Market Coverage, Price and National Welfare Under International Exhaustion of Patents

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1 Trad and vlopmnt Rviw Vol. 6, Issu -, 03, Markt Covrag, Pric and National Wlfar Undr Intrnational Exhaustion of Patnts Rajat Achara This papr offrs a complt mnu of pric and wlfar ranking of markt-basd discrimination and paralll imports of drugs (undr intrnational xhaustion of patnt. It has bn shown that th uniform pric undr paralll imports is unambiguousl lowr than th discriminator prics whn th poor-countr markt is full covrd undr both marktbasd discrimination and paralll imports. This is in sharp contrast to th convntional thortical wisdom, and follows from th fact that undr paralll imports a lowr qualit of drug is innovatd b th patnt-holdr MNC. Thus, paralll imports can, of cours, incras markt accss for th poor, as is oftn argud in favour of implmnting intrnational xhaustion of patnts b th dvloping countris. Convntional wlfar rsults (as in Richardson (00 for xampl, howvr, hold in this ndognous innovation cas, xcpt for that markt-basd pric discrimination ma rais global wlfar vn if no markts ar droppd as a rsult of intrnational xhaustion of patnt rights (or paralll imports. JE Classification: I,, O33, O34 Kwords: Patnts; Paralll Imports; Innovation; Qualit of drug; Pric discrimination.. Introduction Th gains from allowing paralll imports of on-patnt drugs and mdicins that forc th patnt holdr pharmacutical multinational corporations (MNCs to charg partmnt of Economics, Jadavpur Univrsit, Kolkata 70003, India. rajat.achara@gmail.com I thank an anonmous rfr for xtrml hlpful commnts. Thanks ar also du to Maria.C. Garcia-Alonso for hr obsrvations and commnts on som of th issus addrssd in this papr. Th usual disclaimr applis, howvr. Jadavpur Univrsit.

2 Achara / Pric Undr Intrnational Exhaustion of Patnts uniform pric in all markts hav bn dbatd ovr th past fw ars b rsarchrs as wll as polic makrs. Th gnral consnsus in this rgard bing that th richr countris primaril gain from such pric convrgnc bcaus othrwis th MNCs would charg highr prics for th patntd drugs. This provids incntiv for th richr countris to allow paralll imports from th poor countris whr th sam drugs ar sold at lowr prics. Thus, as Richardson (00 dmonstrats, whn th poor countris ar unabl to rstrict paralll xports th uniqu Nash quilibrium will b uniform pricing : Th richr countris undo pric discrimination. Of cours, th intrsts of th rich countris ma b altogthr diffrnt if th ar xportrs of drugs and mdicins. On th othr hand, poorr countris unambiguousl los from paralll imports allowd b th richr countris, and thus it maks sns for thm to prohibit paralll xports. That is, whn th poorr countris can rstrict paralll xports, markt-basd (or cross-countr discrimination is th Nash quilibrium pricing [Richardson (00]. Of lat, Valtti (006 adds a nw dimnsion to th dbat ovr a global rul on xhaustion of patnt rights b stablishing an advrs long run ffct of paralll imports. As th profit of th MNC is lowr undr uniform pricing, paralll imports or intrnational xhaustion of patnt rights x ant lowrs th lvl of innovation of a nw drug. Th corrsponding loss of utilit all around thus is to b wighd against th utilit gains for thos who pa lowr prics undr paralll imports. A similar rsult is stablishd b i and Maskus (006, in th contxt cost-rducing innovation dcision of a MNC: distortions associatd with paralll imports rduc its innovation lvl. Th show that rduction in costrducing R& invstmnt dpnds on transport costs among othr things. For dvloping and dvlopd countris alik, th mor important issu rlatd to paralll imports of pharmacutical drugs and othr halth innovations is th markt accss for thir poor patints. It is primaril bcaus of this markt accss concrn that th dvlopd countris ar kn on allowing paralll imports, dspit in man cass thir own pharmacutical firms mrging losrs as a consqunc. But such a polic of paralll imports whil nsurs markt accss for poor in richr countris is Jlovac and Bordo (005 argu that thr ma not still b complt pric convrgnc sinc th consumrs in th importing countris ma not valu th paralll-importd drugs quall as th valu th drugs marktd b th MNCs. National intrsts rgarding paralll imports diffr vn among th dvlopd or richr countris.. Whras Japan allows intrnational xhaustion, th EU allows rgional xhaustion of patntd goods. Th countris lik USA allow onl national xhaustion of patnts and coprights, and vn incorporat such clauss (th so-calld TRIPS-Plus faturs in bilatral trad ngotiations to protct th intrsts of thir MNC-xportrs [Maskus (000]. Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 30

3 Achara / Pric Undr Intrnational Exhaustion of Patnts apprhndd to dn markt accss to poor in th poorr countris b raising pric thr. Thus, paralll imports sm to bnfit poor patints in th richr countris at th cost of poor patints in th poorr countris. This apprhnsion rgarding trad off btwn markt accss of poor patints in richr and poorr countris follows from th popular blif that arbitrag that paralll imports implis ssntiall causs discriminator prics of an innovatd drug to convrg to a lvl somwhr in btwn. But, whil in man cass such ranking of discriminator and uniform prics ma sm obvious, that it is not a slf-nforcing proposition has rcntl bn dmonstratd b Mukhrj and Pnnings (0 in th contxt of innovation undr licnsing and dcntralizd and cntralizd unions. In th prsnt contxt of innovation of a pharmacutical drug and cross-countr pric discrimination, th advrs innovation ffct of paralll imports shown b Valltti (006 suggsts a similar possibilit. If, for xampl, markts ar full covrd undr paralll imports, and th innovatd qualit is lowr than undr discrimination (as shown b Valltti in cas of partial markt covrag, th uniform pric should b lowrd to induc th burs to participat in th markt. This is in sharp contrast to th convntional thortical wisdom that th uniform pric (rsulting from paralll imports is highr than at last th lowst discriminator pric. Thus, to th xtnt to which paralll imports (or intrnational xhaustion of patnts lowr prics of drugs all around, it can in fact incras markt accss for th poor vrwhr. This is th main focus of this papr. In othr words, in a two-countr world with htrognous st of burs distributd uniforml ovr continuum of incoms and innovation of a qualit of a drug b an MNC, which closl rsmbls th analtical framwork of Valltti (006, th papr xamins whthr thr ar quilibria at which pric of th drug dclins vrwhr as a consqunc of paralll imports bing allowd b th countris. Accordingl, th analsis shds som light on whthr gratr markt accss to an innovatd drug can b a plausibl xplanation of wh vn som of th low-incom dvloping countris lik India allow paralll trad or intrnational xhaustion of patnts, which might sm lss obvious othrwis. Th papr furthr invstigats into implications of this rsult for national wlfar lvls. Sinc th innovatd lowr qualit of th drug rducs national wlfar, dos th gain from lowr pric (and consqunt markt accss is sufficintl high to provid a normativ (or wlfar xplanation for wh most of th dvloping countris implmnt intrnational xhaustion of patnts or allow paralll imports? This national wlfar analsis again contrasts with Valtti (006 who rstricts himslf in driving th condition for global wlfar improvmnt aftr allowing instad of drawing implications of such undr-invstmnt in innovation for national Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 3

4 Achara / Pric Undr Intrnational Exhaustion of Patnts wlfar lvls. At th sam tim, this wlfar dimnsion of our analsis can b sn as xamining th robustnss of Richardson s (00 rsult whn th innovation dcision of th MNC is ndognous. This is thorticall intrsting bcaus th advrs innovation ffct of should lowr th incntivs of th rich countris to undo MB. In this contxt, closl following Richardson (00, w first considr th cas whr th low-pric countr (undr MB cannot rstrict paralll xports, and thn th cas whr it can do so b imposing a paralll-xport tax. In th lattr cas, th issu undr considration is whthr th countr chooss a prohibitiv or a non-prohibitiv xport tax rat. For th abov-mntiond purposs, this papr first xtnds th advrs innovation ffct of paralll imports stablishd b Valltti (006 to all possibl quilibrium configurations including full markt covrag quilibrium. In contrast to Valltti s assumption of all markts bing onl partiall covrd undr both discrimination and uniform pricing, this papr spcifis all quilibrium markt-covrag combinations, offrs a complt mnu of prics and innovation lvls undr markt-basd discrimination (hncforth, MB and paralll imports (hncforth,, and r-stats th advrs innovation rsult. This is don for two rasons. First, as Wauth (996 and Achara (998 argu, th xtnt of markt covrag should b an quilibrium outcom of th profit-maximizing bhaviour of firm(s rathr than an x ant rstriction. This also contrasts with Malug and Schwartz (994 who considrd onl th possibilit of whthr all markts ar bing srvd dpnding on th xtnt of variations in th countr-spcific maximum willingnss-to-pa, but not whthr ach countr markt is srvd full or partiall. But, th xtnt of intra-countr dmand disprsion (which in this papr is rlatd to th intra-countr incom variations dtrmins whthr it is profitabl for th MNC to srv all consumrs in a particular countr or not. Scond, sinc w conciv that lowr innovation lvl undr ma hav a favourabl impact on markt accss for poor all around, it is ncssar to considr all possibl quilibrium markt covrag combinations to chck whthr th markt accss rsult is contingnt upon a particular choic of markt covrag b th MNC. Aftr spcifing all quilibrium markt-covrag combinations, th papr thn stablishs its main rsult: for a sub-st of ths quilibria th uniform pric is actuall lowr than th lowst pric chargd to poor patints in th poorst countr b a discriminator MNC. Th uniform pric undr is unambiguousl lowr than th discriminator prics whn th poor-countr markt is full covrd undr both MB and. This provids a thortical basis for th markt accss argumnt Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 3

5 Achara / Pric Undr Intrnational Exhaustion of Patnts mntiond abov. But whn th poor-countr markt is full covrd onl undr MB, th xtnt of intra-countr dmand disprsion dtrmins th ranking of th uniform and th discriminator prics. Th ssnc of ths rsults is that dos not ncssaril man a trad off btwn markt accss for poor patints in rich and poor countris. Th wlfar analsis, on th othr hand, rvals som intrsting polic dcisions b countris. First, dspit possibilitis of a lowr uniform pric, th poor countr unambiguousl loss from paralll imports. Thus, intrnational xhaustion of patnts allowd b th dvloping countris cannot prhaps b justifid in trms of national wlfar gains. Scond, th rich countr unambiguousl gains, so that, as in Richardson (00, it will undo MB b allowing paralll imports whn th poor countr cannot rstrict it. Third, global wlfar undr dos not ncssaril improv ovr that undr MB. It, in fact, dclins unambiguousl whn th markts ar partiall covrd. This mans, th rich countr cannot compnsat th poor countr to mak globall Parto suprior to MB. Undr full markt covrag, global wlfar incrass onl whn th markt sizs (or intra-countr dmand disprsions ar sufficintl small in th sns dfind latr. This rsult contrasts with Malug and Schwartz (994: Markt-basd pric discrimination ma rais global wlfar vn if no markts ar droppd as a rsult of paralll imports (and uniform pricing. This is bcaus th innovation lvl is lowr whn paralll imports ar allowd b th rich countris. Fourth, whn th poor countr can rstrict paralll xports of th drug to th rich countr b imposing an xport tax, w show that it dos hav an incntiv to prohibit such paralll xports for all paramtric configurations (and, hnc, for all combinations of th xtnt of markt covrag. Thus, th scond rsult of Richardson (00 holds as wll. Ths rsults ar stablishd in th simplst cas of countris having th sam and uniform intra-countr distribution pattrn but diffrnt incom or dmand disprsions. Initiall, w also confin ourslvs with onl two countris to focus on th national wlfar lvls in a tractabl mannr. atr w considr a simpl thrcountr xtnsion of th bnchmark cas to xmplif that a similar xtnsion and gnralization to man countris will not affct th main rsults qualitativl. Th rst of th papr is organizd as follows. In sction w considr th twocountr world conom with uniform incom distribution pattrns, spcif all rlvant quilibria and discuss thir proprtis. Sction 3 xamins th robustnss of Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 33

6 Achara / Pric Undr Intrnational Exhaustion of Patnts th undr-invstmnt rsult for non-uniform incom distribution. Finall w conclud in sction 4.. Unrstrictd Paralll Trading. Th analtical framwork Considr a two-countr world with a rich or high-incom countr ( and a poor or low-incom countr (. Ths countris diffr onl in rspct of th lvls of prsonal incom arnd b th richst consumrs, >, but hav th sam lvl of prsonal incom arnd b th poorst consumrs,. A consumr countr-j with incom [, j ], j,, allocats his incom ovr a composit consumption good and a drug. Th composit consumption good is takn as th numrair and its pric is normalizd to unit. Each consumr bus, if at all, onl on unit of th drug. Th potntial burs in countr-j ar distributd uniforml ovr th rlvant incom rang [, j ] with unit dnsit. Thus, ( j is th xtnt of (intra-countr dmand disprsion. Th drug, which can b of diffrnt qualit indxd b s > 0, is dvlopd b a pharmacutical MNC who has th xclusiv right of its production and sals in both ths countris. Innovation rquirs invstmnt of a sum of mon C in R& that incrass at an incrasing rat with th targt lvl of innovation: C ks ( whr, k is an positiv constant and rflcts th rat of chang in th marginal cost of innovation. Thr ar no production and distribution costs whatsovr. All consumrs vrwhr valu th innovatd qualit of th drug as it dirctl bnfits thm in trms of bttr ffctivnss of curing th disas for which it is usd. Thus it pas for th MNC to dvlop a highr qualit if th additional rvnu at last covrs th additional invstmnt in R&. But, though vr consumr valus a highr qualit drug mor than a lowr qualit drug, ths valuations varis across consumrs with diffrnt incoms. Mor prcisl, following th litratur on qualit choic w assum that richr burs attach an vn highr valuation to a bttr qualit drug rlativ to a lowr qualit drug than do th poorr burs. Assum that such a prfrnc rlationship is linar in incom and qualit 3 : 3 S Shakd and Sutton (98, for xampl. Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 34

7 Achara / Pric Undr Intrnational Exhaustion of Patnts V j (, s s [, j ], j, ( Two commnts ar warrantd at this point. First, this linar prfrnc structur, assumd purl for analtical convninc and tractabilit in trms of closd-form solutions, satisfis all th dsirabl proprtis in a slf-slction modl lik this, such as both th total and marginal utilit ar incrasing in tp (hr, incom, and that th displa th singl-crossing proprt 4. Scond, sinc xcpt for th sunk R& cost, thr ar no othr costs, qualit discrimination is not profitabl for th monopolist vn if it can ffctivl sgmnt th two countr-markts. Th MNC will thus dvlop onl on qualit for all markts. This rsult ma hold vn for positiv and incrasing (marginal production costs 5. Sinc ach bur bus onl on unit of th drug, th nt utilit quals, v j (, s, P j s - P j (3 whr P j is th pric of th drug chargd in countr-j. Not that th prics will diffr onl whn th MNC can practic markt-basd discrimination (hncforth, MB. But whn th countris allow paralll trad of th drug, arbitrag will caus th drug to b paralll xportd from th low-pric countr to th high-pric countr, so that th prics will b th sam vrwhr, P P. Of cours, for complt convrgnc of th countr-spcific prics of th sam qualit drug whn paralll xports and imports ar allowd or unrstrictd, w must assum that th consumrs in th high-pric countr quall valu th drug marktd b th MNC and th on that is paralll-importd. Assuming zro rsrvation utilit for all, consumrs in markt j will not bu th drug if th nt utilit is ngativ. Thus, for an innovatd qualit of th drug, v j (, s, P * 0 dfins th maximum willingnss-to-pa for th drug for consumr with incom such that th consumr bus th drug onl if P j s P * (4 4 For a dtaild discussion of ths proprtis and thir implications, th radrs ar rfrrd to Coopr ( This is in ssnc similar to what Achara (998, 005 had pointd out: whn a monopolist chooss what qualit (or qualitis to produc from a st of availabl qualitis indxd b q [ 0, q] and incurs zro or slowl rising marginal (production cost of qualit, thn it will choos th maximum qualit for all tps within a countr. Th onl choic lft thn is th pric to b chargd. Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 35

8 Achara / Pric Undr Intrnational Exhaustion of Patnts Givn this analtical framwork, w now procd to analz th altrnativ trad, intllctual proprt right and pricing rgims.. Th xtnt of markt covrag t P j and s dnot rspctivl th pric in countr-j markt and th innovatd qualit undr MB. Similarl, lt P and s rspctivl dnot th (uniform pric and th innovatd qualit whn th rich countr allows paralll imports (hncforth, and th poor countr cannot or dos not rstrict paralll xports. * t j b th marginal consumr in countr-j markt who drivs zro nt bnfit from th mnu (P j, s offrd b th MNC to th potntial burs thr. Thus b (4, * Pj j (5 s B th ti-braking rul, th marginal (and indiffrnt consumrs bu th drug. Sinc consumrs with highr incom driv gratr bnfits b th utilit spcification in (, so all ths burs bu th drug as for thm th individualrational constraint (4 is satisfid. But, if < * j, th burs with smallr incom * than j do not bu th drug and th countr-j markt is partiall covrd. On th othr hand, if >, all burs in countr-j bu th drug. * j Thus, in cas of partial markt covrag, givn th uniform and unit distribution, th * total dmand for th drug in countr-j markt is ( j - j. nc, th profit of th MNC quals, P j π Pj j ks (6 j, s For an innovation lvl, profit maximization ilds th following discriminator prics: Pj s j, j, (7 Substitution of (7 in (5 ilds, Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 36

9 Achara / Pric Undr Intrnational Exhaustion of Patnts * j j (8 Th following lmma thn spcifis th paramtric configurations undrling diffrnt combinations of th xtnt of markt covrag at quilibrium undr MB. mma : Undr MB, th MNC covrs a ach countr markt partiall for all < / and charg prics as spcifid in (7; b poor-countr markt full but th rich-countr markt partiall for all Proof: [, / / and charg prics qual to P s and P s / ; c both th markts full for all /, if <, and charg prics qual to Pj s. 6 First two claims follow from th profit-maximizing choic of th xtnt of markt covrag as spcifid in (8. Finall, sinc <, so th cas whr th rich-countr is full covrd is rlvant (i.., / if / < <. Whn th countris allow paralll trad, th MNC is forcd to charg a uniform pric P. t dnot th marginal consumrs in ach countr markt who driv zro nt bnfit from th mnu (P, s offrd b th MNC to all th potntial burs: P s (9 6 Sinc th lowst incom lvl is assumd to b sam vrwhr ( j j,, th MNC chargs th sam pric in both th countris whn both markts ar full covrd. This bcoms a trivial cas sinc thr will b no incntiv for ithr countr to allow paralll imports, and thus is not considrd in pric and wlfar comparisons latr. Full covrag of both markts would hav bn a maningful cas in th prsnt contxt if, for xampl, <, as in Achara and Garcia-Alonso (0. Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 37

10 Achara / Pric Undr Intrnational Exhaustion of Patnts For th sam rason as alrad splld out abov, if < both th markts ar partiall covrd. In that cas, th profit of th MNC quals, P [ + ] ks π P (0 s Procding as bfor, th profit-maximizing uniform pric, for an givn choic of innovation, quals: P ( + s ( 4 ( + 4 ( It is now radil vrifiabl that if <, i.., 3 <, th MNC dos not srv th poor-countr markt. Othrwis, for smallr cross-countr dmand disprsions, i.., for (, 3, both th markts ar srvd. Thrfor, mma : Undr, for all (, 3, th MNC srvs both th markts, with ach countr markt partiall covrd for all < and both th markts full covrd othrwis, whr, ( / 4 +. In rst of th analsis w will assum that <, which mans, first, both th countris will b srvd undr, and scond, both th markts ma b full covrd undr MB. Th diffrnt combinations of markt covrag at diffrnt quilibria and th corrsponding paramtric configurations ar illustratd in Figur. Thus, thr ar four rlvant cass and corrspondingl four possibl sts of quilibrium pric, innovation and wlfar lvls. Th first cas is what has bn discussd in Valltti (006. Th last of ths cass, howvr, is trivial. Sinc th lowst willingnss-to-pa is assumd to b th sam in th two countris, undr full covrag of both th markts th MNC chargs th sam pric s vrwhr vn without paralll imports bing allowd b th countris. That is, whn /, MB is simpl not profitabl. In rst of our analsis w abstract from this trivial cas. W will distinguish btwn th choics in cas II and cas III (from thos in cas I b putting a hat and a tild ovr thm rspctivl. Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 38

11 Achara / Pric Undr Intrnational Exhaustion of Patnts MB Rich-countr markt partiall covrd Rich-countr markt full covrd 0 Poor-countr markt partiall covrd Both th markts partiall covrd Poor-countr markt full covrd Both th markts full covrd Figur : Th Extnt of Markt Covrag at iffrnt Equilibria.3. Innovation and Prics In th first of th thr non-trivial cass illustratd in Figur abov, whr th intracountr dmand disprsion is vr larg, and as a consqunc, both th markts ar partiall covrd undr both th pric rgims, th innovation lvls can b found b maximizing (6 and (0 for th corrsponding pric choics dfind in (7 and ( rspctivl. Mor prcisl, s ( + (3 4k s + 8k ( (4 Whn th intra-countr dmand disprsion is modratl larg ( / < and thus undr MB th MNC full covrs th poor-countr markt but partiall covrs th rich-countr markt, th pric chargd in th formr quals sˆ and consquntl th profit-maximizing choic of th qualit of th drug quals, Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 39

12 Achara / Pric Undr Intrnational Exhaustion of Patnts sˆ arg max ˆ π sˆ ( + sˆ k( sˆ + (5 k 4 Th innovation lvls and prics in othr cass can similarl b drivd. Th quilibrium valus of prics and innovation lvls for diffrnt paramtric configurations ar rportd in Tabl. As shown in th appndix, th undrinvstmnt rsult of Valltti (006 holds for all rlvant rang of dmand disprsion. But th gap btwn th innovation lvls undr MB and dclins with th dclin in th xtnt of th intra-countr dmand disprsion (or th intracountr incom disparit, i.., with highr for an givn. j MB s P P Cas I < Tabl : Equilibrium Pric and Innovation vls ( + 4k 8k 8k ( + ( k 4 ( + ( k 4 s ( + 8k P 3 ( + 3k Cas II < Cas II < + k 4 + k ( k 4 ( k 3 + ( k 4 k + + ( + ( k k ( + Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 40

13 Achara / Pric Undr Intrnational Exhaustion of Patnts This is illustratd in Figur. Undr full markt covrag of th poor countr, s and / s ar th prics chargd b th MNC whn MB can b practicd whras s is th global uniform pric whn is allowd b th rich countr. Thus, for an givn innovation lvl, as riss, th xtnt of th markt (and hnc th profit of th MNC shrinks. Thus, th MNC lowrs th innovation lvl as shown in Figur for all / undr MB and for all undr. Th pric comparison, on th othr hand, is ambiguous. In cas I whr both th markts ar partiall covrd undr both th rgims, th global uniform pric is gratr than th lowst discriminator pric P [, ]. But whn th poor-countr markt is full covrd undr MB (i.., /, th discriminator pric thr riss with. owvr, ( /,, th markts ar still partiall srvd undr so that th (global uniform pric rmains invariant with rspct to th xtnt of dmand disprsion (s Tabl. For all / >, th markts ar full covrd so that th uniform pric riss with just as th discriminator pric chargd in th poor countr, though of cours at a diffrnt rat. For this rang of valus of, it is radil vrifiabl that, Innovation s s Figur : Paralll Imports and Undr-Invstmnt in R& Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 4

14 Achara / Pric Undr Intrnational Exhaustion of Patnts [ ] 0 ~ ~ P P > 4 ~ Thrfor, b th continuit proprt of th quilibrium prics, P ~ ( and P (, thr xists a * ( /, such that P ~ ( * P ~ ( *. nc, for all *, th global uniform pric is lowr than th discriminator prics contrar to th convntional thortical wisdom. This is what w anticipatd arlir. Th intuition bhind this rsult is simpl. Whn it is profitabl for th MNC to srv th ntir markt in th poor countr undr, it must lowr th pric blow th discriminator pric P to induc th poorst burs thr sinc th innovatd drug is now of a lowr qualit varit. That is, th uniform pric undr is lowr than th discriminator prics bcaus of th advrs R& ffct of. Th complt ranking of prics is illustratd in Figur 3 and th algbraic dtails ar providd in th appndix. Pric P P * Figur 3: iscriminator and Global Uniform Prics Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 4

15 Achara / Pric Undr Intrnational Exhaustion of Patnts Th abov rsults ar summarizd in th following proposition: Proposition : a Paralll imports unambiguousl lowr th innovation lvl and th consqunt qualit of th drug for all rlvant paramtric configurations and th xtnt of markt covrag. b Th global uniform pric undr paralll imports is unambiguousl lowr than th countr-spcific discriminator prics whn th poor-countr markt is full covrd undr both MB and rgims (i.., for all. But whn this markt is full covrd onl undr MB (i.., / < <, thr xists a * ( /, such that th uniform pric undr is lowr than th discriminator prics for all *. Proof: Follows from th abov discussion. Thus, paralll imports can, of cours, incras markt accss for th poor, as is oftn argud in favour of implmnting intrnational xhaustion of patnts b th dvloping countris. In th nxt sction, w xamin whthr this markt-accss gain can b so high to provid a normativ justification for such a polic as wll..4 Wlfar Proprtis of Paralll Imports From th prfrnc structur and th consumr st dfind hr, it appars that thr ar thr sourcs of a chang in consumr gains and national wlfar as th pric rgim changs from MB to global uniform pricing. First is th lvl of innovation. Sinc all burs valu highr innovation and consquntl a bttr qualit of th innovatd drug, national wlfar lvls ris with th innovation lvl. Scond sourc of gain is a dclin in pric. Th lowr is th pric of th drug, highr is th surplus for th intra-marginal consumrs, for an givn qualit of th drug. Third sourc is th gratr markt covrag. If pric of th drug dclins or a bttr qualit drug is innovatd, and initiall all th potntial burs wr not srvd, mor lowr-incom burs ar brought into th markt who did not find it worthwhil to bu th drug arlir. Convrsl, if th pric of th drug riss or a lowr qualit of it is innovatd, a fw burs drop out of th markt and th national wlfar dclins. Of cours, chang in th profit of th MNC constituts th othr part of th chang in national wlfar for its nativ countr. owvr, in our national wlfar calculations blow, Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 43

16 Achara / Pric Undr Intrnational Exhaustion of Patnts w nglct this componnt for two simpl rasons. First, this hlps us avoid th issu of location of th MNC. Scond, th dbats ovr th costs and bnfits of paralll imports primaril concrn how th usrs of drugs and mdicins ar affctd b such a polic rgim. 7 owvr, th MNC profit is includd whn th global wlfar is calculatd latr. Thus, national wlfar lvls hr ar simpl th sum of nt wlfar drivd b all consumrs who participat in th markt: W j j * j ( s P d j * whr, j b th marginal consumr in countr-j markt. Th valus of national wlfar lvls in ach of th sub-cass discussd abov ar shown in Tabl blow. Considr first th wlfar of th poor countr. In th first cas, whr th markts ar partiall srvd undr both MB and, paralll imports lowr th qualit of th innovatd drug and rais th pric. Thus, whras som low-incom burs in th poor countr ar now drivn out of th markt, thos who still bu th drug ar wors-off du to lowr innovatd qualit and highr pric. So on all accounts th national wlfar undr dclins blow that undr MB. In th scond cas, paralll import lowrs national wlfar through undr-invstmnt and smallr markt-covrag. Though th uniform pric is lowr for som paramtric valus in this cas, th consqunt gain in nt utilit is not sufficint to compnsat for th utilit losss (s appndix. Finall, in th third cas whr th poor-countr markt is full covrd undr both MB and, thr would b no markt covrag ffct on th national wlfar. But onc again, th utilit loss du to undrinvstmnt undr is largr than th utilit gain du to lowr (uniform pric, thrb lowring national wlfar of th poor countr. Thus, is unambiguousl wlfar rducing for th low-incom countr. Th wlfar loss undr, th magnitud of which dclins, howvr, with th fall in th dmand disprsion (, is shown in Figur 4. 7 Altrnativl, w can think of MNC blonging to th rich countr, but its govrnmnt puts a vr low or zro wight on MNC s profit. Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 44

17 Achara / Pric Undr Intrnational Exhaustion of Patnts Tabl : National and Global Wlfar vls Cas I Cas II Cas II < < < MB Cas II and Cas III W W GW ( + 3k ( + 3k ( + 6k 8k ( ( ( k 4 4 ( ( 3k Cas I and Cas II W T ( 56k + (3 ( k ( + W R ( 56k + (3 ( k ( + GW ( ( 8k k ( + ( + On th othr hand, sinc th global uniform pric is alwas lowr than th discriminator pric chargd to th burs in th rich countr b th MNC, paralll import raiss th national wlfar of th rich countr ovr and abov th lvl undr MB primaril through th favourabl pric ffct. Th utilit gain consqunt upon th lowr pric ovr-compnsats th utilit losss from undr-invstmnt for thos who participat in th markt undr both th pric rgims. Ths wlfar rsults man that th rich countr will undo pric discrimination b allowing paralll imports of th drug whn th poor countr cannot rstrict it. Thus th Richardson (00 rsult xtnds to this cas of ndognous invstmnt dcision with undrinvstmnt in R& undr compard to that undr MB. Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 45

18 Achara / Pric Undr Intrnational Exhaustion of Patnts Wlfar W W Figur 4: Wlfar Ranking of MB and t us now turn to th fficinc proprt of this global-uniform pricing quilibrium. Sinc th poor countr unambiguousl loss, uniform pric undr can at most b potntiall Parto fficint providd, of cours, th rich countr gains from mor than th poor countr loss from it. In such a cas, thr is a scop for th rich countr to compnsat th poor countr for its losss through transfrs (such as contributions to th Global Fund launchd b th Unitd Nations and still gain from. From such a prspctiv it is worthwhil to xamin whthr uniform pricing undr improvs th global wlfar. Th following mma maks a dfinit statmnt in this rgard. mma 3: t GW W + W and GW W + W dnot global wlfar lvls (including th MNC profit undr MB and rspctivl. Thn, GW > GW < ˆ (6a whr, GW < GW [ ˆ, (6b < ŷ <. Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 46

19 Achara / Pric Undr Intrnational Exhaustion of Patnts Proof: S appndix. Thus, global-uniform pricing undr dos not ncssaril improv global wlfar. Onl for small dmand disprsions (or larg valus of, global wlfar is largr undr than undr MB. Thrfor: Proposition : a Whn th poor countr cannot rstrict paralll xports of th patntd drug sold b th MNC, th rich countr will undo MB b allowing paralll imports. A lowr qualit of th drug will b innovatd and sold at th sam pric in vr countr b th patnt-holdr MNC. b Paralll imports and th consqunt global uniform pricing will b (potntiall Parto-fficint onl whn th dmand disprsions ar small in th sns that ˆ, /. [ Proof: Th first part of th proof follows from th obsrvation that th rich countr alwas gains from paralll imports. Th scond part follows from mma Robustnss 3. Mor than two countris To chck whthr th abov rsults dpnd on th two-nss of th world conom, I considr a simpl xtnsion of th world conom to thr-countr cas, which can of cours b furthr xtndd to includ mor countris in th sam mannr as outlind blow. In addition to th poor and rich countris as dfind abov, considr a middl-incom countr having th sam lowst incom lvl but a highst M. Th othr charactristics of th tast htrognit of th potntial burs in this countr ar th sam as thos spcifid abov in th bnchmark cas. For this xtndd world conom, I discuss onl thos sub-cass (as distinguishd in trms of th valu of or th magnitud of dmand disprsions whr th abov-drivd unorthodox pric and wlfar rsults hold. incom lvl (, Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 47

20 Achara / Pric Undr Intrnational Exhaustion of Patnts Procding as bfor it is radil vrifiabl that undr MB th MNC srvs all ths markts partiall < / ; srvs th low-incom countr markt full and th othr two partiall [ /, M ; srvs th low and middl incom countris full and th rich-countr markt partiall [ M /, / ; and srvs all th markts full > /. On th othr hand, undr, all th markts ar partiall covrd > * [ + M + ]/ 6, and full covrd othrwis. Sinc, / < *, so all th markts ar partiall covrd undr both th pricing rgims < /. In this particular cas th innovation and wlfar lvls ar as follows: s + + M (7 4k k s [ + ] + (8 M G W 6 k + + M (9 + M M M M 44k GW [ ] (0 Th undr-invstmnt rsult is immdiat from th comparison of th innovation lvls: s s On th othr hand, 6 ( + ( ( M M > 0 G W - GW 36 k + M + M M > 0 Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 48

21 Achara / Pric Undr Intrnational Exhaustion of Patnts Thus, in this cas of partial covrag of all th markts, paralll imports lowr th innovation lvl. It is also globall Parto infficint as in th two-countr cas discussd abov. To dmonstrat now th favourabl pric ffct of, considr th cas whr [ *, /. Not that * is gratr than M / if ( M is gratr than ( M. For such a paramtric configuration, th prsumd valus of mans that whras onl th low and middl incom countris ar full covrd undr MB b th MNC, all th thr markts ar full covrd undr. Procding as bfor, th quilibrium prics undr th two altrnativ pricing rgims qual: P [ M 8 ] PM s ( 4k [ + + ] P M 3 k ( Whn it is profitabl for th MNC to catr th low and middl incoms countr markts full, as in this particular cas, it chargs th sam pric s in ths markts for an givn innovatd qualit sinc th lowst incom (and hnc th willingnss-to-pa is th sam. A highr pric s /, howvr, is chargd to th burs in th rich countr, for th sam qualit of th drug. That is, du to smallr dmand disprsion in th low and middl incom countris, it dos not pa for th MNC to discriminat btwn ths two markts. But rlativl largr dmand disprsion in th rich countr maks it profitabl to pric out som low-incom potntial burs thr and thus discriminat against th burs who bu th drug rlativ to thos in th othr two countris. W can labl this pricing choic of th MNC as th rgional uniform pricing or partial discrimination. It should thn b obvious that sinc a lowr qualit of th drug is innovatd undr, th global uniform pric that th MNC chargs undr to induc th potntial burs with th lowst incom (sinc in this cas full covrag of th low-incom countr is profitabl must b smallr than th pric th MNC would charg whn a highr qualit is innovatd undr partial discrimination in th sns dfind abov. Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 49

22 Achara / Pric Undr Intrnational Exhaustion of Patnts Th following algbraic xprssion spcifis th magnitud of this quilibrium pric diffrnc: P [ 4 ] P PM P > 0 4k + Ths two cass ar sufficint to illustrat how do th rsults spcifid in Propositions and in th contxt of a two-countr world can xtnd to th thrcountr, and in a similar fashion to th man-countr, world. 3. Export Tax and Paralll Imports So far w hav assumd that th govrnmnt in th low-incom countr cannot prohibit paralll xports of th drug to th rich (and middl incom countr. But trad rstrictions such as an xport tax can b ffctivl usd to rstrict and vn prohibit paralll xports providd of cours thr ar strict monitoring and prohibition of illgal xports and smuggling. Richardson (00 in his homognous good framwork argud that whn th low-incom countris can rstrict paralll xports, th MB will b th (Nash quilibrium pricing. In this sction I xamin whthr this rsult xtnds to this vrticall diffrntiatd good cas. In th analsis blow, w rfr back to th bnchmark modl of two-countr world and assum k for th innovation tchnolog dfind in ( to kp th algbra simpl but without an loss of gnralit. Suppos th -govrnmnt imposs an ad valorm xport tax at th rat t that maximizs th countr s wlfar. Th potntial comptitiv local paralll xportrs now bu th drug at th pric P sold b th MNC in this countr and thn xports it at th pric ( + t P to th rich countr. Thus, whn th rich countr allows unrstrictd paralll imports of th drug from th low-incom countr, th MNC cannot charg th rich-countr burs mor than ( + t P, th pric that th hav to pa for th paralll importd drug. owvr, w assum that whn th rich countr burs fac th sam pric for th drug sold b th MNC in th rich countr and th paralll importd drug, th bu th drug sold b th MNC 8. Thus, for an 8 This choic is assumd hr simpl as a ti-braking rul but can b justifid b th burs prcption that paralll importd drug is not a prfct substitut of th original drug sold b th MNC. Radrs ar rfrrd to Jlovac and Bordo (005 and Maskus (00 for a similar argumnt. Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 50

23 Achara / Pric Undr Intrnational Exhaustion of Patnts givn tax rat, th MNC slls th drug at th pric ( + t P in th rich countr in which cas no drug is actuall (paralll xportd. Thus, th thrat of paralll xports now though rstricts th MNC s abilit to discriminat, it dos not forc it to charg th sam pric vrwhr as whn th -govrnmnt allows fr paralll xports. Th MB rgim and th choics rmain th sam as bfor. Thus, w nd onl to analz th xport tax and rgim, dnotd b T, whr th -govrnmnt first chooss th optimal tax rat and thn th MNC chooss th innovation lvl and th pric of th drug to b sold in th low-incom countr markt, P T. W solv this squntial gam b backward induction mthod. Givn an choic of th xport tax rat t b th -govrnmnt, th following profit maximizing choics of th innovation and th pric lvl b th MNC, whn it srvs th low-incom countr markt, ar radil vrifid: sˆ P T T [ + ( + t ] 4 [ + ( + t ] (3 [ + ( + t ] [ + ( + t ] 3 (4 8 Th xtnt of markt covrag in th two countris qual [ ˆ ( t ] [ ˆ ( t ] ˆ ( t and whr j, j,, is th marginal consumr in countr-j who is indiffrnt btwn buing and not buing: ˆ ( t + ( + t, ˆ ( t ( + t ˆ ( t (5 [ + ( + t ] Of cours, th innovation and pric lvls spcifid in (3 and (4 will b th profit-maximizing choics of th MNC onl for all < ˆ ( t. Othrwis th MNC covrs th low-incom countr markt full (though still catrs th high-incom countr partiall for an positiv xport tax rat. Th choics thn can b radil vrifid as: Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 5

24 Achara / Pric Undr Intrnational Exhaustion of Patnts ~ st [ + ( + t ( + t ] P ~ T [ + ( + t ( t ] (6 (7 + A fw commnts ar warrantd at this point. First, ˆ ( t varis invrsl with th tax rat. This has two implications. Th low-incom countr markt will b srvd b th MNC as long as ˆ ( t <. Sinc ˆ ( t is dcrasing in th tax rat and ˆ(0, so ˆ ( t < t > 0 if <. nc, b th condition statd in mma, viz. <, th MNC srvs th low-countr markt for an xport tax rat imposd b th -govrnmnt. On th othr hand, for an givn, whthr th MNC covrs th low-incom countr markt full or not dpnds on th tax rat itslf. fin a tax rat tˆ ( such that ˆ (ˆ t. Thus, th -govrnmnt can induc th MNC, if it prfrs to, to covr th ntir markt b choosing a tax rat at last qual to tˆ (, and sinc ˆ ( t varis invrsl with th tax rat, this critical tax rat would b highr th smallr is th valu of (i.., th highr is th dmand disprsion in th low-incom countr. This is shown in Figur 4 b th downward sloping curv. Scond, sinc for an givn choic of th pric at which th drug is to b sold in th low-countr, P, th pric at which th MNC slls th drug in th rich countr whn its govrnmnt allows paralll import of th drug incrass monotonicall with th xport tax rat, thr xists a tariff rat that nabl th MNC to charg th sam pric that it would charg undr MB. I labl this tariff rat as prohibitiv tariff rat and undrstandabl its valu diffrs according to whthr undr MB th MNC covrs th low-incom countr full or partiall. In particular, lt tˆ P ~ and t P b such that, ( + tˆ P P P tˆ P (8 ~ ~ ~ ( + tp P P ~ tp (9 Ths prohibitiv tariff rats ar shown b th vrtical and downward-sloping curvs ~ rspctivl in Figur 5. Th rlativ positions and slops of th t P -constraint ~ (rflcting th rlationship ( + t P and th curv labld ˆ (ˆ t ar radil vrifiabl and thus a dtaild discussion on this is avoidd. Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 5

25 Achara / Pric Undr Intrnational Exhaustion of Patnts VII VI V VIII Rgion I Rgion IV ˆ (ˆ t ~ II III t P tˆ P t Figur 5: Prohibitiv and Critical Tax Rats Sinc, as stablishd arlir, th low-incom countr unambiguousl loss whn th rich countr allows paralll imports, th -govrnmnt will gain b imposing th ~ prohibitiv tax rat on paralll xports, tˆ P or t P as dfind abov according as th rlvant valu of, rlativ to allowing fr paralll xports. And for such a prohibitiv tax rat, th -govrnmnt s choic of allowing paralll imports is inconsquntial. Th issu is thn whthr thr xists an non-prohibitiv tax rat that raiss th low-incom countr s wlfar ovr and abov th lvl corrsponding to th prohibitiv tax rat, which, in turn, is qual to th lvl ralizd undr MB. If so, th -govrnmnt chooss that non-prohibitiv tax rat, and thn analzing th choic of th -govrnmnt ovr allowing or MB is maningful. Rfr back to th Figur 5. Sinc < /, th rlvant prohibitiv tax rat tˆ P is lss than th critical rat tˆ, so for this rang of dmand disprsion onl Rgion I is rlvant for discussion. For an t tˆ P, as in Rgions II, III and IV, th MNC th chargs th sam st of discriminator prics P and P, ralizing th sam wlfar lvls for th two countris. Now, for all such combinations of and th tax rat in Rgion I, th following rsults hold as laboratd upon in th appndix: Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 53

26 Achara / Pric Undr Intrnational Exhaustion of Patnts sˆ T > 0 t tˆ P t sˆ T s t P tˆ (30a (30b Th innovation lvl riss with th tax rat for th simpl rason that highr taxs nabl th MNC to discriminat mor btwn th consumrs in th low-incom and rich countris and arn highr profits. Th wlfar lvl of th low-incom countr, on th othr hand, varis with th innovation lvl and th xtnt of markt covrag, whn th MNC partiall covrs th low-incom countr markt (i.., for an choic of th tax rat t < tˆ ( : Wˆ T T sˆ [ ˆ ( t ] Givn that ˆ ( t is dcrasing in th tax rat, b (30a it immdiatl follows that, Thrfor, Wˆ T ( t < W ˆ T (ˆ t P t tˆ P (3 mma 4: For all < /, th -govrnmnt imposs th prohibitiv xport tax rat tˆ P. Proof: S appndix. But for highr dmand disprsion in th low-incom countr, i.., for /, th MNC full covrs this markt undr MB (i.., whn th rich countr dos not allow ~ paralll imports so that t P ( is now th rlvant prohibitiv xport tax. Thr ar now two rlvant sub-cass. First is th sub-cas of modratl high dmand disprsions, [ /,, and th othr is th sub-cas of vr small dmand disprsions, [, /. Sinc for all such modratl high dmand ~ disprsions t P ( > tˆ ( > 0, th -govrnmnt can influnc th MNC s choic of th xtnt of markt covrag b its own choic of a non-prohibitiv tax rat. Prcisl, whn th rich countr allows paralll imports and dmand disprsions ar Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 54

27 Achara / Pric Undr Intrnational Exhaustion of Patnts modratl larg in th sns that / <, for all non-prohibitiv tax rat t < tˆ (, th MNC partiall covrs th low-incom countr markt, and full covrs this markt othrwis. On th othr hand, for vr small dmand disprsions, [, /, th MNC full covrs th low-incom countr markt rgardlss of th xport tax rat whn th rich countr allows paralll imports. nc, th wlfar lvls ralizd for th low-incom countr for diffrnt paramtric configurations ar as follows: [ ˆ ( t ] ˆ ˆ WT st t < tˆ( and [, ~ ~ W T WT st ( t tˆ( and [, (3 ~ ~ W ( > 0 [, T st t and Thus, for an givn valu of, and hnc th xtnt of dmand disprsion, th wlfar lvl of th low-incom countr whn th rich countr allows paralll imports and th MNC covrs its markt full, W ~ T, varis proportionatl with th innovation lvl. Givn th profit-maximizing lvl of innovation b th MNC as spcifid in (6, it is radil vrifiabl that, givn, th innovation lvl, and hnc ~ th low-incom countr s wlfar, is maximum for th prohibitiv tax rat t P (. Thrfor, for all [, /, sinc th MNC srvs all th consumrs in th low-incom countr rgardlss of th rat of xport tax, th -govrnmnt imposs ~ t P ( to maximiz th national wlfar, W ~ T. On th othr hand, for modratl ~ high dmand disprsions, sinc tˆ P > t P ( > tˆ ( and Wˆ T ( t is incrasing in th tax rat t tˆ P, th -govrnmnt s choic of th xport tax rat dpnds on th valu of Wˆ T (ˆ t rlativ to that of W ~ ~ T ( t P. That is, th choic of th tax rat ~ ssntiall boils down to choic btwn tˆ ( and t P. Th following lmma spcifis this choic: mma 5: Wˆ T (ˆ t < W ~ T ~ [,. ( t P Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 55

28 Achara / Pric Undr Intrnational Exhaustion of Patnts Proof: S appndix. Thrfor, Proposition 3: Rgardlss of th siz of its markt (or th dmand disprsion, -, th -govrnmnt prohibits paralll xports. Th -govrnmnt s choic is thus inconsquntial. Proof: Givn (3, th rsult follows dirctl from mmas 4 and 5 and that ~ maximum for th prohibitiv tax rat t P (. W ~ T is That is, whn th -govrnmnt imposs an xport tax to rstrict th paralll xports of th drug from th low-incom to th rich countr, th MB will b th quilibrium pric rgim sinc its choic of prohibitiv rat of tax maks inconsquntial th paralll imports allowd b th rich countr. Thus, th Richardson (00 rsult onc again xtnds to all paramtric configurations. 4. Conclusion B xtnding th arlir work of Valltti (006 to all plausibl paramtric configurations this papr shows that though th undr-invstmnt rsult alwas holds, th innovation lvl for a drug varis with th xtnt of (intra-countr dmand disprsion (and hnc th xtnt of markt covrag. But, th uniform pric (whn paralll trad of th patntd drug is allowd b th countris ma b lowr than th discriminator prics contrar to th convntional thortical wisdom. spit such a possibilit, howvr, th poor countr alwas loss and th rich countr alwas gains from paralll trading. Morovr, global wlfar (including MNC profit ma fall as wll impling that paralll trading of a patntd drug ma not vn b a potntiall Parto suprior rgim compard to pric discrimination. Similar wlfar proprtis of paralll imports hold whn th poor-countr govrnmnt imposs a non-prohibitiv xport tax to (partiall rstrict paralll xports of th patntd drug to th rich countr. Thus, whn th poor countr is not constraind politicall or othrwis, it will undo global uniform pric b prohibiting paralll xports of th drug rgardlss of th paramtric configurations. Thus, MB Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 56

29 Achara / Pric Undr Intrnational Exhaustion of Patnts Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 57 will b th quilibrium pricing rul. This rsult rinstats Richardson (00 rsult in this cas of ndognous R& invstmnt. Appndix: I. Undr-invstmnt undr paralll imports From (3 and (4, it follows that, for <, ( > + k k s s (A. On th othr hand, for / <, givn th valus of innovation lvls as spcifid in Tabl in th txt, it is sufficint to not th following: ( 0 < k s (A. [ ] k s ( + + (A.3 Sinc for this rang of incom lvls, th innovation lvl undr paralll imports rmains th sam as bfor, so ( 0 6 ( > k s s implis that s s > Finall, not that for < <, ( [ ] ( ( 0 4 < + k k k s (A.4 Givn (A. this mans that innovation lvl undr paralll imports falls fastr than that undr MB as riss, as shown in Figur in th txt. On th othr hand, k s s

30 Achara / Pric Undr Intrnational Exhaustion of Patnts nc, <. s > s for < II. Th xtnt of markt covrag and discriminator and uniform prics First of all, not that, < /, discriminator pric in th low-incom countr would alwas b smallr than th uniform pric, though th magnitud of th diffrnc dpnds on how larg is rlativ to. This is radil vrifid from th following st of valus: 3 P ( P ( (A.5 4k P ( < P ( (A.6 8k 3k Morovr, P P [ + ] 0 P 3 > 0, > 4k 3k P 3k [ + + ( ] < 0 nc, P > P (, ], givn <. (A.7 (A.8 On th othr hand, ( /,, using th valu of in ( and th valus of th prics givn in Tabl, it is radil vrifiabl that P 3 3 [ + ] > [ + ] P ( 3 ( (A.9 64k 3k Sinc, as dmonstratd abov, P P for /, b (A.8 and th proprtis of P ( and P ( functions, > / w arriv at th ranking of th discriminator and uniform prics as illustratd in Figur 3 in th txt. Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 58

31 Achara / Pric Undr Intrnational Exhaustion of Patnts III. Wlfar Proprtis of Paralll Imports In cas I, as spcifid in Tabl, it can b radil vrifid that both W and W ar monotonicall incrasing in at an incrasing rat but W riss fastr than W. Sinc W W for, so W > W ovr th rlvant rang, i.., (, ]. Altrnativl, using Scintific Workplac, it can dducd that, W 3 3 W ( ( > 0 (A.0 56 nc, th rich countr unambiguousl gains from paralll imports whn markts ar onl partiall covrd undr both MB and. Whn onl th low-incom countr markt is full covrd undr MB but both markts ar still partiall covrd undr (cas II, first of all not that, wlfar of th low-incom countr monotonicall dclins as riss, W ( [ ( ( ( ] 4k < 0 > and, W ( W ( 8k 56k (A. ( ( + 3 ( + 56k ( > 0 (3 (A. Thrfor, as argud in th txt, sinc W > W /, and W rmains invariant with rspct to changs in <, so b (A. and (A. it follows that W > W [ /, ]. For vn smallr dmand disprsion, wlfar undr paralll imports dclin as wll and attains th sam valu at / as th wlfar undr MB. Thus, th wlfar of th low-incom countr unambiguousl dclins undr paralll imports for all rlvant dmand disprsions. Trad and vlopmnt Rviw, Vol. 6, Issu -, 03 Jadavpur Univrsit. 59