A duopoly of transportation network companies and traditional radio-taxi dispatch service agencies

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1 EJTIR Issu 8(), 08 pp. 96- ISSN: A duopoly of transportaton ntwork compans and tradtonal rado-tax dspatch srvc agncs Thorstn Hlkr Insttut of Transport Economcs, Unvrsty of Münstr, Grmany. Grnot Sg Insttut of Transport Economcs, Unvrsty of Münstr, Grmany. Transportaton ntwork compans commonly ntr th markt for tax rd ntrmdaton and altr th markt outcom. Compard to coopratvly organzd rado-tax dspatch srvc agncs, transportaton ntwork compans run largr flts and srv mor customrs wth lowr fars, whn th fxd costs of th dspatch offc ar rlatvly small. Th sam holds for prvat dspatch frms, whn th fxd costs of a taxcab ar not too small. Ths rsults ar shown n a two-stag duopoly of far and flt sz comptton wth far- and watng-tmdpndnt dmand. Kywords: dgtzaton, rgulatory captur, tax dspatch markt, transportaton ntwork compans.. Introducton Espcally n larg cts, tax rds ar an mportant part of publc transportaton. Popl dmand tax srvcs bcaus thy ar convnnt and fast, thy may not hav a drvng lcns, thy can dsmbark wthout sarchng for parkng, or do not hav accss to a prvat car. Th markt for tax rds can b dvdd nto thr submarkts (Schallr, 007). Th frst s th cabstand markt, found, for xampl, at ralway statons or cty cntrs, whr taxcabs ar watng for customrs n a ln. In Grmany, ths accounts for about prcnt of tax rd starts. Th scond markt s th strt hal markt, whr customrs n cts flag down taxcabs drvng n th strts. In Grman cts, only around tn prcnt of tax rds ar ntatd n ths way. In som Amrcan and Asan cts, ths shar s notably hghr. Th most mportant markt n Grman cts (50-60 prcnt), but also for xampl n Pars or Stockholm (Darbéra, 00), s th dspatch markt. Customrs ordr taxcabs by contactng a tax frm or rado-tax dspatch srvc agncy (RDS) by phon or app. Ths agncs or cntral offcs thn slct a cab for th customrs (Coopr t al., 00). Bcaus th papr analyss th bhavor of such tax ntrmdars, t focuss on th dspatch markt. Thr ar mostly only a fw RDSs n ach cty, so that monopolstc, duopolstc or olgopolstc markt structurs prdomnat. An analyss of th largst Grman cts prsntd n Fgur shows that, for xampl, n Munch and Cologn, narly all tax drvrs and compans us th srvcs of two larg rado-tax dspatch srvc agncs. In Stuttgart and Nurmbrg, only on RDS s prsnt. Smlar forms of th dspatch markt prval, for xampl, n othr countrs of th EU lk Franc and Italy and n th USA (Coopr t al., 00; Frazzan t al., 06). A: Am Stadtgrabn 9, 4849 Münstr, Grmany T: E: thorstn.hlkr@ww.un-munstr.d A: Am Stadtgrabn 9, 4849 Münstr, Grmany T: E: grnot.sg@un-munstr.d

2 Hlkr and Sg A duopoly of transportaton ntwork compans and tradtonal rado-tax dspatch srvc agncs 97 Hamburg Essn Brmn Hanovr 5 3 Brln 3 6 Dussldorf Cologn Dortmund Frankfurt Lpzg Drsdn 4 Nurmbrg Coopratvs Prvat Compans and othrs Stuttgart Munch Fgur. Numbr of RDSs n Grman Cts RDSs can b organzd prvatly or coopratvly and th two typs pursu dffrnt objctvs. Coopratvly organzd agncs dstrbut thr rvnu among all mmbrs (.. all drvrs) and thrfor am to maxmz th proft accrung to ach drvr,.. th avrag proft. Prvat frms tak nto account only th frm ownr s proft, whch s th aggrgat proft of all drvrs. Th markt for tax rds s charactrzd by som spcfcs that should b notd for analytcal purposs. Th dmand for tax srvcs s not only dtrmnd by th far of a rd, th watng tm also plays an mportant rol. Customrs prfr a straghtaway srvc, so that a rd crats a ngatv xtrnalty. Whn a customr occups a taxcab, all othr potntal customrs hav to wat longr than bfor (Orr, 969; Carns and Lston-Hys, 996; Frnandz t al., 006). Contrarws, thr ar conomcs of dnsty; doublng trps and taxcabs rducs watng tm (Arnott, 996). Dpndng on th markt typ, ths xtrnalts ar rgularly not ntrnalzd n th far, spakng n favor of rgulaton. In most countrs, th fars tax drvrs should charg, th numbr of taxcab lcnss and mnmum standards for vhcls ar rgulatd. But rgulaton can b nffcnt as wll. Many conomsts shar th vw that rnt-skng plays a larg rol n tax markt rgulaton (Barrtt, 003; Darbéra, 00; Ctn and Erygt, 03), bcaus tax frms ar abl to captur th rgulatory procss and nsur rgulaton that corrsponds to thr own objctvs (rgulatory captur). W can ntgrat th mplcatons of rgulatory captur wth rgard to th markt ntry of taxcab drvrs nto our modl. Informaton asymmtrs ladng to qualty problms, anothr argumnt n favor of rgulaton, ar not mportant n th dspatch markt, bcaus customrs can choos a partcular company from whch to ordr a tax rd. Th frms thrfor am at a stabl customr rlatonshp and rpat purchass, so thy do not xplot unnformd customrs, but hav an ncntv to satsfy thm. Furthrmor, bad rvws could dtr othr customrs.

3 Hlkr and Sg A duopoly of transportaton ntwork compans and tradtonal rado-tax dspatch srvc agncs 98 Ovr th last fw yars, dgtzaton has nabld nw busnss modls, cratng an ablty to arn mony n th markt for tax rds, spcally n th dspatch markt. Customrs can ordr a tax srvc wth th hlp of a smartphon app lk Ubr or Lyft, and th app oprator allocats a narby drvr to th rqustr. Th rd rout and th far ar usually st by th oprator of ths transportaton ntwork company 3 (TNC), whch arns a fxd shar of th drvr s rvnu. Ths compans dffr n thr busnss modl from th tradtonal RDSs. Whn fars ar not rgulatd, Ubr adjusts th far usng a so-calld surg prcng algorthm to balanc supply and dmand (Hall t al., 05). Cramr and Krugr (06) show that jonng Ubr may ncras capacty utlzaton and thus th productvty of tax drvrs, by rducng mpty drvs and dl tm. Apps clam that thy srv as an ntrfac whr tax drvrs and tax customrs mt, but n fact, by fxng th product (rout) and th prc (far), thy act as an ordnary tax frm. TNCs can compt wth th prsnt rado-tax dspatch srvc agncs n ach town. From a thortcal pont of vw, th quston arss as to what a tax dspatch markt, ncludng transportaton ntwork compans lk Ubr or Lyft, looks lk. RDSs and TNCs hav dffrnt busnss concpts that, as w wll show, rsult n dffrnt flt szs, dffrnt fars, and dffrnt numbrs of rds. Thr has bn som rsarch on modlng th markt for tax rds. Whl, for xampl, Douglas (97), Carns and Lston-Hys (996), Frnandz t al. (006) and Qan and Ukkusur (07) gnratd aggrgatd modls for th strt hal markt, Häcknr and Nybrg (995) and von Massow and Canbolat (00) dvlopd modls for th dspatch markt. Von Massow and Canbolat (00) provd a spatal dspatch modl, whr taxs ar locatd n spcfc zons and rcv ordrs n a crtan chronology. Häcknr and Nybrg (995) dsgnd an aggrgatd modl for an olgopolstc dspatch markt and showd that coopratvly organzd RDSs ar rlatvly lss ffcnt than prvatly ownd RDSs. Anothr larg group of studs ntgratd th spatal structur of tax srvcs nto tax markt modls, spcally for th strt hal markt. Yang and Wong (998) dvlopd a ntwork modl to analyz tax movmnts n cts. Th modl has bn xtndd to consdr dmand lastcty and road congston (Wong t al., 00), markt comptton and rgulaton (Yang t al., 00), mult-prod dynamc tax srvcs wth ndognous srvc ntnsty (Yang t al., 005), multpl usr classs and vhcl mods (Wong t al., 008) and nonlnar prcng (Yang t al., 00a). Wong t al. (005) and Yang t al. (00b) ntroducd mathmatcal modls to consdr th blatral-sarchng bhavor of vacant taxs and customrs n th strt hal markt through mtng functons. Ths modls wr furthr nhancd to analyz th qulbrum proprts (Yang and Yang, 0) and dal wth congston ffcts (Yang t al., 04). H and Shn (05) ncludd th prsnc of an -halng platform n a ntwork modl, and Wang t al. (06) gnratd th prcng stratgs of a tax-halng platform usng th mtng functon. In thr modl, tax drvrs ar fr to us th -halng platform or to do roadsd halng. Th modl most closly rlatd to ours s that of Zha t al. (06). Thy nvstgat th markt mpacts of a monopoly rd-sourcng srvc lk Ubr, and of a duopoly of rd-sourcng srvcs n an aggrgatd modl. Thy stat that rgulatd comptton may not ncssarly lad to lowr prcs and hghr socal wlfar than a rgulatd monopoly. W nclud transportaton ntwork compans n th tax dspatch markt modl of Häcknr and Nybrg (995). In contrast to Zha t al. (06), w compar th markt outcoms of a duopoly of TNCs wth thos of a duopoly of tradtonal rado-tax dspatch srvc agncs. Addtonally, an asymmtrc duopoly of on coopratvly organzd RDS and on TNC and th rgm of rgulatory captur ar consdrd. In our two-stag gam, compans frst choos th numbr of taxcabs n thr flt and thn compt on prc. W compar th markt outcoms and focus on th flt szs or on th markt ntry of tax drvrs n four dffrnt rgms: Th frst s a symmtrc duopoly of coopratvly organzd RDSs that attmpt to maxmz th avrag proft of ach drvr, bcaus thy 3 Ths trmnology was ntroducd by th Calforna Publc Utlts Commt n 03 to classfy Ubr-lk compans.

4 Hlkr and Sg A duopoly of transportaton ntwork compans and tradtonal rado-tax dspatch srvc agncs 99 dstrbut thr rvnu among all mmbrs (Rgm ). By contrast, prvatly organzd RDSs attmpt to maxmz th ovrall proft of ach company/rds (Rgm ). Th thrd rgm s a duopoly of transportaton ntwork compans, whr ach TNC pays taxcab drvrs a fracton of th rvnu and thrfor trs to maxmz rvnu (Rgm 3). Fnally, th rgm of rgulatory captur s addd. W analyz full rgulatory captur by assumng n ths rgm, that two coopratvly organzd RDSs collud and ar abl to captur th rgulatory procss, so that th prc and th numbr of taxcabs ar st to maxmz thr aggrgat profts (Rgm 4). Markt ntry, and vn th prncpl of rvnu sharng, fostr comptton and srv customrs wll n th rado-tax dspatch markt. It can b shown that flt szs ar largr and fars smallr, n a duopoly of transportaton ntwork compans (Rgm 3), than n a duopoly of prvatly organzd RDSs (Rgm ), f th fxd costs of a taxcab ar not too small. Th lvl of fxd costs of an ntrmdary dtrmns th rlatonshp btwn Rgm (coopratvly organzd RDSs) and Rgm 3 (TNCs). Th flt szs n a duopoly of TNCs xcd thos n a duopoly of coopratvly organzd RDSs, f th fxd costs of an ntrmdary ar small. If th fars and numbr of lcnss ar rgulatd, and th rgulaton s capturd by th tax frms (Rgm 4), ths lads to th smallst flt szs of all rgms. In an asymmtrc duopoly of on coopratvly organzd RDS and on TNC, both ncras thr flt szs compard to thos n thr symmtrc duopols.. Th Modl Smlarly to Häcknr and Nybrg (995), w consdr a duopoly of frms that srv as an ntrmdary for tax rds. Each RDS or TNC has f afflatd taxcabs as a flt, and offrs dspatchd taxcab srvcs to customrs wth fars that ar lnar n th quantty q of (homognous) tax rds consumd. Consumrs drv utlty from tax rds and th consumpton of compost good y. Utlty ncrass at a dcrasng rat wth th numbr of trps q and dcrass n watng tm. To smplfy th analyss, a spcfc utlty functon of a rprsntatv consumr that sngl-homs wth tax ntrmdary s assumd: U = y + (w α q )q β Q q δ f. () Th margnal utlty of th frst tax trp s assumd to b w. Ths utlty xcds th varabl costs of a rd (w>c), bcaus othrws, thr would b no qulbrum n th markt. Th dmnshng margnal utlty of addtonal trps s paramtrzd by α. Watng tm dpnds on th quotnt of aggrgat dmand Q of frm and th flt sz f of ths company. Th tchncal ablty to match customrs and taxcabs to rduc dl and watng tm s dnotd by δ. Th margnal dsutlty of th frst scond of watng tm s zro, but th margnal dsutlty ncrass whn mor trps ar dmandd and watng tm rss, whch s paramtrzd by β. Facng a budgt constrant of I = y + p q, whr th compost good y s th numrar, th utlty-maxmzng consumpton of tax rds s q = w p β / δ Q / f. () α If th numbr of consumrs s normalzd to on, th aggrgat dmand for frm s Q = q m, whr m = m s th markt shar of frm and m = -m s th markt shar of frm. Consumrs sarch for th bst combnaton of prc and watng tm, but f both frms ar opratng n th markt, customrs must b ndffrnt btwn th two,.., th ndrct utlts hav to b dntcal: V(p,Q,I) = V(p,Q,I), whch mans that p + β Q = p δ f + β Q. (3) δ f

5 Hlkr and Sg A duopoly of transportaton ntwork compans and tradtonal rado-tax dspatch srvc agncs 00 Solvng ths quaton for th markt shar m lads to m = f (αδ f ( p p ) + β( p w)). (4) β( f p + f p ( f + f )w) Ths valu for th markt shar dtrmns th aggrgat dmand Q of company : Q = δ f (αδ f ( p p ) + β(w p )) j j. (5) β(β + αδ ( f )) In th two-stag gam of ths modl, frms frst choos th numbr of taxcabs n thr flt and thn compt on prc. W do not nclud congston rsultng from dffrnt flt szs n th rgms. On th on hand, largr flt szs should c.p. lad to mor congston. On th othr hand, L t al. (06) hav shown that th markt ntry of a TNC lk Ubr dcrass congston n th urban aras of th Untd Stats, bcaus th traffc of prvat cars shrnks. Thus, th ffct of flt sz on congston s ambguous, thus prvntng a tractabl ncluson n th modl. To solv th dynamc gam of dtrmnng flt szs and prcs w us th mthod of backward nducton and consdr and compar dffrnt typs of frms. RDSs can b organzd coopratvly or prvatly. Morovr, a duopoly of transportaton ntwork compans can b consdrd, or a rgm of rgulatory captur, so that frms collud and maxmz thr aggrgat profts.. Stag : prc comptton At Stag, th total contrbuton margns (TCM) of th compans ar consdrd, bcaus fxd costs for th flt szs and th ntrmdars hav alrady bn pad. In Rgms -3, th two symmtrc compans compt on prc, so that qulbrum prcs can b calculatd. In th rgm of rgulatory captur, thr s no comptton, bcaus th compans collud and ar abl to st a common prc to maxmz th TCMs. RDSs W bgn wth th analyss of a duopoly of RDSs (thr coopratvly or prvatly organzd; Rgm and ). Aggrgat dmand Q lads to a TCM at Stag of th gam of ach RDS that bars varabl costs of c pr tax trp of TCM = ( p c) Q. (6) Th frms maxmz thr TCMs wth rspct to prcs, so that th racton functons p (p j) can b drvd and th qulbrum prcs p (f, ) ar p ( f, ) = c(β + αδ f )(β + 3αδ ) + β(β + αδ ( f ))w β + 6α δ f + 4αβδ ( f ) and th qulbrum quantts ar Q ( f, ) = δ f (β + αδ ( f ))(β + αδ )(w c) (β + αδ ( f ))(β + 3α δ f + αβδ ( f )). (8) Th corrspondng TCM of ach RDS at Stag s βδ f TCM ( f, ) = (β + αδ ( f )) (β + αδ )(c w) 4(β + αδ ( f ))(β + 3α δ f + αβδ ( f )). (9) (7)

6 Hlkr and Sg A duopoly of transportaton ntwork compans and tradtonal rado-tax dspatch srvc agncs 0 TNCs A tax frm that s organzd as a TNC (Rgm 3) bhavs dffrntly. 4 Frst of all, by matchng only customrs and taxcabs, th frm dos not bar th varabl costs of an addtonal trp. Bcaus of that, th total contrbuton margn quals th rvnu accrung to ach company (TCM = R ). On th othr hand, th TNC only rcvs a shar γ of th fars chargd. Thrfor, at Stag, th TNC maxmzs TCM! = γ p Q. (0) Th two TNCs maxmz thr total contrbuton margns wth rspct to prcs and th qulbrum prcs p (f, ) ar β(β + αδ ( f ˆp ( f, ) = ))w β + 6α δ f + 4αβδ ( f ) () wth p / f < 0 and th qulbrum quantts ar ˆQ ( f, ) = δ f (β + αδ ( f ))(β + αδ )w (β + αδ ( f ))(β + 3α δ f + αβδ ( f )). () Th corrspondng total contrbuton margn (rvnu) of ach TNC at th Stag s TCM! w ( f, ) = γ (c w) TCM ( f, ). (3) Comparng quatons 7 and shows: Proposton If th flt szs n a duopoly of RDSs ar as larg as thos n a duopoly of transportaton ntwork compans, tax fars ar lowr n a duopoly of TNCs. Rgulatory captur In many countrs, th fars and th numbr of taxcabs ar dtrmnd by a rgulatory authorty. Accordngly, a rgm wth rgulaton s consdrd. It s possbl that th rgulatory authorty dos not srv th ntrsts of socty as a whol, but s capturd by spcal ntrst groups (Stglr, 97; Barrtt, 003; Ctn and Erygt, 03; Gorck, 07). In Grmany, for xampl, far ncrass n cts ar oftn ntatd by th local RDSs. Poltcal bods thn mostly authorz th applcatons for far ncrass by ths frms. W analyz full rgulatory captur (Rgm 4), by assumng that two coopratvly organzd RDSs collud and ar abl to captur th rgulatory procss so that th prc and th numbr of taxcabs ar st to maxmz thr aggrgat profts. Ths rgm s not quvalnt to th monopoly cas, bcaus th watng tm for customrs dpnds on th flt sz of ach company. In th capturd rgm, thr ar stll two compans and two dffrnt flts. In a monopoly thr s only on flt. Thrfor, dmand s dffrnt vn f th monopoly runs as many taxs as th two duopolsts combnd. In th rgm of rgulatory captur, th dmand s calculatd as follows. Bcaus th frms ar symmtrc and thr s no comptton btwn th two compans (p = p j = p, q = q j = q, f = = f), th markt shars of th two compans ar /, so that n ths cas, Q = / q. Th utlty maxmzng numbr of tax rds (quaton ) thn quals q = (w p)δ f 4αδ f + β. (4) 4 Th varabls of th dffrnt rgms ar dnotd wth th followng accnt marks: Rgm : p ; Rgm :!p ; Rgm 3: ˆp ; Rgm 4: p.

7 Hlkr and Sg A duopoly of transportaton ntwork compans and tradtonal rado-tax dspatch srvc agncs 0 Th rsultng jont total contrbuton margn at Stag s TCM! = ( p c) q. (5) Th maxmzaton of TCM wth rspct to th prc ( TCM! / p = 0) lads to an qulbrum prc of p * = c + w. (6) Th prc n ths rgm s nfluncd only by th paramtrs w and c. Th qulbrum TCM of ach company at Stag s TCM! δ f (c w) = 4(β + 4αδ f ). (7). Stag : flt sz comptton W now analyz th maxmzaton at Stag by usng th rsults of th prc qulbra at Stag. Tax ntrmdars can dtrmn th numbr of taxcabs n thr flt f. It s assumd for all rgms that opratng a tax ntrmdary costs K r, ndpndntly of th numbr of taxcabs and customrs usng th srvc. A taxcab bars fxd costs of K c plus varabl costs of c pr trp. Smlar to Stag, thr s comptton n Rgms -3. In th rgm of rgulatory captur, thr s no comptton, bcaus th compans collud and ar abl to st th flt szs to maxmz th aggrgat proft. In th followng analyss, th rsults for th four rgms ar prsntd. Coopratvly organzd RDSs A coopratvly organzd RDS (Rgm ) maxmzs profts pr taxcab π = TCM K f c K r f (8) wth a frst-ordr condton whch holds f π = TCM / f f TCM f f f TCM + K r = 0, (9) f = TCM K r. (0) f Furthrmor, bcaus RDSs ar only proftabl f TCM -K c f K r, TCM / f K c must hold. For th comparatv statcs of th qulbrum of coopratvly organzd RDSs, s Häcknr and Nybrg (995) or Appndx B. Prvatly organzd RDSs Now consdr a duopoly of RDSs comprsng prvatly ownd frms (Rgm ) that maxmz thr profts by dtrmnng th flt sz. At Stag of th gam, thy follow th sam stratgy as coopratvly organzd RDSs. Howvr, at Stag, thy do not maxmz th avrag proft of a taxcab, but th aggrgat proft!π = f π = TCM f K c K r. ()

8 Hlkr and Sg A duopoly of transportaton ntwork compans and tradtonal rado-tax dspatch srvc agncs 03 Th frst-ordr condton s!π = TCM K f f c = 0. () For th comparatv statcs of th qulbrum of prvatly organzd RDSs, s Häcknr and Nybrg (995) or Appndx B. TNCs At Stag, ach TNC (Rgm 3) fxs th shar γ that t clams from th taxcab drvrs. Th drvrs thn dcd to ntr th markt and to jon a TNC. At th qulbrum, taxcab drvrs who hav to pay th fxd cost of ntry K c as wll as th varabl costs of cq / f and rcv a shar of -γ of rvnu of company, contnu to ntr th markt untl thr proft s zro (s Appndx A for drvaton): Ψ(γ, f ) = ( γ ) γ TCM! f c ˆQ K f c = 0. (3) Th transportaton ntwork company can antcpat th racton of th taxcab drvrs who wsh to jon th TNC f t changs th rvnu shar. Ths shar, as a functon of th flt szs γ (f ), can b dtrmnd from th quaton abov (s Appndx A). It s shown n th Appndx that th mpact of th flt sz on th rvnu shar s ngatv ( γ! / f! < 0) and vc vrsa. If th TNC clams a hghr shar of rvnu, fwr taxcab drvrs jon th TNC. Bcaus ths rlatonshp s bjctv, th TNC dtrmns on of th stratgy varabls γ or f, and th othr s thn dtrmnd as wll. Whras n ralty, th TNC dtrmns γ, w can analyz th bhavor by assumng that th TNC dtrmns f. Th transportaton ntwork company maxmzs ˆπ = TCM! Kr, (4) whch s maxmzd f ˆπ = γ w f f (c w) TCM w TCM + γ = 0. (5) (c w) f In Appndx B, t s shown that th fxd costs K r of th TNC and K c of a taxcab hav no ffct on th flt szs of th TNCs. K r ar sunk costs for th TNC. Furthrmor, th drvrs bar th fxd costs K c of a taxcab, so that thy do not nflunc th flt sz dtrmnaton of th rvnumaxmzng TNC. A rs n varabl costs c lads to hghr prcs and lowr quantts n ths rgm, whl th dmand paramtr w has a postv ffct on th quantty. Rgulatory captur In ths rgm, th proft pr drvr wth th nsrtd qulbrum prc s " π = TCM f K c K r f. (6) Th maxmzaton wth rspct to th flt sz ( π / f = 0) rsults n an qulbrum flt sz of β K f * = r. (7) δ (w c) α K r 4αδ K r Undr th assumptons of th modl, ths flt sz s postv f 0 < K r < (w-c) (6α) holds. An ncras n th paramtr w and th matchng ablty paramtr δ rducs th flt sz. If th wllngnss to pay of th customrs, or th tchncal ablty to match customrs and taxcabs rs,

9 Hlkr and Sg A duopoly of transportaton ntwork compans and tradtonal rado-tax dspatch srvc agncs 04 th RDSs wll, c.p., rduc thr flt sz to maxmz th avrag proft. In contrast, th qulbrum flt szs rs n trms of th cost paramtrs c and K r, and n th paramtr β. Th RDSs choos largr flt szs to sprad th costs ovr a largr numbr of drvrs. If th dsutlty accrung to customrs from watng tm s hgh, th RDSs choos a gratr flt sz as wll, to rduc th avrag watng tm (s Appndx B)..3 Comparson of rgms To compar th flt szs of th coopratvly organzd RDSs (C-RDSs) and th flt szs of th TNCs, w look at th margnal proft of th C-RDS π = TCM / f f f f TCM + K r f (8) at th proft maxmzng TNC flt sz f = f = f *. Th frst-ordr condton (5) can b transformd nto TCM γ = TCM f = TCM γ f, (9) ε f,γ f whr ε f,γ can b calld th rvnu shar lastcty of flt sz. Thrfor, at th proft maxmum of th TNC, quaton 8 s dnotd by π f f = ˆf * whch s ngatv, f = TCM ( ˆf * ) ( ˆf * ) TCM ( ˆf * ) ε f,γ f = ˆf * ( ˆf + K r * ) ( ˆf * ), (30) K r < TCM ( ˆf * ) ε f,γ f = ˆf * = ˆK r. (3) In ths cas, th flt szs of th TNCs ar largr than thos of th C-RDSs. Th oppost s tru f K r s largr than K r. For th TNCs, K r ar fxd costs that do not nflunc th dtrmnaton of flt szs. Th C-RDS maxmzs th avrag proft of a tax drvr. Each drvr has to bar a porton of K r, whch dpnds on th numbr of taxcabs n th C-RDS. If an addtonal drvr jons th C-RDS, ach drvr bars lss of K r. In th cas of hgh fxd costs, th C-RDS has an ncntv to ncras th flt sz, so as to splt costs btwn mor taxcabs. Transportaton ntwork compans optmz wthout consdrng varabl tax costs and thrfor oprat wth lowr prcs, whch usually mpls largr taxcab flts. If K r s larg (K r >K r ), th ncntv for C-RDSs to splt costs ovrcompnsats for th prc comptton ffct, and C-RDS flt szs bcom largr than TNC flt szs. Proposton In a duopoly of TNCs, th flt szs ar largr than n a duopoly of coopratvly organzd RDSs, f and only f K r <K r. In ths cas, th fars ar smallr n a duopoly of transportaton ntwork compans than n a duopoly of coopratvly organzd RDSs. 5 Nxt, w can compar th flt szs of a duopoly of TNCs wth thos of two prvatly organzd RDSs. Th margnal proft of a prvatly organzd RDS!π = TCM K f f c (3) 5 Ths holds bcaus p / f <0, and th TNC fars ar alrady smallr f flt szs ar smlar (s Proposton ).

10 Hlkr and Sg A duopoly of transportaton ntwork compans and tradtonal rado-tax dspatch srvc agncs 05 at th optmal flt szs of th TNCs f = f = f *, usng quaton 9 s!π f f = ˆf * whch s ngatv, f = TCM ( ˆf * ) K c > TCM ( ˆf * ) ε f,γ f f K, (33) * c = ˆf * ε f,γ f f. (34) * = ˆf * In ths cas, th flt szs of th TNCs ar largr than thos of prvatly organzd RDSs. Th oppost s tru f K c s small. As shown n Appndx B, th fxd costs of a taxcab do not nflunc th dtrmnaton of th flt szs of th TNCs. If K c changs, th rvnu-maxmzng company adjusts γ so that th numbr of taxcabs n th flt rmans constant. Prvatly organzd RDSs rduc th numbr of taxcabs n thr flt f K c rss. Proposton 3 In a duopoly of TNCs, th flt szs ar largr than n a duopoly of prvatly organzd RDCs f and only f K c s suffcntly larg. A largr flt mpls that th fars ar smallr n a duopoly of transportaton ntwork compans than n a duopoly of prvatly organzd RDSs as provd n Proposton. Häcknr and Nybrg (995) statd that a duopoly of prvatly organzd RDSs always lads to largr flt szs than a duopoly of coopratvly organzd RDSs (f * >f * ). Ths mans that f th flt szs of th TNCs xcd thos of prvatly organzd RDSs, th flt szs ar also largr than thos of coopratvly organzd RDSs. To compar th rsults of th rgm of rgulatory captur wth a duopoly of coopratvly organzd RDSs, w consdr th partal drvatv π / f at th proft-maxmzng flt sz of th capturd rgm. Ths s postv and lads to th followng rsult: Proposton 4 In a duopoly of coopratvly organzd RDSs, th flt szs ar largr than n th capturd rgm. Th rsults of th modl can b also xpland on th bass of Fgur that dsplays numrcal (wth Wolfram Mathmatca) calculatd racton functons of th flt szs for th paramtr valus α =.4, β = 0.0, δ =, c = 0.65, K c = 0.05, w = and K r = It can b shown that for coopratvly organzd RDSs, f / > 0 holds. In ths cas, th flt szs ar stratgc complmnts. Th oppost s tru for TNCs and prvatly organzd RDSs. Th racton functons hav a ngatv partal drvatv wth rspct to th flt sz of th othr company j ( f / < 0). In ths cas, th flt szs ar stratgc substtuts (s Fgur ). Pont A rprsnts th small flt szs of th compans n th rgm of rgulatory captur (Rgm 4). Th qulbrum n a markt wth two coopratvly organzd RDSs s dnotd by th ntrscton of th racton functons at pont B (Rgm ). Th flt szs ar largr than n th capturd rgm (s Proposton 4). Wth ths paramtr valus, a duopoly of TNCs (pont C) lads to largr flt szs than a duopoly of coopratvly organzd RDSs (B) (s Proposton ). Th largst flt szs can b sn n a markt wth two prvatly organzd RDSs (pont D; s Proposton 3). In th last fw yars, transportaton ntwork compans hav ntrd (or trd to ntr) th markt stll srvd by tradtonal RDSs, whch s an asymmtrc olgopoly of coopratvly organzd RDSs comptng wth TNCs. If w analyz th asymmtrc olgopoly of on C-RDS and on TNC (s qulbra E and F n Fgur ), both compans ncras thr flts to a sz largr than thos n thr symmtrc qulbrums. All drvrs would prfr to b mmbr of th coopratvly organzd RDS, but only a lmtd numbr s accptd.

11 Hlkr and Sg A duopoly of transportaton ntwork compans and tradtonal rado-tax dspatch srvc agncs D f TNC TNC C-RDS C-RDS RDS RDS 0.0 E B C F A f Fgur. Bst rspons functons and qulbra Paramtr valus ar: α =.4, β = 0.0, δ =, c = 0.65, K c = 0.05, w = and K r = Furthrmor, whthr or not RDSs can survv th comptton wth TNCs dpnds not only on opratng costs, whch may b smlar, but also on th tchnqu of matchng drvrs and customrs and changng prcs accordng to dmand. Avalabl mprcal vdnc (Cramr and Krugr, 06; Pck, 07) supports th noton of mor ffcnt TNCs, whch may rsult n an xt of RDSs and th mrgnc of a duopoly or monopoly of transportaton ntwork compans. In th modl, rgm-dpndnt dltas (δ ) could rprsnt ths. Howvr, w dd not mplmnt ths n th modl bcaus t s not clar whthr TNCs can mantan a tchnologcal advantag n th matchng softwar ovr n th long trm as wll. In th currnt transton phas, th TNCs matchng tchnology s bttr, but n th long run, t s lkly that tradtonal tax compans wll b abl to dvlop or buy smlar softwar. From a thortcal pont of vw, t can b shown that th rsults of th modl do not chang sgnfcantly f rgm-dpndnt dltas ar ncludd. Propostons and 4 stll hold. Furthrmor, rgm-dpndnt dltas shft th lmts n Propostons and 3, but th basc rsults rman th sam. 3. Concluson Tax ntrmdars ar th most mportant agnts n th markt for dspatchd tax rds. Tradtonally, ntrmdars hav bn organzd as prvat frms or as coopratvs; nowadays nw frms applyng dffrnt busnss modls succssfully ntr th markt. Bcaus th numbr of tax rds that ar ordrd va transportaton ntwork compans ncrass day by day, w ncludd TNCs n a duopolstc dspatch markt modl and compard th markt outcoms of dffrnt rgms. W fnd that th largst flt szs mrg n th rgm of two transportaton ntwork compans (Rgm 3), f th fxd costs of a taxcab ar rlatvly hgh. In ths cas, th flt szs ar largr than thos of prvatly organzd RDSs (Rgm ). In a duopoly of TNCs, mor tax drvrs ntr th markt and fars ar smallr than n a duopoly of coopratvly organzd RDSs (Rgm ),

12 Hlkr and Sg A duopoly of transportaton ntwork compans and tradtonal rado-tax dspatch srvc agncs 07 f th fxd costs of an ntrmdary ar small. If th fars and th numbr of lcnss ar rgulatd, and th rgulaton s capturd by th tax frms (Rgm 4), ths lads to smallr flt szs than n a duopoly of coopratvly organzd RDSs. Th agncs try to maxmz th proft pr taxcab and thrfor rduc thr flt szs and ras fars. Our study offrs a thortcal xplanaton for th postv mploymnt ffct of TNCs markt ntry that s vdnt from svral studs. Brgr t al. (07) found that whl th numbr of Ubr drvrs n th US ncrasd snc 00, thr ar no ngatv ffcts on th numbr of workrs n convntonal tax srvcs. For Franc and spcally Pars, t s vdnt that th numbr of tax lcnss n fact ncrasd aftr th markt ntry of Ubr (Facta, 06). Ths study s n ln wth th wll-known polcy advc that lbralzaton and th markt ntry of nw frms fostrs comptton, rass th numbr of tax drvrs and ncrass consumr surplus. TNCs oftn clam that thy ar only a platform whr customrs and tax drvrs mt. Accordng to our analyss of tax ntrmdars, TNCs that dtrmn th far, th qualty of cars and drvrs and th rout (whch all consttut th product) and th numbr of taxcabs, ar smlar to a tradtonal tax frm. Howvr, by clamng not to b a frm, som TNCs try to avod complanc wth socal lgslaton, tax lgslaton, mnmum wags and othr lgal workr rghts (Hardng t al., 06). Thus, to support a lvl playng fld, TNCs and RDSs should b subjct to th sam oblgatons and qualty standards. Our modl shds som lght on th postv aspcts of TNCs, but thr s on drawback w should mnton. Thr ar conoms of scal n dspatchng tax rd srvcs that may rsult n a natural monopoly. In combnaton wth th frdom to st prcs n a lbralzd markt, and xtnsv nformaton about customrs, ths s a tmptng bass for abusng markt powr (Darbéra, 05; Hardng t al., 06). So far, at th agncy lvl, th markt n many countrs s oftn only mnmally rgulatd, although thr s a hgh markt concntraton at ths lvl. As long as th numbr of lcnss and th fars ar rgulatd, thr s lttl lway to abus markt powr. But bfor lbralzaton, rgulators hav to nclud a catgory of ntrmdary that ncluds tradtonal RDSs as wll as TNCs of all knds. In Irland, for xampl, ntrmdars must obtan a lcns and n Hungary, thy must satsfy crtan rqurmnts, ncludng fnancal capacty (Frazzan t al., 06). Only th futur wll rval whthr comptton n th markt for dspatchng tax srvcs or comptton from such othr mods of transport as shuttl srvcs, lft srvcs, car sharng or publc transport can prvnt th abus of monopolstc markt powr by TNCs, or whthr govrnmntal acton s rqurd. Rfrncs Arnott, R. (996). Tax travl should b subsdzd. Journal of Urban Economcs, 40(3), Barrtt, S.D. (003). Rgulatory Captur, Proprty Rghts and Tax Drgulaton: A Cas Study. Econmc Affars, 3, Brgr, T., Chn, C. and Fry, C.B. (07). Drvrs of Dsrupton? Estmatng th Ubr Effct. Workng Papr. Carns, R.D. and Lston-Hys, C. (996). Comptton and rgulaton n th tax ndustry. Journal of Publc Economcs, 59(), -5. Ctn, T. and Erygt, K.Y. (03). Th conomc ffcts of govrnmnt rgulaton: Evdnc from th Nw York taxcab markt. Transport Polcy, 5, Coopr, J., Mundy, R. and Nlson, J. (00). Tax! Urban Economs and th Socal and Transport Impacts of th Taxcab. Ashgat Publshng, Ltd. Cramr, J. and Krugr, A.B. (06). Dsruptv Chang n th Tax Busnss: Th Cas of Ubr. Amrcan Economc Rvw: Paprs and Procdngs, 06(5), 77-8.

13 Hlkr and Sg A duopoly of transportaton ntwork compans and tradtonal rado-tax dspatch srvc agncs 08 Darbéra, R. (00). Taxcab rgulaton and urban rsdnts us and prcpton of tax srvcs: a survy n ght cts. th World Confrnc on Transport Rsarch. Darbéra, R. (05). Prncpls for th rgulaton of for-hr road passngr transportaton srvcs. OECD Intrnatonal Transport Forum. Douglas, G.W. (97). Prc Rgulaton and Optmal Srvc Standards: Th Taxcab Industry. Journal of Transport Economcs and Polcy, 6(), 6-7. Facta (06). Taxs and PHV n larg cts - A cas study of Pars. VTC-0604-VE.pdf. Frnandz, L.J.E., d Ca, J.C. and Brons, J.M. (006). A dagrammatc analyss of th markt for crusng taxs. Transportaton Rsarch Part E, 4, Frazzan, S., Gra, G. and Zambon, A. (06). Study on passngr transport by tax, hr car wth drvr and rdsharng n th EU. Fnal Rport for th Europan Commsson, Study contract no. MOVE/D3/SER/05-564/SI Gorck, P.K. (07). Comptton and vstd ntrsts n taxs n Irland: A tal of two statutory nstrumnts. Transportaton Rsarch Part A: Polcy and Practc, 0, Häcknr, J. and Nybrg, S. (995). Drgulatng Tax Srvcs: A Word of Cauton. Journal of Transport Economcs and Polcy, 9(), Hall, J., Kndrck, C. and Nosko, C. (05). Th Effcts of Ubr s Surg Prcng: A Cas Study. Th Unvrsty of Chcago Booth School of Busnss. Hardng, S., Kandlkar, M. and Gulat, S. (06). Tax apps, rgulaton, and th markt for tax journys. Transportaton Rsarch Part A: Polcy and Practc, 88, 5-5. H, F. and Shn, Z.M. (05). Modlng tax srvcs wth smartphon-basd -halng applcatons. Transportaton Rsarch Part C: Emrgng Tchnologs, 58, L, Z., Hong, Y. and Zhang, Z. (06). Do On-dmand Rd- sharng Srvcs Affct Traffc Congston? Evdnc from Ubr Entry. Orr, D. (969). Th Taxcab problm : A proposd soluton. Th Journal of Poltcal Economy, 77(), Pck, J.L. (07). Nw York Cty Drunk Drvng Aftr Ubr. CUNY Graduat Cntr, Workng Papr 3. Qan, X. and Ukkusur, S.V. (07). Tax markt qulbrum wth thrd-party halng srvc. Transportaton Rsarch Part B: Mthodologcal, 00, Schallr, B. (007). Entry controls n tax rgulaton: Implcatons of US and Canadan xprnc for tax rgulaton and drgulaton. Transport Polcy, 4(6), Stglr, G.J. (97). Th Thory of Economc Rgulaton. Th Bll Journal of Economcs and Managmnt Scnc, (), 3-. von Massow, M. and Canbolat, M.S. (00). Farplay: An xamnaton of taxcab drvrs rspons to dspatch polcy. Exprt Systms wth Applcatons, 37(3), Wang, X., H, F., Yang, H. and Gao, H.O. (06). Prcng stratgs for a tax-halng platform. Transportaton Rsarch Part E: Logstcs and Transportaton Rvw, 93, -3. Wong, K.I., Wong, S.C., Bll, M.G.H. and Yang, H. (005). Modlng th Blatral Mcro-Sarchng Bhavor for Urban Tax Srvcs Usng th Absorbng Markov Chan Approach. Journal of Advancd Transportaton, 39(), Wong, K.I., Wong, S.C. and Yang, H. (00). Modlng urban tax srvcs n con-gstd road ntworks wth lastc dmand. Transportaton Rsarch Part B: Mthodologcal, 35(9), Wong, K.I., Wong, S.C., Yang, H. and Wu, J.H. (008). Modlng urban tax srvcs wth multpl usr classs and vhcl mods. Transportaton Rsarch Part B: Mthodologcal, 4(0),

14 Hlkr and Sg A duopoly of transportaton ntwork compans and tradtonal rado-tax dspatch srvc agncs 09 Yang, H., Fung, C.S., Wong, K.I. and Wong, S.C. (00a). Nonlnar prcng of tax srvcs. Transportaton Rsarch Part A: Polcy and Practc, 44(5), Yang, H., Lung, C.W.Y., Wong, S.C. and Bll, M.G.H. (00b). Equlbra of blatral tax-customr sarchng and mtng on ntworks. Transportaton Rsarch Part B: Mthodologcal, 44(8), Yang, H. and Wong, S.C. (998). A ntwork modl of urban tax srvcs. Transportaton Rsarch Part B: Mthodologcal, 3(4), Yang, H., Wong, S.C. and Wong, K.I. (00). Dmand-supply qulbrum of tax srvcs n a ntwork undr comptton and rgulaton. Transportaton Rsarch Part B: Mthodologcal, 36(9), Yang, H. and Yang, T. (0). Equlbrum proprts of tax markts wth sarch frctons. Transportaton Rsarch Part B: Mthodologcal, 45(4), Yang, H., Y, M., Tang, W.H. and Wong, S.C. (005). A Multprod Dynamc Modl of Tax Srvcs wth Endognous Srvc Intnsty. Opratons rsarch, 53(3), Yang, T., Yang, H. and Wong, S.C. (04). Tax srvcs wth sarch frctons and congston xtrnalts. Journal of Advancd Transportaton, 48(6), Zha, L., Yn, Y. and Yang, H. (06). Economc analyss of rd-sourcng markts. Transportaton Rsarch Part C: Emrgng Tchnologs, 7, Appndx A. Drvaton of quaton 3 To drv th rvnu of a tax drvr (frst trm of quaton 3), w can us th nformaton that, n th rgm of two TNCs, th total contrbuton margn quals th rvnu of a TNC (R =TCM ), bcaus th company dos not bar th varabl costs. Th total rvnu (TR), whch ncluds th rvnu of all tax drvrs of on TNC, as wll as th rvnu of th TNC, can b calculatd wth th hlp of quaton 3. Th TNC arns a fracton γ of th total rvnu ˆR = TCM! = γ TR " (35) so that th total rvnu can b xprssd as TR! = TCM ". (36) γ Th tax drvrs arn a shar -γ of th total rvnu and ths s dvdd among f tax drvrs n th flt of TNC. Th rvnu accrung to ach tax drvr (R TD ) can b dtrmnd as ˆR TD = ( γ ) TR! f = ( γ ) γ whch s usd n quaton 3. Solvng quaton 3 for γ lads to TCM ", (37) f γ ( f ) = ρ((β + αδ ( f ))K c ρ + cδ w(αδ + β)(αδ ( f ) + β)) βδ w (αδ + β)(αδ ( f ) + β) (38) wth ρ = β + 3α δ f + αβδ ( f ) and thrfor

15 Hlkr and Sg A duopoly of transportaton ntwork compans and tradtonal rado-tax dspatch srvc agncs dγ df = α ( 4αβ 4 δ ( f )K c + αβ 3 δ (α(4 f +0 f + 5 f j )K c + c w) ) βw (αδ + β)(αδ ( f ) + β) 3 ( ) α 4β 5 K c + 6α 4 δ 5 f j (6α f ( f + 3 f + f j )K c + c ( f )w) βw (αδ + β)(αδ ( f ) + β) 3 ( ) α α β δ 3 (α(8 f f + 57 f f j + 0 f 3 j )K c + c ( f + 3 )w) βw (αδ + β)(αδ ( f ) + β) 3 ( ) α α 3 βδ 4 (α( f )(8 f +3 f + 4 f j )K c + c (0 f + )w) < 0 (39) βw (αδ + β)(αδ ( f ) + β) 3 0 Appndx B. Comparatv statcs Duopoly of coopratvly organzd RDSs It can b shown that for coopratvly organzd RDSs, th margnal utlty of th frst tax trp has a ngatv mpact on th flt szs. Th varabl costs c and th fxd costs of an ntrmdary K r hav a postv ffct on th flt szs, and th fxd costs of a taxcab K c hav no ffct on th flt szs: π f w < 0, π f c > 0, π π > 0, = 0. (40) f K r f K c Th prc of a tax rd rss, f th paramtr w ncrass dp * /dw > 0. Ths s tru bcaus dp * dw = p ( f *, f * ) f f w + p ( f *, f * ) f j w + p ( f *, f * ) w (4) s postv. W assum that a largr flt sz has a ngatv ffct on th prc. Th ffct of w on th flt sz s ngatv, and th drct ffct of w on th prc s postv, so that th total ffct s postv as wll. Th ffcts of th othr paramtrs n ths rgm ar ndtrmnat. Duopoly of prvatly organzd RDSs W can stat wth rspct to th flt sz, that hghr fxd costs K c lad to a smallr flt sz of prvatly organzd RDSs ( π / f K c <0) and n ths cas, K r dos not nflunc th flt szs. In ths rgm, th prc s postvly nfluncd by th varabl costs c: d!p * dc = p ( f! *, f! * ) f f c + p ( f! *, f! * ) c + p (! f *,! f * ) W assum that a largr flt sz has a ngatv ffct on th prc, as shown abov. Th ffct of c on th flt sz s ngatv, and th drct ffct of c on th prc s postv, so that th total ffct s postv as wll. For th quantty, th ffct of c s ngatv and that of w s postv. c (4) d Q! * dc = Q ( f! *, f! * ) f f c + Q ( f! *, f! * ) f j c + Q ( f! *, f! * ) c (43) W assum that a largr flt sz has a postv ffct on th quantty. Th ffct of c on th flt sz s ngatv, and th drct ffct of c on th quantty s ngatv as wll, so that th total ffct s ngatv.

16 Hlkr and Sg A duopoly of transportaton ntwork compans and tradtonal rado-tax dspatch srvc agncs d Q! * dw = Q ( f! *, f! * ) f f w + Q ( f! *, f! * ) f j w + Q ( f! *, f! * ) w (44) W assum that a largr flt sz has a postv ffct on th quantty. Th ffct of w on th flt sz s postv, and th drct ffct of w on th quantty s postv as wll, so that th total ffct s postv. Th ffcts of th othr paramtrs n ths rgm ar ndtrmnat. Duopoly of TNCs It can b shown that for TNCs, th margnal costs c hav a ngatv mpact on th flt szs, and that th fxd costs of an ntrmdary K r and th fxd costs of a taxcab K c hav no ffct on th flt szs: ˆπ f c < 0, ˆπ ˆπ = 0, = 0. (45) f K r f K c In th rgm of TNCs, th prc s postvly nfluncd by th varabl costs c. dˆp * dc = ˆp ( ˆf *, ˆf * ) f f c + ˆp ( ˆf *, ˆf * ) f j c + ˆp ( ˆf *, ˆf * ) c (46) W assum that a largr flt sz has a ngatv ffct on th prc, as shown abov. Th ffct of c on th flt sz s ngatv, and th drct ffct of c on th prc s zro, bcaus th TNCs do not hav to bar ths costs. In ths cas, th total ffct s postv. For th quantty, th ffct of w s postv and th ffct of c s ngatv. d ˆQ * dw = ˆQ ( ˆf *, ˆf * ) f f w + ˆQ ( ˆf *, ˆf * ) w + ˆQ ( ˆf *, ˆf * ) w (47) W assum that a largr flt sz has a postv ffct on th quantty, as shown abov. Th ffct of w on th flt sz s postv, and th drct ffct of w on th quantty s postv as wll, so that th total ffct s postv. d ˆQ * dc = ˆQ ( ˆf *, ˆf * ) f f c + ˆQ ( ˆf *, ˆf * ) c + ˆQ ( ˆf *, ˆf * ) c (48) W assum that a largr flt sz has a postv ffct on th quantty, as shown abov. Th ffct of c on th flt sz s ngatv, and th drct ffct of c on th quantty s zro, so that th total ffct s ngatv. Th ffcts of th othr paramtrs n ths rgm ar ndtrmnat. Rgulatory captur In th rgm of rgulatory captur, th dffrnt paramtrs hav th followng ffcts on th flt sz: f * w < 0, f * c > 0, f * > 0, f * K r β > 0, f * < 0. (49) δ K c has no ffct on th flt sz, and th ffct of α dpnds on th sz of th fxd costs K r. If K r s larg, t holds that f * / α > 0. Th paramtrs affct th prc of a tax rd as follows: p * w > 0, p * > 0. (50) c

17 Hlkr and Sg A duopoly of transportaton ntwork compans and tradtonal rado-tax dspatch srvc agncs K r, K c, α, β, δ hav no nflunc on th prc n th rgm of rgulatory captur. Th dmand for th srvcs of ach RDS dpnds on th followng two paramtrs: Q * > 0, Q * K r α < 0. (5) c, w, K c, β, δ hav no nflunc on th dmand n ths rgm.