First-Mover and Second-Mover Advantages in a Bilateral Duopoly*

Transcription

1 35 The Korean Economc Revew Volume 33 Number 1 Summer Frst-Mover and Second-Mover Advantages n a Blateral Duooly DongJoon Lee Kangsk Cho Kyuchan Hwang Ths study examnes a frst-mover and a second-mover advantage n a vertcal structure n whch each ustream frm trades wth an exclusve retaler and downstream retalers move seuentally. We rovde two man clams. One s that n Cournot (Bertrand cometton the leader s ustream frm sets the nut rce eual to ts margnal cost (eual to ts margnal cost whle the follower s ustream frm sets the nut rce below ts margnal cost (above ts margnal cost. The other s that the follower s (leader s ustream frm enoys hgher rofts than the leader s (follower s ustream frm n Cournot (Bertrand cometton. JEL Classfcaton: D43 L13 L14 Keywords: Frst- and Second-mover Advantage Two-art Tarffs Vertcal Structure 8 I. Introducton We have robably heard of the old roverbs The early brd gets the worm and The second mouse gets the cheese. What do those have to do wth an economc Receved: May Revsed: Aug Acceted: Set We are esecally ndebted to two anonymous referees for careful and constructve comments. The frst author acknowledges that ths research s suorted by Jaan Socety for the Promoton of Scence Grant-n-Ad for Scentfc Research (B Grant Number 15H03396 and Scentfc Research (C 15K The corresondng author also acknowledges that ths work was suorted by the Natonal Research Foundaton of Korea Grant funded by the Korean Government (NRF-014S1A3A Kyuchan Hwang acknowledges a grant from Toka Gakuen Unversty n 015. Frst Author Professor Faculty of Commerce Nagoya Unversty of Commerce and Busness 4-4 Sagamne Komenok-cho Nssn-sh Ach Jaan. Tel: Fax: E-mal: dongoon@nucba.ac. Corresondng and Second Author Professor Graduate School of Internatonal Studes Pusan Natonal Unversty Busandaehak-ro 63 beon-gl Geumeong-gu Pusan Reublc of Korea. Tel: Fax: E-mal: chonu@usan.ac.kr Thrd Author Professor Faculty of Busness Admnstraton Toka Gakuen Unversty Myosh-sh Ach Jaan Tel: Fax: E-mal: hwang@tokagakuen-u.ac.

2 36 The Korean Economc Revew Volume 33 Number 1 Summer 017 theory? Your answer s the frst- and the second-mover advantage n nne cases out of ten. The rme examles of a successful frst mover are Coca-cola ebay Kleenex Kellogg and P&G s dsosable daers. However beng a frst-mover s not a guarantee of a sustanable comettve advantage. Sometmes followers were able to outmaneuver the frst movers and walk away wth a larger market share. The examles of the frst-movers whose market shares were subseuently eroded by the second movers are Nntendo Amazon Google Facebook -hone Mcrosoft Youtube and so on. Durng the last 30 years the arorateness of the eulbrum concet Cournot (Bertrand and Stackelberg n classcal olgooly theory was dealt n varous comettve settngs and has been a maor revval. Ths revson conssts of two man strands. One strand comares the eulbrum ayoffs of the two frms under erfect nformaton. Ths strand ncludes Gal-or (1985 and Dowrck ( From the vewont of frms the strategc decson about whether to move early or late s a very mortant toc. A conventonal wsdom about the frst- and the second-mover advantage s that n a seuental move game the frm who moves frst (leader earns hgher (lower rofts than the frm who moves second (follower f the reacton functons are downwards (uwards slong. The second strand deals wth the ssue of endogenous tmng. In other words the order of move between two gven layers should reflect each layer own ntrnsc ncentve wthout exogenously determned tmng structure. Ths strand ncludes Hamlton and Slutsky (1990 Amr (1995 and Amr and Steanova (006. Ths aer s related to the frst strand and extends the frst- and second-mover advantages n a vertcally related market n whch each ustream frm trades wth ts exclusve downstream frm va two-art tarff contract. Many lteratures n ndustral organzaton have generally suosed that n vertcal searaton each ustream frm charges the franchse fee that can extract the full roft of ts exclusve downstream frm. 3 It s also rare that ustream frms (roducers sell drectly to consumers. Most commonly they sell to dstrbutors who then sell to consumers. Therefore we revsted the frst- and the second-mover advantage n a vertcal structure. Most relatonshs between roducers and dstrbutors consst of sohstcated contracts usng more than the smle lnear rcng rules. The sohstcated contracts are referred as to vertcal restrants. Those are not only to set 1 Albaek (1990 Malath (1993 and Daughety and Renganum (1994 extended ther models to cost uncertanty or sgnalng frameworks by addng an nformatonal trade-off to leader-follower roles. Many studes are secfc olgoolstc settngs. They nclude Boyer and Moreaux (1987 Robson (1990 Deneckere and Kovenock (199 van Damme and Hurkens ( Amr and Grlo (1999 Amr et al. (1999 among others. 3 See for detals Rey and Stgltz ( Rey and Trole (1986 Bonnano and Vckers (1988 and Sagg and Vettas (00 and so on. The examle of exclusve dealng can be seen n car dealersh franchse ndustry and hgh ualty brand-roducts dstrbuton.

3 DongJoon Lee Kangsk Cho Kyuchan Hwang: Frst-Mover and Second-Mover Advantages 37 more general terms of ayments for examle two-art tarffs uantty dscounts and royaltes but also to nclude terms lmtng dstrbutor s decsons for examle resale rce mantenance exclusve dealng and exclusve terrtores. Notably ths aer s the frst study to consder the frst- and the second-mover advantage n a vertcally related duooly. Our study has two related obectves. One s to extend the conventonal model to vertcal structure. The other s to consder whether the classcal results can be sustaned n a vertcal structure or not. The man results are as follows. In contrast to the canoncal results n a one-ter market we fnd that the ustream frm whose downstream frm moves frst (leader earns hgher (lower rofts than the frm whose downstream frm moves second (follower when downstream frms comete n rce (uantty. The ntuton of the result can be exlaned as follows. Let us see the downstream cometton. It s straghtforward that the frst-mover (leader sets larger uantty than the second-mover (follower f the wholesale rces are eual. Ths s the conventonal result. We now turn to the ustream cometton. Notce that each ustream frm can extract all of the rofts from ts downstream frm va two-art tarff. Antcatng downstream cometton the follower s ustream frm sets the wholesale rce as low as t can for ts downstream frm to stand at advantage over downstream cometton. The leader s ustream frm can also do so. In ths case market cometton s so ferce. In the end both frms rofts are lower than those n eulbrum n whch the wholesale rce for follower s lower than that for leader. The remander of ths aer s organzed as follows. Secton descrbes the model. In Secton 3 we consder the benchmark case of the smultaneous-move uantty and rce games. Secton 4 consders the seuental-move uantty and rce games. Fnally the concludng remarks aear n Secton 5. II. The Model There are two dfferentated goods n a market. We have a reresentatve consumer who maxmzes { U( - å = 1 : Î R + } where s the rce good and U ( s a dfferentally strctly concave utlty functon on R + whch s dfferentally strctly monotone n a nonemty bounded regon Q. Let = ( and = ( denote the vector of the uanttes and the retal rces resectvely. A reresentatve consumer by maxmzng U( - å = 1 gves rse to an nverse demand functon = ( = 1 whch s twce contnuously dfferentable n the nteror of Q. Inverse demands wll be downward slong < 0 and the cross effect < 0 ¹. 4 We assume that the nverse demand 4 We assume that the goods are substtutes.

4 38 The Korean Economc Revew Volume 33 Number 1 Summer 017 functon = ( can be nverted to yeld a drect demand functon = ( = 1. The bounded regon n rce sace where demands are ostve wll be denoted by P. Drect demands are gong to be downward slong < 0 and 0 < ¹. We assume that the own effect s larger than the cross effect. > > 0 and > > 0 = 1 ¹. (A1 Consder a manufacturng duooly n whch each ustream frm (.e. manufacturer sells ts roduct to ts own downstream frm (.e. retaler. The nverse and drect demand functon for downstream frm are = ( and = ( ; = 1 ¹ (1 where and are the uanttes and and are the retal rces charged for roduct and resectvely. The margnal cost for each ustream frm s c. For smlcty there are no retalng costs. In addton we assume that each ustream frm rohbts ts downstream frm from tradng and dstrbutng the roduct roduced by the rval ustream frm and that only one downstream frm serves a gven ustream frm. We ost a three-stage game. At stage one each ustream frm offers a contract to ts own downstream frm. The contract s comosed of two varables: wholesale rce w and franchse fee F. At stage two downstream frm (leader sets uantty (retal rce n the seuental move uantty (rce game. Fnally at stage three downstream frm (follower sets uantty (retal rce n the seuental move uantty (rce game. 5 III. Benchmark As a benchmark we frst consder Cournot (Bertrand cometton n whch each downstream frm smultaneously sets a uantty (rce. At stage two gven the wholesale rce w and rval downstream frm s 5 Gven the market structure one could magne all sorts of dfferent varants of seuental-move games. For examle ( ustream frms move seuentally frst then downstream frms move seuentally afterwards ( ustream frm and downstream frm make ther moves then ustream frm and downstream frm move seuentally afterwards ( t may be a beneft for an ustream frm to move frst (second as long as downstream cometton s à la Cournot (Bertrand. Whle there are stuatons where dfferent tmng games may have another soluton t s left to future research to develo the analyss more generally.

5 DongJoon Lee Kangsk Cho Kyuchan Hwang: Frst-Mover and Second-Mover Advantages 39 uantty (rce downstream frm sets the uantty (rce so as to maxmze ts roft. Downstream frm s maxmzaton roblems are as follows: max ( w = [ ( - w ] - F ; = 1 ¹. max ( w = [ - w ] ( - F ; = 1 ¹. where s the retal rce s the uantty and F s the franchse fee. Note that uantty ( s ndeendent of F. The frst-order condton for downstream frm s exressed as follows: ( = ( - w + = 0 ( ( = ( + - w = 0 = 1 ¹. (-1 = 1 ¹. (- We assume that the second-order condtons < 0 ( < 0 are satsfed. Solvng E. (-1 and (- we obtan the unue eulbrum uanttes ˆ ˆ (rces ( ˆ ˆ where the suerscrt ^ denotes the eulbrum at stage two. Let w = ( w w denote the vector of the wholesale rces set by ustream frms at stage one. To understand how w = ( w w affect = ( and = ( let us see the total dfferental of E. (-1 and (-. Dfferentatng E. (-1 and (- we have é ù ú ú é d ù é ù ú d ú = ú. ú ë û ë û ú ë û (3-1 é ù ú ú é d ù é ù ú d ú = ú. ú ë û ë û ú ë û (3- For = 1 ¹ we make the followng assumton. ( ( + < 0 for all n the nteror of Q

6 40 The Korean Economc Revew Volume 33 Number 1 Summer 017 = 1 ¹. (A ( ( + < 0 for all n the nteror of = 1 ¹. (A3 Ths assumton ensures that Cournot reacton functons have sloe less than one n absolute value. Therefore there exsts unue Cournot eulbrum. Note that the assumton does not ut any restrcton on the sgn of the sloe of the reacton functons. 6 Under (A and (A3 the stablty condtons of the eulbrum are satsfed by D D C B ( ( ( ( = - > 0 ( ( ( ( = - > 0 where the suerscrts C and B resectvely denote smultaneous move Cournot and Bertrand game. We have the followng results. d 0 < d > 0 d > 0 d < 0 d < 0 d < 0 d 0 < d < 0. At stage one ustream frm s maxmzaton roblems are as follows: max ˆ w ( ( F u w w = w - c + F s. t. = ( - w ˆ - F ³ 0 and w ³ 0 and max w ( ( F u w w = w - c + F ( ˆ s. t = - w - F ³ 0 and w ³ See for detal Kolstad and Mathesen (1987.

7 DongJoon Lee Kangsk Cho Kyuchan Hwang: Frst-Mover and Second-Mover Advantages 41 Note that the frst constrant s bndng. Therefore we rewrte the maxmzaton roblems as follows: and max u ( w w = [ ( ˆ ( w w ˆ ( w w -c] ˆ ( w w w F s. t. w ³ 0 max u ( w w = [ ˆ ( w w - c] ( ˆ ( w w ˆ ( w w w s. t. w ³ 0 The frst-order condtons are u é ˆ ˆ ˆ ˆ ù ˆ = + ú + - c = 0 ˆ ˆ ë úû u ( ˆ ˆ ˆ ˆ é ù = - c + ú + = ˆ ˆ 0 ë úû = 1 ¹ (4-1 = 1 ¹. (4- We assume that the second-order condton < 0 s satsfed. Solvng E. (4-1 C C C and (4- we obtan the eulbrum wholesale rce w = ( w w and B B B w = ( w w resectvely. u IV. Seuental Move Game 4.1. Seuental Move Quantty Game We now turn to the seuental move uantty game n whch downstream frm (Leader moves at stage two and downstream frm (Follower moves at stage three. At stage three gven the wholesale rce w and ts rval s uantty downstream frm sets the uantty so as to maxmze ts roft. Downstream frm s maxmzaton roblem s as follows: max ( w = [ ( - w ] - F ; = 1 ¹. 1 Note that the uantty s ndeendent of downstream frm s exressed as follows: F. The frst-order condton for

8 4 The Korean Economc Revew Volume 33 Number 1 Summer 017 ( = ( - w + = 0 = 1 ¹. (5 It s assumed that the second-order condton = + < 0 s satsfed. Solvng E. (5 we obtan the eulbrum uantty = ( where the suerscrt denotes the eulbrum of the seuental move game. To see how change n affects let us see the total dfferental of E. (5. Dfferentatng E. (5 we have é ù é ù ú ú ë úû ë úû ( ( ( ( + d = + d. (6 To guarantee the sng of the comaratve statc we need a further assumton. < 0 > 0 < 0 and < 0 = 1 ¹. (A4 These assumtons mean that both roducts are substtutes. 7 In addton to guarantee the stablty condton for a seuental move game we make an addtonal assumton. = ( > c. (A5 Ths assumton means that the eulbrum rce s hgher than the margnal cost of leader. Duooly market wll be sustaned by the assumton. From the second-order condton and (A4 we obtan that é ( ( ù + ú d ú = 0 d ( ( ú <. (7 + ú ë ú û At stage two gven the wholesale rces ( w w downstream frm sets the uantty so as to maxmze ts roft. Downstream frm s maxmzaton roblem s as follows: 7 If the sgn of the cross dervatves s reverse both roducts are comlements.

9 DongJoon Lee Kangsk Cho Kyuchan Hwang: Frst-Mover and Second-Mover Advantages 43 max ( w = [ ( - w ] - F ; = 1 ¹. The frst-order condton for downstream frm s exressed as follows: é ù = ( - w ú = ë úû = 1 ¹. (8 Assume that the second-order condton < 0 s satsfed. Solvng E. (8 we obtan the eulbrum uantty at stage two. Let w = ( w w denote the vector of the wholesale rces set by ustream frms at stage one. To understand how w = ( w w affect = ( let us see the total dfferental of E. (5 and E. (8. Dfferentatng E. (5 and E. (8 we have é ù ú ú é d ù é ù ú d ú = ú. (9 ú ë û ë û ú ë û Under (A the stablty condton of the eulbrum s satsfed by ( ( ( ( D = - > 0. We have d d ( / = < 0. (10-1 D ( / = - > 0. (10- D ( / d = - > 0. (10-3 D ( / d = < 0. (10-4 D At stage one gven the wholesale rce w and the franchse fee F ustream

10 44 The Korean Economc Revew Volume 33 Number 1 Summer 017 frm sets the wholesale rce w and the franchse fee ts roft. It s maxmzaton roblem s as follows: F so as to maxmze w F u = ( w - c + F max s. t. = ( - w - F ³ 0 and w ³ 0. Note that the frst constrant s bndng. Therefore we rewrte the maxmzaton roblem as follows: max w u = [ ( ( ( w w ( w w - c ] ( ( w w s. t. w ³ 0. The frst-order condton s u é ù = + ( c 0 ú + - =. (11 ë úû We assume that the second-order condton < 0 s satsfed. On the other hand ustream frm s maxmzaton roblem s as follows: u w F u = w - c + F max ( s. t. = ( - w - F ³ 0 and w ³ 0. Note that the frst constrant s bndng. Therefore we rewrte t as follows: w max u = [ ( ( ( w w ( w w -c] s. t. w ³ 0. The frst-order condton s 8 8 For the comaratve statc on w and w n eulbrum we need some addtonal assumtons. Wthout any addtonal assumton we consder t wth a lnear demand. Suose a lnear demand functon as = a- - d where s rce s uantty a > 0 and dî (01 whch reresents the degree of roduct dfferentaton. Dfferentatng ustream frm s and s maxmzaton roblem wth resect to w and w resectvely we obtan w = 4 4 [ c( 8-6d + d - d ( 4 - d - d a- ] / ( 16-16d + 3d and ( c - w / ( - d = 0. Therefore w s decreasng n w and w s ndeendent on w.

11 DongJoon Lee Kangsk Cho Kyuchan Hwang: Frst-Mover and Second-Mover Advantages 45 u é ù = + ( c 0 ú + - =. (1 ë úû We assume that the second-order condton < 0 s satsfed. Solvng E. (11 C C C and E. (1 we obtan the eulbrum wholesale rce w = ( w w where the suerscrt C denotes a seuental move uantty game. Notng E. (5 E. (1 can be changed as follows: u é ù = - w + ( w c ú ë û u = ( w - c + = 0. From the above euaton we have the followng result: w C - c = - < 0. (13 In the end we have that w < c. Notng E. (7 E. (11 can be changed as follows: C u ( w w é ù = - w + + ú + ( w - c ë úû C = ( w - c = 0. In the end we have w C = c. (14 We summarze these fndngs n Lemma 1. Lemma 1: Consder a vertcal duooly where one downstream frm (the leader chooses ts uantty before the other downstream frm (the follower. At the sub-game erfect eulbrum of ths three stage game The follower s ustream frm sets the wholesale

12 46 The Korean Economc Revew Volume 33 Number 1 Summer 017 rce below ts margnal cost whle the leader s ustream frm sets the wholesale rce eual to ts margnal cost. Prooston 1: The follower s ustream frm enoys hgher rofts than the leader s ustream frm does. Proof: Let us check the frst order condton for the ustream frm when w = c. Rearrangng E. (11 yelds C u é ù = - w + ( w c ú ë û C Notng that w = c the frst-term and the second-term of the rght-hand sde of the above euaton are eual to zero. We also know that the sgn of the thrd-term s negatve from E. (10-3 and < 0. The frst-order condton that E. (11 < 0 C C when w = c s satsfed. Therefore we obtan the result that w < c at eulbrum. In the end u C ( C C ( C w < u w. Q.E.D. The ntuton behnd Prooston 1 can be exlaned as follows. Let us see the downstream cometton. It s straghtforward that the frst-mover (leader sets larger uantty than the second-mover (follower f the wholesale rces are eual. Ths s the conventonal result. We now turn to the ustream cometton. Notce that each ustream frm can extract all of the rofts from ts downstream frm va two-art tarff. Antcatng downstream cometton the follower s ustream frm sets the wholesale rce as low as t can for ts downstream frm to stand at advantage over downstream cometton. The leader s ustream frm can also do so. In ths case market cometton s so ferce. In the end both frms rofts are lower than those n eulbrum n whch the wholesale rce for follower s lower than that for leader. 4.. Seuental Move Prce Game We now turn to the seuental move rce game. At stage three downstream frm s maxmzaton roblem s max = ( - w ( - F ; = 1 ¹. Note that the rce s ndeendent of F. The frst-order condton for downstream frm s exressed as follows:

13 DongJoon Lee Kangsk Cho Kyuchan Hwang: Frst-Mover and Second-Mover Advantages 47 ( ( = ( + - w = 0 = 1 ¹. (15 It s assumed that the second-order condton = + ( - w < 0 s satsfed. Solvng E. (15 we obtan the unue eulbrum for uantty where the suerscrt denotes the eulbrum at stage three. To understand how affect let us see the total dfferental of E. (15. Dfferentatng E. (15 we have é ù é ù ( ( ë û ë úû + - w ú d = + - w ú d. (16 From (A4 and < 0 we have the followng result: é ù + ( - w ú d = ú > 0. (17 d ú + ( - w ú ë úû At stage two gven the wholesale rces ( w w downstream frm sets the rce so as to maxmze ts roft. Downstream frm s maxmzaton roblem s as follows: max = ( - w [( ( ]- F ; = 1 ¹. The frst-order condton for downstream frm s exressed as follows: é ù = ( ( + ( - w + 0 ú = = 1 ¹. (18 ë úû Assume that the second-order condton s satsfed. Solvng E. (18 we obtan the eulbrum at stage two. Let w = ( w w denote the vector of the wholesale rces set by ustream frms at stage one. To understand how w = ( w w affect = ( let us see the total dfferental of E. (15 and E. (18. Dfferentatng E. (15 and E. (18 we have

14 48 The Korean Economc Revew Volume 33 Number 1 Summer 017 é ù ú ú é d ù é ù ú d ú = ú. (19 ú ë û ë û ú ë û Under (A3 and (A4 the stablty condton of the eulbrum s satsfed by ( ( ( ( D = - > 0. We have d d d ( / = < 0. (0-1 D ( = - > 0. (0- D ( = - > 0. (0-3 D ( / d = < 0. (0-4 D At stage one gven the wholesale rce w and the franchse fee F ustream frm sets the wholesale rce w and the franchse fee F so as to maxmze ts roft. It s maxmzaton roblem s as follows: w F u = ( w - c ( w w ( w w ] + F max [ ( ( [ ( ( ] s. t. = ( w w - w w w ( w w - F ³ 0 and w ³ 0. Note that the frst constrant s bndng. Therefore we rewrte the maxmzaton roblem as follows: w max u = ( ( w w -c [ ( ( w w ( w w ] s. t. w ³ 0.

15 DongJoon Lee Kangsk Cho Kyuchan Hwang: Frst-Mover and Second-Mover Advantages 49 The frst-order condton s 9 u é ù = + ( - c 0 + ú =. (1 ë úû We assume that the second-order condton < 0 s satsfed. On the other hand ustream frm s maxmzaton roblem s as follows: u w [ ( ( ] F u = w - c w w w w + F max ( ( s. t. = ( ( w w - w [ ( ( w w ( w w ]- F ³ 0 and w ³ 0. Note that the frst constrant s bndng. Therefore we rewrte t as follows: w max u = ( ( w w -c ( ( ( w w ( w w s. t. w ³ 0. The frst-order condton s u é ù = + ( - c + 0 ú =. ( ë úû We assume that the second-order condton < 0 s satsfed. Solvng E. (1 B B B and E. ( we obtan the eulbrum wholesale rce w = ( w w where the suerscrt B denotes a seuental move rce game. Notng E. (15 E. (1 can be changed as follows: u é ù = ( - w + ( w c ( c ú ë û u = ( w - c + ( - c = 0. 9 For the comaratve statc on w and w n eulbrum we need some addtonal assumtons. Wthout any addtonal assumton we consder t wth a lnear demand. Suose a lnear demand functon as = [ a( 1- d - + d ] / ( 1- d where s rce s uantty a > 0 and dî (0 1 whch reresents the degree of roduct dfferentaton. Dfferentatng ustream frm s and s maxmzaton roblem wth resect to w and w resectvely we obtan 4 ( c - w / ( - d = 0 and w = [ c( 8-10d + 3d + d ( 1 - d ( 4 + d - d a+ d( - d w ] / ( d + 3d = 0. Therefore w s ndeendent on w and w s ncreasng n w.

16 50 The Korean Economc Revew Volume 33 Number 1 Summer 017 From E. (0-1 and E. (0-3 we have the followng result: w B ( - c - c = - > 0 (3 B In the end we have that w > c. Notng E. (18 E. ( can be changed as follows: u ( w w é ù = + ( - w + ( - w ú ë úû In the end we have é ù é ù + ( w - c + ( w c 0 ú = - + ú = ë úû ë úû w B = c. (4 We summarze these fndngs n Lemma. Lemma : Consder a vertcal duooly where one downstream frm (the leader chooses ts rce before the other downstream frm (the follower. At the sub-game erfect eulbrum of ths three stage game The follower s ustream frm sets the wholesale rce above ts margnal cost whle the leader s ustream frm sets the wholesale rce eual to ts margnal cost. Prooston : The leader s ustream frm enoys hgher rofts than the follower s ustream frm does. Proof: Let us check the frst order condton for the ustream frm when w = c. Rearrangng E. (1 yelds B u é ù = ( - w + ( w c ( c ú ë û B Notng that w = c the frst-term and the second-term of the rght-hand sde of the above euaton are eual to zero. We also know that the sgn of the thrd-term

17 DongJoon Lee Kangsk Cho Kyuchan Hwang: Frst-Mover and Second-Mover Advantages 51 B s ostve from E. (0-3 and > 0. When w = c the frst-order condton B that E. (1 > 0 s satsfed. Therefore we obtan the result that w > c at B B B B eulbrum. In the end u ( w > u ( w. Q.E.D. The ntuton behnd Prooston s the same logc as Prooston 1. Let us see the downstream cometton. It s straghtforward that the second-mover (follower sets lower rce than the frst-mover (leader f the wholesale rces are eual. Ths s the conventonal result. We now turn to the ustream cometton. Notce that each ustream frm can extract all of the rofts from ts downstream frm va twoart tarff. Antcatng downstream cometton the leader s ustream frm sets the wholesale rce as low as t can for ts downstream frm to stand at advantage over downstream cometton. The follower s ustream frm can also do so. In ths case market cometton s so ferce. In the end both frms rofts are lower than those n eulbrum n whch the wholesale rce for leader s lower than that for follower. V. Concludng Remarks We study the ssue of frst- and second-mover advantages n a vertcal structure n whch each ustream frm trades wth ts exclusve downstream frm va two-art tarffs. We show that the ustream frm whose downstream frm moves frst (second sets lower nut rce than ts rval ustream frm whose downstream frm moves second (frst does under rce (uantty cometton. In the end when the goods are substtutes the ustream frm whose downstream frm moves frst (second earns hgher (lower rofts than ts rval ustream frm whose downstream frm moves second (frst under Bertrand (Cournot cometton. Ths result s n stark contrast to the conventonal results of a one-ter market. We conclude by dscussng the lmtatons and extensons of our study. We exogenously comare the eulbrum rofts of two ustream frms under erfect nformaton. If t s ossble to bargan for the nut rce between ustream and downstream what wll haen? In addton we do not consder asymmetrc costs between downstream frms. Fnally t s also nterestng to consder the ssue of endogenous tmng n a vertcal structure. Extendng our model n these drectons s left for future research.

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