Health Insurance as a Two-Part Pricing Contract *

Transcription

1 Healt rae a a Two-Part Priig Cotrat Dari Lakdawalla ad Neeraj Sood RND Corporatio ad NBER gt 2 27 btrat Moopolie appear trogot ealt are arket a a relt of patet liit to te extet of te arket or te preee of ie ipt ad kill. te ealt are idtry owever te deadweigt ot of oopoly ay be oiderably aller ta i oter arket or eve abet altogeter. Healt irae freetly ipleeted a a ex ate prei opled wit a ex pot o-payet per it oed effetively operate a a two-part priig otrat. Ti allow oopolit to ear profit witot ieffiietly otraiig atity. Ti view of ealt irae otrat a everal ipliatio: Low ex pot opayet to ired oer btatially rede deadweigt loe fro edial are oopolie we allate for itae tat te proviio of drg irae lower oopoly lo i te US paraetial arket by ore ta 9 peret; 2 Prie reglatio or atitrt eforeet of oopolie ay be le beefiial i ealt are arket partilarly we ay oer are ired; ad 3 Deadweigt lo fro ealt are oopoly i proportioal to te rate of irae ad will be zero we all oer ave at leat oe irae. For elpfl oet ad ggetio we wi to tak la Garber Daa Golda Geoffrey Joye Toa Pilipo partiipat i te 25 NBER Ser titte Healt Eooi orkop ad partiipat i te Fall 26 NBER Healt Care Progra Meetig. e are gratefl to te Natioal titte o gig for fdig.

2 . trodtio Optial ealt irae otrat balae rik-arig agait te eed for effiiet tilizatio ietive rrow 963; Paly 968; Zekaer 97. Ti balae explai wy otrat do ot etitle poliyolder to liited tilizatio bt itead arge a ex pot it prie or o-payet. Co-payet rede te degree of irae bt i retr prode fewer ditortio i te good arket beae te oer fae a private prie tat partially reflet oial ot. Te trade-off betwee rik-arig ad ietive a bee widely tdied. However ealt irae otrat ave aoter ftio tat i le well-appreiated: te redtio of deadweigt lo. Healt irae reeble a two-part priig otrat i wi a grop of oer pay a pfrot fee i exage for lower prie i te evet of ille. Two-part priig otrat allow a oopolit to ell good at argial ot bt extrat oer rpl i te for of a pfrot payet ee te eial paper by Oi 97. Typially opetitio iprove oer welfare beae it iiize deadweigt lo. te preee of two-part priig owever te oopolit a te ae ietive to iiize deadweigt lo beae a trategy axiize te oer rpl available for extratio. exaple illtrate ti eai i te irae otext. Settig a argial ot opayet ad a prei eal to expeted oer rpl wold for itae allow a fir to extrat te axi poible rpl wile till erig effiiet tilizatio ad zero deadweigt lo. Te ertaity of ealt are dead opled wit ex ate or ex pot ayetri iforatio reate a otratal trtre tat failitate te effiiet extratio of oer rpl. ile argial ot o-payet repreet a ideal ae oberved ealt irae otrat btatially rede te prie faed by ired oer i te preee of arket power ad t deadweigt oopoly lo i ealt are arket.

3 Ti logi i robt to a wide variety of otext. t applie diretly we a oopolit or oligopolit ealt-are provider i itegrated wit a ealt irer. ti ae te ealt-are provider diretly e te two-part irae otrat to extrat rpl. Two proiet exaple of ti vertially itegrated orporate for are: a taff-odel Healt-Maiteae Orgaizatio HMO; ad a paraetial iovator itegrated wit a paray beefit aager PBM tat aage preriptio drg irae. However te ae ietive alo operate o te relatioip betwee a oopolit ealtare provider ad a eparate ealt irae idtry. f irae i opetitively provided a oopolit a e it arket power to ide irae otrat tat extrat axi oer rpl o it bealf. e irae i ot opetitive bot irer ad provider ave trog ietive to axiize te oer rpl available for extratio wi tey te plit aogt teelve. Fially te ore ititio i robt to oo failre i te irae arket like oral azard ad advere eletio. Regardle of te iforatio trtre fir ave ietive to axiize te oer rpl available for extratio. Te ieffiiey of te irae arket lower te total rpl available bt doe ot weake te ietive to axiize extratible rpl. Or relt ave everal iportat ad ovel ipliatio. Firt oopolie i ealt are weter de to patet liited arket ize or itorial fator ave aller deadweigt ot i te good arket. a iportat exaple of ow te teory iflee atal pratie we allate tat providig te average preriptio drg irae poliy to te average ired oer wold lower ired oer deadweigt lo fro paraetial optio by 2

4 ore ta 9%. Moreover i te partilar otext of preriptio drg patet protetio tilate iovatio at le tati deadweigt ot ta i oter arket. Seod breakig p or reglatig oopolie a fewer beefit i ealt are arket we rate of irae are ig. Market power lead to iger ta opetitive irae preia bt old ot affet o-payet ad tilizatio aog ired oer. t reditribte wealt fro ired oer to fir witot oproiig te effiiey of good-proviio. Soiety old do ti reditribtio if it deired by taxig te profit of te oopolit ad reditribtig to ired oer. fat ieffiiey of good-proviio arie oly de to te iopletee of te irae arket; if all oer were ired good old be provided effiietly eve i te preee of oplete arket power. Terefore extedig te availability of irae a be a effetive way to eradiate welfare loe fro oopoly. Tird i te otext of iovatio ealt irae a a two-part priig ee provide a ea to opeate iovator for teir effort wile till erig te effiiet tilizatio of te good tey ivet. Healt are arket ay t be able to eape te typial trade-off betwee ftre iovatio ad tati effiiey. Fially or aalyi provide oe gidae for te optial deig of pbli ealt irae progra wi ogt to et o-payet at or below argial ot ad et irae preia aordig to oiety partilar reditribtive goal. e begi to develop or arget wit te beark ae of firt-bet effiiey i Setio B were all oer are idetial ex ate ad all ex pot eterogeeity i flly obervable. e te itrode ioplete iforatio i Setio C ad ioplete arket power Te eed for patet ad te diffiltie of eoragig iovatio are well-dertood Norda 969; rigt 983. Te effiiey of payig iovator oer rpl a ipliatio for ot-effetivee aalyi wi old aot for te eed to reward iovatio Paly 25; Pilipo ad Jea 26a. 3

5 i Setio D. Setio E oider te ie ie tat arie i te otext of iovative good were two-part ealt irae a affet bot tati ad dyai effiiey. Fially Setio F preet or etiate of deadweigt lo redtio i te US paraetial arket. Setio G olde wit everal ipliatio for ealt are poliy. B. Two-Part Healt rae ad Srpl-Extratio y irer wo a arge bot a prei ex ate ad a o-payet ex pot a eog tool to extrat axi oer rpl ad ere effiiet tilizatio. e firt ake ti poit i te otext of a fll iforatio odel were tere i eiter oral azard or advere eletio. Or iitial etp i very iilar to tat of Gayor Haa-ilo ad Vogt 2 wo ow tat redtio i te prie of edial are beefit oer eve i te preee of oral azard. Coider a eviroet wit fll iforatio ad ideity irae. Fro te ex ate perpetive oer fae a rik of ille ad a ertai dead for a edial reedy. Te edial reedy i proded at otat argial ot eal to MC. irae otrat i a offer of a ex pot o-payet opled wit ideity trafer τ. ti iplet fll iforatio ae te ideity trafer a be oditioal o te oer ealt tate. ex pot o-payet are ot tritly eeary beae te irer old write otrat araterized etirely by a et of ideity payet ad pre-peified edial are atitie. Copayet are t eivalet to expliitly otratig o atity. However te aalyi of ti iple ae elp et te aalytial tage for or diio of ioplete iforatio. Sppoe tere are oer of eare oe idexed by [] ad ditribted iforly over ti iterval. Coer ealt i repreeted by ti idex wi i a rado variable kow ex ate bt revealed to te oer after te irae otrat i praed. Ex pot 4

6 oer tility deped o o-edial optio te atity of edial are oed ad te revealed ealt tate aordig to. Sie iforatio i oplete it arifie o geerality to ae tat tere are jt two tate: ike ad ealt. Te oer i ik wit probability σ. Utility i ea tate i give by ad. Te argial tility of edial are i poitive we ik bt zero we ealty. Ex pot a ik oer wit wealt ad te ealt irae otrat te followig proble: τ τ olve ax Ti i araterized by te firt-order oditio: τ = 2 Ti firt-order oditio ipliitly defie te ex pot dead for edial are a a ftio of ex pot dipoable ioe te o-payet ad ealt aordig to τ. B. Copetitive Otoe f a oer fae a opetitive irae idtry ad a opetitive good arket te otoe i firt-bet. Coer by fll ideity irae at atarially fair prie ad we ik prae te iovatio at argial ot fro te opetitive good-prodig etor. Te followig tree oditio obtai:. Fll irae ideity trafer i te ee tat = ; 2. Effiiet e of edial are were oer fae prie eal to te argial ot of prodtio p = MC ; 3. Zero profit for irer ad edial-provider. 5

7 B.2 Te pat of Moopoly e ow ow tat a oopolit wit ae to a two-part ealt irae otrat will repliate te firt-bet eilibri. Te pedagogially iplet way to dertad ti i to oider a itegrated oopolit wo provide bot ealt are ad irae. S vertial relatioip are ot oo i te ealt are idtry. For exaple Kaier Peraete a taff-odel HMO otrolled oe-tird of te Califoria HMO arket a of 24 Bagarte 25. Siilarly a 999 Federal Trade Coiio tdy fod tat drg opaie owed or ad a igifiat affiliatio wit PBM tat aot for ajority of te PBM ativity. deed i 994 idepedet PBM aoted for le ta 3% of preriptio Levy Te oopolit axiize profit bjet to te oer partiipatio otrait. Te aot of rpl te oopolit a extrat deped o te oer ext available otide optio. itot lo of geerality ppoe tere i oly oe fir providig irae ad ealt are. Terefore te reervatio tility level i wat te oer a aieve der atarky U = σ π σ π were fir profit are π ad we aig owerip of te fir to oer. oter word we ae arket power i oplete i te ee tat tere are o oter fir available to pply ealt are or irae. 3 Ti relt i te oopolit profitaxiizatio proble: ax τ τ σ τ. t. σ MC σ στ τ π σ τ π U 3 2 Sie 994 oe paraetial opaie ave diveted teir tok oldig i PBM bt till aitai trategi iteret i te Martiez Cagig ti aptio affet oly te level of ret eared by te fir wi we ow below to be etral fro te tati poit of view. 6

8 Ti proble a te followig firt-order oditio iplified by ig te oer optiality oditio for : [ τ ]: [ τ ]: [ ]: = MC = = MC 4 Tee eilibri oditio iply tat prie eal argial ot beae ti trategy axiize te oer rpl available for extratio. Te followig arget foralize ti ititio. Sppoe tat > MC. Defie τ τ ad a te otrat vale i te iitial ptative eilibri. Coider te alterative irae otrat tat et eal to MC. log a dead i ot totally ielati te ew otrat ireae ex pot oer rpl by tritly ore ta MC. Terefore tere exit oe ε > MC tat te oer tritly prefer te otrat τ ε τ MC to τ τ. Moreover te ew otrat i tritly ore profitable ta te old oe beae te redtio i te ideity trafer ε exeed te vale of te revee lot fro te prie redtio MC. Te exitee of te alterative otrat otradit te iitial eilibri. Now ppoe < MC. Defie τ τ ad a te otrat vale i ti ptative eilibri. Coider te alterative irae otrat tat et eal to MC. Oe agai if dead i ot totally ielati te oer lo i rpl i tritly le ta MC. Terefore tere exit oe ε ' < MC tat te oer tritly prefer te otrat τ ε ' τ MC to τ τ. Te argial ot otrat i tritly ore profitable for te fir ta te old oe beae i te iitial eilibri te fir i loig MC o ale. Te exitee of te alterative otrat t otradit te iitial eilibri. Terefore = MC. 7

9 Sie te oopolit et te o-payet eal to argial ot te firt-order oditio for τ ad τ iply tat te oer will be flly ired i te ee tat =. Fially profit t be poitive beae te partiipatio otrait bid. Sppoe to te otrary tat profit are zero. Ti iplie tat te oer tility will be eal to tat of atarky wi i lower ta i te firt-bet eilibri. f profit are zero ad tility i lower ta der opetitio te opetitive alloatio offer iger total rpl. Te oopolit old t be ooig a differet alloatio. Te eilibri otrat der oopoly a ow be arized a:. Fll irae ideity trafer i te ee tat = ; 2. Coer fae te prie eal to te argial ot of prodtio p = MC ; 3. Poitive profit for te oopolit-irer by ea of atarially fair preia; Tere i oe reaiig relt to ow: te oopoly alloatio i Pareto-eivalet to te opetitive alloatio. 4 partilar we oer ow te fir oopoly prode te ae level of oer tility a opetitio. Defie Te proble i 3 a be eivaletly rewritte a: π a te eilibri level of oopoly profit. ax τ τ σ τ π. t. σ τ MC σ στ π σ τ π Now oberve tat ti proble i te ae a axiizig te followig over τ π : τ π ad ax τ π τ π σ. t. σ τ π MC σ τ π σ σ τ π τ π 4 By Pareto-eivalee we ea ere tat te oopoly alloatio opled wit oe et of edowet ad trafer prode tility eal to tat der opetitio. 8

10 it a iple age of variable it beoe lear tat ti i idetial to te opetitive irer proble of ooig trafer tat axiize oer tility bjet to a zero profit otrait. Te oer axi tility will t be idetial to tat der opetitio. B.3 Separatig te rae- ad Good-Proder Te preedig aalyi deotrated te e of ealt irae otrat a a ea of rpl-extratio by oiderig a igle fir tat provided bot irae ad good. S a odel i diretly relevat for vertially itegrated fir like taff-odel HMO or paraetial fir itegrated wit PBM bt it relt alo apply to arket were irae ad ealt-are proviio are eparated. alytially we oider te ae of a oopoly good-provider iteratig wit a opetitive irae arket. Later we di ow te relt geeralize to te ae of bilateral oopoly betwee a irer ad good-proder. Bot tee ae prode effiiet otoe. f oer reeive all te fir ret i proportio to teir tilizatio of te good te oopoly ditribtio of reore i idetially eivalet to te opetitive ditribtio. f ot iple tax-ad-trafer ee a prode a eivalet otoe witot reglatig te good arket. Te repreetative irer fae a oopolit ellig te good. egotiatig wit te irer te oopolit i able to peify bot a prie ad a atity or eivaletly a atity ad a total fixed fee. Ti type of otratig i ofte oberved i ealt are arket were atitie are eiter expliitly aed e.g. by a paraetial wolealer or tied to a oliear prie edle e.g. i te for of atity diot rebate ad te like. For exaple otrat betwee PBM ad paraetial fir are of two type o-apitated ad apitated. 5 No-apitated otrat 5 Private-etor etitie tat offer preriptio drg irae overage a eployer labor io ad aaged are opaie ofte ire paray beefit aager PBM to aage tee irae beefit. PBM egage i ay ativitie to aage teir liet preriptio drg irae 9

11 ally peify a lit prie or woleale aiitio ot ad ter for deteriig diot or rebate. Rebate are ally tied to te dollar or it ale of a partilar drg prodt. For exaple growt rebate offer PBM a teeper diot if tey aieve ertai vole target. Capitated otrat o te oter ad peify a fixed payet fro te PBM to te drg opay per ired eber per ot alog wit oe rik-arig arrageet tat deterie additioal payet or oeio baed o atal drg age Levy 999. Te apitated rate obied wit rikarig arrageet effetively reder tee eivalet to two-part priig otrat. Siilarly oplex priig arrageet are alo oo betwee opital ad irer Melik 24. Te ability to et bot a prie ad a atity i iportat. e te oopolit i able to peify oly oe of tee we revert to te aalyi of oopoly artilated by Gayor Haa-ilo ad Vogt 2 were te al oietal loe are irred. 6 te abee of two-part ealt irae peifyig bot prie ad atitie for eterogeeo oer i ite ipratial. Te provider wold eed to peify a differet prie-atity pair or two-part priig e for ea oer. Te two-part trtre of ealt irae provide a atral ad pratial way to tie prie ad atity togeter. Te irer take a give a fixed atity ad a fixed fee aoiated wit tat atity. Sie e i opetig for a otrat fro a oopolit e t axiize i gro profit gro of te fee paid to te oopolit bjet to te partiipatio of te oer. Te oopolit te extrat toe gro profit. f te irer fail to axiize gro profit te oopolit will take i bie elewere. Give te pre-peified atity profit-axiizatio proble a: we a write te irer gro overage ildig aeblig a etwork of retail paraie deigig te pla forlary ad ot arig arrageet o-payet for differet drg ad egotiatig wit paraetial opaie. 6 Tey ow tat eve i te preee of oral azard oer are better off wit opetitio lower prie ta wit oopoly iger prie.

12 G. t. σ = ax τ τ σ τ τ σ ad σ τ σ σ τ στ τ U 5 oiatig te ltiplier ad η wit te two otrait repetively ti proble a te followig firt-order oditio: [ τ ]: [ τ ]: [ ]: = = η = η 6 Note tat tee firt-order oditio are idetial to te ae of te itegrated irer exept tat dg MC i replaed by η. Te evelope teore iplie tat = ση te age i expeted gro d profit aoiated wit a ireae i te oopolit offer of atity. Sie te oopolit a extrat all gro profit e will eate ti argial age i profit to te expeted argial ot of otpt σ MC to toe of te itegrated ae. Forally te oopolit ellig atity eal to G. Te profit-axiizig oopolit olve: akig tee firt-order oditio idetial i able to arge a fee ax G MC σ 7 Te firt-order oditio for ti proble iplie tat G' = σmc or tat η = MC. a relt ti eilibri i idetial to tat proded by te itegrated irer. C. oplete foratio Te preee of ioplete iforatio i largely repoible for idig te two-part trtre of ealt irae. oplete iforatio lead to a eod-bet eilibri bt oopoly wit two-part ealt irae alo aieve ti opetitive otoe. e deotrate te arget by

13 derivig ti relt i te otext of oral azard wi i ex pot ioplete iforatio. Te appedix add advere eletio or ex ate ioplete iforatio. Stdyig te oral azard proble reire iorporatig oe additioal oer eterogeeity. e otie to ae tat oer are idexed by [] ad ditribted iforly over ti iterval. e alo keep te aptio tat te fratio σ fall ik aely all oer for wo σ. Sik oer plae vale o te edial are good wile ealty oer do ot. However iforatio o te everity of ille i ioplete. Patiet wit lower vale of are iker bt te irer aot oberve ti. Terefore eve tog tey ay beefit fro ore irae ta te le ill patiet tere i o way for te irer to ake payet otiget o te derlyig ealt tate. Payet a oly be otiget o te oer oberved deiio to prae te edial good or ot. Ti ake it ipoible to ire all oer flly. Te relt i a eod-bet oltio were te irer arge opayet below argial ot. Ti relt i over-tilizatio relative to te firt-bet bt ti i a eod-bet ea of deliverig oe additioal irae i te fae of iforatioal iopletee. ll oer otie to be ex ate idetial; we relax ti aptio i te appedix were we tdy advere eletio. C. Te Typial Copetitive Proble Coider a repreetative opetitive irer praig edial are fro a opetitive good arket ellig at argial ot ad providig irae witi te iforatioal trtre otlied above. Te fir ooe a o-payet ad prei tat axiize oer tility bjet to a break-eve otrait ad ietive opatibility for te oer. Te irer kow te atity of edial are deaded by oer give te o-payet ad ioe aordig to. Te fir optiizatio proble a be writte a: 2

14 ax MC. t. MC E ad = d 8 oiatig te ltiplier wit te break-eve otrait te firt-order oditio a be expreed a: [ ]: E = MC E E [ ]: d = MC E E 9 Tee firt-order oditio illtrate te tadard trade-off betwee rik-bearig ad ietive i te preee of oral azard. Te left-ad ide of te firt order oditio for alway exeed te left-ad ide of te oditio for beae ad are dereaig i. Ti fat opled wit te two firt-order oditio iplie tat E MC E > E 7 Oberve tat E E E i te expeted effet o of a opeated ireae i te opayet. Sie te opeated dead for edial are i dowward-lopig 8 it follow tat E E E < ad < MC. tr ti iplie tat te argial tility of wealt will be iger ta i te firt-bet aordig to te firt-order oditio for irae. 7 d i a weigted average of were ore weigt i plaed o E it larger vale. 8 Te oer firt-order oditio for edial are optio i E =. Te firt-order effet of a opeated ireae i te o-payet i a ireae i bt o age i or. Terefore te oer t dereae edial are optio i repoe. 3

15 titively te oly way to provide irae i ti liited iforatio ae i to ide over-tilizatio by argig te oer a prie below argial ot. Terefore te beefit of irae t be traded off agait te ot of idig ditortio i te good arket. Ti lead to: Over-tilizatio relative to te firt-bet 2 Higer argial tility of wealt relative to firtbet ad 3 oplete irae. Copetitive arket deliver te eod-bet effiiet alloatio tat axiize oer well-beig bjet to te eooy iforatio otrait. C.2 Two-Part Healt rae wit Moopoly Two-part ealt irae eliiate deadweigt loe aoiated wit oopoly bt it aot olve te itrii iforatioal proble tat lead to oral azard i ti eviroet. a relt a oopolit wit ae to two-part ealt irae priig will ooe a alloatio of reore tat i eod-bet effiiet jt like te opetitive alloatio. Coider a irer wo i alo a oopoly provider of te good wit ertai dead. Te irer axiize profit bjet to a reervatio tility oditio for te oer. Defie U a te level of tility te oer wold attai if e refed te irae otrat ad failed to oe te edial are good. However e ay till ave a lai o te fir profit if e i a areolder. Te irer t olve: ax. t. MC E π d U t i traigtforward to prove te eaial eivalee betwee ti proble ad te opetitive oe o log a oer ow te fir. Forally if we defie π a te eilibri oopoly profit level te above proble i eivalet to: ax π d. t. MC E π 2 4

16 Sbtittig i te reervatio profit otrait allow to rewrite ti a: ax E MC E d 3 wi i exatly eivalet to te diplaed verio of te proble i 8. ore iforal bt perap ore illiatig proof deotrate exatly wy te oopolit ooe to olve te eod-bet Pareto proble. Te reervatio tility oditio a be firt-order approxiated by: d CS 4 were CS i oetized oer rpl. word te oopolit a extrat i total revee o ore ta gro oer rpl fro e of te good. Terefore te oopolit proble der two-part ealt irae priig i eivalet to: ax CS MC E 5 Ti i te eod-bet Pareto proble wi axiize oial rpl give te eooy otratig otrait. Te oopolit a axiize profit by firt axiizig gro oer rpl ad te extratig it. C.3 dvere Seletio Te bai logi of ealt irae a two-part priig alo old p der aoter oo failig of irae arket advere eletio. Or aalyi of oral azard deotrated tat a oopolit wit ae to two-part ealt irae a repliate te opetitive eilibri wit oral azard or ioplete ex pot iforatio. dvere eletio add ioplete ex ate iforatio. ti ae te irer a oberve eiter te everity of ille ex pot or te ex ate differee i te propeity of oer to fall ill. 5

17 i te ae of oral azard two-part priig aot reove te deadweigt lo aoiated wit ayetri iforatio bt it doe reove all te ireetal deadweigt lo aoiated wit oopoly. oter word a oopolit wit ae to te two-part otrat will do jt a well a a opetitive arket i te fae of ayetri iforatio. e ae tere are roially ill patiet type ad ot roially ill patiet type. Fir aot oberve oer type. Defie ad a te ditribtio of roially ill ad ot roially ill people. Te ealt ditribtio for te roially ill i aed to doiate te oter i te firt-order toati ee. irae otrat i a ex ate irae prei opled wit a ex pot opayet. Te appedix deotrate tat opetitio i Pareto-eivalet to oopoly we two-part ealt irae otrat are ed. C.4 Voltary Uirae dvere eletio or ore geerally ex ate eterogeeity allow to aalyze te ipat of irae o or relt. e ave ow trogot tat irae eliiate te deadweigt lo fro oopoly. Obvioly owever oopoly will otie to rede te welfare of te ired. t i traigtforward to ow tat te ired are te oly oer to be ared by oopoly ad tat te deadweigt lo fro oopoly i proportioal to te rate of irae. te tadard Rotild-Stiglitz fraework oidered i or appedix bot type prae oe irae. However if tere i a ot to providig irae ti ay ot be te ae. Sppoe tere i oe traatio ot or load fator o irae o tat a irer ot are eal to λ C were C repreet lai paid ad λ >. Up to ow we ave ipliitly aed tat λ =. Te preee of te load fator reate te poibility tat oe oer will ooe to forego irae. For or aalyi te partilar grop of oer ooig irae e.g. ig-rik ver low-rik i ot rial bt for oitey we otie wit te Rotild-Stiglitz odel i wi tere are roially ill ad ot roially ill patiet. 6

18 Sie te ot roially ill type reeive le oer rpl fro irae tey will be te firt to opt for irae. Sppoe terefore te load fator λ i ig eog tat irae i welfare-redig for te ot roially ill bt till welfare-iprovig for te roially ill. Uder opetitio te roially ill reeive fll irae wile te ot roially ill opt ot of irae ad itead pay argial ot for edial are we eeded. Te ipat of oopoly wit two-part ealt irae otrat are traigtforward: te welfare of te ired roially ill poplatio doe ot age by te arget give earlier i ti etio. partilar opayet rate are et optially ad te prei i ed to extrat oer rpl. However te oopolit will ow ell to te ired poplatio at te tadard oopoly prie beae tere i o irae opay ediatig te traatio. Ti relt i welfare delie for te ired. 9 Defie CS ad CS a te per apita oer rpl ejoyed by te ired der oopoly ad opetitio repetively. f ρ i te proportio of te poplatio ired der opetitio te total oietal lo fro oopoly i give by: ρ CS CS 6 9 Note oe rpriig featre of ti eviroet: eve tog oopoly lower welfare it igt ireae te rate of irae beae it lower te vale of beig ired. Ti doe ot alter te tility of te ot roially ill poplatio wi reai at it reervatio level eve tog it igt affet teir irae tat. Te effet o te rate of irae igt differ if tere i oe itittioal featre tat tabilize a poolig eilibri. a eviroet prei ireae old ae irae aog te ired wo are o te argi. See Tow et al 26 for a aalyi of opital erger ad rate of irae. 7

19 Deadweigt lo i zero if all oer ave at leat partial irae. f ot it i proportioal to te rate of oplete irae. D. oplete Market Power So far we ave oidered te ae of pre oteted oopoly. May ealt are arket are better approxiated by oopoliti opetitio. For exaple two drg opaie igt old patet o differet drg tat treat te ae dieae. Dotor ay bild ie relatioip wit teir patiet wo develop a preferee for oe pyiia over aoter. Patiet ay prefer to go to a opital tat i loet to teir oe. ll tee fator a reate prodt differetiatio i te id of oer. Market power relt bt it i ioplete. ti etio we add oopoliti opetitio to te oral azard iforatio trtre. Moopoliti opetitio age te ditribtio of reore relative to oplete oopoly bt leave itat te relt tat oopoliti opetitor ooe atity o a to axiize extratible rpl. oopoliti opetitor t be idfl tat er toer a defet to te oter fir. Ti liit te aot of rpl available for extratio. However oditioal o oer prae fro er e will otie to et atity o a to axiize teir rpl. To ditill te key idea ppoe we ave two oopoliti opetitor ad B ad two kid of oer wit oe tritly preferrig bt te oter tritly preferrig B. Bot prodt ave te ae argial ot of prodtio. Te fir are itegrated i te ee tat tey bot prode teir good ad provide irae otrat over te. Frter a wit ot patial odel of prodt differetiatio ae tat oer t ooe to e oe or te oter of te prodt bt ot bot tee igt be differet drg pyiia or opital wi aot be eaily ed wit toe of rival. Defie a tility for oer wo prefer ad 8

20 defie B iilarly. f a oer e te wrog good e derive tility i δ were δ <. Sie ea oer a oly oe oe of te good we a ae witot lo of geerality tat irer provide two irae otrat oe tat provide good ad oe tat provide good B. D. Te Seod-Bet Effiiet lloatio Clearly te effiiet alloatio provide ea oer wit er preferred good ad it aoiated irae otrat. Good are old at argial ot to te irer. Ea otrat axiize te tility of te oer bjet to te break-eve otrait of te irer. before te irer kow te atity of good j deaded by a oer of type j i ealt tate give te o-payet ad ioe aordig to j. Te optial otrat for te type j oer axiize: ax. t. j ad j MC j j = j j j MC E j j j j j j j d 7 Ti proble i idetial to te earlier ae of oral azard ad a a iilar oltio araterized by: [ ]: E [ ]: j = j E j j MC E d = j E MC E j j j j j j j j 8 Te irer et a o-payet below argial ot i a effort to provide oe irae. D.2 Eilibri wit Moopoliti Copetitio Te key differee betwee oopoliti opetitio ad te earlier ae of pre oopoly i i te oer reervatio tility level. Te pre oopolit ad oly to garatee te 9

21 oer a tility a e old derive witot oig ay edial are good. Te oopoliti opetitor o te oter ad a to garatee te tility e old derive fro te opetitor otrat. wit ot odel of oligopoly ti reervatio tility level deped o te abee preee ad atre of trategi beavior betwee opetitor. However ti doe ot affet te argial valatio of good oly te level of profit eared by te fir. Te diviio of reore aog te two fir ad te et of oer ave o ipat o effiiey. deed if type oer ow fir all profit extrated are retred to te oer fro wi tey were take. Te relt i te ae eilibri oberved der pre opetitio. j j itot lo of geerality we will deotrate ti reaoig for fir. Defie a te aot of good B B B B tat oer will e we offered te good B irae otrat. Fir te olve: 9.. ax d d t E MC B B B B B B B B = = π π Te deiioakig of te oter fir oly eter iofar a it affet te oer reervatio tility level. f oer ow teir repetive fir ti will ot eve affet te ditribtio of reore. rgig a we did i te ae of oral azard defie π a te optial level of profit tat olve te fir proble. Te proble i 9 a be eivaletly writte a:.. ax E MC t d = π π 2 2

22 Te diplaed verio of ti proble i idetial to te diplaed verio of te opetitive proble i 7. Ti deotrate tat oopoliti opetitio prode te ae alloatio a pre opetitio. D.3 Two-Sided Market Power Otoe ay ot be perfetly effiiet if bot te irae ad provider ide are araterized by ioplete arket power. te ae of bilateral oopoly bot ide otie to ave ietive to axiize oer rpl ad te divide it betwee teelve. However iperfet opetitio o bot ide a reate ie ditortio. For exaple tere ay be trategi ietive for exlive dealig wi i ofte oberved i paraetial arket. Speifi irer award low o-payet to a few drg i a peifi terapeti la. Ti te allow te to extrat ore favorable ter fro te afatrer beae tey a proie iger vole ale f Ellio ad Syder 23. e iplified te proble by oiderig irae poliie for a igle iovatio. Ti iplifiatio arifie o geerality we te irae arket i perfetly opetitive. Eve if ea irae poliy overed a large ber of poible terapie a perfetly opetitive irae idtry wit a large ber of irer old offer a variety of poliie tat overed te preferee of every oer. However wit a liited ber of irer bt a large ber of terapie it i poible tat oe oer igt prefer a et of terapie tat i ot well-overed. Ti poit a be deotrated wit a iple exaple. Sppoe tere are te terapie to treat a igle dieae ad two iovator iovator ell 9 of tee terapie wile iovator B ell oly oe. Tere i a igle irer ad te oer. Ea oer derive $ of rpl fro te terapy e prefer: Nie oer prefer oe of terapie wile te tet prefer B terapy. Sppoe iovator dead a exlive otrat wit te irer. Ti i a redible dead if all $9 of oer rpl i extrated ad if te iovator give te irer $5 of ti 2

23 rpl. ovator B aot at te offer. Te relt i tat tilizatio of B terapy i ieffiiet beae te patiet preferrig B a oly by it diretly ad ot trog a irae poliy. Ti lead to te typial oopoly proble ad te der-proviio it ooly iplie. Ti gget tat arket power i te irae idtry ay be te root ae of ieffiiet tilizatio rater ta arket power o te provider/iovator ide. Ti alo gget tat ieffiiey i te irae idtry will t agait te ability of irae to prode perfetly effiiet otoe. Noetele i atal pratie private irae otrat provide igifiat prie redtio o a large ber of terapie ad treatet eve tog te larget prie redtio igt be reerved for a few preferred drg or provider. Eve o te atal prie diot oberved lead to igifiat redtio i deadweigt lo ad iproveet i effiiey. E. ovatio ajor reao for oopolie i ealt are i te e of patet to eorage iovatio. ile patet iprove dyai effiiey two well-kow ore of dyai ad tati ieffiiey reai Savell ad va Yperele 998. Firt ietive to ivet i reear reai iadeate beae oopoly profit are le ta te oial rpl reated by te iovatio. Seod patet eorage iovatio at te expee of tati ieffiiey fro oopoly lo. Two-part ealt irae a olve bot tee proble i ealt are arket it liit tati ieffiiey by bidizig edial are ad at te ae tie deliver oial rpl to a oopolit i te for of te extrated prei. T it a prode better dyai ietive for iovatio eve wile it dereae te tati ot aoiated wit eoragig iovatio. Te oly dager arie ot fro patet protetio bt fro failre i te irae arket: if ealt irae i ieffiietly eap or over-provided de to goveret bidie for exaple te relt will be exeive aot of iovatio Garber Joe ad Roer 26b. 22

24 E. Te Effiiet lloatio t i well-kow tat opetitio doe ot prode firt-bet otoe wit iovatio. Terefore to allate te effiiet alloatio we t olve te Pareto proble. additio to te trtre developed earlier ppoe tat te good i etio t be developed trog reear. Soiety a ped reore r o te reear proe ad te probability of dioverig te ew good i ρ r. N U i axi tility witot te ivetio. Te firt-bet effiiet alloatio olve te followig eal weigt Pareto proble: ax r. t. ρ r ρ r σ σ σ σ MC σ ρ r r ρ r U N 2 Coditioal o te iovatio beig diovered te effiiet alloatio are all te featre of te firt-bet opetitive eilibri witot iovatio: fll irae ad tilizatio p to te poit were argial beefit eal argial ot. Forally we a araterize it ig te followig iplified firt-order oditio: = ρ' r = MC N [ σ σ U ] = 22 Te tird oditio ie to te iovatio proble tiplate tat te argial vale of ivetig i iovatio i eal to it argial opportity ot. Sie we are oiderig te ae of a igle iovatio we rle ot te poibility of irig agait te failre to iovate wi wold reire te poibility of traferrig reore aro te iovatio ad o iovatio tate. 23

25 E.2 Te Moopoly lloatio wit Two-Part Healt rae bove we owed tat te vertial itegratio of irer wit good-proder ad little ipat o te alloatio provided tat oopolit a egage i oliear priig. Terefore we aalyze ti proble i te expoitioally ipler otext of te itegrated irer-proderiovator. Defiig te iovator realized profit i te evet of diovery a d π ad aig oer ow te fir te itegrated iovator olve te proble: ax τ τ r ρ r. t. σ σ τ MC σ στ r d d τ π σ τ π U 23 U i axi tility for te oer wo ooe ot to otrat wit te iovator. Ti forlatio ae tat i te abee of diovery te fir i iply a opetitive irer earig zero profit. Coditioal o diovery ti fir fae te ae proble a te itegrated irer i Setio B. t are all it firt-order oditio bt add a eilibri oditio for iovatio a follow: [ τ ] : [ τ ] : [ ] : [ r] : ρ' r = MC = = MC σ τ MC σ στ = 24 By te ae arget ade i Setio B.2 we a ow tat = MC. Ti will te iply fll irae aordig to te firt-order oditio for τ ad τ. Ti iplie tat oditioal o diovery te proviio of irae ad te iveted good are Pareto-optial. t reai to ow tat ivetet i reear i alo effiiet. e will do o by owig tat te private retr to iovatio eal te oial retr. 24

26 Te private retr to iovatio i te ex pot retr eared by te iovator or. O te oter ad te oial retr to ivetio i te total oetized gai ejoyed by oer a a relt of te iovatio diovery: π d r d d r r MC π τ σ π τ σ Sie te oer reervatio tility otrait old at eality we kow tat: = d d d d MC π π τ σ π π τ σ 25 Takig firt-order approxiatio to ad we obtai: d π d π r r MC d d d d = π π π τ σ π τ σ Ti deotrate eality betwee te private ad oial retr to iovatio. E.3 pediet to Effiiet ovatio Te aalyi above oidered a reglated bidized ad opetitive irae arket. pratie owever eployer-baed ealt irae preia are ipliitly bidized beae tey are tax-exept. Ti affet te optial level of te irae prei geerally alog wit te ietive to iovate bt it doe ot affet te optial opayet or tati effiiey i te good arket. f oer fae le ta te fll prie of irae oopolit will be able to extrat oer rpl pl te vale of te prei bidy. However oopolit will otie to 25

27 ave ietive to et te o-payet o a to axiize extratible oer rpl. Te relt i tat prei bidie or taxe affet dyai effiiey bt ot tati ieffiiey wi te oopolit a ietive to aitai. Garber Joe ad Roer 26b ave arged ti logi gget tat prei bidie lead to over-iovatio. f te iovator a extrat total rpl i additio to te vale of te prei bidy te retr o iovatio i too ig relative to firt-bet. Te relt i too iovatio bt effiiet proviio of te iovatio tat exit. Notie tat we otie to ave te relt tat two-part priig erae tati loe fro oopoly eve i te otext of iovatio. dditioally a ore opliated odel of te iovatio proe old alo lead to ieffiiey. te tadard odel ed above iovator ogt to appropriate te fll vale of oial rpl. May aalyt ave poited ot tat patet rae pbli bidie ad oter iperfetio a alter ti relt o tat iovator ogt to reeive le ta oial rpl i te firt-bet alloatio. Oter i otrat ave epaized ow little iovator are able to appropriate. Ti i a diffilt etio to reolve i or otext beae otide of te iple odel preeted above tere are a great ay poible odel of te iovatio proe ea wit differet ipliatio. Depedig o te firt-bet rate of appropriatio ae to two-part ealt irae priig ay relt i ieffiietly ig profit. Ti affet te optial tax-adtrafer poliy tat old aopay a ftioig arket for ealt irae te oial plaer a do ietive to over-iovate by taxig te profit of efl iovator. Regardle of dyai ietive two-part priig trog ealt irae otie to ere tati effiiey altog it ay reire orretive to ere dyai effiiey a well. For otratig view i te otext of paraetial ee Garber Joe ad Roer 26a opared wit Pilipo ad Jea 26b. a broader otext ee Sapiro 27 opared wit Norda

28 F. Deadweigt Lo Redtio de to Preriptio Drg rae ti etio we e a tylized odel to allate ow ealt irae lower tati deadweigt lo i te US arket for paraetial were patet reate a oiderable aot of arket power. Speifially we etiate te peretage redtio i deadweigt lo by drg la tat wold obtai if we provided te average ired oer wit te average preriptio drg irae poliy. Ti allatio illtrate te epirial igifiae of or key idea tat ealt irae a igifiatly rede te deadweigt lo fro oopoly priig by lowerig argial prie for oer. e abtrat fro oral azard ad advere eletio i order to fo o effiiey loe fro oopoly aloe. Uig a liear approxiatio to te dead rve deadweigt lo aoiated wit a partilar age i prie ad atity i iply te area of te triagle or p oe 2 alf tie te redtio i prie tie te ireae i atity. Terefore te per apita deadweigt lo witot irae i: dq dp =.5 [ ][ ] DL Q Q P P oi oi oi oi 265 ere Q i atity of preriptio drg oed by ired oer wo fae prie P Q i dead wit perfet opetitio or argial ot priig ad i te oopoly oi ark-p o paraetial prie. Siilarly te deadweigt lo wit irae i: dq dp =.5 [ ][ ] DL Q Q P P i i oi oi 276 red oer fae a prie or opayet of P were i te are of ot bore oi by ired oer. Q i i te atity of preriptio drg oed by ired oer. Te ratio betwee deadweigt lo i te ired ad ired arket i give by: 27

29 DL DL Q Q = Q Q i oi i oi 28 ordig to te above eatio we a etiate te peretage redtio i deadweigt lo de to irae wit te followig paraeter: te are of total drg ot bore by te ired oer 2 te oopoly ark-p o paraetial prie 3 te peretage redtio i optio de to oopoly for ired oer Q Q i ad 4 te peretage Qoi redtio i optio de to oopoly for ired oer. Q To etiate we e data fro te 23 Medial Expeditre Pael Srvey MEPS to etiate te average rate of ot-arig by drg la for braded drg ed by te ired poplatio. Seod log-r geeri prie aed to be eal to argial ot are approxiately % of te prie arged for te orrepodig o-patet drg Lakdawalla Pilipo ad ag 26. T we ae tat te ark-p o paraetial prie i rogly 9%. e etiate te lat two atitie by ig etiated prie elatiitie fro te literatre. Te tadard teory of oopoly wold te iply baed o a 9% ark-p by oopolit a prie elatiity of ired dead arod. or te ivere of te arkp. e e ti elatiity Qi of dead to etiate : te age i atity of drg oed if ired oer are Q oi offered te average drg irae. Te elatiity of dead for te ired oer wo oly fae a fratio of te oopoly prie ay differ fro te optial oopoly elatiity. However Golda et al 24 ave epirially etiated ti elatiity to be.6. e e ti elatiity of 28

30 Q dead to etiate : age i atity of drg oed if ired oer faed Q i argial ot priig. Baed o tee etiate table ow te peretage redtio i deadweigt lo de to irae for te top drg lae. Table : Peretage redtio i deadweigt lo de to irae for te top drg lae. Drg Cla Market Sare verage Cot Sarig Peretage Cage i Deadweigt Lo Top Drg Clae Horoe 5% 29% 9% CNS get 3% 9% 96% tiyperlipidei get 3% 2% 96% Pyoterapeti get 2% 8% 97% Cardiovalar get % 28% 9% Gatroitetial get % 5% 98% Repiratory get 9% 2% 96% ti-ifetive 7% 25% 93% Topial get 5% 24% 93% Coaglatio Modifier 2% 4% 99% ll Braded Drg % 2% 96% Table ow tat te typial irae poliy rretly available i te US a igifiatly rede te deadweigt lo fro oopoly priig of braded paraetial prodt. e etiate tat te typial irae poliy rede deadweigt lo by 96% for all braded drg. Te peretage age i deadweigt lo rage fro 9% for oroe wit te leat geero irae overage to 99% for oaglatio odifier wit te ot geero irae overage. 29

31 G. Colio ad pliatio for Poliy Two-part priig i well-kow a a oltio to te deadweigt lo fro oopoly bt it i freetly ipratial. ealt are arket te oberved trtre of irae otrat provide a ea for aievig te effiiet otoe aoiated wit two-part priig. ile it i ot a paaea for iforatioal proble i te irae arket it a be a effetive oltio to tati deadweigt loe fro oopoly a we ave ow. By partially deoplig oopoly profit fro oer prie two-part ealt irae a play a iportat role i te effiiet delivery of ealt are eve i te preee of arket power. review of ealt are arket i te late 99 igligt tree iterrelated tred: a ireae i aaged are a etod of fiaig ad deliverig are; orizotal oolidatio witi irer opital ad pyiia arket ad blrrig of te vertial dititio betwee tee arket Gayor ad Haa-ilo Or aalyi a iportat ipliatio for aalyzig te potetial oeee of ea of tee tred. Firt or aalyi gget tat te reet ireae i orizotal oolidatio ad arket power of ealt are provider igt ot igifiatly rede oial welfare. Te optial deig of irae otrat a liit or eliiate deadweigt loe fro oopoly i te good arket. To be re oopoly a age te ditribtio of reore if patiet are ot proportioate areolder. However oiety a aieve ay ditribtio it like alog te Pareto-frotier iply by taxig profit ad traferrig te to te appropriate oer. Breakig p te oopoly ay ot be eeary ad eiter i diret prie reglatio. Te retr to breakig p a oopoly are proportioal to te rate of irae oberved i te arketplae. Seod or aalyi gget tat te rie i aaged are ad vertial itegratio of ealt are arket experieed i te 99 provide ie beefit to oiety. te preee of ealt irae deadweigt lo fro oopoly arie oly if: ealt are provider are eparated fro 3

32 irer; ad provider e iple liear priig otrat wit irer. f tee oditio obtai breakig p a oopoly or oligopoly i oially deirable a i Gayor Haa-ilo ad Vogt 2. However te ae otoe a be aieved by eoragig or reirig vertial itegratio betwee te oopolit ad te ealt irae arket. effet givig ore vertial arket power to a ealt are oopolit a atally rede deadweigt lo i ti ae. Fro a poitive poit of view or aalyi gget tat vertial itegratio i ealt are ay be otivated i part by te iproved ability of a itegrated fir to prie-diriiate. Ti a elp to explai wy oe paraetial opaie ave oe to ivet i paray beefit aager ad wy ealt-aiteae orgaizatio itegrate ealt-are proviio wit irae. ovatio i of obvio iportae i ealt are arket. Or aalyi ow tat two-part ealt irae priig alo iprove dyai ietive beae it allow patet oopolit to extrat te axi aot of oer rpl aoiated wit teir ivetio. Te relt i iproved tati ad dyai effiiey. ti otext loger patet ay ave aller oial ot i ter of deadweigt lo fro oopoly bt oiderable oial beefit. Take togeter tee arget gget tat opetitio ay do little to iprove tati effiiey ad tat opetitio eve oopoliti opetitio ay do ar to dyai effiiey. iportat aveat ere owever i tat patet rae or goveret bidie to te irae arket a lead to overiovatio abet orretive Pigovia taxe o iovator profit. Eve o two-part priig trog ealt irae opled wit a orretly oe Pigovia tax will otie to ere bot tati ad dyai effiiey. Te deig of pbli ealt irae ofte oider te trade-off aog optial rikbearig oral azard ad advere eletio. However or aalyi gget tat it ogt to oider ow te two-part ealt irae otrat a bet axiize oial rpl. optially deiged pbli ealt irae ee wold et o-payet at or below argial ot depedig o te extet of oral azard. Te diviio of reore aog oer a te be 3

33 deteried by te edle of preia wi allow te goveret to extrat a or a little oer rpl a it ooe. 32

34 ppedix: dvere Seletio To odel advere eletio ppoe tat oer are eterogeeo ex ate. Tere are roially ill patiet type ad ot roially ill patiet type. Fir aot oberve oer type. Defie ad a te ditribtio of roially ill ad ot roially ill people. Te ealt ditribtio for te roially ill i aed to doiate te oter i te firtorder toati ee. irae otrat i a ex ate irae prei opled wit a ex pot opayet. Te Copetitive Soltio poolig eilibri i ot poible for te al reao Rotild ad Stiglitz 976: give ay ptative poolig eilibri tere i alway a profitable otrat tat attrat oly te low-rik ired. Terefore if a eilibri exit it t be a eparatig eilibri. te opetitive irae idtry ooe two otrat tat axiize te welfare of ea type of aget bjet to ietive opatibility otrait erig te otrat are oe by te orret aget ad break-eve otrait. Te otrat for te roially ill olve: 29 ]: [ ]: [.. ax p d d d t d β γ Ti proble a te followig firt-order oditio: 33

35 [ ]: E [ ]: E γe E = β E γe E p E = β E p 3 Notie tat if te ietive otrait fail to bid tee firt-order oditio are idetial to te eod-bet eilibri wit oral azard. Ti obervatio reveal ow te advere eletio eilibri i affeted by te itrodtio of oral azard. te abee of oral azard fll irae i te beark otoe. Fll irae i ever ietive-opatible beae ig-rik oer alway prefer te fll irae otrat offered to te lower-rik lower-ot oer. Ti explai wy i te tadard Rotild-Stiglitz ettig advere eletio alway ipat otoe. ti ae owever te eod-bet oral azard otrat ay oetie be ietive-opatible. Sppoe for exaple tat te eod-bet otrat ivolve a very ig opayet for te low-rik beae tey ave a igly elati dead ad relatively little irable rik. f o it i poible tat te igrik ired wold prefer teir ow eod-bet otrat to tat offered to te low-rik. ti evet advere eletio wold ave o ipat beae ietive opatibility eerge of it ow aord de to oral azard. Ti wold leave wit te oral azard eilibri otlied above. f owever te eod-bet otrat are ot ietive-opatible we obtai te typial Rotild- Stiglitz oltio i wi te ig-rik oer reeive teir eod-bet otrat bt te low-rik oer reeive oetig wore ta teir eod-bet. Te idiret tility oferred by a peifi otrat i defied by v ad v for te roially ill ad ot roially ill patiet repetively; tee are defied a follow. v ax d 3 e ipoe two aptio tat ake ti eviroet iilar to te Rotild-Stiglitz oe. Firt te roially ill are willig to pay ore for a give age i te opayet rate i te ee tat: 34

36 d d > 32 v v d d Ti i te typial igle-roig property fro Rotild ad Stiglitz 976 aalyi of advere eletio. 2 Seod a give age i te o-payet rate a a bigger ipat o a fir profit o tat: d d d d π = π = E MC E = E MC > d d π = 33 Figre illtrate te eparatig eilibri i -pae. Te rve Z ad Z repreet te zero-profit rve for te ot roially ill ad roially ill repetively. v i te idifferee rve for te roially ill taget to te zero-profit lie ti repreet te optial i.e. eod-bet otrat tat i poible der oral azard. Oberve tat if te eod-bet otrat for te ot roially ill fall o te rve eget tere i o advere eletio proble beae bot eod-bet otrat are ietive-opatible. 2 d = d E w E. Firt-order toati doiae iplie tat te erator i iger for w te roially ill. e ae ti effet otweig te fat tat te argial tility of wealt ay alo be iger for te roially ill. 35

37 Z Z V B MC Figre : Eilibri wit advere eletio ad oral azard. Now oider te ae were advere eletio a a ipat: if te eod-bet otrat for type fall o te rve eget B. ti ae te roially ill will reeive teir eod-bet otrat wile te oter type will reeive te otrat at te iteretio of v ad Z. Eilibri wit Two-Part Moopoly Priig oopolit wo arge a pfrot prei ad a ex pot opayet axiize profit bjet to reervatio tility oditio i.e. partiipatio otrait ad ietive otrait. 36

38 .. ax d d d d d d t d MC d MC 34 Sie ti proble i additively eparable i ad te joit profit-axiizatio proble i idetial to two eparate proble i wi te oopolit axiize profit over ea otrat. Speifially te axiizatio proble i 34 i eivalet to te pair of axiizatio proble below:.. ax d d d t d MC 35 37

39 .. ax d d d t d MC 36 i te oral azard ae it i traigtforward to ow tat tee proble yield Pareto-eivalet alloatio to te opetitive proble. itot lo of geerality we ow ti for te type otrat. To et ot ditribtioal effet we ae tat te repreetative type oer old a lai o all profit tat flow fro otrat wit type oer. Tere ay ot be a well-defied eilibri i te ae of advere eletio bt for or prpoe it ffie to oider te ae were a eilibri exit. f o eilibri exit deadweigt lo fro oopoly i defied. Defie π a te eilibri profit aoiated wit te oltio to 36. f o te 36 i idetial to a proble i wi te fir axiize oer tility bjet to a reervatio profit otrait ad te ietive otrait. Ti proble will alo yield profit eal to π ietive-opatibility ad tility at leat eal to :.. ax d MC d d t d π π 37 Sbtittig te reervatio profit otrait ito te oer objetive ftio yield: 38

40 38.. ax d d t d E MC E Ti proble i idetial to te diplaed verio of te opetitive proble i Terefore te oopoly alloatio i idetial to te opetitive oe. 3 Uder opetitio ad. MC p = = d p 39

41 Referee rrow K. J "Uertaity ad te elfare Eooi of Medial Care." eria Eooi Review Bagarte. 25. "Califoria Healt Care Market Report 25." Califoria HealtCare Fodatio. Califoria HealtCare Fodatio. Ellio S. F. ad C. Syder 23. "Cotervailig Power i oleale Paraetial." MT orkig Paper. Cabridge M: MT. Garber. C. Joe ad P. Roer 26a. "rae ad etive for Medial ovatio." For for Healt Eooi ad Poliy 92: rtile 4. Garber. M. C.. Joe ad P. M. Roer 26b. "rae ad etive for Medial ovatio." Natioal Brea of Eooi Reear orkig Paper 28. Cabridge M: Natioal Brea of Eooi Reear. Gayor M. ad D. Haa-ilo 999. "Cage oolidatio ad opetitio i ealt are arket." Joral of Eooi Perpetive 3: Gayor M. ad D. Haa-ilo 22. "Cage Coolidatio ad Copetitio i Healt Care Market." Te Heiz Sool Caregie-Mello orkig Paper Pittbrg P: Te Heiz Sool Caregie-Mello. Gayor M. D. Haa-ilo ad. B. Vogt 2. "re viible Had Good Had? Moral Hazard Copetitio ad te Seod-Bet i Healt Care Market." Joral of Politial Eooy 85: Golda D. P. G. F. Joye J. J. Eare J. E. Pae M. D. Soloo M. Laori P. B. Lada ad S. M. Tet 24. "Paray beefit ad te e of drg by te roially ill." Jaa 299: Lakdawalla D. T. J. Pilipo ad R. ag 26. "telletal Property ad Marketig." Natioal Brea of Eooi Reear orkig Paper Cabridge M: Natioal Brea of Eooi Reear. Levy R "Te paraetial idtry. diio of opetitive ad atitrt ie i a eviroet of age." Brea of Eooi/Federal Trade Coiio taff report. Brea of Eooi/Federal Trade Coiio. Martiez B. 22. Medo fid tat old tie bid i otrat wit paret Merk after pioff it agree to aitai arket are for Merk ediie. Te all Street Joral. New York. Sboittee o Healt of te Hoe Coittee o ay ad Mea 24. Hopital Priig ad te Uired. Hoe Coittee o ay ad Mea. Mar Norda "vetio Growt ad elfare." Cabridge M: MT Pre. Norda. D. 24. "Speteria Profit i te eria Eooy: Teory ad Meareet." Natioal Brea of Eooi Reear orkig Paper 433. Cabridge M: Natioal Brea of Eooi Reear. Oi. Y. 97. " Dieylad Dilea: Two-part Tariff for a Mikey Moe Moopoly." Qarterly Joral of Eooi 85: Paly M "Te Eooi of Moral Hazard: Coet." eria Eooi Review 583: Paly M. V. 25. "at Meare of Cot ad Beefit for Drg i Cot Effetivee alyi." arto Sool orkig Paper. Piladelpia P: arto Sool. Pilipo T. J. ad. Jea 26a. "Srpl ppropriatio fro R&D ad Healt Care Teology eet Proedre." Natioal Brea of Eooi Reear orkig Paper 26. Cabridge M: Natioal Brea of Eooi Reear. 4

42 Pilipo T. J. ad. B. Jea 26b. "Srpl ppropriatio fro R&D ad Healt Care Teology eet Proedre." Natioal Brea of Eooi Reear orkig Paper 26. Cabridge M: Natioal Brea of Eooi Reear. Rotild M. ad J. E. Stiglitz 976. "Eilibri i Copetitive rae Market: Eay o te Eooi of perfet foratio." Qarterly Joral of Eooi 94: Sapiro C. 27. Patet Refor: ligig Reward ad Cotribtio. Natioal Brea of Eooi Reear NBER orkig Paper. Savell S. ad T. va Yperele "Reward ver telletal Property Rigt." Retrieved Deeber 998 fro SSRN: <ttp://r.o/abtrat=45292> or DO:.239/r <ttp://dx.doi.org/.239/r.45292> Tow R. D. oley R. Felda ad L. R. Br 26. "Te elfare Coeee of Hopital Merger." Uiverity of Mieota orkig Paper. St. Pal: Uiverity of Mieota. rigt B. D "Te Eooi of vetio etive: Patet Prize ad Reear Cotrat." eria Eooi Review 73: Zekaer R. 97. "Medial rae: Cae Stdy of te Tradeoff Betwee Rik Spreadig ad ppropriate etive." Joral of Eooi Teory 2: