

RD

INS

TIT

UTE

FO

R E

NE

RG

Y S

TU

DIE

S

24

Atlantic Basin LNG TerminalsAtlantic Basin LNG TerminalsAtlantic Basin LNG Terminals

Source: Suez

Source: J.Stern (OIES)

4. How much gas is there?

We know that for any resource, the reserves depend on two factors: the market price and the degree of confidence one has in the estimates (Cfr


Chapter 2). It is important to make a distinction between conventional gas and non conventional gas. The next figure (IEA 2009) ranks the different types of gas and their volume for the world.

A distinction (IEA – WEO 2009) is made between:

- conventional gas (estimate of current reserves at present prices and costs) According to the IEA outlook, conventional resources of gas are of the same order of magnitude as those for oil.-

- tight gas: is a resource that can not be profitable developed with vertical wells due to low flow rates (low permeability of the rocks) ; this resource can be exploited using hydraulically fracturing (or cracking open) in order to release the gas. The fracturing is done by pumping into the well water, chemicals and sand at high pressure—this type of gas is being produced since many years in the US and Canada

- shale gas: rock formations that are rich in organic matter and are both source and storage of the gas. The exploitation of this resource requires opening the rock formations and requires more equipment and lots of water to be pumped in the reservoirs. It requires also solutions for the water that is produced together with the gas.

- coal bed methane (CBM): is the natural gas contained in coal beds that are too deep or too narrow to be exploited as coal supply – the production requires again a lot of equipment and water to extract the gas from the coal beds. The production is growing rapidly in the US3. This production can in certain circumstances be combined with the storage of CO2 because fractures in the structure of coal can absorb twice as much CO2 as the methane it initially contained.

- sour gas: gas that contains a lot of H2S and needs extra processing before it can be used – often associated to oil wells

- hydrates: These are crystal-like solids that are formed when methane is mixed with water at low temperature and moderate pressure. They are found offshore and in Arctic regions. The estimates of reserves vary between 2500

3 There have been experiments to produce coalbed methane in the Walloon region and in the Campine region but the productivity was insufficient.


and 20 000 tcm. These are abundant reserves but they will be costly to produce.

This figure (source IEA 2009) combines quantity of reserves and marginal costs. The right had side of the figure gives an idea of the transport costs that need to be added for pipeline and LNG transport.

Aguileras et al (2009) pay more attention to the regions that have in the past not yet explored thoroughly and this results in reserve estimates with an order of magnitude 5 to 10 times higher than the IEA estimates.

The EIA (2011) produced recently a new assessment of the non-conventional shale gas reserves for some regions (see table). We see that in the EU, Poland and France have considerable shale gas reserves. The overall shale oil reserves for the regions studied are 6 times as large as the conventional gas reserves.

The first problem in the exploitation of the non conventional gas reserves is that one needs a lot of land as one needs to drill a lot of wells and equipment. There is also the environmental problem associated to the use of large quantities of water needed for the exploitation. Finally the use of gas itself produces less carbon per unit of energy but the production of non conventional gas is energy intensive and may compensate this advantage of natural gas.



5. Economics of the gas market

The gas industry is characterised by high transport costs and a transport and distribution network that is dedicated to a particular production site and or customers. This explains how the industry developed. We focus here mainly on Europe.

High transport costs Whether one transports gas by pipeline or by LNG tanker, transport operations require always a large upfront investment. One can only start production once the infrastructure is fully in place.

Transport by pipeline is also characterised by economies of scale: the volume that can be transported is more than proportional to the diameter while the costs are also less than proportional to the diameter. Increasing capacity by 10% generates a cost increase of only 6%4 .

In the transport by LNG, there are economies of scale in the liquefaction and regasification plant and in the ships used. Ships have a limited capacity per unit (125-170000 m³) – the number of ships needed depends on the distance.

The hold-up problem for specific transport infrastructure The pipeline constructed to connect one production site with a customer is often very specific: example of Seapipe that connects a Norwegian Gas field to Zeebrugge. In the past this pipe was only meant to supply the Belgian gas company. It is an investment specific for that link without any other possible use.

Costly investments that are specific to serve one customer are at the origin of the so-called hold-up problem. This is the risk that the customer, once the supplier has built the specific transport infrastructure, wants to renegotiate the contract. As the infrastructure can not be used for other purposes, the customer can threaten to pay a much lower price than the price originally agreed. The supplier has no choice but to accept the new deal. One can try to enforce the original contract but the enforcement of international commercial 4 See Van Herterijck, op cit. p64-67


contracts is weak. The main enforcement mechanism is reputation: a customer that does not comply will have problems to obtain new long term contracts.

Another solution that is often used is to ask the customer to participate in the transport investment. This solution was common in Western Europe.

Price discrimination Whenever there is one importer who controls the transport network, this importer can use different prices for the same good delivered to different customers. In this way the importer can maximize his profits. The following graph shows how an importer facing two different clients (industry and residential) can increase his profits by selling at higher prices to the residential sector (higher willingness to pay and lower elasticity of demand) than to the industrial customers (more substitutes available so higher elasticity of demand). In Belgium Distrigas had the legal monopoly for importing gas and sold at different prices according to the type of industrial sector: sectors that could not easily substitute gas paid a higher price. Nowadays such a practice would no longer be allowed and would no longer be possible because Distrigas has no longer the monopoly of gas trading.

Prijsdiscriminatie

MRce

Vraag centrales

MK (invoer)

Q

Prijs, MK

Vraag residentiele sector

Pres

q*re q*cen

MRre

Pce


Netback pricing of natural gas and take or pay contracts An importer can only guarantee to sell a given volume of gas if the price is competitive on his market. When the prices of substitutes vary, one needs a system of price indexation to guarantee the sales. In the gas industry, the importer usually also controlled the transmission network so that he can discriminate prices. Many import contracts used the netback technique to specify the import price of gas. The principle is explained in the following figure where gas is sold to two types of uses: industrial consumers whose alternative fuel is HFO and residential heating customers whose alternative is gasoil. The maximal import price of gas for industrial use is then the consumer price of HFO (containing often a specific tax on sulphur content) minus the transmission cost of gas. The maximal import price of gas for residential use is then the consumer price of gasoil (containing often also a specific tax on oil products) minus the transmission cost and minus the distribution cost. The import price of gas is then a weighted average of the two maximal import prices where the weight equals the share of both types of customers. This is only possible if the importer can price discriminate on his internal market. The figure makes clear that gas exporters and sellers were very much in favour of an environmental tax on oil products. With this guarantee on competitiveness of the imported gas, importers could accept take or pay clauses that force an importer to import a given quantity with a take or play clause: even if not imported it has to be paid.

Price/GJ

Consumer priceGasoil heating

Consumer priceHFO

MaximumConsumer priceGas to industry

Maximum Consumer priceResidential heating

tax

tax

Transmissioncost+ margin

TransmissionCost+margin

DistributionCost+margin

MaximalImport Price cif

MaximalImport Price cif

Netback price principle to determine GAS import price = weighted sum of consumer prices of substitutes – costs of transmission and distribution

Figure: Netback price principle


Take or pay clauses were interesting for the exporters because this allows to guarantee a given volume of sales and this helped to use optimally the production and transport capacity..

A Cournot equilibrium In the European (and Asian) natural gas market there used to be a limited number of suppliers: Norway, Netherlands, Algeria, Russia….for the same product (a GJ of natural gas). How much will each be able to sell? The equilibrium concept that is often used in economics is a Cournot equilibrium. In a Cournot equilibrium every supplier sets the quantity he want to sell, given the quantity that is decided by the other suppliers. He sets this quantity as monopolist on the remaining market. An equilibrium is reached when all quantities produced are mutual best replies: when the quantity sold by him is the best answer to the quantity chosen by the other suppliers and vice versa. This is a non competitive equilibrium.

Take an example5 with two suppliers 1 and 2. In the next figure we determine in a first step the optimal quantity to supply to one given market for supplier 1 for different quantities supplied by firm 2 (0,50,75). For each of the quantities produced by firm 2, firm 1 is a monopolist for the remaining demand and chooses the optimal quantity by equalising marginal revenue and marginal cost. His optimal production will be (50, 25, 12.5). This information can be summarised under the form of a reaction function: what is the optimal production of firm 1 given a production level of firm 2.

5 Example taken from Pindyck & Rubinfeld



LEUVEN

CENTRUM VOOR ECONOMISCHE STUDIEN

MC1

50

MR1(75)

D1(75)

12.5

If Firm 1 thinks Firm 2 will produce75 units, its demand curve is

shifted to the left by this amount.

Q1

P1

What is the output of Firm 1if Firm 2 produces 100 units?

D1(0)

MR1(0)

If Firm 1 thinks Firm 2 will produce nothing, its demand

curve, D1(0), is the market demand curve.

D1(50)MR1(50)

25



MC1

50

MC1

50

MR1(75)

D1(75)

12.5



MR1(75)

D1(75)

12.5



Q1

P1

What is the output of Firm 1if Firm 2 produces 100 units?

D1(0)

MR1(0)



D1(0)

MR1(0)



D1(50)MR1(50)

25



D1(50)MR1(50)

25



Cournot equilibrium: step 1


LEUVEN


Cournot equilibrium – step 2

Firm 2’s Reaction

Firm 2’s reaction curve shows how much itwill produce as a function of how much

it thinks Firm 1 will produce.

Q2

Q1

25 50 75 100

25

50

75

100

Firm 1’s ReactionCurve Q*1(Q2)

x

x


it thinks Firm 2 will produce. The x’scorrespond to the previous model.

In Cournot equilibrium, eachfirm correctly assumes how

much its competitors willproduce and thereby

maximize its own profits.

CournotEquilibrium

Firm 2’s Reaction


it thinks Firm 1 will produce. Firm 2’s ReactionCurve Q*2(Q1)


it thinks Firm 1 will produce.

Q2

Q1

25 50 75 100

25

50

75

100


x

x


it thinks Firm 2 will produce. The x’scorrespond to the previous model.


x

x

Firm 1’s reaction curve shows how much itwill produce as a function of how muchit thinks Firm 2 will produce.




CournotEquilibrium




CournotEquilibrium

The second step consists in setting the two reaction functions together and to find a Cournot equilibrium: what are the mutual best reply production levels: here (25,60). The relative production of the two producers will be a function only of their marginal costs because they fact the same total market demand. A lower marginal cost for firm 1 generates a larger market share in equilibrium.


The Cournot equilibrium is often used to study the natural gas market because supply requires important production and transport investment so that suppliers decide on quantities. An alternative equilibrium concept is the Bertrand equilibrium where production can be easily varied and where firms set prices instead of quantities. The best price a firm can set, given the price set by his competitor is to undercut the price by ε, the equilibrium will be that the price will be equal to the marginal cost of the supplier with the second lowest cost minus ε. In general the Bertrand equilibrium results in prices much closer to the marginal cost than the Cournot equilibrium.

Exercise6: assume 2 producers (Norway and Russia) want to supply the German gas market. The inverse demand function of the German gas market is P=100-0.5(q1+q2) where q1, q2 represent the supply by Norway and Russia. The total costs of Norway are 0.5 (q1)² and for Russia 5 q2. Find the perfectly competitive equilibrium, the Cournot equilibrium and the Bertrand equilibrium.

6. History of the gas market in Western Europe

Because gas transport is expensive and resource availability differs by continents, market development has been very different in Europe, Japan and the US. Here we focus on Western Europe and more particularly also on Belgium.

Before the large gas reserves of Slochteren (NL) were discovered in 1961, natural gas was only used in a few countries (Italy, France and Austria). The discovery of the Dutch gas was the real take off of the natural gas market in Europe. We distinguish 2 periods in this history: before 1973, the period 74-2004 and after 2004.

Before 1973

6 Example taken from Dahl, p268 and served as exam question in the past.


There were massive amounts of gas available in the Netherlands. In order to sell the gas one needed large pipeline investments and an extensive distribution network.

Once the main import pipelines are constructed one starts by supplying first a few big customers as this allows to sell a large volume without large additional transport investments. Gas substituted oil and coal in power stations. The next step is to connect smaller industrial customers and finally smaller consumers.

All European countries opted for an import monopoly with sometimes a partly private ownership (The Belgian Distrigaz was 50% public, and 50% private). The monopoly allowed to benefit from economics of scale in transport and to maximize profits. The profits were important to guarantee a continuous investment in transport networks.


LEUVEN


The West-European Gasmarket before liberatisation

Exporters(countries)

Importers(countries)

Consumers

Netherlands

Norway

UK.

Russia

Algeria

Frankrijk

Duitsland

België

Andere

Industry

Power producers.

Distributioncompanies

houeholds

Small firms

Internationaltransport

NationalTransport + strorageg

One had double monopolies: each exporter was state controlled, together they form an oligopoly (Cournot) and each of the importers had a monopoly in their own country. This situation lasts until 2000-2004.

The national monopolists used their market power to discriminate prices in function of the willingness to pay of the sellers. Power producers that had


cheap coal or HFO as alternative could bargain a better price than industrial customers that have gasoil as alternative. This is also called Ramsey pricing.

Natural gas consumption did grow very rapidly before 1973.

From 1974-2004 The gas demand was growing rapidly because the price of a close substitute (oil products) increased steeply in ‘73 and ‘79-‘80. Initially, prices of gas were not fully indexed on the price of oil products so that demand increased quickly.

One needed additional suppliers. They were found in Norway (Ekofisk, Troll, Sleipner …fields), in Algeria and in Russia.

The high growth in demand led sometimes to unrealistic projected growth rates and bad contracts. The best known example are the first contracts with Algeria. The contracts stipulated sometimes prices for gas fob Algeria that were at the level of the prices of oil substitutes neglecting that the transport and distribution of gas was much more costly than oil. In addition, there was a pay or take clause in the contract. This resulted in financial problems for the importers. In the case of Belgium, Distrigaz was almost bankrupt and went for a long international arbitrage procedure.

Gas price (EU, cif) / Crude oil price (OECD, cif)

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

Ye a r s 19 8 4 - 2 0 0 7

Distrigaz tried to minimize the losses by price discrimination and selling

surpluses at discount prices, if necessary abroad.



LEUVEN


A large Take-or-Pay Contract with a too high price

ca

cn

Pe

Demand

Price

QuantityXa

p1

MR

x1

total quantity to import

Price Algerian gas

Price Dutch gas

Export on spot market

Optimal solution: sell x1 on home marketand xa-xe abroad

This figure illustrates the best solution if there is a very large quantity to be

imported at a too large price. If the importer sells at the import price of

Algerian gas (ca), his sales will be limited and he has to sell the rest as

exports on spot market.

The best the importer can do is to charge the monopoly price p1 where the

Marginal Revenue equals the Marginal Cost and this is here the price on spot

export markets. Most importers were able to discriminate between all types

of clients so that they sold xa at prices that approximate the demand function.

As most trade was between public exporting and public importing companies,

the import contracts were not always economically justified and were used in

order to promote other goals: employment, foreign affairs etc..

One of the complicating factors was the strongly fluctuating oil price. As gas

prices were indexed on oil prices with a delay of some 6 months, gas was very

favourably priced when oil prices were rising and vice versa when oil prices

were decreasing.


Another factor that grew in importance was storage. As gas was imported

from more and more remote areas, the trade off between storage and

transport capacity changed. Importers had the choice between building

minimal storage capacity and a transport capacity in function of the winter

peak of demand or a larger storage and smaller transport capacity.

There was also a continuous attention for environmental regulations and

taxes imposed on oil products and coal as these were important for the

competitive position of gas.

A final important element in terms of demand is the growing use of gas in

power plants: in the new combined cycle gas plants their efficiency is 55-60%

instead of some 40% in conventional plants. This is coupled in some countries

with a nuclear phase out and a concern for CO2 emissions that rules out coal

as alternative fuel for power plants.

Gas consumption in Belgium and Luxembourg

0,0

2,0

4,0

6,0

8,0

10,0

12,0

14,0

16,0

18,0

1967

1969

1971

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

Years 1967-2007

Gas

co

nsu

mp

tio

n in

bcm

per

yea

r


From 2004 onwards

From 2000 onwards the EC requires the liberalisation of the gas trade. This means that large consumers can negotiate their own import contract and the transport company has to grant access to parties that want to use the transport network. We will see in the next section what could be the effects of this liberalisation.

One of the puzzles in the EU gas market is the continued reliance on oil price indexation in gas contracts. The next table shows that in a mature gas market like the US market, prices are more indexed on gas spot markets.

A second important development is the growing dependence on non-EU sources of supply. Russia, North Africa and Middle East will be responsible for 60% and more of our supplies from 2020 onwards. This raises serious concerns. The IEA expects an increase of gas consumption in the European union from 305 bcm in 2006 to 580 bcm in 2030. Its import dependence will rise from 57% now to 86% in 2030. Most of the increase is met by Russia, Africa and Middle East. We discuss the need for more gas imports and the supply of Russian gas more in detail in section 8.


7. Modelling the European gas market

In this section we use the model of Boots et al (2004)7 to study how prices are set after the liberalisation and more particularly, what is the effect of the number of traders on consumer prices. We have chosen this model because it is fully documented and describes the European gas market. Many other models of the gas market use a similar approach.

Structure of the model

The model represents the competition at two levels: first between producers (exporters) to one country and second, within one country between different traders for the same consumers. The following figure represents this dual structure.

Structure of the EU gas model

producer

producer

trader

trader

Household A

Generation A

Industry A

Country A

Country B

Cournot behaviour but eachIs Stackelberg leader wrt traders(they take the reaction of traders into account)GazpromStatoil…

Cournot behaviour in end-useMarkets andPossible price discrimination(1 and sometimes 3 Traders per country)

Transportcosts

DemandFunctionsPer category and per country

“UPSTREAM” “DOWNSTREAM”

Distributioncosts

The European consumer countries are numbered 1,...,n N . In each country,

there are multiple segments (household, industry, power generation), numbered . As a result, there are 1,...,g G N G different markets, each with

its own end-user price.

7 Boots M., Rijkens F., Hobbs B., “trading in the downstream European gas market”, Energy Journal, vol 25, n°3


In the "upstream part", the producers (indexed 1,...,i I ) play a Cournot

game: each takes the sales of the other exporters to a particular market as given and optimizes his profits by selecting a quantity for that market. The producers are only concerned about the border price for each country and each segment – the price they receive for the gas at the border where it enters the country – and do not get involved in the distribution of gas within the country.

Within each country (the "downstream part") there can be 1 or 2 traders, e.g. in Belgium the base case of the model assumes 1 trader, Distrigaz. Traders are numbered . A key feature of the model is that it allows to

increase the number of traders beyond the actual number, to analyze the effects of increasing competition. In each segment, the traders play a Cournot game. If there is only one trader in a given country, then this means a monopoly game.

1,...,r R

The model assumes that producers have a Stackelberg leadership position vis-à-vis traders: producers make their decisions before traders do. When making their decisions, producers already anticipate how their decisions will influence the decisions of the traders. Therefore, in this text, we will first study the behaviour of the traders. Using that information, we will then study the behaviour of the producers.

Downstream: behaviour of traders

The model assumes that each market ng has a linear demand curve, i.e.:

ng ng ng rngr

p y (1)

where is the quantity supplied by trader to market , and rngy r ng ngp is the

resulting market price (end-user price) in market . Note that ng 0ng .

Each trader sets his quantity to maximize profits: r rngy

,

max ( )rng

r ng ng ngy

n grngp bp dc y (2)


Traders decide after producers have decided, and so they take the border prices for each individual country and segment as given. is the

transmission tariff for country and segment , and is also taken as given.

The first-order conditions for to yield the optimal

ngbp ngdc

n

rng

g

y r , are:8

( )rng ng ng ng rng

rng

p bp dc p yy

0

(3)

There are two possible cases: perfect competition and Cournot competition (see section 5 of this chapter).

Under perfect competition, a trader cannot influence the market price by his actions, i.e., the market price is taken as given, hence for each individual trader, we have . Therefore the first-order condition 0ngp (3) reduces to:

ng ng ngp bp dc (4)

In words: under perfect competition, price equals marginal cost of supply. Combining (4) with the demand curve (1), we find:

with ng ng ng rng ng ng ngr

bp y dc (5)

from which we can derive the total quantity supplied by all traders as a function of border price (or vice versa).

Under Cournot competition, a trader takes into account that his quantity decision influences the market price, and as a result a trader may withhold volumes in order to drive up the market price ( 0ng ngp ). In the Cournot

equilibrium each trader maximizes his profits while taking the quantities supplied by other traders as given. Assuming that all traders are identical, we find that:

8 Note that the conditions shown in Boots et al. (2004) are slightly more complicated in order to take into account the

constraint . In this text we ignore this point for the sake of simplicity. 0rngy


1 with

ng ng ng rng ng rng ngr

ngng ng rng ng ng

r ng

bp y y dc

Ry

R

(6)

from which, again, we can derive the total quantity supplied by all traders as a function of border price (or vice versa). This expression is similar to equation (5), but has a steeper slope, reflecting the fact that traders take a monopoly/oligopoly margin. The following figure shows how the consumer demand curve (1) is transformed into curves (5) and (6).

Behaviour traders (“downstream”)

Quantity( yrng)

Price(png, bpng)

Demand function of consumers ng(equation (1))

Perceived demand function for producers if perfect competition in trading (equation (5))

Perceived demand function for producers if 1 monopolist trader (equation (6) with R=1)

Note that equations (5) and (6) are the demand functions perceived by the upstream producers: the curves show which quantities the traders (in total) will buy from producers as a function of border prices charged by producers. Conversely, they show how border prices will change as producers change the quantities exported to different markets.

Upstream: behaviour of producers

Given the perceived demand functions (5) and (6), the producers set quantities (and hence, prices) in each market. The model assumes Cournot


competition between producers: each producer sets a production quantity (i.e., export quantity) to maximize profits, taking the quantities set by others as given. Practically, for a producer, setting a certain production quantity corresponds to investing in a certain amount of developments of gas fields.

The model assumes that producers' marginal production costs are increasing. Furthermore, the long distance transmission costs – to transport gas from the gas fields to the borders of the consuming countries – are assumed to be constant per km per cubic meter of gas. No transmission capacity limits are assumed.

Producers maximize profits:

(7)

, ,

, ,

max

max

ing

ing

i ng in ing i ingq

n g n g

ng ng jng in ing i ingq

n g j n g

bp t q c q

q t q c q

where is the quantity supplied by producer i to market , and is the

transmission cost from producer to country . The function represents

the total production cost as a function of the quantity produced. In case the traders are perfectly competitive,

ingq ng

c

int

i n ( )

ng needs to be replaced by ng . The first-

order condition for maximizing producer i 's profit, is:9

0ing ng jng ng ing in i

jing

q q t cq

(8)

Equation (8) allows us to compute all quantities set by producers, and hence the resulting border prices. We can extend the previous figure to show the quantity decision by a monopolistic producer graphically.

9 The same observation as in footnote 8 applies here.


Resulting equilibrium: illustration for 1 producer and 1 or R traders (R→∞, i.e. perfect competition)

c’ + tin (marginal production & transmission cost)

MR curve for 1 producer, if only 1 trader per country

If only 1 trader per country: double monopoly margins: margin producer (lower part)+ margin importer (upper part)

If perfect competition in trade: only monopoly margin forproducer

png–dcng>bpng(if 1 trader)

Price(png, bpng)

Quantity( yrng , qing)

MR curve for 1 producer, if perfect competition in trade

MR curve for 1 producer, if perfect competition in trade

png–dcng=bpng(if perfect competition in trade)

If producers are a monopoly/oligopoly and traders are perfectly competitive, consumer prices are higher than marginal costs, due to the margin taken by the producers. However, if traders are a monopoly/oligopoly instead of a perfectly competitive industry, consumer prices are even higher, because in that case both producers and traders take a margin. This phenomenon is called double marginalisation: each non-competitive stage of the production process adds a monopoly margin, thereby disregarding the effect of its margin increase on the profit loss of the next stage. In such circumstances, vertical integration of traders and producers would reduce prices, increase consumer welfare and increase total profits (producers + traders). Jean Tirole launched in 1997 the famous phrase: "What is worse than a monopoly? A chain of monopolies."

Empirical specification

In principle, the equations derived above enable us to compute all quantities, end-user prices and border prices, as soon as the demand curves (parameters

ng and ng ), tariffs , transmission costs and marginal production

costs are known. Boots et al. (2004) estimate these parameters based on

actual market circumstances.

ngdc int

ic


First of all, the consumer demand curves can be estimated using the actual volumes, prices, and elasticity per segment. The following table shows the data that is used. Note in particular the large price discrimination between different segments in Belgium.

The following table shows assumptions about production costs, which are based on technical estimates. Producers for which 0i , have a constant

marginal cost of production i up to the point where capacity limits are

reached.


Scenarios and results

Boots et al. (2004) study 4 scenarios, as shown in the following table.

"No price discrimination" refers to a situation in which producers cannot discriminate between border prices for different segments, i.e., an additional constraint is applied: . ,ng nbp bp g

The following table shows the resulting prices in each of the scenarios. Each cell in the table gives the end-user price and the border price for a given segment in a given country.


The first column ("No discr. Benchmark") represents prices if there is perfect competition among traders and among producers. It is interesting to compare this "benchmark" column with the actual prices in 1995, as shown in Table 1. For example, in Germany, the actual 1995 prices are much higher than the "benchmark" prices: in reality, there is no competition and both traders and producers have high margins. On the other hand, in the UK, the simulated "benchmark" prices are close to the real prices, showing that the market is already quite competitive.


The second column, compared to the first column, shows the effect of oligopolistic behaviour of gas producers. The third column shows the extra effect of allowing border price discrimination: introducing border price discrimination leads to much higher price differences between households and power generators. For most countries, actual 1995 prices from Table 1 are close to the scenarios in the second and third columns: oligopolistic producers and competitive traders.

The fourth and fifth column show the effect of oligopolistic behaviour of traders. Profits of traders are zero when they are perfectly competitive, but very large when they have a monopoly/oligopoly. Producer profits are largest when traders are competitive and border price discrimination is possible. The following figure summarizes the welfare effects of the different scenarios.

As mentioned before, the model also enables us to vary the number of traders. The following table shows the prices that result when the number of traders in each market is increased to 3 and then to 9.


The results need to be compared with the fourth column in Table 4. An

increase of the number of traders leads to a decrease of traders' profits, an

increase of producers' profits, an increase in consumer surplus, and in total

an increase of social welfare. If the number of traders were to go to infinity,

the results would converge to the second column of Table 4.

8. The security of European gas supply

Introduction Europe’s dependence on Russian gas imports has been the subject of

increasing political concern after gas conflicts between Russia and Ukraine in

2006 and 2009. We distinguish three issues. A first issue is that some of the

countries through which Russian Gas is exported to the EU (Belarus,

Ukraine) make use of their monopoly position to get better deals (less

expensive gas) with Russia. The second issue is the future supply of natural

gas to the EU: where it will come from and at what conditions. The third

issue is that Russia itself can threaten to interrupt gas supply to EU or

charge higher prices.

Transporting Russian gas to Europe


The next map shows that most Russian gas is exported to the EU via Belarus

and via Ukraine. As former allies of Russia they received Russian gas on

better terms than the rest of EU. When Russia wanted to raise their price to

EU levels, they both have interrupted the gas supply to EU for some time.

This makes both Russia and the EU vulnerable to threats by the transit

countries.

OX

FO

RD

INS

TIT

UT

E F

OR

EN

ER

GY

ST

UD

IES

10

Russian Pipelines via Ukraine and BelarusRussian Pipelines via Ukraine and BelarusRussian Pipelines via Ukraine and Belarus

Source: Stern J. (2007)


OX

FO

RD

INS

TIT

UTE

FO

R E

NE

RG

Y S

TU

DIE

S

12

Blue Stream/South Stream Gas PipelinesBlue Stream/South Stream Gas PipelinesBlue Stream/South Stream Gas Pipelines

Source: Stern J. (2007)

Russia and some of the EU countries have reacted to this threat by building

bypasses that diminish the bargaining power of the two main transit

countries. This is the “Nordstream” pipeline (connecting Russia and Germany

via Baltic sea pipeline) and the project to build a “Southstream” pipeline

(connecting Russia with Bulgaria via Black Sea or via Turkey).

The purpose of these 2 pipelines is different from still another project in the

South-East of Europe and Turkey, the “Nabucco” project. In this EU backed

project the idea is to connect to an alternative source of supply in the Caspian

area. The main problem here will be to have the cooperation of Turkey and of

the local producers in the Caspian area.


OXFORD INSTIT

UTE F

OR E

NERGY S

TUDIE

S

20

Nabucco: a Caspian/Middle East Pipeline NabuccoNabucco: a Caspian/Middle East Pipeline : a Caspian/Middle East Pipeline

Source: OMV

This is the favourite project of all EU politicians and most media commentators

So the purpose of Nabucco is to rely less on Russian gas and not to avoid

dependency on some transit countries.

Where could the EU get its gas supply in the future? The IEA (WEO 2009) looked into the different options to supply natural gas to the EU in

the future. The EU has to get its gas from Russia, Middle East (Qatar) of Africa (mainly

Algeria).

The development of non conventional gas in the US means that these exporters or more

interested to export to the EU. The EU is the major customer of Russian gas.

The figure is also interesting to show how the margins of exporters become much smaller

when they need to supply to remote customers. The nearby suppliers enjoy a rent.



How to deal with unreliable Russian gas supply?

Introduction

Morbee & Proost (2010) assess the potential impact of Russian unreliability

on the European gas market, and how it affects European gas import

strategy.

They study to what extent Europe should invest in strategic gas storage

capacity to mitigate the effects of possible Russian unreliability. The

European gas import market is described by differentiated competition

between Russia and a – more reliable – competitive fringe of other exporters.

The results show that Russian contract volumes and prices decline

significantly as a function of unreliability, so that not only Europe but also


Russia suffers if Russia’s unreliability increases. For Europe, buying gas from

more reliable suppliers at a price premium turns out to be generally more

attractive than building strategic gas storage capacity.

In recent years, security of gas supply has been high on the political agenda

in Europe. Gas import dependence of the European OECD bloc will increase

from 45% in 2006 to 69% in 2030, according to the IEA (2008) Reference

Scenario. Russia plays a crucial role, given that it already supplies more than

half of Europe’s gas imports and that it has the largest proven natural gas.

1

Focus of this paper

Europe needs to import a large share of it gas consumption, especially from RussiaBillion cubic meters (bcm), 2005

* Includes exports to countries such as Switzerland, plus other discrepancies between import and consumption** Mainly LNG from Africa (including Algeria)

Source: BP Statistiscal Review of World Energy, 2006

88

63

49

200

79

122

38 53

212

471

20

Share of EU-25 consumption (Percent)

100100

xx

EU-25consumption

UK

Nether-lands Other

EU-25 production

Total EU-25

production

Exports*

Norwayproduction

Total non-European

gas imports

Russia(pipeline) Algeria

(pipeline) Other**

1919 1313 1010 4242 44 1717 4545 2626 88 1111

We study long-term gas contracting in a non-cooperative setting, using

a partial equilibrium model of the European gas market, with differentiated

competition between one potentially unreliable ‘dominant firm’ (Russia) and

a reliable ‘competitive fringe’ of other non-European import suppliers.

Russia’s potential unreliability is modeled by assuming that there is a

probability d that Russia does not comply with the long-term contracts it has


signed: with probability δ, Russia ‘defaults’ and withholds supply to increase

its price to monopolistic levels for a duration of four months.

The model

Europe is modeled as a large number of uncoordinated gas consumers and

domestic gas producers, with an overarching government that can decide to

invest public funds in gas storage capacity. We assume Europe is a price-

taker with a linear long-run inverse demand curve for gas:

( )p q q

European domestic producers supply an exogenous and fixed quantity Dq ,

and the remaining excess demand Dq q needs to be satisfied by non-

European imports. Short-run demand is also linear, but with a steeper slope

( ) * ( *)SR SRp q p q q

with p*, q* representing the long-run equilibrium.

We assume that decisions on long-term gas import contracts and publicly

financed strategic storage capacity investments are based on a combination of

the interests of importers, end-consumers, domestic producers and taxpayers.

We therefore assume that Europe maximizes the expected total ‘European

surplus’ E[S] :

E with S=CS+ DMax S G

where CS is the consumer surplus, D represents the profits of domestic

producers, and G is the public expenditure on gas storage capacity

investments. _G represents the interests of the recipients of marginal


expenditures out of general government revenue. Note that this equation

assumes risk-neutrality.

Excess demand needs to be satisfied by signing long-term import contracts

with non-European import suppliers. We assume that the non-European

import suppliers have a dominant firm – competitive fringe structure. Russia

is the ‘dominant firm’ and the other non-European gas import suppliers are

grouped together as the ‘competitive fringe. Russia is modeled as a monolithic

entity, i.e. the Russian state is not distinguished from the gas exporter

Gazprom. Russia is assumed to be a risk neutral profit maximizer. Russia is

modeled to be unreliable: once the long-term contracts have been signed,

there is a probability δ that Russia temporarily does not comply with its

supply commitments, i.e. Russia ‘defaults.’ Conversely, there is a probability

(1-δ) that Russia complies with its long-term contracts during the entire

period. All participants know the parameter δ upfront. Russia’s long run

marginal costs of production are assumed constant at . Rc

The competitive fringe is a diversified set of current or potential future non-

European gas import suppliers, including both pipeline and LNG supplies.

Therefore, we assume that – as a group – the competitive fringe is reliable:

even if Russia defaults, the competitive fringe delivers the originally

promised contract quantity at the originally promised contract price0q 0p .

This requires two assumptions. First, we assume that the long-term gas

import contracts between Europe and the competitive fringe are not indexed

on any gas spot market price, which would rise sharply in the event of

Russian default. In practice, this condition is fulfilled since most current

long-term gas import contracts contain little or no indexation on gas spot

market prices. Second, we assume that the competitive fringe players do not

deviate from their contracts. This is a major assumption, which can be

justified by the difference in scale between Russia and each of the other non-


European import suppliers. Each of the other non-European import suppliers

has much less incentive to be unreliable because the market impact of each of

them is much smaller. In addition, a supplier who is perceived as unreliable

could face the threat of being replaced by another supplier in the long term.

Russia, on the other hand, is hard to replace completely in the long term,

even if it behaves unreliably.

The interaction between Europe, Russia and the competitive fringe, is

modeled as a game in three stages. Figure 1 explains the different stages of

the game. In a nutshell: in Stage 1, Europe decides how much to invest in

strategic gas storage capacity; Stage 2 is the stage in which Europe signs

long-term gas import contracts with Russia and the competitive fringe; Stage

3 consists in the execution of the long-term gas import contracts, in which

Russia may or may not comply with the long-term contracts it has signed. We

represent the imported gas quantities by (Russia complies with long-term

contracts), (Russia defaults) and (competitive fringe). The

corresponding prices are denoted

,1Rq

0q,2Rq

,1Rp , ,2Rp and 0p .

Before describing each of the stages in detail, it is important to note that

the stochastic outcome of Stage 3 influences the strategic interaction in Stage

2, because Europe and Russia factor the expected value of Stage-3 pay-offs

into their decisions in Stage 2. In Stage 3, European surplus is either S=S1 or

S=S2 depending on whether Russia complies with its long-term contracts or


not.

In Stage 2, Europe therefore tries to maximize the expected surplus E[S].

This maximization problem can be translated into demand functions for

Russian and other long-term gas import contracts, by finding – for given long-

term gas contract prices – the optimal long-term gas contract quantities that

maximize Europe’s expected surplus E[S] in Stage 3. As for Russia, its

expected profits in Stage 3 are either ,1R R or ,2R R , depending on

whether Russia complies with its long-term contracts or not. Therefore, in the

‘dominant firm – competitive fringe’ game in Stage 2, dominant firm Russia

sets the optimal gas contract quantity to maximize its expected profits RE

in Stage 3, taking into account the long-term gas import contract supply

curve of the competitive fringe and Europe’s above-mentioned demand

functions for Russian and other long-term gas import contracts. European

demand for long-term gas import contracts will turn out to be differentiated

between gas import contracts from Russia and gas import contracts from the


competitive fringe, because their effect in Stage 3 is different. The rest of this

section describes the three stages in more detail.

In Stage 1, Europe decides to foresee a quantity q (in bcm, i.e. billion cubic

meters) of strategic gas storage capacity, to be used as a buffer in case of

withholding of gas supply by Russia. Given the long lead times involved in

the development of storage sites, this decision cannot be postponed until it is

known whether Russia will comply with its contracts or not (i.e. it cannot

wait until Stage 3). Furthermore, in our model, the storage capacity

investment decision takes place before decisions are made regarding the

amounts of long-term gas imports that are contracted from Russia and the

competitive fringe (i.e. before Stage 2). The reason is that investment in

storage capacity is a decision that Europe can make unilaterally. By making

the storage capacity investment decision in a separate stage upfront (Stage

1), Europe gives its storage capacity investment decision an advantageous

Stackelberg leadership position in the strategic game with its gas import

suppliers. In making the decision about storage capacity investment, Europe

takes into account the strategic behavior of Stage 2, and it has perfect and

complete information to do so.

In Stage 2 Europe signs long-term gas import contracts with Russia and with

the competitive fringe. Our approach is non-cooperative, with Europe as a

price-taker in a ‘dominant firm – competitive fringe’ model of the long-term

gas import contract market. Russia, as the dominant firm, puts a quantity

(in bcm per year) on the European market, for which it receives a price ,1Rq

,1Rp (in € per tcm). In making its decision, Russia already takes into account

the subsequent decision of the competitive fringe, who put a quantity (in

bcm per year) on the market, for which they receive a price

0q

0p (in € per tcm).

The prices ,1Rp and 0p are the response of the European inverse demand

functions to the quantities and . The quantity-price pairs ( ) ,1Rq 0q ,1 ,q ,1R Rp


and ( ) represent the long-term gas import contracts signed between

Europe and Russia, and between Europe and the competitive fringe,

respectively. Because of Russian unreliability, the prices

0 ,q p0

,1Rp and 0p do not

need to be the same. Although there are separate inverse demand functions

for Russian and other gas – resulting from the behavior of importers – the

end-consumers face a single price for gas and cannot choose their own mix of

reliable and non-reliable gas. There is a single end-consumer price in each of

the two states of the world in Stage 3.

Stage 3, the final stage of the game, is the execution of the long-term gas

import contracts signed in Stage 2. Stage 3 is the stage that results in actual

pay-offs for the participants to the game. We study one representative year:

although the import contracts and storage capacity investment decisions are

longterm decisions that will hold for multiple years, all volumes and

monetary payoffs in Stage 3 are shown as annual amounts. In a

representative year, there is a probability 1-δ that Russia honors its

commitments, and effectively delivers at a price ,1Rq ,1Rp . This is ‘Case 1’

(Russia complies with long-term contracts). Figure 2 illustrates Case 1

graphically. Dq is the gas supply from European domestic producers, which is

assumed to be exogenous and fixed (inelastic). The shaded area, S1 , is the

European surplus according to equation (3), but without taking storage

capacity investment costs into account. End-consumers pay a single price

corresponding to ,1 0* ,Rp p p , such that demand at price p* is exactly equal

to 0 ,1D Rqq q .

In a representative year, there is also a probability δ of default, in which case

Russia withholds supply to maximize short-run profits. This is ‘Case 2’

(Russia defaults), which is depicted in Figure 3. Assuming that neither Dq

nor q can increase in the short run, Russia can set q ,2R ,1Rq , for which it can 0

command a price ,2 ,1R Rp p . Note that this price is derived from the short-run


demand curve. Europe responds by cutting consumption and using the

maximum amount of stored gas, which is constrained by the storage capacity

qS chosen in Stage 1. The storage capacity investment only covers the cost of

the storage facility and the capital cost of the unused gas, but not the

purchase price of the stored gas itself. The gas withdrawn from the storage

will therefore need to be replaced for future crises, and we assume that this

can be done at some point at a price equal to p0 . Effectively, the price of

using gas from the storage is therefore p0 (in addition to storage capacity


costs, which are sunk). The competitive fringe always delivers q0 at price p0,

whatever happens in Stage 3. As before, this does not mean that identical

end-consumers would pay different prices in the event of Russian default.

Since the marginal unit of gas import supply in the short run in case of

Russian default has a cost ,2Rp (because only Russia could increase supply),

the ‘marginal’ price for end-consumers should correspond to ,2Rp . While this

does create a rent from the fringe supply contracts equal to ,2( R 0 0)p p q , the

rent is part of the European surplus. In total, the European surplus in case of

Russian default is lower than S1 from Figure 2. Figure 3 shows ΔS, the loss in

European surplus due to Russian default. This loss is discussed in more

detail in equation (8) in the next section.

The three stages of the game represent three distinct decisions. We assume

that this three-stage game is played once. In practice, the game is obviously

repeated after a number of years, but because the lead times for gas projects

are very long, we do not consider the repeated game. Finally, if Russia

‘defaults’ (probability δ), the assumption is that this happens only during a

fraction s of the year. For the remaining fraction (1-s) of the year, Russia

respects and ,1Rq ,1Rp .

In summary, our model describes Russia’s unreliability as a potential

‘default’ event, with a probability δ of default. The model takes into account

two ways for Europe to escape from the unreliability of Russian gas supplies:

on the one hand, diversification by signing long-term contracts with the

competitive fringe, and on the other hand, investments in strategic storage c.

The parameters of the model are calibrated on cost data and elasticities from

the literature, the 2007 baseline for volume, and the average price 2003–

2007.


The results

The top half of Figure 4 shows how quantities and prices vary as δ, the

probability of Russian ‘default,’ goes from 0 to 1. The graph also shows the

discount 0 R,1p p p of long-term gas import contracts offered by Russia

compared to contracts offered by the competitive fringe.

For δ=0, there is no risk and there is obviously no price difference between

the contract with Russia and the contracts with the competitive fringe. The

simulation shows that in this case, Europe buys q=135 bcm per year from

Russia and q=94 bcm per year from the other suppliers. This is not too far

from the actual data in 2007 as cited by BP (2008), which mentions 120 bcm

per year from Russia and 95 bcm per year from other non-European import

suppliers. Indeed, until recently, Russia was considered a reliable supplier,

and so it is not surprising that the currently observed market quantities

correspond to the case δ=0.

For δ>0 Russia becomes unreliable. When Russia ‘defaults,’ it delivers only

an annualized amount instead of , at a higher price ,2Rq ,1Rq ,2Rp instead of the

originally agreed long-term gas import contract price ,1Rp . Panel (a) of Figure

4 shows that the quantity withheld would be around 40% and panel (b) shows

that the resulting price increase would be around 40% as well. Although

substantial, such a price increase is only a two-sigma event over three

trading days at gas hubs such as NBP (National Balancing Point, in the UK)

when considering a typical daily volatility of 10%.

As δ increases, Europe increases its volume q0 of long-term gas import

contracts with the competitive fringe, at a slowly increasing contract price p0 .

Meanwhile, Europe procures a smaller volume with long-term contracts

from Russia, even though Russia is obliged to give an increasing discount

,1Rq

p


to ‘compensate’ the risk for Europe. It is obvious why Russia would want to

give the discount: as δ increases, there is a higher chance that Russia can

charge the monopoly price p in Stage 3 (by supplying only a quantity q of

gas). By giving a discount p , Russia can induce Europe to sign the long-


term gas import contracts (despite the unreliability), which puts Europe

in a vulnerable situation. For example, for δ=20%, the Russian contractual

discount is 6.3 EUR/tcm or roughly 4.5% of the price. Despite the discount,

Russia loses market share as δ increases and for δ=57% supply from the

competitive fringe outstrips Russian supply. Clearly, Europe tries to make

itself less dependent on Russia and therefore less vulnerable in the event of

Russian withholding.

,1Rq

Panels (c) and (d) of Figure 4 show the effect on European surplus and on

suppliers’ profits, respectively. Recall that S1 is the European surplus in Case

1 (Russia complies with long-term contracts) while S2 is the European surplus

in Case 2 (Russia defaults). E[S] is the expected value of the European

surplus. For δ=0 and δ=1, we obviously find E[S]=S1 and E[S]=S2,

respectively. As d increases, E[S] decreases: despite the Russian discount and

shifting supply mix, Russian unreliability causes a loss of expected European

surplus. Panel (d) shows Russia’s profits in Case 1 ( ,1R ), Case 2 ( ) and

the expected value E[ ] as well as the profits

,2R

R 0 obtained by the

competitive fringe. Clearly, Russia’s expected profits decrease monotonically

with increasing δ: the negative impact of the Russian contract discount and

loss of Russian market share is not sufficiently counterbalanced by Russia’s

increased likelihood of benefiting from a crisis. The only party gaining from

increased unreliability is the competitive fringe. The competitive fringe

profits increase with increasing δ, because increased Russian unreliability

allows them to sell a larger volume at a higher price.

0

The most important observation is that both Russia and Europe suffer when

δ increases. Although δ is exogenous in our model, the results show that it

would be attractive for both Europe and Russia to invest in a more reliable

relationship.


9. References

Boots M., Rijkens F., Hobbs B., 2004, “trading in the downstream European

gas market”, Energy Journal, vol 25, n°3

Dahl C., 2004, “International Energy Markets”, Pennwell

EIA, 2011, World sale gas resources: an initial assessment of 14 regions

outside the US, April 2011, DOE

IEA ,2009, World Energy Outlook

MIT, 2010, The future of natural gas – an interdisciplinary MIT study,

interim report MIT Energy Initiative

Morbee, J., Proost S., (2010), "Russian Gas Imports in Europe: How Does

Gazprom Reliability Change the Game?", The Energy Journal, vol 31,n°4,

p79-109

Pindyck , Rubinfeld, Micro-economics,

Stern J., 2007, European Gas Security: what does it mean and what are the

most important issues? , CESSA presentation, December, Cambridge

W.Van Herterijck “Aardgas , technische, economische en politieke aspecten”,

ACCO, 2007


Chapter 8 Basic electricity economics

1. Introduction

Electricity is the energy vector where the domestic value added and the domestic flexibility is the largest: one can chose the type of primary fuel to use and one can opt for a particular type of organisation of the sector. We start the chapter with a small introductory section, dealing with conventions and definitions. In the second section we survey the main uses, and the way electricity is generated at EU and world level. Sections 3, 4 and 5 present the basic economics of the electricity market. In section 3 we discuss first peak load pricing and investment in a world where demand is certain. In section 4 we discuss optimal pricing and investment with uncertainty. In section 5 we analyse briefly transport of electricity and the location of consumption and production over space. The emphasis in this chapter is on optimal pricing and investment and not on the market institutions that are needed to implement these optimal allocations. Those are discussed in chapter 9.

In the rest of this chapter we use the following conventions (based on BP statistical review conventions):

1Kwh=3600kJ=860kcal=3412 Btu

1 MTOE produces approx 4.4 Twh


Main uses Electricity as source of power for engines and for lighting has no good substitutes. For some applications natural gas could be an imperfect substitute. For cooking and home heating, gas is a good substitute if it is available. For process heat, except for specific applications, gas is again a good alternative.


Use of electricity Main substitutes

Cooking Gas, coal, firewood

Lighting, power Gas

Home heating Gas, Gasoil, previously coal furnaces

Industrial process Gas, Fuel oil, coal

Transport Oil products

Consumption of electricity is mainly concentrated in the richer Western countries and in the former Soviet countries. The consumption per capita per year in OECD is almost 8000 Kwh while consumption per capita in China is less than 2000 Kwh and in India less than 400 Kwh.

World consumption in 1980 (6800 Twh/year) was less than half the present consumption (15700 Twh/year). The IEA (Outlook 2008) expects the world consumption to double by 2030. Growth in the OECD area would be rather limited to some 1% per year but growth rates in China would be rather 5% per year.

Production of Electricity by fuel Before 1960, coal was the dominant fuel for power production. HFO and gas have taken over first, followed by the expansion of nuclear in the seventies and the eighties. Since early nineties there is a nuclear phase out in large parts of the world following the Chernobyl accident. Since then there is also a revival for gas fired units with the appearance of more performing combined cycle gas turbines that have a conversion efficiency of the order of 55 to 60%..

The next table gives shares of generating technologies in the world and expectations of IEA world outlook (2008). For 2030 the share of coal and gas remain large (which means massive investments), the share of nuclear decreases and one expects renewables to grow from 2% to 7% of total power supply in the world.


1990 2006 2030

coal 37% 41% 44%

oil 11% 6% 2%

Gas 15% 20% 20%

nuclear 17% 15% 10%

hydro 18% 16% 14%

biomass 1% 1% 3%

Wind 1% 4%

Total (TWh)

11811 18921 33265

Source: IEA Outlook 2008

Table 1 Expected electricity generation in the world by type of fuel

One of the main uncertainties is the growth of electricity demand in China and India. BP extrapolated the income elasticities observed in other Asian countries, corrected for improvements in electricity efficiency to make its outlook for China.


3. Trade flows

Trading electricity is mainly regional trade and there are two reasons for

this. First in many countries (EU, USA), the production and transport of

electricity was in public hands or in the hands of a regulated private

monopoly. This production was organised at the level of the state or the

country and trade between regulated national companies was not a priority

even if it could reduce costs. The national control was considered as more

important. Second, electricity is costly to transport over large distances.

In Europe there are traditionally some net exporters (France) and net

importers (Italy, NL, Belgium).

Another important issue not dealt with in this chapter is the cost and

capacity of electricity transmission.


3. Optimal pricing and investment when demand is certain

Peak load pricing and investment with only one type of power plants The demand for electricity is fluctuating strongly within a year: there are

daily, weekly and seasonal variations. As electricity demand can not be

rationed easily, one has to install capacity in function of the peak demand.

This implies that the cost of generating electricity will be different in peak

and off peak periods. An efficient electricity market will signal this difference

in marginal cost to the consumers. Varying prices over time in function of the

marginal cost is called “peak load pricing”. We develop this idea shortly with

a graph, a simple algebraic model and a numerical example.

Assume that peak and off peak are periods of equal length within the year and that

demand in peak does not depend on prices in off peak and vice versa.

peak load pricing

Euro/Kwh

Q

Demand Funct peak

Demand Funct off peak

VariableCost

Optimal price off peak

ExistCap

OptimalCapacity

P* Optimal price in peak for given capacity

P** Optimal price in peak wOptimal capacity

Annuity investmentcost/length peak

P*

Figure 8.1 Peak load pricing and investment

Consider Figure 8.1. First assume there is only one type of plant that can operate and its

capacity is given (“Exist Cap” vertical line in Figure 8.1). Then the optimal price is equal

to variable cost in the off peak period (here the marginal cost of one extra Kwh) and in

the peak period it is equal to the price P* that is needed to ration demand to existing

capacity. This means that in the peak period, prices need to be higher. Peak load pricing


means applying marginal cost pricing over time and charge the variable cost except when

this would give demand levels that are larger than the existing capacity, at that moment,

the peak price has to be raised.

We can also consider what happens if we can extend capacity. Assume that this

configuration of demand functions continues forever. Then it makes sense to extend

capacity up to the point where the marginal benefit of an extra unit of capacity equals the

marginal cost of this capacity. The marginal cost is in this case equal to the annuity of the

investment (equivalent annual cost of one KW of capacity or “rental cost”) divided by the

number of hours this capacity will be used, here length of the peak period). The marginal

benefit is the distance between the demand function and the variable cost. In the presence

of optimal investment we obtain that the price in the peak P** will equal the variable cost

plus the cost of capacity. In the off peak period the price will still equal the variable cost

as no extra capacity needs to be installed to satisfy off peak demand.

Peak load pricing can take different forms: day/night tariff; interruptible demand; etc. –

as there are extra metering cost involved, one leaves the option to the consumer. He will

select what is best for him and for the company. Assume that initially customers

consume more or less evenly in both periods. One could then offer a choice between a

uniform price P°, or a differentiated price between peak and off peak. Those who mainly

consume in the off peak will opt for the differentiated price and so will do those

consumers that can easily reduce their peak consumption.

Figure 8.2 illustrates what happens if one implements average cost pricing rather than

marginal cost pricing. Average cost pricing would mean charging the same price in peak

and off peak. This implies higher prices in off peak period and lower prices in peak

period. This creates two types of inefficiencies: charging above the marginal cost in the

off peak period and rationing of demand in the peak period. This rationing is very costly

as one can not discriminate between high value and low value consumers. When we add

investment possibilities, one will tend to invest more as the peak period is charged only

part of the investment cost for which it is responsible.


peak load pricing vs average cost pricing

Euro/Kwh

Q

Demand Fct peak

Demand Fct off peak

VariableCost

Optimal price off peak

ExistCap

OptimalCapacity

Optimal price peak for givencapacity

Optimal price peak withOptimal capacity

AverageCost pricing

Extra capacityneeded

Figure 8.2 Average cost pricing and investment

To find the optimal price and capacity algebraically (Williamson, 1966), one needs to

solve an optimisation problem. Assuming 2 periods of equal length with low demand L

and high demand H, the demand in each period does not depend on the price in the other

period. Each of these periods generates a net consumer surplus (S-pq) and a producer

surplus pq-bq where b stands for the variable cost. We also take into account the capacity

costs β per unit of capacity. If one considers a representative year, the quantity has

dimension Kwh during one representative hour, the variable cost is fuel cost/ Kwh, the

capacity cost has dimension annuity per 2KW /8760 h. The following expression is the

total economic surplus to be maximised:

, ,Max ( )

. .L H

L L L H H H L L L H H Hq q Q

L L

H H

W S p q S p q p q bq p q bq Q

st q Q

q Q

And this gives the following first order conditions for the optimal quantities and

associated prices:

0 andL L Lq Q p b

0 and

0H H H

L H

q Q p b

Q


Because the capacity is not fully used in the off peak period, the marginal cost of an extra

Kwh is the variable cost. In the peak period, if the capacity is optimally chosen, the price

equals the sum of the variable cost and the capacity cost. The optimal capacity level in

this context means that the sum of the “quasi- rents” λ earned in each period equals the

cost of one unit of capacity β. In our graphical example (Figure 8.1), there was a large

difference between peak and off peak demand functions and the cost of capacity was

rather small – then there is surplus capacity in the off peak period and the quasi rent

earned in the off peak period is zero. If the difference in demand functions is smaller and/

or the cost of capacity larger, there can be quasi-rents in both periods.

Peak load pricing and optimal investment with several types of plants For the production of electricity one can make use of different plants. They differ in the

type of fuel and size. To meet a demand that is not uniform over time it may be more

interesting to classify them in function of the cost of capacity C per unit and their variable

cost c. The variable cost consists principally in fuel costs. Base load units are units with

high cost of capacity and low variable costs. At the other extreme one has peak load units

that have low capital cost and high variable cost. The capacity cost is to be understood as

the full rental cost to have a given capacity (kW) available during a given year. The rental

cost contains the annuity of the plant (so includes the investment cost + interest) plus

insurance and other fixed costs (operators) for a year

We are interested in two questions: 1) what is the best plant mix to meet a given load

profile 2) what does this imply in terms of optimal pricing and capacity?

The optimal mix of peak and baseload plants for a given level of demand is a cost

minimisation problem that is simple when all the power stations are 100% reliable and

one does not need to take into account start up costs. Graphically this can be solved using

a load duration curve and total cost functions per type of plant. The total cost function for

a plant of 1kW of type i is expressed as a function of the time h it is used:

( )i iTC h C c hi


Putting the load curve information (electricity power demand re-arranged in decreasing

order) together with the different cost functions one can select the optimal combination of

the different types of plants by taking for every yearly utilisation rate the least cost plant.

8760 h

8760 h

MW

Total Cost function base load plant of 1kW

Total Cost function of peak plant of 1kW

Euro

Load duration curve

Peak unitcheaper

Base load unit cheaper

Base load plant

Peak load plant

Capacity cost peak plant

CapacityCost base loadplant

Figure 8.3 Optimal plant mix for fixed load demand curve

When demand is price dependent, we can use an extended version of the algebraic

formulation of the peak load pricing problem. We assume that the demands in the peak

(High demand H) and off peak period (Low demand L) are independent. The optimal

choice of capacities needs now to be solved simultaneously with the pricing problem:


, d em an d (M W ) in th e L o w p erio d an d H ig h p erio d w h ere p erio d s h ave sam e u n it len g th

, , , p ro d u ctio n s (M W ) in p erio d s L ,H u s in g p lan ts P (p eak in g ) ,B (b aselo ad )

, cap acity availab le fo

L H

LP L B H P H B

P B

q q

q q q q

Q Q r th e tw o p erio d s o f eq u al len g th (= w h o le year)

( ), ( ) g ro ss co n su m er su rp lu s in d em an d p erio d s L ,H ("area u n d er W T P fu n ctio n ")

, variab le co st fo r a p erio d o f u n it len g th o f a p eak p lan t aL L H H

P B

S q S q

c c n d a b ase p lan t

, cap acity co s ts fo r a year (2 p erio d s o f u n it len g th ) o f p eak in g an d b ase lo ad p lan t

P ro b lem : M ax im ise su m o f g ro ss C S - variab le co sts - cap acity co sts u n d er co n stra in ts b y ch o sinP BC C

g

p ro d u ctio n q u an tities an d cap acity (p rices are d e term in ed im p lic itly b y se lec tin g to ta l p ro d u ctio n

in each o f th e p erio d s)

m ax ( ) ( ) ( ) ( )

( ) (

L L H H P L P H P B L B H B P P B B

L HL L P L B H H P

S q S q c q q c q q C Q C Q

q q q q q

)

( ) ( )

( ) ( )

g en era tin g th e fo llo w in g firs t o rd er co n d itio n s (assu m in g it is o p tim al to u se a ll p lan ts in a ll p erio d s)

(1) 0

(2 ) 0

(3

H B

L P LBL P P L B B

H P H BH P P H B B

L LLL

L

H HHH

H

q

q Q q Q

q Q q Q

Sp

q

Sp

q

)

(4 )

(5)

(6 )

L L P L BP B

H H P H BP B

L P H PP

L B H BB

c c

c c

C

C

The first order conditions tell us what are the properties of the optimal solution.

Obviously, in each period, one follows the merit order: use always first the available

capacity with the lowest variable cost. Here we also determine simultaneously the

capacity of the two plants. Conditions (1) and (2) mean that prices should equal marginal

production cost in that period. The marginal cost is given by equations (3) and (4): it is

the fuel cost plus a quasi rent (or shadow value). The quasi-rent for a given plant in a

given period is the marginal benefit of having one more unit of capacity available during

that period (cfr. interpretation of Lagrange multipliers at the optimum). As in each period

the two plants are used, every type of plant earns quasi-rents in each period. Optimal

capacity is reached when the sum over all periods of the quasi rents (or “value”) equals

the unit cost of capacity. To solve for the optimum we need to solve the system (1) to (6)

and do this for all possible combinations of λ’s as there may be corner solutions where

the peak plant is not used in the low demand period.


An easier special case is where it is optimal not to use the peak plant in the low demand

period:

(0 ) 0

(1) 0

( 2 ) 0

(3)

( 4 )

(5 )

(6 )

( 2 ) (3) (5 )

( 4 ) (5 )

(1) (6 ) [ ]

L P

L LLL

L

H HHH

H

L L BB

H H P H BP B

H PP

L B H BB

HH P P

H BP P B

L H BL B B B B P P B

Sp

q

Sp

q

c

c c

C

C

p C c

C c c

p c C c C C c

c

]

In this case the optimal price (marginal cost) in the High demand period equals the price

of fuel plus the full capacity cost of the peak load plant1. This is indeed the extra cost to

society of satisfying an extra power demand in the peak period. In the Low demand

period we obtain that the price equals the fuel cost + the full capacity cost of a baseload

unit minus the capacity credit for offering low cost capacity in the peak period. This

capacity credit [ P P BC c c equals the savings in capacity costs in the peak period

adjusted for the difference in fuel costs. We illustrate this in Figure 8.4:

1 Price Per Kwh= fuel cost peak plant /Kwh + annual cost capacity/ length of peak period in h.


pH

pL

cB

cP

cP+CP

λHB

λLB

Peak

Base load

8760h

Figure 8.4 Illustration of optimal plant mix with two demand periods

We can use a numerical example to illustrate this point. Assume that demand for capacity

is given by:

125 (200 )

125 (100 )H H

L L

q p

q p

with ,H Lq q in MW and ,H Lp p in EUR/MWh. Assume, a (base-load) power generation

technology with 219000 EUR/MW and BC Bc 25 EUR/MWh is available. In

addition, a peak-load power generation technology with PC 50000 EUR/MW and

60 EUR/MWh is now also availablePc 2 .Unit conversion yields c 262800

EUR/MW and 109500 EUR/MW. Using the formulas calculated above, we have:

P

Bc

EUR EUR312800 71

MW MWhEUR EUR

[ ] 125200 29MW MWh

H P P

L B B P P B

p C c

p C c C c c

2 The parameters of the peak-load technology are taken from the above-mentioned article by Borenstein (2005), assuming USD/EUR parity


and hence, using the demand curves, Hq 16073 MW and Lq 8927 MW. A customer

who agrees to buy a constant amount of power (i.e., the same rate of consumption during

peak and off-peak hours), would pay an average price of 50 EUR/MWh, which is also the

average total cost of the base-load power plant.

How important is peak load pricing and correct capacity choice? Borenstein (2005)

analysed the effects of real time retail pricing with a representative load curve for the US

retail customer and used the following costs for power stations:

He computed the effects of real time pricing for different demand elasticities and found

that real time pricing can easily pay its higher metering costs for the larger consumers.

Figure 8.4 presents the effects on the load duration curve of switching from flat uniform

pricing to real time pricing for 1/3rd of the customers. Borenstein found that gains can be

large – they depend on the elasticity of demand. Time of day pricing (day and night) only

captures a small fraction of the benefits of real time pricing. With real time pricing, total

consumption of electricity could increase.


Effect of switching 1/3 rd of customers from flat to real time pricing

Figure 8.4 Effect of switching from uniform flat to real time of day pricing (source:

Borenstein (2005)).

Can this type of behaviour be decentralised in a market context? This is a question we address in Chapter 9. The answer is “in principle Yes”. If one starts with no initial capacity, a perfectly competitive market would supply the right quantities at the right prices and suppliers would cover their costs. The main assumptions driving this result are the absence of returns to scale in production so that many producers can be active on this market and the absence of reserve capacity requirements.

If one would start from the wrong mix of capacity or a too large or too small capacity, the market mechanism can in principle also achieve the right adaptation over time. If capacity is too large, the quasi-rent would be too small to encourage new investments and capacity would gradually be adjusted downwards. Etc.

Cost of power plants

To decide what type of plant is most appropriate for a given number of hours of operation, one can make a simple “static” comparison of the costs of generating one Mwh. The next table using data from IEA makes such a comparison. In the long term the marginal cost of one Mwh will depend on the availability of the power plant (h/year and technical lifetime), the total


investment cost, the cost of capital (here a simple interest rate), the efficiency of the power plant, the fuel cost and the cost of the CO2 permits.

This table allows to study the importance of each of the parameters. For nuclear, coal and combined cycle gas plant, the availability factor represents the time the machine is not out for planned or unplanned maintenance. For gas turbine, the availability represents the probability the plant is used for peak service. For wind power, the availability factor is a synthesis of wind conditions over the year.

The table allows to make a rough first comparison. What is missing is the effective contribution to the guaranteed capacity (could be only 20% of installed capacity). In reality, the effective utilisation of a power plant will depend on the merit order of the available capacities and of the total demand (cfr. Figure 8.4). A private investor will also take into account his cost of capital and will look into the risks associated to his investment. The risk will depend on the price and variability of the price of electricity.

Simple power plant economics: comparing the cost per Mwh for maximum operating hours per yearsource: IEA

Nuclear coal CC gas gas turb Wind oTechnical parametersCapacity MW 1400,0 750,0 780,0 150,0efficiency % 33,0 41,0 57,0 38,0 10Emission CO2 kg/Gjinput 0,0 93,0 56,0 56,0Technical life years 60,0 40,0 30,0 30,0 2Investment cost €/kw 2928,0 1523,0 763,0 520,0 434Fixed cost of O&M €/Kw 65,0 15,0 11,0 11,0Variable cost O&M €/Mwh 1,2 2,0 1,5 0,4 3

Market parametersfuel cost €/Mwh 3,0 13,0 22,0 22,0Price of CO2 €/ton 25,0 25,0 25,0 25,0 2Interest rate %/100 0,08 0,08 0,08 0,08 0Hours of operation hours/year 7446,0 7446,0 7446,0 1000,0 376

Resultsannuity factor €per Year/€ of investm 0,081 0,084 0,089 0,089 0,annuity €/Kwyear 236,576 127,719 67,775 46,190 442,total fixed cost per Mwh €/MWh 40,5 19,2 10,6 57,2 11total variable fuel cost per hour €/Mwh 10,3 33,7 40,1 58,3 3total variable CO2 permit cost €/Mwh 0,0 20,4 8,8 13,3total cost per Mwh €/Mwh 50,8 73,3 59,5 128,7 14


4. Optimal pricing and investment when demand is

uncertain and availability of plants is uncertain

Demand is not known with uncertainty and power plants can have unforced outages. This is also known as the reserve capacity requirement. In theory one can expand the neo-classical market framework by defining contingent commodities and trade in these commodities. This would mean that one would buy X MW at price p if there is no unforeseen capacity shortage and buy Z MW at price q if there is no capacity shortage.

The problem is that, in case of capacity shortage, it is difficult to suddenly charge higher prices and ration demand in function of the willingness to pay of each customer. This is difficult for two reasons. First the individual WTP’s are not known, second one needs special devices to disconnect individual customers. This implies that if there is a shortage, the average consumer is interrupted, not the consumer that could most easily forego the electricity consumption. We illustrate this in Figure 8.5.

price

Quantity

Demand very high (HH)

Demand high (H)

pH

qHQqHH

qHH

pHH

A

B

D

E

DBE=lost consumer surplus whenThere is efficient rationing and Demand is higher than expected

AEF= expected loss of consumersurplus when there is randomrationing (probability of not safyinga customer in the range OqHH=0Q/OqHH =AF/FpHH

F

0

Figure 8.5 Effect of different types of rationing when prices can not be adapted to peak demand.


Take the case of two demand levels: there is the expected demand qH realised with probability and there is the unexceptionally high power demand qHH

with probability (1 ). Initial existing capacity is fixed at Q. What is an appropriate price and capacity? The problem is that capacity and price in the peak period have to be chosen beforehand.

Assume first that the best solution is to always satisfy demand, whatever its level. This requires that the price in the peak period has to be set at an exceptionally high level (pHH) but this would also generate a high loss of efficiency when the peak demand is at a lower, normal level. The other solution is to go for a lower price (pH) but to increase capacity such that demand is always satisfied (QHH). This would be very costly in terms of capacity.

Assume now that one will not always satisfy demand in the exceptional peak period. Assume that capacity equals Q and that price equals pH. In that case, the demand in the exceptional peak period has to be rationed.

The best option is to use the price mechanism and increase prices up to pHH. The loss of consumer surplus due to insufficient capacity is now limited to area DBE. But it is in general difficult to ration demand efficiently using a higher price. The power cuts are then either at random or proportional. In this case the consumer surplus is much higher and equals AEF: for each consumer in the range 0qHH , a proportion 1-0Q/0qHH will not be satisfied.

For each level of capacity, price and probability distribution of demand one can define the Value Of Lost Load (VOLL) (€ per expected Mwh lost). The optimal solution is to increase the level of peaking capacity up to the point where the reduction of VOLL equals the marginal cost of capacity (annuity peak capacity/duration of load shedding). One can also increase the price so as to balance the marginal reduction in the VOLL and the higher loss of consumer surplus in the normal demand period. There is a loss of consumer surplus in the normal demand period because the full capacity is not used (we assume that the price>fuel cost)

Figure 8.6 shows the different effects at work. Another option is to offer interruptible contracts to those consumers that can easily decrease their demand at short notice. These will be the consumers with the lowest costs of


being curtailed. An interruptible demand contract acts like an increase in capacity.

price

Quantity

Demand very high (HH)

Demand high (H)

pH

qHQqHH

qHH

pHH

A

B

D

E

Reducing the VOLL by installingMore capacity (Q’)and raising the price (p’)

At the cost of increasing the lossof consumer surplus undernormal demand conditions

F

G

0

P’

Q’

pL

PL’

Figure 8.6 Effects of a price increase and a capacity increase

5. Optimal pricing and investment when demand is

uncertain and availability of plants is uncertain

Not only demand can be uncertain, also the availability of plants can be uncertain due to technical failures, unforeseen weather events etc. Assume a load duration curve that is known with certainty..

The probability that demand can not be satisfied fully can be computed by computing all states of the world: this means enumerating all combinations of machines that could have a technical failure. This allows in principle to compute for every production park and a given demand the LOLL. One can again optimize the level of capacity by comparing the cost of extra capacity and the saved LOLL.


6. Production and transport of electricity

For different reasons (cooling, population density, fuel supply) production

can be located at some distance of the consumption location. What are good

economic principles to invest in transport and what are the optimal locations

for production and consumption?

7. References

Borenstein (2005), Long run efficiency of real time Electricity pricing, University of

California Energy Institute , CSEM WP 133 r

Evans J., Hunt L., (eds.) (2009) International Handbook of the Economics of Energy,

Edward Elgar

Stoft S.,2002,, Power system economics, IEEE press

Williamson, O. E., (1966), Peak-load pricing and optimal capacity under indivisibility

constraints, The American Economic Review, p. 810-827

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