Cost Pass-Through with Network Externalities

Transcription

1 Intrnatonal Journal of Busnss and Economcs, 011, Vol. 10, No. 3, Cost Pass-Through wth Ntwor Extrnalts Anna Laura Barald * Dpartmnt of Europan tuds, cond Unvrsty of Napls, Italy Chrstan Rojas Dpartmnt of Rsourc Economcs, Unvrsty of Massachustts Amhrst, U..A. Abstract W analyz th rat at whch cost shocs ar passd through to prcs whn th mart xhbts ntwor xtrnalts. W fnd that th pass-through rat s smallr n th prsnc of ntwor xtrnalts. Also, th dadwght loss cratd by a cost shoc s smallr n a ntwor mart. Ky words: ntwor xtrnalts; cost pass-through; dadwght loss JEL classfcaton: D6; D85; H3 1. Introducton Cost pass-through s an mportant thm n svral flds of conomcs, ncludng ntrnatonal conomcs, ndustral organzaton, anttrust polcy, and publc conomcs. Intrnatonal conomsts hav nvstgatd how th varaton n mportd nput prcs that rsult from xchang rat fluctuatons ar passd through to consumrs and why n many cass such cost shocs ar not fully rflctd n prc changs (.g., Goldbrg and Knttr, 1997). Th mpact of how changs n commodty prcs mpact th prc pad by consumrs s of ntrst to vryon n socty; thr ar many xampls of ths ssu, from how crud ol prc changs affct gasoln th prcs at th pump (.g., Bacon, 1991; Bornstn t al., 1997; Johnson, 00) to how th prc of bf at th farm lvl gts transmttd to th rtal prc (.g., Goodwn and Holt, 1999). In addton, cost pass-through s th cntral concpt n th much dbatd ssu of whthr ffcncy gans can b usd as a vald argumnt n mrgr cass (Kwoa and Wht, 008). mlarly, changs n xcs, or pr-unt, taxs hav a clar rsmblanc to a cost shoc and hnc thr hav bn mportant fforts n th publc conomcs ltratur to undrstand ssus such as th rmnants of th tax pass-through rat and th consqunt ffctvnss for rvnu gnraton or consumpton rducton (Bshop, 1968; Fullrton and Mtcalf, 00). Important xampls of ths ltratur ar cgartt and * Corrspondnc to: cond Unvrsty of Napls, Dpartmnt of Europan tuds, Va dl tfco Casrta, Italy. E-mal: laura.barald@unna.t.

2 178 Intrnatonal Journal of Busnss and Economcs alcohol taxs at both th stat and fdral lvl. Economsts hav xplord from dffrnt angls th thortcal rasons for cost (or pr-unt tax) ovr- and undr-shftng wth analyss that nclud dmand functonal form (Cottrll t al., 001; Dlpalla and Kn, 199), stratgc ntracton (Ptz and Rsngr, 009, Andrson t al., 001), and mnu costs and habt formaton (Ravn t al., 008). In ths papr w add to ths ltratur by thortcally studyng how th pass-through rat can b affctd whn th mart xhbts postv ntwor xtrnalts. In ntwor marts, consumrs wllngnss to pay for th last unt ncrass as th (xpctd) numbr of subscrbrs scalats, mplyng that th ntwor xprncs a slf-sustand growth byond a mnmal numbr of subscrbrs (.., th crtcal mass). W buld comparatv statcs n monopoly and olgopoly marts that xamn whthr th cost pass-through rat s smallr or largr than n a nontwor-xtrnalty countrpart. Th comparatv statc s basd on a cost-sd shft whch can b vwd as a shoc n tchnology or nput prcs 1 or, altrnatvly, th ntroducton (or ncras) of a pr-unt tax (also nown as an xcs tax). In addton, gvn th mportant polcy and socal ramfcatons of cost pass-through outlnd arlr, w complmnt our analyss wth wlfar comparsons. Whn compard to a no-ntwor-xtrnalts countrpart, w fnd that th pass-through rat s smallr n a mart wth ntwor xtrnalts. pcfcally, f a tax ncras causs th sam rducton n quantty n both th ntwor xtrnalts cas and ts standard countrpart, th prc ncras obsrvd n th ntwor xtrnalts cas s smallr. Intutvly, bcaus consumrs dsl a smallr ntwor (as a consqunc of th prc ncras), th prc ncras th mart can bar must b smallr to p th qulbrum quantty chang th sam as n th cas wthout ntwor ffcts. In addton, w also show how th assocatd mart dstorton (masurd by th wlfar loss) cratd by a cost shoc (or a pr-unt tax) s smallr n a ntwor mart.. Ltratur Rvw.1 Cost Pass-Through Th rvw provdd hr s by no mans a comprhnsv ovrvw of th ltratur. Instad, t should b vwd as a brf summary of th thortcal and mprcal fndngs rgardng cost pass-through that rlat most closly to our study. 3 Rlvant Thortcal Rsults Throughout ths artcl w adopt th usual dfnton of pass-through rat (PTR): th ffct of a chang n margnal cost on th qulbrum prc ( p c ). Usng ths dfnton, cost shocs ar sad to b undr-shftd f p c < 1, ovrshftd f p c > 1, and compltly passd-through f p c = 1. 4 In a prfctly compttv mart, cost pass-through can at most b qual to 1, wth th magntud dpndng on th dmand and supply lastcts (Fullrton and Mtcalf, 00). At

3 Anna Laura Barald and Chrstan Rojas 179 th othr xtrm, monopoly, cost shocs can b undr- or ovr-shftd: undr lnar dmand and lnar supply th pass-through rat can at most b 0.50, whras undr a constant-lastcty dmand and constant margnal costs t wll b gratr than 1 (Harrs and ullvan, 1979; Dlpalla and Kn, 199; Bsly, 1998; Cottrll t al., 001; Fullrton and Mtcalf, 00). As n monopoly, olgopoly marts can xprnc undr- or ovr-shftng, albt for a dffrnt rason. Whn stratgc ntracton s mportant and thr s a common cost shoc, frms ract bcaus thy fac hghr costs but also bcaus thr rvals accommodat to th nw nvronmnt. In Brtrand comptton wth dffrntatd products, upward slopng racton functons trggr a multplcatv ffct of th cost shoc that propagats throughout th ndustry and can rsult n ovr-shftng (Andrson t al., 001). In Cournot olgopoly wth homognous products, a postv cost shoc allows frms to scap th prsonrs dlmma by mang vry frm crdbly commt to smallr lvls of producton (ad, 1987). 5 uccssv mart powr n vrtcally sparatd marts can also xacrbat th pass-through rat; th rason for ths s that a cost shoc that occurs at th top of th supply chan s subjct to mor than on mar-up (Ptz and Rsngr, 009). 6 Multpl stmats hav shown consstnt undr-shftng of xchang rats (.g., Engl, 1999; Parsly and W, 001; Goldbrg and Campa, 006). 7 On thortcal xplanaton has to do wth local costs: f mportd nputs ar not too mportant n th producton procss, domstc prcs should not rspond too much to xchang rat fluctuatons (anyal and Jons, 198; Burstn t al., 003; Corstt and Ddola, 004). Anothr has to do wth prc rgdty rsultng from frms dynamc consdratons: producrs st a prc tang nto account both currnt and futur costs as wll as dmand (Dvrux and Engl, 001; Ravn t al., 008). Rlatd Emprcal Fndngs Whl th cost pass-through can occur as a rsult of any typcal cost chang, such as tchnology, wathr, wag ncrass, or any othr chang n nput prcs, rsarch on cost pass-through has bn manly motvatd and studd around spcfc cost chang scnaros: mrgrs, taxs, and xchang rats. Whl thr s a larg mprcal ltratur documntng pass-through rats, thr appar to b two mportant sts of (a pror) at odds fndngs. On th on hand, th ntrnatonal conomcs ltratur suggsts that undr-shftng s a consstnt and wll documntd fndng (.., ovr-shftng dos not occur). On th othr hand, th publc conomcs and ndustral organzaton ltraturs tnd to suggst that ovrshftng s a common phnomnon. 8 On th publc conomcs/ndustral organzaton front, thr hav bn svral studs documntng th PTR. Potrba (1999) rvws a numbr of studs that documnt ovr-shftng. Bsly and Rosn (1998) also fnd vdnc for ovrshftng n svral ndustrs, although Potrba s own analyss ylds mxd fndngs. Barzl (1976) documnts PTR ovr-shftng n th cgartt ndustry whl Hanson and ullvan (008) confrm ths fndng wth mor ald data. 9 Thr hav also bn structural fforts thr documntng or xplanng PTR ovr-shftng (Km and

4 180 Intrnatonal Journal of Busnss and Economcs Cottrll, 008; Rojas, 008). On th ntrnatonal conomcs front, thr ar xtnsv rvws that documnt and xplan PTE undr-shftng (Mnon, 1995; Goldbrg and Knttr, 1997). Mor rcnt fforts hav tan a structural approach (.g., Goldbrg and Hllrstn, 008; Naamura and Zrom, 010); ths last two studs fnd that local costs xplan a larg porton of th undr-shftng pattrn.. Ntwor Extrnalts Whn utlty and/or frms profts ar drctly affctd by th numbr of consumrs and/or producrs usng th sam (or a compatbl) tchnology, ths tchnology s sad to xhbt ntwor xtrnalts (Church and Gangal, 1993; Farrl and olonr, 1985; Katz and hapro, 1985, 1986; hapro and Varan, 1999); consumrs of such a tchnology blong to a ntwor. Th fundamntal da s that th act of jonng a ntwor confrs a bnft to all othr partcpants n th ntwor. Thrfor, ntwor xtrnalts may affct consumrs dcsons whthr to adopt a nw tchnology and/or producrs dcsons whthr to standardz thr products. Communcaton tchnologs ar th man xampl of ntwor goods. Tchnologs that hav strong ntwor xtrnalts gnrally lv longr and hav a rapd growth aftr passng a crtcal dmnson. Ths s th consqunc of a postv fdbac that ntwor ndustrs xhbt: whn th subscrbr s bas of a ntwor grows, an ncrasng numbr of usrs wll fnd t mor proftabl to jon. A natural consqunc n a mart wth a strong postv fdbac s that fwr frms (than othrws) mrg thrby rsultng n ncrasd mart domnanc. Th ltratur on ntwor ffcts usually dstngushs among two typs of ntwor xtrnalts: drct ntwor xtrnalts and ndrct ntwor xtrnalts. Wth drct ntwor xtrnalts th utlty of an agnt connctd to th ntwor good postvly dpnds on th numbr of othr usrs consumng th sam good. Th tlphon mart (both fxd and mobl) as wll as th fax mart xhbt drct ntwor xtrnalts. ubscrpton to a mobl ntwor, for xampl, drctly bnfts xstng usrs of such ntwor, who now hav an addtonal prson wth whom thy may communcat. If thr ar n consumrs connctd to th ntwor, ach usr can potntally communcat wth n ( n 1) usrs; an addtonal consumr thrfor adds n (total) potntal communcatons wthn th systm, and thus nhancs th valu of mmbrshp, assumng that ach usr may at som pont wsh to communcat wth vry othr ownr (Economds, 1996). Wth ndrct ntwor xtrnalts, th valu of a good ncrass as th numbr, or varty, of complmntary goods ncrass: th addton of nw varts of on typ of componnts affcts postvly but ndrctly th utlty of all partcpants through th rducton of prcs. Gnrally, most marts wth ndrct ntwor xtrnalts ar dvdd nto two dstnct sds whch bnft from th ntracton btwn thm. Typcal xampls ar th prsonal computr mart and crdt card ntwors. Katz and hapro (1994) llustrat ths typ of systm wth th hardwar/softwar paradgm, whch can b xtndd to many othr product combnatons such as camras and flm, phonographs and rcords, and tlvson

5 Anna Laura Barald and Chrstan Rojas 181 sts and programmng. Tchncally, th sourc of ntwor xtrnalts ls n consumrs xpctatons about th futur nstalld bas of subscrbrs. For xampl, th dmand for a fax machn s a functon not only of th prc of th product, but also of th xpctd sz of th ntwor to whch th fax machn wll b connctd. Ths mpls that wth ntwor xtrnalts th fundamntal rlatonshp btwn prc and quantty may fal. For ths goods, th wllngnss to pay for th last unt may ncras as th numbr of subscrbrs that ar xpctd to connct to th ntwor rass. Thus th (fulflld xpctatons) dmand-prc schdul may not slop downward vrywhr but t can show an upward slopng porton; as costs dcras on may obsrv dscontnuous xpansons n sals rathr than th smooth xpanson along a downward slopng dmand curv. Ths occurs bcaus, f th numbr of popl who connct to th ntwor s low, thn th margnal ndvdual wllngnss to pay s low (thr ar not many othr popl to communcat wth); f thr s a larg numbr of popl connctd, thn th wllngnss of th margnal ndvdual to pay also s low (vryon ls who has valud t hghr s alrady connctd) (Economds, 1996; Economds and Hmmlbrg, 1995). Fgur 1. Dmand Functon wth Ntwor Extrnalts Fgur 1 shows an llustraton of th shap of th dmand curv just dscrbd. Th ntwor starts at ssntally zro, wth a fw small prturbatons ovr tm. As cost dcrass (du, for xampl, to tchnologcal progrss) th ntwor rachs a crtcal mass (th unstabl qulbrum) that cs up past th low-lvl qulbrum and th systm thn rachs th hgh-lvl qulbrum (as shown by th arrows n Fgur 1). Thrfor th two stabl qulbra ar: (a) zro subscrbrs or (b) th hghst possbl lvl of th ntwor sz (.., whr cost ntrscts th downward slopng scton of th dmand curv). Th mddl qulbrum (whr cost ntrscts th upward slopng sgmnt of th dmand curv) s unstabl bcaus f on prson

6 18 Intrnatonal Journal of Busnss and Economcs dcds to drop out of th ntwor, thn at last on of th rmanng subscrbrs wll fnd t unproftabl to rman connctd and wll lav (th valu of th good s lowr than th cost); but whn ths happns, at last anothr prson wll lav and so on untl th ntwor has no rmanng mmbrs. If, on th othr hand, on prson dcds to jon, anothr mmbr wll fnd t proftabl to jon too, and so on untl th hghst qulbrum lvl s achvd. Thrfor, n ordr to gt th hgh lvl qulbrum from th zro qulbrum, t would not b ncssary for all consumrs to agr n advanc to jon; all s ndd s to achv th crtcal mass, that s, th numbr ndd to gt just byond th unstabl qulbrum. 10 In ths papr, w ma a contrbuton to both th PTR and th ntwor xtrnalts ltraturs by studyng how and whthr a PTR s dffrnt n a mart wth ntwor xtrnalts whr consumrs xpctatons about dmand growth s a crucal lmnt of th mart. To our nowldg, ths papr s th frst attmpt to loo at ths quston. 3. Th Modl In prncpl, w would b abl to study th PTR on both th upward slopng and downward slopng portons of th dmand curv. Howvr, n ordr to hav a manngful and far comparson btwn th ntwor cas and th standard cas, 11 our attnton wll focus on th downward slopng part of th dmand functon. In addton, our focus wll b to study th ffct of a unqu fatur of marts wth ntwor xtrnalts: th rol of consumrs xpctaton rgardng th growth of th ntwor (.., xpctatons about othr consumrs jonng th mart). In partcular, t s possbl that, byond th ffct causd by th curvatur of dmand, consumrs xpctatons wll affct th PTR n ntwor marts. In th analyss that follows w ta a frst stp n comparng th PTR n th standard monopoly and Cournot olgopoly cass to thr rspctv ntwor xtrnalts countrparts by solatng th ffct of consumrs xpctatons from th curvatur of dmand ffct; as w xplan n mor al latr, w do so by rstrctng th chang n quantty du to a cost shoc to b th sam n both cass. W frst drv th dmand for th ntwor good followng th wll-stablshd procdur dscrbd n Economds (1996) and Economds and Hmmlbrg (1995). Bsds bng smpl, th advantag of ths approach s that t nsts th nontwor (.., standard) cas as a spcal scnaro. W assum that ach consumr buys only on unt of th ntwor good and dfn th corrspondng utlty as u ( y, ) = yh( ). Th trm h ( ) s a ntwor xtrnalty functon whch capturs th nflunc of ntwor sz xpctatons ( ) on th utlty lvl; as s standard n th ltratur on ntwor xtrnalts, w assum that h > 0 (a largr xpctd sz of th ntwor rsults n hghr ndvdual utlty) and h 0 (th margnal ntwor xtrnalty s dcrasng n ntwor sz). Th trm y masurs th consumr s snstvty to th ntwor xtrnalty; y s assumd to b unformly dstrbutd btwn 0 and 1. Importantly, th multplcatv spcfcaton of th utlty functon allows for dffrnt typs of consumrs to b affctd dffrntly by

7 Anna Laura Barald and Chrstan Rojas 183 th ntwor xtrnalty. 1 Gvn xpctatons and prc p, vry consumr for whom u ( y, ) = * yh( ) P wll purchas th good. Th ndffrnt consumr ( y ) condton s * gvn by u( y, ) = y h( ) = P. Thus, all consumrs wth y > y * = P h( ) wll purchas th good. Gvn th unform dstrbuton of typs, aggrgat dmand s * gvn by = 1 y, whch s quvalnt to: 1 P =. (1) h( ) Th nvrs dmand functon for th ntwor good s hnc P = (1 ) h( ). n as a functon of ts frst argumnt, ths s just an nvrs dmand functon, and thrfor P = h ( ) < 0 ; howvr, du to th xstnc of ntwor xtrnalts, xpctatons also affct postvly th wllngnss to pay: P = ( 1 ) h > 0. In qulbrum, whn xpctatons ar fulflld ( = ), th dmand functon bcoms P = ( 1 ) h( ). 3.1 Monopoly Consdr a monopoly facng consumr dmand P = ( 1 ) h( ) and convx cost functon C (, t), 13 whr t s a cost-shftng paramtr. W assum that th paramtr t shfts margnal cost only (and not fxd costs); ths spcfcaton fts wll th dvrs cost pass-through scnaros studd by th ltratur: xchang rat changs that ma nputs prcr (or chapr), a cost synrgy assocatd wth a mrgr, or a pr-unt tax ncras. Our assumd dmand functonal form mpls that quantty ( ) s btwn 0 and 1. In ordr to analytcally manpulat th modl, w nd to spcfy a functonal form for h () that satsfs h > 0, h 0, and 0 < 1 and that nsts ntwor and no-ntwor dmands as spcal cass. pcfcally, w us h ( ) = wth 0 1. Whn 0 P = 1, whch corrsponds to th standard monopoly cas wth lnar dmand functon; whn 1 P = (1 ), whch corrsponds to th ntwor xtrnalty cas wth a lnar spcfcaton of th ntwor xtrnalty functon; whn 0 < < 1 P = (1 ), whch corrsponds to th ntwor xtrnalty cas wth a non-lnar spcfcaton of th ntwor xtrnalts functon. 14 tandard Monopoly Cas Gvn th assumd nvrs dmand curv, a monopolst maxmzs π = P( ) C(, t) = (1 ) C(, t) wth frst- and scond-ordr condtons: π P = P + π = C 0. = 1 = 0, C ()

8 184 Intrnatonal Journal of Busnss and Economcs A chang n th cost-shftng paramtr t, whch affcts margnal costs, wll gnrally nduc changs n th qulbrum prc, output, and proft. Hr w drv comparatv statcs rsults for an nfntsmal tax chang. W frst totally dffrntat th frst-ordr condton n () yldng [ ] d = 0. OO t Rarrangng trms obtans: d Ct =, (3) whr th s suprscrpt dnots th standard cas. Wthout loss of gnralty, margnal costs ar assumd to b a non-dcrasng functon of th cost shoc: C 0. Th strct convxty condton of th cost functon mpls that th t dnomnator n (3) s ngatv, thrby mang d also ngatv. Th monopolst optmal absolut pass-through rat s thn P = d > 0. Ntwor Extrnalts Monopoly (Non-Lnar Cas) Th nvrs dmand functon P = ( 1 ), whch s concav, rachs ts maxmum whn = + 1. As statd arlr, to ma a manngful comparson btwn th mart wth a ntwor xtrnalty and ts no-xtrnalty countrpart, w focus th analyss on th downward porton of th dmand curv (.., whn > +1 ). 15 Th monopolst s frst- and scond-ordr condtons ar: 16 π P 1 = P + = (1 )( + 1) + π = ( + 1) 1 ( + )( + 1) 0. = 0, (4) As abov, w totally dffrntat th frst-ordr condton n (4) to obtan 1 [ ( + 1) ( + )( + 1) ] d = 0, whch mpls: t d Ct, 1 (5) ( + 1) ( + )( + 1) = whr th suprscrpt dnots th ntwor xtrnalts cas. As n th standard monopoly cas abov, (5) s ngatv. 17 Th monopolst optmal absolut passthrough rat s: P = 1 K [ ( + 1) ]. (6) As n th standard monopoly cas, th monopolst optmal absolut passthrough rat wth ntwor xtrnalts s postv on th downward slopng porton of th dmand curv ( > ( +1) ) and ngatv whn s locatd on th upward slopng part of th dmand curv ( < ( +1) ). Th xplanaton for th lattr

9 Anna Laura Barald and Chrstan Rojas 185 rsult (whch may sm countrntutv at frst) s th followng. Rcall that th upward slopng part of th dmand curv rprsnts th start-up phas of th ntwor, whr th crtcal mass s locatd; t s n ths porton of th dmand curv that unstabl qulbra ars. Fgur dsplays a ntwor xtrnalts dmand curv and two constant margnal cost lns C 1 and C. Consdr th unstabl qulbrum, A, locatd at th lft ntrscton of C 1 and th dmand curv. An upward shft n th margnal cost functon to C (a cost shoc) pushs th ntwor toward th zro stabl qulbrum (s th arrows n Fgur ) snc A s now blow th nw crtcal mass (gvn by th ntrscton of th margnal cost C and th dmand functon) and th ntwor naturally gos to th zro-quantty qulbrum. Fgur. A Cost hoc wth Ntwor Extrnalts An mportant fatur of our papr s th approach usd to compar th PTR n th standard and ntwor xtrnalty cass. Th pror ltratur on PTR has shown that th magntud of th PTR s, by and larg, du to th curvatur of dmand. nc w ar ntrstd n solatng th ffct of th ntwor xtrnalty on th PTR, w nd to nsur that th dffrnc n th curvatur of dmand btwn th two cass of ntrst s not rsponsbl for our fndng. To do ths, w study th comparatv statc of ntrst, dp, undr th followng condton: d d =. (7) That s, w fx th varaton n quantty du to an nfntsmal cost shoc ( t ) chang to b th sam n th two cass of ntrst. Ths procdur allows us to solat th ffct of ntwor xtrnalts on th PTR whl png th curvatur of dmand constant for th two cass of ntrst. In othr words, f w do not mpos ths condton, a cost shoc wll not only affct th qulbrum prc by dffrnt amounts n th two cass but also affct quantts dffrntly du to dffrncs n th dmand functonal form.

10 186 Intrnatonal Journal of Busnss and Economcs Proposton 1. For th sam chang n quantty (gvn by an nfntsmal varaton n th cost shoc paramtr), th pass-through rat n th prsnc of ntwor xtrnalts s lowr than th pass-through rat n th standard monopoly cas. Proof. Whn (7) holds: dp 1 f [ ( + 1) ] dp, (8) 1 whch occurs whn 1 + ( + 1) > 0. Aftr mathmatcal manpulaton, th condton ndd for (8) to hold s ( 1 ) + (1 ) > 0, whch s always tru. Th ntuton for ths rsult s as follows. A postv cost shoc contracts th supply curv, whch, n turn, mpls a smallr qulbrum quantty and a hghr prc (on th downward slopng porton of th dmand curv). W call ths th standard ffct. Wth ntwor xtrnalts, thr s an addtonal ffct that runs oppost to th standard ffct: f th quantty dcrass (as a rsult of th postv cost shoc), th sz of th ntwor dcrass, and th wllngnss to pay by th margnal consumr also dcrass, thrby nducng a dcras n qulbrum prc. Ths s bcaus th utlty of havng a ntwor good postvly dpnds on th numbr of othr consumrs connctd to th ntwor. Ths ntwor xtrnalts ffct rducs th cost pass-through rat magntud that would b obsrvd othrws. Ntwor Extrnalts: Lnar Cas Th nvrs dmand functon facd by a monopolst producng th ntwor good n ths cas s P = ( 1 ). Ths functon rachs ts maxmum at = 1 and has frst- and scond-ordr condtons: π = 3 C = 0 π and = 6 0. Totally dffrntatng th frst-ordr qulbrum condton obtans L [ 6 ] d = 0, whch mpls d = C 6 t t, whr th L suprscrpt dnots th lnar ntwor xtrnalts cas. Ths last xprsson s ngatv. Thrfor, th corrspondng monopolst optmal absolut pass-through rat s: P L = [ 1 ], whch s postv for > 1 (.., on th downward slopng part of th dmand L curv). For th sam varaton n quantty d = d as n th non-lnar cas, t s asy to chc that th pass-through rat s gratr than th pass-through L rat n th ntwor xtrnalty cas. pcfcally, dp = dp f

11 Anna Laura Barald and Chrstan Rojas 187 d L ( d )(1 ) > 0 ; that s, f > 0, whch s always tru. 3. Cournot Olgopoly wth n Frms Hr, w consdr n dntcal frms producng a homognous good, wth th sam cost structur as n th monopoly cas. tandard Cournot Olgopoly Cas Th dmand functon n ths cas s gvn by P = 1 = 1 ( q + q ). Frm sts ts lvl of output to maxmz ts proft as π = P( ) q ( q, t). Th (symmtrc) frst-ordr condton for proft maxmzaton rsults n dq = C n 1 < 0 qt qq, wth corrspondng pass-through rat gvn by P = ndq > 0. Ntwor Extrnalts Cournot Olgopoly: Non-Lnar Cas Th nvrs dmand functon n ths cas s P = ( 1 ) wth = q + q and q = j q. Frm s frst- and scond-ordr condtons for proft j maxmzaton ar: π q δ π δq = P + q [ = = ( + 1) ] + q 1 ( + 1) q ( + 1) q ( 1) q q = 0, ( + 1) q 1 q q 0. Thus, n (th symmtrc) qulbrum (.., q = q for all frms) th frst-ordr condton bcoms ( nq ) ( nq) + q( nq) ( + 1) q( nq) C = 0 q. To analyz an nfntsmal tax chang, w nd to totally dffrntat th last frst-ordr qulbrum 1 1 condton, whch ylds [ n ( + 1) n + ( + 1) ] dq qq qt = 0 or: dq = qt 1 1 n C ( + 1) n + ( + 1) qq. (9) Rcall that margnal costs ar assumd to b a non-dcrasng functon of th cost shoc paramtr ( C 0 ). Convrsly, local stablty of th qulbrum mpls that qt th dnomnator n (9) s ngatv, thrby mang dq also ngatv. Each frm s optmal absolut pass-through rat s P = 1 1 n ( q )[ ( + 1) ], whch s postv f ( + 1) < 0 ; that s, f > +1 (.., on th downward slopng part of th dmand functon), as n th monopoly cas. Consdr th sam varaton n quantty n th standard and ntwor (olgopoly) cass du to an nfntsmal varaton n th tax paramtr (.., dq = dq ).

12 188 Intrnatonal Journal of Busnss and Economcs Proposton. Whn frms compt n quantts (Cournot comptton) and dq = dq, th optmal pass-through rat wth ntwor xtrnalts s lowr than th optmal pass-through rat n th standard cas. Proof. It s asy now to compar th pass-through rat wth and wthout ntwor xtrnalts whn dq = dq holds: dp q q 1 whn n [ ( + 1) ] dp, 1 whch mpls that 1 + ( + 1) > 0 ; t s straghtforward to vrfy that ths condton always holds. Rsults ar smlar n Cournot wth a lnar ntwor xtrnalts spcfcaton. Appndx A1 contans ths rsults. 3.3 Robustnss: Non-Pur Ntwor Good To nvstgat how robust ar our rsults to a varaton n th dfnton of a ntwor good, w consdr a ntwor xtrnalts (lnar) functon for a non-pur ntwor good: h ( ) = s +, whr s rprsnts th non-ntwor bnfts that a good provds: t masurs th wllngnss to pay for a unt of th good whn thr ar no othr unts sold. Whn s = 0, w ar bac to a mart to a pur ntwor good (dscussd abov). Monopoly Cas Th nvrs dmand functon facd by a monopolst producng th ntwor good s P = ( 1 )( s + ). Ths functon rachs ts maxmum at = 1 s. Th monopolst s proft s π = P( ) (, t), wth frst- and scond-ordr condtons: δπ δp = P + = s s + 3 δ δ δ π = s 6 δ 0. = 0, Totally dffrntatng th frst-ordr condton obtans [ s 6 ] d = 0. Aftr rarrangng trms, ths last xprsson t bcoms d = C s 6 < 0 t. Accordngly, th monopolst s optmal absolut pass-through rat s P = ( δ t)[1 s ], whch s postv for > 1 s (a quantty lvl locatd on th downward slopng part of th dmand curv). In th standard monopoly cas, th nvrs dmand functon s P = ( 1 ) s, whch rsults n:

13 Anna Laura Barald and Chrstan Rojas 189 d Ct = s and P = s. Proposton 3. Whn d = d, th pass-through rat n th standard monopoly cas wth a non-pur ntwor good s gratr than th pass-through rat n th corrspondng ntwor xtrnalty cas. Proof. Th condton d = d holds f * = Thrfor, dp = dp f s( d ) ( d )(1 s ) > 0, that s, f < 1, whch s always tru bcaus * = 1 3. Furthr, t s asy also to chc that th sam proposton holds n th Cournot olgopoly cas wth a non-pur ntwor good. Appndx A contans th proof. 4. Wlfar Analyss Th motvaton for carryng out wlfar comparatv statcs s justfd by th mportanc of pr-unt taxs n th pass-through ltratur. W consdr two wlfar masurs: (1) th xcss burdn of a pr-unt tax wth and wthout ntwor xtrnalts and () wlfar varatons (du to a pr-unt tax chang) n a standard monopoly mart and n a monopoly wth ntwor xtrnalts. Th dffrnc btwn th xcss burdn and th wlfar analyss s that th formr tas nto account tax rvnus (thrby bng a comparson of total soctal wlfar consumrs, producrs, and th govrnmnt), whl th lattr only focuss on th wlfar of consumrs and producrs (.., t xcluds tax rvnus). W carry out ths scond calculaton snc n many cass polcymars may b ntrstd n th ffcts of pr-unt taxs on ach group of agnts rathr than n th sum Excss Burdn Th xcss burdn of taxaton s th ffcncy cost, or dadwght loss, assocatd wth taxaton. In ths scton w compar, n a monopoly stuaton, th ncrmntal xcss burdn of a pr-unt tax wth and wthout ntwor xtrnalts. Fgur 3 llustrats a standard nvrs dmand curv and th corrspondng margnal rvnu (MR) curv for a monopolst. 0 uppos margnal costs (MC) ar constant. Th ntal margnal cost s C 0, whch ntrscts MR whr = 0 ; th corrspondng prc s P 0. Pror to a pr-unt tax ncras, th xcss burdn s th ara bc (gratr than zro bcaus prc xcds MC). Aftr th mposton of a tax (whch shfts MC up to C 0 + t ), prc ncrass to P 1 and quantty dcrass to 1, whl th ncrmntal xcss burdn s th ara abcd; algbracally, ths ara can b approxmatd by th followng formula:

14 190 Intrnatonal Journal of Busnss and Economcs 1 P abcd ( P0 C0) P = ( P0 0) + ( ). Fgur 3. Excss Burdn Analyss To compar th monopoly stuaton wth and wthout ntwor xtrnalts, w consdr, as n th analyss abov, th sam varaton n th quantty du to th mposton of a tax, that s d = d = d. Proposton 4. Th ncrmntal xcss burdn of an xcs tax s gratr n th standard monopoly cas than n th corrspondng ntwor xtrnalts cas. Proof. Th ncrmntal xcss burdn du to a tax postvly dpnds on P. Gvn that w hav shown that dp > dp, ths rsult mpls that th dadwght loss assocatd to a tax s always lowr n a mart wth ntwor xtrnalts. Ths rsult s mportant from a publc polcy prspctv snc t stats that f govrnmnts nd to dcd btwn taxng a mart that s subjct to mportant ntwor xtrnalts and a standard mart (and f polcymars car about dadwght loss), taxaton of th ntwor mart should b avodd. W furthr dscuss th mplcaton of ths rsult n th concluson. 4. Wlfar Varaton W now consdr th varaton n wlfar n a monopoly mart n both th standard and ntwor cass whn thr s a chang n th pr-unt tax. Th da s to s how ntwor xtrnalts affct th varaton n wlfar for both consumrs and producrs.

15 Anna Laura Barald and Chrstan Rojas 191 tandard Monopoly Cas nc n th standard monopoly cas th dmand functon s lnar, C s gvn by th xprsson C = ( 1 ) (1 P) = (1 ), and ts chang du to a pr-unt tax varaton s C = ( ) < 0. Th monopolst proft s π = (, t) and ts varaton to a tax chang s π = ( )(1 ) ( C ) < 0. Th sgn of ths last xprsson dpnds on th magntud of C and C, thrfor t s a pror not prdctabl. Th varaton n th wlfar du to a varaton n a pr-unt tax, aftr som manpulaton, s thn W = ( )(1 ) ( C ). Whl th xprsson n parnthss n th last quaton can mathmatcally b ngatv, thrby mang W (possbly) postv, t s conomcally unlly. Not that th trm 1 s smply th mar-up snc 1 = P, and w xpct a monopolst to b opratng wth a postv mar-up. Ntwor Extrnalts: Non-Lnar Monopoly Cas Lt us start wth th cas whr th ntwor xtrnalts functon s not lnar, that s h ( ) = P = (1 ). Wlfar ( W ) s th sum of th consumr surplus ( C ) and th monopolst s proft (π ): Consquntly, th varaton n th wlfar du to an nfntsmal varaton n a pr-unt tax s: W C = + π. In ths non-lnar cas, th C s gvn by th followng xprsson: C = Pd P = Thus, th varaton n C du to an nfntsmal varaton n th pr-unt tax s: [ + 1) ] C +1 = (, whch s always ngatv on th downward slopng part of th dmand curv Th monopolst proft s π = (, t) and ts chang du to a + 1 varaton n th pr-unt tax s π = ( )[( + 1) ( + ) ] ( C ). Th sgn of ths xprsson s not prdctabl for th sam rason statd arlr. Th rsultng chang n wlfar du to a varaton n a pr-unt tax, aftr + 1 som manpulaton, s W = ( )( ) ( C ). By th sam rasonng w usd n th standard monopoly cas abov, ths xprsson wll b ngatv. Proposton 5. Undr th sam chang n quantty du to an nfntsmal varaton n

16 19 Intrnatonal Journal of Busnss and Economcs th cost shoc paramtr (.., dq = dq ), th chang n total wlfar n th ntwor xtrnalts monopoly cas s gratr than th chang n wlfar n th standard monopoly cas. Proof. Th comparson of th wlfar varaton s gvn by: W W > + 1 C C ( ) > + ( 1 ), (10) whch, aftr manpulaton, mpls ( 1 )( 1) < 0, whch s always tru at d = d. W also show that, whn comparng th varaton n th C n th standard and ntwor xtrnalty (monopoly) cass, th condton C > C always holds, 1 whl th rlaton btwn th varaton n th two monopoly profts s nrmnat; mportantly, (10) also holds n th lnar xtrnalty cas wth a pur and non-pur ntwor good, as wll as n th Cournot olgopoly cas. Implcatons Equaton (10) ndcats that whl wlfar losss n th cas of a pr-unt tax ncras ar largr (mor ngatv) n th standard cas (consstnt th xcss burdn analyss), wlfar gans (du to an ncras n subsds) ar also largr n th standard cas (nconsstnt wth th xcss burdn analyss). 3 Th rason for th dscrpancy wth th xcss burdn analyss (n th cas of a pr-unt subsdy ncras) s that th dadwght loss analyss ncluds both changs n tax rvnus (or subsdy paymnts) and changs n wlfar. To s how to rconcl ths analyss, rcall that a prc dcras, as a rsult of a pr-unt subsdy ncras, s largr n th standard cas; ths mans that subsdy paymnts ar largr n th standard cas (larg nough to offst th largr wlfar gan n th standard cas). nc th sgn of proft chang as a rsult of a pr-unt tax chang s nrmnat, th rsult n (10) s manly drvn by th smallr (n absolut valu) consumr wlfar chang; snc w hav controlld for th rol of dmand curvatur on th PTR, ths rsult mans that a smallr PTR n th ntwor cas s du to consumrs xpctatons about ntwor growth. 5. Conclusons Cost pass-through s a y conomc comparatv statc. Th rsults of ths papr contrbut to th growng and nfluntal cost pass-through ltratur by showng that ntwor xtrnalts can b an mportant rmnant of th passthrough rat. Cost pass-through can b nfluncd by both dmand and supply condtons; snc ntwor xtrnalts ar fundamntally a dmand-sd

17 Anna Laura Barald and Chrstan Rojas 193 phnomnon, our analyss can b classfd as a dmand-drvn factor of cost passthrough. pcfcally, th cost pass-through rat s smallr n a mart wth ntwor xtrnalts than n a no-ntwor-xtrnalty countrpart; an mportant fatur of our study s that ths rsult s robust to svral dmand spcfcatons and mart structurs and that t dos not dpnd on th dffrnc n curvatur of dmand btwn th two cass consdrd. Our rsults also suggst that whn facng a pr-unt tax dcras (.., a subsdy ncras), consumrs would, all ls qual, prfr to consum a standard good (ovr a ntwor good); but thy would prfr a ntwor good (ovr a standard good) othrws. Th rason for ths fndng s that, gvn th sam quantty chang, a prunt subsdy ncras (dcras) wll dcras (ncras) prc by a smallr amount n th ntwor good cas than n th standard cas. Fnally our analyss can b nformatv for polcymang. 4 If ntrvnton va pr-unt subsds s chosn, and f th govrnmnt only cars about wlfar (and not tax rvnu, or subsdy paymnts), t would prfr, all ls qual, to ntrvn n a standard mart rathr than n a ntwor good mart (f t had to fac such a choc). Convrsly, f pr-unt taxs ar chosn, and f wlfar s th only consdraton, th govrnmnt would prfr a ntwor mart ovr a standard mart. On th othr hand, f govrnmnt cars about dadwght loss, t wll prfr a ntwor good mart ovr a standard good mart rgardlss of th typ of ntrvnton (pr-unt tax or pr-unt subsdy). Fnally, govrnmnt ntrvnton through taxaton can b crtcal f th ntwor s facng th upward slopng scton of th dmand curv: an ncras of th xcs tax can ma th ntwor dsappar, but a subsdy can propl t to stabl growth. Of cours, our analyss s not wthout cavats. Frst, w lmt our attnton to Cournot olgopoly as ths cas s mor tractabl than th dffrntatd product Brtrand modl. cond, thr ar a numbr of othr ralstc mart faturs that w assum away such as th vrtcal structur of th mart, dynamc consdratons (from both dmand and supply sd), as wll as stratgc ntry dcsons. Appndx A1. Cost pass-through analyss n Cournot olgopoly wth a lnar ntwor xtrnalts spcfcaton. In ths cas, th nvrs dmand functon s P = ( 1 ) wth = q + q and q 1 = j q. Frms hav th sam cost structur as n th monopoly cas. Frm j has frst- and scond-ordr condtons: π q δ π δq = P + q [1 ] q = 4 q q q = 0. + q q q = 0,

18 194 Intrnatonal Journal of Busnss and Economcs Thus, n th symmtrc qulbrum, th frm s ncssary condton bcoms nq ( nq) + q nq = 0 q. Totally dffrntatng th frst-ordr qulbrum condton, w hav [ n + 1 qn 4nq ] dq = 0 qq qt, whch, aftr rarrangng trms, bcoms: dq Cqt =, (a) n + 1 qn 4nq qq whr C 0 ; local stablty of th qulbrum mpls that th dnomnator of (a) t s ngatv. Thus dq s ngatv. Th frm optmal absolut pass-through rat s thus P = n( q )[1 nq], whch s postv f 1 nq < 0, that s, f > 1 (.., on th downward slopng part of th dmand functon). As n th monopoly cas, w consdr th sam varaton n quantty (n both th ntwor and standard cass) du to an nfntsmal varaton n th cost-shoc paramtr. Thn, * th quaton dq = dq s satsfd for = n + 1 n +. It s asy to show that dp dp. A. Cost pass-through analyss n Cournot olgopoly wth non-pur ntwor goods. Th nvrs dmand functon s P = ( 1 )( s + ) wth = q + q and q 1 = j q. Frms hav th sam cost structur as n th monopoly cas. Totally j dffrntatng th frst-ordr condton, w obtan: dq Cqt = (1 s)(1 + n) nq( n + ) qq. Th frm s optmal absolut pass-through rat s thus P = n( q )[1 s nq], whch s postv f 1 s nq < 0, that s, f > 1 s (.., on th downward slopng part of th dmand functon). In th standard Cournot cas, th dmand functon s P = ( 1 ) s wth = q + q and dq = C s( 1+ n) qt qq, and th optmal PTR s P = sn( q ). As statd throughout th papr, w consdr th sam varaton n quantty (n both th ntwor and standard cass) du to an nfntsmal varaton n th costshoc paramtr. Thn, th quaton dq = dq s satsfd for 5 * = n + 1 ( n + ). It s asy to chc that dp dp. Indd dp dp f sn( q ) > n( q )[1 s nq], whch mpls that * < 1 s always tru bcaus = n + 1 ( n + ). A.3 Wlfar analyss, monopoly cas wth lnar ntwor xtrnalty spcfcaton. Hr, w drv th varaton n consumr surplus ( C ), proft, and wlfar n th monopoly cas wth a pur ntwor good as a rsult of a pr-unt tax chang. (Th drvaton s smlar wth a non-pur ntwor good.) Th dmand wth functon s P = ( 1 ), whl consumr surplus s gvn by C = Pd P

19 Anna Laura Barald and Chrstan Rojas = ( 3) (1 ). Th varaton n th C du to an nfntsmal varaton n th tax paramtr s C = ( )( 1), whch s ngatv for > 1 ; that s, on th downward slopng part of th nvrs dmand curv. 3 Th monopolst proft s π = (, t) and ts chang du to a varaton n th tax s π = ( )[( 3 ] ( C ) wth a sgn that s not a pror prdctabl bcaus t dpnds on th magntud of C and C. Rcallng th xprsson for C and proft n th standard cas, w can compar th varaton n th C, proft, and wlfar du to an nfntsmal varaton n th tax paramtr n both cass. Whn = (whch s tru whn * = 1 ): C C > bcaus ( 1) > ; π π C C < bcaus ( 3 ) < (1 ) W W >. and A4. Wlfar rsults n Cournot olgopoly cas wth a non-lnar ntwor spcfcaton. and Th nvrs dmand functon n ths cas s P = ( 1 ) wth = q + q q 1 q. Consdr th symmtrc cas j q = q = q. Th C s: j = j C = = ( ) Pdq Pq nq dq ( nq) dq q( nq) + q( nq) = n q n q n q + n q Th varaton n th C du to an nfntsmal varaton n th tax paramtr s C = ( q )[( nq) ( nq) ( + 1)( nq) + ( + )( nq) ], whch s always ngatv on th downward slopng part of th nvrs dmand curv. + 1 Th proft of a gvn frm s π = q( nq) q( nq) (, t) and ts chang + 1 du to a varaton n th tax s π = ( q )[( + 1)( nq) ( + )( nq) ] C. Lt us now consdr th standard olgopoly cas. Th consumr surplus s C = ( 1 ) nq and th corrspondng proft s π = q( 1 nq) (, t), wth C = nq( q ) and π = ( q )(1 nq ) C. Aftr mposng =, w can say that W > W holds f:

20 196 Intrnatonal Journal of Busnss and Economcs q [( nq) ( nq) ( + 1)( nq) + ( + )( nq) ] + 1 [( + 1)( nq) ( + )( nq) ] q + q π > nq + q = (1 nq C, C ), whch s tru f ( 1)(1 ) < 0, a rlatonshp that always holds. It s straghtforward to prov th sam rsult wth th lnar spcfcaton of th ntwor xtrnalts functon. Nots 1. Cost shocs ar common n ndustrs charactrzd by ntwor ffcts. An xampl of ths s th tlcommuncatons ndustry, whch s oftn subjct to xognous shocs du to tchnology nnovatons (a ngatv cost shoc) or to volatl xchang rats that affct th prc of mportd nputs (such as qupmnt).. W provd rfrncs to mor comprhnsv rvws throughout ths scton. 3. nc pr-unt tax changs and cost shocs hav quvalnt mathmatcal tratmnts, publc conomcs studs (on taxs) and ndustral organzaton studs (on costs) hav sgnfcant ovrlap; for ths rason, although w only rfr to cost pass-through, w ntrchangably rfr to studs n both ltraturs n ths scton. 4. An altrnatv concpt usd to study ths ssu s pass-through rat lastcty (PTE), whch s dfnd as ( p c)( c p). Th concpt PTR s commonly usd by th ndustral organzaton ltratur, whras PTE s typcally adoptd by th ntrnatonal conomcs ltratur. Wthout loss of gnralty for our analyss blow, w adopt th formr. 5. As notd by Andrson t al. (001), ad (1997), and Fullrton and Mtcalf (00), howvr, n ths cass th condtons for ovr- or undr-shftng also dpnd on th dmand curvatur. 6. For a rcnt rvw of factors affctng PTR s Kosc and Cahll (006). 7. Whl undr-shftng n ths ltratur focuss on PTE, PTR stmats n ths ltratur sm to suggst that undr-shftng s stll a common fndng (.g., Naamura and Zrom, 009; Goldbrg and Hllrstn, 008). 8. Whl thr hav not bn attmpts to rconcl ths two apparntly opposng vws, thr ar two lly rasons. Frst, th two ltraturs consdr dffrnt typs of cost shocs: ntrnatonal conomsts study xchang rats whras publc conomsts ar prmarly concrnd wth xcs taxs. cond, th ndustral organzaton ltratur focuss on PTR (.., p c ), whl ntrnatonal conomsts hav (typcally) studd PTE (.., ( p c)( c p) ). Clarly, unlss mar-ups ar zro, PTE wll b smallr than PTR. 9. Dlpalla and O Donnll (001) also analyz th PTR n th cgartt ndustry. 10. Rogrs (003) dfns th crtcal mass as th mnmal numbr of subscrbrs (adoptrs) of an ntractv nnovaton for th furthr rat of adopton to b slf-sustanng; that s, ntwor ffcts can gnrat multpl stabl qulbra sparatd by an unstabl on, th crtcal mass. 11. To smplfy xposton w wll hncforth oftn rfr to th ntwor xtrnalty cas smply as th ntwor cas.

21 Anna Laura Barald and Chrstan Rojas Ths assumpton dvrgs from that of Katz and hapro (1985) and Cabral (1990), who us an addtv utlty spcfcaton, so that all consumrs rcv th sam bnft from th ntwor xtrnalty. 13. C = ( C ) > 0 and C = ( C ) > Th last two cass rprsnt a pur ntwor good (.., th good has no stand alon valu). W latr addrss th non-pur ntwor good cas. 15. To s ths, not that P > 0 whn 0 < ( + 1) whl P < 0 whn ( + 1) < Th scond ordr condton π = ( + 1) ( + )( + 1) 0 holds f > ( + ). Thrfor t always holds whn > ( +1) (snc ( + ) s smallr than ( +1) ), whr w concntrat our analyss blow. 17. pcfcally, t s straghtforward to chc that th dnomnator of th (5) s always ngatv for th cas that s of ntrst for our analyss: ( + 1) < * = 1 3 s on th downward slopng part of th dmand functon f 3 1> 0, or whn > 1 3 (a condton that s not too rstrctv). 19. An xampl of ths s whn polcymars gv mor wght to consumr wlfar, as s th cas n anttrust polcy. 0. To b consstnt wth our arlr analyss, w compar th two cass of ntrst on th downward slopng porton of th dmand curv (.., whr th two cass ar comparabl). 1. In comparng th two C, aftr algbrac manpulaton, t can b shown that ( 1) + ( 1) < 0 always holds.. appndcs A3 and A4. 3. Rcall that W s ngatv. 4. W do rcognz, howvr, that polcymang s subjct to subtlts that would ma th followng mplcatons mor or lss rlvant. For xampl, th polcymar may hav objctvs othr than wlfar or dadwght loss (tax rvnu, or consumr wlfar, for xampl). Also, t s obvous that polcymars do not always fac taxaton dcsons among th two typs of marts w consdr. * 5. ls on th downward slopng porton of th dmand curv f s ( n + ) 1 > 0. Rfrncs Andrson,. M., A. d Palma, and B. Krdr, (001), Tax Incdnc n Dffrntatd Product Olgopoly, Journal of Publc Economcs, 81(), Bacon, R. W., (1991), Rocts and Fathrs: Th Asymmtrc pd of Adjustmnt of UK Rtal Gasoln Prcs to Cost Changs, Enrgy Economcs, 13, Barzl, Y., (1976), An Altrnatv Approach to th Analyss of Taxaton, Th Journal of Poltcal Economy, 84(6), Bsly, T. and H. Rosn, (1998), als Taxs and Prcs: An Emprcal Analyss, NBER Worng Papr, No Bshop, R. L., (1968), Th Effcts of pcfc and Ad Valorm Taxs, Th uartrly Journal of Economcs, 8(), Bornstn,., A. C. Camron, and R. Glbrt, (1997), Do Gasoln Prcs Rspond Asymmtrcally to Crud Ol Prc Changs? Th uartrly Journal of

22 198 Intrnatonal Journal of Busnss and Economcs Economcs, 11(1), Burstn, A. T., J. C. Nvs, and. Rblo, (003), Dstrbuton Costs and Ral Exchang Rat Dynamcs durng Exchang-Rat-Basd tablzatons, Journal of Montary Economcs, 50, Cabral, L. M. B., (1990), On th Adopton of Innovatons wth Ntwor Extrnalts, Mathmatcal ocal cncs, 19, Campa, J. M. and L.. Goldbrg, (005), Exchang Rat Pass-Through nto Import Prcs, Th Rvw of Economcs and tatstcs, 87(4), Church, J. and N. Gandal, (1993), Complmntary Ntwor Extrnalts and Tchnologcal Adopton, Intrnatonal Journal of Industral Organzaton, 11(), Corstt, G. and L. Ddola, (004), Exchang-Rat Fluctuatons and Pass- Through, Mtng Paprs, No. 495, octy for Economc Dynamcs. Cottrll, R., L. Egan, and W. Buchold, (001), Byond Illnos Brc: Th Law and Economcs of Cost Pass-Through n th ADM Prc Fxng Cas, Rvw of Industral Organzaton, 18(1), Dlpalla,. and M. Kn, (199), Th Comparson btwn Ad Valorm and pcfc Taxaton undr Imprfct Comptton, Journal of Publc Economcs, 49(3), Dlpalla,. and O. O Donnll, (001), Estmatng Tax Incdnc, Mart Powr and Mart Conduct: Th Europan Cgartt Industry, Intrnatonal Journal of Industral Organzaton, 19(6), Dvrux, M. and C. Engl, (001), Endognous Currncy of Prc ttng n a Dynamc Opn Economy Modl, NBER Worng Papr, No Economds, N. and C. Hmmlbrg, (1995), Crtcal Mass and Ntwor z wth Applcaton to th U Fax Mart, Dscusson Papr, EC-95-11, trn chool of Busnss, N.Y.U. Economds, N., (1996), Th Economcs of Ntwors, Intrnatonal Journal of Industral Organzaton, 14(6), Engl, C., (1999), Accountng for U.. Ral Exchang Rat Changs, Journal of Poltcal Economy, 107, Farrll, J. and G. alonr, (1985), tandardzaton, Compatblty, and Innovaton, RAND Journal of Economcs, 16(1), Fullrton, D. and G. Mtcalf, (00), Tax Incdnc, NBER Worng Papr, No Goldbrg, P. K. and R. Hllrstn, (008), A tructural Approach to Explanng Incomplt Exchang-Rat Pass-Through and Prcng-To-Mart, Amrcan Economc Rvw, 98(), Goldbrg, P. K. and M. M. Knttr, (1997), Goods Prcs and Exchang Rats: What Hav W Larnd? Journal of Economc Ltratur, 35, Goodwn, B. K. and M. T. Holt, (1999), Prc Transmsson and Asymmtrc Adjustmnt n th U.. Bf ctor, Amrcan Journal of Agrcultural Economcs, 81, Hanson, A. and R. ullvan, (008), Th Incdnc of Tobacco Taxaton: Evdnc

23 Anna Laura Barald and Chrstan Rojas 199 from Gographc Mcro-Lvl Data, Worng Papr, Gorga tat Unvrsty. Harrs, R. G. and L. A. ullvan, (1979), Passng on th Monopoly Ovrcharg: A Comprhnsv Polcy Analyss, Unvrsty of Pnnsylvana Law Rvw, 18(), Johnson, R. N., (00), arch Costs, Lags and Prcs at th Pump, Rvw of Industral Organzaton, 0, Katz, M. L. and H.. Rosn, (1985), Tax Analyss n an Olgopoly Modl, NBER Worng Papr, No Katz, M. L. and C. hapro, (1985), Ntwor Extrnalts, Comptton, and Compatblty, Amrcan Economc Rvw, 75(3), Katz, M. L. and C. hapro, (1986), Tchnology Adopton n th Prsnc of Ntwor Extrnalts, Journal of Poltcal Economy, 94, Katz, M. L. and C. hapro, (1994), ystms Comptton and Ntwor Effcts, Journal of Economc Prspctvs, 8, Km, D. and R. Cottrll, (008), Cost Pass-Through n Dffrntatd Product Marts: Th Cas of U.. Procssd Chs, Journal of Industral Economcs, 56(1), Kosc, G. and M. Cahll, (006), Economcs of Cost Pass through and Damags n Indrct Purchasr Anttrust Cass, Th Anttrust Bulltn, 51(3), Kwoa, J. and L. Wht, (008), Th Anttrust Rvoluton: Economcs, Comptton, and Polcy, 5th Edton, Oxford Unvrsty Prss. Mnon, J., (1995), Exchang Rat Pass-Through, Journal of Economc urvys, 9(), Naamura, E. and D. Zrom, (010), Accountng for Incomplt Pass-Through, Rvw of Economc tuds, 77(3), Parsly, D. C. and. W, (003), A Prsm nto th PPP Puzzls: Th Mcro- Foundatons of Bg Mac Ral Exchang Rats, NBER Worng Papr, No Ptz, M. and M. Rsngr, (009), Indrct Taxaton n Vrtcal Olgopoly, CEIFO Worng Papr, No Potrba, J. M., (1999), Front Mattr to Tax Polcy and th Economy, n Tax Polcy and th Economy, Vol. 13, NBER Chaptrs. Ravn, M.,. chmtt-groh, and M. Urb, (008), Incomplt Cost Pass-Through undr Dp Habts, CEPR Dscusson Paprs, No Rogrs, E., (003), Dffuson of Innovatons, 5th Edton, Nw Yor: Fr Prss. Rojas, C., (008), Prc Comptton n U.. Brwng, Th Journal of Industral Economcs, 56, anyal, K. K. and R. W. Jons, (198), Th Thory of Trad n Mddl Products, Amrcan Economc Rvw, 7(1), ad, J., (1997), Proftabl Cost Incrass and th hftng of Taxaton: Equlbrum Rspons of Marts n Olgopoly, Th Warwc Economcs Rsarch Papr rs, Th Unvrsty of Warwc, No. 60. hapro, C. and H. R. Varan, (1999), Informaton Ruls: A tratgc Gud to th Ntwor Economy, Boston, MA: Harvard Busnss chool Prss.