Interdependence of the Sawlog, Pulpwood and Sawmill Chip Markets: an Oligopsony Model with an Application to Finland

Transcription

1 Slva Fennca 35(2) research artcles nterdependence of the Sawlog, Pulpwood and Sawmll Chp Markets: an Olgopsony Model wth an Applcaton to Fnland A. Maart. Kallo Kallo, A.M nterdependence of the sawlog, pulpwood and sawmll chp markets: an olgopsony model wth an applcaton to Fnland. Slva Fennca 35(2): The nterdependence of the markets for pulpwood, sawlogs and sawmll chps s analysed usng a short-run model, whch accommodates the alternatve competton structures of wood buyers. We propose that mperfect competton n the pulpwood market tends to make the sawmlls owned by the pulp and paper companes larger than the ndependent ones, even n the absence of transactonal economes of ntegraton. The mpact of the wood market competton pattern on the profts of the forest owners and forest ndustry frms depends upon a frm-capacty structure, wood supply elastctes, and busness cycles n the output markets. The numercal applcaton of the model to the Fnnsh softwood market suggests that nfleblty of producton capactes tends to make the wood demand rather nsenstve wth respect to prce. Only the large frms, whch all produce both pulp and sawnwood, may have olgopsony power under some condtons. ntegrated producton can ncrease competton n the sawlog market va the wood chp market. Keywords wood market, olgopsony, forest ndustry Author s address Helsnk School of Economcs, Department of Economcs and Management Scence, P.O. Bo 1210, FN Helsnk, Fnland E-mal maart.kallo@hkkk.f Receved 9 October 2000 Accepted 23 January ntroducton Forestry and the forest ndustry are of consderable economc mportance n many countres, not the least because they provde ncome and mportant job opportuntes n rural areas. Hence, there s a need for effcent wood markets. The spatal olgopsony power of the wood buyers has often been recognsed as a possble source of wood market neffcency. Due to the landntensve character of forestry and scale economes n pulpwood processng, pulpwood supplers n partcular often have relatvely few potental buyers for the product. Despte the possblty of small-scale producton n sawmllng, the sawlog market can also be concentrated. Dversfcaton 229

2 Slva Fennca 35(2) research artcles by pulp and paper producers nto sawnwood producton s one source of sawlog market concentraton. The ncentves for ntegrated producton of pulp and sawnwood can be many. f stumpage sales are the domnant sales pattern n the wood market, ntegraton facltates allocaton of the dfferent wood types from a sales lot to alternatve end-uses. ntegraton may also reduce the transacton costs afflated wth the echange of an mportant raw materal of the pulp ndustry, sawmll chps. But as we wll dscuss n ths paper, ths ntegraton may be also motvated by mperfect competton n the wood market. Competton n the wood market has been studed n countres wth a sgnfcant forest sector. Some studes have amed to eplctly quantfy the mpacts of mperfect competton n the wood market on socal welfare. Brännlund (1989) suggests a consderable socal loss, gven the assumed monopsony n the Swedsh pulpwood market. Murray (1995a) estmates the welfare effects of a pulpwood market olgopsony and partal vertcal ntegraton of the pulp ndustry wth roundwood resources n the U.S. Hs results ndcate very small welfare dstortons, but consderable dstrbutonal mpacts. Regardng studes on the degree of market power, Murray s (1995b) study on the U.S. markets for pulpwood and sawlogs ndcates a mld but statstcally sgnfcant level of olgopsony power n the pulpwood market, but compettve sawlogs markets. Bergman and Brännlund (1995) suggest that the Swedsh pulpwood market has been more olgopsonstc durng recessons than booms. Størdal and Baardsen (2000) propose that the Norwegan sawlog market has been non-compettve. Ronnla and Toppnen (2000) do not reject the compettve market hypothess for the Fnnsh pulpwood market, but present some evdence for a non-compettve sawmll chp market. Smulatons of the Fnnsh pulpwood market from 1988 to 1997 n Kallo (2001) suggest that the market may have been non-compettve durng the recesson years. The wood market studes typcally eamne the markets for pulpwood and sawlogs separately, whle they may consder the nterrelaton of these two markets through cross-prce effects (e.g., Kuuluvanen et al. 1988, Brännlund 1989). Despte sawmll chps beng an mportant raw materal source for the pulp ndustry 1), the role of the chp market as a lnk between the two roundwood markets has attracted lttle attenton. n ths paper, we eamne wood market competton whle accountng for the nteracton of the markets for sawlogs, pulpwood and chps. Our goal s to gan a better understandng of how the use of chps s reflected n roundwood prces, quanttes traded and the performance and szes of the market players under alternatve competton hypotheses. We wll frst address ths ssue by analysng a theoretcal market model where the wood buyers are dvded nto frms producng sawnwood only and nto frms that produce both pulp and sawnwood. We wll show, for nstance, that when sawmll chps are an mportant nput n the pulp ndustry, the pulpwood prce should be nested n the sawlog prce. We wll also suggest that under the non-compettve wood markets, pulp producers ntegrated wth sawnwood tend to choose a larger sawnwood output than ndependent sawmlls. To eplore the real-world mplcatons of the model and the phenomena that can emerge due to the wood market nteractons, the model s appled to recent data on the Fnnsh softwood market. n ths contet, we also dscuss the mplcatons for the market competton of the current buyer structure n the Fnnsh wood market. n Secton 2, we present and analyse a wood market model where the demand sde conssts of vertcally ntegrated and non-ntegrated forest ndustry frms. n Secton 3, the model s talored to represent the Fnnsh softwood market. The results of the numercal eperments are presented n Secton 4. Secton 5 concludes. 2 Model Consder an ndustry wth two types of frms. For the frms, pulp s a prncpal product, but to dversfy and to obtan fleblty n wood procurement, they also produce sawnwood. The frms,e E produce sawnwood only. A fed nput a s of sawlogs s requred to produce one unt of sawnwood. As a by-product, share r of 1) n Fnland, for nstance, sawmll chps accounted for 25% of the total wood use n the pulp ndustry n 1998 (The Fnnsh Forest Research 1999). n Sweden the respectve fgure for 1997 was 30% (Skogsstatstsk årsbok 1999). 230

3 Kallo nterdependence of the Sawlog, Pulpwood and Sawmll Chp Markets: an Olgopsony Model sawlog nput a s s converted to sawmll chps,.e., one unt of sawnwood output gves an output of ra s unts of chps. To produce pulp, frms use a fed amount a m of pulpwood or chps per one unt of pulp output. n the short run, the producton of sawnwood and pulp by a frm s lmted by the frm s producton capacty. Due to the assumpton of fed wood nput proportons, these producton capactes can also be epressed as mamal wood processng capactes. We denote the pulpwood processng capacty of frm by K m and sawlog processng capacty by K s. n addton to wood and captal, the ndustry usenergy, labour and other materals n pulp and sawnwood producton. The margnal unt costs of frm due to the use of these non-wood nputs are assumed constant and they are denoted c m n pulp producton, and c s n sawnwood producton. The frms are assumed to take sawnwood and pulp prces, p s and p m respectvely, gven. Hence, there s perfect competton n the market for outputs. Roundwood s suppled to the ndustry by numerous prvate forest owners. Ther wllngness to sell roundwood s assumed to depend on the stumpage prce of wood and on factors Z, whch are eogenous to the forest ndustry. The stumpage prce for sawlogs w s can be epressed by the nverse supply functon w s = w s (X s, Z), where X s denotes the total supply of sawlogs. Respectvely, the stumpage prce for pulpwood w m s determned as w m = w m (X m, Z), where X m denotes the total supply of pulpwood. Assume that these nverse supply functons are ncreasng n quantty,.e., w m ' = w m / X m > 0, and w s ' = w s / X s > 0. n addton to stumpage prce, other woodrelated costs are ncurred from harvestng the wood and transportng t to mll. We denote the dfference between the mll prce and stumpage prce of pulpwood by d. Furthermore, we assume that the mll prce of chps w h s ted to the mll prce (w m + d) of pulpwood so that w h = w m + d b. Assumng sawmll chps to be a perfect substtute for roundwood, b 0 s a possble mark-down term, whch results from pulp mlls payng a non-compettve prce for chps. The net unt prce of chps receved by ndependent sawmlls s gven as w h l, where l s the unt cost of transportng chps from a sawmll to a pulp mll. For, let m, h and s denote the nput of pulpwood, the nput of chps purchased from the ndependent sawmlls, and the nput of sawlogs by producer, respectvely. Smlarly, for e E, let s e be the sawlog nput. n a market clearng equlbrum, the pulpwood supply X m equals the total pulpwood demand,.e., X m = Σ m, and the supply of sawlogs X quals the demand for sawlogs by ntegrated and ndependent sawmlls,.e., X s = X s + X s E, where X s = Σ s and X s E = Σ e E. The total nput of purchased wood chps Σ h s denoted by X h. We assume that the market for chps clears,.e., we requre that X h = rx s E. A frm may recognse that ts own wood demand has an mpact on the total wood demand and thereby on the market prce. We denote the frm s conjectured mpact of ts own nput decson on the total wood demand n the markets for pulpwood by X m / m = γ m and for sawlogs by X s / s = γ s. n a compettve pulpwood market frms act lke prce takers. n ths case γ m = 0 for all. For a compettve sawlog market γ s = 0 for all respectvely. n a quantty settng Cournot olgopsony γ m = 1 for all, and γ s = 1 for all and for all E for pulpwood and sawlogs, respectvely. Hence, under the Cournot conjecture, each frm consders only ts own mpact on the total pulpwood or sawlog demand. Let us now formulate the mathematcal models for the wood buyng frms and dscuss the alternatve wood market equlbra. We assume that all the frms mamse ther profts. To smplfy notaton, we nclude the nonstumpage costs of sawlogs drectly n the margnal costs c s of sawnwood producton, but keep the respectve unt cost d for pulpwood apart from c m. For an ntegrated frm, proft V s gven by V r ps cs s pm cm m + h + s = ( ) + ( )( ) as am w ( w + d ) ( w + d b ). s s m m m h Note that s / a s s the sawnwood output and ( m + h + r s ) / a m s the pulp output of frm. To further smplfy notaton, we denote (p s c s ) / a s = π s and (p m c m ) / a m = π m. Then the proft () 1 231

4 Slva Fennca 35(2) research artcles mamsaton problem of the frm s: Ma V r w m h s = ( πs + πm s) s,, + ( π m wm d) m + ( π w d+ b) st.. s m m h ( 2) K () 3 s m + h + rs Km ( 4) rx ( 5) h s E h j j The wood nputs are constraned by the wood processng capactes as gven by Eqs. (3) and (4). n addton, n Eq. (5), the use of purchased chps s lmted to the resdual amount that s avalable to the frm from the total chp quantty rx s E after the rvals use of chps. Let us denote the Lagrange multplers for constrants (3) (5) by µ s, µ m and µ h respectvely. n an equlbrum s, m and h satsfy the followng Karush-Kuhn- Tucker optmalty condtons, whch employ the slack varables δ s, δ m and δ h : π + rπ w w ' γ µ rµ + δ = 0 ( 6 ) δ s s m s s s s s m s = 0 ( 7) s π w w ' γ ( + ) d µ + δ = 0 ( 8 ) m m m m m h m m ( rxs E ) µ = 0 ( 17) j h j h h,,, µ, µ, µ, δ, δ, and δ 0. s m h s m h s m h Before gong to the problem of ndependent sawmlls, let us consder an eample. f frm does not buy any chps,.e., h = 0, even when there s a postve resdual supply of chps for the frm, t follows from Eq. (17) that µ h = 0. Consequently, f the pulpwood market s non-compettve so that γ m > 0, Eqs. (8) and (10) mply that δ m > 0, f m > 0. Therefore, from Eq. (9) we must have m = 0. A Cournot frm buys all the chps avalable to t from the market at a prce w m + d b before t starts buyng pulpwood from the stumpage market. Snce ths concluson holds for all frms, the clearance of the chps market s guaranteed, f m > 0, for any. ndependent sawmll e E, mamses ts proft V e as: ma e Ve = π + ( wm + d b l) r ws ( 18) s st.. K, ( 19) 0. Denotng the Lagrange multpler for constrant (19) by µ s e and ntroducng a slack varable δ, the Karush-Kuhn-Tucker condtons for an optmal soluton are: δ m m = 0 ( 9) π w d+ b µ µ + δ =0 ( 10) m m h m h π + rw ( + d l b) m w w γ µ + δ ' s s 0 ( 20) δ h K = 0 ( 11) s h 0 ( 12) s ( K ) µ = 0 ( 13) s s s Km m h rs 0 ( 14) ( K r ) µ = 0 ( 15) m m h s m rxs E 0 ( 16) j h j h δ e s e s = 0 ( 21) K 0 ( 22) ( K ) µ = 0 ( 23) e 0, µ, δ 0. s From now on, whle eamnng market equlbra, we lmt our consderaton to an ndustry where all the frms are actve n the market equlbrum,.e., we assume that all the frms and e E are producng sawnwood and that all the frms 232

5 Kallo nterdependence of the Sawlog, Pulpwood and Sawmll Chp Markets: an Olgopsony Model are producng pulp as well. Hence we are nterested n the cases where the slack varables δ s and δ m of constrants (6) and (8) are zero for ntegrated frms, and where slack varable δ s e s zero for non-ntegrated frm E. We also assume that all the frms hold the same wood market conjecture..e., γ s = γ s for all ntegrated and ndependent sawmlls and γ m = γ m for all pulp producers. Hence γ s = 1 and γ m = 1 refer to Cournot markets, whereas γ s = 0 and γ m = 0 refer to perfect competton. Constrants (6), (8) and (20) become: πs + rπm ws w' sγ ss µ rµ = 0, s m π w w' γ ( + ) d µ = 0, m m m m m h m π + rwm + rd rb rl ws w ' γ µ = 0, e E. s s (') 6 (') 8 ( 20') Let us denote by m, s, h, π m, π s, µ m and µ s the averages of the ntegrated frms for varables m, s, h, parameters π m, π s and shadow prces µ m and µ s respectvely. n a smlar manner, we denote the averages of the actve ndependent sawmll E by s E, π s E and µ s E. Wth some rearrangng, aggregatng across frms n Eqs. (6') and Eqs. (8'), and aggregatng across frm E n Eqs. (20') we obtan: w = π γ w' ( + ) d µ ( 24) m m m m m h m w = π + rπ γ w' µ rµ ( 25) s s m s s s s m w = π + rw + rd rb rl γ w' µ ( 26) s s E m s s s E s E The value of the opton to use sawmll chps n pulp producton enters the sawlog prce equatons (25) and (26) and ncreases the sawlog prce. n an unconstraned compettve equlbrum µ m = µ s = µ s E = 0 and γ m = γ s = 0. (For no frm to have a postve shadow prce for ts producton capactes, the actve frms must have dentcal margnal revenues π s and π m of wood use.) Then for Eqs. (25) and (26) to hold smultaneously, substtuton of the pulpwood prce from Eq. (24) to Eq. (26) mples that the ndependent sawmlls only produce f π s E π s rb + rl. Consequently, f b > 0 or l > 0, the ndependent sawmlls have to be more cost-effectve or they have to prce dfferentate to obtan a better prce for ther product than the ntegrated sawmlls to successfully compete wth them. Consder now an unconstraned olgopsony n the sawlogs market. Substtutng the pulpwood prce from Eq. (24) to Eq. (26), we obtan the result that the ntegrated and ndependent sawmlls are of the same sze n the sawlog market f π s E = π s + rb + rl, when the pulpwood market s compettve. mperfect competton n the pulpwood market ncreases the sze of the ntegrated sawmlls wth respect to ndependent sawmlls. n the Cournot market for sawlogs, the long-run dfference between the average sze of ntegrated and ndependent sawmlls n terms of sawlog use s 2) : s s E = ( πs πs E + γ mrw ' m( m + h ) + rb + rl) w' s ( 27) We now demonstrate that dependng on the output market condtons, the sawlog prce can decrease or ncrease due to non-compettve behavour of the ntegrated frms n the pulpwood market. We also propose that non-compettve behavour n the sawlog market may ncrease the pulpwood prce. An Eample wth a Sawlog Prce That s Decreasng Due to a Non-Compettve Pulpwood Market Consder frst the case wth perfect competton n all markets, so that γ s = γ m = b = 0. Assume all frms to be actve wth dle capacty, so that µ m = µ s = µ s E = 0. The compettve sawlog prce w s P s obtaned by substtutng compettve pulpwood prce w m P to Eq. (26) as: 2) Due to scale economes n the pulp and paper ndustry, the wood consumpton n pulp producton by a sngle frm may be substantal. n Fnland, for nstance, the average pulpwood nput by a producer s close to 10 mll. m 3 annually, whle the proporton of wood chps r can be taken to be between Hence the mpact of the non-compettve wood market behavour on the relatve szes of the sawmlls can be non-neglgble. 233

6 Slva Fennca 35(2) research artcles w = π + rw + rd rl ( 28) s P s E m P f the pulp ndustry now shfts to Cournot behavour, pulpwood prce w m C becomes w = w w' ( + ) µ ( 29) m C m P m m h m f the pulpwood prce decreases suffcently because some large frms cut output substantally, some small pulp producers may ncrease ther producton and become capacty-constraned. That s why µ m enters Eq. (29). Nevertheless, because w m ' > 0 and µ m > 0, the Cournot prce cannot be hgher than the compettve prce. Therefore, snce w m C < w m P, the sawlog prce adjusts downwards as follows: w = w + r( w w ) ( 30) s C s P m C m P An Eample wth a Sawlog Prce That s ncreasng Due to a Non-Compettve Pulpwood Market Consder now the case where the busness cycle n the pulp market s favourable wth a capactyconstraned pulp ndustry, but assume that each ntegrated sawmll has dle capacty. f there were more pulp capacty, ntegrated sawmlls would be able to produce more. n other words, the pulp capacty also lmts the sawnwood output. n ths case, the compettve sawlog prce s: w = π + rπ rµ ( 31) s P s m m f the pulp ndustry now shfts to Cournot competton n the wood market, and f ths mples dle capacty both for sawnwood and pulp, t follows that µ m = 0. Then the sawlog prce ncreases to the unconstraned compettve level, where w s = π s + rπ m. Hence, t s possble that mperfect competton n the pulpwood market wll ncrease the sawlog prce. mpact of Non-Compettve Behavour n the Sawlog Market on Pulpwood Prce f we gnore the possblty of usng sawlogs as a drect substtute for pulpwood, mperfect competton n the sawlog market may not decrease pulpwood prce. n the short run, the compettve pulpwood prce depends solely on the margnal product value of pulpwood n pulp producton and on the producton capacty. Hence, the sawlog prce level does not nfluence the pulpwood market drectly. However, t can nfluence the pulpwood market va the chp market. f the olgopsony decreases sawnwood producton, the supply of sawmll chps wll be reduced n the same proporton. The cut n the nput of chps may be replaced partly or entrely by pulpwood, whch may ncrease the pulpwood prce. Ths behavour wll be seen n the numercal applcaton of the model to the Fnnsh wood market. 3 Numercal Applcaton Let us now descrbe the numercal applcaton of the model to the Fnnsh softwood market. The market for the hardwood speces wacluded because mports form such an mportant part of the ndustral use of hardwood. n 1998, roughly 50% of the hardwood and 6% of the softwood used by the forest ndustry were mported (The Fnnsh Forest Research 1999). To capture the producton structure of the Fnnsh forest ndustry n a more detaled manner, the model n Secton 2 watended to nclude two pulp grades and two mechancal forest ndustry products. The products are sawnwood, plywood, chemcal pulp and mechancal pulp and they are referred to wth sub-ndces s, v, m and y, respectvely. The ncluson of two more products means that addtonal decson varables are needed for each frm n the model formulaton. n Secton 2, m s the frm s pulpwood nput n (chemcal) pulp processng, h s the frm s nput of purchased chps n (chemcal) pulp processng, and s s the frm s nput of sawlogs n sawnwood processng. To smplfy calculatons, we assume that all the sawmll chps are consumed n chemcal pulp processng, although n Fnland chps are used n mechancal pulpng as well. n 1998, chemcal pulpng accounted for 76% of total chps use (The Fnnsh Forest Research 1999). Then, the addtonal varables for frm are the pulpwood 234

7 Kallo nterdependence of the Sawlog, Pulpwood and Sawmll Chp Markets: an Olgopsony Model Table 1. Producton n 1999 and assumed annual producton capactes n 2000 (1000 t, 1000 m 3 ) for softwood products n Fnland by frm. Sawnwood Plywood Sulphate pulp Mechancal pulp Output Capacty Output Capacty Output Capacty Output Capacty UPM-Kymmene Stora-Enso Metsä-Serla Vapo Others Total nput n mechancal pulp, y, and the sawlog nput n plywood producton, v. New parameters correspondng to etended product groupng are requred respectvely. The Append shows how the new varables and parameters enter the proft mamsng problem of the ntegrated (Eqs. (A.1) (A.5)) and non-ntegrated (Eqs. (A.6) (A.8)) frms. The ndustry Data The Fnnsh forest ndustry s concentrated n nput markets. Three large forest ndustry frms buy practcally all the pulpwood and sawmll chps and ther share of the sawlog demand s over 50%. Table 1 presents the producton n 1999 (based on the Fnnsh Forest ndustry Federaton, 2000c and 2000d) and assumed capactes of the frms for the softwood products n The fgures account for holdngs n any jontly owned mlls. Myllykosk Paper has been ncluded wth Metsä-Serla, due to ther allance. Unless mentoned elsewhere, our source for capacty data was the www-pages of the Fnnsh Forest ndustres Federaton (2000a). The fgures n Table 1 were used to defne the wood processng capactes K m, K y, K s and K v of the chemcal pulp, mechancal pulp, sawnwood and plywood producers, respectvely. Our data source aggregates softwood and hardwood sulphate pulp capactes. The capacty was allocated between the grades followng ther shares of the mll s producton n Mechancal pulp s ntegrated wth paper and paperboard producton. The ntegrated paper and paperboard capacty lmts ts demand and producton. ts capactes were defned as follows. Frst, we calculated the mll capacty utlsaton rates for paper and paperboard contanng mechancal pulp. For ths we used the producton volumes for 1999 (The Fnnsh Forest ndustry Federaton, 2000c) and the producton capactes for 2000 (The Fnnsh Forest ndustry Federaton, 2000a). Ths capacty utlsaton rate was also assumed for the mechancal pulp capactes of the mlls, whch were then calculated from the mlls mechancal pulp producton n For large sawnwood producers (members of the Fnnsh Forest ndustry Federaton) we used the capactes for 1998, usng the Fnnsh Forest ndustry Federaton (1998) as a basc source. These fgures were updated usng the data publshed by the web-stes of the ndvdual companes n August 2000, whenever such data were avalable. For the rest of the producers, all of whch are relatvely small, we defned the aggregated producton capacty assumng the average capacty utlsaton rate to be same as that of the larger producers. Ths capacty block was dvded to 200 smaller unts n the model. Plywood capactes are not of great sgnfcance wth respect to wood use. Half of the wood used n plywood producton was softwood n 1998 (The Fnnsh Forest Research 1999). Lackng the wood use data for 1999, we assumed that 50% of the plywood producton was also softwood plywood n For Metsä-Serla, we obtaned the softwood plywood capacty from a web-ste of ts subsdary Fnnforest n August For UPM-Kymmene, we used the 50% softwood assumpton to dsaggregate the soft- 235

8 Slva Fennca 35(2) research artcles wood producton capacty from the total plywood capacty. The wood nput per one unt of output has been qute stable n the forest ndustry. Due to substtuton between wood and the other producton factors, and due to dfferences between the mlls n ther wood use effcency and respectve varaton n the mlls actvty levels, there can be slght annual varaton. Based on the data by the Fnnsh Forest ndustry Federaton (2000a) we used the coeffcents, a y = 2.8 m 3 /t and a m = 5.6 m 3 /t for pulpwood nput n mechancal pulp and chemcal pulp, respectvely, and the coeffcents a s = 2.25 m 3 /m 3 and a v = 3.0 m 3 /m 3 for sawlog nput n sawnwood or plywood, respectvely. The coeffcent of 5.3 m 3 /t was gven for sulphate pulp by the source above, but that fgure also ncludes the hardwood pulp wth lower wood nput. The pulp yeld of wood n softwood chemcal pulpng s appromately half of that n mechancal pulpng (e.g., Saarno, 1999). For the chps output coeffcents we employed the values r v = 0.4 and r s = 0.36 per one m 3 of sawlogs used n plywood and sawnwood producton. These fgures were calculated from the data by the Fnnsh Forest ndustry Federaton (n 1999a and 2000d). Roundwood Supply Econometrc studes have establshed a postve correlaton between wood stumpage prce and supply from the prvate forests, whch supply over three-quarters of the softwood n Fnland. Toppnen and Kuuluvanen (1997) obtaned prce elastcty estmates for short-term pulpwood supply as follows: 0.4 durng but over 2.0 for the perod from 1976 to For the sawlog supply, Kuuluvanen et al. (1988) obtaned a prce elastcty of 0.53, and Tkkanen and Vehkamäk (1990) obtaned a prce elastcty of The studes usng more recent tme-seres data have gven med results. n Toppnen and Kuuluvanen (1997), the sawlog supply elastcty was found to be nsgnfcant or very small and n Toppnen (1998) t wastmated to be of the order of 1.9. We represent the wood supply wth two nverse supply functons (.e., functons for wood prces), one for the pulpwood prce and one for the sawlog prce. The producton data n Table 1 and the nput coeffcents above gve the reference demands: 27.8 mll. m 3 for sawlogs and 26.1 mll. m 3 for pulpwood. These quanttes were used together wth reference market prces to form nverse wood supply functons of lnear form: w s = M s + β s X s for sawlogs, and w m = M m + β m X m for pulpwood. The supply functon parameters (M s, M m, β s and β m ) were defned to equate the prce elastcty of wood supply n the reference pont wth a gven prce elastcty estmate, for whch we eplored a range of values. The base case reference prces were weghted averages of pne and spruce stumpage prces from prvate forests n 1999: 250 FM/m 3 for sawlogs, and 109 FM/m 3 for pulpwood. The purchased quanttes were used as weghts. These data were based on the Fnnsh Forest Research nsttute (2000). We tested the senstvty of the results wth respect to other reference prce levels as well. Product and nput Prces From 1978 to 1998, the real prces of forest products n Fnland obtaned ther peaks durng the last ten years, sawnwood beng an ecepton. The mamum and mnmum values were obtaned smultaneously for pulp and pulpwood. For sawlogs, the mnmum and mamum prces were attaned smultaneously wth the lowest and hghest pulpwood prces, respectvely. To encompass market cycles and also uncertanty n cost data, we consder three alternatve scenaros: hgh (HGH), average (AVG) and low (LOW) output markets. Table 2 shows the data employed to defne margnal revenue parameters for wood use, π m, π y, π s, and π v n chemcal pulp, mechancal pulp, sawnwood and plywood, respectvely, n the scenaros. The same parameters were used for both the ntegrated and non-ntegrated producers. Snce pulp s an ntermedary product, our procedure encompasses the assumpton that the prce of pulp entrely reflects the value of pulp n paper and paperboard producton. Solvng the Model We assume ether perfect competton or Cournot 236

9 Kallo nterdependence of the Sawlog, Pulpwood and Sawmll Chp Markets: an Olgopsony Model Table 2. Prces and varable producton costs other than stumpage costs (FM/m 3 or FM/t n 1998 money) employed n defnng the margnal revenues of wood use n scenaros HGH, LOW and AVG. Sawnwood Plywood HGH LOW AVG HGH LOW AVG Prce Energy Labor Fed wood Other Margn Mechancal pulp Sulphate pulp HGH LOW AVG HGH LOW AVG Prce Energy Labor Fed wood Other Margn Source: Prces are mnmum, mamum and average eport unt values n from the Statstcal Yearbook of Forestry. For sawnwood and plywood, the cost data were obtaned by dvdng the total nonwood costs n the ndustral Statstcs 1998 by the producton quantty. For mechancal pulp, the non-wood costs are averages of thermo-mechancal pulp and groundwood pulp and they are calculated usng the technology defntons n Saarno (1999). For sulphate pulp the costs have been calculated on the bass of the technology defntons n Saarno (1999) and Jaakko Pöyry Consultng (1992). Fed wood costs nclude the harvestng and long-dstance transportaton costs of roundwood. The harvestng costs were obtaned from Metsäteho Oy and the long-dstance transportaton costs are from the Fnnsh Statstcal Yearbook of Forestry Margn refers to proft margn before the stumpage costs of wood and captal costs. competton n the roundwood markets. The market for sawmll chps s compettve n the base case (parameter b = 0), but to eplore the nfluence of non-compettve prcng of sawmll chps we also nvestgate cases wth b > 0. We use the fgure l = 30 FM/m 3 for the average transportaton cost of chps from a sawmll to a pulp mll. Ths was roughly the average costs of longdstance transportaton (FM/m 3 ) for roundwood n Fnland n 1998 (the Fnnsh Forest Research 1999). To fnd the market equlbra for the alternatve competton hypotheses, we frst formed the Karush-Kuhn-Tucker optmalty condtons of the problems of the ndvdual frms. Then, usng the GAMS software package (Brooke et al. 1992), we solved a mathematcal programmng problem, whch conssts of these condtons and the market clearng condtons for wood chps, sawlogs and pulpwood (Eqs. (A.9) (A.11) n the Append). Any feasble soluton for ths problem s a market equlbrum. 4 Smulaton Results Ths secton descrbes and compares the smulated market outcomes n alternatve competton patterns of the wood buyers. We let the output market cycle and the prce elastctes of wood supply vary. Results for Prce Elastctes of Wood Supply of 1.0 or above Facng untary elastc or more elastc roundwood supply functons, the smulated forest ndustry produces at full capacty under all output market 237

10 Slva Fennca 35(2) research artcles condtons and competton patterns. Due to a rather elastc wood supply, no frm s able to gan from olgopsonstc behavour n any market. Hence, f a frm cuts ts wood demand n order to pay less for wood, the decrease n the wood costs cannot offset the decrease n varable profts caused by the decreased sales. Results for Prce Elastctes of Supply of 1.0 for Pulpwood and below 0.5 for Sawlogs Let us look at a case where the prce elastcty of the pulpwood supply s 1.0, and where the prce elastcty of the sawlog supply vares from 0.3 to 0.5. Wth an elastcty of 0.5, the Cournot outcome dffers from the compettve outcome only n scenaro LOW. Wth an elastcty of 0.3, the olgopsony also contracts ts sawlog demand under better market condtons. Fg. 1 graphs the mpacts of the olgopsonstc behavour on the roundwood demand n scenaro LOW. Fg. 2 presents a comparson of the aggregated profts n the alternatve competton patterns relatve to perfect competton when the sawlog prce elastcty s 0.3. All the ndependent sawmlls are well below the Cournot frm sze of our eperments, whch n terms of sawlog nput s roughly 5 mll. m 3 (4.5 mll. m 3 ) n the average (low) market for a sawlog prce elastcty of 0.3. Ther behavour s unaffected by the competton pattern. However, as vdent from Fg. 2, they are the bggest wnners n relatve terms f the larger companes behave non-compettvely n the sawlog market. Whle mperfect competton n the sawlog market reduces sawnwood and plywood output, t also decreases the supply of chps. As shown n Fg. 1, the demand for pulpwood ncreases. The resultng ncrease n pulpwood prce dlutes some of the gans from mperfect competton n the sawlog market for the ntegrated frms. n Fg. 2 the forest owners are slghtly better off when there s Cournot competton n both markets than n the case of Cournot competton n the sawlogs market only. The two largest sawlog buyers cut ther sawlog demand more under sawlog market olgopsony than under olgopsony n both roundwood markets. Aggregaton of profts hdes frmlevel dfferences. Two of the three ntegrated Mll. m Sawlog prce elastcty pulpwood-11 sawlogs-11 pulpwood-10 sawlogs-10 Fg. 1. Change (mll. m 3 ) n the demand for pulpwood and sawlogs n scenaro LOW, when the ndustry shfts from compettve behavour to Cournot olgopsony n the sawlog market (10) or n the both sawlog and pulpwood markets (11). Pulpwood prce elastcty s fed at 1.0. producers clearly have the largest profts when there s a Cournot olgopsony n the sawlog market only, whle the largest pulp producer makes roughly the same proft n both the sawlog market olgopsony and n the entre roundwood market olgopsony. Results for Prce Elastctes of Supply of 1.0 for Sawlogs and below 1.0 for Pulpwood Let us keep the sawlog prce elastcty untary and eperment wth pulpwood prce elastcty. n scenaro AVG, the pulp companes produce at full capacty under the Cournot olgopsony when we employ the lowest econometrc prce elastcty estmate for the pulpwood supply n Fnland, 0.4. n scenaro LOW, however, the pulpwood consumpton s then 5.6 mll. m 3 (20%) lower n the Cournot pulpwood market than n the compettve market. n the low market, the largest pulp producer cuts ts pulpwood nput slghtly wth an elastcty of 0.9. The second largest pulpwood buyer contracts ts producton when we reduce the pulpwood prce elastcty to 0.5. The sawlog prce and demand reman unaffected n all the cases. 238

11 Kallo nterdependence of the Sawlog, Pulpwood and Sawmll Chp Markets: an Olgopsony Model 180 % 160 % 140 % 120 % 100 % 80 % 60 % 40 % 20 % 0 % 20 % 40 % H FOR A L H A L H A L VF NF Fg. 2. Change (%) n the ncome of forest owners (FOR) and n the profts of ntegrated (VF) and non-ntegrated (NF) frms n the hgh (H), average (A) and low (L) output markets when the ndustry shfts from compettve behavour to Cournot competton n the sawlog market only (10) or n the pulpwood and sawlog markets (11). Results for the supply elastctes of 1.0 for pulpwood and 0.3 for sawlogs Colluson of ntegrated Frms (Monopsony) Now consder a case where all the ntegrated frms form a wood-buyng cartel. n the pulpwood market, ths means a monopsony. Facng untary elastc wood supply functons, the cartel would produce practcally at full capacty n scenaros AVG and HGH, whle n scenaro LOW the cartel would cut ts roundwood demand. Then the Cournot behavour n the sawlog market only s not sustanable. Due to the resultng ncrease n pulpwood prce, the cartel makes less proft than under perfect competton. When both wood markets are olgopsonstc, the cartel contracts ts pulpwood demand by 28% and ts sawlog demand by 9% from the compettve levels. Gven the average output markets, the current pulp capacty n Fnland roughly equals the optmal monopsonstc capacty when the prce elastcty of the pulpwood supply s 0.8 (The capacty utlsaton by the monopsony s then 99.8%). Gven that the sawlog market s also olgopsonstc, the current ntegrated sawmll capacty s optmal to the monopsony pulp ndustry f the sawlog prce elastcty s about 0.7. Hence, then the capacty s n full use. f the sawnwood capacty of the pulp ndustry were dsntegrated and used by an ndependent sawmll, sawnwood producton would decrease by crca 17%. Non-Compettve Prcng of Sawmll Chps For non-compettve prcng of chps to have a short-run nfluence on the producton and harvest levels, the mark-down n the chp prce has to be consderable. n scenaro LOW, the non-ntegrated sawmlls are most vulnerable to non-compettve prcng of chps. Then, gven a untary elastc sawlog and pulpwood supply, the frst mpact on the sawnwood producton quanttes s seen for mark-down b = FM 200. Then the largest ndependent sawmll cuts ts sawnwood producton under the Cournot competton, but not under the compettve market. t thus seems that the short-run mpacts of the non-compettve chps market are manly dstrbutonal. ntegrated forest ndustry companes make more proft, ndependent sawmlls make less proft, but forest owners ncome s unaffected. Whle the mpact on the forest owners s neutral n the short run, the small sawmlls may be left to face ths potental problem alone. Nevertheless, there can be long- 239

12 Slva Fennca 35(2) research artcles run effects, shown as a decrease n the sze of the sawmllng sector. Further Senstvty Analyss Let us fnally test the senstvty of the results wth respect to some other prcng schemes. The wood nput n 1999 s stll used as a reference quantty. When the wood supply functons are benchmarked to the average real prces n the perod from 1988 to 1998, 109 FM/m 3 for softwood pulpwood and 218 FM/m 3 for sawlogs, the pulpwood supply functon remans unchanged. Epectedly, the behavour of the pulpwood buyers s unaffected. The sawlog prces are lower, and all the scenaros are more favourable to the sawmllng ndustry. Even leslastc sawlog supply functons than before are requred to make the olgopsonstc behavour attractve n the sawlog markets. n scenaro LOW, the sawlog supply elastcty has to be decreased to 0.4 to make the largest buyer contract ts sawlog nput n Cournot. When we keep the sawlog reference prce at 250 FM/m 3 and choose a pulpwood reference prce of 141 FM/m 3, the prce spread between the two wood grades (FM 109) equals the average spread durng The poston of the pulpwood buyers s now weakened. Under a untary elastc pulpwood supply, Cournot behavour n the pulpwood market now decreases the pulpwood demand by 4.7 mll. m 3 (16%) n LOW, but not at all n the other scenaros. n scenaro AVG, the pulpwood prce elastcty has to be 0.6 or less to make the Cournot outcome devate from the compettve outcome. 5 Dscusson We presented and analysed a forest sector model that lnks the markets for sawlog and pulpwood va the market for sawmll chps. The model was used for a numercal analyss of the Fnnsh softwood market under alternatve competton patterns. Both the analytcal and numercal results suggest that due to the lnkage of the sub-markets, the mpact of the alternatve competton patterns on the performance of the market players s not e ante predctable; t depends on the frm-capacty structure, the output market cycle and on the wood supply elastctes. The analytcal model suggests that the value of the opton to use sawmll chps as an nput n pulp producton should be nested n the sawlog prce. f there are transacton costs n the echange of chps between the frms or f the pulp ndustry marks down the chp prce, ndependent sawmlls have to obtan a hgher margnal revenue from wood use than the sawmlls owned by pulp companes to compete wth them. Olgopsonstc behavour n the sawlog market allows the operaton of sawmlls wth dfferng margnal product values for sawlogs n the market. However, f the pulpwood market s non-compettve, sawmlls owned by the pulp producng companes tend to be larger than the ndependent sawmlls, even n the absence of transactonal economes of ntegraton. Ths can ncrease the buyer-sde concentraton n the sawlog market. However, because a sawmll ntegrated wth a pulp company may choose a consderably larger output than what s optmal for a respectve ndependent olgopsonstc sawmll, the ntegraton can also be welfareenhancng n ths case. The prncpal purpose of the numercal analyss was to eplore the phenomena that can emerge n the wood market due to the use of chps and due to ntegrated pulp and sawnwood producton. Snce the model was talored to represent the Fnnsh softwood market wth ts most recent frm-capacty structure, some suggestons may be drawn regardng the Fnnsh tmber market. Accountng for the sawlog market competton, the study also etends the work n Kallo (2001). When consderng our results, ther senstvty wth respect to the choce of wood supply elastctes and to the use of a lnear appromaton of the wood supply curve, should be borne n mnd. Frst, gven the current structure of the Fnnsh roundwood market, t seems that one should be worred about the short-run welfare mpacts of mperfect competton manly durng recessons. Under the average market condtons the ndustry s capacty-constraned for a rather plausble set of elastctes, whch makes the demand for wood rather nsenstve wth respect to prce. Then the 240

13 Kallo nterdependence of the Sawlog, Pulpwood and Sawmll Chp Markets: an Olgopsony Model market power ssues have manly dstrbutonal mpacts n the short-run. Snce the pulpwood processng capacty equals the monopsony capacty n the average market condtons for a rather plausble pulpwood supply elastcty of 0.8, ths result seems not to be very senstve wth respect to the assumed level of conjectural varaton. Nevertheless, n order to enhance wood market stablty durng recessons, further mergers between pulp producers should not be encouraged. The Fnnsh sawlog market s less concentrated on the buyer sde than the pulpwood market, and the sawlog supply has to be very nelastc to render market power to the buyers. ndependent sawmlls are too small to nfluence wood prce. Possbly, they face non-compettve prcng of sawmll chps, whch mght affect the sze of the sawmllng sector and the structure of the roundwood demand n the long run. A wder array of market opportuntes for sawmll chps would be a remedy to ths potental problem. There are some ndcatons that the pulp producton capacty has reached the lmts of ts growth potental n Fnland. Rough estmates based on natonal forest resource accountng suggest that the domestc pulpwood resources were practcally n full use durng (The Fnnsh Forest Research 1997). An ndustry specalst, Desen (1998, p.25) wrtes that the accepted opnon n the forest ndustry s that sgnfcant epanson of [pulp] capacty based on addtonal wood removals wll no longer be possble after the md 1990s. Provded that ths pcture of the stuaton s realstc, quantty-settng olgopsonstc competton should not have sgnfcant long-run welfare mpacts n the pulpwood market. Regardng the outcome, t s not mportant, whether the growth n domestc pulpwood demand s constraned by the domestc wood resources or whether t s constraned by the reluctance of the olgopsonstc pulp ndustry to add further capacty. We modelled the wood market at an aggregate natonal level. Also, whle the volume of foregn trade n softwood tmber has been relatvely low, we assumed that the supply functons of pulpwood and sawlogs manly represent domestc sources. There s, however, some evdence of the Fnnsh market for pne and spruce pulpwood beng dvsble nto regonal sub-markets wth dfferng prce structures (Toppnen and Tovonen 1998, Tll, Tovonen and Toppnen 2000). Ths can be the sgnal of a non-compettve wood market behavour at the regonal level. On the other hand, Thorsen (1998) proposes that the strong law of one prce holds between spruce sawlogs markets n Fnland and Sweden. Whle ths can, for nstance, be a reflecton of the common eport markets of sawnwood, t does not prove the estence of the spatally ntegrated sawlog market (See dscusson n Trole 1990, p.13). Nevertheless, the ntegrated markets are less lkely to be neffcent than the non-ntegrated ones. Furthermore, our analyss leaves any questons nfluenced by the current and future developments n roundwood mports and eports subject to further studes. Acknowledgements The author thanks Markku Kallo and the two referees of ths journal for ther valuable comments on earler versons of ths paper. References Bergman, M. & Brännlund, R Measurng olgopsony power. An applcaton to the Swedsh pulp and paper ndustry. Revew of ndustral Organzaton 10: Brännlund, R The socal loss from mperfect competton the case of the Swedsh pulpwood market. Scandnavan Journal of Economcs 91(4): Brooke, A., Kendrck, D. & Meeraus, A GAMS, a user s gude. The Scentfc Press. Desen, M. (ed.) Economcs of the pulp and paper ndustry. Book 1. n Papermakng scence and technology. Helsnk. Fapet. 186 p. The Fnnsh Forest ndustres Federaton Key to the Fnnsh forest ndustry. Helsnk. 1999a. Envronmental report. Sawmllng and panel products ndustry. Statstcs for Espoo. 1999b. Envronmental report. Paper and pulp ndustry. Statstcs for Espoo. 2000a. nformaton on the 241

14 Slva Fennca 35(2) research artcles n August, b. The Fnnsh forest ndustry facts and fgures. Helsnk 6/ p. 2000c. Envronmental report. Paper and pulp ndustry. Statstcs for Espoo. 2000d. Envronmental report. Sawmllng and panel products ndustry. Statstcs for Espoo. The Fnnsh Forest Research nsttute [Fnnsh forest sector economc outlook]. Metsäsektorn ajankohtaskatsaus Helsnk Research Centre, Report p. (n Fnnsh) The Fnnsh Statstcal Yearbook of Forestry Helsnk [Newsletter of forestry statstcs Purchases and prces of wood, December 1999] Metsätlastotedote Puun ostot ja hnnat, joulukuu Helsnk. (n Fnnsh). Jaakko Poyry Consultng The data for the Fnnsh forest sector model. Unpublshed document. Kallo, A.M Analysng the Fnnsh pulpwood market under alternatve hypotheses of competton. Canadan Journal of Forest Research 31: Kuuluvanen, J., Hetemäk, L., Ollonqvst, P., Ovaskanen, V., Pajuoja, H., Salo, J., Seppälä, H. & Tervo, M The Fnnsh roundwood market: an econometrc analyss. Fnnsh Economc Papers. 1: Murray, B.C. 1995a. Olgopsony, vertcal ntegraton, and output substtuton: welfare effects n U.S. pulpwood market. Land Economcs 71(2): b. Measurng the olgopsony power wth shadow prces: U.S. Markets for pulpwood and sawlogs. The Revew of Economcs and Statstcs 77: Ronnla, M. & Toppnen, A Testng for olgopsony power n the Fnnsh wood market. Journal of Forest Economcs 6: Saarno, A Choce of strategc technology nvestment case of pulp producton technology. Acta Unverstats Lappeenrantaenss p. + appendces. Skogsstatstsk årsbok Offcal statstcs of Sweden. Natonal Board of Forestry. Størdal, S. & Baardsen, S Concentraton and market power n the Norwegan sawlog market Forthcomng n Scandnavan Forest Economcs 38. Thorsen, B.J Spatal ntegraton n the Nordc tmber market: long-run equlbra and short-run dynamcs. Scandnavan Journal of Forest Research 13: Tkkanen,. & Vehkamäk, S The effects of economc and forest polcy on roundwood supply. Proceedngs, UFRO Workng Group S Montreal. p Tll, P., Tovonen, R. & Toppnen, A [ntegraton of the regonal wood prce changes n Fnland]. Puun hntavahteluden alueellnen yhtene vyys Suomessa. Metsäteteen akakauskrja 3/2000: (n Fnnsh). Trole, J The theory of ndustral organzaton. Fourth edton. Massachusetts nsttute of Technology. 479 p. Toppnen, A ncorporatng co-ntegraton relatons n a short-run model of the Fnnsh sawlog market. Canadan Journal of Forest Research 28: & Kuuluvanen, J Structural changes n sawlog and pulpwood markets n Fnland. Scandnavan Journal of Forest Research 12: & Tovonen, R Roundwood market ntegraton n Fnland: a multvarate contegraton analyss. Journal of Forest Economcs 4(3): Total of 30 references 242

15 Kallo nterdependence of the Sawlog, Pulpwood and Sawmll Chp Markets: an Olgopsony Model Append Etended frm models (Notaton as n Sectons 2 and 3) The proft mamsng problem of a vertcally ntegrated frms s: Ma V = π + π + π ( + + r + r ) + π s s v v m m h s v v y y s, v, m, y s w ( X )( + ) ( w ( X ) + d)( + ) ( w ( X ) + d b) s s s v m m m y m m h ( A1. ) st s v K s K v + + r + r K m h s s v v m ( A. 2) ( A. 3) ( A. 4) y K y ( A. 5),,,, s v h m y 0 The proft mamsng problem of an ndependent sawnwood or plywood producer e E s: ma Ve = π + π + ( w + d b l)( r + r ) w ( X )( + ) ( A. 6) st.. v e v e m s v v e s s v e v e K K v e ( A. 7) ( A. 8) Etended market clearng condtons The market clearng condtons for sawmll chps, pulpwood and sawlogs, respectvely, are: = ( rs + rvv e ) ( A. 9) h e E ( m + y ) = Xm ( A. 10) and ( s + v ) + ( + v e ) = X e E s (A.11) 243