Quantity-setting Oligopolies in Complementary Input Markets - the Case of Iron Ore and Coking Coal

Transcription

1 Quantty-settng Olgopoles n Complementary Input Markets - the Case of Iron Ore and Cokng Coal AUTHORS Harald Heckng Tmo Panke EWI Workng Paper No. 14/06 February 2014 Insttute of Energy Economcs at the Unversty of Cologne (EWI)

2 . Insttute of Energy Economcs at the Unversty of Cologne (EWI) Alte Wagenfabrk Vogelsanger Str Cologne Tel.: +49 (0) Fax: +49 (0) Correspondng Author Tmo Panke Insttute of Energy Economcs at the Unversty of Cologne (EWI) Tel.: +49 (0) Fax: +49 (0) ISSN: The responsblty for the workng papers les soley wth the authors. Any vews expressed are those of the authors and do not necessarly represent those of the EWI.

3 Quantty-settng Olgopoles n Complementary Input Markets - the Case of Iron Ore and Cokng Coal Harald Heckng a, Tmo Panke a, a Insttute of Energy Economcs, Unversty of Cologne, Vogelsanger Strasse 321, Cologne, Germany. Abstract Ths paper nvestgates the benefts of a merger when goods are complements and frms behave n a Cournot manner both n a theoretcal model as well as n a real-world applcaton. In a settng of two complementary duopoles a merger between two frms each producng one of the goods always ncreases the frms total proft, whereas the remanng frms are worse o. However, allowng for a restrcton on one of the mergng frms output, we proof that there exsts a crtcal capacty constrant () below whch the mergng frms are nd erent to the merger, () above whch the merger s always benefcal and () the lower the demand elastcty s the smaller ths crtcal capacty constrant becomes. Usng a spatal mult-nput equlbrum model of the ron ore and cokng coal markets, we nvestgate whether our theoretcal fndngs may hold true n a real market as well. The chosen ndustry example s partcularly well suted snce (a) goods are complements n pg ron producton, (b) each of the nputs s of lttle use n alternatve applcatons, (c) nternatonal trade of both commodtes s hghly concentrated and (d) a few (large) frms are actve n both nput markets. We fnd that due to lmted capacty, these frms gan no substantal extra beneft from optmsng ther dvsons smultaneously. Keywords: Cournot olgopoles, parallel vertcal ntegraton, complementary nputs, appled ndustral organsaton, mxed complementarty problem JEL classfcaton: C61, D43, L22, Q31, Q Introducton The research presented n the paper at hand s nspred by an nterestng example of an ndustry wth complementary nputs, namely ron ore and cokng coal. Both goods are ndspensable nputs Correspondng author: Emal address: tmo.panke@ew.un-koeln.de, (Tmo Panke) We would lke to thank Felx Hö er for hs helpful comments and suggestons. Furthermore we would lke to thank Johannes Trüby for sharng hs dataset on the cokng coal market and Robert Germeshausen for provdng excellent research assstance.

4 when makng crude steel usng the so-called oxygen route,.e., producng frst the pg ron n a basc-oxygen furnace and second usng the pg ron n a blast furnace to create the fnal product, crude steel. Ths ndustry example s of partcular nterest because () the goods are complements, () each of the nputs s of lttle use n alternatve applcatons, e.g., power plants typcally use coals of d erenty qualty, () nternatonal trade of both commodtes s hghly concentrated and (v) a few (large) frms are actve n both nput markets (parallel vertcal ntegraton),.e., produce both ron ore and cokng coal, although none of them s vertcally ntegrated n the producton of steel. Ths market settng rases at least one mportant queston: Do frms beneft from behavng parallel vertcally ntegrated, or put d erently, s a merger between two frms, where each of the frms produce a d erent complement, proftable? In order to answer ths queston, our analyss comprses two steps: Frst, we use a smple theoretcal model to nvestgate the proftablty of a merger n a settng wth complementary goods. In ths model, we consder two homogeneous Cournot duopoles of complementary goods and assume the demand for the composte product to depend lnearly on ts prce. We consder two cases, one wth unlmted capactes and one ncorporatng a bndng capacty constrant on one of the mergng frms output. Comparng total profts of the frms n a stuaton wth or wthout a merger allows us to answer our research queston from a theoretcal pont of vew. The actual markets for ron ore and cokng coal are however more complex as () both markets have more than two supplers, () there are multple parallel vertcally ntegrated frms, () producton costs are heterogeneous, (v) both markets are spatal wth multple demand and supply regons and (v) several producers face a bndng capacty constrant. We therefore, second, develop and employ a spatal, mult-nput olgopoly smulaton model of the ron ore and cokng coal market, calbrated wth data from a unque data set for the years 2008 to We run the model for a range of assumed demand elastctes to assess profts of the ntegrated companes n both cases,.e., the smultaneous (equvalent to the merger stuaton) and the separate optmsaton (equvalent to the non-merger stuaton) of the busness unts. Further, we compare the smulaton results of three specfc market settngs to the actual market outcomes. Besdes one perfect competton scenaro, we assess one scenaro assumng separate optmsaton of all ntegrated frms, and the other one 2

5 assumng smultaneous optmsaton of the ntegrated companes busness unts. We then assess whch of the three scenaros best explans the actual market outcomes wth regard to trade flows, producton volumes and prces of the two commodtes. Concernng trade flows, we use three statstcal measures to evaluate whch settng provdes the best ft. The theoretcal model confrms the result that a merger of two companes, each producng one of the complementary nputs, leads to hgher profts than the sum of the two separate frm s profts. In other words, no merger-paradox exsts when goods are complements and capactes are unconstraned. However, f one of the mergng frms capacty s lmted, we prove that there exsts a crtcal capacty constrant () below whch mergng s nd erent from not mergng, () above whch the merger s always benefcal and () the lower the demand elastcty s the smaller ths crtcal capacty constrant becomes. Applyng the smulaton model for the ron ore and cokng coal market, we fnd that smultaneous optmsaton (equvalent to the merger stuaton) generates addtonal benefts compared to separate optmsaton (equvalent to the non-merger stuaton) the lower the assumed demand elastcty gets. However for demand elastctes beyond -0.5 to -0.6 the benefts of smultaneous optmsaton tend to zero. Comparng smulaton results and actual market outcomes for the years 2008 to 2010, no evdence of compettve behavour on a frm level s found, whch allows us to contnue wth the two Cournot scenaros. In terms of trade flows, prces and producton volumes the separate optmsaton scenaro provdes a more consstent ft wth actual market outcomes than the smultaneous optmsaton scenaro although one scenaro does not unambguously domnate the other one. Takng nto account low or zero extra benefts of smultaneous optmsaton for the demand elastctes that yeld the best ft, plus organsatonal and transactonal costs of smultaneous optmsaton, t s lkely that ntegrated frms optmse ther ron ore and cokng coal dvsons ndependently. Our research s nspred by the extensve lterature on the theory of complementary olgopoles, wth the semnal publcaton by Cournot (1838) as a startng pont. More recent papers on the topc of strategc behavour and complementary goods were nspred by Sngh and Vves (1984), who develop a duopoly framework that allows the analyss of quantty- and prce-settng olgopoles 3

6 assumng goods to be substtutes, ndependent or complements. Buldng on Sngh and Vves fndng, a whole body of lterature emerged devotng ts attenton to analysng the problem of complementary monopoles under d erent setups. However, the settng, n whch we are nterested, s d erent from the ones assumed n most of the papers belongng to ths strand of lterature: In our settng, supply of each complement s charactersed by an olgopoly,.e., there are few substtutes for each complement, whle most of the papers belongng to the body of lterature refered to above assume each complementary good to be produced by a monopolst. Salnger (1989) s among the few to use a smlar settng as ours. In addton to the theoretcal lterature, several emprcal papers have been publshed dealng wth the analyss of ron ore and cokng coal tradng (e.g., Toweh and Newcomb (1991), Labson (1997), Graham et al. (1999) and Trüby (2013)) and the e ects of mergers n the ron ore ndustry (Fuza and Tto, 2010). However, to the best of our knowledge, there has not yet been a publcaton that deals wth the strategc nteracton between both markets and none applyng the theory of complementary nputs to a real-world settng. Consequently, ths paper contrbutes to the lterature n three ways: Frst, we provde nsghts nto the e ect of capacty constrants on the proftablty of a merger between frms producng complementary goods and behavng n a Cournot manner. Second, ths s the frst study applyng the theory of complementary quantty-settng olgopoles usng the example of the ron ore and cokng coal market. Thrd, we develop a spatal mult-nput equlbrum model that has been calbrated usng a unque data set for the years and accounts for the complex nteractons and the spatal nature of both markets, allowng us to smulate the exercse of market power on a frm level. The remander of ths paper s structured as follows: Secton 2 ntroduces our theoretcal framework and establshes our theoretcal fndngs. The thrd secton motvates our ndustry example, explans the structure of the smulaton model used to model the ron ore and cokng coal market and descrbes the numercal data used n ths study. Secton 4 analyses the results obtaned from the model smulatons. More specfcally, Subsecton 4.1. analyses, from the perspectve of ndvdual frms, the mpacts of smultaneous or separate optmsaton on the frms profts. Subsecton 4.2. assesses whether prce-takng behavour or smultaneous or separate optmsaton of the nte- 4

7 grated frms best explans actual outcomes of the ron ore and cokng coal market. Subsecton 4.3. brefly dscusses the strategc mplcatons of these fndngs. Fnally, Secton 5 concludes. 2. Quantty-settng complementary olgopoles In the settng we are nterested n, supply of each complement s charactersed by a quanttysettng (Cournot) olgopoly,.e., each of the two complementary goods s homogeneous. Furthermore, the settng s charactersed by the exstence of a number of parallel vertcally ntegrated frms,.e., companes whch produce both complements. Consequently, we model two smultaneous Cournot equlbra both of whch nfluence the composte good s demand and thus the prce of the two complementary goods. The approach chosen n ths paper resembles the one n Salnger (1989), who uses a smlar settng of complementary olgopoles to nvestgate how d erent defntons of the terms upstream and downstream change the mpact of a vertcal merger on competton. Followng Salnger (1989), we assume players actve n one nput market to take the prce of the other complement as gven, thus we = 0. Ths assumpton mples that we abstract from the tragedy of the antcommons problem. The problem was frst descrbed by Sonnenschen (1968), who ponted out the dualty between a Bertrand duopoly wth substtutes and a Cournot complementary monopoly. Sonnenschen (1968) showed for a setup n whch each complementary good s produced by one monopolst and each monopolst maxmses ts proft by choosng the optmal quantty of ts good, an ncentve arses to undercut total output of the other complement. In hs settng an oversupply of one of the complements would cause ts prce to drop to zero (or to margnal costs f they are assumed to be greater than zero), leavng all the profts to the other complement s suppler. In the end, ths would lead to a race-to-the-bottom n quanttes. The unque Nash-equlbrum where such a devaton s not proftable s one where no frm produces at all. Ths somewhat paradox (and unrealstc) result reles heavly on the e ect that even the slghtest excess supply of one of the goods lets ts prce drop to zero. An e ect whch already Sonnenschen hmself referred to as somewhat obscure Ths remark can be found n footnote 4 of Sonnenschen (1968). 2 Another nterestng aspect of complementary goods and Cournot competton was frst brought forward by Sngh and Vves (1984). They develop a duopoly framework that allows to analyse quantty- and prce-settng olgopoles 5

8 Next, we frst wll quckly recall the market outcomes for the case of olgopolstc nput markets, n whch frms produce only one complement and compete by settng quanttes and no capacty constrants exst. Second, we derve optmal quanttes and prces n a settng that features one parallel vertcally ntegrated frm,.e. a frm that produces both complements. In Subsecton 2.2, we frst nvestgate f the ntroducton of a bndng capacty constrant on one of the complementary goods of the parallel vertcally ntegrated frm may change the favourablty of a vertcal merger. Second, we propose and proof three conjectures charactersng the proftablty of a merger A model of two complementary duopoles wth no capacty constrants To llustrate what e ect parallel vertcal ntegraton,.e., a merger between frms that produce d erent complementary goods, has on outcomes n a quantty-settng complementary olgopoly, we start out by consderng a smple market that conssts of four symmetrc frms (N = M = 2) producng two complementary goods. Two frms (c n ) produce complement C (cokng coal) and the remanng two frms ( m ) produce the other complement I (ron ore). Producton costs are assumed to be zero. Complements I and C may be combned n fxed proportons (here: one unt each) to produce the composte good p (pg ron),.e., t holds true that x p = x = x c wth x c = P N n xn c and x = P M m xm. In addton, we assume full compatblty among the complements and perfect competton n the market for the composte good, such that NxM composte goods exst, h PM all of whch are avalable at prce p p = p + p c. Thus each complement s prce (p m xm,p c h PN and p c n xn c,p ) depends on the supply of the complement ( P M m xm or P N n xn c ) as well as the prce of the other complement. However, the prce of the other complement s perceved as a cost component due to the = 0. We also rule out that there s product d erentaton n the composte good market, thus all NxM composte goods are perfect substtutes as well. Intally, we do not assume the compos- (Bertrand, 1883) assumng goods to be substtutes, ndependent or complements. The two authors proof that n the case of a complementary monopoly companes prefer to o er prce nstead of quantty contracts, as ths maxmses ther profts. Amongst other thngs, Häckner (2000) shows that ths fndng also holds true under more general assumptons ncludng a settng wth more frms (each producng one complementary good). In ths paper both nput markets are charactersed by olgopoles wth frms havng producton constrants. Therefore, f frms were assumed to engage n Bertrand competton and producton capacty would be unconstraned prces of each complement would equal margnal costs and, thus profts would amount to zero. In the case of capacty constrants t has been shown that frst-order condtons for proft maxmsaton may have a knk, such that equlbra may not be well defned. Therefore, companes would prefer quantty contracts over prce contracts n our settng. 6

9 Fgure 1: Market structure wth ndependent ownershp te good s nverse demand functon to be of a specfc functonal form. Consequently, the proft functons of the four frms are gven by m = p x m (1) cn = p c x n c. (2) Takng, for example, the frst partal dervate of the proft functon of frm 1 yelds the followng frst-order @x 1 = p x 1 = 0 (3) wth x m beng the ron ore producton of the compettors. Due to the assumpton that the frms engage n Cournot competton, t holds true 1 we assume = 0, hence Equaton 3 smplfes to = 0. As dscussed prevously, n our 1 = 1 x 1 =0. (4) 7

10 In order to derve the market results we assume the demand functon to be lnear n form,.e., p p = a bx p. The frst partal dervate of the proft functon of frm 1 yelds the followng frst-order condton, whch due to the assumed symmetry looks analogue for the other 1 = p bx 1 =0. (5) Solvng the resultng system of equatons allows us to derve equlbrum output and prces under ndependent ownershp: x p = x = x c = a 2b, p c = p = a 4 and p p = a 2. (6) In order to llustrate the e ects of parallel vertcal ntegraton, we now consder a setup n whch one frm produces both complements, as depcted n Fgure 2. The proft functon of the parallel Fgure 2: Market structure wth one ntegrated frm vertcally ntegrated company (PVI), n ts general form,.e. wthout a specfc functonal form of the (nverse) demand functon, s gven by PVI = p x PVI + p c x PVI c. (7) 8

11 Takng the frst partal dervate of Equaton 7 wth respect to x PVI and x PVI c PVI c = p + = p @x PVI c We already know that p x PVI PVI c = pc PVI PVI c = 0 m x m n c c n x n PVI x PVI x PVI c c PVI c p c = 0 (8) p =0. (9) = 0. Keepng n mnd that n ths example a factor ntensty (fn) of 1 s assumed, n case of a parallel vertcally ntegrated PVI PVI c = fn = 1. Thus, an ntegrated frm knowng that an ncrease n one of the complements output needs an equally large ncrease of the other complement n order to ncrease the output of the composte good, would always fnd t benefcal to ncrease output of both goods at the same tme. Assumng a lnear nverse demand functon of the composte good and usng Equatons 8 and 9, respectvely, the resultng frst-order condtons PVI = a 2bx PVI bx 2 + p c = p + p c bx PVI = 0 PVI c = a 2bx PVI c bx 2 c + p = p + p c bx PVI c =0. (11) Takng a closer look at the Equatons 10 and 11, we see that due to the complementarty of the goods, n order to maxmse ts overall profts the parallel vertcally ntegrated frm has to take nto account not only the producton of ts drect compettors, but also the prce of the complementary good. Solvng agan the resultng system equatons allows us to derve equlbrum output and prces under parallel vertcal ntegraton: x p = x = x c = 2a 5b, p c = p = a 5 and p p = 2a 5. (12) By comparng the equlbrum solutons,.e., wth (Equatons 12) and wthout parallel vertcal ntegraton (Equatons 6), we fnd that parallel vertcal ntegraton results n hgher supply of the composte good and, therefore, of the two complementary nputs, whch n turn leads to lower 9

12 prces. Hence, a merger between two frms producng complementary goods ncreases consumer welfare. Prce of composte good Prce of complements Quantty (x p = x = x c ) Table 1: Market outcomes Independent ownershp a 2 a 4 a 2b Each frm s output x m = x n c = a 4b Each frm s proft m = c n = a2 16b One parallel vertcally ntegrated frm x PVI PVI = 4a2 25b 2a 5 a 5 3a 5b = x PVI c x 2 = x2 c = a 5b = 2a 5b 2 = c 2 = a2 25b Whle consumers proft by the merger, the frms that are not part of the merger lose market share and make less proft. Ths s due to the fact that the merger e ectvely nternalses a negatve externalty. The externalty s negatve due to the the fact = 0 (see also Salnger (1989)). If a company, producng one of the complements, chooses to reduce ts output, the producton of the composte good s reduced as well, thereby rasng the composte good s prce. Ths ncreases the prce of the company s complement, whle the other complement s prce s not changed (because = 0). However, due to the reducton of the composte good s output, the output of the other complement s reduced. Consequently, reducng the output of one of the complements causes a negatve externalty on the frms producng the other complement. Consequently, the PVI company, nternalsng ths negatve externalty, s wllng to supply a larger amount of both nputs, whch then leads to a reducton of the output of the remanng ndependent companes (see Table 1). Another nterestng aspect s that, n contrast to Cournot olgopoly wth substtutes and no capacty constrants, there s no merger paradox,.e., profts of the new merged frm are always larger than the combned profts of the two sngle frms, agan due to the nternalsaton of the negatve externalty. Summng up, we recalled that a parallel vertcally ntegrated company maxmses ts profts by optmsng output of both goods accountng for the negatve externalty of reducng the output of one of the complements on the other. In the case wth no capacty constrants, we showed that 10

13 a merger between two frms producng d erent d erent complements s always proftable,.e., t ncreases overall proft of the frms Proftablty of a parallel vertcal merger As shown n Subsecton 2.1, the proftablty of a merger arses from ncreasng the ntegrated frm s output of both complements wth respect to the case of ndependent ownershp. Therefore, the queston arses whether a constrant restrctng the potental output of one of the two complements may alter the result that the merger s benefcal. In order to do so, we need to recall from Subsecton 2.1 that, frst, an unconstraned ntegrated frm behaves n a manner smlar to a Stackelberg leader,.e. by takng nto account the negatve externalty of the two complements, he ncreases hs output compared to the case wth no merger (see Table 1). Second, the ntegrated frm maxmses ts proft by supplyng the same amount of both complements (n case of a factor ntensty of both goods of 1),.e. t provdes both complements as a bundle. However, n case of a bndng capacty constrant on one of the complements, the frm could also choose to supply d erent quanttes of ts two goods. Consequently, one can rewrte the proft functon of the parallel vertcal ntegrated frm from the prevous subsecton (Equaton 7) as: PVI =(p + p c )x b + p x PVI + p c x PVI c (13) wth x b referrng to the amount of bundled sales suppled to the market, thus t represents at the same tme sales of ron ore as well as cokng coal, whle x PVI and x PVI c need not be sold at a smlar rato. Thus the frm s total ron ore and cokng coal output amounts to x b + x PVI x b + x PVI c, respectvely. In the followng, usng Equaton 13 and a lnear demand functon, we would lke to nvestgate the proftablty of a merger n the event of a bndng capacty constrant n more detal. Therefore, we propose three conjectures that we wll proof subsequently: Conjecture 1 Gven a specfc lnear demand functon, there exsts a crtcal capacty lmt, x b, that causes the mergng frms to be nd erent between the merger and not mergng,.e. profts do not change due to the merger. For capacty lmts lower than x b profts reman unchanged by the merger as well. and 11

14 Conjecture 2 Gven a specfc lnear demand functon, for every capacty lmt ˆx b that fulflls ˆx b > x b, a merger s proftable despte a bndng capacty constrant. Conjecture 3 The less elastc the lnear nverse demand functon of the composte good, the lower becomes the crtcal capacty constrant, x b. Concentratng frst on Conjecture 1, we need to show that for a gven lnear nverse-demand functon of the composte good, there s a capacty lmt to one of the complements x b 3 that causes the d erence between the sum of the two separated frms profts, c 1 + 1, and the proft of the merged frm, PVI, to be zero. For ths purpose, we start by dervng the equlbrum proft of PVI usng the frst-order condtons of the three frms (one ntegrated and two ndependent PVI = bx PVI bx b + p = 0 PVI c = bx PVI c bx b + p c = 0 PVI = bx b bx PVI b bx PVI + p c + p = 0 (16) Assumng a bndng capacty constrant on the ron ore output of the ntegrated frm (x b ), the frst and thrd frst-order condtons (Equatons 14 and 16) wll not be needed as the frm s optmal ron ore output s x b (hence, x PVI = 0), otherwse the capacty constrant would not be bndng. Knowng that the frst-order condtons of the non-ntegrated frms reman unchanged (see Equaton 10) and usng p p = p + p c as well as Equaton 15 yelds p = 2a 3bx b 5, p c = a + bx b, x PVI c = x b + a 5b. (17) Therefore, the ntegrated frm s maxmum proft functon n case of a bndng capacty constrant s PVI = a2 + 12abx b 25b 14b 2 x 2 b. (18) 3 We use x b snce f the capacty constrant on one of the complements s bndng, the frm wll choose to produce at least the same quantty of the other complement, hence t wll supply x b -bundles. 12

15 We know from Subsecton 2.1 that the proft of two unconstraned ndependent ron ore and cokng coal frms amounts to 2 a2 16b = a2 8b wth each frm supplyng a 4b (see Table 1). In order to proof Conjecture 1, we thus need to show that when the capacty constrant s x b = a 4b the ntegrated frm equals the profts of the two ndependent frms: profts of PVI = a2 + 12ab a 4b 14b 2 a 4b 25b 2 = 4a2 7a2 8 25b = 25a b = a2 8b, (19) whch s the case. Now, f we consder two ndependent frms wth one of them beng constrant n ts output, e.g., the ron ore frm (x 2 ), the functon of the maxmum profts s the same as n the case of no merger (see Appendx C). In other words, f the capacty lmt equals the optmal quantty n the case of ndependent frms or s lower, profts of the frms reman unchanged by the merger, whch s what we wanted to proof. Regardng Conjecture 2, we need to show that for capacty constrants that are hgher than x b profts of the merged frms are hgher than n the case of no merger. We already know that the optmal output of the unconstraned ntegrated frm s 2a 5b. Takng a look at equlbrum output of x PVI c stated n Equaton 17, we see that x PVI c s zero for ˆx b > a 4b, because output n ths model s restrcted to be non-negatve. Therefore, total output of the ntegrated frm s equal to ˆx b for ˆx b > x b = a 4b. In ths case, equlbrum prces and the ntegrated frm s profts are gven by p = p c = a bˆx b, PVI = 2aˆx b 2bˆx 2 b 3 3 for ˆx b > x b. (20) Hence, for ˆx b > x b t holds true that the profts of the ntegrated frm change PVI = 2a 4bˆx b 9 for ˆx b > x b, (21) b > 0 for a 4b < ˆx b < 2a 5b, whch proofs Conjecture 2. Fgure 3 llustrates the profts of the ntegrated and two ndependents frms dependng on the ron ore capacty. Focussng now on Conjecture 3, we would lke to show that the steeper the nverse demand functon the lower the optmal quanttes suppled n case of no merger a 4b (see Table 1) and thus 13

16 Fgure 3: Profts of the ntegrated versus two ndependent frms the lower the capacty constrant that renders the profts of an ntegrated and two non-ntegrated frms equal. Therefore, we need to establsh the relatonshp between the rato of a, the maxmum wllngness-to-pay, and b, the slope of the nverse demand functon, and the assumed (absolute) pont elastcty. Snce t can be easly shown that a and b n the lnear demand case can be wrtten as: a = p ref + b x ref (22) b = p ref x ref 1 wth >0, (23) wth p ref and x ref beng a reference prce and demand, respectvely, t holds true that a b =(1+ ) x ref. (24) Consequently, the lower the elastcty n the reference pont,,.e., the steeper the lnear nverse demand functon, the lower the optmal quanttes when frms optmse ther quanttes separately. Thus, the less elastc the lnear nverse demand functon of the composte good, the lower the crtcal capacty constrant, x b becomes (Conjecture 1). The ntuton behnd ths fndng s that the steeper the demand functon,.e. the lower the pont elastcty, the lower the equlbrum output. The lower the equlbrum output s the less restrctve s the capacty constrant. Furthermore, the 14

17 less restrctve the capacty constrant of the ntegrated frm, the longer the e ect of smultaneous optmsng (avodng margnalsaton of both dvsons). 3. A spatal equlbrum model of the global ron ore and cokng coal market 3.1. Steelmakng and the markets for ron ore and cokng coal In general, there are two man routes to produce crude steel, whch s an alloy of ron and carbon. 4 One opton, also referred to as the oxygen route, s an ntegrated steel-makng process nvolvng blast furnace (BF) producton of pg ron followed by a basc oxygen furnace (BOF). Alternatvely, an electrc arc furnace (EAF) process may be appled (the so called electrc route ), whch manly uses recycled steel (steel scrap) for steelmakng, and may also use drect reduced ron (DRI) to substtute steel scrap. Roughly 30% of global steel supply s produced usng EAFs, wth the remander relyng on ntegrated steel-makng. The man d erence between the two producton methods s that the basc oxygen steelmakng process s self-su cent n energy,.e., the energy s generated durng the process by the reacton of oxygen and carbon, wth coke beng the man source of carbon. Ths s not the case wth EAF steelmakng, as an EAF manly reles on the use of electrcty for meltng the steel scrap and DRI. Therefore, no coke s used n electrc arc furnaces. Aganst the background that coke s essentally cokng coal wthout mpurtes, t s obvous that almost the entre global cokng coal supply s used n coke ovens and, therefore, n the basc oxygen steelmakng process. Furthermore, due to ts chemcal propertes and the exstence of cheaper alternatve coal types (manly thermal coal and lgnte), cokng coal s not used n electrcty generaton. Albet to a lesser extent, ths also holds true for ron ore, wth the reason beng that the major part of total steel scrap supply s used n EAFs, thereby reducng the need for drect reduced ron. In 2012, pg ron producton amounted to 1112 Mt, whle drect reduced ron producton was 71 Mt,.e., DRI accounted for 6% of global ron producton (WSA, 2013). Consequently, ron ore and cokng coal are complementary goods needed to produce pg ron, wth both nputs beng (almost exclusvely) used n ths sngle applcaton. 4 The nterested reader s referred to Fgure A.1 n Appendx A for a graphcal overvew of the two most mportant steelmakng processes and the requred nputs. 15

18 Furthermore, both markets, the one for ron ore as well the one for cokng coal share two nterestng characterstcs: Frst, nternatonal trade of both commodtes s hghly concentrated, as the bggest four exportng companes n the cokng coal and ron ore market were responsble for 45% and 67% of total trade volume n 2010, respectvely. Second, three global mnng companes, namely BHP Bllton, Ro Tnto and Anglo Amercan, are among the top four exportng companes n both markets. Hence, not only are they parallel vertcally ntegrated companes,.e. they produce both complementary nputs, but, n addton, they may have consderable market power. Gven the settng of complementary nputs and market concentraton, ntegrated companes actve n both markets may have ncentves to maxmse ther profts by smultaneously choosng ther ron ore and cokng coal producton volumes and not separately,.e. by dvson or busness unt Model logc and formulaton The partal equlbrum model presented n ths secton s programmed as a mxed complementary problem (MCP). The model ams at maxmsng annual profts of the global mnng companes producng ron ore and cokng coal subject to producton constrants and gven the varous costs along the supply-chan, such as seaborne and nland transport costs. Secton 2, albet n a smplfed settng (.e., non-spatal market, wth only one consumng regon and homogeneous players) already dscusses a frm s proft functon under ndependent ownershp and parallel vertcal ntegraton. Here, the dscusson of the model focuses only on the frst-order and the market clearng condtons, thus we do not explctly wrte down the respectve proft functons. Smlar to the model presented n the prevous secton, we assume that the composte good s prce ( d,y )ndemand regon d lnearly depends on the composte good s (pg ron) demand (whch s equal to pg ron producton p d,y ). Thus, d,y = nt d,y slo d,y p d,y. 5 6 The model dstngushes the physcal transports of nput factor by mnng company c n year y produced n mne m to a demand market d (tr c,,m,d,y ) and the sales of a company to a market 5 Although all sets, parameters and varables used throughout ths subsecton are explaned n the text, the reader s referred to Table B.1 n Appendx B for an overvew of the nomenclature. 6 To keep the formulae as smple as possble, all parameters used n the model descrpton have been adjusted for the factor ntensty. 16

19 (sa c,,d,y ). If the frm s optmsed smultaneously, t can also sell both compostes as a bundle (sa b c,d,y ). Transports tr c,,m,d,y are constraned by the annual producton capacty cap c,,m,y of mne m. Hence, the amount of transported volumes s subject to the followng constrant cap c,,m,y X tr c,,m,d,y 0 8c,, m, y (µ c,,m,y ), (25) d2d thereby µ c,,m,y represents the value of an addtonal unt of producton capacty at mne m n year y, whch may also be nterpreted as a scarcty rent of producton capacty. For each nput, the sum of transported volumes to a demand market has to equal the sales of each company. If smultaneous optmsaton s enabled the parameter sm c s equal to 1. X tr c,,m,d,y = sa c,,d,y + sa b c,d,y sm c 8c,, d, y (v c,,d,y ), (26) m2d thereby v c,,d,y can be nterpreted as the physcal value of the transported goods,.e. the sum of producton costs, scarcty rent and transport costs. A mnng company s only wllng to produce and transport a good to a market f the sum of producton costs, scarcty rent and transport costs s covered by the resultng physcal value n the c,,m,d,y = v c,,d,y + pco,m,y + tco,m,y + µ c,,m,y 0? tr c,,m,d,y 0 8c,, m, d, y. (27) Each mnng company c maxmses ts proft by sellng volumes to demand regon d as long as the prce of the nput factor (,d,y ) exceeds the value of the good v c,,d,y. In case the company s assgned market power (whch s ndcated by settng the bnary parameter cva c,y equal to one), d,,y must not only exceed physcal delvery costs but also the company s mark-up, whch depends 17

20 on the slope of the composte good s demand functon (slo d,y ) and sales volume of the company (sa c,,d,y and sa b c,d,y sm c n case smultaneous optmsaton s c,,d,y = d,,y cva c,y slo d,y (sa c,,d,y + sa b c,d,y sm c) + v c,,d,y 0? sa c,,d,y 0 8c,, d, y. (28) If an ntegrated mnng company decdes to optmse ts dvsons smultaneously t has to decde addtonally about the amount of bundles of complementary nput factors t sells to each market. The prce of both nput factors,.e. the bundle has to equal the olgopolstc mark-up (see Equaton 16) plus the physcal value of both b c,d,y = X + X! X ( d,,y ) cva c,y slo d,y (sa c,,d,y )+sa b c,d,y sm c v c,,d,y 0? sa b c,d,y 0 8c, d, y. (29) Fnally, n order to model an olgopoly n complementary goods the model encompases three market clearng condtons: d,y = nt d,y slo d,y p d,y? d,y free 8d, y (30) p d,y = X c2c (sa c,,d,y + sa b c,d,y sm c)?,d,y free 8, d, y (31) d,y + X 2I,d,y 0? p d,y 0 8d, y. (32) These market clearng condtons determne three thngs: Frst, Equaton 30 determnes the prce of pg ron ( d,y ) usng the nverse lnear demand functon. Second, Equaton 31 states that each nput s total sales (ncludng bundles of nput factors) to demand regon d needs to equal total pg ron demand (p d,y ). Ths equaton s used to model ron ore and cokng coal as complementary goods, wth the composte good beng produced usng a fxed-proporton producton technology. Fnally, Inequalty 32 needs to be ncorporated to establsh the relatonshp between nput factor prces (,d,y ) and pg ron prce ( d,y ). For smplfcaton, we assume that the pg ron prce s 18

21 fully explaned by the prces of ron ore and cokng coal,.e. does not nclude any further margnal costs for the producton process. Ths does not e ect the results qualtatvely though as the fnal product s prce s of no further mportance for our analyss Data and scenaro settng Ths subsecton descrbes the data of the ron ore and cokng coal market that we use n the numercal smulaton. The dataset comprses demand, producton and transport data of the years 2008 to Demand data Iron ore consumpton data n nternatonal statstcs (e.g., World Steel Assocaton (WSA)) s usually specfed n metrc tons thereby abstractng from the ron content n the ore (Fe-content). Ths however complcates our analyss: As we are nterested n ron ore consumpton as an nput n pg ron producton, t necesstates nformaton on the amount of pure ron contaned n the consumed ore. For example, a country has an annual consumpton of 1 mllon tonnes (Mt) of ron ore. It s suppled by one producer delverng 0.7 Mt of 40% Fe and another delverng 0.3 Mt of 60% Fe. Thus, the country consumes 0.46 Mt of pure ron. A second country also consumes 1 Mt of ron ore, but the materal has an ron content of 65% Fe. Hence the country consumes 0.65 Mt of pure ron. Even though both countres consume 1 t of ron ore, the pure ron consumpton as an nput for pg ron producton s nearly 50% hgher n the second country. To cope wth ths problem, we use annual pg ron producton data provded by WSA as a proxy for the actual ron ore consumpton, thereby assumng that 1 Mt of pure ron s consumed to produce 1 Mt of pg ron. Concernng cokng coal we do not face ths problem as we account for cokng coal consumpton specfed n energy unts (IEA, 2012). However, t s necessary to defne the factor ntensty of cokng coal n pg ron producton. Comparng cokng coal consumpton and pg ron producton we assume a factor ntensty of 70% whch means that 0.7 Mt of cokng coal are needed to produce 1 Mt of pg ron. 19

22 We assume that n the smulaton model both ron ore and cokng coal are exclusvely used for pg ron producton. In realty, 6% of global annual ron ore producton serves as nput for socalled drect reduced ron (DRI). Concernng cokng coal, IEA statstcs suggest that some mnor quanttes (4% globally) of cokng coal are used for power generaton as well. We correct our data for ths n the followng to lmt complexty of our analyss. For the same reason, we abstract from stockng of ron ore or cokng coal that can be observed n both markets. As stated n chapter 3, lnear prce-demand functons for pg ron are requred n order to smulate d erent market settngs. To derve those country specfc demand functons we stck to an approach whch has been wdely used n lterature on market models programmed as a mxed complementary problem (MCP): Usng a reference prce, a reference volume and an elastcty yelds slope and ntercept of the demand functon. We use the annual pg ron producton as reference volume. The reference prce s however more d cult to obtan snce we are not nterested n the real pg ron prce (contanng prce elements such as labour costs) but only the part of the prce that can be explaned by those nput factors beng n the scope of our analyss,.e. the prces of ron ore and cokng coal. The reference prce s therefore calculated as follows p p = p + p c. (33) The annual average prces of ron ore and cokng coal are derved based on nformaton from BGR ( ) and BREE (2011) Producton data We nclude detaled ron ore producton data contanng mne-by-mne producton costs and regon specfc ron contents (World Mne Cost Data Exchange, 2013). Concernng cokng coal we ntegrate the dataset of Trüby (2013) comprsng mne-by-mne producton costs as well. The producton costs have to be nterpreted as free on board costs.e. nland transport costs are already taken nto account. Addtonally, we analyse hstorc ron ore and cokng coal producton data of the most mportant export companes such as Vale, Ro Tnto, BHP Bllton (BHPB), Anglo Amercan/Kumba, XStrata or FMG usng ther annually publshed producton reports. 20

23 Usng those data sources n addton to annual country specfc producton and export volumes (ron ore: WSA (2010, 2011, 2012), cokng coal: IEA (2012)), we obtan a detaled and nearly complete dataset of both factor market s supply sde. Fgure 4: Iron ore and cokng coal FOB cost curves of major exporters n 2008 However, for two major producng countres t s d cult to access detaled mne sharp producton data n both markets: Chna and Inda. For Chna, World Steel Dynamcs (2011) provdes us wth cost and capacty nformaton on ron ore producton d erentatng between several cost levels. Concernng Chnese cokng coal producton and both nputs n Inda, we use the annual ron ore producton from WSA respectvely the annual cokng coal producton from IEA (2012), however not d erentatng between d erent mnes. Ths smplfcaton does not severely a ect our analyss as both n Chna and n Inda there s no domnant ron ore or cokng coal producer that has a sgnfcant nfluence on global trade. Therefore, we assume an atomstc supply sde n 21

24 those two countres,.e. ron ore and cokng coal producers from both countres are modeled as compettve players. Players modeled as Cournot players are Vale, RoTnto, BHPB, FMG, Anglo Amercan (Kumba), CSN, LKAB and SNIM n the ron ore market and Ro Tnto, BHPB, Anglo Amercan and XStrata n the cokng coal market. In lne wth Trüby (2013), we model US cokng coal exporters as one Cournot player (US CC), snce the man export ports and the nland transport rals are controlled by one player and market power s assumed to be exerted va the nfrastructure. Other smaller and mostly domestc producers are assumed to market ther producton volumes as compettve players. Fgure 4 shows the global FOB supply cost curves of major ron ore and cokng coal exporters n Note that ths fgure does not reflect the seaborne traded ron ore volumes exactly snce exporters also partly supply ther domestc markets as well. We observe that regardng producton costs the bg three ron ore exporters Vale, Ro Tnto and BHP Bllton are for most part n the lower half of the global FOB cost curve Transport data The IOCC dataset comprses dstances between major export and mport ports usng a port dstance calculator. Addtonally, the dataset contans freght rates of 2008 to 2010 of bulk carrer transports on numerous shppng routes. Usng freght rates and transport dstances we calculate a proxy for the seaborne transport costs. For most of the nland transport routes, costs are already accounted for snce the cost data are free on board (FOB),.e., the costs comprse producton, nland transport and port handlng costs. The only excepton s nland transports from Russa to Europe respectvely Chna where ral freght rates are used. To lmt model complexty, we do not explctly account for capacty lmtatons of nether port nor ral nfrastructure nor shp capactes. We mplctly assume that scarce bulk carrer capactes are already represented by the freght rates. Capacty lmtatons of export port or ral nfrastructure both are subsumed under the producton capacty of a producton regon. For example, f a producton regon has a capacty of 100 and the accordng port only has a capacty of 80, the producton capacty we use n our model s

25 4. Results of the appled analyss 4.1. The proftablty of parallel vertcal ntegraton n the ron ore and cokng coal market We apply our computatonal model to nvestgate whether or not frms beneft from behavng parallel vertcally ntegrated. Therefore, n a frst step, we smulate the ron ore and cokng coal market for the years 2008 to 2010 to derve the proftablty of the ntegrated companes Anglo Amercan, Ro Tnto and BHP Bllton. Snce the strategy choce of the compettors mght nfluence the proftablty of the own strategy, we model a smple statc smultaneous game wth two stages. In the frst stage, each ntegrated company chooses between two strateges: optmsng smultaneously (SIM) and optmsng separately (SEP). In the second stage, all companes n the ron ore and cokng coal market (also companes actve n only one of the markets) set the producton quanttes, thereby knowng each of the ntegrated companes strategy choces, SIM or SEP. Thus, n total we smulate 8 model runs and use each company s total proft margn as payo functon. 7 The queston arses f the proposed two-stage game s a realstc representaton of the market. Is an ntegrated company able to credbly commt optmsng both dvsons separately and can ths be observed by the other players? The commtment for separate optmsaton could be realsed by ncentve contracts for the dvson managers, e.g. by remuneraton dependng on proftablty of the dvson. Although these contracts are unlkely to be seen by the other players, separate optmsaton could be observable by foundng a subsdary company for e.g. the ron ore busness. Ideally, the holdng would sell mnor shares of the subsdary n order to further ncentvse that each dvson s optmzng tself separately. Although n realty, ron ore and cokng coal busnesses of ntegrated companes are rather subdvsons 8 than subsdares, the strategy SEP could per se be commtted to n a credble and observable way. Fgure 5 llustrates the proftablty of choosng SIM over SEP for each of the three ntegrated companes gven the other companes strategy choces and the assumed demand elastcty (nota- 7 Snce we have no data about fxed costs of ron and cokng coal mnng, we focus on the proft margn,.e. prce mnus margnal costs tmes quantty sold. Ths s su cent for our analyss snce we only compare d erences of proft margns whereas fxed costs only change the level of the total profts. 8 Interestngly, for both Ro Tnto and BHP Bllton, the head o ces of the ron ore dvsons are stuated n Perth, the coal dvsons n Brsbane and the holdngs n Melbourne. 23

26 ton: b = BHP Bllton, r = Ro Tnto, a = Anglo Amercan, 1 = SIM, 0 = SEP). The proftablty s derved as the d erence n proft margns between opton SIM and opton SEP. These results seem to confrm Conjecture 3 from 2.2: The more nelastc the demand s, the hgher s the addtonal beneft of choosng SIM over SEP. Wth an ncreasng demand elastcty the addtonal beneft of SIM converges to zero. 9 Fgure 5: D erence n profts of optmzng smultaneously (SIM) or separately (SEP) dependng on the other ntegrated companes strategy. As stated n 2.2, capacty constrants of at least one of the complementary goods seem to be one explanaton for the decreasng proftablty of strategy SIM. For BHP Bllton, for example, the ron ore capacty s bndng n all three years as soon as the demand elastcty (n absolute terms) s hgher than 0.5. Ro Tnto s cokng coal capacty s bndng n all of the scenaros and the ron ore capacty becomes bndng for elastctes of 0.3 and 0.4 and hgher. Ths mght be an 9 For BHP Bllton, we observe slghtly negatve values for the years 2008 and Ths phenomenon can be explaned by numercal reasons durng the soluton process of the model. The loss when choosng strategy SIM seems neglgble snce t s at hghest 1% of the proft margn. 24

27 explanaton why the addtonal beneft of strategy SIM s generally hgher for BHP Bllton than for Ro Tnto A comparson of three market settngs So far, the model results revealed that SIM s a benefcal strategy for ntegrated companes f the demand s rather nelastc or, n other words, f the producton capacty of both complementary goods s not scarce. However, the outcomes of SIM and SEP are equal when hgher demand elastctes are assumed. In the followng, to fnd evdence whether or not ntegrated players optmse ther ron ore and cokng coal dvsons smultaneously, we nvestgate whch of the strategy choces and whch demand elastctes best represent hstorcal market outcomes. Therefore we compare model results and hstorcal market outcomes,.e., prces, trade flows and producton volumes. In total, we focus on three market settngs n ths secton: Frst, we nvestgate whether noncompettve behavour s observed n both the ron ore and the cokng coal market. Hence, we run a scenaro n whch all players n the market behave n a perfectly compettve manner ( Perfect competton ),.e., act as prce takers. Second, we run another two model smulatons each assumng Cournot behavour n both markets. One n whch Anglo Amercan, BHP Bllton and Ro Tnto behave as parallel vertcally ntegrated frms ( SIM ) and another one n whch each of those frms ron ore and cokng coal busness unts optmse ther profts separately ( SEP ). By comparng model outcomes to actual prce, producton and trade data for the tme perod from 2008 to 2010, we am at dentfyng the settng that has the better ft wth the realsed values. To compare trade flows we use three statstcal tests dscussed n Appendx D. 10 Startng wth the analyss of the Perfect competton settng, we fnd that the test statstcs of the F-test allow us to reject the null hypothess ( 0 = 0 and 1 = 1) on a 99.9% level for both goods n all years and elastctes (Table 2). Interestngly, whereas ths result s confrmed by hgher Thel s nequalty coe cents and lower Spearman rank correlaton coe cents n the case of ron ore n all years, ths s not the case wth cokng coal trade flows n 2008 (Fgure 6). 10 The nterested reader s referred to Appendx E for a seres of tables dsplayng trade flows for both commodtes at a demand elastctes of -0.5 as well as actual trade flows n the respectve years. 25

28 However, consderng prces and producton n the perfect competton settng (PC) n addton to the trade flows, we conclude that the two market settngs, n whch players behave n a noncompettve manner, outperform the perfect competton settng. The model when run wth all players actng as prce takers cannot reproduce ron ore prces for most part of the elastctes that were nvestgated (Fgure 7). In addton, total producton of both commodtes s too hgh n ths market settng and, more mportantly, the model cannot capture producton behavor of the largest company n each market (Fgure 8),.e., Vale n the case of ron ore and BHP Bllton n the case of cokng coal: For almost each assumed demand elastcty, these producers produce up to full capacty. Table 2: P-values of the F-tests ( 0 =0and 1 = 1) for a wde range of elastctes Cokng Perfect competton Separate Smultaneous coal e = ** 0.00*** 0.00*** 0.08* 0.04** 0.03** e = *** 0.00*** 0.00*** * 0.04** * 0.44 e = *** 0.00*** 0.00*** e = *** 0.00*** 0.00*** e = *** 0.00*** 0.00*** e = *** 0.00*** 0.00*** e = *** 0.00*** 0.00*** * e = *** 0.00*** 0.00*** * * 0.08* e = *** 0.00*** 0.00*** * 0.08* 0.05* 0.07* e = *** 0.00*** 0.00*** 0.10* * 0.06* 0.04** 0.06* Iron Perfect competton Separate Smultaneous ore e = *** 0.00*** 0.00*** e = *** 0.00*** 0.00*** e = *** 0.00*** 0.00*** e = *** 0.00*** 0.00*** e = *** 0.00*** 0.00*** ** 0.19 e = *** 0.00*** 0.00*** 0.09* 0.01** *** 0.09* e = *** 0.00*** 0.00*** 0.04** 0.00*** 0.09* *** 0.05* e = *** 0.00*** 0.00*** 0.02** 0.00*** 0.05** 0.08* 0.00*** 0.03** e = *** 0.00*** 0.00*** 0.01*** 0.00*** 0.05** 0.06* 0.00*** 0.03** e = *** 0.00*** 0.00*** 0.01*** 0.00*** 0.01** 0.06* 0.00*** 0.01** Sgnfcance levels: 0.01 *** 0.05 ** 0.1 * Concernng the comparson of the SIM and the SEP settng, the pcture s more ambguous. Startng out by lookng at the results of the hypothess tests for ron ore trade flows, one may be 26