Optimal Extraction Paths of Coal

Optimal Extraction Paths of CoalChapter 1 Introduction1.1. MotivationAccording to the World Energy Outlook (WEO 2007)1, global cytosine dioxide ( carbon dioxide) discharges go forth gain by 1,8 % per year from 2005 to 2030, and 2 % per year for the block 2030-2050.2 From 12.446 Mt of CO2 equivalent in 2002, emissions de pct reach 15.833 Mt in 2030 for OECD countries an average plus of 1,1 % per year. CO2 is the most important anthropogenic greenho aim accelerator (GHG), which is contributing to global warming. The primary source of the ext expiryd atmospheric submersion of CO2 since the pre-industrial period results from fossil fuel use, with land-use change providing anformer(a) significant but sm comp permitelyer contribution.3 Continued greenhouse gas emissions at or higher up current rates would cause further warming and induce more(prenominal) changes in the global climate system during the 21st century.4According to the Nuclear Energy Agency and the supranationa l Energy Agency the origin multiplication sector give contribute to almost half the increase in global emissions between 2002 and 2030, and pass on remain the hit biggest CO2-emitting sector in 2030. In OECD countries, its emissions entrust forward motion from 4.793 Mt of CO2 in 2002 to 6.191 Mt of CO2 in 2030, but the sh ar will remain constant.5Today, power generation emits 65 % of industrial emissions of CO2 in OECD countries and is kindredly to become submissive in countries strategies to reduce greenhouse gas emissions.6 One of such instruments is the Kyoto Protocol.Under the United Nations Frame crap collection on Climate Change (UNFCCC), more than 180 countries produce recognised the need to stabilise the concentration of GHG in the atmosphere, which atomic number 18 causing climate change. The Kyoto Protocol to the UNFCCC, was adopted at the trine session of the throng of Parties in 1997 in Kyoto, Japan. It entered into force on 16 February 2005 with 184 Parti es of the Convention who live ratified to date.7The major hold of the Kyoto Protocol is that it stations binding targets for 37 industrialized countries (including Germany) and the European Community for reducing GHG emissions. These amount to an average of phoebe bird percent of the 1990 levels on the whole told everywhere the five-year period 2008-2012.8The Kyoto Protocol includes specific flexible mechanisms such as Emissions Trading, the Clean victimisation Mechanism (CDM) and Joint Implementation (JI) for the countries to be able to reach their mandatory emission limits.Emissions transaction, as set out in Article 17 of the Kyoto Protocol, allows countries that absorb emission units to sp atomic number 18 emissions permitted to them but non apply to sell this excess capacity to countries that exceed their targets. Thus, a new commodity was created in the form of emission reduction or removal assets. Since CO2 is the principal greenhouse gas, people speak simply of trading in carbon. Carbon is now tracked and traded like any otherwise commodity. This is know as the carbon food market.9 In European countries the emissions trading system is the European Union Emissions Trading Scheme (EU ETS), the largest system nowadays.The CDM, delimitate in Article 12 of the Protocol, allows a country with an emission reduction or emission point of accumulation commitment under the Kyoto Protocol ( attach B Party) to implement emission reduction find outs in developing countries. such(prenominal) projects can earn saleable certified emission reduction credits, each equivalent to one salary ton of CO2, which can be counted towards meeting the Kyoto targets.A CDM project activity big businessman involve, for example, a rural electrification project using solar panels or the installation of more energy-efficient boilers.10The JI mechanism, defined in Article 6 of the Kyoto Protocol, allows a country with an emission reduction or limitation commitment under the Kyoto Protocol (Annex B Party) to earn emission reduction units from an emission-reduction or emission removal project in another Annex B Party, each equivalent to one ton of CO2, which can be counted towards meeting its Kyoto target.JI offers Parties a flexible and follow-efficient wets of fulfilling a part of their Kyoto commitments, while the host Party benefits from foreign coronation and technology transfer.11Germany is one of the worlds largest energy consumers and ranks third in total CO2 emissions within the G-7, after the the States and Japan.12 Annually, Germany produces around 850 millions tons of CO2 equivalent gases, which is approximately 2,8 % of all worlds CO2 emissions.13 On 31 whitethorn 2002, the Kyoto Protocol was ratified by Germany. After entering it into force Germany has played an active role in the European and world carbon markets.Electricity production in Germany is largely based on sunburn exhaustible imaginativenesss, causing high CO2 emi ssions. That makes the issue of CO2 trade crucial for German power botanys and the economy in whole.In 2008, the total amount of earthy electricity supplied in Germany was around 639,1 TWh14, that is slightly higher in comparison to the previous year. Nevertheless, during last years thither is a tendency of increase in electricity supply (See bow 1).The electricity supply in Germany is based on several(prenominal) technologies and fuels. The distribution of net electricity supply in last years in Germany is shown in Table 1. Electricity production in 2008, as in previous years, was based mainly on blacken-fired (hard combust and lignite) steam turbine (43,6 %) and nuclear (22,3 %) power plants.15Energy sourceSince the share of the sear based power plants in Germany is large and the amount of electricity produced is still growing, the impact of the CO2 emissions trade on the economy of these plants is genuinely significant.According to data provided by the Nuclear Energy Age ncy and the International Energy Agency, the deter exploit for blacken is rising during the economic life poster of the coal-firing plants.16 This rise partly can be cause by rise to poweral CO2 cost.The largest impact of the emissions trading on the electricity generation cost is felt by the lignite-fired power plants followed by the hard coal-fired power plants, since lignite while burning is producing more emissions than hard coal.17 With an assumed emission legal injury of 20 /tCO2 the power generation costs of the lignite-fired power plant would increase by 63 % from 25,4 /MWh to 41,4 /MWh, whereas the generation costs with hard coal-fired would rise by 48 % from 30,2 /MWh to 44,8 /MWh.18The matchedness of the coal-fired plants is in like manner learnd by including the CO2 equipment casualtys into the costs. 1 represents peripheral cost curve based on the total installed capacity and facilities operating costs for Europe.19 As can be stick outn, the addition of CO2 harm to the production costs can make coal power plants less competitive. The sequence of most of electricity plants stays the same after addition of 20 /tCO2 to the costs, though coal based power plants move to the side of less competitive plants.These facts and evident changes originate many questions such as side by side(p) how long will electricity from fossil fuels stay competitive, how the pedigree of fossil fuels is influenced by CO2 wrongs.1.2. Problem definitionFrom all of the above it can clearly be seen that the CO2 equipment casualty is influencing the economic value of coal and its yield trend.20 Questions this thesis is dealing with are how the lineage lane is simulateed by the CO2 damage, and what the best path of using coal is. For many companies, i.e. in coal dig and coal utilizing, this question is essential, since they already face significant changes in profitability. The thesis is aimed at describing the optimum declension path of exhaustible ima ging (coal) without and accordingly with CO2 work outations. That will allow to compare and to see the changes in paths. Coal-related industries will be contended here, but similarly the approaches can be used for other exhaustible fossil fuels.Since coal is an exhaustible election, for describing its optimal ancestry path we will use the exhaustible mental imagery economic guess, to be more precise, Hotellings guess, which de termines the optimal root path of exhaustible imageryfulness. Hotellings encounter is one of the mandatory conditions of optimality of the extraction path. The optimal extraction path means that the miner is maximising his profit if he follows this path. alike that, we widen the scope of the work and change the condition of maximising the profit and look at the causal agency when a miner aims to prolong the life-time of the mine as much as possible. We will also consider different markets types competitive and monopoly. For formling all the scena rios in the mentioned conditions, a single mine which is situated in Germany will be used, and we will assume that all coal is burned at the power plant for production of electricity which belongs to the same company as the mine.1.3. RelevanceWe aim to determine how the EU ETS is influencing the extraction path of the coal and its value. This question is very important for the mine owner, as it allows him to choose the right dodge for production and exploitation, depending on the new market conditions with costs for CO2. That is essential for the economic survival of the miner. And for us, the task is thence to determine the influence of CO2 footing on the extraction path of a coal mine. First, we will construct the model without consideration of CO2 price in two different market conditions, and later on we include CO2 price considerations. As mentioned before, we will discuss the case when a miner wants to maximise the life-time of the mine. The reasons for that might be to sa ve jobs or g overnmental directives. This case also will be canvas in different markets.1.4. GoalsThe goal of the work is to construct simplified models, on the base of Hotellings hold guess, which will determine the optimal extraction paths of coal and extraction paths leading to maximization of life-time, for one single mine situated in Germany in different market conditions without and with CO2 price consideration. Afterwards, on the base of models including into them mathematical data, we aim to show the scale of the CO2 price affecting the extraction path.1.5. StructureThe current chapter, chapter one, gives an basis into the root, determines the goals of the topic, explains the motivation of the enquiry through in the work, supports it with topical data.The second chapter contains the theoretical base for the further research. It describes Hotellings rule extraction of exhaustible visionfulnesss, discusses the crucial points of the theory, and gives the basic model of optimal extraction of exhaustible resource.In the third chapter, models of optimal extraction of coal in different conditions are developed. At the beginning, the models represent the optimal extraction path of competitive market and then monopoly market. Next, cases are discussed in which the company is maximising the life-time of the mine also in two market types. Afterwards, the CO2 price is integrated into the models, and the change in extraction paths is described. At the end, two numerical examples are given, and calculated to find two optimal extraction paths without CO2 and then with it.The last chapter, chapter four, gives the summary of the whole master thesis and its results.Chapter 2 The theory of exhaustible resources 2.1. OverviewThis chapter is dedicated to Hotellings theory itself, since we use it to determine extraction paths of coal. It contains the theoretical background for further models construction, and allows to understand the theory deeper. Next, Hotellings rule is discussed. Afterwards, we discuss different parameters which can influence the rule, since these considerations are necessary for construction of the models and making appropriate assumptions for them. At the end of this chapter the basic model of optimal extraction of exhaustible resource is given. On the basis of this model, in the following chapter, we will build models with considerations of different market conditions and CO2 price.The main questions of the economics of exhaustible resources are what is the optimal rate of exploration of the resource by company, the price path of the exhaustible resource and how does it change with time? These are the questions which we are interested in. And since coal is exhaustible resource, this theory is applicable to our case.Exhaustible resources are those that are available in fixed quantities. They dont exhibit significant growth or renewal over the time. Coal is exhaustible resource its amount in adheres is fixed and doesnt grow over time. Pindyck distinguishes between exhaustible and non-renewable resources21 by noting that, while the latter do not exhibit growth or regeneration, new militia can be acquired through exploratory effort and discovery.22 Since the first one is more wide spread, in this work the term exhaustible resources will be used for indication of this type of resources.In 1914 L. C. aged dealt with questions of natural resource economics. He examined the supply behaviour over time of an individual extractor who anticipates a sequence of real prices and attempts to maximize discounted profits.23 Harold Hotelling extended Grays theory by predicting the sequence of market prices that Gray took as given in his work The economic science of Exhaustible Resources in 1931, which then became a seminal paper on the economics of exhaustible resources.242.1.1. Hotellings ruleHotellings rule, as described in his paper entitled The Economics of Exhaustible Resources, is an economic theory, poi nting out how the prices should behave under a specified (and very restrictive) set of conditions.25It states that competitive mine owners, maximizing the present value of their initial bears, should extract a quantity such that price of the exhaustible resource rise at the rate of interest.26 In other words, if we assume that P0 is the initial price of the resource, Pt is the price of resource at some point of time, i is interest rate, then27(1)Hotellings rule is based on the following assumptions28 the mine owners objective is to maximize the present value of his current and early profits. This requires that extraction takes place along an efficient path in a competitive industry equilibrium, which implies that all mines are identical in terms of costs and that they are all price takers in a perfect and instantaneous market of information. the mine is perfectly competitive and has no control over the price it receives for its production. mine production is not cumber by existin g capacity it may produce as much or as little as it likes at any time during the life of the mine. the ore deposit has a ca sinalized value. That is, a copper or gold deposit in the ground is a capital asset to its owner (and society) in the same way as any other production facility. Furthermore, he assumed that the richest and most fond deposits would be mined first, and that increasing scarceness (after exhaustion of the best mines) would add capitalized value on inferior deposits, which could then be mined. the resource stock is homogenous and consequently there is no suspiciousty about the size, grade and tonnage of the ore deposit. Current and future prices and extraction costs are known. This implies that an ore body has uniform quality or grade throughout and that there is no change in grade of the ore as mining proceeds. Miners and grade control officers, who endeavour to supply the mill only with ore above a certain grade, recognize this fifth assumption to be major d eparture from reality. The topic of uncertain reserves is discussed in more details in subsection 2.1.5 of the thesis. The sixth assumption is that the costs of mining or extraction do not change as the orebody is depleted. Again, this assumption does not recognize that all mines face increasing costs as the ores are depleted. Underground mining costs increase as the mining face becomes longer and deeper and moves further away from the shaft system, while in open pit operations haul roads become longer and pits become progressively larger and deeper. A rider to Hotellings assumption that the bare(a) unit (standard mining unit) is accessible at the same constant cost, is the assumption that the marginal cost of extraction in this particular case is zero. In addition, it implies that the market price and the rate of extraction are connected by a stable, downward sloping demand curve for the resource.29 In this constrained model the size of the remaining stock declines without ever being augmented by exploration discoveries. To the topic of cost of extraction is also dedicated the section 2.1.4 of the thesis. The final assumption is that there is no expert improvement during the life of the mine and that no new additions to the resource stock are contributed by exploration. Sections 2.1.7 and 2.1.8. are discussing technological progress and backstop resources, which are also connected to technological progress.Hotellings model predicts a widely distributed rise in commodity prices over time. The model has been used by numerous authors as a useful reference point in discussions on the various dimensions of mineral supply and availability. Among the factors that the model helps come in are that30 Prices are a useful indicator of scarcity, if markets are fiting easy (section 2.1.3 is discussing the question of resource scarcity) The effects of exploration and technological innovation significantly and importantly influence mineral availability over time Mar ket structure matters (competition versus monopoly) Mineral resources are not homogeneous Backstop technologies limit the ground level to which prices can increase Substitution is an important reaction to increased scarcity Changes in demand influence price and availability.In other words, the model provides a vehicle for introducing the various dimensions of mineral supply and scarcity.31 scarcely since Hotellings rule uses a number of assumptions, it might not coincide with reality completely. The next part discusses the experimental validation of Hotellings rule.2.1.2. Empirical validation of Hotellings ruleAll the assumptions of the model mentioned before diminish the potential value of the application of the model for the miner in the real world. In an attempt to validate Hotellings rule, much research effort has been directed to empirical testing of that theory. except unfortunately, till now there is no consensus of look coming from empirical analysis.32One way of testing Hotellings rule seems to be clear collect time-series data on the price of a resource, and see if the proportionate growth rate of the price is equal to r. This was done by Barnett and Morse. They found that resource prices including iron, copper, silver and timber fell over time, which was a most flurry result for proponents of the standard theory.33 Other research came up with absolutely different results which could not assess whether the theory is right or wrong.But the problem is far more challenging than this to settle, and a direct psychometric test of resource prices is not a reasonable way to proceed. The variable Pt in Hotellings rule is the net price (or rent, or royalty) of the resource, not its market price. Roughly speaking, these are related as followspt= Pt +b (2)where pt is the gross (or market) price of the extracted resource, Pt is net price of the resource (unextracted), and b the marginal extraction cost. According to the equation (2), if the marginal cost of extraction is fall, pt might be falling even though Pt is rising. So, evidence of falling market prices cannot, in itself, be regarded as nullify the Hotelling principle.34This suggests that the right data to use is the resource net price, but this is an unobservable variable as well as i. So its possible to construct a proxy for it, by subtracting marginal costs from the gross market price to arrive at the net price. This difficult approach was pursued by a number of researchers. Slade made one the earliest studies of this type. She concluded that some resources have U-shaped quadratic price paths, having move in the past due to changes in demand or costs of extraction, but later rising.35 The other study of this type is by Stollerys, which generally supported the Hotelling hypothesis with an example of the nickel market by calculating the resource rent per ton of nickel.36 Thirdly, Halvorsen and Smith tested the theory and concluded, that using data for the Canadian metal m ining industry, the empirical implications of the theory of exhaustible resources are strongly rejected.37If it can be shown that prices for exhaustible resource did not rise at the rate i, it does not necessarily mean that Hotellings rule is not right. There are several circumstances where the resource prices may fall over time even where Hotellings rule is being followed. For example, a sequence of new mineral discoveries could lead to a downhill path of the resources net price. Pindyck first demonstrated that in his seminal paper. If the resource extraction takes place in non-competitive markets, the net price will also rise less quickly than the discount rate. And in the front end of technical progress continually reducing extraction costs, the market price may fall over time, thereby contradicting a simple Hotelling rule.38Named before facts show numerous contradictions which researchers face while dealing with Hotellings rule. But inspite of all these problems, the theory rem ains appealing. In their conclusion, Devarajan and Fisher state that Hotellings article is the sole source of work in a vigorously growing branch of economics.39 Solow stated that, Good theory is commonly trying to tell you something, even if it is not the literal truth.40 So although the economics of exhaustible resources does not cover the real world of mining and mineral extraction to any large extent, it is still worthwhile to re-examine the theory. Also, many studies relaxed the assumptions of Hotelling, which introduced flexibility and widened the scope of the model applications.41Next some of the most important factors influencing the Hotelling model will be discussed.As can be clearly seen from formula 1, the main variable is the price of the resource. On what does it depend? Which parameters percentage is it? As in the thesis will be considered a single mine case, in the discussion we take into consideration mainly single mine factors, which are scarcity rent ( see sectio n 2.1.3) cost of extraction (see section 2.1.4) uncertain reserves the amount of the resource left in the mine, discovery of new reserves (see section 2.1.5) demand in the market (see section 2.1.6) technological progress (see section 2.1.7) backstop technologies (see section 2.1.8) market structure competitive (see section 3.3.1) or monopoly (see section 3.3.2)Now we have a closer look at these parameters, since further description of the scenarios in different markets might require taking some of the facts into consideration.2.1.3. Resource ScarcityHotellings rule is determining the price of exhaustible resource and the extraction path of it. This price, along with other costs, covers resource scarcity, and a large part of the Hotellings theory is dedicated to resource scarcity. Since it may influence the price of the resource and the extraction path, we discuss it more in details.Worries about resource scarcity can be traced back to medieval times in Britain, and have surfaced p eriodically ever since. The scarcity of land was central to the theories of Malthus and other classical economists.What do we mean by resource scarcity? One use of the term to be called absolute scarcity holds that all resources are scarce, as the availability of resources is fixed and finite at any point in time, while the wants which resource use can satisfy are not limited.42But this is not the usual meaning of the term in general discussions about natural resource scarcity. In these cases, scarcity tends to be used to allude that the natural resource is becoming harder to obtain, and requires more of other resources to obtain it. The relevant costs to include in measures of scarcity are both private and external costs. It is important to recognize that, if private extraction costs are not rising over time, social costs may rise if negative externalities such as environmental degradation or depletion of common property resources are increasing as a final result of extraction of the natural resource. Thus, a rising opportunity cost of obtaining the resource is an indicator of scarcity let us call this use of the term relative scarcity.43There are several indicators that one might use to assess the degree of scarcity of particular natural resources, and natural resources in general including somatogenic indicators (such as reserve quantities or reserve-to-consumption ratios), marginal resource extraction cost, marginal exploration and discovery costs, market prices, and resource rents.Scarcity is concerned with the real opportunity cost of acquiring additional quantities of the resource. This suggests that the marginal extraction cost of obtaining the resource from existing reserves would be an appropriate indicator of scarcity. Unfortunately, no clear proof about scarcity can be drawn from extraction cost data alone. Barnett and Morse, studying marginal resource extraction costs, found no evidence of increasing scarcity, except for forestry.44The most commonly used scarcity indicator is time-series data on real (that is, inflation-adjusted) market prices. It is here that the affinity between tests of scarcity and tests of the Hotelling principle is most apparent. Market price data are readily available, easy to use and, like all asset prices, are forward-looking, to some extent at least. Use of price data has threesome main problems. First, prices are often distorted as a consequence of taxes, subsidies, replace controls and other governmental interventions. Reliable measures need to be corrected for such distortions. Secondly, the real price index tends to be very sensitive to the choice of deflator. Should nominal prices be deflated by a retail or wholesale price index (and for which basket of goods), by the GDP deflator, or by some stimulus price index such as manufacturing wages?45The third major problem with resource price data is that market prices do not in general measure the right thing. An ideal price measure would reflect the net price of the resource. Hotellings rule shows that it rises through time as the resource becomes progressively scarcer. But net resource prices are not directly observed variables, and so it is rather difficult to use them as a basis for empirical analysis.46Stern distinguishes two major concepts of scarcity exchange scarcity and use scarcity. Rents and prices measure the private exchange scarcity of stocks and commodities, respectively, for those wishing to purchase them. They are not necessarily good measures of scarcity for society as a whole or for resource owners. though originally intended as an indicator of the classical natural or real price, unit cost can be reinterpreted as an indicator of use scarcity. Unit cost or related measures are possible indicators of use scarcity but are not perfect either as a social scarcity indicator they do not reflect downstream technical improvements in resource use, availability of substitutes, or, as in the case of price, t he impact of environmental damage associated with resource extraction and use on welfare. All individual indicators of scarcity have limitations. There is no correct way to measure resource scarcity.472.1.4. Cost of extractionThe cost of extraction of an exhaustible resource is discussed in this section, since these costs, similarly to resource scarcity, are also included in the price of resource. Any changes in them can affect the resource price and the extraction path of it, and further we need to make appropriate assumptions.A number of researchers have attempted to provide deterministic explanations for deviations from the Hotelling price path based on the properties of the extraction cost function Solow and Wan (1976), Hanson (1980), and Roumasset, Isaak, and Fesharaki (1983). They argue that, holding technology and knowledge of the stock of the resource constant, the most easily accessible sources of the resource will be exploited first. This suggests that extraction costs sho uld rise over time, and this will affect the resource price path Dasgupta and Heal (1974, 1979). However, extraction costs alone-unless changed unexpectedly-do not explain why prices have not risen.482.1.5. Uncertain ReservesThe change in reserves may influence the resource scarcity value, the price of the resource and demand in the market, any of these changes affects the Hotellings rule. We discuss reserves change to have demote understanding of it, as then we need to make an assumption about it to construct the model.Changes in extraction and exploration technology all affect the size of the stock of proven, or extractible, reserves. This uncertainty about the reserve base contrasts with another underlying assumption in the Hotelling model. Constant real appreciation in exhaustible resource prices is derived in this model because the reserve stock is known with certainty (as are the demand function and extraction costs). In practice, however, reserves are not known with certaint y and have increased dramatically over time, often in large, discrete leaps.49The effect of uncertain reserves on the optimal depletion path has been examined in a number of studies. An unanticipated shock to reserves can cause a berth among optimal paths. A sudden, unanticipated increase in proven reserves causes the price trajectory to fall to assure full resource exhaustion. Observed prices in these models fall sharply when the discovery is made.50In addition to unanticipated shocks to the reserve base, a number of these models address the impact of endogenous exploration behaviour on the resource price path. As shown by Arrow and Chang, exploration tends to accelerate as the stock of known reserves declines and the price of the resource rises. With major new discoveries, exploration tends to slow until scarcity again becomes important.51 The implied price path, therefore, is one that rises and falls, with little apparent trend.As pointed out by Pindyck, uncertainty about the st ock of reserves is consistent with observed price behavior, although such uncertainty does not fully explain that behaviour.52 Clearly, reserve shocks have played an important role in preventing the Limits to Growth scenario from occurring by consistently raising the size of the resource stock. The timing of reserve discoveries and shifts in price trajectories, however, do not coincide precisely as the theory would predict. Announcements of large new deposits have sometimes caused prices to move, but often there is little immediate response.53In any case, the frequency with which shocks to the reserve base have occurred either because of luck or because of the endogenous response of enhanced exploration activity raises an important issue regarding the degree to which these resources really are exhaustible. The steady rise in reserves, despite growing demand, which depict a steady upward trend in consumption), may argue for decreasing scarcity value of the resource over time.54D.B. R