WEC19 Sydney-Paper 608

8/7/2019 WEC19 Sydney-Paper 608

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POTENTIAL INVESTMENTS IN CLEANING FOSSIL FUEL

(LE POTENTIEL D'INVESTISSEMENTS POUR NETTOYER LE COMBUSTIBLE FOSSILE)

By

DR. AWWAD A. ALHARTHI & MOHAMMED A. AL-FEHAID

Saudi Arabian Oil Company (SAUDI ARAMCO)

The authors would like to thank Dr. MahmoudOsaimi, Mr. Timothy W. Martin, Mr. Richard A. Horner and Mr. James W. Ragland for their valuablecomments and assistant. Special thanks are to Mr.Gregory Sullivan and Mr. Mahdi Al-Asfour for their valuable contributions. Any error remains our responsibility.


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ABSTRACT

The purpose of this paper is to investigate the long standing debatebetween fossil fuel producers and renewable energy advocates on howthe world demand for energy is best met. The optimal way to meet theworld energy demand is defined in this paper as one that maximizes theworld society well being. The society of the world is said to be better off ifboth taxes on and subsidies to energy providers are eliminated. Thepaper starts with a summary of the driving forces behind energy demandand supply followed by world energy demands outlook. These twosections laid the ground for the mathematical presentation of the twotypes of energy sources from which long term profit functions, long-runenergy supply functions and welfare measures are derived. Thetheoretical finding supports the view that focus should be on cleaningfossil fuel based energy in the short to medium-term and graduallydevelop future energy technologies. As full spectrum data is not availableto perform econometric estimation for the derived functional forms, wehave chosen to provide a numerical example at the end of the paper toinsure better understanding of the papers contents.


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ABSTRAIT

Le but de cet article est dexaminer le dbat de position long entre lesproducteurs de combustible fossile et les dfenseurs d'nergierenouvelables sur la faon dont la demande du monde de l'nergie est lemieux satisfaite. La manire optimale de satisfaire la demandenergtique du monde est dfinie en cet article en tant qu'un quimaximise le bien-tre de socit du monde. La socit du monde seraitmeilleure au loin, si les impts sur et les subventions aux fournisseursd'nergie sont limines. Le papier commence avec un sommaire desforces de conduite derrire la demande et l'approvisionnement d'nergie,suivi par les perspectives prochaines de la consommation d'nergie. Cesdeux sections tendent la terrain pour la prsentation mathmatique desdeux types de sources d'nergie desquelles le bnfice long termefonctions, fonctions de longue dure d'approvisionnement en nergie etles mesures de bien-tre sont drivs. La conclusion thorique soutientla vue que lattention doit tre mit sur le nettoyage de combustible fossiledans le court moyen terme et graduellement dvelopper de futurestechnologies d'nergie. Car les pleines donnes de spectre ne sont pasdisponibles pour effectuer l'valuation conomtrique pour les formesfonctionnelles drives, nous avons choisi de fournir un exemplenumrique la fin du papier pour assurer une meilleure comprhensiondu contenu de papier.


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Table of Contents:(Table de contents)

1. Introduction (Introduction)

2. Supply & Demand Driving Forces (Les forces de

conduite derrire la demande et lapprovisionnement delnergie)

2.1 Geopolitics (Gopolitiques)

2.2 Economics (Economiques)

2.3 Environment (Environment)

3. 2000-2100 Energy Outlook (Les perspectives de lnergiepour 2000-2100)

4. Emission-Free Energy Based Model (Un modle pour

zro mission)

4.1 The Fossil Fuel Investor (Investisseurs dans lescombustibles)

4.2 The Alternative Energy Investor (Investisseurs danslalternatives dnergies)

4.3 Welfare Analysis (Analyse de bien-tre)

4.4 Numerical Analysis (Analyse numrique)

5. Conclusions (Conclusions)

6. References (Rfrences)


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Potential Investments in Cleaning Fossil Fuel(Le potentiel d'investissements pour nettoyer le combustible fossile)

1. Introduction (Introduction)

The worlds demand for energy is forecast to double in the next fifty years and estimated

reserves of conventional (fossil fuel) and renewable energy combined are needed to meetexpected demand. Growth in demand for energy in its current form may be quite costly froman environmental perspective. As such, many energy producers, governments andenvironmentalists share the same concerns and have participated directly or indirectly insupporting research in technologies often through partnership and collaboration that canminimize the negative impact on the environment. Market penetration of new technology-based fuels is slow and damage to the environment continues to grow due in part to lower investment in technologies relating to conventional energy sources, such as coal, oil and gas-based energy.

The challenges facing energy providers and consumers are tremendous. Energy producersand consumers alike have invested heavily to build the worlds extant energy infrastructure,making it economical to consume energy at affordable prices and keeping the world economy

growing at an acceptable rate. Past investment in the conventional energy infrastructure isestimated to be in the hundreds of billions of US dollars if clean fuels and environmentalchallenges are to be met simply to comply to tightening regulatory framework. Under investment without incentives is possible due to uncertain economic returns and regulatorychanges. Replacement of new infrastructures able to produce alternative non-fossil sourcesof energy is expected to lead to increased energy supply costs. The willingness to pay suchcosts has not yet been displayed. Such a massive outlay of funds has the potential to bringthe world economy to its knees. In the current world economic and political environment,there is a fairly limited set of alternatives. The most pragmatic approach is to jointly fundresearch to find the technologies that are capable of utilizing the energy resources availableto preserve world economic growth and protect the environment. While self-interest isperhaps the single most important geopolitical motivator, it must be put aside. In these daysof increasing regional interdependence and uniting world economies, nationalistic self-interest

must give way to a more self-critical focus on the global social, environmental and economicoutlook. To do so, diversification of investment to include all potential sources in the entireenergy spectrum is required. A pragmatic approach to energy technology development mustbe adopted, encompassing the development and deployment of cleaner conventional fueltechnology as well as the increasing investment in the development of non-fossil fuel-basedenergy sources.

We will discuss in this paper that significant economic benefits can be realized if societyfocuses short and medium-term investment and efforts on cleaning fossil fuels, which in turncontribute to the economic growth and welfare of the entire world while supporting the energyneeds of impoverished regions. Capitol resources generated from the continuance andacceleration of this approach should be channeled increasingly into the development of futureenergy technologies.

Energy is a necessary ingredient for fueling economic and social development for both theindustrialized and developing worlds. It is essential to ensure that adequate supplies of energy at affordable prices are available while protecting the environment against harmfulemissions and pollutants. Fossil fuel reserves of the world will be adequate to meet the worlddemand for these commodities for at least the next hundred years, according to the USGS.The major challenge is determining the amount of investment and its direction. Should mostinvestment and energy policies be focused upon identifying alternative fuels and developingthe massive infrastructure required to support them or to utilize the existing cheap sources of energy and direct part of the investment and research and development into the extractionand cleaning of these fuels?

Before answering this question, the driving forces behind energy supply and demand must beexplored first, followed by energy outlook. Section three denotes the mathematical


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presentation, welfare analysis and numerical example while section four summarizes thefindings and states possible extension to the work.

2. Supply and Demand Driving Forces (Les forces de conduite derrire la demande etl'approvisionnement d'nergie)

The final source of energy is an important part of our daily life, regardless of its origin. Thevarious sources of energy compete in the marketplace at prevailing market prices that aredetermined not only by demand and supply forces but also by external factors that tend tomove prices away from market equilibrium. Although these external forces are strong enoughto distort market equilibrium, investments in the various sources of energy continued. Thechallenge facing the producers of the various energy sources is the ability to find a commonground that insures fair income distribution and energy availability at affordable prices. It isthis common ground that both consumers and producers must strive to find. The way toembark on a starting point is to look at the driving forces that are causing the differences. The

power behind these differences is presented in the following triangular chart (Figure I) madeup of geopolitical, economic and environmental vertices.

Figure I

Fossilfuel

Taxes

Environmental

Prices

Renewablesubsidies

EconomicsInventories

DemandSecurity

SupplySecurityGeopolitics

The dynamic links between the driving forces(Les liens dynamiques entre les forces)

As can be seen from the chart above, these interests are linked together and areinterdependent. To understand the links between the contributing elements, lets describehow each is developed and how they negatively impacts both producers and consumers.

2.1 Geopolitics (Gopolitiques):It is apparent that geopolitical events during the 1970s have scarred the collective memory of oil consuming nations. Our collective consciousness has been conditioned to believe thatenergy sources are not only scarce because they are of limited volumes, but also due to alack of confidence in the security of the supply, even in the face of consistent evidence to thecontrary. This belief amongst consuming countries has resulted in a complete departure fromthe economic theory which states that the optimum way to extract natural resources is toutilize the most economical source first to maximize the benefits at a minimum cost. Thisdeparture made consuming nations focus on how to replace fossil fuels, primarily because alarge portion of proven reserves exist in unstable regions of the world, with alternatives thathave proven to be impractical to meet increasing demand for energy due to hugedevelopment and infrastructure costs when compared with conventional energy sources.While supply interruption concerns have proven to be unfounded in the past two decades,consuming nations continue to use the development of alternative fuel sources as a pretext tomaintain and even increase punitively high tax rates on fossil fuels. This commonmisperception regarding supply and demand security, frequently promoted by political


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considerations within consumer nations, has affected the overall perception of energyeconomics. Fortunately, recent efforts toward enhancing dialogue and understandingbetween the consumers and the producers of energy have had a positive effect and concernsabout energy security are gradually waning.

2.2 Economics (Economiques):The second driving force is economics, where consuming nations are worried about theimpact of high-energy costs upon their economy and producers are concerned aboutsustainable demand. These concerns tend to widen the gap between the two even in thepresence of the World Trade Organization (WTO) where one would expect mutual interestand the rules of WTO to win out over regional concerns. Governments on both sides becomeprofit maximizing and capture value for their own nations well being either through hightaxation or high prices for energy. This tends to put downward pressure on world economicgrowth as final consumers are paying the cost by cutting their spending on all other goodsand services to pay their energy bills. Distorted picture of inventories affects the true demandand supply outlook and force a cycle of adjustments to the supply to correct for the distortedprices. This phenomenon could appropriately be resolved by allowing more transparency inenergy information exchange between consumers and producers.

Based on the principle of economic evaluation that aims to maximize the welfare of thesociety, if two alternatives sources of energy were available to meet the societys energyrequirements with different costs (consisting of the cost of production (extraction), processing,transportation, storage and distribution), the source with higher net benefit (total benefitsminus total costs) should be utilized first. Given the huge investment and technology requiredto produce, process and transport alternative fuels, utilizing fossil resources first to supplysocietys needs, until alternative fuels become economically feasible and comparable to fossilfuel in terms of net benefit to the society, provides significant economical advantages over any alternative currently being pursued or contemplated 1.

2.3 Environment (Environnement):The last and most abused element is the environment, where consuming nations use it as apretext to double-charge end users under the umbrella of reducing CO 2 emissions from fossilfuels. These taxes, which supposedly are levied to fund research and projects for the purposeof identifying the right technologies, are misused and directed to different purposes other thanwhat they were intended for. Even if emission policies are effectively administered, theincome is often spend to encourage energy product switching, rather than address theimmediate concern of improving air quality. Such action serves as a disincentive for fossilenergy suppliers to make the forward investments necessary to meet consuming nationsclean energy use expectations. The combination of applied and planned taxes on fossil fuel-based energy, and subsidies to renewable forms of energy will eventually lead to lessinvestment in fossil fuel energy, which will result in tightness of supplies that in turn have anadverse effect on the world economy, especially that of the industrialized world. Other major environmental problems, such as nuclear waste, with proportionally disastrous impact werenearly shelved and ignored in favor of reducing dependence on fossil fuel.

It is clear that returning to the basic, sound and proven economic and technological principlesis required for the benefit of the world society. A new emphasis on cleaning what is knownand available rather than continuing high expenditure completely on the unknown and theunattainable at an unsustainable rate with high degrees of uncertainty associated with

1 David Ricardo first established the above basic economic principle in the eighteenth centurywhen he discussed the basis of the economic rent. He applied this principle to the agriculturalland, saying that when parcels of land having different degrees of fertility are available, thesociety should cultivate the most fertile land first, since the cost of cultivation of such land isthe lowest and produces higher value products. As population increases, society mustcultivate inferior land to meet the food requirements of the growing population. In this case,

rent will be higher for the higher quality lands in proportion to the difference in the degree of fertility. Later, economists generalized this principle to all commodities that are produced in asociety.


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delivering economic successful outcomes. Negligent policy will inevitably lead todiseconomies within developing national economies. Thus a disciplined development of alternative energy non fossil fuels is desirable and beneficial to the society based upon futureprojected demand forecasts; while addressing the immediate need associated with clean upof cheap fossil fuel use. Namely, the focus should be on both cleaning extant fossil fuelresources and utilizing the enhanced revenue stream produced by a more efficient utilization

of our existing infrastructure investment to fund the search for practical, economical and cleanalternatives.

3. 2000-2100 Energy Outlook (Les perspectives de lnergie pour 2000-2100):

World energy demand is satisfied by different sources of energy. The share of these distinctsources of energy varies based on economic and environmental factors. Nuclear andrenewable make the lowest share, followed by coal, while petroleum-based energy sourcesform the largest share. Improvements in technology have contributed greatly to increasingsupply and slowing down growth in demand for energy, but its impact on the level of consumption has been limited in recent years due to the higher costs for the development of new technologies necessary to simply address regulatory concerns, without regard to thelatency of development and introducing new solutions. It is apparent that improvement in non-

fossil fuel technologies cannot be achieved on worldwide scale in the next few decades giventhe sizable increase in the cost associated with such new technologies and its impact on theworld economy and development. As demand for energy is driven largely by the need for sustaining positive economic growth and development, the exponential growth of the worldpopulation is leading to higher energy demand. In this section we will examine a forecast of energy demand for this century as a base case and then apply the scenario of diversificationof investment.

We examined the results of several long-term forecasting models, specifically the MARKAL;AIM & IIASA/WEC study entitled Global Energy Perspective. The latter study was conductedin two phases, from 1993 to 1995 and from 1995 to 1998. We looked at its scenarios, takinginto account the results of the more recent outlooks as well.

We assume in the following outlook that there will be no major policy shifts and that theconsumption of energy will only be subject to the following constraints: Population growth,sustainability of the economic growth, availability of energy resources and extractioneconomics, which include the effect of technology advances in this field.

For this purpose we assumed the UN medium population growth projection, which shows thatthe world population will reach around 10 billion by mid-century, after which population growthwill slow. This growth is combined with two facts: Two additional trends are anticipated toemerge; that urbanization will increase and that an increasing percentage of the populationwill be 60+. Collectively, these factors are projected to result in higher energy consumption.(See figure II)

Figure II

POPULATION

4000

6000

8000

10000

12000

1990 2010 2030 2050 2070 2090

Millions

0.00%

0.50%

1.00%

1.50%

2.00%%

Millions Growth rates


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The economic growth for this outlook is assumed to be approximately 2-3% annually for thewhole world. The industrialized nations are expected to sustain their economic growth around2%, while the economy of the developing world is expected to grow around 4% on average.The expected growth in energy consumption (especially fossil fuel) will be over 3% annually.It is important to note that economic growth is expected to slow at the end of the century due

to energy supply limitation. (See figure III.)

Figure III

GDP

0

100000

200000

300000

400000

500000

1990 2010 2030 2050 2070 2090

Bill US$97

1.5%1.7%1.9%

2.1%2.3%2.5%2.7%2.9%3.1%

%

GDP-Bill US$97 Growth rates

As mentioned earlier, it is assumed that there will be adequate resources of fossil fuels to lastuntil the end of the century and beyond, nevertheless, the economics of oil and gas resourceextraction will have an impact on their demand and consequently on their growth rates.

Coal will gain more share in the second half of the century compared to oil and gas. Nuclear energy consumption is also forecasted to decline gradually due to the awareness of theaccumulation of the nuclear hazardous waste over the years.

Renewable energy resources, which include hydroelectricity, biomass, solar, hydrogen-basedenergy and others will compete fiercely with coal and oil in the last two decades of thecentury. The overall picture of total energy demand as shown in Table-I is forecasted to growat healthy rates until mid-century and then slow down to nearly 1% because of advances inefficiency technology and resources limitations. (See Table-I and Figure IV)

Table-IWorld Total Energy Consumption

(La demande totale d'nergie)

Mboe/day1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100Oil 69 80 89 98 108 117 126 135 141 146 148 149Natural Gas 38 47 59 77 102 138 184 227 260 290 319 341Coal 47 50 54 59 66 73 82 92 104 118 135 157Nuclear 10 13 15 15 16 17 19 21 22 23 22 21Other 13 17 21 27 33 43 54 67 85 106 133 168Total World 178 206 238 276 325 389 464 542 612 683 758 835


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Figure IV

ENERGY CONSUMPTION GROWTH RATES

-1.00%-0.50%0.00%0.50%1.00%1.50%2.00%2.50%3.00%3.50%

2000 2020 2040 2060 2080 2100-1.00%-0.50%0.00%0.50%1.00%1.50%2.00%2.50%3.00%3.50%

Oil Natural Gas CoalNuclear Other Total World

4. Emission Free Energy Based Model (Un modle pour zro mission):

As was established in previous sections, the world is said to have two commercial sources of energy: Fossil fuel-based energy (crude oil, coal and gas) and renewable energy sources(solar, fuel cell, hydrogen, etc.). World society is searching for optimal methods to meetprojected energy demand at the lowest possible cost. Energy policies that are bothenvironmentally friendly (zero emission) and can be obtained at the same or lower price thanthe current energy market price (inclusive of taxes and subsidies) are key goals. Fossil fuelconsumption growth rates are projected to decline at the same rate that renewableconsumption increases, unless the growth in demand exceeds the growth in renewableenergy supply.

Two key stakeholders exert tremendous influence in the world energy market. Fossil fuelproducers claim that the only way to meet future energy demand with zero emissions and atthe lowest possible cost is to invest in cleaning fossil fuel-based energy. Their views arebased on the facts that the infrastructure and distribution systems are already in place andonly current variable costs (maintaining the system running) and investments to stripemissions are all what is required to achieve this goal. These producers contrast this to theimmense costs incurred by not only funding the building of a new infrastructure and newdistribution systems, but also to identifying and standardizing on a currently non-existingcommodity, the alternative fuel itself. The opposing group, on the other hand, claim that fossilfuel-based energy source will be depleted shortly and the world will run out of such energysooner or later. They argue that the world society would be better off by identifying another source of energy before it is too late. While fossil fuel producers agree with this view, theypoint out that the world is far from running out of fossil fuel and it will be some hundred yearsbefore that happened according to some reliable estimates. They argue that the world isbetter off economically by focusing on cleaning fossil fuel first and at the same time pursueresearch and development for alternatives at a rate that would have minimal impact on theworld economy. In this paper, we investigate qualitatively the problem facing the two groupsand demonstrate, based on pure economic considerations, which of the two types of fuelsmaximizes not only the producers/investors long-run profit but also the overall welfare of world society.

To start the analysis, we assume a fixed quantity of fossil fuel-based energy, implying that allreplaced reserves are ignored. Consumption of fossil fuel-based energy at time t is a fractionof total available stock and such consumption increases at a rate that is driven by globaleconomic growth and is constrained by consuming nations taxation policies aimed atcurtailing emissions and as a source of income. Whether these policies are in the bestinterests of the individual and specific economy is open for debate and is beyond the scope of


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this paper. The growth rate in energy demand is assumed to be a decreasing function of energy price P, that is that the higher the price, the lower the growth in consumption.

Consumption of fossil fuel-based energy produces pollution E and E increases whenconsumption increases. Doing nothing will lead to higher pollution regardless of therestrictions on consumption. This is so because the world economy is driven by energy and

therefore one cannot realistically assume lower energy consumption and higher economicgrowth at the same time. Emissions and taxation provide incentives for fossil fuel-basedenergy investment to strip emissions (produce zero emission-based energy) to meetenvironmental requirements as a first objective and also to reduce the cost to the end-user through the elimination of environmental taxes as a second objective. Achieving theseobjectives are said to make the society of the world better off and insure worldwidesustainable economic growth.

4.1 Fossil Fuel Investors (Investisseurs dans les combustibles):In order to achieve their objectives, fossil fuel-based energy producers and private non-fossilfuel producers corporations must be willing to take on new investment policies so as toproduce the required commodity in a perfect competitive market. While the commodity isalready in use but with unpleasant characteristics (emissions), the producers are assumed to

undertake a reproduction of the commodity to meet the desired objective of zero emission.Independent corporations and investors see the opportunity of finding the right technologyand are taking part in the efforts in the hope that they can sell their technology to fossil fuelproducers. For this purpose we employ the widely used Cobb-Douglas production function.

(1) LAK Q F = Equation (1) represents the new form of the required fossil fuel (zero emission) as a functionof labor L and capital K. The additional variable A denotes total factor productivity (TFP) andcan be interpreted in the same way as the error term in the neoclassical regression. Namely Aaccounts for anything else that is not captured by the other two variables in the function. Theparameters and denote the degree of homogeneity. At a given capital rent r and a labor

cost w, the profit maximization for fossil fuel investors using (1) can be stated as follow:

(2)rK wLK ALPrK wLQP FFFF ==Max

The newly introduced variable P F is the current market price for fossil fuel and is given as partof total price paid by end consumer.

+= FMF PP 0> and (3)*PPF

Where is the taxes imposed on consumption to reduce emission and P MF is the end user (consumer) price. The actual market price charged by producers is therefore less than the

final paid price due to taxes. It is assumed that current taxes will continue when the new fossilfuel (Q F ) first introduced to the market. The price P F must be equal to or greater than somethreshold P* below which producers of fossil fuel will be incurring cost rather than profit andonly larger producers remain in the market. As smaller and high-cost producers reduce their outputs or exit the market, prices are assumed to recover to exceed the assumed threshold.For example, currently, when refined oil products prices decline bellow a certain level, refinerstend to cut back their throughputs until prices recover. Also note that smaller crude oilproducers have been known to exit the market when crude oil prices decline below somelevel, and reappear when prices increase beyond this threshold level. These are basic factscharacterizing any competitive market.

Assuming capital and labor are variables, the necessary, first-order conditions for (2) is to setthe marginal value product of each factor (the output price times the marginal products factor

of production) equal to their respective prices, or equivalently to set the slope of the profit


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function with respect to labor and capital equal to zero

01 == wLAK P

L FF

(4)

01 == rLAK P

K FF

From the above first order condition, we have:

KrK LAPF = and

LwK LAPF = (5)

Solving for K we have

rLw

K =

Substituting the value for K into the second equation in (4), we have 2

rr

LwALPF =

1

(5)

Solving for L, we get 3

11

11 +

=

FAPwr

L (6)

=11

1

11

1

1

rwPA

F

and

=11

1

11

11

rwPAK F

Using (5) and (6) we have 4

2 . Expanding powers in (5), we have: which make it easier to solve for L as given by equation (6).

rwrALPF =+ 1111

3 . The long hand version of L is given by: 111

1

1

11

11

1

+

+

+

++

+

=

wr PAL F and

when terms are rearranged we have (6). The final result for K is stated in its final formwhere the long hand derivations are omitted, as they are similar to that for L.

4 . The first part of equation (7) is expanded to

give:( ) ( ) ( ) ( )

11

1

11

1

11

1

11

11

11

1 ++

+

++

+

+

+

+

+

+

++ +

++

=

wrPA F which

can be reduced to: 111111

11

+

+

+++ +

=

wrPA F Further simplification of this gives us the last form of equation (7).


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==

11

1

11

11

11

1

11

1

1

rwPA

rwPAAP

KrK LAP

F

FFF

(7)

= 111

11

1

rwPA F

Now we have all we need to find the long run profit function for fossil fuel based energyinvestors. From (5), (6) and (7), we have:

+

=+=+

++++

1111

11

1111

/ /

1 1

rwPA

rwPA

rK

wLrK wL

F

F

and by rearranging terms, the profit function is given by:

( ) ( )

= 111

1

11

1,,rwF

PAFPrwF (8)

Equation (8) expresses fossil fuel based energy investors profit as a function of the pricesand the parameters of the production function and TFP. Investors require the profit capitalratio to be greater or at least equal to the cost of capital r .

4.2 Alternative Energy Investors (Investisseurs dans lalternatives dnergies):The problem facing the alternative fuel based energy investors is different as they

need to invest in producing the energy commodity and fund the required distributioninfrastructures. The other problem facing such investors is the amount of capital required andtheir reliance on subsidies in both producing and selling the commodity.

The alternative fuel investors problem is specified based on the same functional form with thefollowing differences. Producers of such commodities are faced with larger requirements for capital. Such producers lack the in-place capital available for fossil fuel based energy; thegood itself need to be produced versus a one already in use and the infrastructures needed tobe built for it. The following presents the alternative fuel producers/investors model.

LK AJ Q A = (9)

Where J denotes the additional investments and the other variables are the same as in thecase of fossil fuel investors. Assuming investors face the same capital and labor cost, thelong run profit function for the alternative fuel based energy investors is given by:

( ) ( )K J rwLLK AJ PK J rwLQP AAAA +=+=Max (10)


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First order conditions are:

01 == wLK AJ P

L AA

(11)

01 == rLK AJ P

K AA

01 == rLK AJ P

J AA

Solving simultaneously for L, K and J and rearranging terms, we have 5

( ) ( ) ( ) ( )

+

=11

1

11

11

rwPAL A (12)

Solution for K is given by:

( ) ( ) ( ) ( )

= 11

111

11

rwPAK A (13)

Solving finally for J, we have

( ) ( ) ( ) ( )

=1

1

11

1

1

rwPAJ A (14)

Substituting L, K and J into the production function we have 6

+

+

+++

=

11

11

11

1

rwPAAPPLK AJ AAA(15)

+

++

+

++

11

1

1

1

11

rwPA A

5 . The long hand form of the three variables are:

1111

11

111

11 ++++++

+++

+++

+++++=

wrPAL A ,

11

11111

11

11

+++

++++++++

++++=

wrPAK A and

11

11111

11

11

+++

++++++++

++

++

=

wrPAJ A .

6 .( )( ) ( ) ( ) ( )

111

111

11 ++

+

+

++

+

+

+++

+++

=

wrPAPLK AJ AA ( ) ( ) ( )( ) ( ) ( )( ) ( )

111

111

111

++

++

++

++

++

++

++

+

111111

1

1

1

+++

+++

+++++++

++

++

=

wrPA A

111

11

1 +++

++++

++

=

rw

PA A


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( )( )

( ) ( )

+

= 11

11

1

1

rwPA A

Now we have

rJ rK wLLwKrJr / / /

++=++

and

rJ

rK

wL

PLK AJ A / / /

===

111

11

1

/ / /

+++

++

=++

wr

PAr

J r

K w

LA

1111

11 ++

+

++

+

wr

PA A

1111

11

++

+

++

+

wr

PA A

Therefore the alternative energy investors profit function is given by:

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

+

= 11

1

1

1

1

1,,rw

PAPrw AAA (16)

Taking the derivative of the two profit functions with respect to price P , the supply functionsfor the two energy types are:

( ) ( )

( )

( )

+

=

111

1

*

1

rwPAQ F (17)

( ) ( )( )

( )

+

++

=

111

1

*

1

rwPAQ A (18)

The above two supply functions represent the supply of energy that meets the world energydemand and maximizes each producers profit. Given perfect market competition (price of theenergy commodity, labor and capital costs are the same for both producers of the twoenergies), one would expect AF > due to the additional cost of capital J an alternativebased energys investors need. The magnitude of the difference between the two profits is aquestion of empirical work, which is under investigation. The two profits are compared on the

basis of relative measurement distortion and absolute measurement respectively:1

F

A


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+= FMF PP and the cost to individuals is given by:

( ) FFFMFF QPQPC +==

As we have pointed out above, one of the objectives for investors in emission-free fossil fuelis to reduce the final price paid by the individuals. And since there is no reason for taxes onfossil fuel to continue as the fuel becomes environmentally friendly, investors and individualswill be in a position to demand the removal of such taxes. As taxes decline, cost to finalconsumers decrease and the individual is said to be better off the lower the tax.

In contrast, alternative energy depends on subsidies to keep it competitive with fossil fuelbased energy. That is, end consumers are faced with the following market price:

+= AMA PP

( ) AAAMAA QPQPC +==

where > and covers the additional cost to produce the alternative energy and thesubsidies paid by tax payers to make the alternative energy compatible with fossil fuel basedenergy. Thus, alternative energy is more expensive to consume as far as the society of theworld is concerned,

Figure VPrice Welfare

Fossil Fuel

P += FMF P ++ PP

+= AMA PPAlternative

Time Time(a) (b)

since such subsidies can be expended in other sectors to promote the general welfare of world society. In order for the alternative based energy to retain competitiveness, subsidiesmust increase at parity or higher rate than the decline in the tax rate imposed on fossil fuel-based energy. The above discussion is presented in figure V. The first graph on the left (a)shows the societal cost of alternative energy is increasing as subsidies must be inflated at thesame level that tax declines. The dashed line shows that as taxes decrease, the final price toend consumer declines to the market price, while subsidies must increase to retain thecompetitiveness of alternative energy. Note that the graph on the right (b) is a mirror image of the one in the left, which demonstrates that the society wellbeing is enhanced through thelower cost of fossil fuel-based energy but negatively impacted by higher subsidies toartificially support alternative energy. The dashed line reveals that improvements in thesocietal well-being accelerate as taxes go to zero, while the solid line shows how society isnegatively impacted as the cost of alternative fuels increases.

In the following section we will present an application of the above theoretical presentationsusing the data in section two of the paper.

4.4 Numerical Analysis (Analyse numrique):


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As complete data is not available at this time, we use information presented in the secondsection of the paper to derive estimates of the parameters of the model. The demand data,which is assumed to equal the supplied quantities, is used to find the different values of theparameters at different point in time. Thus, the values of the parameters are energy demanddependents. That is, any change in the quantity demanded at any point of time will changethe values of the parameters. The following table shows the estimated parameters values and

the assumed constant market price and cost of labor and capital respectively. Under theassumption that both investors in fossil fuel emission technology and alternative energyproduction and distribution systems face the same capital rental rate r, labor cost w andmarket price P, it remains to identify the size of the parameters so as to test which investmentis more profitable. Since investors in the alternative fuel-based energy require additionalcapital J whose share in the production function is required to be higher in order to replacefossil fuel-based energy and given the current market share of the alternative fuel-basedenergy, it is apparent that the higher the capital requirements the higher the cost andtherefore the lower the profit. Using w, P, r and energy demand forecast (section II above),the derived parameters estimates for the two supply functions are given in table II. Since wehave assumed variable Labor and Capital, we allow the associated parameters to changeover time in order to pin point required labor and capital combination that meet the requiredenergy demand at any point of time.

Table IIEstimated parameters and assumed price and costs(Prix et cot assumes, et estimation des paramtres)

Date A w p r 1990 6.21E-01 3.93E-01 4.65E-01 2.75E-01 9.49E-02 5.33E-01 2 30 0.072000 5.40E-01 4.58E-01 4.15E-01 2.73E-01 1.02E-01 5.32E-01 2 30 0.072010 6.36E-01 3.86E-01 4.72E-01 2.71E-01 9.98E-02 5.31E-01 2 30 0.07

2020 6.50E-01 3.64E-01 4.91E-01 2.71E-01 9.97E-02 5.30E-01 2 30 0.072030 6.08E-01 4.24E-01 4.42E-01 2.72E-01 1.01E-01 5.31E-01 2 30 0.072040 6.61E-01 3.55E-01 5.01E-01 2.71E-01 1.00E-01 5.31E-01 2 30 0.072050 6.37E-01 3.77E-01 4.84E-01 2.72E-01 1.01E-01 5.31E-01 2 30 0.072060 6.28E-01 3.92E-01 4.72E-01 2.72E-01 1.01E-01 5.32E-01 2 30 0.072070 6.61E-01 3.55E-01 5.03E-01 2.72E-01 1.01E-01 5.31E-01 2 30 0.072080 6.61E-01 3.56E-01 5.03E-01 2.72E-01 1.01E-01 5.31E-01 2 30 0.072090 6.47E-01 3.68E-01 4.94E-01 2.72E-01 1.01E-01 5.32E-01 2 30 0.072100 6.48E-01 3.68E-01 4.94E-01 2.73E-01 1.01E-01 5.32E-01 2 30 0.07

The parameter associated with current investment in the alternative energy is smaller reflecting the smaller share of the alternative energy currently, but larger for the additionalrequired capital as indicated in table II above. The parameter associated with fossil fuelcapital requirement is also large, but slightly lower than that for the additional capital requiredfor the alternative energy production, although the required world energy demand is the samefor both. That is, we have assumed that if the world energy requirements are to be met byeither type of energy, then what is the most suitable way of meeting such demand. In other ward, we assume full replacements to find out what choice maximizes the investors profit andat the same time maximizes the society well being.

Comparison between the two profit functions based on table II, gives us net profit for the twoinvestors exclusive of tax and subsidies, which will be discussed later in the welfare section.We have simulated the two profit functions under different quantities of demand for energyand found that the summation of the parameters of the model for both types of energy areless than one, implying decreasing return to scale. The results are consistent with the energymarket, as one cannot expect to more than double output if input factors were to be doubled.A higher cost is found to associate with the additional capital requirements for the alternative


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energy based fuel. The following table denotes the two profits and the absolute differencebetween the two.

Table-IIIBillions of $US

(Milliards des dollars Amricains)

Date F

A

1990 0.76 0.52 -0.24 0.692000 0.77 0.57 -0.21 0.732010 1.00 0.69 -0.31 0.692020 1.19 0.81 -0.38 0.682030 1.29 0.92 -0.37 0.722040 1.68 1.14 -0.55 0.682050 1.94 1.33 -0.61 0.692060 2.23 1.55 -0.68 0.702070 2.65 1.79 -0.86 0.682080 2.96 2.00 -0.96 0.68

2090 3.23 2.20 -1.03 0.682100 3.53 2.41 -1.12 0.68

It is clear from the table that there are more incentives to invest in cleaning fossil fuel-basedenergy than investing in the alternative fuel-based energy, as the profit from investing incleaning fossil fuel is about one third higher compared to investing in the alternative basedenergy. The derived two profit functions can be compared on the bases of price, parametersand cost of labor and capital. Furthermore, from table III, the gap between the two profitsgrows larger as we go further in the future despite fixed price and costs facing the twoinvestors as can be seen in figure-6.

Figure VI

Profit Comparison

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

Billion US$

Fossil Fuel Alternatives Delta

In the above, we demonstrated that profit from investment in fossil fuel-based energy not onlyby far exceeds that of investing in the alternative fuel energy, but also is increasing. It remainsto apply the data to investigate which investment will maximize the welfare of the society of the world. To see that, we will include both tax and subsidies in the analysis using the abovedefined functional forms. Table IV shows final prices paid by end consumers taking intoaccount tax and subsidies. The first column denotes an assumed fixed price, the maximumprice an end consumers should be charged and it should cover all production cost plus profit.This is the value used in the profit maximization for both investors and it has resulted in

positive profit for both. The second column denotes the tax rate imposed on fossil fuel. It isassumed that tax rate is double the maximum price an end consumer should pay.


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Table IVPrices (in US$) with and without taxes and subsidies

(Prix avec et sans impts et subventions dollars Amricains)

Date p pMF pM A 1990 30 25.00 25.00 55 552000 30 30.00 30.00 60 602010 30 22.50 37.50 53 682020 30 17.00 43.00 47 732030 30 12.50 47.50 43 782040 30 7.50 52.50 38 832050 30 2.50 57.50 33 882060 30 0.00 57.50 30 882070 30 0.00 57.50 30 882080 30 0.00 57.50 30 882090 30 0.00 57.50 30 882100 30 0.00 57.50 30 88

The tax is assumed to decline at an increasing rate as the new form of fossil fuel (emission-free) enters the market. Subsidy is denoted in the third column and it is assumed that suchsubsidy is equal to tax, to insure the compatibility of the alternative fuel-based energy. Astaxes decline, subsidies must increase at the same level tax decreases; otherwise, alternativefuel producers will not be able to compete with fossil fuel. While end users may incur some of the alternative higher costs, the real loss is to the society as a whole as such subsidies couldbe redirected to other welfare programs.

Table VCosts and benefits to the society in billions of $US

(Cots et bnfices pour la socit - Milliards des dollars Amricains)Date Final Cost of Fossil Fuel

Final Cost of Alternative

Benefits to Society fromconsuming Fossil

Totalenergy

1990 10680 10680 0 1782000 11330 13390 2060 2062010 12495 16065 3570 2382020 13800 19320 5520 2762030 15438 23563 8125 3252040 17505 29175 11670 3892050 19720 35960 16240 4642060 21680 43360 21680 5422070 22950 50490 27540 6122080 23905 58055 34150 6832090 24635 66325 41690 7582100 25050 75150 50100 835

The last two columns in the table denote the real costs to the society. Table V comparescosts and benefits to the society of the world from consuming either type of energy. It is clear that investment in cleaning fossil fuel based energy maximizes both investors return and thewell being of the world society.


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5. Conclusions (Conclusions): Given the estimated growth in the world demand for energy,all sources of energy must be utilized to meet such

increasing demand. Demand for energy is best met through more investments

being directed to technologies for cleaning fossil fuel basedenergy so as to reduce emissions as well as maintaining anacceptable worldwide economic growth.

Utilization of energy sources is best accomplished viasystematic movements according to economic theory. Thecheapest sources of energy must be brought to the marketfirst and its consumption must continue until its productioncosts exceed the cost of the production of its substitutes.

Theoretical and numerical analysis show that investors andthe society of the world are better off through investments incleaning fossil fuel based energy.

The paper can be extended in many ways. For example, onecan employ Option Theory to compare investments in bothenergy sources, employ Optimal Control theory and find thetime path for investments as well as finding the optimumswitching time from fossil fuel to alternative fuel, useavailable data and estimate the annual rate of penetrationand the associated costs and benefits to the society of theworld and one may use different investment functional formin the present content of the paper and derive an alternativesolutions.

As we know of no existing work of the type presented in thispaper, we still have benefited from the sited literature.


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Authors:

Name: Dr. Awwad A. AlharthiPh.D. in econometrics and Mathematicaleconomics. University of Colorado 1991.1992-Now: Corporate Planning Dept. inSaudi Aramco.Areas of work include, project evaluation,

environment, WTO, crude oil pricing andeconometric modeling.

Name: Mr. Mohammed A. Al-FehaidM.Sc. in Mathematics 1985.1978-1990: King Fahad University ofPetroleum & Minerals.1990-1997: Ministry of Petroleum.1997-Now: Corporate Planning Dept. in

Saudi Aramco. Areas of work include marketfundamentals, statistical analysis.

Documents

WEC19 Sydney-Paper 608