Vol., No.9, 1110-1119 (010) doi:10.436/ealt.010.9164 Healt Effect of uer fee on atient welfare and efficiency in a two tier ealt care market Eugenia Amorfu Kwame Nkruma Univerity of Science and Tecnology, Kumai, Gana; eamorfu@gmail.com Received 6 Marc 010; revied 7 May 010; acceted 9 May 010. ASTRACT Ti i a teoretical aer examining te effect of uer fee on atient welfare and ocial welfare under tree form of rovider reimburement: full cot, roective ayment and cot aring. Te aer extend Rickman and McGuire (1999) by introducing uer fee to te ublic ector and maintaining te aumtion tat rovider can work in bot te rivate and ublic ealt ector. Contrary to reviou tudie, ti tudy ow tat efficiency i oible under te full cot reimburement. Te aer alo ow te condition under wic efficiency i oible under eac reimburement ceme. Patient welfare can imrove wit te introduction of uer fee wen ervice in te ublic and rivate ector are comlementary. Keyword: Uer Fee; Two Tier Healtcare; Mixed Financing; Proective Payment; Cot Saring 1. INTRODUCTION Many countrie ave te two tier ealt care ytem: te coexitence of ublic and rivate ealt care ector. And over te year, ublic ealt care reform in many countrie a involved a witc from fully financed ytem to mixed one [1,]. Suc a witc i oberved in bot indutrialized and develoing countrie. Te mixed financing ytem involve making te atient bear at leat art of te cot of care rovided in te ublic ector. Te intention i to artly relieve te government of te burden of funding ublic ealt care and at te ame time reduce exceive ue of care tat migt exit under te fully funded ytem. Variou ayment ceme are alo ued in te ublic ealt ector to ay ealt care rovider. Te uroe of ti aer i to find te imact of atient direct ayment at te oint of urcae, in te ublic ealt ector, on te efficiency of tree ayment ceme: full cot reimburement, roective ayment and cot aring in a two tier ealt care ector. Examle of mixed financing ytem in indutrialied countrie conit of a combination of comulory ocial ecurity ytem covering a ackage of eential ervice and rivate inurance olicy to cover te ret. Te atient ten a to ay remium and co-ayment [3]. Some of te indutrialied countrie tat ave adoted ti include Autralia, Italy, and te United State (in te Medicare lan) [3]. In develoing countrie te mixed financing ytem in general involve introduction of uer fee. Many Sub-Saaran countrie uc a Cote d Ivoire, Kenya, and Nigeria ave adoted ti ytem. Tere i coniderable teoretical literature on te effect of rivate inurance (wit co-ayment) on uality of care and te efficient roviion of ervice (e.g., [4-8]. Wile tee analye centred more on te effect of inurance on uality and efficiency of ervice tan on te reimburement ceme, oter examined te role of different reimburement ceme in te efficient roviion of ervice [9-17]. Te uetion ten i doe te effect of mixed financing ytem on efficiency deend on te tye of reimburement ceme to rovider. To anwer te uetion, te current aer extended a model on a two tier ealt care ytem in [16] tat examined te effect of te rivate ealt care ector on te efficiency of rovider reimburement ceme. Te extenion involve te introduction of a uer fee to te ublic ector. Reference [16] in turn, wa an extenion of [18], wic examined te effect of reimburement ceme on te uly of ervice in te ublic ector. In teir tudy, te ublic ealt care wa a fully funded ytem (e.g., te National Healt Service in te ritain) and o te atient did not ay for te ervice received. Reference [16] extended [18] by including a rivate ector wile maintaining te full funding ytem in te ublic ector. Te ecific interet in te aer ten i to examine ow teir reult of te two reviou aer would be affected wen a uer fee i included in te ublic ector. Coyrigt 010 SciRe. Oenly acceible at tt://www.cir.org/journal/health/
E. Amorfu / HEALTH (010) 1110-1119 1111 Earlier tudie tat examined ealt roduction in rivate and ublic ector wit uer fee in te ublic ector include [18-0]. Reference [18] reented an emirical model in wic effort wa not obervable and atient ad to cooe medical contract for ealt care roviion from government and miion oital in te Cameroun. Reference [0] alo reented an emirical tudy, wic examined ow te introduction of uer fee to te ublic ector affect uality and acceibility of ervice. In a teoretical model in wic ublic ector ervice are covered artly by comulory ocial inurance, artly by rivate inurance and artly by out-of-ocket, [1] examined te condition for otimal rate of ocial inurance and rivate coinurance. Following [16] te current aer focue on tree form of rovider-reimburement ceme: full-cot reimburement, roective ayment and cot aring.. METHOD Ti i a model of mixed ealt care market, ublic and rivate, tat allow yician to work in bot ector. Let rereent ublicly rovided ealt care received by a rereentative atient and rereent rivately rovided ealt care. Te atient receive benefit, (,), from treatment and ay for it according to te marginal benefit it rovide: (.), for treatment in te rivate ector and (1-) (.) for treatment in te ublic ector, were 0 < < 1 i te fraction of te fee aid by te government. Tee fee do not ave to eual te full cot of treatment. Te atient could ave artial inurance and bear only art of te cot of treatment. Wat i imortant i tat te atient bear ome cot for treatment in bot ector. (.) a oitive marginal roduct, wit uniue maxima in and, < 0, < 0. Treatment, and, can be comlement, (.) > 0, ubtitute, (.) < 0 or unrelated (.) = 0. Treatment are comlement if, for examle, te yician ue te ublic ector to reuet te atient to do ome tet in te rivate ector 1 Note tat N can be negative wen ervice are comlement and i very large. Ti cae i not examined. I do not ue te aumtion in [16] tat atient do not earc among alternative yician but becaue yician care about te welfare of atient tey do not carge a monoolit rice. In te current model, te yician care for te atient rereent i care for etic of treatment.ti revent te yician from carging monoolit rice. A own in (11) te yician would carge a monoolit rice if U N = 0. Ti i conitent wit [3], were te yician i contrained by atient information. In [3] even toug, atient cannot evaluate te marginal benefit from treatment from a given yician tey can evaluate te abolute utility uon treatment. Patient can oberve te utility of oter atient after treatment. If atient of one yician end u wit a lower utility on average tan oter ten te yician looe atient. 3 In order to avoid te imlied reuirement tat te marginal cot in te two ector be eual, I do not aume contant marginal cot for te roviion of treatment a in [16]. to el wit diagnoe in te ublic ector. Wen te yician ue, for examle, te rivate ector to treat an illne tat can be treated in te ublic ector ten and are ubtitute. Te atient net benefit i: N (, ) (, ) (, ) (1 ) (, ) (1) Wit te excetion of te lat term on te RHS, wic rereent te fee in te ublic ector, (1) i identical to te atient net benefit in [16]. Te marginal net benefit are: N(, ) (, ) (1 ) (, ) (, ) 0 1 () N (, ) (, ) (1 ) (, ) 0 (3) Pyician are regulated and are often exected to follow a code of etic wit te uroe of taking te atient interet into account wen cooing treatment. Following [] it i aumed tat te yician care about te etic of treatment. Tu, te yician care about te well-being of i atient, N(,), a well a te rofit of i ublic oital, and rivate ector rofit, : R ( ) (1 ) (, ) c ( ) (4) were R() i te revenue tat te ublic oital receive from te government. Again wit te excetion of (1 ) (,) (4) i identical to te ublic oital rofit in [16]. Te rivate rofit, owever, i te ame a tat in [16]: (, ) c( ) (5) were c (i) > 0, c (i) > 0 (i =, ), 3 and and ave uniue maximum in and reectively, te marginal rofit are: (1 ) (, ) or < 0 (6) ' R ( ) (1 ) (, ) (, ) c '( ) or > 0 (7) were R () > 0. (, ) 0 (8) (, ) (, ) c'( ) 0 (9) Te yician utility function i U(,, N), wit U N > 0, U 0, U 0, U NN < 0, U 0, and U P P 0. Te yician cooe and to maximize i utility. Te firt order condition are: U U U N 0 (10) N U U U N 0 (11) N Coyrigt 010 SciRe. Oenly acceible at tt://www.cir.org/journal/health/
111 E. Amorfu / HEALTH (010) 1110-1119 U U N U (1) N y ubtituting (1) into (10) and rearranging roduce: N MRS N N N (13) were MRS N = U N /U > 0. E.13 define a locu {,} tat maximize te yician utility. Wit te excetion of te econd term on te RHS, (13) i identical to wat [16] obtained. Ti econd term aear ere becaue te incluion of a fee in te ublic ector make, wic i zero in [16], oitive, negative or zero, in te current model, deending on weter and are comlement, ubtitute, or unrelated reectively. Te term in bracket are te magnitude of te loe of te rivate ector io-rofit ( / ) and te atient indifference curve (N /N ). Te welfare function, W(, ) = (, ) c() c(), i ued to find efficiency under te variou reimburement ceme. It i aumed tat te welfare function i concave and a uniue maxima in and. Efficiency reuire tat te following firt order condition for te maximization of te welfare function are atified: (, ) c 0 (14) (, ) c 0 (15) 4 Te tree yician reimburement rule in te ublic ector and teir effect on euilibrium and rovided by te yician are now examined. Te reimburement rule are full-cot reimburement, roective ayment, and cot aring. Te atient in [16] did not ave to ay fee in te ublic ector and o te full-cot reimburement involved te government roviding enoug revenue to cover te cot of roduction. In te current model, owever, te full-cot reimburement, involve te ublic oital receiving R() from te government to cover art of te cot not covered by te uer fee. Proective ayment involve te government giving a fixed amount of revenue, G, to te oital regardle of te total cot of roduction and of te total fee collected. Te cot-aring rule i a combination of roective ayment and cot reimburement. Te government give fixed revenue, G, and ten ay for a fraction of te cot of roduction. Under eac rule, (13) i ued to examine 4 were c and c rereent te marginal cot of and reectively. 5 ecaue te marginal net benefit in ti model differ from toe in Rickman and McGuire te atient indifference curve in ti model are alo different. Te indifference curve in Rickman and McGuire loe downward wen and are ubtitute and uward wen tey are comlement (U-aed indifference curve). In Rickman and McGuire N >0, weter and are ubtitute or comlement; N > 0 wen tey are ubtitute and N < 0 wen tey are comlement. ow te and coen by te yician affect otimality from te oint of view of te atient and ociety. Te atient indifference curve are downward loing for bot comlement and ubtitute 5. Ti i becaue te loe of te indifference curve i N /N and wit N > 0, N > 0 regardle of te relationi between and. Figure 1(a) and 1(b) ow te io-rofit for te yician rivate rofit. Te loe of te io-rofit (- / ) deend on weter treatment are ubtitute or comlement. A own in (8) and (9), i oitive wen treatment are comlement and negative wen tey are ubtitute; i oitive wen i very mall and become negative a it i increae. Tu, wen treatment are ubtitute, te io-rofit loe uward wen i mall and downward wen increae wit rofit increaing a fall. Te ooite occur wen treatment are comlement. Wen treatment are comlement te io-rofit loe downward wen i mall and uward a increae wit rofit increaing in. Tee are own in Figure 1. 3. RESULTS AND DISCUSSION 3.1. Full Cot Reimburement Under ti rule, te government rovide te revenue reuired to cover art of te cot of roduction tat te uer fee could not cover. Hence = 0 and o = 0; i.e., te yician cooe to maximize ublic oital rofit. Euation (13), ten, become: N 0 MRS N N (16) N Rearranging (16) roduce: MRSN N N (17) MRSN N N Notice tat wen = 0, te two loe in bracket in (16) are eual, and te reult are identical to toe in [16], i.e., te yician cooe and to euate te loe of te io-rofit and te atient indifference curve. Suc reult i oible in te current model if and are unrelated, i.e., if (, ) = 0 imlying tat = 0. It i of interet to examine te otimality of euilibrium and from te atient and ociety erective wen ervice are comlement, > 0, and wen tey are ubtitute, < 0. E.17 ow tat in euilibrium te difference between te loe of te iorofit and indifference curve deend on te ign of. Wen treatment are ubtitute, < 0, te io-rofit curve i teeer tan te atient indifference curve. Te reulting lower te atient welfare comared to [15] a well a [16]. Reference [15] owed tat in te ab- Coyrigt 010 SciRe. Oenly acceible at tt://www.cir.org/journal/health/
E. Amorfu / HEALTH (010) 1110-1119 1113 (a) (b) (c) Figure 1. (a) Private io-rofit curve for ubtitute; (b) rivate io-rofit curve for comlement; (c) atient indifference curve for ubtitute and comlement. ence of a rivate ector and a uer fee, te otimal coen by te yician coincide wit wat te atient would cooe under full information, i.e., at te oint were net marginal benefit i zero. However, by including te rivate ector, [16] owed tat te yician reallocate treatment between te rivate and ublic ector uc tat te atient marginal net benefit in euilibrium i oitive; ence, from te atient erective, te coen by te yician i ub-otimal. In te current model, te incluion of a uer fee furter increae te atient marginal net benefit. Te atient, ten, get le and lower welfare tan in [16]. Figure (a) ow te euilibrium treatment from eac ector wen treatment are ubtitute. For comlement N > 0, N > 0 and > 0 and o in euilibrium te atient indifference curve i teeer tan te io-rofit. Te atient, ten, receive le uly of bot ervice tan e would ave coen imelf. Ti i contrary to [16] were te atient received overuly of and underuly of. It i tu not clear if te atient i wore off or better off in ti model tan in [16] wen ervice are comlement. Te euilibrium i own in Figure (b). Te difference between te ign of in [16] and te current aer make an imortant oint. Wit = 0 in [16], te uantity of coen by te yician doe not affect te rofit of te ublic oital. Te introduction of uer fee in te current aer, owever, make te ublic oital rofit deendent on te uantity of ervice ulied in te rivate ector wit ublic rofit decreaing in wen ervice are ubtitute and increaing wen ervice are comlement. Wen ervice are ubtitute, te two ector comete for ervice and o every unit of rivate treatment ulied rereent a lo of fee to te ublic ector. Wit comlementary ervice, owever, te two ector become artner and o an increae in uly of rivate treatment i accomanied by an increae in uly of ublic treatment and tu increae te amount of fee received by te ublic oital. Since te yician i agent to te ublic a well a te rivate oital, a cange in te yician beaviour tat deend on te relationi between te ervice rereent te conflict of interet tat exit in te agency relationi. Suc conflict of interet can adverely affect te ublic oital if te yician ut more weigt on rivate rofit tan ublic rofit wen ervice are ubtitute. Wen ervice are comlement te two oital become artner and o any conflict of interet i eliminated. Tu, te tandard notion tat yician a incentive to create artificial ortage in te ublic ector in order to increae ervice in te rivate ector i relevant wen ervice are ubtitute. Te efficiency of te euilibrium i now conidered by uing (16): Coyrigt 010 SciRe. Oenly acceible at tt://www.cir.org/journal/health/
1114 E. Amorfu / HEALTH (010) 1110-1119 (a) (b) Figure. (a) Full cot euilibrium for ubtitute; (b) full cot euilibrium for comlement. N 0 MRSN N N (16) y ubtituting (9) into (16) and rearranging (16) become: MRS N v (18) MRS N N N were v = c. Auming efficiency in te rivate ector, v = 0, it i of interet to find out if efficiency in te ublic ector i alo acievable. Ti i done by etting v = 0 and ubtituting (), (3), (6) and (8) into (18) 6 Note tat rice elaticity of demand for i: and olving for : (1 ) 1 (1 ) (1 N ) MRS MRSN (19) Te ign of deend on weter ervice are comlement or ubtitute a well a on te ize of MRS N. For ubtitute, < 0 < c wen MRS N 1 and for comlement, < 0 < c i oible wen MRS N < 1. However, > 0 c i oible wen ervice are ubtitute and MRS N < 1 or wen ervice are comlement and MRS N > 1. For comlement wen MRS N = 1, < 0 < c wen > and demand for i inelatic 6. Similarly, > 0 c wen < and demand for i elatic. MRS N = 1, mean tat te yician ut eual weigt on te ublic oital urlu and atient utility, wen cooing treatment. Reference [15], call ti beaviour erfect agency. Recall tat MRS N = U N /U, and o MRS N >1 wen te yician ut more weigt on te atient net benefit tan ublic oital urlu. Similarly, MRS N < 1 wen te yician ut more weigt on te ublic oital urlu tan te atient net benefit. A decribed in [15], uc imerfect agency i likely, becaue te oital often a a tronger bargaining ower on te yician tan te atient. Hence te analyi will focu on te cae were MRS N 1. Perfect agent i ued to refer to te cae in wic MRS N = 1 wile imerfect agent refer to te cae in wic MRS N < 1. For ubtitute, (19) ow tat wen te uly of i efficient te yician overulie if e i a erfect agent. In te ame way te yician can overuly wen for comlementary ervice e i an imerfect agent or i a erfect agent, >, and demand for i inelatic. For bot ubtitute and comlement efficiency in bot ector can be ruled out under tee circumtance. However, efficiency i oible wen roviding ervice tat are ubtitute and te yician i an imerfect agent. Wen ervice are comlement erfect agency combined wit elatic demand for and a le uly of tan i reuired for efficiency. Tee reult are imortant in everal reect. Firt, contrary to [16], were efficiency in bot ector i not oible under te full-cot reimburement rule, efficiency in bot ector i oible in te current model under te full cot. Ti give credibility to te argument tat cot control olicy on te demand-ide in te form of uer fee, coinurance, and deductible i eential to reducing te exceive ue of care tat exit under te full cot reimburement ceme wit full inurance in te ublic ector. However, even toug efficiency i Coyrigt 010 SciRe. Oenly acceible at tt://www.cir.org/journal/health/
E. Amorfu / HEALTH (010) 1110-1119 1115 oible it i acieved at te exene of te atient welfare. Ti i not urriing becaue te uer fee force te atient rater tan te rovider to internalize any externality tat exited in te market. A already exlained, te uer fee reduce te euilibrium uly of ervice and ti make te atient wore off. Secondly, imerfect agency i reuired for efficiency. Unlike [16] a well a [15] were te agency role i not able to acieve efficiency under full cot reimburement, imerfect agency i crucial for efficiency in te current model. In [16], efficiency in te rivate ector i only acievable at te exene of overuly of ervice in te ublic ector. Te oibility of efficiency in te current model ten imlie tat wen ervice are ubtitute, te introduction of uer fee in te ublic ector contraint te yician from overulying ervice to te extent of ulying te amount tat maximize ocial urlu a long a te yician i an imerfect agent. Te uer fee ten tranfer any cot caued by te imerfection of te agency unto te atient. Tirdly, te elaticity of demand for ublic ervice i imortant for efficiency wen ervice are comlement. For comlementary ervice, te uer fee maximize ocial urlu by reducing overuly a long a te yician i a erfect agent wen demand for i elatic and te euilibrium uly of i le tan. Wen ervice are comlement and tere are no cloe ubtitute te reulting inelatic demand for make even erfect agency unable to acieve efficiency in te ublic ector. Ti weaken te ability of te uer fee to acieve te efficiency and o weaken te argument for cot control on te demand ide wen ervice are comlement. Te reult are alo contrary to wat [4] and [5] found in comaring full cot reimburement wit roective ayment. Tey ow tat cot-reimburement like fee-for-ervice i caracterized by overuly becaue it doe not rovide te rovider incentive to economize on te uantity of ervice. Like [15] tey did not ave uer fee in teir model. 3.. Proective Payment Under ti rule, te government give a fixed amount of revenue, G, to te ublic oital regardle of cot of te roduction and revenue collected from uer fee. Tu, (4) become: 7 Note Note tat a fall in caue an increae in rivate rofit wen ervice are ubtitute. y uing te oitive loed ortion of te io-rofit it i oible to obtain imilar reult if te rivate io-rofit curve i allowed to ift to te left and indifference curve remain uncanged. 8 Te underlying aumtion i tat 0, i.e., te and maximize atient benefit if cot were zero, making te term in te uare bracket oitive. G (1 ) (, ) c( ) (0) Te reulting marginal rofit wit reect to i negative: (1 ) (, ) (1 ) (, ) c'( ) 0 (1) E.13, ten, become: (1 ) (, ) (1 ) (, ) c'( ) N MRSN N N Rearrange to get: c'( ) (1 ) (, ) (1 ) (, ) MRS N N MRS N N MRS N N N N () (3) Wit te excetion of te firt term on te left and ide (LHS), (3) i identical to (13). Ti (oitive) term determine te difference between te euilibrium and under te full-cot ayment ceme and te roective ayment ceme. Again, te relationi between te loe of te indifference curve and te io-rofit deend on weter ervice are ubtitute or comlement. For ubtitute, te coefficient of te io-rofit loe i le tan one. Tu, (3) ow tat, under te roective ayment ceme, te euilibrium and occur at a oint were te io-rofit i teeer tan te indifference curve but not a tee a under te full-cot ceme. Ti i own in Figure 3(a) a (ii) wic a le and more tan te full cot euilibrium 7. Ti reult i euivalent to [16]. Wen ervice are comlement, te coefficient of te io-rofit loe in (3) i greater tan one imlying tat in euilibrium te iorofit i flatter tan te indifference curve but not a flat a under te full cot. A own in Figure 3(b) a ii, te euilibrium and are bot le tan toe of te full cot and for a given level of rivate rofit, te atient end u on a lower indifference curve tan te full cot euilibrium. Ti again i conitent wit te reult of [16]. To determine te efficiency of ti euilibrium (), (3), (6), (8), and (9) are ubtituted into (3) et = c (i.e., efficiency in te rivate ector), and rearranged to roduce: k (1 MRSN ) (1 ) (4) were k = c = 0 i reuired for efficiency in te ublic ector. E.4 ow tat k = 0 wen MRS N = 1. However, k > 0 wen MRS N < 1 and k < 0 wen MRS N > 1 8. Efficiency in te ublic ector deend Coyrigt 010 SciRe. Oenly acceible at tt://www.cir.org/journal/health/
1116 E. Amorfu / HEALTH (010) 1110-1119 (a) (b) Figure 3. (a) Proective ayment euilibrium for ubtitute relative to tat of full cot; (b) Proective ayment euilibrium for comlement relative to tat of full cot. on te agency beaviour of te yician and not on te relationi between te ervice. Perfect agency i reuired for efficiency in te ublic ector wile imerfect agency roduce too little in euilibrium. Given tat te yician i an imerfect agent, (4) ow tat term in te uare bracket increae wen te rice elaticity of demand for increae 9. A te demand for ervice in te rivate ector become more elatic te imerfect agent ulie an otimal amount of rivate ervice at 9 Note tat, ubtituting ti into (4) and differ- entiating wit reect to ε yield (1 ) 0. te exene of too little uly of ublic ervice regardle of te relationi between te ervice. Tee reult are alo imortant. Firt, comared wit te cot reimburement cae, te diincentive tat accomanie te roviion of under te roective ayment caue te imerfect agent to cut down te overuly of tat exit under te cot reimburement wen ervice are comlement a well a te otimal uly of wen ervice are ubtitute uc tat too little i roduced weter ervice are comlement or ubtitute. Second, te reult ere are contrary to [16] were efficiency in bot ector i oible under te roective ayment wen ervice are ubtitute regardle of te agency tye of te yician. Tird, te reult are imilar to [15] in tat erfect agency i reuired for efficiency. Reference [15] argue tat te need for erfect agency weaken te argument in favour of roective ayment ceme. Te influence of oital on yician beaviour i manifeted in te cange in ervice rovided by yician in accordance wit cange in te ayment ceme to oital. Tu, yician are more likely to be imerfect agent tan erfect agent imlying tat efficiency cannot be actualized under te roective ayment. Te reult alo rovide intereting comarion wit [10], [16] and [1]. Reference [10] reent a model in wic all firm (oital) roduce omogeneou roduct but differ by te cot of roduction. He conclude tat roective ayment, becaue it make ayment indeendent of te oital cot, i otimal. Reference [16] conider a model wit eterogeneou atient, in term of cotline, tat can be treated wit varying effort wit demand reonding to te variation. Managerial effort i reuired for te enancement of uality and reduction of cot. Hi reult ow tat roective ayment can elicit te efficient effort if te rovider a to treat all atient. Selden reult, owever, owed tat roective ayment i not otimal even under full inurance. Te uetion ten i wat ize of can lead to efficiency in te ublic ector, under te roective ayment, given efficiency in te rivate ector. Ti i found from (4) by etting k = 0 and olving for : ( ) * (5) ( ) Tu, tere i an otimal at wic efficiency in bot ector i oible under te roective ayment regardle of te tye of agency role layed by te yician a well a te relationi between ervice. Obviouly, * < 1. Note, owever, tat * increae a te elaticity of demand for rivate ervice fall regardle of te relationi between te rivate and ublic er- Coyrigt 010 SciRe. Oenly acceible at tt://www.cir.org/journal/health/
E. Amorfu / HEALTH (010) 1110-1119 1117 vice 10. Ti i intereting becaue (4) ow tat given tat te yician i imerfect, a fall in te elaticity of demand for rivate ervice caue te yician to increae ervice in te ublic ector given an otimal uly of ervice in te rivate ector. Tu, (5) imlie tat a te ervice in te rivate and/or te ublic ector become neceitie (and o le elatic) efficiency demand tat te government reduce te uer fee for ublic ervice. Ti i conitent wit [16] tat wen = 1 efficiency i oible under roective ayment regardle of te tye of agency. 3.3. Cot Saring Under ti rule, te government make a fixed ayment, G, and cover a fraction,, of te cot of roduction: R ( ) G c ( ) (6) Te ublic oital rofit become: G (1 ) (, ) ( 1) c( ) (7) were 0 < < 1. Te government can increae, G, and reduce uc tat te total ayment remain contant. Note tat = 0 imlie roective ayment wile G = 0 and = 1 rereent full cot reimburement. Te marginal rofit i: (1 ) (, ) (1 ) (, ) (1 ) c'( ) 0 (8) E.13 become: (1 ) c'( ) (1 ) (, ) (1 ) (, ) MRSN N (9) MRSN N N MRS N N N Wit te excetion of - c (), (9) i identical to (3). E.9 ow tat for ubtitute te io-rofit i teeer tan te atient indifference curve but not a tee a under te roective ayment. Wen ervice are comlement, owever, te io-rofit i flatter tan te atient indifference curve but by lower degree tan under te roective ayment. Tee are own a iii in Figure 4(a) and 4(b): Tu, atient are wore off under cot aring tan under full cot but are not a wore off a under roective ayment. Following [16], it i imortant to conider te ize of 10 Te elaticity of demand for i: = ; [ ( ) ] * 0. (a) (b) Figure 4. (a) Cot aring euilibrium for ubtitute, relative to toe of full cot and roective ayment; (b) Cot aring euilibrium for comlement relative to toe of full cot and roective ayment. at wic otimality can be acieved in te ublic ector given tat te rivate ector i otimal. Ti i obtained by ubtituting (), (3), (6), (8) and (9) into (9) and etting k = 0: (1 )( ) * (1 MRSN ) c'( ) (30) Clearly * i zero wen te yician i a erfect agent in wic cae roective ayment i otimal. Coyrigt 010 SciRe. Oenly acceible at tt://www.cir.org/journal/health/
1118 E. Amorfu / HEALTH (010) 1110-1119 However, * cannot be one 11, i.e., cot aring can be ued to enure otimal uly of ervice. It i otimal for te government to ue a combination of fixed fee and incentive ayment to reward te oital becaue ti force rovider to internalize te externalitie tat lead to underuly under roective ayment (Selden 1990; [15] 1986) and overuly under full cot reimburement. Euation (30) ow tat te ize of * doe not deend on te relationi between ervice i.e., it i otimal for te government to a on te ame fraction of cot for ubtitute and comlement. In [16] efficiency in bot ector reuire tat * = (1- MRS N ). Ti i identical to wat [15] recommend for efficiency in te ublic ector wen tere i no rivate ector. Tu, in Rickman & McGuire, te otimal fraction of cot tat i aed on to rovider doe not deend on te relationi between te ervice. Te term in te uare bracket in (30) rereent te effect of te uer fee in te ublic ector on te ize of *. Note tat wen = 1 (30) become * = (1 - MRS N ), wic i te ame a in [16] a well a in [15]. Wit te term in te uare bracket le tan one, * in te current model i le tan tat in [16]. Tu, wen tere i a uer fee in te ublic ector, efficiency reuire tat le revenue be retained to induce otimal roviion of ublic ervice for bot ubtitute and comlement tan wen tere i no uer fee. Note tat te econd term in te uare bracket increae in te elaticity of ervice in bot ector 1. Te * ere i ubject to te ame etback a in [15] a well a [16] in tat information on an unobervable variable, te yician utility, i reuired. However, te effect of elaticity on * in te current model reduce te deendence on information on te yician utility. Te reence of te oitive term in te bracket wic deend on elaticity reduce te range witin wic * fall. Tu, under te uer fee ytem in te ublic ector in a two-tier ytem, cot aring can enure efficiency in bot te ublic and rivate ector regardle of te relationi between ervice in te two ector. Ti i alo intuitive. Comared to te full cot reimburement ytem (were G = 0 and = 1), te fall in marginal revenue reulting from letting * < 1 give te imerfect agent te incentive to reduce te overuly of comlementary ervice wile maintaining uly of ubtitute at te efficient level. For comarion wit roective ayment, (were G > 0 and = 0) te increae in marginal revenue from etting * < 1 induce te imerfect agent to increae ervice. 11 Ti i baed on te aumtion tat 1 (1 ) 0 and ( ) c'( ) (1 ) 1 0 c'( ) 4. CONCLUSIONS Many recent ealt care reform introduce uer fee to te ublic ector. Ti aer examined atient welfare and efficiency under different rovider reimburement ceme in te ublic ector in a mixed ealt care ytem were te atient bear cot for treatment in bot te ublic and rivate ector. Te aer extended reviou tudie by introducing uer fee in te ublic ector. Te rovider reimburement ceme examined are full-cot reimburement, roective ayment and cot aring. Te reult ow tat efficiency i oible under te full cot reimburement ceme if te yician trade off ublic oital urlu for atient net benefit wen ervice are ubtitute and trading off atient net benefit for ublic oital urlu or being a erfect agent wen ervice are comlement. Ti i contrary to te reult in reviou tudie were tere i overuly of ervice in euilibrium in te ublic ector under te full cot reimburement. Under te roective ayment efficiency i only oible wen te fraction of cot not covered by te uer fee i at it otimal level. Similarly, under te cot-aring ceme, efficiency occur only if te fraction of cot tat te government ae on to rovider i at it otimal level. Ti i imilar to te reult in reviou tudie; owever, te otimal fraction in ti aer i le tan tat in reviou tudie. Of te tree reimburement ceme, te atient i wort off under te roective ayment and a te iget utility under te full-cot reimburement. In general te introduction of uer fee in te ublic ector make te atient wore off wen ervice are ubtitute. However, it i not clear weter te uer fee make atient wore off or better off wen ervice are comlement. REFERENCES [1] eley, T. and Gouveia,. (1994) Alternative ytem of ealt care roviion. Economic Policy, 03-58. [] Zweifel, P. and reyer, F. (1997) Healt economic. Oxford Univerity Pre, Oxford. [3] Petretto, A. (1999) Otimal ocial ealt inurance wit ulementary rivate inurance. Journal of Healt Economic, 18(1), 77-745. [4] Holmer, M. (1984) Tax olicy and te demand for ealt inurance. Journal of Healt Economic, 3, 03-1. [5] Zuckerman, S. (1987) Commercial inurer and all-ayer regulation evidence on oital reone to financial need. Journal of Healt Economic, 6(3), 165-187. [6] Gravelle, H. (1999) Caitation contract: acce and uality. Journal of Healt Economic, 18(1), 315-340. [7] Cernick, H.A., Holmer, M.R. and Weinberg, D.H. (1987) Tax olicy toward ealt inurance and te demand for medical ervice. Journal of Healt Economic, 61-5. [8] Selden, T.M. (1999) Premium ubidie for ealt inur- Coyrigt 010 SciRe. Oenly acceible at tt://www.cir.org/journal/health/
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