The Japanese Subcontracting System, Competition and Asymmetric Equilibrium

Transcription

1 Workng Paper 10 The Japanese Subcontractng System, Competton and Asymmetrc Equlbrum Tatsuhko Naru 1, DongJoon Lee, and Tatsuya Kkutan 3 February Graduate School of Busness and Management, Kyoto Unversty Postgraduate Student, Graduate School of Economcs, Kyoto Unversty 3 Graduate School of Economcs, Kyoto Unversty

2 The Japanese Subcontractng System, Competton and Asymmetrc Equlbrum Tatsuhko Naru 1, DongJoon Lee, and Tatsuya Kkutan 3 Abstract Ths paper examnes two manufacturers competton wth ther own afflated suppler n duopoly. Each manufacturer purchases ntermedate goods from ts own afflated suppler. A cost reducton nvestment takes place before the ntermedate goods are produced by each suppler. We llustrate the asymmetrc equlbrum, n the sense that the ntermedate prces pad from manufacturers to supplers are dfferent. The asymmetrc equlbrum arses n the effcent envronments of the cost reducton nvestment. Under the asymmetrc equlbrum, a manufacturer settng a lower component prce has a compettve advantage. We also explan two nterestng results of a comparatve analyss. One s that the larger the demand becomes, the less output the advantageous manufacturer produces, whle the more output the dsadvantageous manufacturer produces. The other s that the worse the cost condton becomes, the more output the advantageous manufacturer produces, whle the less output the dsadvantageous manufacturer produces. JEL classfcaton: L13, L5, L6 Keywords: Japanese Subcontractng System; Asymmetrc Equlbrum; Compettve advantages 1 Graduate School of Busness and Management, Kyoto Unversty. E-mal:naru@ecno. kyoto-u.ac.p Postgraduate Student, Graduate School of Economcs, Kyoto Unversty. E-mal: 3 Graduate School of Economcs, Kyoto Unversty. E-mal: kkutan@ecno.kyoto-u.ac.p

3 1 Introducton Heterogeneous phenomena are wdely spread n our real world. Therefore, economsts have been studed and consdered as an mportant area of ther research. Emprcal studes also suggest that frms, whch have dfferent technologes, szes, capacty, and strateges, and so on, compete n the same ndustry. The phenomenon arses even wthn a frm. For example, some employees are facng on strong ncentves, whle the others are provded wth weak ncentves. To our regret, such dfferences have been manly taken as exogenous rather than endogenous varables n theoretcal economcs. So, ths paper addresses ths logcal gap n a duopoly. Ths paper deals wth a competton between two manufacturers wthn the Japanese subcontractng system. The Japanese subcontractng system s characterzed by a cooperatve relatonshp between the manufacturer and the suppler. In addton, the suppler's skll-and-ablty plays a greatly mportant role n the manufacturer s performance 4. The result of ths paper n the ven of earler contrbutons that have sought to explan ntrandustry heterogenety of frms n envronments where frms have dentcal opportunty sets. For nstance, Mlls (1990) demonstrates that heterogeneous plant szes can emerge n equlbrum capacty expanson of a growng ndustry, even though scale economes gve larger plants a unt cost advantage. Salop and Stgltz (1977) examne the consequences of mperfectly 4 See Asanuma (1985a, 1985b), Womack et al. (1990), Cusmano and Takesh (1991), and Nshguch (1994) for the Japanese subcontractng system. They show the mportance of a cooperatve relatonshp between automakers and supplers as well as of the supplers skll-and-ablty n the Japanese subcontractng system. In partcular, the suppler s skll-and-ablty n ths paper focuses on the cost reducton nvestment adoptng pror to producng the ntermedate. Each manufacturer provdes ts afflated suppler wth several supports to accumulate and upgrade the suppler s skll-and-ablty. We regard the manufacturer s support as a pecunary transfer, F, from the manufacturer to the suppler. 1

4 nformed consumers n a toursts and natves model, where some frms choose hgh prces and small scale by caterng to the poorly nformed consumer segment, whle other frms choose low prces and large scale as they attract well-nformed consumers. Under non convexty attrbuted to the moral hazard between prncpal and agent, the best response to other frms provdng strong ncentves can be to provde weak ncentves (Hermaln, 1994). Under the cost tradeoff between the fxed cost and the varable cost, f ther technology set s nsuffcently convex, heterogeneous equlbrum s attanable (Mlls and Smth, 1996) 5. They also showed that uncertanty about demand or costs favors the emergence of heterogeneous frms. From the socal welfare s standpont, equlbra tend to have too lttle heterogenety. Gal-Or (1999) consdered an olgopoly market competng wth dfferentated but competng products. If the demand between two products s moderately correlated, asymmetrc equlbrum may arse; one frm establsh ts own sales force, whle the other has ts ndependent sales force. He also showed that vertcal separaton s more lkely than vertcal ntegraton when ther products are hghly substtutable. Ths paper s summarzed as follows; ths paper shows that asymmetrc equlbrum, n the sense that the ntermedate goods (parts or component) prces pad from manufacturers to supplers are dfferent. The asymmetrc equlbrum arses n the effcent envronments of the cost reducton nvestment. Under the asymmetrc equlbrum, a manufacturer settng a lower component prce has a compettve advantage n duopoly. Ths paper also suggests two nterestng results of a comparatve analyss. One s that ncrease n demand makes the advantageous manufacturer, who sets the prce of the ntermedate to lower, reduce ts Cournot equlbrum output, whereas t nspres the dsadvantageous manufacturer to ncrease ts Cournot equlbrum 5 The model s smlar to our model. The man dfference between ours and thers s that the technology set n our model s contnuous, whle ther technology set has only two cases; hgh and low technology set.

5 output. The other s that the worse the cost condton becomes, the more output the advantageous manufacturer produces, whle the less output the dsadvantageous manufacturer does. The rest of ths paper s organzed as follows. Secton descrbes the model. In secton 3, t s shown that asymmetrc equlbrum exsts n a duopoly. Secton 4 characterzes equlbra and deals wth a comparatve analyss. Concludng remarks are n Secton 5. The Model Consder two manufacturers producng a homogeneous fnal product. The nverse demand functon s specfed as follows: p=a-b(q +q ) (1) where p s the prce of the fnal goods, a and b are postve constants, q are the output of each manufacturer. q and Each manufacturer purchases an ntermedate for the fnal good from ts own afflated suppler. We assume that a procurement contract between them conssts of a unt of the parts prce w and a pecunary transfer F. To put t precsely, when each manufacturer ka(k=,) offers the procurement contract to ts suppler ks(k=,), t proposes the contract consstng of the ntermedate prce w k and the pecunary transfer F k6. For smplcty, we regard the pecunary transfer as a lump-sum payment. A cost reducton nvestment takes place before the ntermedate goods are produced n ths model. The nvestment can decrease the margnal cost of the ntermedate. For a complete explanaton, suppose that the nvestment amount s x k. Then, the margnal cost becomes c-x k. The nvestment costs tx k / where t s a strctly postve constant. For smplcty, the cost of transformng the 6 See Naru et al. (009) for detals. 3

6 ntermedate goods nto the fnal goods s normalzed to zero. We also assume that each unt of the fnal good requres exactly one unt of the ntermedate goods. For the condtons that the S.O.C s satsfed and all varables are non-negatve, specfcally, these assumptons take the followng forms: Assumpton 1. bt 1. a 5bt Assumpton.. c [Fgure 1 here] A more detaled descrpton of the tmng of the three-stage game s gven as follows: In stage 1, each manufacturer offers a take-t-or-leave-t contract 7 to ts Keretsu suppler. In stage, each suppler determnes ts cost-reducng nvestment. Then, each manufacturer chooses hs output level n stage 3. The payments and the ntermedate goods are transferred between them accordng to the ntal contract between stage and stage 3. We focus on sub-game perfect equlbra for ths game. 3 The Analyss In the thrd stage, manufacturer A chooses an output level for the fnal product n order to maxmze ts proft gven the output of a rval frm. Then, frm A s maxmzaton problem s: Max ( a b( q q ) w ) q F, w. r. t. q,, 1,;. () A where the subscrpt A denote the manufacturer. 7 The manufacturer offers to ts suppler a procurement contract whch ncludes the prce of an ntermedate good w and a pecunary transfer. F 4

7 From the frst-order condton that π A / q =a-bq -bq -w =0, the reacton functon s gven by q (q )=(a-bq -w )/(b) The above two reacton functons yeld the equlbrum outputs as solutons to the thrd-stage game: q q ( a w w ) (3-1) 3 ( a w w ) (3-) 3 The prce for the fnal good and the manufacturers payoffs are obtaned by substtutng Eq. (3-1) and Eq. (3-) nto Eq. (1) and Eq. (): ( a w w ) p,, 1,;. (4-1) 3 ( a w w ) A F,, 1,;. (4-) 9b What s mportant to note from Eq. (4-1) s that q q ff w w Eq. (4-) show how the margnal procurement cost w affect ther output levels. Concsely speakng, the hgher frm A s margnal procurement cost w s, the more frm A s output q s, and vce versa. It s also worth notng from Eq. (3-1), Eq. (3-) and Eq. (4-1) that 5

8 q >0 w <(a+w )/ p>w q >0 w <(a+w )/ p>w The above equatons mply that the prce for the fnal product s hgher than the margnal procurement cost of each frm n order to have a postve output level. We turn then to the second stage game. In stage two, suppler S makes an nvestment for reducng ts margnal cost before the ntermedate goods are produced. Therefore, suppler S chooses the nvestment level x n order to maxmze ts proft. Suppler S s maxmzaton problem s ( w c x )( a w w ) tx Max S F, w. r. t. x (5) 3b Ths yelds the Cournot-Nash equlbrum nvestment level as solutons to the second-stage game: ( a w w ) x ( w, w ) (6-1) 3bt The second-order condton s gven by S w t 0. The margnal cost and the payoff for suppler S are obtaned by substtutng Eq. (6-1) nto suppler S s margnal cost functon and Eq. (5): (3bct a w w ) c ( w, w ) (3-6-) 3bt 6

9 ( a w w )( a w w 6bt( w c)) S ( w, w ) F. (3-6-3) 18b t From Eq. (6-1), the nvestment level x of frm s affected by frm s nvestment level x postvely, and vce versa. Concsely speakng, Eq. (6-1) mples that the hgher the ntermedate procurement prce w s, the less suppler S's nvestment amount x s, whle the more suppler S s s, and vce verse. We now turn to the frst stage game. Manufacturer A chooses ntermedate goods prce w and pecunary transfer F to maxmze ts own proft gven two constrant condtons that ts suppler S s proft and ntermedate goods prce w are nonnegatve. Manufacturer A s maxmzaton problem s Max A (a - w w ) 9b - F, w.r.t. w and F s.t. S (a - w - w )(a - w w 18b t 6bt(w - c)) F 0, and w 0 Note that the frst constrant condton s bndng. Therefore, the Eq. (7) can be reduced as follows: (a - w w ) Max A 9b s. t. w 0 (a - w w )(a - w w 6bt(w 18b t - c)), w.r.t. w The frst-order condtons 8 s gven by 8 A 4(bt -1)w The second-order condton 0 w 9b t (bt>1). s satsfed by the Assumpton 1 7

10 w A A w {6bct - a(bt w 0, and w ) 4(bt -1)w (bt )w } 0, 9b t 0 (7) It s worth notng that w A {6bct - a(bt ) (bt )w } 9b t f w =0. Therefore, the reacton functons can be rewrtten as: {6bct a(bt ) (bt )w } w (w ) f 6bct a(bt ) (bt )w (8-1) 4(bt -1) w (w ) 0 f 6bct a(bt ) (bt )w (8-) It s also worth notng that f6bct a(bt ) 0, Eq. (8-) should be satsfed for gven w 0. Therefore, the case corresponds to a corner soluton: w O w O 0 (9) where the superscrpt O denotes corner soluton. If, on the other hand, 6bct a(bt ) 0, the reacton functons are obtaned from Eq. (3-8-1), respectvely, as follows: 6bct - a(bt ) (1) w(w 0) 0 and 4(bt -1) w (bt ) w () 0, [ ] 1 ff bt[ ]. w 4(bt -1) w [Fgure here] Fgure shows the reacton curves n 1<bt< that support the varous equlbra. 8

11 Note that the ntersecton of two reacton curves s a symmetrc equlbrum but t s unstable. Two ponts, whch corresponds to {0,(6bct-a(bt+))/4(bt-1)} and {(6bct-a(bt+))/4(bt-1), 0}, of the vertcal and the horzontal axs support asymmetrc equlbra. If bt>, the equlbrum ntermedate goods prce s, therefore, the ntersecton of two reacton curves as follows: 6bct - a(bt ) w * w *. 5bt - Fgure 3-3 shows the reacton curves n bt> that support a symmetrc equlbrum. Note that the equlbrum of {6bct-a(bt+)}/(5bt-) s stable. [Fgure 3 here] Let us then see the case that bt=. We know that two reacton curves are completely dentcal. Therefore, mult equlbra occur n ths case. We turn to the case that 1<bt<. If w (w )=0, w {6bct-a(bt+)}/(bt+) should be satsfed. Ths lead to two asymmetrc equlbra n the sense that each manufacturer set ts ntermedate goods prce to be dfferent: w ** 0 6bct - a(bt ) w **, 4(bt 1), 1, ;. We also obtan another equlbrum that two reacton curves, w (w ) and w (w ), ntersect at w =w ={6btc-a(bt+)}/(5bt+) 9. Puttng what we mentoned above together, when 1<bt<, there exst three 9 It s worth notng that f bt<, {6btc-a(bt+)}/4(bt-1) {6btc-a(bt+)}/(bt+). 9

12 Cournot-Nash equlbra. 6bct - a(bt ) w * w * (5bt ) 6bct -a(bt ) (w * *, w * *) 0, 4(bt 1) 6bct -a(bt ) (w * *, w * *), 0 4(bt 1) (10-1) (10- ) (10-3) However, t s worth notng that the symmetrc equlbrum descrbed by Eq. (3-10-1) s unstable n the nterval that 1<bt<. Proposton 1: Gven Assumpton 1 and Assumpton, 1. If 6bct a(bt ) 0, there exsts a corner soluton, w O=w O=0.. If 6bct a(bt ) 0, (a) There exsts a symmetrc equlbrum w *=w *={6bct-a(bt+)}/(5bt-) when bt>. (b) There exst mult equlbra when bt=. (c) When 1<bt<, there exst two stable asymmetrc equlbra, 6bct - a(bt ) 6bct - a(bt ) (w **, w **), 0 and (w **, w **) 0, 4(bt 1) 4(bt 1). The regons that support asymmetrc equlbra, 1<bt<, means the effcent envronments of the nvestment. To put t concsely, as b s the slope of demand curve and t s the effcency parameter of the nvestment, the asymmetrc equlbra are lkely to happen when the slope of demand s gentle or the effcency parameter of the nvestment s small. 4 Comparatve Analyss n Equlbra In the prevous secton, we llustrated that the asymmetrc equlbra arse n 10

13 1<bt<. To begn wth, we analyze comparatve statcs n equbra. 4.1 Corner Soluton As we explaned n Proposton 1, f 6bct a(bt ) 0, the equlbrum ntermedate goods prces are w O=w O=0. Substtutng them nto Eq. (4-1), Eq. (4-), Eq. (4-3), Eq. (6-1), Eq. (6-), and Eq. (6-3), we obtan equlbrum nvestment amount, equlbrum margnal cost, equlbrum output amount, equlbrum fnal goods prce, equlbrum payoff, and equlbrum pecunary transfer, respectvely c x O O O q O x a/3bt (11-1) O O c (3bct a)/3bt (11-) q a/3b (11-3) p O a/3b (11-4) O O a{(bt 1)a - 6bct} A A (11-5) 18b t O a(6bct a) F (11-6) 18b t O F Now, we easly check that the optmal values of all varables obtaned above are non-negatve under Assumpton 1, Assumpton, and the condton for the corner soluton whch s 6bct<a(bt+). From Assumpton, n fact, t can be proved to be c O=c O>0. Note that (bt+)<(bt+1). Then, t s obvous that O A O A 0 from the condton that 6bct<a(bt+). We now turn to the comparatve statcs. The parameter a shfts demand up and down. Increase n a demand (a) nduces supplers to make more nvestments. It also causes the prce of the fnal goods to ncrease. More nvestments wll nduce manufacturers to produce more outputs and to gan more payoffs. Suppose that the parameter of cost (c) shfts upward. The rse n the parameter of cost (c) wll reduce ther payoffs as a result of ncrements of 11

14 ther pecunary transfer. However, note that t does not drectly affect equlbrum nvestment level, equlbrum output level, and prce of fnal good. 4. Symmetrc Equlbrum Under the condtons that 6bct>a(bt+) and bt>, Cournot equlbrum ntermedate goods prce s 6bct a(bt ) w * w * (1-1) 5bt Substtutng t nto Eq. (4-1), Eq. (4-), Eq. (4-3), Eq. (6-1), Eq. (6-), and Eq. (6-3), we have equlbrum nvestment level, equlbrum margnal producton costs, equlbrum output amount, equlbrum fnal goods prce, equlbrum payoff, and equlbrum pecunary transfer, respectvely (a c) x* x * 5bt (1-) 5bct a c* c * 5bt (1-3) t(a c) q* q * 5bt (1-4) {(bt )a 4bct} p* p * 5bt (1-5) t(bt 1)(a c) * * (5bt ) (1-6) t(bt 1)( a c) A* A* (5bt ) (1-7) Now, we can easly check that the optmal values of all varables obtaned above are non-negatve under Assumpton 1 and Assumpton. Let us see the 1

15 effect of the demand parameter (a) on all the optmal varables. Increasng the demand parameter (a) wll reduce the ntermedate goods prce and the margnal cost. If there s an ncreased demand for the fnal goods, each manufacturer wll ncrease ts output n order to acqure more profts. It nduces each suppler to ncrease the cost reducton nvestment. The ncremental nvestment results n decreasng n the margnal cost and the ntermedate goods prce. From the fact that c *-w *=bt(a-c)/(5bt-)>0, each manufacturer sets the ntermedate goods prce to be lower than the margnal cost. Increasng the demand parameter (a) wll ncrease output amount, nvestment level, and payoff. Next, suppose that the parameter of cost (c) shfts upward. It s also obvous that ncrease n cost parameter (c) wll decrease output amount, nvestment level, and payoff. Furthermore, ncreasng the demand parameter (a) and the cost parameter (c) wll rse up the fnal goods prce. 4.3 Asymmetrc Equlbrum Under the condtons that 6bct>a(bt+) and 1<bt<, there exst two stable asymmetrc equlbra. Substtutng t nto Eq. (4-1), Eq. (4-), Eq. (4-3), Eq. (6-1), Eq. (6-), and Eq. (6-3), In equlbrum, the ntermedate goods prce, the nvestment levels, the margnal producton costs, the output amounts, the fnal goods prce, manufacturers payoffs, and pecunary transfers s gven by w 6bct a(bt ) ** (13-1) 4(bt 1) w ** 0 (13-) x ** x a c ** (13-3) (bt 1) bct a( bt) (13-4) 4bt(bt 1) 13

16 c bct a ** (13-5) (bt 1) ** c q a( bt) bct(3 bt) (13-6) 4bt(bt 1) t(a c) ** (13-7) (bt 1) ** q bct a( bt) (13-8) 4b(bt 1) bct a( bt) p ** (13-9) 4(bt 1) t(a c) A ** (13-10) 8(bt 1) {bct ( bt)a}{bt(5 bt)c ( bt)(bt 1)a} A ** (13-11) 3b t(bt 1) t(bt 1)(a c) F ** (13-1) 8(bt 1) {bct ( bt)a}{bt(4bt 5) ( bt)a} F ** (13-13) 3b t(bt 1) Now, we can easly check that all optmal varables obtaned above are non-negatve under Assumpton 1, Assumpton, and the condton for asymmetrc equbra, 6bct>a(bt+) 10. When manufacturer A sets the ntermedate goods prce to be zero and manufacturer A sets t to be postve, the characterstcs of the asymmetrc equlbrum can be descrbe as follows. Proposton : Gven 1<bt<, 6bct>a(bt+), Assumpton 1, and Assumpton, the asymmetrc equlbra are characterzed by; 1. x **>x **. q **>q ** 10 See Appendx for a detal. 14

17 3. c **>w ** and c **>w **=0 4. * ** A * A Proof) Under the condtons that 6btc>(bt+)a and 1<bt<, we have x **-x **={6btc-(bt+)a}/4bt(bt-1)>0 (14-1) q **-q **={6btc-(bt+)a}/4b(bt-1)>0 (14-) c **-w **={bt(a-c)+a}/4bt(bt-1)>0 11 (14-3) Furthermore, under a>c, note that bt(3-bt)c-(+bt-b t )a={6btc-(bt+)a}+b t (a-c)>0. Then, we have 6btc - (bt )a} bt(3- bt)c - ( bt - b t )a} A **- A ** 0 (14-4) 3b t(bt -1) In the end, manufacturer A who sets the ntermedate goods prce to be zero enoys more proft, output, and nvestment than those of manufacturer A who sets the ntermedate goods prce to be postve 1. Let us see the effect of some parameters on the asymmetrc equlbra values. Suppose that the parameter of demand (a) shfts upward. Manufacturer A wth a postve ntermedate goods prce wll ncrease ts output amount through settng the ntermedate goods prce down. Increasng the output amount nduces ts suppler S to make more aggressvely n cost reducton nvestment. More nvestment not only wll result n the margnal producton cost to come 11 It s obvous that c **>w **=0. 1 Note that c**<c**. 15

18 down but also that manufacturer A s payoff to ncrease. Unlke manufacturer A s postve response to demand parameter s ncrease, manufacturer A wth a zero ntermedate goods prce reduces ts Cournot equlbrum output amount. Note that manufacturer A and manufacturer A are n Cournot competton by changng ther ntermedate goods prces. When demand ncreases, manufacturer A can not decrease ts ntermedate goods prce down because t already set a zero. Another mportant thng s that ncrease n demand parameter (a) decreases the prce for fnal goods. Secondly, let us see the effect of cost condton (c) on all varables. Suppose that cost condton (c) shfts upward. It wll ncrease the ntermedate goods prce for manufacturer A. Therefore, t wll decrease Cournot equlbrum output amount for manufacturer A. It wll nduce ts suppler S not only to decrease nvestment level but also to ncrease margnal producton cost. In the end, the payoff for manufacturer A wll decrease. Unlke decreasng Cournot equlbrum output as manufacturer A s response to worse cost condton, manufacturer A wth a zero ntermedate goods prce wll ncrease ts Cournot equlbrum output level because t takes advantage poston n Cournot competton wth the rval frm A. Increasng the output amount nduces ts suppler S to make more aggressvely n cost reducton nvestment. More nvestment wll result n not only that the margnal producton cost wll come down but also that manufacturer A s payoff wll ncrease. It s also nterestng to have the postve effect of cost condton (c) on output of manufacturer A. However, note that ncreasng the cost condton (c) wll reduce the total output amounts and wll ncrease the fnal goods prce. Hybrd cars have varous advantages over conventonal vehcles, such as fuel effcency, low cost per a mle, and envronmental benefts. However, the hybrd cars also have dsadvantage over the conventonal automobles. From the manufacturer s pont of vew, t takes hgh cost for manufacturer to produce the hybrd cars. The same can be sad for the luxury cars, such as Lexus whch s the most expensve among the Japanese automobles. In ths case, our model 16

19 proposes that the advantageous frm produces more hybrd cars and more luxury cars than the dsadvantageous frm produces. Let us see a more detaled economc phenomenon. From 005 to 008, Toyota s market strategy s clearly dfferent from Honda s market strategy n the domestc passenger car market. Totally, the market sze n the domestc market has been decreasng, especally plunged n 008 by the global fnancal crss caused by a collapse of the US sub-prme mortgage and the reversal of the housng boom. In the mddle of decreasng the market sze, the market share of the normal passenger car 13 ncluded the hybrd car, the luxury car, and no lght car for Toyota has been ncreasng, whle the market share of the lght car for Toyota has been decreasng rapdly from 005 to 008. The reverse can be sad for Honda. Fgure 4 and Fgure 5 suffcently support the above phenomenon. [Fgure 4 and 5 here] 5 Concludng Remarks Ths paper analyzed Cournot competton between homogeneous manufacturers wth ther own Keretsu suppler. Ths paper dealt wth a model n whch a cost reducton nvestment took place before the ntermedate goods was produced. We llustrated that asymmetrc equlbrum arose n the sense that two manufacturers set ther ntermedate goods prces to be dfferently. It had been llustrated that the exstence of asymmetrc equlbrum by usng trade-off relatonshp between fxed cost and varable cost (Mlls and Smth, 1996). Ther technology choce s selected one of the alternatves. However, our asymmetrc equlbrum s generated n the contnuous technology set. They obtaned ths result wth nsuffcently convex technology set and random varable, whle we acheved t wth suffcently convex component prce set and contnuous varable. 13 The Japan Automoble Dealer Assocaton classfes the passenger car nto two categores; normal passenger car and lght passenger car. 17

20 The afflated relatonshp between a manufacturer and a suppler has been regarded as a hybrd organzaton between vertcal ntegraton and market. It has played a greatly mportant role n the rapd growth perods of the Japanese economy. So, ths paper focused on a theoretcal model lnked wth Keretsu procurement. In the model, we llustrated that asymmetrc equlbrum arose n the sense that the ntermedate goods prces pad from manufacturers to supplers was dfferent. It seems to explan the performance dfferences between Japanese automakers n the domestc market. We also explaned two nterestng results to comparatve statc analyss. One was that the larger the demand becomes, the less output amount the advantageous manufacturer produces, whle the more output amount the dsadvantageous manufacturer produces. The other was that the worse the cost condton becomes, the more output the advantageous manufacturer produces, whle the less output the dsadvantageous manufacturer produces. Appendx It wll be explaned that all parameters of asymmetrc equlbrum are non-negatve, herenafter, under the condtons that (1) 1<bt, () <a/c, (3) 6bct>(bt+)a, and (4) bt<. It wll be proved that a/c<bt, to begn wth, under the condtons (1) and (3). 0<bt(bt-1) s satsfed under the condton (1). Let s add 6bt to the equaton and dvde t nto (bt+). Rearrangng t, we obtan 6bt/(bt+)<bt. Under the condton (3), therefore, ths leads a 6bct bt (A-1) c ( bt ) Secondly, t wll be proved that a/c<bt/(-bt) s satsfed, under the condtons (1), (4), and (A-1). 1<bt< leads to (-bt)<1. Rearrangng and Multplyng t by bt, we obtan bt<bt/(-bt). From Assumpton 1 and bt<bt/(-bt), t s proved to be 18

21 a bt bct (A-) c ( bt) Thrdly, t wll be proved that a/c>bt(3-bt)/(-bt) s satsfed, under the condtons (1), (). Suppose that x=bt and f(x)=a/c. Then, ths leads to f(x)=x(3-x)/(-x). Dfferentatng t wth respect to x, ths s easly seen to be f ( x) 4( x 1)( x 3). x ( x) The functon f(x) s decreasng functon n the nterval between 1<x<. Therefore, the value of the functon f(x) has, when x=1. From the condton (), therefore, t s obvous a c bt(3 bt) (A-3) ( bt) Lastly, t wll be proved that all parameters, Eq. (13), of asymmetrc equlbra are non-negatve on the bass of these results. It s manfest that the component prces (w **,w **; w **>0=w **) are non-negatve from the condton (3). Cost reducton nvestments (x **,x **; x **>x **>0) s non-negatve from the condtons (1), (), and Eq. (3-14-1). Margnal costs are non-negatve from the condtons Eq. (A-1) and (A-). Quanttes (q **,q **; q **>q **>0) are apparent from the condtons (1), (), and Eq. (14-). The prce of fnal good s non-negatve under the condton Eq. (A-). Manufacturers payoffs * * * 0 are non-negatve from the condtons (1), (), and Eq. (14-1). A * A It s obvously proved that all varables are non-negatve. 19

22 Reference Asanuma, B. (1985a), The Organzaton of Parts Purchases n the Japanese Automotve Industry, Japanese Economc Studes, Summer pp Asanuma, B. (1985b), The Contractual Practce for Parts Supply n the Japanese Automotve Industry, Japanese Economc Studes, Summer pp Baker, G. P., R. Gbbons, and K. J. Murphy (00), Relatonal Contracts and the Theory of the Frm, Quarterly Journal of Economcs, Vol. 117, pp Bettgnes, J. (006), Product Market Competton and Boundares of the Frm, Canadan Journal of Economcs, Vol. 39, pp Bonanno, G. and J. Vckers, (1988), Vertcal Separaton, Journal of Industral Economcs, Vol. 36, pp Brander, J and B. Spencer (1983), Strategc commtment wth R & D: the symmetrc case, Bell Journal of Economcs, Vol. 14, pp Chen, YongMn (001), On the Vertcal Mergers and ther Compettve Effects, Rand Journal of Economcs, Vol. 3, pp Chen, YongMn (005), Vertcal Dsntegraton, Journal of Economcs & Management Strategy, Vol. 14, pp Cusmano, M. and A. Takesh (1991), Suppler Relatons and Management: A Survey of Japanese, Japanese-Transplant, and U.S. Auto Plants, Strategc Management Journal, Vol. 1, pp Dyer, Jeffrey H. (1996), Does Governance Matter? Keretsu Allances and Asset Specfcty As sources of Japanese Compettve Advantage Organzaton Scence, Vol. 7, pp Economdes, Ncholas and Steven C. Salop (199), Competton and Integraton among Complements, and Network Market, Journal of Industral Economcs, Vol. 40, pp Ern, Anderson (1985), The Salesperson as outsde Agent or Employee: A 0

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28 market share 60% Fgure 4. Market Shares for the Passenger Car except the Lght Car 50% 40% 30% Honda Nssan Toyota 0% 10% 0% Source: Japan Automoble Dealers Assocaton market share 60% 50% 40% 30% 0% 10% 0% Fgure 5. Market Shares for the Lght Car Honda Nssan Toyota Source: Japan Automoble Dealers Assocaton 6