Using Market Structure to Regulate a Vertically Integrated Monopolist

Transcription

1 Using Markt Structur to Rgulat a Vrtically Intgratd Monopolist by Sang H. L and Jonathan H. Hamilton Dpartmnt ofeconomics Univrsity offlorida Gainsvill FL USA May 1998 W thank David Sappington, Sanford Brg, and an anonymous rfr for many hlpful commnts. Th scond author thanks th Univrsity offlorida Collg of Businss Administration and th Public Utility Rsarch Cntr for financial support for this rsarch.

2 Abstract A natural monopolist whos cost is privat information producs a good which is combind with anothr good that can b producd by th monopolist or by othr firms. Th agncy that rgulats th monopolist can impos any ofsvral diffrnt markt structurs in th industry: intgratd monopoly, vrtical sparation with fr ntry downstram, or libralization downstram (both intgratd and indpndnt production). Whn svral firms produc downstram, a Coumot quantity-stting gam with fr ntry dtrmins th markt pric. W driv th optimal contracts to offr th monopolist undr all thr markt structurs and xamin th influnc ofdownstram cost diffrncs on accss prics. W thn study th optimal rgulatory policy whr th rgulator can condition th downstram markt structur on th monopolist's cost rport to th rgulator. Th optimal rgulatory policy awards a monopoly to a low-cost upstram firm, but rquirs fr ntry downstram ifth monopolist rports high upstram costs. Thus, th choic ofmarkt structur is an additional tool to limit rnt xtraction by th monopolist. Simulation analysis rvals th possibility ofsignificant wlfar gains from this additional rgulatory tool.

3 1. Introduction Sinc Baron and Myrson (1982), asymmtric information modls hav bn a major focus ofrsarch on monopoly rgulation. Work by Lwis and Sappington (1988a, 1988b, 1989, 1997) and Laffont and Tirol (1986, 1990a, 1990b, 1994) has addd gratly to our undrstanding ofincntiv rgulation. Rcnt policy initiativs attmpt to rstructur traditional rgulatd industris, particularly by rducing th dgr ofvrtical intgration. In svral industris, sgmnts ofth industry that had bn part ofa natural monopoly ar now opn to fr ntry by compting firms. Somtims th original monopolist has bn barrd from ntring th comptitiv sgmnt. In tlcommunications, th 1984 divstitur compltd th opning of intr-lata long distanc markts, but th Baby Blls wr prvntd from offring longdistanc srvic. Now comptition is coming to vn mor ofth industry. In lctricity, svral rgulatory commissions' rtail whling proposals ffctivly drgulat parts ofth gnration sctor, but incumbnt monopolists rtain control ofdistribution and rmain subjct to rgulation. Our goal is to analyz how th xistnc ofpotntial comptition affcts a rgulator's dcision rgarding markt structur in a ntwork industry and how markt structur itslf can b usd to limit rnt xtraction. On branch ofth xisting litratur considrs th trms on which to prmit small-scal ntry in on sctor. In a full information framwork, Willig (1979) studis intrconnction by compting supplirs and strsss th fact that stratgic bhavior may lad th ntwork oprator to dtr socially bnficial ntry. Baumol and Sidak (1994) discuss similar issus in th framwork ofrailroad accss pricing. Thir fficint componnt pricing rul (ECPR) stats that an ntrant should pay th incumbnt its full opportunity cost (incrmntal rvnus minus incrmntal costs) for us ofth ntwork. Whil this prohibits unconomic ntry, it placs 1

4 littl comptitiv prssur on th monopolist Armstrong and Doyl (1995) discuss a numbr of limitations ofth ECPR. Whil full information provids a usful bnchmark cas, incorporating information asymmtris btwn firms and th rgulator is important. Laffont and Tirol (1994) analyz accss pricing in a hiddn action modl ofmultiproduct monopoly rgulation. Whn public funds hav a social cost du to th dadwight loss oftaxation, th optimal accss pric must xcd marginal cost, vn though th rgulator has complt information. Morovr, thy study th impact ofth rgulator's incomplt information about th monopoly's cost structur on th monopoly's informational rnts. Vickrs (1995) studis accss pricing ruls in th Baron and Myrson (B-M) (1982) modl in which th rgulator dos not know (upstram) marginal cost. Vickrs compars vrtically intgratd monopoly with an imprfctly comptitiv downstram sctor with and without th monopolist producing downstram. All firms, including th monopolist, who produc downstram hav constant marginal cost and a positiv fixd cost. Ths firms ngag in Cournot comptition with fr ntry.! On qustion is whthr th monopolist should b allowd in th drgulatd downstram sctor. Anothr qustion is whthr th prsnc ofth fring firms who ar only activ downstram always nhancs wlfar. As long as th rgulator can dictat that ithr th monopolist or th fring firms b shut down, to incras xpctd wlfar th rgulator may prmit scond sourcs ofproduction in th drgulatd downstram markt to ITwo sourcs ofinfficincy must b valuatd for th wlfar comparison ofvrtical intgration and vrtical sparation: th information asymmtry, which allows th monopolist to gt distributionally costly rnts, and imprfct comptition downstram, which lads to xcss ntry (duplication ofth fixd costs). Vrtical intgration has disadvantags for rasons rlatd to anti-comptitiv incntivs to rais rivals' costs, but it may b advantagous to rduc duplication offixd costs insofar as it allows gratr productiv fficincy. S Vickrs (1995). 2

5 rplac, or to produc alongsid, th xisting monopolist.2 Sction 2 dscribs our modl that combins B-M monopoly upstram with Cournot oligopoly downstram. W allow marginal production costs downstram to diffr btwn th monopolist and fring firms. 3 Th rgulator knows both downstram costs; th only privat information is upstram marginal cost. Whil it may b difficult to obsrv costs ofntwork opration, th tchnology ofcombining ntwork accss with anothr input may b a simpl tchnology. W considr cass whr th monopolist is mor or lss fficint in th downstram sctor. Ifthr ar conomis ofscop, th monopolist would b mor fficint. Ifth monopolist has highr labor costs (prhaps du to union contracts), th monopolist would b lss fficint. Sction 3 studis optimal contracts undr thr diffrnt markt structurs: (1) vrtically intgratd monopoly; (2) vrtical sparation--th monopolist is xcludd from downstram production; and (3) vrtical intgration with libralization--th monopolist and th fring can both ntr downstram production (w call this simply libralization in th rmaindr ofth papr).4 This last structur includs two variants, dpnding on whthr or not th rgulator controls th monopolist's downstram activity. Th rgulatory instrumnt is th offr to th monopolist ofa schdul spcifid by th monopolist's choic ofaccss pric. Ifth monopolist's downstram output is contractibl, vrtical intgration and vrtical sparation ar spcial cass of libralization. Ifth monopolist is mor fficint than fring firms in th downstram markt, 2For rcnt thortical studis on scond sourcing problms, s Anton and Yao (1987), Dmski, Sappington, and Spillr (1987), Auriol and Laffont (1992), and McGuir and Riordan (1995). 3W follow Vickrs's (1995) framwork, xcpt that w allow downstram production costs to diffr btwn th upstram monopolist and th fring. 4Armstrong, Cowan, and Vickrs (1994, Ch. 5) discuss a numbr ofconcptual issus involving th choic btwn intgration and sparation or libralization in ntwork industris. 3

6 libralization yilds optimizd xpctd wlfar ofvrtical intgration and thus vrtical intgration is optimal. Furthrmor, ifth monopolist is lss fficint but clos to fring firms, vrtical intgration may still b optimal, saving fixd costs downstram. Howvr, ifth monopolist is significantly infficint than fring firms, libralization yilds optimizd xpctd wlfar of vrtical sparation and thus vrtical sparation is optimal. Whn th monopolist's downstram output is not contractibl, nithr vrtical intgration nor vrtical sparation ar nstd in th libralization structur. Sinc th rgulator facs an additional constraint -- th monopolist's first ordr condition in th downstram Coumot gam, noncontractibl libralization downstram output can not yild any highr xpctd wlfar than libralization with contractibl downstram output. Dspit this, th noncontractibl form of libralization is rlvant. 5 Ifth monopolist is mor fficint than fring firms in th downstram markt, vrtical intgration dominats libralization. Undr vrtical sparation and libralization, th optimal accss pric diffrs from marginal cost pricing ofaccss du to th informational asymmtry btwn th rgulator and th monopolist, th downstram markt dmand function, and fixd costs. W xamin th ffcts ofdownstram cost diffrncs on th optimal accss pric undr libralization. In particular, with linar dmand, th mor fficint th monopolist is and th lss fficint th fring is at th downstram lvl, th highr ar th accss pric and th monopolist's pric-cost margin. Morovr, th mor fficint th monopolist is and th lss fficint th fring is at th downstram lvl, th fwr firms ar in th downstram markt and, to that xtnt, lss duplication offixd costs occurs. 5Undr contractibl libralization, th rgulator can giv th monopolist an advantag by allowing it to commit to a lvl ofoutput in advanc ofth fring firm's choics. In practic, it may b ncssary to allow vryon to compt on th sam footing downstram. 4

7 In Sction 4, w rstrict our attntion to linar invrs dmand and show that diffrncs in th lvl ofxpctd social wlfar undr libralization and vrtical sparation dpnd on paramtr valus ofth dmand and cost function at th downstram lvl, but not on th ralization ofth monopolist's upstram cost. Hnc, ifall rlvant information about th invrs dmand function and costs at downstram lvl ar known, th ranking of markt structurs btwn libralization and vrtical sparation in trms ofxpctd wlfar is dtrmind at th outst, irrspctiv ofth ralization ofth monopolist's upstram marginal cost. In Sction 5, w xtnd our analysis to dsign an optimal policy whn both markt structur and th monopolist's compnsation dpnd on th monopolist's upstram marginal cost rport. W rfr to this as a hybrid rgim. Th rlvant choics facing th rgulator ar: (1) vrtically intgratd monopoly vrsus vrtical sparation; or (2) vrtically intgratd monopoly vrsus libralization. W focus on th formr cas bcaus ithr vrtical intgration or libralization dominats th othr in th lattr cas. Th ky point is that, undr th hybrid rgim, th rgulator considrs not only vrtical conduct (pricing), but also vrtical structur. 6 By implmnting th optimal rgulatory policy that uss th choic ofmarkt structur as an additional tool to limit rnt xtraction by th monopolist, th rgulator can incras xpctd social wlfar significantly. 7 6In vrtically rlatd markts, thr ar two major qustions. Th qustion ofvrtical conduct is how to rgulat th trms on which th monopolist givs accss to th othr firms and th qustion rgarding vrtical structur is whthr to allow th monopolist into th drgulatd downstram sctoro S Armstrong, Cowan, and Vickrs (1994). 7Our rsult shows larg fficincy gains for th hybrid mchanism, compard to Bowr's (1993). H studis marginal bnfits of crtain contracting instrumnts in procurmnt modl such as full commitmnt, slf slction, multipl cost obsrvation, and comptition, and finds small diffrncs btwn th mchanisms. On major diffrnc is that h considrs two-priod modls in which th principal (th buyr) can updat th contract using information acquird in th first priodo 5

8 2. Th Modl A rgulatd industry producs a singl homognous product. Assum thr ar no incom ffcts, and dnot invrs dmand by P ( Q), which w assum to b twic diffrntiabl. To mak ach unit ofth good rquirs on unit ofan input supplid by an upstram monopolist and on unit ofanothr input providd by a downstram producr. Th firms in th industry includ a vrtically intgratd monopolist (in both th upstram and downstram sctors ifth rgulator prmits it) and othr producrs who can frly ntr th downstram sctor (which w rfr to as fring firms). W assum that all marginal costs ar constant. Lt 8 dnot th monopolist's upstram marginal cost (th marginal cost ofntwork opration with rspct to output). Lt wand v qual th downstram marginal costs ofothr inputs usd by th downstram monopolist and th fring firms, rspctivly. Hnc, ifth monopolist (hrinaftr, M) chargs fring firms an accss f a for th upstram input, fring firms' marginal cost ofproduction ofth final good is a + v, whil M's own marginal cost ofproduction ofth final good is 8 + w. Any firm (including th monopolist) that ntrs th downstram markt must pay a fixd cost K. Lt n dnot th numbr offirms in th downstram markt, which will b dtrmind ndognously by a zro profit condition for th fring firms Th Rgulatory Environmnt Th upstram marginal cost,, is th monopolist's privat information throughout our analysis. Th rgulator knows only that has th distribution function F( 8), with a support 8W ignor any intgr constraints on n. 6

9 on [ft, ]. W assum that F ( ) is continuous, diffrntiabl, and strictly incrasing. To kp our analysis tractabl, w assum a uniform distribution for : Assumption 1. 8-ft Th upstram marginal cost, 8, has a distribution function: F () =-- a-ft (1) W also confin our analysis to paramtr valus for which it is optimal to hav positiv output. Assumption 2. For all 8 E [fr, 8], it is nvr optimal to hav zro production in th upstram and downstram markt. 9 With asymmtric information, th rgulator's problm is to maximiz an xpctd valu of social wlfar which is a wightd sum ofconsumrs' surplus and firms' profits. Social wlfar quals: w=s(q) + x 1t, x E [0, 1] 10 (2) whr S(Q) and 1t dnot consumrs' surplus and Ms profit, rspctivly. II 9por diffrnt markt structurs, th critical uppr bound on diffrs, so w postpon stating th prcis bounds until latr in th papr. 10If x < 1, th rgulator favors consumr intrsts ovr M s intrsts. With this spcification, a transfr ofa dollar from consumrs to M would rsult in a loss of (1 - x) dollars. S Baron (1989). I1By assuming fr ntry in th downstram markt, th fring firms's comptitiv profits ar zro and ar omittd. W assum that n is continuous to avoid intgr problms. 7

10 2.2 Th Downstram Cournot Gam Undr th policy options ofvrtical sparation or libralization, firms in th downstram sctor playa Coumot quantity comptition gam. Lt ql and q2 rprsnt th quantitis of final goods supplid by th monopolist and ach comptitiv fring firm, rspctivly. Lt Q dnot th aggrgat quantity supplid in th downstram markt. Thus, Q = ql + (n - 1)q2 undr libralization and Q=nq2 undr vrtical sparation. First, th rgulator sts an accss pric, a, for th upstram good by offring th monopolist a mnu ofchoics which dtrmins th accss pric. If q1 is contractibl, th rgulator offrs a mnu {a, q1(a), T(a)} whr T(a) is th transfr (positiv or ngativ). If q1 is not contractibl, thn th rgulator offrs a mnu {a, T(a) } A Rprsntativ Fring Firm Onc th accss pric is st, ach idntical comptitiv fring firm chooss its output to solv: Max q2 [P(Q)-a-v]q2-K whr Q = ql + (n - 1) q2 and ql is ithrms downstram output choic or th output lvl prscribd by th rgulatory contract ( qi is zro undr vrtical sparation). Th first ordr condition for profit maximization and th zro profit condition ar: P - a - v = - P /q2 [P(Q)-a-v]q2=K. (3) (4) To simplify notation, dfin tp( Q) == J-P /( Q) and k == (7(. Thn conditions (3) and (4) bcom: k q =-- a = P - v ~ q;( Q) k, 2 q;(q), 8 (5)

11 2.2.2 Th lvlonopolist Whn th rgulator slcts libralization., ifth monopolist's downstram output choic ql is not contractibl, M solvs: Max [p( Q) w ] q 1 - K. ql Th first ordr condition is: (6) In this cas, quation (5) and (6) dtrmin th downstram quilibrium as a function ofaccss pric, a. Whn th mnu spcifis ql' th monopolist's downstram output is tid to th accss pric, and quations (3) and (4) dscrib th downstram quilibrium as a function of q1. 3. Optimal Contracts W now modl th contracts in two sttings dpnding upon whthr or not th monopolist's downstram output is contractibl. 3.1 Libralization with Contractibl qt If M s downstram output q1 is contractibl, th rgulatory mchanism involvs thr policy instrumnts: {Q(a), ql (a), T(a)}.12 Sinc Ms profit consists ofth profits from slling ntwork accss to fring firms and from slling final product in th downstram markt, plus th transfr, Ms profit quals: n C (8) = Max a (a - 8)(n - 1)q2 +[P(QC(a)) - 8 -w ]ql(a) + TC(a)-K = Max (a - 8) Q C ( a) + [ P (Q C ( a )) - w - a ] q1(a) + T C ( a) - K, a 12Th policy instrumnts ar quivalnt to {Q(), q 1( ), T()}, whr Q( ) is M s total upstram production. 9

12 whr th suprscript C dnots that th markt structur is libralization with contractibl ql' Onc th rgulator sts an accss pric., Cournot comptition downstram and th fr ntry condition dtrmin th final good pric. Thn M s incntiv compatibility condition is givn by a1tc ( 8 ) / a8 = - Q C (8 ). Intgrating by parts with th binding individual rationality condition c - 1C () =0, M s xpctd profit quals: (7) Hnc xpctd wlfar undr libralization quals: EW C = f{u(q c(8)) - (8 + w) QC(8) + [v + q;(q c(8)) k - whql (8) - Qc(8) ] ft - K~(ql (8)) - (1 - a)(8 - ft) Qc(8) } { ~ ft } d8 (8) whr ~ ( q1) is an indicator function that is qual to 1 if q1 > 0 and 0 othrwis. 13 Th only constraint th rgulator must considr is q 1 E [0, Q]. Thn, pointwis optimization of(8) with rspct to q1 and Q, subjct to q1 E [0, Q] yilds th following rsult: Proposition 1 1) Vrtical intgration and vrtical sparation ar spcial cass oflibralization in which q1 = QC and q1 = 0, rspctivly. 2) Ifth monopolist's downstram marginal cost xcds fring firms' marginal cost by tp(q) k (w - v > <p( Q c) k), thn q1 =0 is optimal for all (vrtical sparation). 13If q 1 = a is th optimal cas, th monopolist dos not spnd th fixd cost to ntr downstram production. 10

13 3) If w - v < q;( Qc) k, q1 = 0 is optimal if E [ [ v + q;( Q C ( 8 )) k - w ] Q C ( 8) ] - K < 0, whil q1 = QC is optimal if E [ [ v + q;( Q C ( 8 )) k - w ] Q C ( 8 ) ] - K> O. Ifth monopolist producs a positiv downstram output, ql =QC is optimal (vrtical intgration). (All proofs ar containd in th Appndix.) Th bnchmark shows that th thr diffrnt rgulatory rgims ar diffrnt cass ofa singl problm in which th monopolist's downstram output is contractibl. Whn ql is contractibl, ifw maximiz (8) with rspct to ql' w typically hav a cornr solution, with ql = Q or q1 = 0, as long as v + q;( Q) k - w dos not chang sign for diffrnt valus of Vrtically Intgratd Monopoly Ifvrtical intgration is optimal, pointwis optimization of(8) yilds th optimal pric in stat : pi(8)=8+w+(1-a)(8-ft), (9) whr th suprscript I indicats that th markt structur is vrtically intgratd monopoly. Equation (9) implis that th rgulator sts th final good pric abov marginal cost (8 + w) in such a way to rduc th firm's rnts whn its costs ar low. For w =0, (9) is simply th B-M rsult for a monopolist with unknown cost Vrtical Sparation Undr th markt structur ofvrtical sparation, th numbr ofth firms in th downstram markt is n = q;( Q) Q / kand th total amount offixd costs incurrd in th 11

14 downstram markt is 11 K =tp(q) k Q.14 Th rgulator sts an accss pric qual to: a S ( 8) = 8 - l ~ (Q S (8)) k E + (1 - x)( 8 - ft) (10) 2 whr S dnots vrtical sparation and E == - QP II (Q) / pi (Q) IS th lasticity ofth slop ofinvrs dmand. 15 Th rsulting final good pric is: (11) Not that th accss pric is highr with concav invrs dmand (E < 0) than with convx invrs dmand (E > 0) through th trm - ~ ~(Q s) k E. W may considr this trm as a mans ofbalancing wlfar loss bcaus, whn th rgulator rducs th numbr ofunits of output to limit M s rnt on th upstram input, th amount by which th final good pric incrass riss mor rapidly with convx invrs dmand than with concav invrs dmand. 3.2 Libralization with Noncontractibl q1 Ifth monopolist's downstram output dos not affct th upstram contract, th rgulator can not induc th monopolist to choos an output lvl which dos not satisfy M s first ordr condition for th downstram Coumot gam. Hnc M s optimization problm is: n L (8) =Max a (a - 8)QL(a) +(P(QL(a)) -w -a ]ql(a,8) + TL(a)-K whr L dnots libralization with noncontractibl q1 and q1(a, ) is th monopolist's quilibrium choic in th downstram Coumot gam. Onc th rgulator sts an accss pric, th 14Sinc ach idntical fring firm producs a quantity qual to q2' for a givn lvl of output Q s, th numbr offirms in th downstram markt is dtrmind by n = Q S / Q2' From (5), q2 = k / tp(q s), so th numbr offirms is n = q;(q s) QS / k. 15For xampl, E = 0 with a linar dmand and E = (b + 1) / b with a constant lasticity dmand, Q = ap -b. 12

15 final good pric is dtrmind by Coumot comptition and fr ntry. Thn M s incntiv compatibility condition is givn by a TIL (8 ) / a8 = [ v + q;( QL(8)) k - w ] / P /( QL( 8)) - QL(8).16 To avoid countrvailing incntivs for th monopolist, w confin our analysis to a paramtr rgion in which atil() /a dos not chang sign. I7 Assumption 3. ati L (8) = v+q;(ql(8))k-w -QL(8)<O p/(ql(8)) a for all 8E[!!,8]. In othr words, w rul out pooling solutions. Not that w - v > q;( Q L) k is sufficint, but not ncssary, for Assumption 3 to hold. W will assum that Assumption 3 holds throughout th rmaindr ofth papr. L - With th individual rationality condition 1t () = 0, M s xpctd profit quals: (12) 16From th first ordr condition (5) and (6), ~ =p - v - q;( Q) k and P - w - 8 = - P /(Q) q 1. Hnc w can rwrit M s profit as 1t () = Maxa (a - 8)Q L ( a ) + [ v + q;( QL(a ) ) k - w ] [ P (QL(a)) w ] / - P /(QL(a )) + T L(a) - K and gt th incntiv compatibility condition. 17Whn countrvailing incntivs aris, pooling gnrally charactrizs th quilibrium contract and agnts' prformanc is distortd both abov and blow fficint lvls. S Lwis and Sappington (1989). W xclud this cas to illustrat th potntial ofndognizing markt structur mor clarly. 13

16 With Ms first ordr condition and (12), xpctd wlfar quals: E W L = J{U( QL( 8)) - ( 8 + w) QL( 8) + [v + lfj( QL( 8 )) k - w ] [q1 ( 8) - QL( 8) ] ft -K-(l-a)(8-ft) [QL(8)+ v+lfj(ql(8))k-w] } {~} d. (13) _pl(ql(8)) - ft Lmma 1 Suppos that th monopolist's downstram output is not contractibl. 1) Ifth monopolist is sufficintly fficint so that w - v < q;( Q) k, vrtical intgration dominats libralization for all cost rports. (If w - v > <pc Q) k, th rvrs ffcts occur.) 2) Libralization with contractibl ql dominats libralization with noncontractibl ql. Whn q1 is not contractibl, nithr vrtical intgration nor vrtical sparation is a spcial cas of libralization. Vrtical intgration ithr dominats or is dominatd by libralization dpnding on v + q;( Q) k zw. Not that, bcaus it uss on lss instrumnt, libralization with noncontractibl q1 can not yild highr xpctd wlfar than libralization with contractibl q1. Whn q1 is not contractibl, th xpctd wlfar-maximizing rgulator considrs not only fixd costs associatd with fring ntry but also th diffrncs in production fficincy downstram. Th rgulator sts an accss pric qual to: a L (8)=8+(V-W)(1-SE)+lfJ(QL(8))k[ 1- ~(l +S)E] [ V +.!- q;( Q L ( )) k ~ w ] + (1 - a) ( - ft) E, ~pl(ql)ql() (14) 14

17 whr s dnots th ratio of Ms output to Q, s == ql / Q. Th rsulting final good pric is: pl(8)=8+v+(v-w)(l-se)+tp(ql(8))k (2- ~(l +s)e] V +..!. q;( QL ( 8 )) k - tv ] + (1 - a) (8 - fr) E. [ _pl(ql)ql(8) (15) W can now compar outcoms undr th diffrnt institutional sttings. Th main issu hr is to show how diffrncs in production fficincy ( = v - w) affcts th optimal accss pricing rul. Proposition 2 Suppos that th downstram dmand is linar. 1) Th optimally rgulatd accss and final good prics undr libralization and undr vrtical sparation diffr by v + q;( Q) k - w. 2) Undr libralization, th rgulator incrass both th accss pric and th final good pric by th diffrnc in marginal costs. Hnc, ifth monopolist is mor fficint downstram, th monopolist's pric-cost margin and markt shar incras. Fwr fring firms ntr and lss duplication offixd costs occurs. (If v < w, th rvrs ffcts occur.) 3) If v + qj( Q) k - w > 0, th downstram markt has fwr fring firms undr libralization than undr vrtical sparation. (If v + q;( Q) k - w < 0, th rvrs ffcts occur.) Not that, whn th downstram markt dmand is linar, th optimal accss pric undr vrtical sparation (a S ( )) allows for only M s information rnt, whil th optimal accss pric undr libralization ( a L ( )) accounts for not only M s information rnt but also diffrncs in production fficincy downstram and fixd costs associatd with fring firms' ntris. Hnc, ranking wlfar undr libralization and vrtical sparation dpnds on whthr th rduction in 15

18 th duplication ofth fixd costs dominats th gratr pric-cost margin. Proposition 3 Assum that 1 - se> ) Ifth invrs dmand curv is concav (E < 0) and th monopolist is mor fficint than fring firms, th rgulator raiss th accss pric by mor than v - w, but rducs th monopolist's information rnt rlativ to th cas oflinar dmand. 2) Ifth invrs dmand curv is convx (E> 0) and th monopolist is mor fficint than fring firms, th rgulator raiss th accss pric by lss than v - lv, but incrass th monopolist's information rnt rlativ to th cas oflinar dmand. 4. Analysis of Profits and Wlfar In this sction, w will rstrict our attntion to linar invrs dmand. Suppos that th downstram markt has a linar invrs dmand curv: P = A - BQ (A > 0, B > 0). Hnc th corrsponding aggrgat utility from consumption will b U( Q) = A Q - (B/ 2 ) Q 2, ignoring an arbitrary constant. 4.1 Comparison ofwlfar Lt W f ( ), W s(), and W L ( ) dnot social wlfar conditional on th monopolist's upstram cost undr th markt structur ofvrtical intgration, vrtical sparation, and libralization, rspctivly. For xampl, social wlfar undr vrtically intgratd monopoly is 18For convx dmand curvs with constant lasticity, th condition may not hold unlss th monopolist's downstram markt shar is small For concav dmand curvs, it always holds. 16

19 8" givnby W I (8)=U(QI(8))-(w+8)Ql(8)-K-(l-a) f QI(8)d8. Thcontractibl q1 libralization policy is always ithr vrtical intgration or vrtical sparation, so w do not nd to considr it sparatly, Thn wlfar changs as 8 changs undr ach rgulatory policy in th following mannr: Lmma 2 Suppos that th dmand curv is linar. 1) Th drivativ of social wlfar with rspct to undr libralization is th sam as that undr vrtical sparation. Any comparisons ofwlfar undr vrtical sparation and libralization ar indpndnt of 8 (W s (8):( W L (8) ifandonlyif K:( 3(v+bk-w)2). 2B 2) If v + b k - w > 0, social wlfar dcrass fastr as incrass undr vrtical intgration than undr vrtical sparation and libralization. In othr words, awi(8) < aw s ( 8) = aw L ( 8) < O. (If v + b k - w < 0 a8 a a ' th rvrs ffcts occur.) Lmma 2 provids us with som important simpl ruls to choos among markt structurs. Sinc W S (8) and W L (8) dcras at th sam rat as incrass, if WS(ft) > WL(ft), libralization can b xcludd from th rgulator's policy options, and if WS(ft) < WL(ft), sparation can b xcludd. Furthr, whn v + b k - w > 0, if WI(ft) < W S(ft) (or WI(ft) < WL(ft)), th rgulator would choos ithr vrtical sparation or libralization rathr than vrtical intgration bcaus W1(8) dcrass fastr than W S ( ) and W L ( ) as Incrass. 17

20 4.2 Comparison of M's Profit undr Diffrnt Markt Structurs Lt us now considr 1\1's profits undr ach markt structur. With linar invrs dmand, from (9), total output in stat undr vrtical intgration is: Ql(8) = (l/b)[a -w + (1 - a)ft - (2 - a)8]. Thn Ms profits conditional on 8 undr vrtical intgration is as follows: { A - w + (1 - x) - (2 - a) } n;\8) = J B - d8. B (16) Similarly, Ms profit functions undr vrtical sparation and libralization ar as follows: s J {A -v-bk+(1-a)ft-(2 -a)8 } L TC()= d =TI(). B B (17) Lmma 3 1) M s profit undr vrtical sparation is th sam as that undr libralization (n s ) = n L )). 2) If v + b k - w > 0, Ms profit undr vrtically intgratd monopoly is highr than undr vrtical sparation and libralization for all S (rc1(s»max {TI s (8), TI L (8)} \j S E [ft, 0]). (If v + b k - w < 0, th rvrs ffcts occur.) 3) If v + b k - w> 0, Ms profit undr vrtically intgratd monopoly dcrass fastr as 8 incrass than undr vrtical sparation or libralization ( an;!(8) < an;s(8) v + b k - w < 0, th rvrs ffcts occur.) as a as an;l ( 8». (If Th first rsult in Lmma 3 follows from th fact that pric and output chang in offstting ways with linar dmand. From (11) and (15), P L () = p s) + v + b k - w (th sam is also tru 18

21 for accss prics a L () and a S(8)). With linar dmand, th diffrnc in th output lvls is indpndnt of 8: Q L ( 8) - Q S ( 8) = - (v + b k - w ) / B. If v + b k - ltj > 0, th optimal final good pric (quantity) undr libralization is highr (lowr) than that undr vrtical sparation. Howvr th intgrand of Ms xpctd profit function (12) is QL ( 8) + (v + b k - w ) / B and quals th intgrand of M s xpctd profit function undr vrtical sparation QS ( ). Thrfor M s profit is th sam undr both markt structurs. Th rgulator xactly offsts M s highr arnings in th downstram markt by adjusting th nt transfr. On avrag, if v + b k - w > 0, vrtical intgration is th most profitabl markt structur for th monopolist, but its profit is mor snsitiv to upstram cost than with downstram production by th fring. Th rgulator can xploit this fatur in a particular way, which w dvlop in th nxt sction. 5. A Hybrid Rgim In th prvious sction, assuming linar dmand in th downstram markt, w analyzd accss pric, profit, and social wlfar for ach rgulatory policy whr th rgulator has x ant chosn a markt structur, irrspctiv ofth monopolist's cost rport. Would it b socially bnficial to allow comptitors to hav accss to th intgratd firm's ntwork for all cost ralizations? As Vickrs (1995) points out, thr ar two undrlying conomic ffcts: th information asymmtry, which allows th monopolist to xtract rnts, and imprfct comptition, which lads to xcss ntry (with duplication offixd costs). Can th rgulator gain significantly by conditioning th markt structur on th ralization ofth cost charactristic ofth firm? Considr a hybrid rgim in which th rgulator can allow both vrtical structur and th contract 19

22 paymnts to vary with th cost rport. From Lmma 1, w know that a hybrid rgim can not dominat intgration or libralization sinc on ofths rgims dominats th othr for all cost rports. Lmma 2 indicats that w can furthr rduc th st ofpolicy options in hybrid rgims to ons with vrtical intgration and vrtical sparation. To simplify our analysis, w confin ourslvs to a subst ofth no-pooling rgion in paramtr spac with linar dmand: Assumption 4 v+bk-w>o. Assumption 4 guarants that, as incrass, social wlfar dcrass fastr undr vrtical intgration than vrtical sparation (Lmma 2) and that th monopolist's profit undr vrtical intgration is highr than undr vrtical sparation but dcrass fastr (Lmma 3). 5.1 Hybrid Rgim with Vrtically Intgratd Monopoly and Vrtical Sparation Suppos that, whn th monopolist's upstram cost is at its lowr bound, th ranking of social wlfar is: WI(ft) > W,S(ft). Sinc WI() dcrass fastr than W S (8) as 8 incrass, th ranking can switch so that WI(8) < W S (8). S Figur 1 for an illustration. In this cas, th qustion ariss whthr th rgulator can xploit this and blnd th two markt structurs togthr dpnding on th cost rport. Suppos that th rgulator offrs M a mnu that changs th allowd markt structur if M's rportd cost is highr than a critical valu 8* E [ft, 8]. In particular, th rgulator adopts monopoly if E [ft, 8*], and vrtical sparation othrwis. Th ida is that th rgulator can us th choic ofmarkt structurs as an additional tool to limit th monopolist's rnt xtraction and incras xpctd social wlfar. Lt 20

23 E W H dnot xpctd social wlfar undr th hybrid rgim. For M s rportd valu ofcost 8 E [fr, 8 * ], M arns th profit ofth vrtically intgratd monopoly, TC 1 ( 8 ). For (3 E (8 *, 8"], sinc only fring firms ar allowd in th downstram markt, M s profit will b TC S ( 8) and th individual rationality condition binds with n S (8") =a.19 W must modify th incntiv compatibility (I) and individual rationality constraints (IR) to accommodat th structural chang at 8 * : IC* or s an (8) = _ QS( 8) for 8 E (8*, a] a8 8* whr n J (8) = f QI(8) d8 + n S (8*) for 8 B n S (8) = f QS(8) d8 for 8 E (8*, a] for 8 E UL 8*] and 8 E [8*, a]. Each incntiv compatibility condition is continuous and diffrntiabl on ach connctd intrval of 8. ffi* Th condition n 1 (8*) = rc s (8*) insurs that thr is no incntiv in th nighborhood of 8* to misrport costs to gain from th switch in markt structur. Figur 2 illustrats profit as a function of 8 undr such a policy. It is worth noting that, undr th hybrid rgim, M s 19Ifw considr an industry whr fring firms do not nd units ofan input providd by a monopolist for thir production, th binding individual rationality condition should b rc 1 (8*) =o. 21

24 incntiv to xaggrat its cost is dampnd bcaus M has to shut down its downstram sctor for (3 E (8*,8] Th Rgulator's Problm With th modifid individual rationality condition, lt W I (,*) dnot wlfar undr vrtically intgratd monopoly for E [ft, * ]. Sinc W S() rmains unchangd for 8 E (*, 8], th rgulator's objctiv function bcoms: iv{;c:x 6* EW H C8*) = J W I C8, 8*)jC8)d8 + J W S (8)jC8)d8 ft 6* (18) (s th appndix for dtails). Sinc th rgulator's problm is to choos a critical valu * optimally so that xpctd social wlfar is maximizd, maximizing xpctd wlfar with rspct to * yilds th first ordr condition: Proposition 4 Suppos that th following condition holds: W I (ft) > W S (ft). Thn th optimal markt structur for th maximization ofxpctd wlfar uss a hybrid rgim ofvrtical intgration and [2A -v-w-bk+2(i-a)8](v-w+bk)-2b 2 k 2 - sparation if < * = - < 8. In othr - 2(2-a)(v-w+bk) cass, th optimal policy is ithr vrtical sparation or intgratd monopoly for all cost rports. 22

25 In contrast with th cass whr markt structurs ar takn as givn, Proposition 4 shows how using markt structur as a contract instrumnt can affct th bhavior ofth rgulatd firm in th conomy. Prviously, th optimal accss pricing rul limitd th rgulator's rol to M s vrtical conduct. Undr th hybrid rgim, howvr, th rgulator can us th thrat ofntry by fring firms and xclusion ofth monopoly from th downstram markt and thrby nhanc xpctd wlfar Exampl To illustrat th magnitud ofth gains from th hybrid policy, w now prsnt som simulation rsults. Suppos that th invrs dmand function is P = 58 - Q and is uniformly distributd on th intrval [1, 15]. For th paramtr valus, x =0.5, v =5, W = 10, K =400 (k =20), WI(ft) > WS(ft) and vrtical sparation dominats libralization. Optimization ofth hybrid rgim yilds an intrior solution with 8* = Th rgulator strictly dtrs any ntry by th fring if ~ *, and it xcluds th monopolist from th drgulatd sctor and allows th fring to tak ovr th ntir downstram markt othrwis. Expctd wlfar undr vrtically intgratd monopoly and vrtical sparation ar and 249.5, rspctivly. Howvr, xpctd wlfar undr th hybrid rgim is Th following tabls indicat how th valu ofxpctd wlfar varis as ach paramtr changs in ach rgulatory rgim for th givn xampl. (1) Expctd wlfar with diffrnt wights on Ms profit (x) (Tabl 1) Th largr x is, th mor M s profit counts in xpctd social wlfar and th smallr is th 23

26 wlfar loss from th transfr" Hnc, as M s rnts bcom lss objctionabl, fwr distortions will b imposd. Expctd wlfar undr ach rgulatory policy incrass as a incrass, partly bcaus th monopoly rnts count mor in wlfar. As w incras a, th valu of {1 * also incrass, favoring th monopolist. Howvr, th absolut xpctd wlfar gain ofth hybrid policy ovr th bst singl markt structur policy is monotonically dcrasing with rspct to a. At a nar zro, limiting rnt xtraction-is highly valud whil, at a = 1, fficincy is highly valud. (2) Expctd wlfar with diffrnt costs at th downstram lvl (v and w) (Tabl 2 and 3) As a fring firm's marginal cost ( v) incrass, xpctd wlfar undr vrtical sparation and th hybrid rgim dcrass and policy switching occurs at a largr valu of *. Thrfor, ifth fring firms ar lss fficint rlativ to th monopolist, vrtically intgratd monopoly is mor likly to b adoptd for th optimal markt structur ofth industry. Th sam lin ofrasoning applis to dcrass in M s marginal cost (w) at th downstram lvl. (3) Expctd wlfar with diffrnt fixd cost (K) (Tabl 4) Sinc w assum a fixd cost for all ntrants in th downstram markt, it is costly to opn sgmnts to comptitors in trms ofduplication ofth fixd costs. As K incrass, xpctd wlfar undr ach rgulatory policy dcrass. Howvr, th optimal switching point (* ) will dtrmind by whthr M s pric-cost margin ffct dominats th duplication ofth fixd cost ffct. This xampl is a cas whr M s pric-cost margin ffct dominats th duplication of th fixd cost ffct. 24

27 5.2 How th Hybrid Rgim Compars with Libralization W saw arlir that libralization with contractibl q 1 is dominatd by ithr vrtical intgration or vrtical sparation (Proposition 1) and that libralization with noncontractibl q1 is dominatd by libralization with contractibl qi (Lmma 1). Hnc, ifvrtical sparation dominats libralization, undr som conditions, th hybrid rgim dominats both vrtical intgration and vrtical sparation. Thus, it is th optimal policy among all thos w hav studid. 6. Conclusion Optimal rgulation undr asymmtric information ofa vrtically intgratd monopolist can includ rgulation of vrtical structur as wll as vrtical conduct. In a simpl combination of B-M rgulation and Coumot oligopoly, ifth rgulator drgulats th downstram markt, th optimal rgulatd accss pric and final good pric ar highr than whn th rgulator adopts vrtical sparation. A wlfar comparison oflibralization and vrtical sparation dpnds on whthr th rduction in th duplication offixd costs dominats th gratr pric-cost margin. Sinc th wlfar comparison oflibralization and vrtical sparation is indpndnt ofth monopolist's upstram marginal cost, th rgulator's task rgarding vrtical structur is to choos ithr sol or multipl sourcs ofproduction in th drgulatd markt. Th hybrid rgim considrs both th information asymmtry and imprfct comptition in th downstram markt. Th rgulator can incras xpctd social wlfar as long as th rgulator can shut down ithr th monopolist or (potntial) fring firms, or lt both produc final goods. In contrast with th cass with fixd markt structurs, th hybrid xampl whr ithr th monopolist or th fring srv th ntir downstram markt shows how incntiv issus can 25

28 affct th rgulatd firm's comptitiv nvironmnt. W hav shown that a low-cost monopolist is rwardd with monopoly downstram markt and a high cost monopolist is xcludd from or facs comptition in th downstram markt, vn though it is th monopolist's upstram cost that affcts this choic undr th hybrid rgim. Our analysis prsums that fr ntry ndognously dtrmins th numbr offirms in th downstram markt. W also assum that th industry producs a singl homognous product. In practic, howvr, ach firm may fac a capacity constraint and hav a markt powr for its own product. Ifw assum that th monopolist has a fw potntial comptitors oflarg-scal, thn comptitors would also arn oligopoly profits undr quantity comptition. Thn th duplication offixd costs might not b crucial in th wlfar comparison ofintgratd monopoly and vrtical sparation. Endognous incntiv mchanisms for othr nvironmnts rmain an important topic for futur rsarch. 26

29 Tabl 1: Expctd wlfar as th wight on M s profit ( a ) changs: v=5, w=10, K=400(k=20), 8E[1,15], and P=58-0. x 8* EW H EW I EW s Wlfar gain (%)* *Th last column is calculatd by [E W H - max {E W I, E W s} ] / max {E WI, E W S }. Tabl 2: Expctd wlfar as a fring firm's cost (v) changs: a=o.5, w=10, K=400(k=20), 8E[1,15], and P= v 8* EW H EW I EW s Wlfar gain (%) For this xampl, if v> 6, social wlfar undr libralization is gratr than undr vrtical sparation. 27

30 Tabl 3: Expctd wlfar as M s cost at th downstram lvl (ly) changs: a=0.5, v=5, K=400(k=20), 8E[I,I5], and P= ly 8* EW H EW I EW s Wlfar gain (0/0) *For this xampl, if w < 9, social wlfar undr libralization is gratr than undr vrtical sparation. Tabl 4: Expctd wlfar as th fixd cost (K) changs: a =0.5, v =5, w = 10, E [1, 15], and P =58-0. k 8* EW H EW I EW s Wlfar gain (%)

31 w) ws() o 1.---: _ Figur 1: 29

32 11: (8), I I I I I 1 I I i~~ I ~~ : ~~ I ~~ I ~~ I...!..~ i ~~ I ~~ I..~ \.. I I I I I! L----: ""--- ~_ o 8* Figur 2: Ms incntiv compatibility condition undr th hybrid rgim: 8* 11/(8)=f QI(8) d8+n s (8*) for 8 E [ft,8*]. 8 30

33 Appndix A. Drivation of Incntiv Compatibility Condition maxiitllz Whn q 1 is contractibl, th monopolist undr libralization chooss its accss f to 1tc ( 8) = Max (a - 8) QC ( a) + [ P (Q C ( a)) - w - a ]q1(a) + T(a) - K. a By using th nvlop thorm, Ms incntiv compatibility constraint is: With th binding individual rationality condition n C(8) = 0, intgration ofth monopolist's incntiv compatibility constraint ovr [8, 8] yilds its profit function: 1t C (8) = f QC(8) d8. Whn q1 is noncontractibl, th monopolist producs th quilibrium choic in th downstram Coumot gam: q1 = [ P(Q L) w ]/ - pi(q L). From (5), sinc a = P ( QL) - V - q;( QL) k, w can rwrit th monopolist's profit as follows: n L (8) = Max a (a - 8) QL(a) + TL(a) - K Thn, th nvlop thorm yilds Ms incntiv compatibility condition as follows: Hnc, with th binding individual rationality condition TIL () =0, intgration ofth monopolist's incntiv compatibility condition ovr [8,8] yilds th monopolist's profit function: TI L ( ) = fo { QL ( 8) + v + tp( QL ( 8 )) k - w } d. _pl(ql(8)) 31

34 B. Proofs Proof of proposition 1 rspct to ql Th problm of optimizing xpctd social wlfar undr contractibl libralization with and Qcis: - ~c; {{ U( Q C ( 8)) - (8 + w)q C ( 8) + [ v + qj( Q C ( 8 )) k - w ][q1 ( a) - Q C ( 8) ] - K ~ (q1) - (1 - x) (8 - ft) QC ( 8) } ~ d8 8-ft s.t. I if ql > 0 q1 E [ 0, Q] and ~ (q 1 ) = 0 { if ql = o. Diffrntiating EW c with rspct to ql yilds: i) If v+q;(qc)k-w<o, thn aewc/aql<o andthus ql =0 is optimal for all 8 (vrtical sparation). ii) If v + q;( Qc) k - w > 0, thn ae W C / aq1 > O. Ifth monopolist producs a positiv downstram output, th monopolist spnds K to produc downstram. Hnc, q1 =0 IS optimal if E [[ v + qj( Q C ( 8)) k - w ] ] Q C ( 8) - K < 0 whil q1 = Q C is optimal if E [[ v + qj(q C(8)) k - w]] QC(8) - K> 0 (vrtical intgration). Whn vrtical sparation is optimal, xpctd social wlfar quals: EWS = f {U (Q S ( 8)) - [ 8 + v + qj( Q S ( 8)) k ] Q S ( 8 ) ft _ (1 - a)(8 - ft) Q S(8) } { ~ ft } d8. Optimizing E W S with rspct to Q S(8) yilds th optimal accss f and final good pric: a S(8) = 8 - ~ qj( Qs) k E + (1 - a)(8-8) and 2-32

35 Similarly, whn vrtical intgration is optimal, xpctd social wlfar quals: EW I =!{U(QI(8)) - (8 +w)qi(8) -K - (1 - a)(8 - ft)qi(8) } { ~ ft } d8 and optimizing E W I with rspct to QI (a) yilds: pi(a) = +w + (1 - a)(8 - ft). Lmma 1 1) Comparing WI(a) and W L (a), wl (a) has th additional trms: [ v + <p( Q L) k - w ] ( q1 - Q L) and - (1 - a) J v + <p( Q L) k - w d 8. _pl(ql) Thus, tak th optimal Q L ( 8) undr noncontractibl libralization and substitut it for Q I ( a) in WI (a). If v + qj( Q(8 ) ) k - w > 0 for all B, w 1 ( QL( )) > WL( QL( a)) bcaus 8" L [ V + <p( Q L ( 8 )) k - w ][q (a) - Q L ( a ) ] < 0 and - (1 - a)j v + <p(q ( 8 )) k - w d 8 < 0 1 (} _pl(ql(8)) (aslongas a<1). Also WI(QL(a)) < W 1 (QI(a)) sinc QL(a) is fasibl, butnot optimal, undr vrtical intgration. Thus, W I ( ) > W L ( a) if v + qj( Q( 8 ) ) k - w > 0 for all 8. Not that, vnthough v<w, W I (a»w L (8) as long as v+qj(q(8))k-l'v>o for all a. If v + tp( Q())k - w < 0, thn W 1 ( )< WL ( 8 ) by similar rasoning. 2) Contractibl libralization allows choic of ql by th rgulator who can sustain th outcom undr noncontractibl libralization. Hnc, wlfar must b at last as grat undr contractibl libralization. 33

36 Proof of Proposition 2. 1) From (10) and (11), optimal accss and final good prics undr vrtical sparation ar a S() = + (1 - x:) ( - ft) and P S() = + v + qj( Q S()) k + (1 - x:) ( - ft), rspctivly. From (14) and (15), optimal accss and final good prics undr noncontractibl libralization ar a L (8) = + v + qj( QL ()) k - w + (1 - x:) (8 - ft) and p L () = v + 2 qj( Q L (8)) k - w + (1 - x:) ( - ft), rspctivly. Hnc optimally rgulatd accss and final good prics ar highr or lowr undr libralization by v + qj( Q(8 )) k - w. 2) Compard to th cas whr v =w, th rgulator incrass both th accss pric and th final good pric by th diffrnc in marginal costs (v - w ) undr libralization. Lt CF ( =a L ( 8) + v) and M ( =8 + w) dnot th ovrall marginal costs ofth fring firms and th monopolist, rspctivly. Thn, CF will ris or fall by twic th chang in v ( acf / av = 2) du to an incras in accss pric, whil M will chang xactly by a chang in w (JC1\tf/Jw=I). From (15), itis J(pL--w)/Jv>O and a(pl-8-w)/jw<0 with linar dmand (E =0). Th sam is tru for a L (8). If v>w, th monopolist's pric-cost margin will b vn highr than othrwis. Sinc th numbr offring firms in th downstram markt undr libralization is dtrmind by n L - 1 = (Q L - q1 ) / q2 and th monopolist producs th downstram output by q1 = [p L ( ) w ] / - P L ( 8 ), th highr v IS, th highr is th final good pric. And, th highr th final good pric is, th gratr is q1 and th smallr is th numbr ofth fring firms. 3) If v+qj(q)k-w>o, QS(8»QL(8) bcaus p L (8»p s (8). Th numbr of fring firms in th downstram markt undr vrtical sparation is dtrmind by n S = Q S / q2. Thn, sinc QS>QL>QL_ qi and qj(q) is constant, Q2 L =q2 S =klqj(q) and nl<n S. 34

37 Proof of Proposition 3 1) With a concav invrs dmand curv (E < 0), if v> w in quation (14), th mor fficint monopolist is favord by th rgulator by mor than actual cost diffrnc bcaus (v - w)( 1 - se) > (v - w). Howvr, th mor fficint monopolist gains lss informational rnt than with linar invrs dmand bcaus (v - w) E < O. If v < w, th rvrs ffct _pl(ql)ql occurs. 2) With a convx invrs dmand curv (E> 0), ifv > w in quation (14), th lss fficint fring firms ar favord by th rgulator bcaus (v - w)( 1 - se) < (v - w) sinc 1 - se> O. Howvr, th mor fficint monopolist gains mor informational rnt than with linar invrs dmand bcaus (v - w) E > O. If v < w, th rvrs ffct occurs. _pl(ql)ql Proof oflmma 2 1) Sinc U(Q) =AQ - (B/2)Q2 and QS ( 8) = ( 1/B) [A - v - bk + (1 - x)ft - (2 - x) 8], social wlfar undr vrtical sparation is W S (8) = U(Q s(8)) - (8 + v + b k)q s(8) - (1 - ct) f Qs(8) d8 =(1/2B)[A -v-bk+(i-x)ft-(2 -x)8][a -v-bk-(i-x)ft-a8] - (1 - ct) f QS(8) d8. Thn: aws ( 8)/a = - ( 1/B) [ xa - x v - x bk - 2 (1 - x)2 ft + (2 - x) (1-2 x )]. Similarly, sinc QL (8) = ( 1/B) [A - 2 v - 2 b k + w + (1 - a)ft - (2 - x) ], social wlfar undr libralization downstram is: 35

38 W L () = U(QL (8)) - (8 + v + bk) QL (8) + (v + b k - tv) (P - w - )1B - K -(I-a) J{QL(8)+(v-w+bk)/B} d8. =(1/2B) [A - 2v +w - 2bk + (1 - o:)ft - (2-0:)0]- [~-w-(i-o:)ft-o:o]-k + ( 1IB) (v + b k - w) [2 v + 2 b k - 2 w + (1-0:) (8 - fl.)] -(I-a) J{QL(8) +(v+bk-w)/b} d8. Thn, it is straightforward to show: aws(o)lao = - (lib) [o:(a - v - bk) - 2(1-0:)2 ft + (2-0:)(1-20:)0] Not that QS ( 0) = QL ( 0) + (v + b k - w) lb. Thn, w find: W S (8) - WL(O) = -(3/2B)(v +bk-w)2 +K. Thrfor, W S(8) ~ W L (8) dos not dpnd on th monopolist's upstram marginal cost,. Hnc ws ( 8) ~ W L ( 8) if and only if 3 (v + b k - w) 2 K. 2B 2) From (9), Q 1(0) =( 1IB) [A - w + (1-0:)ft - (2-0:) ]. Thn: W I (8) = U(Q 1(8)) - (8 + w)q 1(8) - K - (I - a) J Q1(8) d8 = (1 /2B) [A - w + (1 - o:)ft - (2-0:) 0] [A - w - (1 - o:)ft - 0: 0] - K () -f Q/(8) d8, and aw I ( )Ia = - ( 1/B) [ x (A - w) - 2 (1-0:) 2ft + (2 - x) (1 ~ 2 x )]. If v+bk-w>o, aw I (8)<aW s (8) = aw L (8)<o. a ao ao 36

39 Proof of Lmma 3 1) To prov that TIs(8) = TIL (8), it is sufficint to show that QL ( 8) + (v + b k - w ) / B =QS ( 8 ). From (13) and (19), With linar dmand, sinc P L (8) = + 2 v + 2 b k - w + (1 - x) ( - ft), QL () + (v - w + bk)/b = ( 1/B) [A - v - bk + (1 - x)ft - (2 - x) ] = Qs(8). 2) Sinc TI S (8)=TI L (8), it is sufficint to show that Q/(8»Qs(8) if v+bk-w>o.from(9)and(11), ps(8)_pi(8)=v+bk-w. Hnc QI(8»Qs(8) if 1 S L - V + b k - w > O. Thrfor TI (8) > n (8) = 1t (8) for all 8 E [ft, 8). 3) From (16) and (17), an l (8)/a8=(I/B)[A -w+(1-x)ft-(2-x)8] and ans ( 8) / a8 = ( 1/B) [A - v - bk + (1 - x) ft - (2 - x) 8 ]. If v + b k - w > 0, ani(8) / a8 < a TIs(8) / a8. Sinc TIs(8) = TIL (8), atil(8) / a8 < a TIL (8) / a8 also holds. Proof of Proposition 4 For E [ft, 8*]: whr W / (,8*) = U[Q/(8)] - (8 + w ) Q/(8) - K '" _ - (1 - x) f QI() d - (1 - x)1t s (*) rcs(*) = f Qs() d. Similarly, for E (8*, 8] : Ws() = U(Q s)) - ( + v + bk) Q s) - (1 - x) f Q S) d. Pointwis optimization with rspct to Q yilds Q 1(8) = ( 1/B) [A - w + (1 - x) ft - (2 - x) 8] undr vrtically intgratd monopoly and 37

40 Qs(8) = (lib) [A - v - bk + (1 - a)ft - (2 - a)8] undr vrtical sparation. Not that QI on th intrval 8 E [ft, 8*] is th sam as th on drivd from (9). Th rgulator offsts a chang in M s profit undr vrtically intgratd monopoly by adjusting th nt transfr. Thn social wlfar undr th hybrid rgim is as follows: i) for E [ft, 8*], WI(8,8*) = (1 /2B) [A - w + (1 - a)ft - (2 - a)8] [A - lv - (1 - a)ft - a ] - K * - (1 - a) I{(1I!)[A - w + (1 - a)ft - (2 - a)8] } d8 8 -(1-a) I {(l/b)[a -v-bk+(1-a)ft-(2 -a)8]} d8 * ii) for E (8*,8], W S (8) =(1/2B) [A - v - bk + (1 - a)ft - (2 - a)8] [A - v - bk - (1 - a)ft - a8] -(1 - a) I{(1/B)[A - v - bk + (1 - a)ft - (2 - a)8] } d8. W thn obtain: I " awl(8,8*) df(8) + W I(8*)j(8) - WS(8*)j(8) aew H a8* = ft a8* [2A - v - b k - w + 2 (1 - a)ft - 2 (2 - a)* ] (v + b k - w) - 2 b 2 k 2 = 2B(8 - fr) Thrfor xpctd social wlfar undr th hybrid rgim is maximizd whn th rgulator offrs M a mnu that contains th possibility ofshutting down M s downstram sctor if M s rportd cost is highr than a critical valu: 8 * = [2A - v - b k - w + 2 (1 - a)ft](v + b k - w) - 2 b 2 k 2 2(2-a)(v+bk-w) Furthr th assumption of v + b k - w > 0 guarants th scond ordr condition ofth a 2 EW maximization problm: H = - (2 - a) (v + b k - w) < 0, a8*2 38