THREE ESSYS IN INDUSTRI ECONOMICS ND PUBIC POICY by CHEWNET BUNCHI B.E., Kng Mongkut s Insttute of Technology adkrabang, 1996 M.E., Kasetsart Unversty, 004 N BSTRCT OF DISSERTTION submtted n partal fulfllment of the requrements for the degree DOCTOR OF PHIOSOPHY Department of Economcs College of rts and Scences KNSS STTE UNIVERSITY Manhattan, Kansas 015
bstract Ths dssertaton comprses of three essays n ndustral economcs. My frst essay analyzes socal effcency of entry nto a downstream olgopoly of a vertcal market structure, where an upstream suppler sells an essental nput to all frms producng downstream. In the downstream markets, a multproduct frm s both a monopoly n ts own product and a leader n a dfferent product market wth free entry of followers. We show that n the presence of scale economes, entry s socally nsuffcent. The nsuffcency of entry s due to the fact that entry generates a busness-creatng effect sgnfcantly large enough to domnate a busness-stealng effect, regardless of whether the upstream suppler's nput prcng strategy s dscrmnatory or unform. Ths suggests that entry regulaton as a publc polcy s socally undesrable n the downstream olgopoly of a vertcal market structure. My second essay examnes dfferences n welfare mplcatons between dscrmnatory and unform nput prce regmes n vertcally related markets where a multproduct frm operates downstream n two separate markets: one s a monopoly and the other s an olgopoly wth entry of new frms. In the analyss, we analyze how the downstream entry nto the olgopolstc market affects socal effcency. In an open economy, whether the nput prce regme s dscrmnatory or unform, entry s always socally excessve n the presence of scale economes. Ths contrasts wth the exstng studes n the lterature that entry s always socally nsuffcent n an open economy wth the presence of scale economes. Focusng on the scenaro where vertcally ntegrated producer () adopts a nonforeclosure strategy, my thrd essay shows that downstream entry s socally nsuffcent despte scale economes and the margnal cost dfference between the and ts retal compettors. The non-foreclosure equlbrum arses when the 's wholesale proft from the sales of an
essental nput s suffcently large and the shares the proft wth ts downstream compettors. For the case of an open economy where the s a foregn frm, downstream entry contnues to be socally nsuffcent. Entry regulaton s therefore socally undesrable, but a producton subsdy encouragng downstream entry s shown to be a welfare-mprovng polcy.
THREE ESSYS IN INDUSTRI ECONOMICS ND PUBIC POICY by CHEWNET BUNCHI B.E., Kng Mongkut s Insttute of Technology adkrabang, 1996 M.E., Kasetsart Unversty, 004 DISSERTTION submtted n partal fulfllment of the requrements for the degree DOCTOR OF PHIOSOPHY Department of Economcs College of rts and Scences KNSS STTE UNIVERSITY Manhattan, Kansas 015 pproved by: Major Professor Dr. Yang-Mng Chang
Copyrght CHEWNET BUNCHI 015
bstract Ths dssertaton comprses of three essays n ndustral economcs. My frst essay analyzes socal effcency of entry nto a downstream olgopoly of a vertcal market structure, where an upstream suppler sells an essental nput to all frms producng downstream. In the downstream markets, a multproduct frm s both a monopoly n ts own product and a leader n a dfferent product market wth free entry of followers. We show that n the presence of scale economes, entry s socally nsuffcent. The nsuffcency of entry s due to the fact that entry generates a busness-creatng effect sgnfcantly large enough to domnate a busness-stealng effect, regardless of whether the upstream suppler's nput prcng strategy s dscrmnatory or unform. Ths suggests that entry regulaton as a publc polcy s socally undesrable n the downstream olgopoly of a vertcal market structure. My second essay examnes dfferences n welfare mplcatons between dscrmnatory and unform nput prce regmes n vertcally related markets where a multproduct frm operates downstream n two separate markets: one s a monopoly and the other s an olgopoly wth entry of new frms. In the analyss, we analyze how the downstream entry nto the olgopolstc market affects socal effcency. In an open economy, whether the nput prce regme s dscrmnatory or unform, entry s always socally excessve n the presence of scale economes. Ths contrasts wth the exstng studes n the lterature that entry s always socally nsuffcent n an open economy wth the presence of scale economes. Focusng on the scenaro where vertcally ntegrated producer () adopts a nonforeclosure strategy, my thrd essay shows that downstream entry s socally nsuffcent despte scale economes and the margnal cost dfference between the and ts retal compettors. The non-foreclosure equlbrum arses when the 's wholesale proft from the sales of an
essental nput s suffcently large and the shares the proft wth ts downstream compettors. For the case of an open economy where the s a foregn frm, downstream entry contnues to be socally nsuffcent. Entry regulaton s therefore socally undesrable, but a producton subsdy encouragng downstream entry s shown to be a welfare-mprovng polcy.
Table of Contents st of Fgures... x cknowledgements......x Dedcaton... x Chapter 1 - Socal Effcency of Downstream Entry n Vertcally Related Markets wth Multproduct eaders...1 1.1 Introducton...1 1. The Smple Model of Vertcally Related Markets...4 1..1 Downstream Entry under Input Prce Dscrmnaton...5 1.. Downstream Entry under Unform Input Prcng...11 1.3 Concludng Remarks...17 Chapter - Input Prce Dscrmnaton vs. Unform Prcng n Vertcally Related Markets wth Downstream Entry...19.1.Introducton...19. The nalytcal Framework.....1 Input Prce Dscrmnaton...3.. Unform Input Prcng...8. 3 Concludng Remarks...34 Chapter 3- Welfare Implcatons of Downstream Entry When Vertcally Integrated Frm dopts a Non-Foreclosure Strategy...35 3.1 Introducton...35 3. Model...37 3.3 Downstream Entry When the s a Foregn Frm...43 3.4 Concludng Remarks...47 References...48 ppendx - ppendx of Chapter 1...50 ppendx B- ppendx of Chapter...55 ppendx C- ppendx of Chapter 3...57 v
st of Fgures Fgure.1 Entry s socally nsuffcent... 5 x
cknowledgements Ths dssertaton could not be accomplshed wthout the help of these people. The frst person I wsh to thank s my major advser, Dr. Yang-Mng Chang. Thanks for all of hs advce and support, whenever I needed gudance and was n troubled stuatons, my advser always stands by for me. I wsh to thank my commttee members, Dr. Phlp G. Gayle, Dr. Jeffrey Peterson, and Dr. ele Shen, as well as outsde charperson, Dr. aure Johnson, for provdng advce and suggestons for my dssertaton. I would lke to thank all professors, frends and staffs n Economcs Department and all of my Tha frends at K-State for helpng and supportng me along those years of my study. I would lke to express my deep apprecaton to "dad" and "mom," Dr. and Mrs. Donald and orene Stutevlle, for takng good care of me durng my stay here. Fnally, I wsh to thank my sponsor, the Natonal Broadcastng and Telecommuncatons Commsson of Thaland, for provdng full fnancal support to my study of Ph.D. n economcs at Kansas State Unversty. I wsh, one day n the comng future, I wll have a chance to pay back for these people who have supported me. x
Dedcaton I dedcate my dssertaton to my parents, my brother and ssters. x
Chapter 1 - Socal Effcency of Downstream Entry n Vertcally Related Markets wth Multproduct eaders 1.1 Introducton Whether entry nto a market s socally excessve or not consttutes an mportant regulatory ssue to governments or polcy makers of many countres. 1 Economsts have helped dentfy a set of prmary varables that determne the welfare mplcatons of entry under mperfect competton. These varables nclude the presence of scale economes, market structure (n terms of the number of frms), competton models adopted by rval frms, as well as dfferences n margnal costs of producton between competng frms, etc. The semnal contrbuton by Mankw and Whnston (1986) ndcates that under olgopoly wth no nteger constrant, the presence of scale economes makes entry socally excessve. Ghosh and Morta (007) demonstrate for the case of a successve vertcal olgopoly that free entry equlbrum can be socally nsuffcent rather than excessve. Herweg and Muller (01) show that entry can be ether socally nsuffcent or excessve, dependng on whether there s nput prce dscrmnaton and whether the number of frms n the downstream ndustry s exogenously gven. Mukerjee (01) shows that n the absence of scale economes, entry s always socally nsuffcent. In the presence of scale economes, Mukerjee (01) further ndcates that entry remans to be socally nsuffcent when the margnal cost dfferental between market leader and followers s sgnfcantly large. In ths paper, we examne socal effcency of downstream entry n vertcally related markets. Specfcally, we analyze and compare effects that alternatve nput prcng regmes (dscrmnatory vs. unform) have on downstream entry n order to see f entry s socally 1 See, for example, Suzumura and Kyono (1987) and Suzumura (1995). 1
excessve or nsuffcent. s n Mukerjee (01), we pay specal attenton to competton between a market leader and followers. But unlke Mukerjee (01), we consder that a market leader s a multproduct frm n both of the downstream output markets. We further examne the scenaro where an upstream nput monopolst supples an essental nput to all frms producng downstream. In the downstream markets, a multproduct frm s both a monopoly n ts own product and a leader n a dfferent product market wth free entry of followers. The upstream monopolst may adopt a dscrmnatory prcng strategy by chargng dfferent nput prces between the multproduct frm and the followers. lternatvely, the upstream monopolst may adopt a unform prcng strategy for ts nput, chargng an dentcal prce to all downstream buyers. We wsh to see whether dfferences n nput prcng regmes affect the welfare mplcatons of downstream entry dfferently. It should be mentoned that the standard logc behnd prce concessons s appled to nput prcng determned by an upstream monopolst suppler. Ths mples that downstream frms whose markets have lower demands are apt to receve an nput prce concesson. Thus, when one market has hgher demand than another market, under nput prce dscrmnaton the multproduct frm (the leader) would receve nput prce concesson. That s, the nput prce for the multproduct frm s lower than that for the followers. On the other hand, under unform nput prcng, f the olgopolstc market wth free entry has a hgher demand than the monopoly market, the nput prce for the multproduct frm (the leader) wll be hgher than that for the frm under nput prce dscrmnaton. Ths s because the prce concesson s appled to all frms equally. However the downstream followers wll get a lower nput prce under unform nput prcng than under nput prce dscrmnaton. The pros and corns between unform prcng and prce dscrmnaton upon socal welfare have long been debated. rya and Mttendorf (010)
show that nput prce dscrmnaton can provde welfare gans by gvng prce concessons to less effcent frms. They ndcate that when markets have lower demand and lower competton, prce dscrmnaton stfles the socal effcency by shftng output to less compettve markets. Ths noton contrasts to Bork s (1978) defendng about prce dscrmnaton and concludes that the unform prcng can offer sgnfcant welfare benefts. Whereas Katz (1987), Yoshda (000) and Vallett (003) also support the noton that prce dscrmnaton can provde welfare benefts by sphonng the producton to the less effcent sources. part from two alternatve nput prcng regmes, t s nstructve to see economc reasons behnd the nsuffcent and excessve entry. There are two effects assocated wth entry: one s a busness-stealng effect and the other s a busness-creatng effect. busness-stealng effect arses when entry steals busness from an ncumbent whch suffers a loss n the volume of sales. On the other hand, a busness-creatng effect emerges when entry creates busness to an ncumbent by ncreasng ts volume of sales. From the perspectve of a socal planner, every busness system has both busness-stealng and busness-creatng effects assocated wth entry. It s mportant to dentfy condtons under whch one effect domnates the other. If entry s such that the busness-stealng effect s domnated by the busness-creatng effect, entry s deemed to be socally nsuffcent. On the contrary, f the busness-stealng effect domnates the busnesscreatng effect, such entry s socally excessve. In our analyss, we consder the case that all frms n the downstream olgopolstc market ncur set-up costs and that the upstream nput suppler adopts ether a dscrmnatory or a unform prcng scheme. We show that the busnessstealng effect s domnated by the busness-creatng effect, wth the consequence that entry nto the downstream olgopoly of a vertcal market structure s socally nsuffcent. We therefore 3
nfer that downstream entry regulaton s not socally effectve from the welfare maxmzaton perspectve. The remander of ths chapter s organzed as follows. Secton 1. descrbes the model of a vertcally related market structure. In Secton 1.3, we dscuss welfare mplcatons of downstream entry when the upstream nput suppler adopts ether a dscrmnatory or a unform nput prcng scheme. Secton 1.4 concludes. 1. The Smple Model of Vertcally Related Markets We consder a smple vertcal structure n whch there s an upstream monopoly suppler sellng an essental nput to all frms producng downstream. In the downstream markets, a multproduct frm s a Stackelberg leader n an olgopolstc market for a homogenous good (denoted as ) and s a monopoly n ts own product (denoted as B ). There are potental entrants wantng to produce good. If an entrant decdes to enter the olgopolstc market, t ncurs a fxed cost k( 0), and behaves as a Stackelberg follower. We wsh to examne welfare mplcatons of entry nto the downstream olgopolstc market of a vertcal structure. For analytcal smplcty, we assume that the producton cost of the upstream monopoly suppler s zero and that all frms n the downstream markets requre one unt of the essental nput to produce one unt of output. We further assume that the leader and followers n the olgopolstc market ncur set-up costs and that all the followers n ths market are dentcal n all aspects. The (nverse) demand n the downstream olgopolstc market s assumed to be lnear: P q q, where P s prce of product, and n 1 q and q are the quanttes of the good 4
produced by the leader and the th follower ( = 1,, n) respectvely, represents the sze or demand of the market. The (nverse) demand n the downstream monopoly market s taken to be: P y, where P and y B B B are the prce and quantty of product B, and represents ts B market sze or demand. Two alternatve prcng schemes may be adopted by the upstream suppler sellng an essental nput, X. One s dscrmnatory prcng, under whch one nput prce w s charged to the multproduct leader and another nput prce w s charged to each of the followers n the olgopolstc market, where w w. The other s unform prcng, under whch an dentcal prce w s charged to all nput buyers. The analyss nvolves a three-stage game. t stage one, the upstream nput monopolst sets ts prces that maxmze total profts. t stage two, the multproduct leader makes ts output decsons to maxmze jont profts from the two downstream markets. t stage three, each entrant as a follower n the olgopolstc market determnes ts output to maxmze ndvdual proft. In what follows, we employ backward nducton to solve for the subgame perfect Nash equlbrum for each nput prcng scheme. 1..1 Downstream Entry under Input Prce Dscrmnaton Under ths regme, dscrmnatory nput prces are charged to the multproduct leader and each follower n the olgopolstc market. Gven nput prce w, the th follower at the thrd stage of the game chooses output q to maxmze ts total proft, assumng that the leader s output q and the outputs of all other followers reman unchanged. The proft maxmzaton problem of the th follower s: 5
n w 1 Max q q q q k. Solvng for the optmal output level of the th follower yelds q q w n 1 for 1,..., n. (1) Gven a dfferent nput prce w, the multproduct leader at the second stage of the game solves the jont proft maxmzaton problem: n Max [( q q ) w ] q ( y w ) y k, B { q, y } 1 where q s gven n (1). Under the assumpton of symmetry that followers are dentcal n all aspects, we solve for the leader's equlbrum outputs: q y w n 1 nw, (a) w B. (b) Usng (1) and (a), we calculate output of each follower as q n 1 w n w n 1. (c) From (a) and (c), we see that an ncrease n w rases the output of the leader and lowers the output of each follower. Smlarly, an ncrease n w rases the output of each follower and lowers the output of the multproduct leader. t the frst stage of the game, the upstream nput monopolst determnes an optmal prcng structure, { w, w }, by solvng the followng proft maxmzaton problem: Max ( w q w y ) nw q, w, w s 6
where q, y, and q are respectvely gven n (a), (b), and (c). The frst-order condtons wth respect to w and w lead to the optmal nput prces: w n Bn 3n 4 1, (3a) w n Bn 3n 4 3 1, (3b) where the subscrpt represents the case of nput prce dscrmnaton. Under dscrmnatory prcng, the optmal nput prces reflect a two-fold averagng across both downstream markets and frms. Substtutng the nput prces from (3a)-(3b) back nto (a)-(c), we have the equlbrum outputs of the leader and the followers respectvely: q n B n 43n 4 5 6, (4a) y B n n 43n 4 5 6, (4b) q 4 1 n. (4c) To determne the total amount of the nput, X, sold to all the downstream buyers, we note that X q y nq under the assumpton that one unt of output requres one unt of nput n producton. Substtutng q, y, and q from (4a)-(4c) nto ths expresson yelds X (n1) ( n1). 4 n 1 B (4d) Ths fndng contrasts wth the result of rya and Mttendorf (010). The authors show that under Cournot competton, nput prces reflect only the averagng of demand condtons of the two downstream markets. 7
Makng use of (4a)-(4d), we have the comparatve statcs of downstream entry: n q B n 3 4 ( )0 n y B n 3 4 q ( )0 n 4 1 0, n when ( ), (5a) B when ( ), (5b) B (5c) X n 4 1 0. n (5d) Equatons (5a) and (5b) ndcate the dfferences n demands between the two downstream markets when entry affects the equlbrum outputs of the leader. If demand n the olgopolstc market exceeds that n the monopoly market, entry ncreases the leader s output n the olgopolstc market but decreases ts output n the monopoly market. Ths suggests that entry generates a busness-creatng effect n the olgopolstc market but a busness-stealng effect n the monopoly market. If, nstead, demand n the olgopolstc market s lower than demand n the monopoly market, entry generates a busness-stealng effect n former market and a busnesscreatng effect n the latter market. These two conflctng effects thus depend on the market demand dfferental. Nevertheless, for any dfferences of demand condtons between the two downstream markets, entry generates both effects to the leader from each market equally so that the equlbrum outputs of the leader are ndependent of entry. For each follower, we have from (5c) that entry generates a busness-stealng effect. For the upstream suppler, we have from (5d) that entry generates a busness-creatng effect. The net equlbrum profts for the nput suppler, the downstream leader and ts competton are gven, respectvely, as 8
S n n n n n n 4 7 B 3 B 4 8 4, 8 3 4 1 n n (6) 4n 37n 7n 40 5n 89n 104n 40 0n 84n 11n 48 16 3 4 1 3 3 3 B B n n k, (7) 16 n 1 k. (8) Next, we analyze how downstream entry affects socal welfare by comparng the equlbrum number of followers under market condtons, denoted by n, and the one determned by the socal planner, denoted by n ˆ. If s greater than n ˆ, entry s socally excessve; but f n equals n ˆ, entry s socally optmal; f n n s less than n ˆ, entry s socally nsuffcent. We frstly determne the equlbrum number of followers under market condtons. Usng the zero-proft condton, k 0, 16 n 1 (9a) we solve for the number of the followers n the free-entry equlbrum as n 1. 4 k (9b) 1 Next, we determne the socally optmal number of the followers from the socal planner s perspectve. The objectve s to maxmze overall welfare, whch s taken to be the sum of the upstream nput suppler s profts, the profts of the leader the followers n the downstream markets, and consumer surplus n both markets. That s, the socal planner solves the followng welfare maxmzaton problem: 9
Max SW = n CS CS, {} nˆ s B s where,, and are gven by (6), (7), and (8), respectvely, CS ( q nq ), and CS B ( y ). Takng the frst-order dervatve of SW wth respect to n, settng the resultng expresson to zero, we have 4 3 4 3 4 3 (40n 39n 5n 498n 176) B(10n 46n 78n 58n 16) B(4n 1n 1n 4 n) k 0. 3 16(3n 7n4) (10) Ths FOC defnes the socally optmal number of the entrants (denoted as n ˆ) n the downstream olgopolstc market. Evaluatng the left hand sde of (10) at the pont where n n as gven n (9b), we show n ppendx -1 that SW n 1 n 1 4 k 0. The strct concavty of the socal welfare functon mples that the equlbrum number of the followers under market condtons s less than the socally optmal number of the followers. That s, n nˆ. We thus have PROPOSITION 1. Under nput prce dscrmnaton wth the presence of scale economes and a multproduct leader n a downstream olgopolstc market, entry nto the downstream market s socally nsuffcent. The ntuton behnd Proposton 1 s as follows. Under nput prce dscrmnaton, downstream entry generates the busness-creatng effect to beneft the upstream nput suppler. Ths result emerges, regardless of dfferences n demands between the downstream markets. For the leader servng both of the downstream markets, f demand n the olgopolstc market exceeds 10
demand n the monopoly market, entry generates a busness-creatng effect n the olgopolstc market and a busness-stealng effect n the monopoly market. If, nstead, demand n the monopoly market exceeds demand n the olgopolstc market, entry generates a busnesscreatng effect n the monopoly market but a busness-stealng effect n the olgopolstc market. Hence, from the leader's perspectve, entry has a busness-creatng effect n the market wth a hgher demand and a busness-stealng effect n the market wth a lower demand. Nevertheless, for the leader the busness-creatng effect and the busness-stealng effect cancel out each other, for any dfferences n demands. Consequently, entry does not have any busness effect for the leader. For the followers, however, entry always results n a busness-stealng effect regardless of dfferences n market demands between the two output markets. The strength of both busness effects s shown to depend on the dfferences n demand condtons of the two downstream markets. Ths mples that both busness effects drectly affect overall welfare. We thus can nfer that under dscrmnatory nput prcng wth scale economes and market leader, the busness-creatng effect always domnates the busness-stealng effect, wth the consequence that entry s socally nsuffcent. 1.. Downstream Entry under Unform Input Prcng Under ths regme, the upstream suppler charges an dentcal prce for ts nput to all downstream frms. Gven nput prce w, the follower th for = 1, n chooses ts output q to maxmze ts own proft, takng the outputs of rval frms as gven. Formally, the th follower s proft maxmzaton problem s: Max q w q k n q 1 q 11
Usng the FOC for the th follower, we solve for ts output as a functon of the leader s output: q wq n 1 (11) The multproduct leader determnes ts output decsons by choosng q and y that solve for the followng jont proft maxmzaton problem: n q w Max q wq y w y k B { q, y } n 1 The FOCs wth respect to q and y yeld the equlbrum outputs of the leader as q w, (1a) y B w. (1b) Usng (11) and (1a), we calculate the output of each follower to be q w n 1 (1c) The upstream nput monopolst determnes an optmal prce solvng the followng proft maxmzaton problem: Max s q y nq w (13) w Substtutng (1a)-(1c) nto s n (13), we set the dervatve optmal nput prce as d dw to zero and solve for the s n 1 B n 1 w. (3n ) (14) 1
where the subscrpt represents the case of unform prcng. The result n (14) ndcates that the equlbrum nput prce reflects a two-fold averagng across both downstream markets and frms. Substtutng w from (14) back nto (1a)-(1c), we obtan the equlbrum outputs of the leader and each follower as follows: q y q B n Bn 43n 4 3 1, n n 43n 5 3 1, n Bn 43nn1 4 3 1. (15a) (15b) (15c) To determne the total amount of the nput X sold by the upstream suppler to all downstream buyers, we note that X q y nq. Substtutng q, y, and q from (15a)-(15c) nto ths expresson yelds B 4n 1 n 1 n 1 X. (15d) From (15a)-(15d), we have the comparatve statcs of downstream entry: n q B n 4 3 ( )0 n y B 4 3 ( )0 n when ( ), (16a) B when ( ), (16b) B 3n 6n 3 1n 18n 7 q B n 4 3n n1 ( )0 when ( ), (16c) B 13
X n 4 1 0. n (16d) Equatons (16a) and (16b) ndcate that dfferences n demands between the downstream markets play an mportant role n determnng how entry affects the equlbrum outputs of the market leader. When the two markets are dentcal n demands, entry exerts no effects on the leader s output decsons. However, when dfferences of the demand condtons between olgopolstc market and monopolstc market are small, entry reduces the outputs of the leader n both markets slghtly. In addton, f ths dfference s sgnfcantly large, entry lowers the outputs of the leader n both markets extremely. On the other hand when the dfference of the demand condtons between monopoly market and olgopolstc market s small, entry wll ncrease the outputs of the leader for both markets slghtly and when ths dfference s sgnfcantly large, entry wll extremely rase the outputs of the leader n both markets. For each follower, we have from equaton (16c) that entry wll ncrease the output only when the demand condton of monopoly market s sgnfcantly larger than olgopolstc market and entry wll decrease the output for vce versa. Because the unform prcng reflects a two-fold averagng both across markets and across frms, entry affects the nput prce and the strength of whch depends on the dfference n demand condtons between the downstream markets. If the dfference s sgnfcantly large, the strength of ths effect wll be extremely strong. For the upstream suppler, we have from equaton (16d) that entry wll always ncrease the total amount of the nput to be sold n both of the downstream markets. Consequently, there s a busness-creatng effect resultng from entry. In concluson, under unform prcng, f the demand condton of olgopolstc market s larger than monopolstc market then all frms n the downstream market wll ncur the busness-stealng effect except the upstream suppler that wll have the busness-creatng effect. But f the demand 14
condton of the monopolstc market s larger than that of the olgopolstc market, all frms n the downstream market and upstream suppler wll ncur the busness-creatng effect. The net equlbrum profts of the suppler, the leader, and the th follower for = 1, n are gven, respectvely, as S n Bn 8n13n [ 1 1 ], (17) (4n 4n 9n 10) (5n 56n 41n 10) (0n 50n 4n 1) k, 16( n1)(3n) (18) 3 3 3 B B n Bn n n [ 4 3 1 ] 16 1 3 k. (19) Next we show how entry affects socal effcency by comparng the equlbrum number of followers under market condtons, denoted by n, and the one determned by the socal planner, denoted by n. To solve for the equlbrum number of followers under market condtons, we use the followng zero-proft condton: n Bn n n [ 4 3 1 ] k 0, 16 1 3 (0a) and fnd that 4 B 0 k 16 B 8 B 16 k 8 kb 16 k n. 4 k (0b) For determnng the socally optmal number of the followers, we assume that the objectve of the socal planner s to maxmze overall welfare, whch s the sum of frm profts and consumer surplus n the vertcally related markets. That s, the socal planner solves the followng welfare maxmzaton problem: 15
Max SW = n CS CS, {} n S B S where,, and are gven by (17), (18), and (19), respectvely, CS ( q nq ), and CS B ( y ). Takng the frst-order dervatve of SW wth respect to n, settng the resultng expresson to zero, we have 4 3 4 3 4 3 (38n 149n 01n 115n 4) B(5n 19n 7n 17n 4) B(11n 1n 6n 8n 4) k 0. 16( n1)(3n) (1) Ths FOC defnes the socally optmal number of the entrants (denoted as n ) n the downstream olgopolstc market. Evaluatng the left hand sde of (1) at the pont n n as derved n (0b), we show n ppendx - that SW n nn 0. Ths mples that the equlbrum number of the followers under market condtons s less than the socal optmal number of the followers. That s, n n. s a result, entry under ths regme s socally nsuffcent. PROPOSITION : Under unform nput prcng wth the presence of scale economes and a multproduct leader n a downstream olgopolstc market, entry nto the downstream market s socally nsuffcent. The ntuton for the proposton s as follows. Under unform nput prcng, entry can create the busness-creatng effect to the suppler for any dfferences of the demand condtons between the two downstream markets. For the leader, when the demand condton n downstream monopoly market s larger than downstream olgopolstc market, entry wll create the busness- 16
creatng effect for both downstream markets. However, entry wll create busness-stealng effect for both downstream markets when the demand condton n downstream olgopolstc market s larger than downstream monopoly market. The strength of both effects wll depend on the dfference of the demand condtons between the two downstream markets so the larger of the dfference of the demand condtons, the stronger of the busness effects. For the follower, entry generates a busness creatng effect only when the dfference of the demand condtons between the downstream monopoly market and downstream olgopolstc market s sgnfcantly large. Otherwse, entry generates a busness-stealng effect nstead. s a result, when there s a sgnfcantly dfference of the demand condtons between the two downstream markets, entry generates a sgnfcant effect on socal welfare. However, when there s a sgnfcant dfference of the demand condtons between the two downstream markets, the busness-creatng effect always domnates the busness-stealng effect and entry s always socally nsuffcent. 1.3 Concludng Remarks In ths paper, we focus our analyss on a vertcally related market structure to examne the socal effcency of downstream entry under dfferent nput prcng regmes provded by the upstream suppler. Competton n the downstream olgopolstc market s characterzed by a Stackelberg leader-follower game wth the leader beng a multproduct frm operatng as a monopolst n ts own product market. We show that n the presence of scale economes the alternatve nput prce regmes (dscrmnatory vs. unform) dd not determne the effect of downstream entry to the olgopolstc market on socal welfare; entry s always socally 17
nsuffcent for both prcng regmes. s a result, entry regulaton may not be justfed n a downstream olgopoly of a vertcal market structure. 18
Chapter - Input Prce Dscrmnaton vs. Unform Prcng n Vertcally Related Markets wth Downstream Entry.1 Introducton The prmary objectve of ths paper s to analyze how alternatve nput prce regmes (dscrmnatory vs. unform) and downstream entry affect socal effcency n vertcally related markets. The vertcal structure s composed of a foregn upstream suppler sellng an essental nput to domestc downstream purchasers operatng n two dfferent markets, one s olgopolstc and the other s monopolstc. In the olgopolstc market, an ncumbent frm and entrants engage n Cournot competton. In the monopoly market, the ncumbent frm sells a dfferent product n ts own market. The upstream suppler has the optons of choosng between a dscrmnatory nput prcng and a unform nput prcng. One of these phenomena can be frequently observed n developng countres when they have to mport an essental nput such as crude ol to produce fnal products n domestc markets. We consder the case that demand n the olgopolstc market s greater or dentcal to demand n the monopoly market. For analytcal smplcty, we assume that the margnal cost of the upstream suppler s zero and that all frms n the olgopolstc market have an dentcal set-up cost. The upstream nput suppler has the optons of offerng ether unform or dscrmnatory nput prcng to each frm producng downstream. 3 The consderaton of an alternatve nput prcng regme s consstent wth that rya and Mttendorf (010). Under nput prce 3 Ths nput prce dscrmnaton whch s one of the most common forms of prce dscrmnaton, thrd-degree prce dscrmnaton, means that dfferent buyers are charged wth dfferent prces but each buyer pays a constant amount for each unt of the nput they bought. Ths s dfferent from frst degree prce dscrmnaton and second degree prce dscrmnaton. For frst degree prce dscrmnaton, the seller wll charge a dfferent prce for each unt of nput when the prce charged for each unt of nputs s equal to the maxmum wllngness to pay for that unt. For the second degree prce dscrmnaton, the seller wll charge dfferent prces to each buyer and these dfferent prces wll depend on the number of unt of nput bought, but not across customer. 19
dscrmnaton, each frm s offered dfferent nput prces and the offerng reflects an averagng of the demand condtons n whch each frm operates. Under unform nput prcng, each downstream frm s offered an dentcal nput prce and such offerng reflects a two-fold averagng, across both markets and across all frms. rya and Mttendorf (010) also show that prce concesson wll accrue to the weaker nput buyers whose output markets have lower demand. Thus, under unform nput prcng and the olgopolstc market has a hgher demand than the monopoly market, the nput prce for the multproduct frm wll be ncreased. s a result, the multproduct frm has a hgher ncentve to produce more under nput prce dscrmnaton than under unform nput prcng. The ncreased motvaton for producton of multproduct frm under nput prce dscrmnaton s welfare-enhancng. In our study, n whch there are entrants nto downstream olgopolstc market, the number of entrants exerts a sgnfcant effect on the optmal nput prce under the unform prcng regme but not on the optmal nput prce under a dscrmnatory regme. The effect of downstream entry on nput prce under unform nput prcng s shown to depend on the demand condtons between the downstream markets. If the demand condton of the olgopolstc market s hgher than that of the monopoly market, downstream entry ncreases the optmal nput prce charged by the nput suppler. If the demand condtons of the two output markets are dentcal, downstream entry has no effect on nput prce. The ncrease n nput prce resultng from the entry s shown to be a key factor that creates ether the busness-stealng effect 4 or the busness-creatng effect 5 to each downstream frm. 4 The busness-stealng effect exsts when the equlbrum strategc response of exstng frms to new entry results n ther havng a lower volume of sales. 5 The busness-creatng effect exsts when the equlbrum strategc response of exstng frms to new entry results n ther havng a hgher volume of sales. 0
Under nput prce dscrmnaton, however, downstream entry generates an mpact to the downstream olgopoly market through () a busness-creatng effect to the upstream suppler and () a busness-stealng effect to the ncumbent frm and entrants. great deal of contrbutons has studed how entry affects socal welfare. In ther semnal work, Mankv and Whnston (1986) show that under olgopolstc homogenous market wth no nteger constrant and the presence of scale economes, entry s socally excessve so that entry restrctons are often socally desrable. Ghosh and Morta (007) demonstrate that under a successve vertcal olgopoly model ncorporatng vertcal relatonshp between ndustres, the free entry equlbrum can be socally nsuffcent rather than excessve. Mukerjee (01) shows that n the presence of scale economes, f the margnal cost dfference between the leader and the follower s sgnfcantly large, entry s always socally nsuffcent and n the absence of scale economes, entry s always socally nsuffcent. Herweg and Muller (01) show that entry can be ether socally nsuffcent or excessve by permttng prce dscrmnaton n nput markets and takng the downstream ndustry as exogenously gven. Next we wll present some artcles mentonng about the comparatve advantage and dsadvantage of unform prcng and prce dscrmnaton onto socal welfare. Subsequently, Bork s (1978) defenses about prce dscrmnaton and concludes that the unform prcng can offer sgnfcant welfare benefts. Whereas the authors who support the noton that prce dscrmnaton can provde welfare benefts by sphonng the producton to the less effcent sources compose of Katz (1987), Yoshda (000), rya and Mttendorf (010) and Chen, Hwang and Peng ( 011). Katz (1987) demonstrates that ntermedate good prce dscrmnaton may shft prces n a way that reduces output n the fnal good market and thus lower consumer s surplus and 1
welfare. However, ths prcng regme may ncrease welfare by preventng socally neffcent ntegraton. Yoshda (000) shows that n a specal case, when all downstream frms can be ordered n effcency, prce dscrmnaton always reduces both the total output of the fnal good and welfare level. Nevertheless, n a general case, nput-market prce dscrmnaton can lower or rase the total output of the fnal good and welfare level. rya and Mttendorf (010) demonstrate that prce dscrmnaton can provde welfare gans by gvng prce concessons to less effcent frms. They show that when the markets have lower demand and lower competton, prce dscrmnaton wll stfle the socal effcency by shftng output to less compettve markets. Chen, Hwang and Peng (011) show that nput prce dscrmnaton can create postve effect to socal welfare under the condton that the postve output allocaton effcency effect outweghs the negatve producton effcency effect. The remander of ths chapter s organzed as follows. Secton. descrbes the model. Secton.3 presents the results. Secton.4 concludes.. The nalytcal Framework We consder a smple vertcal structure n whch there s a foregn upstream monopoly suppler sellng an essental nput to domestc buyers n two downstream markets: one s an olgopoly and the other s a monopoly. In the downstream olgopolstc market, there s Cournot competton between the ncumbent frm and entrants. The ncumbent frm n the olgopolstc market also operates as a monopolst n ts own product market. For analytcal smplcty, we mpose the followng assumptons: () the producton cost of the upstream monopoly suppler equals to zero, () all downstream frms requre one unt of nput to produce one unt of fnal output, () demand n the olgopolstc market s greater or equal to demand n the monopoly
market, (v) the ncumbent frm and entrants n the downstream olgopolstc market ncur a set up cost k and all entrants n ths market are smlar. et the (nverse) demand n the downstream olgopolstc market be gven as 1 n P q q, where P s market prce, q and q are the quanttes of the output produced by the ncumbent frm and the th entrant (for = 1, n) respectvely, and represents demand condton of the market. The (nverse) demand n the downstream monopoly market s assumed to be P B B y, where P and B y are prce and quantty of the ncumbent frm, B represents demand condton of the monopoly market. The foregn upstream monopoly suppler can provde two regulatory nput prcng regmes between nput prce dscrmnaton and unform nput prcng. Under nput prce dscrmnaton, the suppler can provde dfferent nput prces to each downstream frm; n ths case, the ncumbent frm and entrants pay w and w respectvely. Under unform nput prcng, the suppler wll provde the same nput prce to all buyers; n ths case, each frm pays w for each unt of nput. In the followng analyss, we employ backward nducton to dentfy the subgame perfect Nash equlbra...1 Input Prce Dscrmnaton Under ths nput prcng regme, the suppler charges separated prces for nputs to the ncumbent frm and entrants. Gven nput prce w, the th entrant for = 1, n chooses ts output q to maxmze ts total proft and takes ts rval output q as gven. Formally, frm th problem s: n w 1 Max q q q q k. 3
Smlarly, gven nput prce w, the ncumbent frm chooses ts outputs q and y to maxmze ts total proft and takes ts rval output q as gven. Formally, the ncumbent frm problem s: n q q wq Max y w y k. B { q, } y 1 Solvng for the outputs of the th entrant and the ncumbent frm, we have q w w n for 1,..., n, (1a) q y w n 1 nw, n w B. We fnd that for the downstream olgopolstc market, an ncrease n w and (1b) (1c) w wll rase the outputs of the entrant and ncumbent frm respectvely. w, w The suppler maxmzes the followng expresson to determne nput prces s Max w q y nw q, where q, q, and y are gven n (1a), (1b), and (1c), respectvely. Solvng for the nput prces yelds, (a) 4 B w 3. 8 B w (b) Based on the dscrmnatory nput prces n (a) and (b), we see that the nput prces reflect an averagng of demand condtons n the downstream markets and that entry nto the olgopolstc markets have no effects on nput prces. 4
PROPOSITION 1 Under nput prce dscrmnaton, the optmal nput prces reflect an averagng of demand condtons that each frm operates and downstream entry exerts no effect at all on these nput prces. The ntuton for Proposton 1 s as follows. Under nput prce dscrmnaton, the nput prces reflect an averagng of demand condtons that each frm operates whch s consstent wth the results of rya and Mttendorf (010). Because the ncumbent frm operates n two separate markets and demand condton n one of whch s lower, the frm obtans a prce dscount on nput prce from the upstream nput suppler. The ncumbent has a stronger ncentve to ncrease ts producton under nput prcng dscrmnaton than unform nput prcng. The nput prce dscount s one of the factors that affect overall welfare as a motvaton for the ncumbent frm to shft the producton to lower demand market. Substtutng (a)-(b) back nto (1a)-(1c), we calculate the equlbrum levels of outputs for the ncumbent frm, the th entrant (for = 1, n), and the total nput: n6bn 8 q, (3a) n y 3B, 8 q n, n Bn 4n 1 X. (3b) (3c) (3d) Makng use of (3a)-(3d), we have the comparatve statcs of downstream entry: n q 0, n (3e) 5
n y 0, (3f) n q 0, n (3g) X n 0, n (3h) Equatons (3e)-(3h) ndcate that entry lowers the output levels of the ncumbent frm and entrants but ncreases the total nput n the downstream markets. Hence, entry generates a busness-stealng effect to the ncumbent frm and entrants, but a busness-creatng effect to the upstream suppler. However, entry does not affect the outputs of the ncumbent frm n the downstream monopoly market. The net equlbrum profts for the suppler, the ncumbent frm, and the th entrant for = 1, n, are respectvely: 3n n n4 16n B B s, (4a) n 8n0 5n 0n0 4n 0n4 B B k, (4b) 3 n k for 1,..., n. 4n1 (4c) Next we examne the effect of downstream entry on socal welfare. Usng equaton (4c), we have the followng expressons for the zero-proft condton and the equlbrum number of followers under the market soluton: 6
k 0, 4 n1 (5a) n. (5b) k To evaluate whether n n the downstream olgopolstc market s socally excessve or nsuffcent, we assume that there s a socal planner wth an objectve of maxmzng overall welfare by an optmal number of followers. Gven that the upstream nput suppler s a foregner frm, ts proft does not consttute a component of domestc welfare. The welfare maxmzng number of the followers can be obtaned by solvng the followng problem: B Max SW = n CS CS n whch s n 15n 64n60 15n 60n60 16n 68n7 Max 64 n B B The frst-order condton for welfare optmzaton s: k n 1. SW n B n n B k 0. 16 n 3 (6) Evaluatng the frst-order dervatve n at the pont the value of n satsfes the zeroproft condton n (5b), we have SW SW n n k n n 16n 3 [ 5 6 B ] 0. (7) The strct concavty of the socal welfare functon mples that entry s socally excessve. We thus have 7
PROPOSITION Under nput prce dscrmnaton, f the upstream nput suppler s a foregn frm but the multproduct frm and entrants are domestc frms, entry s always socally excessve for the domestc country, wth the scale economes. The ntuton for Proposton s as follows. When the upstream nput suppler s a foregn frm, ts proft wll be excluded from the welfare functon. s a result, the domestc country determnes ts socally optmal number of entry by maxmzng the sum of consumer surplus from olgopolstc market and monopoly market and total net profts of multproduct frm and entrants. Snce more entry decrease the outputs and profts of multproduct frm and entrants, both of these effects create excessve entry of entrants n domestc country... Unform Input Prcng Under ths nput prcng regme, the suppler provdes the nput prce to all frms equally. Gven ts nput prce w, the th entrant for = 1, n chooses ts output q to maxmze ts total proft, takng ts rval output Max q w q k. n q 1 q q as gven. Formally, frm th s problem s: The ncumbent frm determnes the quanttes of products q and y to be sold n downstream olgopolstc market and the monopoly market by maxmzng ts overall profts takng as gven ts rval output q. Formally, the ncumbent frm s proft maxmzaton, problem s: n q Max q w q y w y k. B { q, y } 1 Solvng for the output levels of the th entrant and the ncumbent frm yelds 8
w q n for 1,..., n, (8a) w q n, (8b) y B w. (8c) The foregn suppler maxmzes ts total proft by determnng an optmal nput prce w solvng for the followng problem: Max q y nq w w s, where the quanttes of the nput demanded by the downstream frms are gven n equatons (8a)-(8c). Solvng for the optmal nput prce yelds n n 1 B w. (9) 6n8 Based on w n (9) under unform prcng, we see that the nput prce reflects a two-fold averagng both across markets and across frms. We, therefore, have PROPOSITION 3 Under unform nput prcng n a vertcal market wth downstream entry, the optmal nput prce reflects a two-fold averagng both across markets and across frms. The ntuton for proposton 3 s as follows. Under unform nput prcng, the nput prce wll reflect a two-fold averagng across markets and across frms. Under ths nput prcng regme, the upstream nput suppler wll provde the same nput prce to all frms and when the number of frms ncreases, the unform nput prce wll be ncreased. Nevertheless for the entrants, the unform nput prce s stll lower than dscrmnatory nput prce so the entrants prefer to produce under unform nput prcng than dscrmnatory nput prcng. On the other hand for the ncumbent frm, the unform nput prce s hgher than dscrmnatory nput prce so 9
the ncumbent frm prefers to produce under dscrmnatory nput prcng than unform nput prcng. Substtutng w from (9) back nto (8a)-(8c), we obtan the equlbrum outputs of the ncumbent frm, the th entrant (for = 1, n), and the total nput. These results are recorded as follows: n Bn 3 4 ( ) 3 q, n n (10a) B(5n6) ( n 1) y n, (10b) 43 4 n Bn 3 q, 3n 4 n (10c) X (n) ( n) B. (10d) 4n Makng use of (10a)-(10d), we have the comparatve statcs of downstream entry: q n n n n n 3n 10n8 B(3 1 1) (1 36 8) 0, (10e) n y B ( )0, 3n 4) when ( ), (10f) B q n n n n n 3n 10n8 B(3 1 1) (1 36 8) 0, (10g) X n 0, n (10h) Equatons (10e)-(10h) ndcate that under unform nput prcng, entry and demand condtons between the downstream olgopolstc market and the downstream monopoly market wll have the sgnfcant effect to the outputs of the ncumbent frm and the entrants. For the 30
ncumbent frm, when the demand condtons of the two downstream markets are equal, there s no effect from the entry to the output n the downstream monopoly market but entry wll decrease the output n the downstream olgopolstc market. Furthermore, when the demand condton of the downstream olgopolstc market s larger than the downstream monopoly market, entry wll reduce the outputs for both markets. For the entrant, entry wll decrease the output when the demand condton of downstream olgopolstc market s sgnfcantly larger or dentcal to the downstream monopoly market. Because the unform nput prcng reflects a two-fold averagng both across markets and across frms, when the suppler provdes the unform nput prce to the buyers, entry wll have sgnfcant effect to the nput prce and the strength of ths effect wll depend on the dfference of the demand condtons. If the demand condton of the downstream olgopolstc market s sgnfcantly larger than the downstream monopoly market entry wll extremely ncrease the nput prce. For the suppler, entry wll ncrease the total nputs that wll be sold n both downstream markets for any dfferences of the demand condtons. Next, we calculate the net equlbrum profts of the suppler, the ncumbent frm, and the th entrant (for = 1, n). These results are recorded as follows: n Bn 1 s 8 3n 4 n, (11a) E F k, (11b) 16 n 3n 4 where E 4 ( 4 6 3 9 60 40) 5 (5 4 3 3 76 80 3 n n n n B n n n n B), F (0 4 14 3 31 B n n n 384n 19), and 31
n Bn n n 3 k. (11c) 4 3 4 The equlbrum number of downstream entrants under market condtons s determned by the followng zero-proft condton: n Bn n n 3 k 0. (1a) 4 3 4 Solvng for the optmal number of entrants yelds 4 B 0 k 16 B 16k 8 B 16 k 8 kb n. (1b) 1 k To evaluate whether n n the downstream olgopolstc market s socally excessve or nsuffcent, we contnue to assume that the socal planner's objectve to maxmze overall welfare by solvng the followng problem: B Max SW = n CS CS. n That s, Max a b c B B n 3n 3n4 k n 1, where a n n n n 4 3 76 50 160 196 480, b n n n n 4 3 79 51 10 164 480, c n n n n 4 3 9 61 1480 1536 576. The frst-order dervatve of SW s: 3
SW d B e B f n 8(3n 10n8) 3 where k, (13) d n n n n 4 3 10 18 04 360 19, e n n n n 4 3 11 8 8 80 18, 4 3 f n n n n 46 16 35 19 576. Evaluatng the frst-order dervatve SW n n (13) at the pont where the value of n satsfes the zero-proft condton n (1b), we have SW n nn g Bh B j 0, 3 3 8 3 4 n n (14) where g n n n n 4 3 106 590 18 118 384, h n n n n 4 3 5 38 108 136 64, j n n n n 4 3 47 8 616 576 19. The strct concavty of the socal welfare functon mples that entry s socally excessve. We, therefore, have PROPOSITION 4 Under unform nput prcng, f the upstream nput suppler s a foregn frm but the multproduct frm and entrants are domestc frms, entry s always socally excessve for the domestc country, wth the scale economes. The ntuton for Proposton 4 s as follows. Under unform nput prcng and the upstream nput suppler s a foregn frm, entry s always socally excessve. Because entry wll reduce both output and proft of the multproduct frm and entrants, both of these effects create excessve entry of entrants n domestc country. 33