The Economics of Inter-City Competition in Financial and Distribution Markets

Transcription

1 Journal of Economcs and Management, 016, Vol. 1, o. 1, The Economcs of Inter-Cty Competton n nancal and strbuton Markets Eddery Lam epartment of Economcs, Rochester Insttute of Technology, U..A. Ch-Yn Wu epartment of Economcs, eng Cha Unversty, Tawan We ntroduce a model of nter-cty competton wthn a multdmensonal framework. More specfcally, we extend a sngle-sector model to one comprsng two sectors, namely, a fnancal sector and a dstrbuton sector n a three-stage sequental-game framework. There are two types of nfrastructure, wth one for each sector. The government of each cty can buld the nfrastructure necessary to ncrease the compettveness of the relevant sector. However, gven that resources are lmted, each cty has to decde on whch type of nfrastructure to buld, as well as on whch elements of that type they wsh to nvest n. Under ths framework, we show that the relatve abundance of resources, the ntal costs of provdng servces, and the relatve effectveness of the nfrastructure determne the amount of nfrastructure the government decdes to buld, and thus the outcome of the game. Keywords: nter-cty competton, multdmensonal framework, publc nfrastructure JEL classfcaton: 1, 1, O1 Receved Aprl 4, 015, revsed August 10, 015, accepted August 11, 015. Correspondence to: epartment of Economcs, eng Cha Unversty, 100 Wenhwa Rd., eatwen, Tachung, Tawan, 4074; Tel: ext. 4491; e-mal: chynwu@fcu.edu.tw.

2 86 Journal of Economcs and Management 1 Introducton Ctes consttute an mportant economc jursdcton n a country because cty and local governments provde the basc nfrastructure that facltates busness actvtes. In general, ctes are the most populous and most prosperous areas n a country. Arguably, ctes have enabled cvlzatons to grow and prosper, and have made the world economy what t s today. Interestngly, ctes compete n varous economc dmensons (e.g., to be a fnancal center, a dstrbuton headquarters, or an Olympc Cty), regardless of whether located wthn the same country and or n dfferent natons. or example, the long-standng competton between ydney and Melbourne s often quoted as a classc example of nter-cty rvalry wthn a country, regardng both commercal and cultural perspectves. urthermore, rankfurt, the headquarters of the European Central Bank, has been competng wth London to become Europe s premer fnancal center. Among the major ctes n Asa, Hong Kong and ngapore have been servng as hubs and nternatonal gateways, as well as competng to be the largest fnancal center n East and outheast Asa. 1 As a result, ssues related to nter-cty competton across natonal boundares have become ncreasngly mportant. Many studes have examned the economcs of ctes, abstracted from the topcs of economc geography. In general, these studes can be dvded nto the followng two categores: those that study ctes that compete wth each other and those that study ctes that cooperate for mutual beneft. In the case of competton, ctes try to undercut rvals by lowerng ther producton costs. The governments of the ctes consttute one of the mportant components when ntervenng n the competton. Martn and Rogers (1995) state that publc nfrastructure affects the locaton of ndustres and the trade wthn and between countres. Long and Wong (009) show that governments provde the nfrastructure that lowers the costs of local frms n order to enhance ther compettveness. Moreover, the provson of publc nputs s 1 The Global nancal Centres Index (GCI) ranks ew York, London, Hong Kong, and ngapore as the top four global fnancal centers n 015. or example, see ujta et al. (1999) and Krugman (1991) for dscussons of theoretcal economc geography models, and Behrens and Thsse (007) and Bosker et al. (010) for the new economc geography models.

3 The Economcs of Inter-Cty Competton n nancal and strbuton Markets 87 able to enhance the productvty of prvate nputs and nduce an agglomeraton effect (see, e.g., Brakman et al. (00, 008), enge et al. (009), and Ott and oretz (010)). In the case of cooperaton, ctes can trade nputs, ntermedate goods, and fnal goods. In ths case, the man concerns are whether ctes should dversfy ther producton and how labor should be dstrbuted between ctes. Anas and Xong (003) show that the transportaton costs for nputs and fnal goods determne whether ctes should dversfy ther producton. If the transportaton costs of nputs are low, ctes should dversfy ther producton. However, f the transportaton costs of fnal goods are low, ctes should specalze n terms of producton. Cavalhes et al. (007) show that trade costs, communcaton costs and commutng costs determne the szes of ctes, as well as the allocaton of frms wthn ctes. In ther model, t s possble for several ndustral dstrcts to appear wthn the same cty. Henderson (1974) has developed a theoretcal model to analyze the optmal sze of ctes, and has found that the optmal sze s determned by the owners of captal. If the captal owners also form part of the labor force, then the optmal cty sze tends to be smaller. On the other hand, f the captal owners are purely nvestors, conflcts of nterest between the labor force and nvestors may lead to an undesrable equlbrum n whch the cty sze s not optmal. nally, Grajeda and heldon (009) provde an emprcal study on the relatonshp between trade openness and the sze of a cty. However, ther results are not consstent, and depend on the econometrc models they estmate and the data they use n the developng countres versus developed countres. It appears that relatvely lttle research has been conducted to analyze the economc geography of nter-cty competton between natons. The recent contrbuton by Long and Wong (009) s an excepton. They develop a spatal model to analyze the strategc rvalry between ctes located n dfferent countres tryng to become the major dstrbuton center n a regon. Ths study extends the sngle-sector model of cty competton developed by Long and Wong (009). In our analyss, we explctly consder the resource constrants facng two cty governments across multple dmensons. pecfcally, each government maxmzes ts objectve functon by strategcally dstrbutng lmted resources wthn two dfferent sectors: a fnancal sector and a dstrbuton sector. Governments can assst frms n these sectors by expendng resources to

4 88 Journal of Economcs and Management buld the nfrastructure relevant to the sector. These nfrastructures reduce the servce costs of the respectve sectors and ncrease the compettveness of frms n the sectors. Here, we analyze nter-cty competton n terms of the two sectors usng the sequental game structure. Whle t would be desrable to use the smultaneous game structure, as n Long and Wong (009), the complexty and ntractablty of the resultng mathematcs prevents us from dong so. Therefore, we solve ths model under the sequental game structure. We show that f the resources of one cty are more abundant than those n the other cty, ceters parbus, ths cty tends to domnate both the fnancal and dstrbuton sectors. Gven that a cty s resources may reflect ts sze and prosperty, our analyss mples that larger and wealther ctes are more lkely to become both dstrbuton and fnancal centers. In addton, we derve the condtons under whch one cty domnates the fnancal sector, whle the other domnates the dstrbuton sector. The remander of ths paper s organzed as follows. ecton presents the analytcal framework of competton between two ctes n the fnancal and dstrbuton markets. In ecton 3, we examne the case n whch one cty captures both markets. ectons 4 and 5 analyze duopolstc competton n the fnancal market and n the dstrbuton market, respectvely. Then, n ecton 6, we dscuss how government resource constrants affect the domnance of local frms n the fnancal and dstrbuton markets. Lastly, ecton 7 concludes the paper. The Model ollowng Long and Wong (009), we analyze the competton between two ctes, denoted as cty (orth) and cty (outh), 3 where the dstance between the two s normalzed to unty. Cty s located at pont 0 and cty s located at pont 1. There exsts a contnuum of nvestors/producers who are unformly dstrbuted between the two ctes. Each cty s assumed to have a sngle dstrbuton frm. To allow for nter-cty competton n multple dmensons, we also ncorporate a fnancal sector nto our model by consderng that each nvestor has to acqure a 3 It s possble that ctes coordnate to produce a better outcome. or example, ew York Cty s the fnancal captal, whle Washngton s the man poltcal center n the Unted tates. We exclude ths type of coordnaton n ths study.

5 The Economcs of Inter-Cty Competton n nancal and strbuton Markets 89 loan from a fnancal frm (located n cty or ) to fnance producton. or analytcal smplcty, there s a sngle fnancal frm n each cty. Assumng that each nvestor produces one unt of a homogeneous good, the nvestor has to decde whether to sell the product locally or to export t. If an nvestor decdes to export the good, he has to hre a dstrbuton frm (referred to as dstrbutor or ) to dstrbute t to the rest of the world. The world prce of ths homogeneous good s taken to be hgher than ts local prce. 4 In offerng a producton loan to each nvestor, fnancal frm or charges, and ncurs a servce cost C ( ), where or. It s costly for an nvestor to collect nformaton about fnancal servces, and ths cost s postvely related to where the nvestor s located. or nstance, nvestors have to travel to a cty for negotatons or to sgn contracts. If an nvestor s located at pont x, the cost of travelng to cty s ( C ) x. Ths can be regarded as the cost of acqurng or researchng nformaton about the fnancal frm n cty. Ths cost s ( C )(1 x) f nvestor x obtans nformaton about fnancal frm. In provdng the servce of dstrbutng the good for an nvestor, dstrbutor or charges and ncurs a cost C ( ), where or. If an nvestor s located at pont y, the shpment cost to cty s ( b )(1 y). ( b ) y and to cty s nally, there s a government n each of the two ctes. A cty government (referred to as government or ) can help ts fnancal and dstrbuton frms become more compettve by buldng the necessary nfrastructure. By nfrastructure, we do not lmt ourselves to physcal nfrastructure, such as a new arport. ophstcated legal and fnancal systems can certanly help reduce the operatng costs of a fnancal frm. Thus, mprovements to these systems are also consdered to be part of the relevant nfrastructure. We consder two types of nfrastructure: I and servce cost, whle nfrastructure cost. pecfcally, we assume that: I. Infrastructure I I helps to reduce the fnancal frm s helps to reduce the dstrbuton frm s servce C C ( I ), (1) 4 We assume that the fnancal and dstrbuton servces provded by cty and cty are dentcal. The only dfference s the costs of the varous servces.

6 90 Journal of Economcs and Management C C ( I ), () j where C s the servce cost of frm j (=, ) n cty (=, ), and C j s j frm j ' s servce cost n the absence of any nfrastructure. ymbol denotes the j effectveness of nfrastructure I n reducng the cost to frm j of provdng ts j servce n cty. Another nterpretaton of s that t reflects the comparatve advantage of one sector over other sectors. Equatons (1) and () ndcate that each cty government s capable of reducng the operatng costs of local frms by buldng a more effcent nfrastructure. However, gven the lmted resources avalable, each government has to decde whch type of nfrastructure to buld, as well as whch elements of that type they wsh to nvest n..1 The Three-tage Game We consder a three-stage sequental-move game. We provde more detaled explanatons of each stage of the game n the followng subsectons. ote that f an nvestor decdes to export hs product to the rest of the world, he has to hre both a fnancal and a dstrbuton frm. However, f the costs of hrng these frms outwegh the benefts, he decdes not to undertake the nvestment. It s possble for an nvestor to hre a fnancal frm only. In ths case, the nvestor decdes to sell hs goods locally. () rst tage At the begnnng of ths game, each cty government determnes whch type of nfrastructure to buld and the elements of the type n whch they ntend to nvest. We assume that the man objectve of government or s to maxmze the total proft of ts fnancal and dstrbuton frms. As mentoned earler, a cty government can help both types of frms become more compettve by buldng the relevant nfrastructure for each frm. The nfrastructure helps reduce the servce costs of the respectve frms, allowng them to offer lower prces to nvestors. However, each government has lmted resources. enote R as the (exogenous) 5 amount of 5 Gven that ths s a one-tme game, we assume that the amount of resources avalable to each cty s exogenous. In a repeated game, one can argue that the amount of resources s endogenous. In other words, the prosperty of each sector wll affect the amount of resources each cty has n the next perod.

7 The Economcs of Inter-Cty Competton n nancal and strbuton Markets 91 resources avalable to government (=, ). The objectve of government s to choose I and { I, I } I to maxmze the followng constraned optmzaton problem: max ( ) (3) subject to R I I, (4) where j s the proft of frm j n cty. Here, R can be used to reflect the sze of a cty. If the ctes are smlar n terms of ther sze and the effectveness of ther respectve nfrastructures, t s lkely that ctes and wll share the fnancal and dstrbuton markets equally. However, f one cty s much larger than the other and, thus, has more resources, t s lkely that the larger cty wll capture both markets. In a later secton, we derve the condtons that determne whch of these scenaros wll emerge. () econd tage In the second stage of the game, each fnancal frm decdes how many nvestors to serve, as well as an optmal prce to charge. Recall that an nvestor has to acqure a loan from a fnancal frm to fnance producton. If an nvestor fnds that producton s unproftable, he wll not apply for a loan. Ths condton lmts the maxmum prce the fnancal frm can charge to nvestors and, hence, consttutes a constrant on the frm s proft maxmzaton decson. enote as the prce fnancal frm charges to nvestors, and x as the number of nvestors served by the frm. Let P be the compettve prce at whch nvestors can sell ther goods locally. The objectve of fnancal frm s to choose followng problem: and x to solve the max x s ( ) ( ) C dx C x 0 (5) {, x } subject to C P x. (6) or analytcal smplcty, we assume that the fnancal frm s servce cost, C, s ndependent of the number of nvestors served by the frm. However, ths servce

8 9 Journal of Economcs and Management cost s a functon of nfrastructure I, as descrbed by equaton (1). ote that ( C ) x n equaton (6) s the cost to the nvestor at locaton x of obtanng nformaton about fnancal frm. mlarly, we can express the proft maxmzaton problem faced by fnancal frm by replacng () Thrd tage x wth (1 ) and changng the subscrpt to. x In the thrd and last stage of the game, dstrbutor or has to decde how many nvestors to serve, and at what prces. In our settng, the number of nvestors s dependent on the equlbrum outcome of the second stage. If an nvestor decdes not to obtan any loan from a fnancal frm, he wll not hre any dstrbutor ether, smply because he s not producng. Let * P be the compettve prce of the homogeneous good n the world market. Under the assumpton that * P P, there s an ncentve for the nvestors to export. Gven the servce prces charged by the dstrbutors, the nvestors wll not hre the dstrbuton frms f they realze that exportng s unproftable. Ths condton mposes a constrant on the prce that a dstrbutor can charge. The constraned proft maxmzaton problem that dstrbutor solves s: max y ( ) ( ) C dy C y 0 (7) {, y } subject to * C b P ( x ) y. (8) mlarly, we can set up the constraned proft maxmzaton problem for dstrbutor by replacng ote that y wth (1 ) and by changng the subscrpt to. y y s the number of nvestors served by dstrbutor. We also assume that a dstrbutor s servce cost, C, s ndependent of y. However, ths servce cost s a functon of nfrastructure I as gven by equaton (). The term s the prce that dstrbutor charges. The term ( b ) y s the cost of shppng the good to cty. The budget constrant n (8) s slghtly dfferent from that for a fnancal frm as dscussed earler. nce an nvestor has to acqure a loan from a fnancal frm for producton, the nvestor has to subtract the cost of hrng a fnancal frm, ( ( C ) x ), n calculatng the proft from exportng. The budget

9 The Economcs of Inter-Cty Competton n nancal and strbuton Markets 93 constrant holds only when an nvestor hres dstrbutor or otherwse the nvestor wll just sell hs product locally. 3 Monopolstc nancal rm and strbuton rm As n game theory, we use backward nducton to solve the three-stage game. We focus our analyss temporarly on a sngle cty case by assumng that the fnancal and dstrbuton frms n cty are neffcent to the pont where they do not offer any servces. In ths case, fnancal frm and dstrbutor become monopolstc servce provders. Three possbltes of nterest to our analyss are as follows: 1) Both fnancal frm and dstrbutor serve ther respectve markets completely; ) nancal frm serves ts market completely, but dstrbutor serves ts market partally; 3) Both fnancal frm and dstrbutor serve ther respectve markets partally. 6 In what follows, we dscuss the whole market case and the partal market case separately. We begn our analyss wth dstrbutor at stage three and then fnancal frm at stage two. (.s)thrd stage: dstrbutor strbutor s able to serve the entre dstrbuton market f and only f: 3b * C P C x. (9a) Ths s the scenaro where y 1. Gven ths condton, we derve the prce that dstrbutor charges to the nvestor by solvng the constraned proft optmzaton problem (see equatons (7) and (8)): * C b P x. (9b) strbutor serves the market only partally f and only f: 6 ote that, under ths settng, t s not possble to have a case n whch the dstrbuton frm serves the whole market and the fnancal frm serves only a part of the market. Investors are requred to hre a fnancal frm f they want to start producng. However, snce the fnancal frm decdes to serve only a part of the market, some nvestors must be left out and, thus, wll not hre a dstrbuton frm because they are not producng anythng.

10 94 Journal of Economcs and Management 3b * C P C x. (9c) In ths scenaro, strbutor determnes and y that maxmze proft n equaton (7) subject to the constrant n equaton (8). The solutons are: * 1 [ P ] [ C Cx ], (9d) * 1 y [ ( P C ) x ]. (9e) b 3 3 In the above two cases, servce prce depends on x, the number of nvestors who are served by dstrbutor. The dstrbutor has to take nto account the servce prce that fnancal frm charges,, n the second stage of the three-stage game. (.s)econd stage: fnancal frm nancal frm s able to serve the entre fnancal market f and only f: 3C P C. (10a) Ths s the scenaro n whch x 1. Gven ths condton, we solve the constraned proft maxmzaton problem (see equatons (5) and (6)) for the prce that fnancal frm charges to the nvestors: C P. (10b) nancal frm serves the market only partally f and only f: 3C P C. (10c) nancal frm determnes and subject to the constrant n equaton (6). The solutons are: x that maxmze proft n equaton (5) C P, (10d) 3 3 ( x P C ). (10e) 3C

11 The Economcs of Inter-Cty Competton n nancal and strbuton Markets 95 Case I: Both frms n cty serve ther respectve markets completely In ths case, x 1 and y 1. The servce prce charged by fnancal frm s gven n equaton (10b). To determne the servce prce charged by dstrbutor, we substtute equaton (10b) nto equaton (9b) and set x 1 to obtan: b * P P. We calculate profts for fnancal frm and dstrbutor whch are gven, respectvely, as: C * b P C and P P C. (11) Case II: Only fnancal frm serves ts market completely In ths case x 1 and equaton (10b) also defnes. To obtan substtute equaton (10b) nto equaton (9d) and set x 1 to obtan: 1 3 3, we * [ P P] C. (1) To obtan y, we frst set (1) nto equaton (9e) to get: x to be 1 n equaton (9e). We then substtute equaton 1 C 1 y P P b * [ ( ) ]. (13) We calculate the proft for dstrbutor as follows: * 1 * C 1 ( P P C ) [ ( P P) ]. (14) 3 b In ths case, the proft for fnancal frm s dentcal to that n the prevous case: C P C. (15) Case III: Both frms n cty serve ther respectve markets partally In ths case, s gven from equaton (10d) and (10e). The proft for fnancal frm s: x s gven from equaton

12 96 Journal of Economcs and Management ( P C ) ( P C ). (16) 3 3C To derve y, we substtute equatons (10d) and (10e) nto equaton (9e) to get: 1 * 4 y ( [ P P C ] C. b 3 9 mlarly, to obtan to get:, we substtute equatons (10d) and (10e) nto equaton (9d) * 4 1 ( P P) C C We calculate the proft for dstrbutor as follows: * 4 1 * 4 [ ( P P) C C ] ( [ P P C ] C. (17) b 3 9 (.s)rst stage Here we only consder Case I n whch fnancal frm and dstrbutor serve ther respectve markets totally. Recall that ther proft functons are gven, respectvely, as: where C P C, (18) * b P P C, (19) C and equatons (1) and (). C are the costs of provdng servces by the frms as defned n The objectve of government s to choose followng proft maxmzaton problem: I and I that solve the max ( ) I I subject to {, } R I I, where and problem yelds: are gven n equatons (18) and (19). olvng the above

13 The Economcs of Inter-Cty Competton n nancal and strbuton Markets 97 I I R ( ), (0) R ( ). (1) The equlbrum servce costs for fnancal frm and dstrbutor are gven, respectvely, as: C C C R s ( ), C R s ( ). We can use above equatons to calculate and. 4 uopoly n the nancal Market We proceed to examne the case n whch the fnancal frms of two ctes compete n the fnancal market. We consder the whole market scenaro where every nvestor s completely served by the same fnancal frm (ether or ). It s necessary to determne the crtcal nvestor who s ndfferent between fnancal frm and fnancal frm. The nvestor, denoted as x, wll be ndfferent f: d C C x (1 x ) d d. () olvng for x yelds: d 1 1 ( ) C. (3) x d Ths equaton s smlar to equaton (19) for the case of dstrbuton frms dscussed n Long and Wong (009). There are three possbltes: 1) Case I: If, then x 1 and fnancal frm serves the entre C d fnancal market. nancal frm charges the servce prce, ( ) f P, and P ( C ) f P. C

14 98 Journal of Economcs and Management ) Case II: If, then x 0 wth fnancal frm servng the C d entre fnancal market. nancal frm charges the servce prce, ( C ) f P, and P ( C ) f P. 3) Case III: If, then fnancal frm serves the nvestors located C at (0, x ) and fnancal frm serves those at ( x,1). d d As llustrated by Long and Wong (009), we derve the reacton functons of both the fnancal frm and dstrbutor by solvng the followng problem: C Max ( C ) x C subject to P x 0 C. The reacton functons of the respectve frms are: and C 1 R ( ) [ C ], 4 C 1 R ( ) [ C ]. 4 otce that R ( ) ntersects ( C ) when C (3 ) C. In other words, f * C dervaton shows that f (3 ) C, fnancal frm captures the entre market. A smlar C * (3 ) C, fnancal frm captures the entre fnancal market. Accordng to the lmted prcng proposton as shown n Long and Wong (009), f condton (9a) holds and P C (3 ) C, then fnancal frm captures the entre market by chargng a servce prce lower than the monopoly prce. Wth the above lmted prcng proposton, we derve the equlbrum condton for the second stage of ths game. Assume that both fnancal frms at ths second stage compete n Bertrand fashon by choosng servce prces smultaneously. We obtan smlar results to those n Long and Wong (009). Assumng the condton (9a) holds: 1) If C C (3 ) C, fnancal frm captures the entre market. Accordng to the lmt prcng theorem, f C P, fnancal frm charges the

15 The Economcs of Inter-Cty Competton n nancal and strbuton Markets 99 servce prce, C ( C ). On the other hand, f C P, the fnancal frm charges the monopolstc servce prce, P ( C ). ) mlarly, f C C (3 ) C, fnancal frm captures the entre market. Accordng to the lmt prcng theorem, f C P, fnancal frm charges the servce prce, C ( C ). On the other hand, f C P, fnancal frm charges the monopolstc servce prce, P ( C ). 3) nally, f C C (3 ) C, none of the two fnancal frms captures the entre market. It follows from the reacton functons that we have: C 1 ( C C ), 3 C 1 ( C C ). 3 5 uopoly n the strbuton Market In ths secton, we consder cases n whch a fnancal frm, ether or, captures the entre fnancal market. In other words, the partal fnancal market s not consdered here. urthermore, here we only consder the whole market soluton for the dstrbuton market. mlar to the prevous secton, we characterze the nvestor who s ndfferent between dstrbutor or dstrbutor. The nvestor, located at pont ndfferent f and only f: y, wll be d b C b C y x (1 y ) x d d. (4) To nvestor y, the cost of hrng dstrbutor s dentcal to the cost of hrng d dstrbutor. ote that on both sdes of equaton (4), the fnancal servce prce,, and the cost of obtanng nformaton, ( C ) x, are cancelled out. Ths s due to the assumpton that, at the second stage, there s only one fnancal frm (ether or ) capturng the entre fnancal market. olvng for y yelds: 7 d 7 Ths result s smlar to that of Long and Wong (009).

16 100 Journal of Economcs and Management 1 1 ( ) b. y d Here there are three nterestng possbltes, gven that only one fnancal frm domnates n the fnancal market: 1) If C C (3 ) b, dstrbutor captures the entre dstrbuton market. Accordng to the lmt prcng theorem, f C servce prce, C ( b ). On the other hand, f charges the monopolstc servce prce, P ( b ). P, dstrbutor charges the C P, dstrbutor ) mlarly, f C C (3 ) b, dstrbutor captures the entre dstrbuton market. Accordng to the lmt prcng theorem, f C P, dstrbutor charges the servce prce, C ( b ). On the other hand, f C P, dstrbutor charges the monopolstc servce prce, P ( b ). 3) nally, f C C (3 ) b, none of the dstrbutors s able to capture the entre dstrbuton market. It follows from the reacton functons that we have: b 1 ( C C ), 3 b 1 ( C C ), 3 * where P P ( C ) x. 6 How Government Resources Affect Market omnance Up to ths pont, our analyss s smlar to that of Long and Wong (009), wth the excepton of havng two markets n a sequental game. In ths secton, we examne how a cty s resource constrant determnes how much of a partcular market the cty can capture. or smplcty, we only consder two cases: (, ) and (, ). In each case, the frst element denotes the frm that domnates the fnancal market. or nstance, f the frst element s, the fnancal market s domnated by fnancal frm. mlarly, the second element denotes the frm that domnates the dstrbuton market.

17 The Economcs of Inter-Cty Competton n nancal and strbuton Markets The nancal Market Analyss of Case (, ) In ths case, both the fnancal and dstrbuton markets are captured by the frms from cty. Ths s dentcal to the prevous case n whch the frms located n cty are so ncompetent that the frms n cty are monopolstc servce provders n ther respectve markets. Therefore, the equlbrum amounts of nfrastructure bult by government for the dstrbuton and fnancal markets are, respectvely: I I R ( ), (5) R ( ). (6) Accordngly, the frms respectve costs of provdng servces are: C C C R s ( ), (7) C R s ( ). (8) ow, recall that fnancal frm captures the entre fnancal market f and only f: 3 C C C. (9) Let us assume that cty decdes on the amounts of nfrastructure and costs of provdng servces n a smlar way. That s: j j j j C C ( I ). Here, j can be ether or, dependng on the market assocated wth the cost. In order to guarantee the market domnance of fnancal frm, t must be the case that even f cty devotes all ts resources to buldng a fnancal nfrastructure,

18 10 Journal of Economcs and Management fnancal frm remans compettve enough that condton (9) contnues to hold. If cty dedcates all ts resources to construct a fnancal nfrastructure (.e., R I C ), then C becomes: C ( R ). (30) ubsttutng equatons (8) and (30) nto condton (9), we have: C ( R ) R 3 ( ) C. C s Then, rearrangng the terms yelds: R ( )( ) (C s C 3 ) ( ) C R. (31) Condton (31) consttutes the suffcent condton under whch the frms from cty capture both markets. Ths may occur when () cty has more resources than cty, () the fnancal nfrastructure of cty s more effectve than that of cty, or () cty has an advantage n terms of ts ntal servce cost ( C ) over that of cty ( C ), and s able to overcome cases where cty may have more resources than cty. By symmetry, the fnancal and dstrbuton frms n cty capture ther respectve markets entrely f and only f: R ( )( ) (C C 3 ) ( ) C R. (3) The above fndngs permt us to establsh the followng proposton: Proposton 1: If the relatonshp between the amount of resources ( R ) avalable to cty and the amount of resources ( R ) avalable to cty satsfes condton (31), then the fnancal and dstrbuton frms located n cty capture ther respectve markets entrely. Consequently, the frms located n cty do not capture ether market. By contrast, f the relatonshp between R and R satsfes condton (3), then the fnancal and dstrbuton frms located n cty capture ther

19 The Economcs of Inter-Cty Competton n nancal and strbuton Markets 103 respectve markets entrely, and the frms located n cty do not capture ether market Analyss of Case (, ) ext, we consder the case n whch fnancal frm captures the fnancal market and dstrbutor captures the dstrbuton market. Gven that the dstrbuton market s domnated by dstrbutor, there s no ncentve for government to nvest resources n the local dstrbuton nfrastructure to help ts dstrbutor lower ts operatng costs. Instead, government decdes to allocate all avalable resources to construct the fnancal nfrastructure (.e., R I ). We can justfy ths stuaton usng backward nducton. uppose that government has to determne the amount of resources to be allocated to construct the dstrbuton nfrastructure. By backward nducton, government starts the game backwards, and examnes the thrd stage frst. Gven the parameters, government knows that ts dstrbuton frm cannot compete n the dstrbuton market. Therefore, ts optmal strategy s to expend all avalable resources on the fnancal nfrastructure. However, n the thrd stage, t s unclear whether government wll expend all ts resources on ts dstrbuton nfrastructure. Therefore, for fnancal frm to domnate the fnancal market, t must be the case that, even f government expends all ts resources on enhancng ts fnancal nfrastructure, fnancal frm remans compettve enough to capture the entre fnancal market. we have: By substtutng equaton (30) nto condton (9) and replacng I wth R, C ( R ) 3 R C. C s After rearrangng the terms, we have: R ( ) C 3 ) C R. (33) (C By symmetry, fnancal frm captures the entre fnancal market and dstrbutor captures the entre dstrbuton market f:

20 104 Journal of Economcs and Management R ( ) C 3 ) C R. (34) (C We summarze the above condtons and combne them nto Proposton 1a: Proposton 1a: If condton (33) holds, fnancal frm captures the entre fnancal market. urthermore, n the case n whch the frms located n cty capture both markets, condton (31) must hold. By contrast, f condton (34) holds, fnancal frm captures the entre fnancal market. urthermore, condton (3) must hold for the frms located n cty to capture both markets. nally, f both condtons (33) and (34) fal to hold, then nether frm s able to domnate the fnancal market. gure 1 presents a graphcal llustraton of the aforementoned fndngs. Lne AB represents condton (33). or any dstrbuton of resources (, ) R R (that les to the rght of lne AB, fnancal frm captures the entre fnancal market. Lne C represents condton (31). or any dstrbuton of resources lne C, the frms n cty capture both markets. (, ) R R to the rght of Cty domnates both markets G o sngle frm domnates the B E fnancal market Cty domnates both markets 0 A C gure 1: The strbuton of Government Resources Affects the Market omnance

21 The Economcs of Inter-Cty Competton n nancal and strbuton Markets 105 The next case s where fnancal frm domnates the fnancal market. Condton (3) and condton (34) are represented by lne GH and lne E, respectvely. or any allocaton of resources (, ) R R that les to the left of lne E, fnancal frm captures the entre fnancal market. In addton, f such a resource dstrbuton also les to the left of lne GH, both markets are domnated by the frms n cty. nally, for any dstrbuton of resources (, ) R R that les between lne AB and lne E, no sngle frm s able to capture the entre fnancal market. In other words, ths s the area where the fnancal market s shared between the two ctes. It s nstructve to nvestgate how the effectveness of the fnancal nfrastructure n a cty affects the market domnance of the fnancal sector. Here, we focus on the case for cty. If the fnancal nfrastructure n a gven cty becomes more effectve, ceters parbus, the value of ncreases. Ths case may emerge when, for nstance, cty has a new polcy-maker who s more capable than hs predecessor. Intutvely, an ncrease n the effectveness of the fnancal nfrastructure wll enhance the ablty of fnancal frm to capture the fnancal market. In terms of condton (33), a larger makes the rght-hand sde of the nequalty smaller. In other words, t becomes easer for cty to domnate the fnancal market. gure provdes a graphcal nterpretaton of ths fndng. An ncrease n shfts the lne AB to AB. Thus, the area between AB and AB ndcates the gans from ths mprovement.

22 106 Journal of Economcs and Management R B B 0 A A R s gure : An Improvement n nancal Infrastructure Enhances the Market omnance of the nancal ector However, t s unclear whether an ncrease n wll also help cty capture the dstrbuton market. On the one hand, equaton (5) ndcates that an ncrease n ncreases other hand, the ncrease n I. Consequently, dstrbutor becomes more compettve. On the reduces the amount that government nvests n the fnancal nfrastructure. Ths makes condton (31) more dffcult to satsfy. In other words, t reduces the ablty of cty to capture both the fnancal and dstrbuton markets. The net result depends on the relatonshp between and : () If, an ncrease n mproves the lkelhood that cty wll capture both markets; () If () If, an ncrease n both markets; market., an ncrease n reduces the lkelhood that cty wll capture has no effect on capturng the dstrbuton

23 The Economcs of Inter-Cty Competton n nancal and strbuton Markets 107 We summarze these fndngs n the followng proposton: Proposton : An ncrease n mproves the lkelhood of cty capturng the entre fnancal market. However, t s ambguous whether ths mprovement wll also help cty capture the dstrbuton market. Corollary : An ncrease n, j, reduces the lkelhood of cty capturng the entre fnancal market. j We can prove Corollary by analyzng the mprovement n perspectve of cty. from the ext, we examne how the relatve effectveness of the fnancal nfrastructure nfluences the domnance of the fnancal market. uppose that decreases. Ths decrease may be caused by an ncrease n, a decrease n, or both. If t happens because of an ncrease n or smultaneous changes n and, from condton (33), gure shows how ths change ncreases the compettveness of fnancal frm. On the other hand, f the decrease occurs because of a decrease n, then the graphcal representaton s slghtly dfferent. In ths case the slope becomes steeper, but the ntercept remans unchanged. gure 3 llustrates ths change. Recall that condton (33) s used to graph lne AB. Wth ths ncrease n the slope, the lne swtches to AB. As n the prevous case, the area between lne AB and lne AB represents the gan from the mprovement n the effectveness of the fnancal nfrastructure. However, t s ambguous whether ths mprovement wll also assst dstrbuton frm n capturng the dstrbuton market. Proposton apples f ths mprovement s caused by an ncrease n or by smultaneous changes n and. However, f ths mprovement s caused by a reducton n, condton (31) tells us that ths reducton helps the frms n cty to capture both markets. We summarze ths result n the followng proposton: Proposton 3: An mprovement (A reducton) n the relatve effectveness of the fnancal nfrastructure helps (prevents) cty capture the fnancal market. Whether the magntude of ths ncrease (decrease) wll enhance the market domnance depends on the source of the mprovement. evertheless, t s ambguous how changes n relatve effectveness affect the market domnance of the dstrbuton

24 108 Journal of Economcs and Management sector. R B B A R s gure 3: A eclne n the Rval Cty s nancal Infrastructure Enhances the Market omnance of the nancal ector ext, we examne how changes n the ntal cost affect the fnancal market. It s reasonable to assume that the ntal cost s postvely related to the hstory of the cty. Establshed ctes have lower ntal costs than newer ctes. Therefore, one can argue that by examnng the ntal cost dfferental, we can evaluate how the hstory of the cty affects the fnancal market. We contnue to use cty as an example, and suppose that the ntal cost dfferental, C s C, decreases. It follows from equaton (33) that ths decrease causes a parallel shft n lne AB to the left, as shown n gure 4. Ths change n the ntal cost dfferental helps fnancal frm to serve more nvestors n the fnancal market. The gan n market share s measured by the area between lne AB and lne AB. Moreover, an nvestgaton of equaton (31) reveals that ths decrease n the ntal cost dfferental also helps dstrbutor capture the dstrbuton market. nce the term on the rght-hand sde of equaton (31) becomes smaller, t s more lkely that the nequalty condton s satsfed. We summarze ths fndng n the followng

25 The Economcs of Inter-Cty Competton n nancal and strbuton Markets 109 proposton. Proposton 4: A decrease (An ncrease) n the ntal cost dfferental of provdng servces helps cty to capture (prevents cty from capturng) both the fnancal and dstrbuton markets. R B B 0 A A R s gure 4: An Improvement n the Intal Cost fferental Enhances the Market omnance of the nancal ector 6. The strbuton Market In ths secton, we examne how government resource constrants affect the dstrbuton market. Gven that we consder a three-stage sequental game, we assume that fnancal frm captures the entre fnancal market. That s, equaton (33) holds. 8 As n ecton 6.1, we consder only two cases, namely, (, ) and (, ) Analyss of Case (, ) 8 Cases of partal fnancal markets are gnored owng to ther mathematcal complexty.

26 110 Journal of Economcs and Management In ths case, the frms n cty domnate both markets. Ths case s dentcal to the one n whch the frms n cty have monopolstc power over ther respectve markets. As a result, the amount nvested by government n the dstrbuton nfrastructure s dentcal to that n equaton (0): I R ( ). (35) The equlbrum servce cost for dstrbutor s: C C R s ( ). (36) ow, recall that n analyzng the duopoly n the dstrbuton market, the frms n cty capture both markets f and only f: 3 C C b. (37) or cty to domnate both markets, t must be the case that, even f cty devotes all avalable resources to buldng ts dstrbuton nfrastructure, dstrbutor remans suffcently compettve to capture the entre market. ubsttutng nto C yelds: C R I C ( R ). (38) ext, by substtutng equatons (36) and (38) nto equaton (37), we have: C ( R ) C R 3 s ( ) b. Then, rearrangng the terms yelds: R ( )( ) (C C 3 ) ( ) b R. (39) If the frms n cty wsh to domnate both markets, condton (39) must hold. In

27 The Economcs of Inter-Cty Competton n nancal and strbuton Markets 111 addton, recall from the prevous secton that condton (31) must also hold for cty to capture both markets. Therefore, gven that cty captures the fnancal market, both condton (31) and condton (39) must hold for cty to capture the dstrbuton market as well. mlarly, suppose cty captures the entre fnancal market. Then, the followng condton must hold: R ( )( ) (C C 3 ) ( ) b R. (40) Once agan, we know from the prevous secton that condton (3) must hold for cty to capture both markets. We can summarze these fndngs n the followng proposton: Proposton 5a: uppose condton (33) holds and cty captures the entre fnancal market. Then, cty wll also capture the dstrbuton market f condtons (31) and (39) are satsfed. mlarly, assumng that condton (34) holds and cty captures the entre fnancal market, cty wll also capture the dstrbuton market f condtons (3) and (40) are satsfed. 6.. Analyss of Case (, ) Ths s the case n whch cty domnates the fnancal market, but cty domnates the dstrbuton market. By backward nducton, we know that the optmal strategy for cty s to not nvest n the nfrastructure of the dstrbuton market (.e., I 0 and C s ). However, what about cty? By just observng the game n the C thrd stage, t s unclear what government should do. Thus, government wll move back to the second stage. Once government observes the second stage, t realzes that t cannot compete n the fnancal market. As a result, government wll allocate all avalable resources to mprovng the dstrbuton nfrastructure (.e., I R ). Gven ths condton, we have: C C ( R ). (41)

28 11 Journal of Economcs and Management It follows from the analyss n the secton on the duopoly n dstrbuton that case (, ) emerges f and only f: 3 C C b. (4) Replacng C wth C s and substtutng equaton (41) nto equaton (4), we have: C s C ( R ) 3 b. Then, rearrangng the terms yelds: R (C Cs ) 3 b.. (43) Thus, the above equaton consttutes the suffcent condton under whch case (, ) arses. In addton, gven that fnancal frm domnates the fnancal market, condton (33) must also be satsfed. There are three possbltes: Case I: If ( ) (C ) Cs (3 ) b 0, the terms on the rght-hand sde of equaton (43) become non-negatve. gure 5 llustrates ths case. Lne AB represents condton (33), and lne C represents the lne that satsfes both condtons (3) and (40). Lne E represents condton (43). We know that case (, ) must satsfy both condton (33) and condton (43). The area that satsfes both condtons s between BE and and bounded below by E. In addton, the area bounded above by E and lyng between BE and represents the case n whch fnancal frm domnates the fnancal market, but frm captures the entre dstrbuton market. Case II: ( ) (C ) Cs (3 ) b 0. In ths case, the rght-hand sde of equaton (43) s non-postve. gure 6 llustrates ths case. The obvous dfference between ths case and the prevous case s the non-exstence of a partal dstrbuton market. In ths case, the dstrbuton market s domnated by ether dstrbutor or dstrbutor. The above fndngs are descrbed n the followng proposton. Proposton 5b: uppose cty domnates the fnancal market and condton (33)

29 The Economcs of Inter-Cty Competton n nancal and strbuton Markets 113 holds. If both the suffcent condtons n (31) and (39) hold, cty captures both markets. If ether condton (33) or condton (39), or both, fal to hold, then there are two cases: () If ( ) (C Cs ) (3 ) b, a partal dstrbuton market does not exst. In other words, the dstrbuton market s domnated by dstrbutor. () If ( ) (C Cs ) (3 ) b, then a partal dstrbuton market exsts. R B (,) ψ C Cs + 3 ψ b E (,P) (,) A gure 5: The Case n Whch Ctes May hare the strbuton Market C R s

30 114 Journal of Economcs and Management R B (,) (,) 0 A C R s gure 6: The Case n Whch Ether Cty or Cty omnates the Entre strbuton Market By symmetry, we summarze the stuatons n whch cty domnates the entre fnancal market. Proposton 5c: uppose cty domnates the fnancal market and condton (34) holds. If both condton (3) and condton (40) hold, cty captures both markets. If ether condton (3) or condton (40), or both, fal to hold, then there are two cases: () If ( ) (C C ) (3 ) b, then a partal dstrbuton market does not exst. In other words, the dstrbuton market s domnated by dstrbutor ; () If ( ) (C C ) (3 ) b, then a partal dstrbuton market exsts. 7 Concludng Remarks In ths study, we extend the model of Long and Wong (009) to allow for a multdmensonal analyss, where two ctes compete to become the dstrbuton center and the fnancal center. We show that f the resources of one cty are more

31 The Economcs of Inter-Cty Competton n nancal and strbuton Markets 115 abundant than those of the other cty, ceters parbus, ths cty tends to domnate both markets. Ths concluson s reached under the assumpton that cty governments effcently use ther lmted resources to undertake cost-reducng nvestments n nfrastructure. Gven that the resources a cty has avalable may reflect the sze and the prosperty of the cty, our analyss mples that larger and wealther ctes are more lkely to become both the dstrbuton and fnancal centers. We observe ths phenomenon n the real world. or nstance, ngapore, rather than Manla, s the man fnancal market n outh East Asa. We further show that an mprovement n nfrastructure enhances the compettveness of ether the fnancal or the dstrbuton sector. Ths result s not lmted to cases that nclude physcal nfrastructure, such as buldngs. It also apples to, for example, legal and/or economc systems n a cty. A better legal system helps mprove the compettveness of local frms n nternatonal markets by provdng assurances and trust, as observed frequently n the real world. One of the common features of major fnancal ctes such as ew York, Hong Kong, Tokyo, and London s ther sophstcated legal systems. Our smple model provdes a possble explanaton as to why these ctes are capable of beng major players n the fnancal ndustry, both regonally and globally. Lastly, we should menton some caveats and, hence, potentally nterestng extensons to the proposed model. rst, we assume n our smple analyss that two competng ctes share a smlar geographcal background. However, ths s not realstc, because geographcal locaton affects the types of ctes and the compettveness of frms located wthn the ctes. or example, almost all major ctes n the world today are located along a coastlne. One could argue that the ntal costs n the model reflect some degree of geographcal advantage, but these advantages are not suffcent to explan how locaton affects market outcomes. Thus, a more complete framework that ncludes spatal competton should be consdered n future research. Another possble extenson s to ncorporate producton technology nto the analyss. In ths case, the qualty of labor and the return on captal may be mportant n determnng whether ctes can be major players n ther respectve markets. Economes of scale n producton may also play a crucal role n the equlbrum outcome of market competton. urthermore, whle we only consder two ctes and two sectors n our study, real-world stuatons are more

32 116 Journal of Economcs and Management complex than ths. Therefore, t would be nterestng to see how the solutons would change f we were to extend ths model beyond two ctes and two sectors. We postulate that whle the mathematcal form wll be more complcated, the basc prncples wll reman the same. nally, ths study can be extended by examnng how the nfrastructures of one sector provde postve externaltes to other sectors. or example, buldng more schools n a sector wll boost the qualty of workers n other sectors. In ths sense, rather than competng for resources, sectors may complement one another, whch wll affect the optmal allocaton of resources. Acknowledgements We thank the edtor, two anonymous referees, and Yang-Mng Chang for very helpful comments and suggestons. Any remanng errors are our own. References Anas, A. and K. Xong, (003), Intercty Trade and the Industral versfcaton of Ctes, Journal of Urban Economcs, 54, Behrens, K. and J.. Thsse, (007), Regonal Economcs: A ew Economc Geography Perspectve, Regonal cence and Urban Economcs, 37, Bosker, M.,. Brakman, H. Garretsen, and M. chramm, (010), Addng Geography to the ew Economc Geography: Brdgng the Gap between Theory and Emprcs, Journal of Economc Geography, Brakman,., H. Garretsen, and C. van Marrewjk, (00), Locatonal Competton and Agglomeraton: The Role of Government pendng, Workng Paper 775, CEfo. Brakman,., H. Garretsen, and C. van Marrewjk, (008), Agglomeraton and Government pendng, In: Brakman,. and H. Garretsen, (eds.), oregn rect Investment and the Multnatonal Enterprse, MIT Press. Cavalhès, J., C. Gagné, T. Tabuch, and J.-. Thsse, (007), Trade and the tructure of Ctes, Journal of Urban Economcs, 6, enge, R., M. von Ehrlch, and M. Wrede, (009), Publc Input Competton and Agglomeraton, Regonal cence and Urban Economcs, 39,

33 The Economcs of Inter-Cty Competton n nancal and strbuton Markets 117 ujta, M., P. Krugman, and A. J. Venables, (1999), The patal Economy: Ctes, Regons, and Internatonal Trade, Cambrdge, MA: MIT Press. Grajeda, M. R. and I. heldon, (009), Trade Openness and Cty Interacton, Workng Paper, MPRA Paper Henderson, J., (1974), The ze and Types of Ctes, Amercan Economc Revew, 64, Krugman, P. R., (1991), Increasng Returns and Economc Geography, Journal of Poltcal Economy, 99, Long,. V. and K. Y. Wong, (009), A Tale of Two Ports: The Economc Geography of Inter-Cty Rvalry, Revew of Internatonal Economcs, 17, Martn, P. and C. A. Rogers, (1995), Industral Locaton of Publc Infrastructure, Journal of Internatonal Economcs, 39, Ott, I. and. oretz, (010), Productve Publc Input, Integraton and Agglomeraton, Regonal cence and Urban Economcs, 40,