The effect of market conduct on international steam coal trade

European Economic Review 24 (1984) 39-59. North-Holland

Charles D. MOLSTAD University of Ihois,

Champaign, IL 61820. USA

Los Alamos Nationa; Laboratory, Los Alamos, NM 87545, US.4 Received November 1982, Snal version received August 1983 Iris paper is concerned with the determinants of international steam coai !rade. Most quantitative work in explaining such trade has been stymied by the apparent fr’!~e of the competitive model to account for observed and anticipaled trade flows. In general. authors have sought institutionat explanations for this failure. The hypothesis explored by this paper is that the exercising of market power by certain agents in the market can iead to trade patterns consistent with those observed and anticipated. This hypothesis is expiored through a simple model of imperfelct market equGbrium. In addition to nerfect competition, we examine Cournot-Nash monopoly (South Africa), duopoly (South Africa, Australia]! and duopcly/monopsony (South Africa, Australia, Japan) with a competitive hinge of prod~~ccr~ I LX. Canada, Poland, China, Colombia), Using the equilibrium model of coal trade, we eanrnrne these .market structures and evaluate the extent to which they cdn explain existing and anticipated trade patterns.

One of the key economic questions in international commodity trade is how to explain observed trade patterns. This question is motivated by a desire to forecast trade and understand how governmental pohcies can influence that trade. Several decades of research, much of it related to ~l~a~r~ trade, heave led to frustration with the simple comLztitive model of tra where the least-cost supplier captures an importing c’ou For many commodities, this behavioral model neither observations nor explains observed trade patterns. theories of ra concentrated on ljeveloping ii trade patterns. consumer behavior to explain 0

0014-2921 ? t,‘U. 1 @TJ1984, Elsevier Science Publishers B.V. I?lorth-

two contributions to this literature. irst, we investigate rfections in acconnt~n~ for trade in a ie~rn’ coal marker. As in the case of rnod~~ of tradie is unsatisfactory for explaining historic patterns. We evaluate the hypothesis that patterns of by the exercise o rket power by various agents in ft:conclude that simple ass @ions about market conduct are ssary) to :replicste historic and anticipated trade nd purpose of this paper is to su st a new way of computing level:s of trade in the presence of imperfect competition. We a inqerfect competition spatial equili.brium made1 as a non-linear and use an existing algorithm to solve for xt ~~~o~, background on the steam coal market is presented. discussion is -used to develop the hypothesis that the er deterrmines trade. In section 3 a model of reaction which is used as the basis for the results

the rise in the real price of oil and natural g,as over the gast decade, as s~ii~~ to coal as a principal alternative source of energy. The of coal has been encouraged in countries with plentiful domestic ~~rczs (such as the US) and in countries with negligible domestic ~a~an~=This has Ied te; modest international tra.de in steam ctations of more s&&&ant trade over the coming decades. ominatqd international coal trade ~~c~u~on of steam coil situation is changing due in 1arg.T t years. Table 1 shows steam ezoalexports partment of Energy ew by a third from I 9S2 due in larg.! other US gover~m$~t forecasts

ChB.

Kohad

and D.S. Abbey. The irltcrnational steam coal trlr$e

41

[Enteragency Coal Export Task Force (1981)3 and Australian for epartment of Trade and Resources t1981)]. One can co ta that the international market is currently rather sm appears to be growing rapidly. Coal has the poterhl fur being a ver ficant commodity in international trade, particularly if oil prices remain big A basic problem in understanding the development of the internatio~ steam coal market can be appreciated by examining the role of the Unite States in that market. There is much interest in the US in the extent to which the US will be an exporter of coal. Table 1 indicates that the US share Table 1 Steam coal exports (lo6 tonnes). Country -Australia Canada Republic of South Africa UrLted States to Canada Ur:!:ed States excluding Canada Polandb China United Kingdon” USSR Other Total

1979” 1980” 199V --5.9 9.4 83.9 1.0 1.2 3.6 15.9 211.4 63.2 11.0 10.3 10.9 61.8 2.4 15.2 20.0 19.5 15.8 0.3 0.6 9.1 7.0 2.3 3.8 n.a. n.a. 0.9 25.6 n.a. n.a. --58.3 77.3 286.1 _-

%urce: Abbey (1983). bExports to the West only. ‘Total exports, principally steam coal. dProjections from US Department of Energy ( 1982). Table 2 Estimated producer costs of delivering coal to Europe and Japan.”

Country of origin

Ocean transport

Tklivered

0.35 0.115 0.30

0.35 1.00 0.60

‘15 2.10 1.85

0.65 0.15 0.30

0.45

Mine-moutb

Inland transport

1.55 0.95 0.95 I.05 0.95 0.95 1.30

--

A. To Europe us East coast

Australia South Africa B To Japan us -west Coast Australia South Africa esteri Canada

___ 198tX$,‘10yJoules. So

price9.

2.1 1.50 : 85 2.s5 ---. ._.~lll_-----~tera~e~~~ Coal Export Task Force

32

Clr.D. Kolstvd and D.S. Abbley, The international steam cd t

trade

has been around 25%. The 1980 sha.re is higher

although this mai be due at least in part to xxhced straha and ~‘~~a~d,and the inability of South Africa to illlcrep1snls in wo

internationali market to rise to 38% by the year 2000 ~~~ CoalI cohort Task Force ~~9$~~~.The pro lem is that these and anticipated US shares of the steam al market woulld ihleonsistent w&h produc:tion cost information. As shown in merican coal (does not appear to be particulariy cost uth African or Australian coal in either Europe or Japan porters of coal). Indications are that this situation asisteven after significant resource depletion. 1’ --_--.P-.P P _the

Fig I. InframargGlal vs. monopolistic production.

retatioiss of the data in table 2 are possible. If resources are n Australia and South Africa to physically supply the et without the invoivement of the fringe (North America), rket is competitive, Australia and South sbo~~d be the only exporters of coal.’ However, if resources a.:e rctz in Australia and South Africa, so that fringe wotild be necessary now or in the near future, then c theory suggests that these twc producing amarginal and that Ricardian rents should in a competitive market.’ This can be hypothetical demand cur s are drawn (A : a iow cost producer ( > and a higher ns to have constant marginal production costs. IWand sad Colombia, can compete in certain regional Cdl t~~~~]~ the remahcler oi the decade is expected to be int in the future the Me e’s future

is involved in

Their aggregate supply curve is shown in the figure. If the dem;anJ curve is a price pz for both produsers is consistent with competihe producer surplus earned by A.4is economic rent owe*der, if the dema curve is A, iht3l pricing at p2 is inconsistent with co etitive behavior whir;: would result in the price p1 (ignoring the future trajectory of prices). Beca.use of thy large amount of coal resources in South Africa and Australia, extractable at low cosb, it would appear that these two countries alonle could supply the bulk of the international market for some time to come, and thus that these counirres are not inframarginal producers in th;: conventional sense4 Co!-c;equently, on the basis of the producer costs presented in table 2, we must conclude that North American participation in the Japanese and Europearl markets is inconsistent with perfect competition.

In

the Ias!. section:

we saw that although the in’ternational steam coa market might appear to be competitive, the perfect competition model of trade does not account for current or anticipated trade patterns. Most authors attribute this failing to institutional fz.ctors such as an inability to increase export port capacity or non-economic buying preferences. For instance, in projecting coal trade patterns, a typical approach is to assume that export capacity is constrained, particularly in 1’4ustralia and South Africa. If demand is higher than constrained output levels, the higher cost suppliers will enter the market. This is the approach taken by the I:S Department of Energy (l93Z) to project US coal expsorts. To ensure LS participation in the market, output from all other exporters is constrained. Similarly, the ICF’ CorItoration (1981) constrair.s only South African and Australian exports to develop their forecasts. In an analysis of the effects of’ deregulating US railroads, the NERA Corporation (198i.) takes a slightly different approach by assuming that certain exporlers face sharply rising costs from rapid increases in exports. This electively coGtrains csports, although not at a predetermined level. Constraints undoubtedly exist 11~ short-run capacity, but it is difficult to determine anti justify constraints on long-run capacity. A somewhat plausible explanation for the participation of suppliers in the market is the desire of consumers 13 reduce (l98I) assumes consumers will obtain diversifying supply. I otal impcrts from a sin Finite elasticity of Force (~9$1) suggests that 4Tt,e common view is that tk\leinternational coal market is crrmpetiti~s. a view hased on [Yap: abunc!ant endow wide di§tri~~ti~~ of resources and the large r?mmber of ~~~~~~d~~~~ producers (companies) iaa?rolved in co A~~~~~q~coal tia;n in and bet suffkzient Pee of cad to tend towards long-run marginal cost.’

ClU!l. K&ad

and LM. Abbey, The internutional steam. coal trade

roducts from d rent supplier countriess Reddy of stit~tio~ betw~~~ US and Acstralian ass~m~t~ons can force the market ons used in. the above studies have the desirable a sizeable market share for the US. Unfortunately, r czd hoc,>and dificult to ~~~lant~tativ~~y the arssumptions require data that are very diffic:ult n&on capacity at scme future point in umptions sbout market operation are antification, particularly the question of ith the possiblle exceytion of the Reddy (1976) work,

ark.et conduct that has not been examined in any ade: literature is that of imierfect competition. Imperfect ion has often bean argued as determining trade in other ities, ~a~icularly grains. 6 The grain trade situation is strikingly coal trade: trade flows do not seem to be explainabl,e on t competition. M&alla’s (1966) early attempt to explain It. trade patterns suggested that Canada and the US act as a alter setting wheat prices which other producers follow. Alaouze et al, extend this to a cooperative triopoly involving Australia. In both are hypothesizec! which result in a determinate and trade flows. Carter and Schmitz (1979) counter that Japan protean Economic Community act as non-cooperative duopsonists. asic idea behind all of this work is that trade is determined by the f the market, in terms of the nature and extent of market power articipants. This contention is supported by the beha.vior of the ,rn a structural perspective appears to be the competitive model of trade explains observed owever, one problem witii assuming that trade can imperfect competition is that there are a variety c: about oligopohstic behavior and strategy, each rent set of eq~~lib~~rn prices and trades. guish otherwise identical products on demand involving a fnite elasticity of

of

2.4. Structure

oJ’ the steam ma1 market

Dissatisfaction with the model of perfect competitmn in explaining stea coal trade patterns and experience in understanding trade in other commodities suggest that a model of imperfect competition may better explain observed and a&ipated trade patterns. I-Iowever, before one can consider the model of imperfect competition it is necessary to examine the structure of the market to see if any participants have the potential for exercising market power. There are se many producing companies in the international steam coal market that no one of them would appear to have enough of a market share to manipulate the market. However, there are a few institutions in the market, principally national governments or producer associations, with significant potential to exercise market power. In South Africa. virtually all output is from mines operated by members of the Transvaa’ Coal Cwners Association (TCOA). The TCOA operates as a domestic cartel, assigning production quotas, and marketing member output. The TCOA is also the principal owner of the export shipping terminal. To top this off, th’e South African government has a system of export licenses for coal [Abbe] and Kolstad (1983)3. Whether there is potential to exercise market power in Australia is iess obvious, although there is concentration in the coa! industry.s Labor unions or railroad,s could also extract rent, and the government has a system of export licenses (although they do not currently appear to be particularly constraining on exports). On the consuming side. a number of countries have a single or major national buyer of foreign coal (e.g. Japan, France and Spain). National utilities dominate buying in many other countries. 3. A mocbel~ of i It is a hypothesis of this paper that current and anticipntzd patterns of coal. trade, including significant US exports, are consistent with rational economic behavior on the part of producers and consumers. We are interested in examining the extent to which the use of market power by one or more participants in the market can lead to significant US participation in the international market. Our approach ii to define a model of the steam coal market an test the effect of a variety of types of market crsn tsade patterns. -We do this for 1980 and 19%). Us!ng several sta compare trade under different market conduct assumptions wit (1980) data and forecast year is t

e market. Our approach is to let steam COLIdemand s it ~~ct~~~~y was in 1980 or as forecast for 1990, dribe a model equilibrium trade patterns as a function of et conduct. We then compare these ‘forecast’ trade with ‘actual’ trade patterns and accept or reject particular eses about market conduet. rium and th!e complementarity

probkm

cc:ad

trade model presented here is a spatial equilibrium model but not sense. Neatly all spatial equilibrium models utilize to find an equilibrium set of prices and udge (1971) and Thompson (1981)]. This works petitive partial equilibrium (by maximizing consumer ai;d ?;roducer su ;us) or even an equilibrium for the case of a single list or monopsorrist (b:y maximizing producer or consumer surplus). unately, most imperfect tnarket situations involve a number of agents, tane~~usly maximizing their objectives based on certain assumptions eh,avior. In general such markets can be es [Friedman (1982)]. Even assuming strategies are kn~~~n and can be specified, such games are difficult to solve (for an WWiththe exception of a zero-sum, two-person game, such KS ca,nnot .in genePal be couched as the maximization of a single r approach to finding an equilibrium is to (a) hypothesize an strategy for each agent, (b) define the conditions under which I maximize his objective, and (c) solve for an equilibrium set of and quantities which simultaneously satisfies th.e maximization ions for all agents. This is in the spirit of general equilibrium analysis, re a. set of prices. and quantities is sought which simultaneously cs the objectives of all agents in a physically feasible manner (no emand) given price-taking behavior [see Manne et al. (1980)]. sence, the Kuhn-Tuclker conditions for each agent’s maximization and solived simultaneously. For mstance, consider the

,r) over the variables

Ch.D. K&tad

and D.S. Abbey, The international steam coal trade

Kuhn-Tucker conditions for this maximization prabkm aU/dq~

s 0,

(iJU/dqt)qj =O,

qi 2.0,

47

are

Vi.

(

lc)

Our assumptions about strategies and objectives are simple enough so that the entire set of equilibrium conditions can be put into the form of eq. [ !cj. Thus, in mathematical terms. the model consists of a set of equations of the form S;;(i)Zi

=O,

Vi,

W

where 1;: is a function of the vector of variables Z. We seek a r;olution to eq. (2a) such that z and fare non-negative,

In other words, we seek a non-negative vector z such that f(z) is nonnegative and the inner product of f(z) and z is zero. The set of eqs. (2) is the generic non-linear compleinentarity problem and is a standard way of formulating general equilibrium problems [see Scarf and Hansen ( 1972)]. Bimatrix games can also be formulated in this manner [Cottle and Danrzig (1974)J If f is a.Sj[ine(linear) the eqs. (2) define a linear complementarity problem for which efficient algorithms are available. A number of general equilibrium models have ‘been solved as linear complementarity problems [Dantzig et aI. (1979) and Mathieson (1982)J. Mathieson (1982) has experimented with solving the non-linear complzmentarity problem through successive linearizakions of J 3.2

The World Steam Con1 Trade Model

Based on our previous discuss.ion of the strucrure of the steam coal market, an assumption of the WorX Steam Coal Trade Mod consumers and producers act competitively as price t.akers. o\bever, producing or consuming countries can extract monopoly rent. This assumption allows us to deal with aggregate regional*“\ supply an functions. We do not need TVdeal with individual producers or co the subnationali levee. There are of course many ways for cou.niries to extract monopoly ren 63,in&ding the use of ex~ort~import licenses or of which can support any level of exports OF imports. In the m o-w, rent is ass rther detail on osu regionsof ltc moitd are individual coua-ies subnational level and some correspond to several countries.

atthou,gh

so

Cb,D. &had!

48

and LAS,Abbey, The international steam1coal trade

consists of a number of pro ucing and consuming r ther by a ~ra~!;~Qrt~t~o~network, S~v~~~~types of coal each ~rold~~~in~: gion to satis demand in the consuming eitzman (19%) have shown, Cremer and e mode1 is static. ~~~~~~~~5~ effects are sm~l, iittle accuracy is lost through a static Eysis of mono~~y power relative to a dynamic: analysis. Conditions for ~~~b~~rnin the market are straightforward competitive conditions, except a tariff is irrwserd on certain exports or imports and the level of the is ~~et~~~ned endogenously in the model. The behavioral model for ff setting is that of reaction function equilibria [see Friedman reducing regions know the slope of the demand curves in the ey *serve amd conjecture the behavior of other producers in Isges in their rariff level. Similarly, consNumersknow the slope ucer’s supply curves. The simplest conjecture that can be made is that a particular producer assumes that as he varies his tariff, f all other producers will not change [and similarly for s, there are four ba&z sets of equations in the model: producer profit itions, consumer utility maximizing conditions, interrlegional nditions, and tax revenue maximizing conditions. Taible 3 a synopsis of the endogenous .:nd exogenous variables used. in the 1. The model is described below in terms of the four sets of equations. a and c~ffi~~e~~tassumptions are described in an appendix. ’ 2.1~ ~~~~~r

2 .

tin of is

q-dmdity

rodidions

the d’ consumers (regions) f&es a local price for coal, jj. If the sitive in the jth region, demand as a function of price must be Table 3 Wsdd parmeters

to coanirner j

and variables.’

(%,‘1ci9 hules)

-coal to poducer i ($/tonne) ucer i to consumer j (!G/tonne)

g k-coal in region i as a I’unction of the production rate

equal to th,:*quantity

consumed,

Rere and throughout this, section, racilitate writing the comptementarity

dummy variables condition.

(e.g. uj) are used to

3.22. Producer profit mtaxirnizfltio~n conditions The standard condition for profit maximizing behavior is that marginal cost equals marginal revenue. In the case of R competitive market, margina revenue is price. Recall that we assume for conceptual purposes that marke power is exercised by the taxing authority, nc!t individual producers. T first-order coniiitions for producer profit maximization are Wik =

(Cik(Sik)-fiik) 10,

Wi&Si&

-0.

(4)

In other words, price equals marginal cost unless no prodrlction takes place. It is also necessary to assume that quantities shipped to consumers are consistent with production levels,

This condition states that exports must be equal to production unless the price is zero in which case some production may be freely discarded. 3.3, Ttzx revenue maximiztztion As the model is describ,ed here, market power is exercised through export taxes. The case of an important tax can be developed in a simiiar inanner. For simplicity. >weassume the taxing authority can price discri!~i~atc., setting a different tax rate for different destinations. ~~i~~~ti~~~ Arguments can be made on both sides as to w or a uniform taut is most appropriate. If market power in. reality is exerci~ through a tax, then t e same tax rate for all coal mi If market power is e rcis;ed directly by producers, might be most appropriate since many sales are Q

C.f+.D.Kc fstad and D.S. Abbey, Tfw internationaf steam cotif fvade

For an

export tax,

tax

revenue

forre

on i

isgiven by

ine the tax rate that maximizes revenues, this e(quation is t to the tax rates, constraini.ng tax rates lto be nonconditions for a revenue maximum involve the s with respect to tax rate, The change in q with the slope of the residual demand curve in region j for This slope can be completed from the slope of the j adjusted by how region j’s competitors may react s price. The slope of the residual demand curve in

is the conjectural variation; i.e., rij is the change in quantity to j from all other producers with a change in quantity supplied to j man (1982) or Intriligator (1971)J For perfect competition (ol: - 1; i.e., any redunction in output is assumed to r. The Cournot-Nash behavioral model assumes We ean now write tba f a- .u-st-ordet condition for a maximum of eq. e assume that changes in taxes to one country do not aifect exports to

compkated, in some cases ii si.mplifies r Cournot-Nash behavior with only (ri

j

=

0)

3.4. Price tf&iency conditions ecause we deal with two sets of prices, one for consumers and one for ,producers, it is necessary to link these sets of prices to assure consistency.

The interpretation of this equation is that if any ;rade takes place between a purchasing and a consuming region, the difference between producer and consumer prices must be precisely the sum of transport costs and taxes, and in any even.t canuot be greater than this sum.

A? was indicated earlier in this paper, the competitive model does not appear to explain current or anticipated steam coal trade flows. As was also indicated, studies of trade in ocher commodities suggested that alternate assumptions about market conduct can explain trade patterns. In this section we explore this hypothesis by examining how trade flows dialer from the perfect competition case under three alternate models of imperfect competition. On the producer side, it would appear that the Relpublic of South Africa (RSA) is in the best position to exercise monopoly power, not only because of its apparent cost advantage in delivering steam coal but also in terms of institutions which are already in place to exercise that power. Australia is a second producer which has thf, potential to exercise market power. prrncipally because of its cost advantage. Institutional mechanisms for exercising power appear to be less developed in Australia than in the RSA. On the consumer side, Japan is the dominant consumer of steam coal in Asia. Furthermore, iu Japan there is a high degree of coordination among the few coal importers. ‘!f’hissuggests the three cases we will examine. One is the case cf the RSA act.ing as a monopolist w;rh all other producers acting competitiveiy. 1 second case is that of a. non-cooperative duopoly involving the RF.<, and Australia with all other producers acting competitively. The third case i:s that of the RSA and Australia acting as duopohsts and Japan acting as d power completely dominates morropsonist. Japan’s monopsony

settiing export

aud import

taxes, production

levels and shipment

since in reality ay not be sure at the part of the tora will react to fc~rtnn~~~~y, there ;are also deficiencies with the Cournot-Nash el, the most glaring of which relates to d.eterring the entry of the instance,, the strategy of setting price inge enters is not a Cournot-Nash since the oligopolist is taking3 ~scount of ‘how the fringe will react to o&t’s price and quantity decisions. Xevertheless, the Cournotcl is a good ttarting point for an examinaj;ion of the effects of S

of

e iniui?ive appeal ~~O~~jtO~~ bdlaQiC9~. It PmZkSSOKII

involves solving the World Steam Coal Tracle Model h of these three differe:nt mark& structures plus the perfect ure. The model i,s solved for 1980 based on actual import for 1990 based on DOE projected demand. A description tions and solution technique for the model is relegated to 4 presents the basic results of the analysis for the years 1980 and the table, export market shares are forecast from the four major ng areas (plus an ‘other’ category) to the two major consuming ese trade matrices reflect only international trade and not so shown is a base l,cvel of trade - actual trade shares and DOE’s projection of tra6e shares for 1990.’3 To determine ch of the fuur models best explains trade, we will use two measures to s with the base level of trade, the Theil rman rank correlation coefficient. The3 (1961) inequah coefficient has been widely used to compare ts with actual values. uch insight can be gained using the inequality r hypothesis testing in ‘our case because it lity coefficient (U) is in essence the rootuared error between elements of the predicted and actual trade ent lies b’etweenzero and one. Perfect quality coefficient. Further insight is y ~a~~u~~at~~the variance (Us) and covariance (UC) proportions of Suppose predicted values are plotted agains? et forecasting, all points would lie along a 45” line. icates the spread of points about this 45” line. in the appendix, there are actually several dozen producing and consuming for the purposes of table 4. b.ased on their expert assessment of s. We thus use thw I^orecasts as a t that ekmenls of the &are matrices

Ch.D. K&ad

and DA Abbey, Tl!e international sit-am coal trade

52

The variance proportion indicates the extent to which the slope of a regression line through the points deviates from one. Thus, in some sense. ttw higher thg covariance proportion (a ma.ximum of one), the better the forecast since one would expect some random component in forecasts. A second statistic is the S?earman rank correlation coeficient [Conover (l980)3, which is a non-parametric statistic. Pairing each element of the actual (A) and predicted (P) trade matrices, we can vilew these pairs (aij,Pji) as samples from a bivariate distribution. Regressing pi i against aij we obtain We can then test the null hypothesis that a!=0 and "=Gt+@~,j$Vii* ;L 1.‘” Unfortunately, this is not altogether satisfactory, because the elements of the predicted trade matrix are not independent nor is there a conventional population from which the sample is being taken. Nevertheless, the statistic along with the Theil inequality coefficient should give us good insight on the performance of the four models of market conduct. 4.1. 1980 trade Referring to table. 4, it can be seen that the competitive model gives trade patterns .which diverge considerably irom actual trade. In this case, the RSA and Australia capture 67% of the market compared to their actuai share of 39%. The other three market conduct assumptions give better mat&(; to actual trade (in terms of the Theil inequality coefficient) although nom is a dramatically good match to actual trade shares. Testing ;he null hypol,hesis that a model predicts actual trade, we can reject the hypothesis at the S’, level for all models except the du3poly case. Of so;ne importance is the dramatic increase in the covariance proportion for the three imperfect competition cases. The ‘low covariance proportion for the ccnlpetitive case reflects the tendency for the competitive model to underestimate small trade shares and overestimate large trade shares. i.Llthough ilmperfect competition assumption results in very significant i:inprovements in trade shares (relative to the competitive case), in ali cases the: RSA is shown to have a bigger markci share than in fact was the case in 19KO.This is probably due tot the fact that in 1980, the international steam cos.l market was far from equilibrium. The market wai a nex one and y rapidly in recent years and, for p land ceased exports of coal. Apparently io meet demand because o!t’vomited port facil~t~cs.It appears 4 ‘5Let A and P be the actual and predicted trade matrices. reqxctively, with elements ‘J;, land pi;. Assume each (aij,pij) pair i:? independent (a strong assumptior! is our case). Let 5 dr~ii p he thtb mean value of pij computd from rhe sample. Given the datiQnSl?ip !:, ~1 -we can estimate z and 8. Since SL =O and 5 2 p, we wish to test the ntill r-I’B@ij-Pl+Eljr lnd test the extent 81hkwrrelaPion b921k~rcra hy ?othesis that /?= 1. To ent. For Olshc;152 Or d wnpk oF ii/C 11’11. N’, level). /pj>W.i15 (ai the IV I, irieli) null hypothesis can cr IpI> 0.6364 (at the 5’;; level). Cpjj

and

Europe Europe East Asia East Asia East Asia East Asia East Asia

LSKQX

Europe Europe

USA Canada WSA Australia Other USA Canada R5.2 Austmba Bthw Total traddt (lo6 tonnes) Theil inequality coefhcient Covariance proportion Spearman rank coo,relaiion coeficientc 1980 Fw 1980 1580 I980 1980 1980 198LI 1980 1980 1980 1980 1980

1980

Year 0.15 0.01 0.22 0.07 0.19 0.04 0.01 0.04 0.06 0.01 84

Base level of tradeb

-

0.35 -0.85

0.12 0.04 105 0.40

-

0.55 -0.19

-

Competitive

0.04 0.34 0.07 0.23 0.14. 0.0s 88 0.28 0.71 -0.87

0.01

RSA

:: 0:w 0.06 84 0.25 0.54 -8.53

0.08 WI 0.37 0.01 0.24 -

MA, Australia

0.05 86 0.28 0.53 - 0.75

iA5

-

0.35 0.01 0.24

0.04 0.04

A, Australia, Japan

Nash oligopolists/oligoynists

Market conduct

steam coal market shares as a function of market conduct.

TO

1980 and 1990 international

From

-.

Table 4

CC&. Kofstad and D.S. Abbey, The in~ernatimsl seam coal trade

Ch.D. Kob~tad and D.S. Ahb~y,

The intcrnati’orrai steamcoal trade

orst JO rn~l~~~ntons in 1980. This capacity limit is expected to be with using actual trade :Iata CO 1985. This illustrates the eses absnt market operat icularily in a market as young rna,t~ona~steam coal market. .&_

7 19

trad!e

urse of the recent volatility in the intern,ational steam coal market, it a~~r~~~ate to examine projected trade based on an ‘expert’ isn of’ the market. We have thus taken the UltS Department of (1$382) forecast of 1990 overall1 steam coal import demand, traide shares from the various market conduct assumptions and :d these trade patterns to US Department of Energy’s (19812) r&en from table 4, the competitive market model behaves poorly level, we cannot accept the (alternate) hypothesis ode1 gives trade shares similar to ‘actual’ trade. The models perform only slightly betrer, principally in rms of higlher covariance proportions and lower correlation coefficients. the duopoly/monopsony conduct *assumption gi-ires very good ot only is the Theil inequality coefficient lower than all other models, t the covariance proportion is very high. This conclusion is also supported ion of the trade matrices and the very loves Spearman rank understood by examining the four types of market ndltct. The main iob1emwitb the competitive,case is the excessive market of the two low-cost producers, the RSA and Australia. The case of monopoly shifts much of the exports of the RSA uver to Australia. The ly case has the desired eflrect of shifting RSA and Australian exports rica. How-ever in the duopoly case, East Asi.a (princlpa.lly ssiveIy away from its neighbor, Australia. With Japan exercising msnopsony power, this imbalance is corrected and we see trade hat are fairly consistent with projected 1990 trade. nopsony case, the RSA increases prices t.o Europe by s and less than $5 per tonne to y less than $I,0 per tonne to all of i2s c~sto~~ers, urves are so flat, the J,apanese The effect of treating as 8 is t extracting rent

e

asic

resse

alysis is hQw to account for past

Ch.D. Kolstaa’ ma! D.S. Abbey, The internationul stem coal trade

59

and anticipa.ted patterns of trade in steam coal. The hypothesis examined is that market conduct can explain these trade patterns. We have shown thiat a number of simple and common models of market conduct fa11to yiei ‘desired’ trade patterns. However, it appeared that when the RSA, Australia and Japan each exercise market power (non-coopera,tiveiy), trade patterns are very similar to actual or anticipated patterns. Of course, we have ccrtai~ly not proved the converse of this hypothesis, that observed trade patterns are due to a particular type of market conduct. Another result of our analysis has policy implications for fringe producers such as the US. We have shown that exercising ma+* power can increase the share of the market for the competitive fringe. This suggests that it is in the best interest of the fringe to encourage other producers to capture rnonopoiy rent. Finally, we have demonstrated a new way of computing spatial equilibrium in markets operating in other than perfect competition. It is hoped this approach can be successfully utilized in examining other markets. eta& of the World Coal Tra

Odd

In this appendix, we present a briei overview of the particulars of the World Coal Trade Model which was described in section 3. Most applied models are in a continual state of improvement, particularly with regard to model parameters and coefficients. Since the international steam coal market is so young, we expect sources of data used for this model to evolve rapidly. Nevertheless, it is useful ‘to indicate the general sources of data used in the analysis presented in this paper. For more complete documentatio mterested readers are referred to Koistad et al. (1983). Four types of coal are considered in the model: low-sulfur bituminous, subbituminous, lignite, and high-su!fur bituminous. Only the first two these are considered to be tradeable internationally. These coals can produced for export in ten coal supply regions. Coal supply in six of these regions (three US regions, Western Canada, the Republic cf Sout and Australia) is represented by a linear marginal cost curve for e tvipe giving marginal cost as a function of the rate of extraction of coal. These supply curves have been estimated (~on_ec~~~~ornet~ca~l~I~ b the Energy Information Administration (HA) of the US Depart Energy. Estimates of mine to port tra~sp~rt c&s were curves. Modest inelaistic supply was hypothesized for regions (Poland, Colombia, China and Ldonesia). emand for coal i each of 21 regions I6 is re

Easternws. c’entral Republic of South Africa.,and other Aftica.

5s

anstant

Ch.D. K&ad

and D.S. Abbey, ‘The intermtional steam coal tmie

elasticity demand function. These demand functions were developed m coal of -0.6. stration ( 198 I) calculated forecast- consumption s by region determine ifsr steam coal. given rhe assumed price elasticity. Prioe and and CUIWSfor 1 sed for the 1980 case. countries importing in ed to import steam coal (particularly iin Europe). These inelastic and were subtracted from overall steam ere assli~~ed to

canoe ocean port wac,associated with each producer and each consumer. ~~~~~swere made about the capacity of each of these ports in terms of :ressel size. Thus, the maximum vessel size for a particular route based on the minimum capacity at the origin and destination. This the c0st of moving coal over that route. The model is mkd using a version of Lemke’s algorithm for solving the ~~~~r complementarity proble:m Domlin (1976)]. Since demand is nonlinear, the problem is successively linearized until convergence to a solution is realized. Such an approach has been used very successfully for general m problems by athieson (1982). Solution time (for a single time problem) varies h the assumptions about market conduct and divergent: criteria but takes ‘on the order of 30 to 45 minutes of CBYJtime C-VAX computer. Such a problem would involve approximately 250 ts and variables.

s Alamos National Laboratory

report (Los

S and Charles D. Kolstad, 1983, The structure of international steam coal atural Resources Journal, 23,859-891. AS. Watson and N.H. Sturgess, 1978, Ohgor>oly pricing in the world wheat &r&an Journal of Agricultural Economics 60, May, 173-185. n, P’auf S., 1969, A theo of demand for products distinguished by place of Papers 16, Marc,., 159476. 1981, Coal demand study, June (Australian stent conjectures, American Economic Review Andrew Schmitz, 1979, important tariffs and price formation in the world Am~ca~ Journal of A~,~~~~t~r~llEconomics 61, Aug., 517-5X!. 80, Practicai nonpa:rametric statistics (Wiley, New York). ComE;lementary pivot theory of mathematical eds., Studies in optimization (Mathematical e monopol,y price or world oil, European

Ch.D. Kol’stad

apld D.S. Abbey, The ~r~~ernaticwal steam coal trtidf

59

Dantzig, O.B., B.C. Eaves. and D Gale, 1979, An algorithm f<*ra piece+& linear model of Iirade with negative prices aad bankruptcy, M nthematical Progral;*ming 16, 190-209. Energy Information Ad,ministration, 1981, 1981 annual report to Congress, US ‘~epartm~:nt of Energy report DOE/Ella-0173;81) (Washington, DC). Friedman, J.F., 1977, Oligopoly and the theory of games (North-Holland, Amstero jm). Friedman, James, 1982, Oligopoly theory, in: Kenneth J. Arrow and Michaei E; Xritrsligator, eds., Handbook of mathematical economics, Vol. 2, (North-Holland, Amsterdam) 491-534. Houck, J.P., M.E. Ryan and A. Subotnik, 1972, Soybeans and their products: hfarkets, mod& and policy (University of Minnesota Press, Minneapolis, MN). ICF, Inc., 1981, Potential role of Appalachian producers in the steam coal export market: Task no. 1, international steam coal trade analysis, Report piepdred for the Appalachian Regional Commission, Nov. (Washington, DC). Interagency Coal Export Task Force, 1981, Interim report of the Interagency Coal Export Task Force, US Department of Energy report DOE/FE-O01 2, Jan. (Washington, DC). Intriligator, Michael D., 1971, Mathematical optimization and economic theory (Prentic+Hall, Englewood Cliffs, NJ). K.olstad. Charles D., David S. Abbey and Robert Bivins. 1983, Modeling international steam coal trade, Los Alamos National Laboratory report LA-9461-M& Jan. (Los-Alamos. NM). IMcCalla, A.F., 1966, A duopoly model of world wheat pricing, Journal e>fFarm Economics 48. 71 l-727. Manne, A.S., H. Chao and R. Wilson, 1980, Computation of competitive equilibria by a sequence of linear programs, Econometrica 48, Nov., 1595 1615. Mathieson, Lars, 1982, Complementarity and economic equilibrium: A modellir,g rormat and ar. algorithm, Preliminary draft, Jan. (Department of Operations Research, Stanford University. Stanford, CA). hdurphy, Frederic H., Hanif D. Sherali and Allen L. Soyster. 1982. A mathematical programming approach for determining oligopolistic market equilibrium. Mathematical Programming 24,92-106. National Coal Board (IEA Services) Ltd., 1981, IEA 1981 coal research report I London]. NERA Corporation, 198L Statement of National Economic Research Associates on behalf of the Coal Exporters Association and the National Coal Association, filed Tegarding Interstate Commerce Commission consideratioa of railroad exemption on export coai. Ex parte no. 346, sub. no. 7, Dec. (Washington, DC). Reddy. N.N., 1976, Japanese demand for US cob.1. A market-share model, Quarterly Revir‘w ol; Economics and Business 16, Spring, 514. Saris, Alexander H., 1981, Empirical models 3f international trade in agricultural commtdltw.. in: A.F. IVIcCalla and T.E. Josling, eds., Imperfect markets in agricultural trade (Allenhr+l Osmun & Co., Montclair, P;J). Scarf, Herbert and Terje Hansen, 1973, The computation of economic equilibria Wale Fn~\rr-ll\ Press, New Haven, CT). Schmitz, A., A.F. McCalla, D.O. Mitchell and C. Carter, 1981, Grain export cartels ~Balhnpcr. Cambridge, MA). Takayama, T. and GO. Judge, 1971, Spatial and temporal price and allocation models (NorthHolland, Amsterdam). Theil, Henri, 1961, Economic forecasts and policy (North-Hoiiand, Ams!erdam). ‘Thompson, Ro&rt L., 1981, A survey of recent US developments in i.r;ternationa! a@ctiltu:di trade models, US Department of Agriculture, Bibliography and literaWc of .Agricuiture report no. 21, Sept. (Washington, DC). ‘romlin, Jr&n A., P&ust implementation of Lemke’s method for thr, linear complementarit> report SOL 76-24. Sept. (Dep:irtmrrnt of problem, Syster;:i:s Qp imization Laborator) Operations Rese *rch, Stanford I!niversiny. Stanford. C.4’. US Department of Energy, F9!2, US coal exports: Projections arid documentation. Report DOE/EIA-03 17, March (Washin,gton, DC).