Introduction to the Energetic-Transition: A critical
overview of some energetic transition models.
Yacoub Bahini∗
August 25, 2013
Abstract
Keywords: energetic transition, renewable energy, factors’ productivity, energy efficiency, economic growth.
JEL Classification: .
∗
CES, Universuty Paris 1. E-mail: [email protected]
1
1
Introduction:
In this analyse we will make an overview on the concept of energetic transition
by other authors. We will particularly focus on the work of U. Chakravorty,
B. Magn and M. Moreau (CMM) in their paper :”A Hotelling model with
ceiling on the stock of pollution”, and the model of O. Tahvonen and S. Solo
(TS) in their work ”Economic growth and transition between renewable and
non-renewable energy resources”.
The choice of these two papers as references comes from the fact that they
deal with the problem of energetic transition with different ways, and they
represent some of the recent literature in this field. The two models will be
studied separately to shows advantages and limits of each approach.
The literature studying the extraction of non-renewable energies (NRE)
sources - such as fossil fuel - has grown over the last 40 years due to the
Oil-price chocks of the 1970s, and more recently due to the recognition of the
dangers of climate change. Despite the increasing number of these studies and
their advanced levels, they are still without clear classification of their specific
objectives. In other words, the results of every model depends normally on
the structure and assumption of the adopted approach, what imply that their
finding may diverge. The present paper is not trying to give a proposed organizational frame of this literature, but rather to discuss some of the energetic
literature finding concepts, notably those of energetic transition between NRE
and RE, with the aim to introduce some Key-difference between these models.
It is important for policy-makers (Governments, International community...) to know more on the relation-ship between energy consumption and
economic growth in order to design effective energy and environmental policy.
I. Ozturk has shown that empirical studies, of energy consumption-economic
growth and electricity consumption-economic growth nexus, highlight that although the positive role of energy growth has become a stylized fact, there
are some methodological reservations about the results from these empirical
studies. He concludes that a general observation from these studies is that the
literature produced conflicting results and there is no consensus neither on the
existence nor on the direction of causality between energy consumption and
economic growth. However, its conclusion derived from electricity consumption and growth nexus for the country-specific studies show that causality is
running from electricity consumption to economic growth in most of these
studies. Consequently, we may conclude that electricity is a limiting factor
to economic growth and, hence, shocks to energy supply will have a negative
impact on economic growth.
W. Nel and C. Cooper in their analyze, based on an explicit economic
growth model and focused on Energy security and Global warming that are
considered as the 21st century sustainability threats, predict, with divergence
from 20th century equilibrium conditions, that economic growth and socioeconomic Welfare will be stabilized only under optimistic assumptions that
demand a paradigm shift in contemporary economic thought and focused attention from policy-makers. These optimistic assumptions can be resumed
in technological change and Human behaviors. It can be concluded that
2
the global warming may be acceptable and profitable compared to the socioeconomic consequences of not exploiting fossil fuel reserves to their full technological potential.
An another major aspect of the literature of exhaustible resources, especially fossil fuel energy, is the debate about the very known traditional scarcity
rent. R. Hart and D. Spiro, in their paper ”The elephant in Hotelling’s room”,
show that scarcity rents seem to have been marginal or non-existent historically, that they almost certainly do not dominate resource price today and
that, at very last, there will be other factors shaping resource prices in the upcoming decades. In fact, different empirical methods had confirmed this issue.
The almost constant price trend of exhaustible resources effectively rule out
pure Hotelling resource and is suggestive of low scarcity rent (see for instance
Krautkraemer, 1998).
They have shown, under the fact that a constant ad-valorem-tax has non
effect on the extraction path (Dasgupta and Heal, 1979), that the scarcity
rent is in reality pushed down, but the deficit is filled precisely by the tax, and
the over all effect is that income flows are transformed from resource owner
(rents) to the regulator (taxes). This implies, since a changing tax rate may be
politically unfeasible, that a cap- and-trend system is preferred over taxation
for curbing CO2 emission. And that anything that creates expectation of lower
future demand for Hotelling resource - such as the announcement of future
taxes or R&D investments in finding substitutes for the resources - will lower
the scarcity rent, and thus tend to reduce the price and raise consumption in
the present.
Furthermore, we will show that the scarcity rent path can be strictly decreasing under the strength of others factors, contrary to Hotelling prediction.
Because of scarcity of NRE and growing environmental problems, many researchers advocate a rapid transition to RE resources. The problem is weather
the RE can provide anywhere the level of primary energy costs of energy forecast by various official organizations in a business-as-usual world. Thus, one
has to wonder if the optimal level of RE will reach the level of energy consumption presently forecasted for a few decades? Do the costs of RE and NRE
are the main true indexes of substituability? Should be there a limit (upper
bound) of the RE installed capacity?
There is also a substantial literature based on the idea that changes in
interest rate should be positively correlated with resource’s price increase if
the scarcity rent is significant. The majority of these papers find no such a
correlation 1 . The few papers that do find support for the existence of a
scarcity rent do not support that it is a dominant component 2 .
Chermack and Patrick (2001) and Ellis and Halvorsen (2002) have supported this finding too, by another different approach, by treating the resource
in the ground as one among several input for the production of the finished
resource, in which case the marginal cost saving from increasing extraction
(saving costs on other inputs) should be equal to the scarcity rent.
1
1See Sole and Tille, 2009; Heal and Barrow, 1980, 1981; and Harvorsen and Smith 1984,
1991.
2
See for example Stollery, 1983
3
The literature of exhaustible resources, and in particular that of the energetic transition seems to give a very large and divergent results (or finding)
concerning the optimal sustainable energy transition, especially over the last
few decades, during which the literature in this field has known an important
widening and development.
The first thing one should have to make, concerning this large and unclassified literature, is to distinguish between the theoretical models (in particular
the dynamic growth models), and the empirical based model approaches. The
former deal with the optimal allocation of resources under assumptions proper
to each model. The later aims, in general, to explain the real relation-ship between resources allocation and economic growth, the key factors influencing
energy conservation, inter-substitution between different type of energies, the
main factors behind RE development and so on, based on historical data.
As the remaining of this paper will treat the Theoretical-Models, we would
like to stay a moment with Salomon and Krishna 3 , giving important and
essential rules end lessons from historical shifting between major energies, to
build up a successful energetic transition.
Although our reluctance to characterize all historical shifting between energies, presented in the Salomond and Krishna paper, as energetic transition,
because of their reversibility as we will see in what follow, their paper presents
one of the most useful analyzes presenting the main factors determining policy instruments that had influenced introduction of a new energy systems.
Salomon and Krishna made a rapid survey of historical shifting between energies since the down civilization, considering the wide sens of energy sources4 .
.
History of human use of energy shows that peoples are not required to
keep using a particular source if better option become available, and most of
these historical shifts between energies lasted over a century or longer, while
the energetic transition of 21st century as it seems will need to be more rapid
(Salomon and Krishna (2011). They 5 aimed to highlight the main factors
behind past transitions, and recognizes that little is known about how to
accelerate the energetic transition.
It is in this point that occur the role of the theoretical growth energetic
transition models 6 .
They focus more on the first major energy transition from wood to fossilfuel in the 18th century, and the three modern ”partial transitions” that occurred in some countries (Brazil, which shifted successfully from Oil-based
transportation system to Sugarcane-Ethanol system, France which shifted successfully from Oil-fired electric power to nuclear power, and finally the United
State,which attempted unsuccessfully to shift from foreign Oil to a mix do3
In their impressive ”the coming sustainable energy transition: history, strategies, and
out-look”, 2011
4
These sources have included the sun, wind, water, human and animal muscle, wood,
grasses, dung, agricultural crops, animal fats and tallow, and eventually fossil fuel (Solomon
and Krishna, 2011.
5
Solomon and Krishna (2011)
6
The two model that will be studied in this work will show that theoretical growth
energy transition models can give a very divergent results, and our next paper will propose
an optimal dynamic extraction different from these two models.
4
mestic energy resources).
The 18th century transition was driven by British urbanization, commerce,
technological innovation, and the discovery of major fossil fuel resources. It
lasted almost two century when fossil fuels surpassed the total supply of
biomass fuels to become the primary global energy resource. The main causes
behind this transition was ”High labor costs, increasing scarcity of regional
wood supplies, and difficulty in shipping wood due to its low energy density
provided the initial impetuses for slow and arduous transition that occurred as
the process of industrialization played out in the UK” (Solomon and Krishna
(2011). The industrial revolution, derived eminently and decisively from the
development and use of the steam engine, was indispensable to achieve this
transition. This transition was widespread and covered all sectors even at
different rates. The success of this passage to fossil fuel was due to some key
factors, that can be resumed in technological evolution in all sectors and the
support of government and nations.
The modern energy transition examples are limited in some developing
coun- tries, and characterized by their partiality (transition in some sectors
and not all) and differentiation from one country to another (transportation in
Brazil, Electricity in France), that can question if a real word wide transition
to sustainable energies can be achieved. The modern transition has began effectively in 1925 when Brazil had utilized bio-ethanol as a transportation fuel,
even after Ward War II, it was largely ignored as petroleum-based fuel became inexpensive. When the OPEC Oil chock occurred in 1973-74, Oil export
prices were raised by 70 % with deep cuts in production, eventually quadrupling Oil price (Yergin, 1991, pp. 606-607), causing adverse macroeconomic
impact around the word, as a global recession followed.
Several nations developed programs to wean themselves off of foreign Oil
in order to ensure that any adverse effects would not recur, among them the
countries that have been taken as example by Salomon and Krishana. The
Brazilian’s Bio-ethanol fuel experience represent one of the most important
modern (partials) energy transitions, because it target the transportation sector which has important share in aggregate energy demand (27% in the word
global energy demand ”Word energy outlook (2010)”, and 32% in Brazil energy demand ”Earth Trends-Country Profile (1999)) and has limiting ability
to use renewable energies, at least until now.
The origin of Brazilian’s ethanol program dates to November 14, 1975,
when it initiated its National Alcohol Fuel Program (Proolcool)(Salomon and
Krishna, 2011), starting with 0,9 billions liters of ethanol to exceed 27 billion
litters by 2009 (Gee and McMeekin, 2011). Passing by a recession between
the late of 1980’s and during the 1990’s because of collapse of global Oil prices
and significant rise in word sugar prices, the ethanol production return to
increase by 2002. The percentage of alcohol-based cars sales, rapidly increased
from 1% of total sales in 1979 to 96% by 1985, collapse to fall to 0,1% by
1998, and then re-increase rapidly to 56% by 2005 (Solomon and Krishna,
2011). The ethanol-fuel contribute actually to more than 14% of Brazilian’s
road transport fuels. The non stability of development of ethanol bio-fuel
in Brazil’s experience shows the strong sensibility and reversibility of this
5
transition, that demonstrates that development of ethanol-bio-fuel requires a
contentious change in strategic policies.
Contrarily to the irregularity of Brazilian’s transition experience, the French’s
one was most regular, knew a continuous growth and gained more and more
ground in the electricity sector since the launch of the nuclear program by the
beginning of 1970’s.
With 58 nuclear reactors that were built during the last three decades,
the total energy supply in France grew from less than 5 million tonnes of Oil
equivalent (Mtoe) to over 100 Mtoe by 2008 (IEA, 2010) to cover more than
78% of electricity generation and 43% of France’s total energy supply (IAE,
2010). France is currently the second largest producer of nuclear energy after
the US, but the share of nuclear energy account only for 8% of US total energy
supply. Thus France brought successfully its goal by significantly reducing its
energy dependence on Oil-Import.
However, these two ”partial transitions” (Brazil and France) did not occur
without confronting some obstacles. In France, the nuclear energy program
”did met hostility from a broad spectrum of French society that included trade
union, local residents, environmental groups and many scientists (Kitschelt,
1986, Hayes, 2006), because of fear about reactor safety (The effects of radioactivity on human health and the environment), the concerns about disproportional distribution of advantages (and costs) from nuclear power (Hdjilambrinos, 2000, P. 1116) and uneconomic nuclear technology (in its earlier
stage of development).”(Salomon and Krishna with some modifications)
The Brazilian’s transition, from Oil-fuel to ethanol based fuel, had been
supported by the totality of Brazilians, political leaders and economic actors,
contrarily to French’s program at its beginning. The only worry of Brazilian’s
transition was defining the adequate policy (economic and technological) to
achieve their objective. As regard to the US, the most ambitious program,
Project Independence, suggested in November 7, 1973 by President Richard
Nixon 7 did not come close to meeting its goals. The domestic Oil and gas
production plummeted, the accuracy and usefulness of Project Independence
Modeling System (PIES) came into question by prominent economists (e. g.
Hausman, 1975) and by the end of 1970s net import petroleum increased to
43.1% from 34.8% in 1973 (EIA, 1974).
To understand elements behind successfully managed energy transition,
a series of studies 8 developed a Multilevel perspective (MLP) theory, which
consist of three inter-linked dimensions in a nested hierarchy 1. niche - inno7
Wen he said: ” Let us set as our national goal, in the spirit of Apollo, with the determination of the Manhattan Project, that by the end of this decade we will have developed the
potential to meet our own energy needs without depending on any foreign energy sources
(Nixon, 1973, P. 920).
8
e. g. Geel, 2002, 2005, Verbong and Geel, 2007, Geel and Schot, 2007, Verbong et al.
2008.
6
vations9 , 2. Socio-technical-regime10 , 3. Socio-technical-landscap 11 .
France and Brazil had largely succeed their transition because the Three
MLP factors12 reinforced each others along with their transition dynamic.
Government of these two countries provided strong support and subsidies,
funded R& D to develop technologies, and launched many publicity campaigns.
Furthermore, their transition programs gained public support, even with some
difficulty at least at the beginning, especially in the French case.
The macro level seems to have been in favor of these two programs, despite
some drop-off in consumer support for alcohol-based cars in the late 1980s in
Brazil, because of collapse in Oil prices, that was surpassed by alternative
policy mechanism notably in the beginning of 2000s decade (Solomon and
Krishna).
The US strategy has failed because of trying to increase the development
of large number of domestic energy sources, that limited the niche innovation,
and made it difficult to obtain a consensus on energy alternatives. The increased US reliance on Non-OPEC oil sources and collapse of Oil prices in the
mid 1980s, government support for developing alternative energy sources and
increasing fuel efficiency in motor vehicle collapsed (Kash and RyKroft, 1984).
Further more, the type of governance and county’s institutions played a major
role in the country’s ability to control an effective transition policy. Thus, the
more an economy is centralized the greater its ability to control energy supply
and consumption pasterns, and thus transition between major sources more
rapidly. This was the handicap of the US to reach its energy-independence
goals. Most of Word’s countries seems to have had the same problems because
of their decentralized structure.
In what follow, we will discuss two chosen models (Theoritical-Models),
which deal with the problem of the energetic transition in different ways.
We characterize the first as ”Environmental Energetic Transition Model (EnvETM)” and the second as ”Technological Energetic Transition Model(TETM)”,
and we end with a general discussion.
Presenting these models should lead us to highlight some of the main factors influencing the optimal energetic transition between the non-renewable
and renewable energies.
Thus we should be able to answer the following questions, even partially:
What are the main forces driving the energetic transition? is it the scarcity
of the natural resources? or is it the internalize of the environmental problems?
is it purely economic profitability? Or others?
9
The micro-level, where new technologies (novelties) energy and are typically protected,
sub- sidized or otherwise promoted by government, such as bio-fuel or nuclear power. Radical
niche innovations can provide the seeds for major energy system changes (Verbong and Geels,
2007).
10
The meso-level, which constitute three interlinked dimensions, i. e.: a networks of
actors and social groups, formal, normative and cognitive rules, and material and technical
elements. Path dependency and technological lock-in are the norm in energy systems.
11
The macro-level, which is the exogenous environment that usually changes slowly, over
many decades, and influence the dynamics at the niche and regime levels(thought not vice
versa). these factors include the macro-economy, deep cultural pasterns, and macro level
political develop- ments.
12
These factors include the macroeconomic, deep cultural patterns, and macro level political development
7
Can one say that any model in which there is a substitution between energies is a model of energetic transition? What is the criteria of credibility so
that a model explains best the optimal energetic transition? Do all used approaches, to explain the transition, explain the dynamics of economic growth?
In other world, can we accept that the dynamic of energy consumption explain
the social welfare level whatever the constraints and assumptions? Then, can
we say that there are some incredible models?
Part I
Environmental Energetic Transition
Models (EnvETM): Ex. U.
Chakravorty, B. Magn and M.
Moreau (CMM’s) model:
2
Introduction:
The Chakrovarty and al. paper present an extension of the Hotelling by adding
a backstop resource, internalizing the environmental damages and the ceiling
on stock pollution, and giving a possibility to abate. As in Hotelling, the
CMM’s model predict an increase in energy prices (before the backstop becomes economic), but with a different rates and levels.
The increasing price in Hotelling, due to the scarcity of exhaustible resource
(that decrease the rate of extraction), was understood until now as to giving
more value to the resource as R. Sollow (1974) said ”A pool of oil or vein of
iron or deposit of copper in the ground is a capital asset to society and to its
owner”. CMM shows that environmental degradation increases the level of
price and its growth rate more than when only scarcity was considered. It is
clear that more the NRE is GHG emission intensive more the price level and
its rate increase. Since we cannot accept that the dirty give energy source
more value, we should change the concept that increasing price do necessarily
means increasing value.
When talking about optimal allocation we must not forgot the inter-generational
equality. R. Sollow raised by saying ”In my own work on this question,I have
sometime used a rather special criterion that embodies sharp assumptions
about inter-generational equity: I have imposed the requirement that consumption per head be constant through time, so that no generation is favored
over any other, and asked for the largest steady consumption per head tat
can be maintained for- ever, given all constraints including the finiteness of
resources” (R. Sollow, 1974).
This is an arithmetical or logic based instincts justice, but all the literature
models tel us that the best way to allocate an exhaustible resource is not by
sharing it equitably (between infinite living people), at least until now. Some
generation should profit more that others. This means that instead of sharing
8
reserves of exhaustible resource on an infinity of living consumers (consumption will tends to zero), it will be better that only some generation will profit
from the resource to have a considered consumption level (>> 0), and by the
continuity of live (continuity of humanity require energy consumption at every
time as paramount necessity) the exhaustible resources must profit to the first
generation. That support logically the exhaustible resource model finding.
In the CMM model, the authors aim to propose an approach that can
will be adopted in international environmental agreements. So, they try to
highlight the optimal conditions to be implemented to preserve the quality of
environment along of the dynamic pollution.
The constraints on stock of pollution and abatement cost play the main
role to define the optimal level of NRE along the extraction path. That why it
is characterized by its environmental occupation. This fact can be seen clearly
when they say ”We characterize the solution to the textbook Hotelling model
when there is a ceiling on the stock emission”.
The model predict that there should be some different stages of extraction
and price path, depending on the level of pollution, the stock of NRE resource
and the different costs (of abatement, backstop resource...). The simultaneous
use of both energies (NRE and RE) occur only at advanced stage of NRE
resource extraction, before which extraction of NRE decrease (in almost all
cases) that could mean a decreasing of economic growth (considering that the
economic growth and energy consumption are complementary). Although that
this model present one of the more recent and developed approach dealing with
environmental problem and energetic transition, we will show, in this paper,
that it is very limited with regard to explanation of the impact of energetic
transition on economic growth.
In spite of its environmental aim, this model give us some important points
of views of the energetic transition dynamic as we shall see in what follows.
3
Problematic of CMM:
As it was said briefly in the introduction, the CMM model is characterized
by its environmental occupation. Thus, the constraint on aggregate emission
coming from consumption of NRE resources, plays the main role in the shifting
between energies. This is clearly said: ”Little attention has been paid to the
problem of how a limit on the stock of emission may alter the sequence of
extraction of a fossil fuel and the backstop resource over time”13 .
Furthermore, they focus their analysis on some literature of the models
that specify damage function caused by the use of non-renewable resources,
and some empirical works on global warming. For the former, they have given
the following works among others:
• Forster (1980): He consider that pollution has a negative effect on the
utility function, but clean energy has no role except in the terminal
phase.
• Sinclair (1994)and Ulph and Ulph (1994): they have examined the time
13
CMM
9
profile of the carbon tax in an infinite horizon framework, but without
backstop resource.
• Hoel and Kverndokk (1996) and Tahvonen (1997): have analysed the
path of optimal carbon taxes in a model with a NRE resources and
a clean back- stop. Using Stock-dependent extraction costs, they show
that there may be a period of simultaneous extraction of the non-renewable
resource and a clean backstop.
For the empirical works on global warming they have retained a general
equilibrium framework that does not explicitly recognize the scarcity of fossil
fuels, or model the problem by imposing exogenous carbon taxes (e. g. see
Manne and Richels, 1991; Nordhaus and Yang, 1996; Chakravorty et al., 1997).
We have no objective to comment these references, but rather to strengthen
our hypothesis on the claim of CMM’s model.
4
The work of CMM:
The work of CMM can be considered as one of the important point of view
modeling the optimal extraction of the scarce energetic resources.
In fact, the CMM’s model present the continuity of Hotelling model with
internalizing environmental damages caused by emission of green house gases.
They consider three scenario, first the case where demand is increasing (ID),
secondly the case where demand is constant (CD), and third case in which
demand is decreasing (DD).
The model predict that energy price will never exceed the price of the
backstop or RE resource, that it is considered constant over time and relatively
more expensive compared with NRE.
As the price still lower than the cost of backstop resource, the price path
depends on whether the ceiling on the stock of pollution is binding, it is not
binding but will be binding in future, and if the ceiling is not binding and
will never be binding. We will see the path of price during this work for the
three scenarios, but one can underline that the price, in general, is increasing.
The CMM’s model, according to our understanding, introduces some new
concepts, of ”environmental rent”14 and ”abatement rent”, which we will see
in description later in this paper.
Even if the CMM’s model considers the only energetic sector, and thus
considers only energy commodity, it advance an important approach to the
energetic literature by introducing the ceiling on the stock of pollution, and
the possibility of abatement that makes it possible to increase consumption
of dirty NRE energetic resource more than when abatement was not possible.
The introduction of backstop resource, or renewable resource, is one of the
more important characteristics of this model too.
Let us present others points that the model help to introduce:
• Prices are useful indicators of scarcity. furthermore, its path can indicate
the level of social interest towards the environmental problems.
14
In this analyse we do not distinguish between rent and tax.
10
• The price rate must depend on the level of pollution stock, abatement
cost, NRE stock and backstop energy cost.
• The NRE resources are not homogeneous,
• Back stop technology allows to stabilizes energy price, and thus the
energy’s consumption growth,
• substitution is an important response to increased scarcity,
• change in demand influences price and availability,
• The level of energy price, cost of abatement and the scarcity rent are a
keys indicators of the dynamic of extraction of NRE resource,
• The extraction path of NRE resource depends on evolution of demand,
• The cost level of renewable resources is an important indicator to the
NRE extraction path.
• The constant costs of NRE and RE, and the relatively low cost of NRE
imply depletion of NRE resource in finite time.
• The short term evolution of expected level of demand has important
influence on the extraction and price paths.
• Energy taxes must follow the extraction stage and the level of pollution.
In other words, the model provides a vehicle for introducing various dimension of energy supply and scarcity of NRE resource with conservation of
environmental quality, and an abundant backstop technology.
5
CMM’s assumptions:
CMM established several economic assumptions for their model that do not
necessarily reflect the reality of the energetic sector, and as in the Hotelling
model, it is hardly surprising that the rule cannot be verified experimentally15 .
• The CMM’s model assumes firstly that energetic resource owner’s objective is to maximize the present value of its current and future consumption, differently with the Hotelling that aims to maximize the profit.
This require that extraction of NRE resource and utilization of RE resource take place on an efficient path in a competitive energy market
equilibrium, which imply that energetic producers are identical in terms
of costs and that they are all price takers in perfect and instantaneous
market of information.
• Secondly, the energetic sector is perfectly competitive and has no control
over the price received from for its production.
15
RCA MINNIT
11
• The third assumption is that extraction of NRE resource and the production of RE are not constrained by existing capacity, they may produce as
much or as little as they like, at any time for the renewable, and during
the live of existing NRE resources.
• The forth assumption is that coal deposit has a capitalized value. That is
the coal deposit in the ground is a capital asset to its owner (and society)
in the same way as other production facility. Furthermore, they assume
that richest and most accessible deposit would be extracted first, and
that increasing scarcity (after exhaustion of the most accessible coal)
would confer capitalized value on inferior deposit which could be extracted.
• Fifth, they assumed that the resource stock of NRE resource is homogeneous and consequently there is no uncertainty about the size, grade and
energetic value of their deposit. Furthermore, they assume homogeneous
renewable resource, that is that RE resource is produced with constant
cost over time, that would not reflect the reality of technological evolution. Current and future prices and extraction or production costs are
known. This imply that NRE and RE energies has uniform quantity and
there will be not a continual improvement of the efficiency and the costs
of both energies.
• The sixth assumption is that the cost of NRE resource does not change
as the deposit is depleted, and the cost of RE resource does not change
with time by ”the learning by doing” experience for example. Thus,
this assumption does not recognize the fact that all NRE resources face
increasing costs as they are depleted and the deposit become more and
more hardly accessible, and that RE resource face their cost decreasing significantly as their propagation become more and more important.
Furthermore, the assumption that marginal unit is accessible at the same
cost, imply that marginal cost of extraction in this particular case is zero.
In addition, it imply that market price and the rate of extraction are connected by a stable downward slopping demand curve for the resource16 .
• The seventh assumption is that there is no technical improvement during the life of coal and that no new additions to resource stock are contributed by resources exploration. Thus, as The Hotelling model, the
CMM’s model seems tend to diminish the potential value of the application for companies or countries involved in the non-renewable energy
resource extraction.
• CMM’s model, as Hotelling, neglect all economic sectors other than the
energetic sector, and neglect the fact that energy consumption is influenced by others main factors, such that the technological characteristics
of production for example, that constrain the level of production, and
consequently limit the level of energy by considering the strong complementarity between energy and others production factor.
16
Solow, 1974, P.3.
12
• Fifthly, the CMM’s model assume that the non-renewable and renewable
resources are perfectly substitutable, that can go away from reality, at
least when considering actual technological level.
• Lastly, the model assume that the degree of pollution can be perfectly
known, and that the effect of abatement on reducing pollution is also
perfectly known, that diverge from reality because of difficulty to verify
the pollution level precisely.
Whatever the limits of CMM’s model, it still be one of the best extension
models of Hotelling. It can help understanding the way to deal with the problem of environmental damage caused by extraction of dirty energy resources,
and can help the international community to implement an efficient environmental policy. It define the optimal carbon taxes and the permit of emission
taxes dependently on the level of pollution with consideration of the backstop
resource. With their elegant analysis, CMM provide economists of energetic
transition a strong structure to build more advanced thought on this problematic, and confirm what solow said ”Good theory is usually trying to tell you
something, even if is not the literal truth”.
6
The extraction and price paths in the CMM’s
model:
In this part we will discuss in depth the results of CMM’s model concerning
the optimal consumption path and price path of both renewable and nonrenewable energetic resources.
In each scenario of exogenous demand (ID, CD and DD), dynamic consumption pass by some different and consecutive stages that we describe below. The number of periods is almost six, depending on some exogenous data.
The most important among them are the following:
• Expected exogenous evolution of demand, that is the utility function is
dependent of time17 .
• The level of the stock of NRE resource.
• the cost of backstop resource, that is greater than the cost of nonrenewable resource,cr > ce .
• The maximum consumption rate of non-renewable resource, X̄, when the
constraint on the ceiling of pollution is binding, Z̄, and its correspondent
price p¯t .
We will discuss also in this section the meaning of increased price and
level of production of the backstop energy. So, we will discuss on the sense or
meaning of the scarcity rent and the role of backstop energy.
17
One should notice that there is a difference between demand and consumption. If consumption does not reach the level of demand then we have some deficit.
13
Do we have to understand the scarcity rent, the ”environmental rent” and
”abatement rent” 18 , as an increased value of the non-renewable resource, as
it was understood right now?
In fact, in Hotelling, the scarcity was always considered as Solow (1972)
pointed out that ”a mineral deposit, whose value arise from the potential for
extraction and sale, is a capital asset to its owner and society”19 . Always
according to Solow ”the only way to a resource in the ground can produce a
current return for its owner is by appreciating in value”20 . Such understanding
must be revised and discussed.
As was said in the introduction of this part, adopting this logic the Coal’s
rent (scarcity + environmental) must be greater than the Oil’s one. Knowing
that Coal is more intensive than Oil in term of GHG emission, we can be sure
that Oil will be more preferable socially (with considering the same reserve of
Oil and Coal). CMM model suggest that the price level of Coal is bigger than
Oil’s, and it increase most rapidly, that mean that Coal deposit have more
economic value than Oil’s, that diverge from society choice.
That we want to say is that increasing price does not mean giving more
value to a given exhaustible resource deposit. Increasing price means limiting
extraction of NRE and not appreciating in value. The price is an attracting
force that conduct the extraction of NRE to a given (Optimal) level. The
level in Hotelling pure model is zero-extraction level. We will show more on
this on the next part of this paper, and in our next paper that propose a new
transition-model.
So, in the CMM’s model and Hotelling model, the non-renewable resource
try to tell us ”Keep me in the ground” by its price voice and the Environment
would like to tell us ”Do not pollute”.
6.1
The different periods of extraction:
Here we present the different periods of extraction presented by the CMM’s
model, to help referencing our analysis in what follow.
The first period in which the constraint or the ceiling of the stock
of pollution is not binding, but there is a continual degradation of the
environment. That is that the ceiling will be binding. In this case only
coal is used in different scenarios.
The second period when ceiling is binding, is divided in three different
stages, whose succession and apparition depends on the considered cases.
The abatement period which may occur only when ceiling is
binding and the level of extraction of non-renewable resource is
more important than its critical value x̄. Furthermore it will never
be optimal to abate when the renewable resource is competitive, i.
e. when abatement occur only non-renewable resource can be used.
18
The scarcity rent was historically known by the Hotelling work, but for the ”environmental rent” and ”abatement rent” we have introduced them as new concepts.
19
RCA Minnit
20
Solow (1972) P.2
14
The only use of non-renewable resource without abatement
in which the extraction is constant at its critical value x̄.
The simultaneous use of both resources in which extraction
of non-renewable resource continue at its critical value x̄ until exhaustion.
After the binding ceiling period there may occur the last two possible
periods:
The third period that follow the Hotelling standard period with the
only use of non-renewable resource.
The forth and last period that is characterized by the restrictive use
of renew- able energy.
6.2
The modified Hotelling price and the consumption path:
Hotelling had demonstrated that price of an exhaustible resource (or value
of an exhaustible resource in the ground) must grow at the market rate of
interest. It is known by the famous Hotelling r-percent rule: Pt = P0 ert where
Pt is the price in the period t, P0 is the initial period price, and r is the market
rate of interest.
”It is important to note that this relation hold only when if extraction costs
are zero. More generally, net price rise at the rate of interest for all version of
the model (zero extraction cost, constant positive costs, rising costs). Thus the
net price, λ = p − mc, which is the market price minus the cost of extracting
one ton of ore (marginal cost) should be expected to grow exponentially at the
rate of interest”21 . That was just a reminder of Hotelling rule, whose CMM’s
model constitute a real extension.
In fact, the CMM’s model suggest that energy price must grow as long
as the price does not reach the constant cost of the backstop energy, except
at the ceiling on the DD scenario, on which one use only the non-renewable
resource with constant extraction. On what follow we describe each period.
The forth and last period (P4 ):
In this period we use only the renewable resource, it is the last phase
in each scenario. It occur just after the non-renewable resource is completely
depleted. The exhaustion of the non-renewable resource is one of the important
characteristics of the CMM’s model. It is a direct result of the constant costs
of the two energies, and the relative low cost of the non-renewable resource
compared with the renewable energy cost.
Assumption of constant cost can be considered as a highly explosive regarding the fact that non-renewable resource should get an increasing cost,
and the renewable resource should get an decreasing cost. Constant price of
RE mean that the energy consumption (only use of RE) will be constant (Increasing, decreasing) in the CD (ID, DD), that is an important result of CMM.
This give the adequate price policy to be made after achieving transition.
The standard Hotelling period (P3 ):
21
R.C.A. Minnit
15
In P3 , the remaining stock of non-renewable resource is small enough, such
that the ceiling still inactive from the beginning of this phase. So, there is
no difference between CMM’s model and Hotelling model during this time
interval. Thus the price follow the ”r-percent Hotelling rule”: P̆t = ce + λ0 ert .
With ce is the extraction cost of non-renewable resource and λ0 is the initial
scarcity rent.
As in Hotelling, the marginal cost should include the amount paid in fixed
and variable costs, wages, taxes, dividends and fair market return, sufficient
to induce to invest in energy resource development in the first place. ”The
simple case of net price has been extended to mean that the royalty for the
marginal unit of extraction, will rise at the rate of interest. This is exactly
the definition of royalty. It is a decline in value of natural resource as a result
of the extraction of one unit of the resource. The energy producer should in
this case be happy to pay royalty to the owner of the resource, because it is
a benefit he never aimed for. In reality ”mine owners” are both to pay this
amount to the owner of the resource, usually on the form of royalty to the
government, as they view it as a return to be appropriated because of their
entrepreneurial skill and risk they bear in mineral investment ventures”22 .
This stage of extraction (P3 ), if it occur, it will be just before the last
period whose price is constant at the level of the cost of the backstop resource
(cr ).
This imply that the CMM’s model predict that the price should not grow
indefinitely, it will be obstructed by the constant cost of backstop resource
once it becomes competitive.
P3 occur only in the case of high renewable energy’s cost (cr > P̄t ), and
it consists rather in a transitional period between the ceiling period (P2 ) and
the final period of only use of renewable resource (P4 ). That is that just in the
end of P3 the stock of non-renewable resource will be completely exhausted.
The P3 period embody the property of the continuity of the extraction path.
In this period, the extraction path is decreasing in both CD and DD scenarios. In the ID scenario we cannot conclude about property of the extraction
path, that present one of the limits of the CMM’s model.
The ceiling binding period (P2 ):
During the P2 period, the ceiling on the stock of pollution is binding, and
CMM’s model predict three possible sub-periods of the optimal path to control
the greenhouse emission. The apparition or not of these sub-periods depends
on the levels of the following price indicators:
Pet (at ): Which is the price (marginal utility) corresponding to the maximum
consumption rate of coal if the stock of pollution, Z, is at its upper
bound Z̄, and abatement is equal to at .
Pet Which is the price (marginal utility) corresponding to the maximum
con- sumption rate, x̄, of coal when the stock of pollution is at its upper
bound Z̄, and there is no abatement.
cr which is the cost of renewable resource.
22
Minnit
16
In what follow we present the description of each period, and indicate the
succession of these sub-periods in each case and scenarios.
The abatement sub-period (P2−1 ):
Abatement occurs only if its cost is sufficiently competitive and is done
only when the ceiling on the stock of pollution is binding. This period is also
characterized by increasing price: P̆t = ce + λ0 ert + ζca ,where P̆t is the energy
price when abatement occur, ζ is the pollution per unit of coal consumed, and
ca is the unit cost of abatement.
It is clear that this price P̆t is higher than Hotelling’s price ( P˜t). Thus even
if abatement is the most effective mean to deal with increasing environmental
damage, its corresponding price will still relatively higher than the Hotelling
price. It exceed the Hotellig by the marginal cost of abatement, that is :
P̆t = P̃t + ζca .
Thus, one can call this ”The Abatement Rent” (AR), because if one consider it as a tax, it will not be clear who pay it, so the AR is a kind of disguise
tax. The AR is constant over P2−1 period, that mean that the price P̆t is
just a shifting of the graph of the standard Hotelling price. In this period
the increasing rate of price is caused only by the scarcity rent. Thus, one can
conclude that the AR increase the level of price, but do not change the growth
rate of price. That is it will not be optimal to increase or decrease the growth
rate of price by the effect of abatement cost.
Since when abatement occur only the non-renewable energy can be used
and only the excess of extraction, at = x̆t − x̄, is abated, and in the end
of abatement period x̆t = x̄ in almost all cases because of continuity,we can
conclude that ”the latest abated unit is more costly than the former one”
during all this interval. Thus the model predict that the first pollutant pay
less than the last one, that can be socially inequitable.
It is important to note that the extraction path during P2−1 is decreasing
in both CD and DD scenarios, and it seam to be the same for ID scenario
because of the fact that x̆t > x̄ at the beginning, and that x̆t = x̄ at the end
of this period in almost all cases.
The sub-period of only use of non-renewable resource without
abate- ment (P-2-2):
In this case, the optimal extraction path of non-renewable re- source is
constant at the level of maximum consumption rate of coal, x̄, when the ceiling
is at its upper bound Z̄, and there is no abatement. In this case, the price path
depend on demand behaviour. It is increasing on the ID scenario, constant for
CD scenario, and decreasing for DD scenario. In all cases, the consumption
rate still constant at x̄.
If we take the case of CD for example, we see that the price is constant
while we use the only NRE source. This is explained by the high level of price
compared with the Hotelling standard model. Thus, this price level allow to
more energy consumption comparing to the ceiling constraint on the stock of
pollution, but once the price reach the Hotelling’s price level, it will re-increase.
This stage of consumption can be considered as a transitional period between the ceiling binding period (P2 ) and the Hotelling period (P3 ), or the
final period (P4 ) of only use of renewable resource. This period can also be
17
qualified as a period of exhaustion of non-renewable resource. This is true
for both CD and DD scenarios. In ID scenario this hold for almost all cases
depending on the level of the renewable resource cost and the rate of growth
of P̄ .
Even in the case of the ID scenario, the P2−2 period still a transitional
period that aims to exhaust the non-renewable energy resource, and its occurrence on the time line depend on the abatement cost and the level of renewable
energy cost. The model don’t precise the price path exactly on the ID and
DD scenarios that present another limit.
The sub-period of simultaneous use of both resources without
abatement (P-2-3):
This period is characterized by ceiling binding on the stock of pollution,
and a competitive renewable resource. The optimal policy to limit the carbon
emission is to fill the exceed demand (over x̄) by the renewable. Thus the
consumption of non-renewable resource must be constant at the x̄ level. The
price is constant along this interval at the level of the cost of renewable resource
cr , that present the upper bound of the energy price in all periods and cases.
This period, if it occur, it should be the last period before exhausting
non- renewable resource, except in one of the cases during the DD scenario,
in which P2−3 occur just before P2−2 . So, P2−2 and P2−3 can be considered
as the exhausting periods of non- renewable resource, and their occurrence
depend on their corresponding prices competitiveness.
The first period with ceiling non-binding and increasing environmental damage (P1 )
The first period is that of the only use of non-renewable resource with a
sufficiently high rate of extraction. It is characterized by a continuous degradation of the environment quality, and thus by augmenting the stock of pollution toward its upper bound Z̄. The energy price, in this period (P1 ), has the
most highly increasing rate compared with all other periods, that is it increase
rapidly: P = ce + λ0 ert − ζµ0 e(r+α)t . We call this later term (−ζµ0 e(r+α)t )
the ”Environmental Damage Rent” (EDR), that consist of the amount that
be must paid for the society (or government) to permit a pollution.
It is clear that EDR must grow with a rate greater than the rate of interest,
notably equal to the interest rate plus a positive constant α corresponding to
the auto-regeneration of the environment. This result is not intuitive, since the
increase of the parameter of auto-regeneration, α, should normally decrease
the price because of the pollution constraint will be loosen, while the parameter
α has the strict contrary impact (Ż = ζxt − at − αZt ).
When α increase, the effect of the marginal pollution caused by the marginal
0
consumption must decrease. With other words, for α > α the marginal unit
of consumption, at the same stage, have lower damage impact when consider0
ing α than when considering α . The fact that EDR rate is greater than the
SR show that environmental damage problem must have more consideration
than resources’ scarcity, at least during this period.
It is clear that in all scenarios, the stock of pollution is increasing during
this period, that explain the increasing price of energy.
18
7
Conclusion:
It was clear that CMM’s model attempt to extending Hotelling theory to the
case when the stock of pollution is constrained. It gives a strong base to a
useful environmental policy insight. Among its important results is that the
extraction path must pass by multiple different stages, depending on RE cost,
whether the NRE is highly or lowly polluting and its stock level.
The CMM’s model gives a useful proposal of carbon emission taxation, and
show that it must depend on the stage of extraction. Furthermore, we have
concluded some important results from CMM’s model, notably the fact that
scarcity rent must be understood out-of its traditional meaning, the introduction of environmental rent and abatement rent and their effects on extraction
and price path.
Although the importance of CMM’s model, it do not represent our research
objective, notably ”The energetic transition and its impact on the economic
growth”. In fact, this model is characterized by its environmental particularity, and does not explain clearly or sufficiently the impact on the economic
growth. The only link that can be established between this model and economic growth is that the level of energy consumption can reflect the level of
produced goods, with the strict complementary assumption between energy,
as production factor, and other production factors such as capital for example.
The only consideration of energy sector present a simplistic assumption
regarding the complexity of energy use, and neglect other factors affecting the
energy consumption such as the technology constraint, for example.
Furthermore, the model predict a jumping on RE use from zero to a given
level, that may be technically unfeasible. Thus, instead of giving an optimal
evolution of the capacity of production of RE, the model consider that we can
produce as much as we like, because of the abundance of RE.
Lastly, the authors have not distinguished, in they analysis, between the
substitution between energies (Gas, Oil, Solar..) and the energy transition
(NRE to RE), whose we will talk about in the end of this paper.
8
Which is greener, Flatter or stepper extraction
path?
Before leaving this part devoted to environmental models, it is of importance to
mention the concept of green paradox, evoked by Sinn, in his working paper
”Public policy against global warming”, and to evoke some contradictions
concerning the meaning of extraction path flattens. Sinn says that historically,
the literature on the climate change considered only the demand side and
neglect the supply side. Thus, it considered the only partial equilibrium in
the word wide energy market.
So, ”Alternative methods of generating usual energy from wind, water, sunlight or biomass may also depress the price of energy in the world markets and
stimulate demand elsewhere, but, as assumed they do not affect the extraction
path, the general equilibrium reaction of world energy markets must be such
that the alternative energy produced simply is consumed in addition to the
19
energy con- tained in fossil fuel. There is a contribution to economic growth
and mankind’s well being, but not towards a mitigation of the greenhouse effects”. (Sinn 2007) The introduction of global warming in Sinn’s model, seems
to have a positive impact by postponing the extraction of energy resources, i.
e. with less extraction in the present but a lower decline there after.
The ”Green Paradox” appears when a changing (increasing) tax rate is
introduced. That have as a result a highest demand change rate in the time,
that means more extraction today and less extraction in the future comparing
with the case without changing tax. Thus, the problem of global warming is
exacerbated rather than mitigated.
The ”Green Paradox” give us an important finding that we have to consider
while implementing an environmental policy, because of the fact that some of
proposed policies can be, controversially, anti-environmentalist.
Despite the importance of this finding (Green Paradox), it could have a
weak point of Sinn’s model, notably the fact that with a given proven reserves
of NRE, we connote impose an initial level of extraction. I. e. that, in this
model, the initial level of extraction should be given endogenously, respecting
the optimal price path and the condition that both extraction level and initial
reserves must tends to zero continuously, the possible initial extraction level
is unique. With these assumptions, the flatter extraction path should be the
green one. But when regarding CMM’s model, that was presented above, we
can see that the flatter extraction path has not the same interpretation as in
Sinn’s model.
In fact, in the CMM’s model, the extraction path depends not only on the
reserves quantity but also on the level of pollution and the cost of REs. In
the CMM’s model the steeper extraction path mean that the environmental
damages caused by marginal extraction unit is high, and the more increasing
price means limiting extraction of NRE to introduce earlier possible the RE,
contrarily with Sinn’s price path meaning.
So we can conclude that the price signal in these both models (Sinn’s
and CMM’s) has the strict contrary information. To more understand this
phenomenon in CMM’s model, we can see’ in CD scenario, for example, when
abatement occur, the extraction path becomes more flatter than before, that
means less decrease in extraction because of less environmental damages.
Thus CMM’s model tend to flatten more the extraction path if the environmental damage is less considerable, while Sinn’s model flatter more the
extraction path when the environmental damage is more considerable. This
contradiction may be caused by the clean backstop and natural regeneration
capacity of the atmosphere considered by CMM.
20
Part II
Technical Energetic Transition
Models (TETM): Ex. O. Tahvonen
and S. Salo (TS’s) model
9
Introduction:
In this part of present paper, we will present rather briefly the TS’s model:
”Economic growth and transition between renewable and non-renewable energy resources”.
This model was chosen because it deals with the problem of the transition between energies with a new approach different from the CMM’s model
and most of tradi- tional models. Thus, it allows us to discuss a new approach
showing the complexity of the energetic transition. The model studies optimal
path of non-renewable and renewable energy use, starting with the unique use
of renewable energy (that diverge from our vision: that we rather qtart with
the non-renewable use). They consider a very long run of energy consumption starting before the industrialization epoch (before 18s century) until our
modern epoch.
The changing costs (by concavity) of both energies and the production
function play the main role to define the optimal path in this model. The
importance of TS’s approach is that it change radically the classical vision
of the optimal NRE resource extraction theory. They shows that scarcity do
not drives the energy’s path path, and that the extraction path of NRE can
be U-shaped differently to the Hotelling based models that predict rather a
decreasing extraction over time.
TS’s model predicts, starting with the only use of RE, an increasing economic growth that rise energy demand and the choke price for NRE. Until
reaching a given level (choke price), the NRE energy become economic and,
due to the growing demand, there occur a switch to simultaneous use of RE
and NRE energy with an initial increase in the NRE use. The NRE use starts
from zero and return to zeros in finite or infinite time.
They (T&S) introduce also the concept of economic reserves (of NRE),
that present the used physical quantity of the NRE resource. The amount
of economic reserves is endogenous and depends on RE substitute, technology
and past economic development. Furthermore, this model (TS’s) predicts that
extraction (of NRE) ”requires resources which, with small capital stock, may
have very high values in terms of foregone consumption and investment. This,
together with low demand, implies that the initial use of NREs with small k∞
is low”.(TS) ”The size of economic reserves increases because the choke price
increases along increasing capital stock and a larger fraction of physical stock
becomes economically recov- erable”.(TS)
The TS’s model is closer to our proposed model (Next paper) in the sense
that it considers another economic sector other than the energy sector, and its
21
consideration of the level of technology, although the big difference between
theme.
10
Problematic of TS’s model:
Tahvanon and Solo (TS) have explained in their introduction that the environmental problems, caused by emission of greenhouse gases coming from the use
of exhaustible resources, present the main target of their model. So, they
attempt to contribute to more understanding of the growing environmental
problem with some divergence of the Hotelling-based models.
In fact, the structure of the model can not be characterized by environmental purpose, but it is rather designated by its technological line. That is
that production technology plays the main role, among others, to determine
the optimal path. Furthermore, the level of greenhouse emission can be evaluated only by the extraction level of non-renewable resource and there is no
other environmental constraint in the model.
The main divergence between the TS’s model and and Hotelling- based
models is that TS predict that the scarcity-rent of an exhaustible resource can
firstly increase and then decreases to zero, contrarily to Hotelling that predict
an increasing scarcity-rent over time.
TS’ model shows that the extraction of NRE can increase first from zero
to a given level before its exhaustion, then decrease to zero, that diverge from
Hotteling that predict a monotonically decreasing extraction. Furthermore,
TS’s model do not require depletion of NRE reserves, but gives rather the
notion of economical reserves.
However, this can not be a sufficient argument to question the Hotelling
scarcity rent, because this change is due to the presence of an economical
context strictly different from those was considered in traditional models, that
we should see during this paper. So, we will show that this change of the rate
of scarcity rent should be understood as an evolution and not as a negation
of the Hotelling rent meaning. In our model (next paper), we should present
another different comprehension of the Hotelling rent.
11
The TS’s model assumptions:
The TS’s model aims to maximize the social welfare too, by maximizing the
consumption efficiency of the unique consumption good of economy. There is
one productive sector whose production function is P , and use capital and energy as productive factors (k, e). There are two different perfect substitutable
sources of energy, the renewable ,q, and the non-renewable, s.
Differently from the CMM’s model, TS’s model assumes a non constant
costs of energies. The marginal costs of two types of energies are strictly
increasing and concave, but not depending on the time.
Despite the importance of the increasing marginal costs assumption, the
marginal cost of a given quantity of energy is the same over time and neglect
the fact that the costs must be changed in the future. Notably it seem to
be increasing for non-renewable because of more deeper fossil resources, and
22
decreasing for renewable because of technical evolution and experiences. Furthermore, the TS’s model neglect the depreciation of the capital and con- sider
an abundant renewable energy, that diverge from reality.
Another implausible assumption is that the cost of using the most favorable
renewable energy are assumed to be equal or lower than the cost of using the
first unit of non-renewable, that cause directly the fact that we must start
with the only use of renewable and then we shift to a simultaneous use of both
energies with increasing non-renewable use at the beginning and then decrease
to zero in finite or infinite time. That is not reflecting the reality according
to our knowledge, and go away from our central objective of transition from
non-renewable to renewable energy.
12
The steady state:
The TS’s model is characterized by a unique possible interior steady state.
Equations characterizing the steady state are the followings: Pe (k, s)−C(x) =
0
0; Pe (k, s) = F (s) and r = Pk (s).
Where x is the remaining stock, C(x) is marginal cost of extraction, and
0
F is the marginal cost of renewable.
At the steady state the chock price, or the marginal cost of energy, should
equalize the marginal cost of extraction of non-renewable resource. Furthermore, this marginal cost of energy equalize the marginal cost of renewable
energy. The last equation means that the marginal cost of capital (or the
marginal productivity of capital), at the steady state, is equal to the interest
rate r.
This later condition implies that the rate of interest has a positive impact
on the level of the capital at the steady state (k∞ ). That means that bigger
(resp. lower) is the rate of interest r, the lower (resp. bigger) is the level of
k∞ , that is technically questionable because the intuitive effect of interest rate
on the level of k∞ should be strictly the opposite. Our model (Next paper)
predict the contrary effect, that is that bigger (resp. lower) is the rate of
interest r, bigger (resp. lower) is the level of k∞ .
Physically, the steady state present the level of non-economic reserves of
NRE toward which we converge in finite or infinite time. Thus the steady
state correspond to the last phase of extraction of NRE when extraction is
zero (or infinitesimal). ”There is a limiting cases, of course, in which demand
goes asymptotically to zero as the price rises to infinity, and the resource is
exhausted only asymptotically. But it is neither believable nor important” (R.
Sollow, 1974).
13
The optimal extraction path:
In TS’s model, the extraction path of non-renewable resource has always an
inverse U-shape. The use of non-renewable resource increases from zero until
reaching a certain level and then begin to decrease to zero in finite or infinite
time.
23
The non-renewable energy occur only when energy price exceed or equalize
the chock price of non-renewable. That is Pe ≥ C(x)(orG = Pe −C(x) = 0) TS
shows that the maximum level of remaining stock of non-renewable resource at
the steady state (x∞ ) is strictly positive. Thus the remaining reserve should be
positive and lower than x∞ (x∞ ∈ [0; x∞ ]), depending on the initial conditions
(specially the level of capital) and the chock price level.
Because of the finding of their model (TS’s model), concerning the optimal
extraction path, the authors make questionable the implication of the traditional models of scarce resources which assume a strictly decreasing extraction
of non- renewable resource. And they also criticize the increasing scarcity rent
by showing that it can take an inverted U-shape too.
Although the importance of their results (TS) considering the extraction
path and scarcity rent, one should not understand it as a contradiction with the
Hotelling rule, but one should rather take it as an evolution of the Hotelling’s
rules meaning.
In fact, the smooth switch between the energies is due to the increasing
endogenous energy demand toward a steady state, and the properties of increasing marginal cost of extraction. The later is likely increases less than
the former. In simultaneous use of both energies, when the extraction starts
to decrease because of its relatively increasing cost, the more and more less
expensive renewable energy and limited consumption (that converge to e∞ )
implies that scarcity rent begin to fall toward zero because of the other forces
that tends to limit the use of the scarce resource. Thus, these factors take-of
from the scarcity rent its role as a scarce resource protector.
The finding of our model (next paper) is that the extraction of scarce
resource must be kept at a given rate (or converge toward it) as long as it is
possible whatever the relative marginal prices.
14
The non-renewable resource price path:
The TS’s model predicts a ”generalized Hotelling rule”, that the price of NRE
in term of output must increase monotonically along the optimal solution at
regime of simultaneous use of both resources. While the price in term of
current utility may, in general, increase or decrease. They show an example
when the price in term of current utility initially decreases and then increases.
”The marginal costs of producing energy from renewable exceeds the marginal
extraction costs of nonrenewable, the difference being the resource rent” (TS).
The rent always decreases to zero, that why T&S question the traditional
concept that it is a true index of scarcity. One should say again that the finding
of TS’s model on the fact that scarcity rent increase firstly then decrease
toward zero, do not deny the fact that rent is a true index of scarcity rent.
The decreasing rent is forced by others economic factors, the principal
among them is that economy must converge to a steady state, that is energy
demand is limited or bound from above, and by the fact that, by assumption,
the cost of the first marginal unit of non-renewable is higher than that of
renewable, which force to limit the use of non-renewable, and so decrease the
(scarcity) rent. We have seen the quite similar results in the CMM’s model
24
when energy price was stable in the CD scenario with the simultaneous use of
both energies.
15
Technical change:
TS present in their paper a case of technical change by leaning on the following
two assumptions:
- The level of extraction-specific technological knowledge (n1 ) that accumulate due to learning by doing extraction (n1 = q), and
- The level of technological knowledge (n2 ) associated with the level of
productive capital (n2 = k).
Generally, this technological change does not affect the path form of extraction of non-renewable resource and the scarcity rent, but affect the rate
of extraction and the rate of growth of the scarcity rent along the time. The
technical change accelerate the deletion of non-renewable because of decreasing extraction cost due to the accumulation of extraction-specific technological
knowledge, jointly with ever growing capital stock.
Another important result, is that along the regime of simultaneous use of
both energies, technical change in resource extraction imply a decreasing price
of energy during the beginning of simultaneous use of both energies, although
the price increases back toward the chock price as t → +∞ differently of the
case of no- technological change when the price increase permanently.
This mean that technical change has a non-permanent positive effect on
the scarcity rent. That is that, in the beginning of simultaneous use period,
the technical change decrease the price more than the scarcity rent increase
it. This imply also a more carbon emission in unit of time in presence in
technological change than in its absence, at least at the beginning period of
simultaneous use of both energies.
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Conclusion:
TS’s model present a quite different approach from the traditional Hotellingbased models. Despite its amazing context, we start with the only use of RE
( or the fact that they consider the very long run of energy use starting by the
pre-industrialist period) , it give us a new vision of energetic transition.
Among their important results, with regard to the environmental problems,
is that the optimal extraction path do not imply the exhaustion of NRE. There
must be always a preserved physical reserves that are known as non- economic
reserves.
The decreasing scarcity rent, at least after a given time, changes radically
the traditional rules of exhaustible resource’s theory. On other hand, it is
important to express that the inverse U-shape of extraction of NRE in TS’s
model (starting from zero) is not necessarily different to the extraction path
form the Hotelling based models (monotonically decreasing). In fact when
we consider that the capital is significantly high ( after industrialization), the
extraction path of NRE must start with a strictly positive value and then
decrease monotonically.
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The authors present their result as a critic to the Hotelling rules, that we
have shown not to be necessarily true, i. e. that their result must present
a new meaning of Hotelling rules. In other world, the increasing price must
be known as an attracting force to take-back the extraction to a given level
proper of each model. Among the important things in this model is that it
propose a smooth shifting between energies. So, there is no a jumping as in
the CMM’s model.
Furthermore, they show that the convergence of energy consumption toward a steady state is depending not only on energy supply but also on the
level of capital. This is why we consider it as a ”Technological Energetic
Transition Model (TETM)”.
Although that TS’s model is more closer to our model (Next paper) than
CMM’s, in the fact that they are both characterized by their technological
presence, it seems to be away from our objective. In fact, energetic transition
in this model (TS) is not going from NRE to RE, because they assume a lower
cost of RE than NRE, that mean that they consider the old RE (of the preindustrial period), while the RE sources that we consider are the new form
that was not largely known before.
Furthermore, the abundance of RE energy is limiting the importance of
this model (TS). We want to know the optimal rate of RE development. The
neglected depreciation of capital present a further limit of this model too.
Part III
Discussion:
The aim of this paper was not to criticize nor to privilege one energetic transition approach to another, but rather to try to clarify our concept (or meaning)
of the Energetic-Transition.
We also want to say that there are a big difference between ”substitution
be- tween energies” and ”The Energetic Transition”. In substitution between
energies we should not distinguish between RE and NER, because we consider
the large form of energies whatever their characteristics. Substitution is the
shifting between energies in the short term that do not demand a technological
change, it is reversible.
While the energetic transition mean that there is a radical structural
change, so it is generally not reversible. It can be realized only on the middle
or long term. We also aimed to call-up for a classification of the literature
models that deal with the Energetic-Transition problems. Within the framework of this objective, we have presented the CMM’s and TS’ models that
gives a very different results. The former is characterized by its environmental
approach (Environmental Energetic Transition Model ”EnvETM”) and the
later by its technological constraint (Technological Energetic Transition Models ”TETM”). An example of empirical models was also briefly presented in
the beginning of this paper.
This paper is also considered as an introduction to my project research
(The energetic transition and its impact on economic growth). We will pro-
26
pose a model that deal with this problem with different approach that try to
overcome same limits of these models. Notably, the constraint on RE energy
installed capacity, and both type of energy use: The energy as production
factor and energy used for the private consumption (households).
Our central questions about the Energetic-Transition are: Does the ineluctable energetic transition will have a positive or negative impact on the
social welfare? What are the conditions under which the transition should
stimulate economic growth? Do we have optimally to force or delay RE development? What should be the optimal growth rate of the RE share in the
aggregate energy demand? What should be the effect of internalizing the social
damage causing by GHS emission on the RE development? All these questions remain without convincing answers nor a consensus among the scientific
community.
Nevertheless that the literature gives us a solid base to establish the future
approach to deal with the energetic transition, that we tried to resume in the
following lessons.
1. The first lesson is that the results of each energetic transition model
depend on its conception of the energetic system.
2. It is important to differentiate between Theoretical-Economic-Growth
Transition- Model and Empirical-Transition-Models. The former deal
with the optimal allocation of resources, while the later try to present
the main factors driving the historical transition experiences.
3. The level of energy consumption can, implicitly, reflect the level of the
social welfare.
4. The expected energy demand has an effect on the extraction and price
path.
5. There should be an optimal level of RE dynamic share within the aggregate energy consumption.
6. There should be an optimal level of extraction of NRE too.
7. The price level is an important indication of the stage of the extraction
of NREs.
8. The price’s change rate can help precising the level of environmental
damages.
9. Internalizing environmental impacts increases price level. The corresponding marge can be known as environmental rent (tax).
10. The relative low cost of NRE, compared with the RE, along the consumption path means its depletion in finite time.
11. The scarcity rent does not necessarily reflect the level of remaining stock
of NRE resource. So, it is not always a true index of scarcity.
12. The RE promotion policy (as feed-in-tariff for example) seems to have a
positive effects on the RE development.
27
13. The learning by doing experience is an essential driving force for the
diffusion dynamic of RE technologies.
14. The taxes rate and rents should follow the stage of extraction and the
level of social damage caused by GHE.
15. The transition to renewable energies seems to be largely constrained by
the material availability as, for example, the silicon for the silicon-basedphoto- voltaic panels.
16. the global worming may be acceptable and profitable compared to the
socio- economic consequences of not exploiting fossil fuel reserves to their
full tech- nological potential.
17. An strong support from government, especially in subsides and R&D, is
indis- pensable to achieve energy transition programs.
18. The support and awareness of peoples is crucial to achieve energy transition programs too.
19. The macroeconomic conditions have a direct impact on energy transition
programs.
20. To success an energy transition program one should focus only on some
sectors of the economy and not all. A very ambitious program covering
all economic sectors risk to fail.
21. The type of governance and institutions influence directly the energy
tran- sition programs. And it seems that more centralized is the country,
more is its capability to control the program.
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