a limited time period as a sort of “defense mechanism”30 against the new entrant Russia between mid-2004 to mid-2005. But when the optimal withholding became too great or would have attracted more entrants the market became competitive again in the second half of 2005. This is in line with the results of Chapter 2 where perfect competition better represents the global trade flows in 2005 and 2006.
In this analysis we considered only the benefit the “big three” may have had by using market power through quantity. However, as we have observed in Section 3.4 this quantity effect may have been accompanied by an unusual increase of Colombian (and to some extend South African) F.O.B. prices. Higher Colombian prices would make the quantity effect stronger or require less of a quantity effect for the same amount of additional profit.
However, there is no theoretical model to our knowledge where such a divergence can be reproduced without breaking some assumption of the perfect market, especially perfect information and rationality of players.
3.7. Conclusions the entry and the production capacity expansions of a new fringe producer, Russia.
We find this exercise of market power to be an occurrence limited in time as in the years 2003 and 2006 a competitive model is a better representation of the actual market outcome. Also this punctual strategic behavior does not seem to be an issue that would require the action of competition authorities since entry in the market is relatively easy. Static models can deliver some insights in market power issues but in our case more complex models where capacities are not fixed could also be helpful to analyze the investment and entry dynamics.
We found in Chapters 2 and 3 that market power is not a fundamental and structural issue in the global steam coal market. Thus, in the following Chapter 4 we introduce, based on the assumption of perfect competition, a model of the global steam coal market with a higher dimension in two aspects. The “COALMOD-Word” model provides a virtually complete coverage of demand as it also includes domestic markets, and the time horizon is not static for one year anymore, but runs until 2030 with endogenous investments.
3.A Appendix
3.A.1 Proofs
Proof of proposition 1
Given the first-order conditions: b−2qi−qj −C0(qi)−riqi = 0and
b−2qj−qi−C0(qj)−rjqj = 0, and symmetry (C0(qi) =C0(qj) =c)we obtain following expressions:
qj = b−q2+ri−c
j and ri = −b+2q−qi+qj+c
i
Replacing the expression ofqj inri yields following expression forri: ri=−2 +2+r1
j − −b+c+
b 2+rj−2+c
rj
qi
Now to obtain the obtain the profit maximizing value of qi we modify the optimization problem of playeri by integrating the above expression ofqi, so that the firm can choose its profit-maximizing quantity given the other firms CVrj :
maxqi
Πi= h
b−
qi+b−q2+ri−c
j
i
qi−C(qi)
∂Πi
∂qi =b−qi− b−q2+ri−c
j +
−1 +2+r1
j
qi−c= 0 qi= −b+c−br−2−2j+crj
j
Integrating this expression ofqi in the above expression ofri, yields, after simplification:
ri=−2+r1
j
Proof of proposition 2
Assuming that the capacity constraint Kj >qj of playerj is binding thenKj =qj. Then expression ri from the proof of proposition 1 can be rewritten as:
ri=−2−−b+c+Kq j
i
Accordingly, the new optimization problem of player iis:
maxqi
Πi= [b−(qi+Kj)]qi−C(qi)
∂Πi
∂qi =b−2qi−Kj−c= 0 qi= b−K2j−c
Integrating this expression ofqi in the above expression ofri, yields, after simplification:
3.A. Appendix
ri= 0
If the capacity is not binding whenri= 0, given anyrj, then it will never be since
∂qj∗/∂ri >0. A reduction ofri leads to a lower qj∗.
Proof of proposition 3
Assuming now that the firm are asymmetric with heterogeneous cost functions of the form C(qi) = (Cinti+1/2Cslpiqi)qi withCinti >0 the marginal cost’s intercept and Cslpi >0 the marginal cost’s slope, we obtain:
qj = 2+rb−qi−Cintj
j+Cslpj andri= b−2qi−qj−Cint−q i−Cslpiqi
i
Replacing the expression ofqj inri yields following expression forri:
ri=−2−Cslpi+2+Cslp1
j+rj − b−Cinti−
b
2+Cslpj+rj−2+Cintj
Cslpj+rj
qi
Now to obtain the obtain the profit maximizing value of qi modify the optimization problem of playeriby integrating the above expression of qi, so that the firm can choose its profit-maximizing quantity given the other firms CVrj :
maxqi
Πi= h
b−
qi+2+rb−qi−Cintj
j+Cslpj
i
qi−(Cinti+1/2Cslpiqi)qi
∂Πi
∂qi =b−qi− b−q2+ri−Cintj
j+Cslpj +
−1 +2+r 1
j+Cslpj
qi−Cinti−Cslpiqi = 0
qi=
b−Cinti− b
2+rj+Cslpj+2+Cintj
rj+Cslpj
/
2+Cslpi− 2
+rj+Cslpj
Integrating this expression ofqi in the above expression ofri, yields, after simplification:
ri=−2+Cslp1
j+rj
If for the calculated value of ri,qj = 0 becausep < Cintj, then since∂qi∗/∂ri <0 and
∂qi∗/∂rj >0 and because Cslpi>0, playerican increase it’s profit by reducing it’s quantity and increasing the market price untilp+=Cintj withan infinitesimally small number, which represents the limit-pricing strategy.
Proof of proposition 4
Assuming two firms i= 1,2 that are symmetric with zero production costs andaand b respectively the demand curve slope and intercept. The profit function Π1 is:
Π1= (b−a(q1+q2))·q1
The first order condition is:
∂Π1
∂q1 =b−a(q1+q2)−a·q1= 0
Using the symmetry of the player q1 =q2, thenqNi = 3ab andΠNi = 9ab2. This is the non-cooperative Cournot-Nash solution we will use for the following Nash Bargaining game, still assuming symmetry:
ΠN B=
(b−2·a·qi)·qi−9ab2
·
(b−2·a·qi)·qi−9ab2
∂ΠN B
∂qi =
(b−2·a·qi)·qi−9ab2
·(b−2·a·qi−2·a·qi)·2 = 0
The above equation has multiple solution. However, since we want the players to be better off than in the Cournot case the first expression of the product has to be positive, hence:
b−2·a·qi−2·a·qi = 0, thereforeqiN B = 4ab .
Now the we calculate the results for the Cartel model with q1+q2=Q: ΠC = (b−a·Q)·Q
∂ΠC
∂Q =b−a·Q−a·Q= 0 Thus, Q= 2ab and qCi = Q2 = 4ab .
We therefore proved that qiC =qiN B = 4ab .
3.A. Appendix
3.A.2 Market data
Table 3.4: Steam coal trade flows to Europe in million tons and import market share of South Africa and Colombia
2002 2003 2004 2005 2006 2007 2008 2009 To Europe
South Africa 54.5 58.9 55.9 53.0 55.2 48.6 38.4 30.6
Colombia 21.4 24.5 25.6 26.5 28.5 31.8 29.8 34.0
Russia 22.7 28.5 41.3 48.7 58.0 60.0 60.4 61.1
US 4.5 2.5 3.7 2.4 3.4 5.5 12.9 11.1
Indonesia 11.0 12.4 13.6 14.2 20.6 17.1 15.5 12.8
Australia 9.8 12.2 10.4 7.6 6.5 7.7 6.4 5.0
Sum 123.9 139.0 150.5 152.4 172.1 170.7 163.5 154.6 S. Afr.+Col. 75.9 83.4 81.5 79.5 83.7 80.3 68.2 64.5 Share
S. Afr.+Col. 0.61 0.60 0.54 0.52 0.49 0.47 0.42 0.42 To India
South Africa 3.8 2.9 0.7 2.4 3.6 7.7 7.8 20.6
Source: IEA (2011a)
Table 3.5: Export volumes in million tons and export market share of the “Big Three”
2002 2003 2004 2005 2006 2007 2008 South Africa
Anglo American 15.7 18.6 17.4 20.3 22.8 24.0 22.3 BHP Billition 23.6 22.8 20.5 21.9 20.3 18.8 12.4
Xstrata 12.6 13.8 12.9 13.5 13.2 13.7 12.3
Total S.A. Exports 68.5 70.9 67.0 70.9 68.1 65.1 59.4
Total Big 3 52 55 51 56 56 56 47
Share Big 3 0.76 0.78 0.76 0.78 0.83 0.87 0.79 Colombia
Anglo American 6.9 8.7 9.6 10.1 11.0 11.3 11.5
BHP Billition 5.4 8.2 8.2 8.7 9.5 9.9 10.5
Xstrata 9.2 9.9 10.5
Glencore 6.0 8.0 9.7 8.5
Prodeco (Glencore) 5.0 5.0 5.0 5.0 5.0 13.5 13.5 Total Col. Exports 36.5 45.6 50.9 53.6 62.0 64.6 67.8 Total Big 3 30.3 38.6 42.1 42.3 45.7 55.8 57.5 Share Big 3 0.83 0.85 0.83 0.79 0.74 0.86 0.85 Source: company annual reports 2002-2008
A Techno-economic Analysis using the COALMOD-World Model: The End of “Cheap Coal”?
4.1 Introduction
This chapter introduces a tool to analyze the future developments of the international steam coal market, the “COALMOD-World” model.31 The model includes virtually all producing and consuming regions in the world by modeling domestic markets along with the globalized seaborne market to see their interaction. The time horizon is 2006 until 2030. COALMOD-World is a multi-period model that simulates yearly market outcomes, trade flows and prices for the years 2006, 2010, 2015, 2020, 2025 and 2030, as well as investments in the coal sector’s production capacity and transport infrastructure. Trade flows and investments may be subject to various capacity or expansion constraints. We assume profit maximizing players who optimize their expected and discounted profit over the total model horizon. In the model we integrate a wide range of geological, technical and economical data and mechanisms that aim at a more realistic depiction of the future coal market than is realized in previous models. We include the main drivers of the market such as future demand. Geological data is integrated in the form of reserves, heterogeneous coal qualities and with an endogenous costs mechanism that depends on cumulative production and investments. Technical constraints also influence the model outcomes and the whole model framework is grounded in economic theory and game-theoretic concepts.
We apply the model to two scenarios: one that sees global demand of coal continuously increasing and another where the demand stabilizes after 2015. As in both cases demand increases in Asia, especially in India and China, one main result of our modeling exercise is an increase of the international seaborne trade both in absolute terms and in relative
31This chapter is an updated and modified version of Haftendorn et al. (2010) and a modified version of the forthcoming article Haftendorn et al. (2012a).
4.1. Introduction terms compared to global consumption. We also expect an increase in imports from Asia as well as a shift of global trade flows toward that region. Another significant result is that until 2030, the end of cheap coal will not be caused by geological reserve constraints but rather by infrastructure constraints. Especially in the scenario of a continuously increasing global coal demand driven by Asia and China, the market may not be able to supply enough steam coal due to restrictions in the expansion of mining and transport capacities. These restrictions affect not just domestic supply in India and China but also the global seaborne suppliers such as South Africa. Stabilizing world coal demand after 2015 will lead to a less tight future market situation. A stabilization of future coal demand will be beneficial both to the climate and to the global energy supply costs by keeping coal relatively cheap.
Our research is motivated by the fact that international trade and global demand for steam coal is mainly driven by demand in Asia. Thus, we want to be able to identify how the interplay between domestic supply, exports and imports driven by demand as well as by supply costs and constraints will influence future trade flows and prices. Another area where we hope to make a contribution is to the discussion about “the end of cheap coal”
outlined in the eponymous comment written by Heinberg and Fridley (2010) in Nature. The authors argue that “useful coal may be less abundant than has been assumed” (p.
367). The authors cite three recent studies that predict a more or less imminent end of cheap and available coal through decreasing global production levels and rapid reserve depletion (Patzek and Croft, 2010; Höök et al., 2010; Mohr and Evans, 2009). These studies are based on the concept of the Hubbert curve first described by M. King Hubbert (1959). The core mathematical assumption of this model is that cumulative resource production follows a logistic growth path that derived with respect to time yields the well-known symmetrical bell shaped curve of yearly production output; the summit of the curve representing the “peak” of the yearly production rate. Thus, it is mathematically possible to estimate the shape of the curve and thus the peak year as well as the ultimately recoverable reserves, defined as the surface under the curve, based solely on historical production data.32 This simple technique is subject to controversy. Its proponents claim that “the Hubbert curves are based on [...] production and not on ill-defined and subjective [...] ‘reserves’ ” and that “historical production trends reflect the prevailing economics prior to the time of production” (Patzek and Croft, 2010, p. 3111). However, its opponents, such as Lynch (2003), state that the “work of the Hubbert modelers has proven to be incorrect in theory, and based heavily on assumptions that the available evidence shows to be wrong. They have repeatedly misinterpreted political and economic effects as reflecting geological constraints, and misunderstood the causality underlying exploration, discovery and production” (p. 30). We do not intend to settle the general debate about the Hubbert curves but rather make a critical evaluation of the three aforementioned papers using this method for coal. We give an overview of the papers starting with the earliest predicted “peak coal”, finishing with the one with the latest
32A description of the mathematical transformations is given in Claerbout and Muir (2008)
peak date.
Patzek and Croft (2010) predict the global coal peak as early as 2011. The method-ology used is the closest to the one described by Hubbert. The authors use historical production data to fit Hubbert curves for each coalfield and then sum the data up. Hence the name “multi-Hubbert cycle analysis”. To be able to perform this summation, the au-thors assume that coal mines are “independent of each other” in terms of production.
We find this to be a rather strong assumption. For example a power plant located in Southern China that is able to choose between domestic coal from northern Shanxi or imported coal from Indonesia will make an economic calculation based on the extraction and transport costs. Thus, if coal from Indonesia is cheaper to source, the higher pro-duction from Indonesia will cause lower propro-duction in Shanxi, ergo the mines are not independent. Also there may be some problems with using only historical production data. The imminence of the predicted peak in China, also 2011, may be due to the fact that infrastructure constraints, reforms and price regulations that can slow down production are interpreted as geological depletion. Indeed, Peng (2011) found that the effect of the recent coal market deregulation, while power prices are kept regulated, is that “under pressure of price increases from domestic coal suppliers the power sector responded by going to overseas markets to purchase coal”. Interestingly, another study by Lin and Liu (2010), also using the Hubbert curve methodology, predict a much later time for the peak, between the late 2020s and the early 2030s. Patzek and Croft (2010) also concede that “Hubbert cycle predictions almost always underpredict the true future production rate of a resource” but argue only verbally why new production capacity will be hard to put in place due to transport or environmental restrictions. This is essentially a question of investment dynamic that the Hubbert curve model is not able to integrate.
Also, past production can only represent past economic situations. The simple Hubbert model fails to integrate paradigm shift that will affect the future production pattern such as the carbon constraints of climate policy or the high economic growth in Asia.
Höök et al. (2010) use a more refined model as they integrate past production and reserve estimates for the Hubbert curve fitting. In the “standard case outlook” the authors predict the peak around 2025-2030. The global production level at that time is in the same range as other projections such as the IEA (2010) World Energy Outlook Current Policies scenario. The authors discuss reserves estimates extensively and show how they developed over time. The underlying reserve estimations of the “standard case outlook”
is more restrictive than the ones of national geological services such as the USGS or the German BGR and does not account for the expansion of the reserves. Thus, the authors also model a “high case outlook” with a doubled reserve base. Logically the peak is further in the future, around 2040. But the estimated annual production values also increase and after 2015 these values are significantly higher that the estimates of the IEA (2010) World Energy Outlook Current Policies scenario that represents the worst case in climate policy. The Hubbert method, by trying to fit a bell curve, overestimates future production. This is caused by the fact that realistic demand projections are not included
4.2. Equilibrium Modeling of Energy Resource Markets