Quality ovisio i Two-Sie Maets: the ase of Maage ae Micea I. Macu * Deatmet of Ecoomics, Uivesity of Floia, 33 Mathely Hall.O. ox 74, Gaiesville, FL 36, 35 39-4, micea@.ufl.eu Job Maet ae Octobe 8 STRT I evelo a two-sie maet moel to stuy the ole laye by iiect extealities i shaig the icig a uality ecisios of maage cae ogaizatios. I fi that maage cae uality, access to hysicias, a hysicia eimbusemets ecease whe the cost of oviig uality o the oulatio health is iceases. These eceases ae moe oouce whe the exteality exete by octos o atiets is lage, whe olicyholes cae moe about uality, a whe the suly of hysicias is moe elastic. The esults may hel to uesta the iceasig ublic issatisfactio with maage cae. They uescoe the imotace of imlemetig a moitoig the achievemet of uality staas i the face of ogoig iceases i health iss associate with a agig oulatio. JEL classificatio: I; L Keywos: Two-Sie Maets; Extealities; Quality; Maage ae; vese Selectio * I am vey gateful fo the commets a suot I eceive fom huog i, Safo eg, James Seale, a esecially Davi Saigto. y emaiig eos ae my ow.
. Itouctio Diect extealities, such as those exete by isue iiviuals o othe membes of the same isuace ool though moal haza a/o avese selectio, have log bee aalyze i health cae maets. This aticle focuses o iiect extealities betwee octos a atiets a the two-sie atue of maage cae maets. Two-sie maets ae maets i which thee ae two-way iiect extealities betwee the aticiats i a maet that iteact though a itemeiay latfom. The umbe a/o uality, o some othe chaacteistic of membes o oe sie of a itemeiay s etwo affects the utility of eollees o the othe sie. case i oit is a maage cae ogaizatio MO that ees to attact both octos a atiets. atiets cae about the availability of octos. t the same time, octos cae about the umbe of atiets eolle i the maage cae la. The esece of iiect extealities leas to imotat eatues fom fuametal esults i taitioal micoecoomics. Fo examle, eatues fom magial cost icig may ot ecessaily eflect maet owe. Such eatues coul also eflect the elative magitue of the iiect extealities exete by each sie mstog [6]. The icig stuctue i twosie maets is ofte sewe i favo of oe sie, whose cosumtio is subsiize fom the eveues collecte o the othe sie. Most softwae latfoms a iteet otals oeate i this mae. Recogizig the imotace a coseueces of the iiect extealities is essetial to avoi the fallacies of alyig the oe-sie logic to two-sie maets Wight [4]. See ow [963], Zechause [97], Ellis a McGuie [993], Ma a McGuie [997], Ma a Rioa []. See Rochet a Tiole [3] fo a fomal efiitio of two-sie maets.
Maage cae iffes fom othe two-sie maets because the MO s execte cost is lie to the execte beefit eive by eollees though thei health is. I cotast, the cost of oucig a commoity lie a vieo game is the same egaless how much games ejoy the game. Theefoe, the health is of olicyholes is of aticula imotace i aalyzig maage cae. This health is, i tu, ees o the uality of health cae ovie by the MO, the size of its hysicia etwo, a the isuace emium it chages. To ate, two-sie maet moels have focuse almost exclusively o the icig ecisios of itemeiaies. 3 The stuy by ezzio a igatao [7] is a excetio. They stuy uality ovisio by cometig hositals i a hoizotal iffeetiatio moel with egulate isuace emiums. To my owlege, aey a Rochet s [6] aalysis of cometitio betwee maage cae ogaizatios is the oly othe two-sie aoach to health cae maets. I exte the liteatue by aalyzig a MO s ofit maximizig choice of uality of sevice. Quality hee eflects the egee to which the MO assists hysicias i oviig health cae sevices. It ca be thought of as a uality-iceasig iut sulie by the MO, such as iagostic tests o sohisticate health ifomatio ocessig, stoage, a etieval. I fi that the less elastic is the suly of octos with esect to eimbusemets, the moe eollees cae about uality, a the lowe the iiect exteality exete by octos o atiets, the moe the MO ca euce hysicia comesatio whe iceasig uality a maitai the same emium a umbe of eollees, aticulaly at low levels of uality elative to eimbusemet. 3 Evas a Schmalesee [5], a Rochet a Tiole [5] ovie a oveview of the two-sie maets liteatue.
I my moel, a icease i the magial cost of oviig uality eceases the amout of the uality-iceasig iut ovie by the MO. This i tu eceases the effectiveess of hysicias, which leas to lowe hysicia eimbusemets a fewe octos i the efee etwo. Iiviuals ae uwillig to ay the same isuace emium as befoe, a the ema fo maage cae shifts owwas. The isuace emium eceases, but the ecease oes ot fully comesate fo the eceases i uality a umbe of hysicias. Thus, the MO euces the is of its atiets mix to avoi oviig the moe costly uality. Fo oulatios moe at is of becomig ill, as is the case of the agig oulatio of the Uite States, the MO ovies sevices of lowe uality, ays lowe hysicia eimbusemets, a iclues fewe ovies i its efee etwo. The isuace emium eceases, but the MO fis it ofitable to eoll some highe is iiviuals. The eceases i maage cae uality, access to octos, a eimbusemets to hysicias ue to iceases i the oulatio health is a i the cost of uality ovisio ae moe oouce whe the exteality exete by octos o atiets is geate, whe iiviuals cae moe about uality, a whe the elasticity of the suly of octos with esect to eimbusemets is geate. Thus, although MOs ovie sevices of highe uality a access to moe octos i maets whee iiviuals cae moe about uality a access to octos, these maets ae also the oes most affecte whe the cost of uality ovisio a oulatio health iss icease. The esults illustate the ole laye by iiect extealities i shaig the icig a uality ecisios of maage cae ogaizatios a may hel to uesta the gowig ublic issatisfactio with maage cae. They uescoe the imotace of imlemetig a moitoig the achievemet of uality staas i the face of ogoig iceases i health is 3
ue to oulatio agig, a that of ajustig the ates ai by govemet ogams lie Meicae a Meicai accoig to the health is of maage cae eollees. The est of the stuy is ogaize as follows. Sectio esets the geeal moel. Sectio 3 esets the esults fo iso-elastic istibutios of atiets health iss a hysicias cost of teatmet. Sectio 4 coclues.. The Moel Thee is a cotiuum of iiviuals of mass that iffe accoig to thei obability of becomig ill,,. The obability of becomig ill is istibute accoig to the cumulative istibutio fuctio F, with twice cotiuously iffeetiable obability esity fuctio f that is ositive eveywhee i,. The execte utility of tye iiviuals fom joiig the MO ees o the umbe of hysicias eolle i the maage cae etwo, the isuace emium they have to ay, a the uality of sevice ovie by the MO : 4,,, U. Fo simlicity, I assume atiets ay o out of ocet costs i the fom of coisuace, coaymets, o euctibles. The moel thus abstacts fom moal haza a avese selectio issues that have bee extesively aalyze elsewhee i oe to focus o etwo exteality asects of maage cae. The aamete etemies the magitue of the exteality exete by octos o atiets. Doctos o ot facto ito thei ecisio-maig the effect thei aticiatio has o the utility of olicyholes. The size of the ovie etwo mattes because the MO oes ot ay 4 s it is aaet fom the utility secificatio, the moel abstacts fom icome effects. This assumtio is ot icomatible with global is avesio a health isuace ema fom iiviuals if the obability of gettig ill is small, the isuace emium is small, a the cost of teatmet is lage aey a Rochet [6]. 4
fo ay teatmet that its eollees might eceive outsie its etwo. The moel thus catues the case of a health maiteace ogaizatio HMO. lage etwo of hysicias may lowe atiets tasotatio costs, o icease the lielihoo that atiets will fi hysicias matchig thei efee style of teatmet. Thee is easo to believe iiviuals feel stogly about the choice of ovies MOs offe. oce about limite choice of ovies has eve omte some states to eact laws esuig that willig hysicias ae ot exclue fom maage cae etwos the so-calle y Willig ovie laws, a atiets have access to ovies of thei choice Feeom of hoice laws. 5 The utility of olicyholes also ees o the uality of cae ovie by the MO. The uality vaiable i this moel catues the egee to which the MO assists hysicias i oviig health cae. It ca be thought of as a uality-iceasig iut sulie by the MO, such as iagostic tests o sohisticate health ifomatio ocessig, stoage, a etieval. Maage cae ogaizatios use vaious meas to cotol costs, fom e-authoizatio of oceues to utilizatio eview. While these ae meat to icease efficiecy a ecease the cost of health cae, they may also estict the ovisio of health cae by hysicias a thus otetially affect the uality of teatmet. Quality issues have ot laye a omiet ole i two sie maet moels to ate, as stuies have focuse maily o the ceit ca iusty a electoic latfoms. 6 Howeve, uality of sevice is a aticulaly citical issue i health cae, a hece meits caeful attetio. Thee is a cotiuum of hysicias of mass > that iffe i thei cost of teatig atiets c µ µ, whee > is the highest cost icue by ay octo fo teatig a sigle 5 6 Some estictios aly eve ue y Willig ovie laws. ovies have to have a cetai uality cetificatio a have to be willig to accet the same cotactual coitios eimbusemets, e-authoizatio etc. as eolle hysicias of the same uality. excetio is the stuy by ezzio a igatao [7]. 5
atiet. The factio µ [,] of this maximum cost icue by tye µ hysicias is istibute accoig to the cumulative istibutio fuctio Gµ, with coesoig esity fuctio gµ which is assume to be cotiuously iffeetiable a ositive eveywhee. 7 To focus o the uality ovie by the MO, I assume that octos o ot iffe i tems of uality. To this e, I also assume that octos act i the best iteest of thei atiets a o ot egage i simig loweig the uality of sevice they ovie o umig the actice of efusig to teat high cost atiets. The utility that a hysicia eives fom teatig a atiet is the iffeece betwee the eimbusemet ai by the MO i the fom of a fee fo sevice, a the cost of teatmet cµ: 8 v µ c µ. The MO oes ot obseve atiet a hysicia tyes. Howeve, the istibutios of atiet a octo tyes ae commo owlege... atiets Decisio Maig If they choose to o so, iiviuals ca secue health cae sevices fom a alteative ovie, calle la. la ovies sevices of uality, a access to a etwo of hysicias of size, i exchage fo a emium. la might be viewe as a taitioal isuace la which gives eollees access to all the octos i the maet o Meicae fee fo sevice FFS, whose emium, uality, a umbe of hysicias the MO taes as give. I assume emiums ae sufficietly high that atiets choose ot to joi both las, a the MO fis it ofitable to offe a lowe uality of sevice a umbe of octos i oe to attact 7 8 The cost cµ catues both moetay a o-moetay costs of teatmet. Fo simlicity, I assume octos have costat magial costs of teatig atiets. The esults of the moel woul ot chage if the MOs ai hysicias a fixe amout e yea e eollee egaless whethe iiviuals see teatmet o ot caitatio, athe tha a fee fo sevice. 6
iiviuals with lowe obability of gettig ill. To avoi cofusio, i what follows I will efe to the MO as la o MO, a iex its chaacteistics accoigly. atiets joi MO if they eive a highe level of execte utility fom joiig it tha fom joiig la : U U. 3 Give the alteative offee by la, the MO chooses to ovie a lowe uality of sevice etwo size combiatio such that it attacts iiviuals with lowe obability of gettig sic:. 4 MO chages a lowe isuace emium tha la, othewise o atiets will joi MO. Theefoe, thee exists, fo which iiviuals ae iiffeet betwee joiig MO a joiig la :,,,,,. 5 atiets of lowe health is joi MO, while atiets of highe health is > joi la. Emiical eviece suggests that maage cae las have bee successful i attactig a mix of atiets with lowe health is tha taitioal health isues Mille a Luft [994], Glie [], Deb a Tivei [6], a Liu a Zimme [6] a thei isuace emiums ae ofte substatially lowe ltma, utle, a Zechause [3]... hysicias Decisio Maig I assume hysicias face o caacity costaits. oseuetly, they eoll i the etwo of MO if the utility they eive fom teatig atiets is oegative: v µ c µ. 6 7
Oly hysicias fo which the moetay a o-moetay cost of teatig atiets is lowe tha the eimbusemet e atiet µ will joi the MO s efee etwo. The umbe of hysicias that joi MO is thus:. 7 G I assume MO oes ot obseve the cost of teatmet of each hysicia a caot efeetially iect atiets towas cetai hysicias e.g., those that have the lowest cost of teatmet. Moeove, atiets ae eually liely to go to ay hysicia because teatmet is fee oce the emium has bee ai, a hysicias ae assume to be of the same uality. Theefoe, hysicias eollig i the efee etwo of MO exect to eually shae cases i the MO with the othe eolle hysicias. The total utility a hysicia of tye µ exects to get fom joiig MO is the ouct of the execte utility e atiet v a the execte case loa D : V µ v µ D µ f. 8 G hysicias utility thus ees o the umbe a tye of eollees. Iiviuals o ot tae this iiect exteality ito accout whe eciig whethe to eoll i the MO..3. ofit Maximizatio I assume MO is a fo-ofit MO, a thus maximizes its ofits give by: [ ] Π f, 9 whee is MO s e atiet cost of oviig uality, which is iceasig a covex i. 8
9 The fist oe coitios chaacteizig MO s ofit maximizig choice of emium, eimbusemet, a uality ae give by: Π f F F Π f f F ' Π f f F whee 3 4 5 ae the total eivatives of with esect to,, a. Sufficiet coitios fo ofit maximizatio ae ovie i the aeix. Euatios - eflect the familia micoecoomic aaigm that the ofit maximizig fim chooses the isuace emium, hysicia eimbusemet, a uality such that the magial beefit of each istumet euals its magial cost. Fo examle, iceasig uality allows MO to attact moe iiviuals F fom which it collects emium, a
factio of which will ee teatmet which costs, i aitio to the icease costs of oviig uality to all olicyholes ' f Euatio. While these esults ae ituitive, they iffe fom the familia micoecoomic theoy of oe-sie maets though the esece of iiect exteality effects. The ofit maximizig emiums, eimbusemets, a uality ee o the iiect exteality hysicias exet o olicyholes, a the exteality exete by olicyholes o octos. Whe eciig whethe to joi MO, iiviuals o ot tae ito accout the effect of thei ecisios o the utility of octos i the MO s etwo. Similaly, hysicias o ot tae ito accout the ae beefit olicyholes woul ejoy fom beig able to choose amog a lage etwo of ovies. The fist oe coitios ca be ewitte i the familia Ramsey fom η, 6 whee η F 7 F is the elasticity of the umbes of eollees with esect to the isuace emium. The moe elastic is the umbe of eollees with esect to chages i the isuace emium the lowe will be the mau chage by MO. hysicia eimbusemet has tae the lace that usually belogs to the magial cost of teatmet i oe-sie maet moels. The utility of olicyholes ees o the eimbusemet ai to octos by MO though its effect o the umbe of octos i the efee etwo
g. 8 Similaly, the utility of octos ees o the isuace emium ovie by MO though its effect o the umbe a tye of olicyholes F. Two-sie maet moels so fa have focuse o the otimal icig ecisios of itemeiaies. The eset moel also aalyzes the otimal choice of uality of the itemeiay MO. The utility of hysicias fom joiig MO ees iiectly o the uality of sevice ovie by MO to atiets though its effect o the umbe a tye of olicyholes F Euatio. ombiig the fist oe coitios fo ofit maximizatio yiels ' f f F. 9 This i tu ca be ewitte to aalyze the taeoffs face by MO whe choosig the uality of sevice a hysicia eimbusemet: cst cst '. Iceasig the uality of sevice ovie to atiets allows the MO to euce the eimbusemet e atiet it ays octos, chage the same isuace emium a attact the same umbe of atiets. Similaly, iceasig the eimbusemet attacts moe octos which
ovie olicyholes aitioal utility, allowig the MO to euce the uality of sevice it offes a maitai the same umbe of atiets a isuace emium. Usig Euatios 4 a 5, Euatio ca be ewitte as: ' cst cst. ' The highe the magial cost of oviig uality a the lowe the elasticity of the umbe of octos with esect to eimbusemets, the moe the MO ca euce aymets to its octos whe it iceases uality a maitai the same emium a umbe of eollees. lso, the moe eollees cae about uality highe a the less they cae about the umbe of octos lowe, the moe the MO ca euce eimbusemets whe iceasig uality a ee the same emium a umbe of eollees, aticulaly at low levels of uality elative to eimbusemet. 3. Iso-Elastic Distibutios of Health Ris a ost The moel ca be solve fully fo the case i which the istibutios of atiet a hysicia tyes ae iso-elastic a uality is ouce with costat magial cost, i.e., F, µ µ G, '. 6 These owe istibutios ae a coveiet way to summaize the cocetatio of high-is atiets a high-cost hysicias i the maet aey a Rochet [6]. Distibutios with highe omiate those with lowe i the sese of fist oe stochastic omiace. The highe is the elasticity of the istibutio of atiet tyes the highe is the execte umbe of illess cases. Similaly, the highe is, the elasticity of the istibutio of hysicia tyes, the highe is the execte umbe of octos with high cost of teatig atiets.
3 Solvig the moel yiels the followig solutio see eix fo eivatios: 7 8 9 ] [ 3 3
The followig oositios escibe the imact of chages i aametes of iteest o MO s eimbusemet, uality, umbe of octos, magial health is, a isuace emium. They ae summaize i Table. The oofs of these oositios ae setche i the aeix. The esults wee eive usig Mathematica 5. seaate file etailig the eivatios is available fom the autho uo euest. oositio. Whe iiviuals cae moe about uality highe o access to octos highe the MO ovies moe of the uality-iceasig iut, ays highe eimbusemets, a attacts moe octos. The magial health is isue by the MO eceases as moe iiviuals choose the alteative la. s iiviuals become moe cocee about the uality of the health cae they eceive, the MO ovies moe of the uality iceasig iut. This iceases the magial utility of octos, so MO ays highe eimbusemets a attacts moe octos. Similaly, the iiect exteality exete by octos o atiets oes ot affect solely the umbe of octos i MO s etwo. Whe olicyholes cae moe about the umbe of octos, the MO fis it ofitable to ovie octos with moe of the iuts they ee to bette teat atiets. Howeve, if iiviuals cae moe about uality o access to octos, moe of them will choose the alteative la that ovies highe uality of sevice a access to moe hysicias. oositio. The MO euces the is of its mix of atiets whe the elasticity of the suly of hysicias with esect to eimbusemets iceases. Just as fims chage lowe ices whe ema fo thei oucts is moe elastic, the MO ays highe eimbusemets to attact octos whe the suly of octos is moe elastic. I the moel, catues both the elasticity of the suly of hysicias a the cocetatio of octos with high teatmet costs. Moe octos have high teatmet costs whe is geate. ecause it is moe costly to attact hysicias the MO isues fewe iiviuals a euces the health is of its atiet mix. 4
The effect of a icease i o eimbusemet, the umbe of octos, a the uality ovie by the MO is ambiguous. Deceasig eimbusemets o eeig them costat may be ofit maximizig if the umbe of octos a thus the willigess to ay of olicyholes oes t ecease too much. If a ecease i eimbusemet woul lea to a lage ecease i the umbe of octos a i the olicyholes utility a willigess to ay, the the MO may fi it ofitable to icease eimbusemet, eve if the et effect is still a euctio i the magial health is isue by the MO. oositio 3. MO ovies less of the uality-iceasig iut, ays lowe eimbusemets, attacts fewe octos, chages a lowe isuace emium, a isues iiviuals with lowe health is whe its magial cost of oviig uality iceases. The MO eceases eimbusemets a attacts fewe octos because octos ae less efficiet whe they eceive less of the uality-iceasig iut, a the magial utility eive by olicyholes fom access to octos eceases. The ema fo maage cae shifts owwas, as iiviuals willigess to ay fo maage cae eceases. The isuace emium eceases as a esult, but the ecease oes ot fully comesate fo the ecease i olicyhole s utility ue to lowe uality a fewe hysicias. Thus, the MO euces the is of its atiets mix a isues fewe eole i oe to avoi oviig the moe costly uality. Of aticula imotace is the way i which the istibutio of health iss i the oulatio affects the isuace emium, eimbusemet, uality ovie, as well as the umbe a mix of atiets seve by the MO. Moe eole ae at is of becomig ill as a esult of the agig of the US oulatio. I the moel this coesos to a shift i the istibutio of health iss towas highe health iss, catue by a highe value of. The istibutio of health iss fo highe statistically omiates those with lowe i the sese of fist oe stochastic omiace. omaative statics with esect to ca illustate the effects of 5
oulatio ageig, o allow fo comaisos betwee maets with iffeet istibutios of health iss. oositio 4. Whe the health is of the oulatio iceases the MO ovies lowe uality, ays lowe eimbusemets, attacts fewe hysicias, chages a lowe isuace emium, a fis it ofitable to attact some iiviuals with highe health is. Whe it faces a highe umbe of illess cases, the MO ties to cotol costs by eucig uality, ayig lowe eimbusemets, a oviig access to fewe octos. These eictios of the moel ae boaly cosistet with the gowig ublic issatisfactio with the uality of health cae ovie by maage cae ogaizatios, a thei attemts to cotol costs though a vaiety of mechaisms such as maatoy efeals a e-authoizatio oceues. ecause the olicyholes willigess to ay eceases whe uality a access to hysicias ae euce, the MO chages a lowe isuace emium. ecause thee ae fewe low-is a moe high-is iiviuals whe iceases, the MO isues some iiviuals with highe health is. oositio 5 escibes the factos that etemie the magitue of the chages i uality, eimbusemet, a umbe of octos. oositio 5. The ecetage eceases i MO uality, eimbusemet, a umbe of octos ue to iceases i oulatio health is o i the magial cost of uality ovisio ae geate whe eole cae moe about uality highe, whe the exteality exete by octos o atiets is geate highe, a whe the cocetatio of octos with high teatmet costs is highe highe. 9 oositio showe that the MO ovies highe uality a access to moe hysicias i maets i which iiviuals cae moe about uality a access to hysicias. oositio 5 shows that these ae also the maets i which the eceases i uality a access to hysicias 9 The exteality exete by the eollmet of a aitioal octo i MO s etwo, the magial utility of olicyholes with esect to the umbe of octos, iceases whe iceases if the umbe of octos i the etwo is geate tha oe ssumtio 63 i the eix. Similaly, ssumtio 64 i the eix esues that the magial utility of uality iceases whe iceases. 6
ae moe oouce, as the MO ties to cotai costs whe the oulatio health is iceases fo easos such as oulatio agig. oositio 6. The MO ays highe eimbusemets, attacts moe octos, ovies moe of the uality iceasig iut, isues moe olicyholes, a chages a highe isuace emium whe the umbe of octos i the maet iceases. The MO ays highe eimbusemets whe the umbe of octos i the maet iceases because the same icease i eimbusemets attacts moe octos i its etwo. This i tu iceases the utility of olicyholes, moe of whom eoll i maage cae. The isuace emium iceases as a esult of the icease i the olicyholes willigess to ay. This is a somewhat couteituitive esult because the icease suly of a iut esults i a highe ice fo the goo ouce. The ey iffeece fom the usual settig is that the umbe of octos also affects the magial utility a thus the willigess to ay of olicyholes. oositio 7. The MO ays lowe eimbusemets, attacts fewe octos, ovies less of the uality iceasig iut, isues fewe olicyholes, a chages a lowe isuace emium whe the maximum cost of teatmet iceases. While the ecease i the isuace emium chage by the MO is somewhat suisig, it is ue to the absece of icome effects i the moel, a to the fact that the MO taes the alteative la s uality, etwo of octos, a isuace emium as give. This limits the MO s ability to icease its isuace emium. The MO the esots to uality euctios a euce access to hysicias to cutail costs. This famewo is aoiate fo aalyzig the behavio of maage cae ogaizatios give the choices mae by the ete fo Meicae a Meicai Sevice egaig the taitioal Meicae fee fo sevice la. Futue eseach shoul moel the stategic iteactio betwee health isues to stuy also the alteative la s choice of uality, umbe of octos, a isuace emium. 7
4. oclusio This ae has eveloe a two-sie maet moel of maage cae to aalyze the behavio of a ofit maximizig MO i the esece of iiect etwo extealities betwee octos a atiets. evious two-sie maet stuies have focuse o the icig ecisios of itemeiaies. Give the cucial ole laye by uality i etemiig the health is of olicyholes, I aalyze both the MO s icig a its uality ecisios. The MO s choice of uality, emiums, a eimbusemets ees o the istibutios of atiet health iss a hysicia costs. It also ees o the magial cost of oviig uality, the utility eive by atiets fom the uality of health cae sevices, the magitue of the iiect exteality exete by octos o atiets, a the elasticity of the suly of hysicias with esect to eimbusemets. I the case of iso-elastic istibutios of atiet health is a hysicia cost of teatmet, a icease i the cost of oviig uality eceases the uality ovie by the MO, which euces the effectiveess of hysicias, the magial utility eive by olicyholes, a thus the eimbusemet a the umbe of octos i the efee etwo. The ema fo maage cae sevices shifts owwa, a the isuace emium also eceases. Howeve, the ecease i emium is smalle tha the ecease i atiet utility ue to lowe uality a umbe of hysicias i the etwo. Thus, the MO euces the health is of its atiet mix, a avois oviig, at least i at, the moe costly uality. Fo oulatios moe at is of becomig ill, as is the case of the ageig oulatio of the Uite States, the MO ovies sevices of lowe uality, ays lowe hysicia eimbusemets, iclues fewe ovies i its efee etwo, yet fis it ofitable to isue some highe is iiviuals. 8
lthough MOs ovie sevices of highe uality a access to moe octos i maets whee iiviuals cae moe about uality a access to octos, these maets ae also the oes i which the MO euces uality, eimbusemets, a access to hysicias moe aggessively to cutail costs whe the cost of uality ovisio o oulatio health iss icease. These esults may hel to uesta the iceasig ublic issatisfactio with maage cae. They uescoe the imotace of imlemetig a moitoig the achievemet of uality staas, as well as ajustig the caitatio ates ai by govemet ogams lie Meicae a Meicai to accout fo health is. While most of the eseach o two-sie maets has so fa bee theoetical, thee is a gowig emiical two-sie maet liteatue Rysma [4], Rysma [7], haa & olla-wexle [8]. Yet to my owlege thee is o emiical stuy aalyzig the twosie maet asects of maage cae. Give the otetial imotat imlicatios of iiect extealities, emiical stuies woul be useful to gauge the elative magitue a the ole laye by iiect extealities i health cae maets. EDIX Iso-elastic Distibutios of Health Ris a Teatmet ost Deivatio of the ofit Maximizig Solutio To bette uesta the esults, the moel is solve assumig iso-elastic istibutios of atiet a hysicia tyes F a G c c, a costat magial costs of oviig uality '. It is easiest to exess the isuace emium chage by the MO i tems of uality, eimbusemet, a the cutoff obability fom Euatio 5 a solve the moel with esect to uality, eimbusemet, a the cutoff obability of illess. We have 9
3 a the MO s ofit is [ ] Π f. 33 Relacig f i Euatio 33 a itegatig yiels: Π. 34 The fist oe coitios with esect to,, ae: [ ] Π. 35 Π. 36 ' Π. 37 Simlifyig, we get:. 38. 39 '. 4 ombiig Euatios 39 a 4 we get: '. 4 Taig ito accout that ', we ca exess uality i tems of eimbusemet:
. 4 Relacig Euatios 4 a 7 ito Euatio 39 a solvig fo eimbusemet yiels:. 43 ecause we ca comute the umbe of octos i the efee etwo:. 44 Relacig the exessio fo the eimbusemet fom Euatio 43 ito Euatio 4 yiels the followig exessio fo the uality ovie by MO :. 45 Substitutig Euatios 43, 44, a 45 ito Euatio 38 a solvig fo the magial health is of MO s atiets yiels
46 Fially, substitutig i Euatio 3 yiels the solutio fo the isuace emium ] [ 47 Sufficiet oitios fo ofit Maximizatio ote that the eomiato i Euatios 46 a 47 ca be witte as [ ] > D, 48 whee the seco euality comes fom Euatio 39. The eomiato is ositive sice MO offes lowe uality a umbe of octos tha the alteative la, a so ae a as a esult. We also ee < 49 to guaatee that <.
3 The seco oe eivatives of MO s ofit fuctio with esect to,, a ae: [ ] Π. 5 Π. 5 Π ''. 5 Π. 53 ' Π. 54 Π. 55 Taig Euatio 38 ito accout, Euatio 5 ca be witte: < Π. 56 The Hessia matix of the MO s ofit fuctio is: '' H. 57 The iagoal elemets of the Hessia matix ae egative if ' ', < <, < <, a < <, 58 that is, if the cost of oviig uality is covex, a the utility of eollees exhibits imiishig etus to uality a eimbusemet. Futhemoe, all the etemiat mios ae ositive
4 ue these assumtios if the utility of olicyholes also exhibits eceasig etus to scale, that is if >. 59 The fact that the etemiat mios ae ositive is obvious with the excetio of the oe coesoig to the seco eivatives with esect to uality a eimbusemet, which ca be witte as: [ ] '' '' > H Det. 6 Ue the coitios i Ieualities 58 a 59 the Hessia matix i Euatio 57 is egative efiite. These coitios togethe with the fist oe coitios i Euatios 35, 36, a 37 ae sufficiet coitios fo ofit maximizatio. The followig assumtios o the aametes ae mae i aitio to the sufficiet coitios fo maximizatio: >, > 6 > 6 < 63 <. 64
ssumtio 6 is eee to guaatee that < G <. ssumtio 63 esues that > a the utility of olicyholes is highe fo highe values of. This allows us to iteet a icease i as a icease i the exteality exete by octos o atiets. Similaly, ssumtio 64 guaatees that > a olicyholes eive a highe utility fom uality whe iceases. Ieualities 6, 63, a 64 ca be simultaeously satisfie if > a the magial cost of the uality iceasig iut is ot too lage <. 65 Ue all these assumtios, the imact of chages i aametes of iteest o the MO s eimbusemet, uality, umbe of octos, magial health is, a isuace emium is summaize i Table. The followig sectio setches the oofs of the mai oositios. The esults wee eive usig Mathematica 5. Fo bevity, oly the mai esults of the eivatios ae esete. seaate file etailig the eivatios is available fom the autho uo euest. oof of oositio Diffeetiatig Euatios 43 though 47 with esect to it ca be show that l >. 66 l >. 67 l >. 68 l l <. 69 5
{[ l l ] }. 7 Oe woul exect the MO s isuace emium to icease whe olicyholes cae moe about uality highe because the MO s uality a umbe of octos icease a the magial health is eceases. The chage i MO s isuace emium is ambiguous because the utility of the alteative la also iceases whe atiets cae moe about uality. small eough ecease i eimbusemet coule with small iceases i uality a umbe of octos ca lea to a ecease i the magial health is whe the alteative la s uality a umbe of octos ae lage eough. Diffeetiatig Euatios 43 though 48 with esect to to stuy the effects of a icease i the exteality exete by octos o atiets yiels l > l > 7 7 l > 73 l l < 74 {[ l l ] }. 75 The chage i MO s isuace emium whe olicyholes cae moe about access to octos highe is ambiguous fo easos simila to those fo which the chage i MO s isuace emium is ambiguous whe olicyholes cae moe about uality highe. The utility fom joiig the alteative la also iceases. 6
oof of oositio Diffeetiatig Euatios 43 though 47 with esect to yiels l l 76 l l l 77 l l 78 l l < [ l l ] 79. 8 The sig of the eivatives ees o the magitue of l l, with the excetio of the cutoff health is. The MO euces the magial health is it isues whe the cocetatio of high teatmet cost octos iceases. oof of oositio 3 Diffeetiatig Euatio 45 with esect to, we see that the MO ovies less of the uality iceasig iut whe the magial cost of uality ovisio iceases. <. 8 The eimbusemet ai to hysicias also eceases: <. 8 7
The easo is that the euctio i the amout of the uality iceasig iut ovie by the MO also imiishes the magial utility of hysicias. Theefoe, the umbe of hysicias i the MO s etwo also eceases: <. 83 With lowe uality a access to fewe octos the magial willigess to ay of olicyholes eceases, a so oes the isuace emium chage by the MO: [ ] <. 84 Howeve, the ecease is such that the MO isues a mix of atiets with lowe health is, as ca be see by iffeetiatig Euatio 46 with esect to a simlifyig: { } < 85 Fially, the MO attacts a smalle umbe of iiviuals: F <. 86 oof of oositio 4 Diffeetiatig Euatios 43, 44, a 45 with esect to it ca be show that <. 87 Whe the cocetatio of high-is atiets iceases the MO euces uality a iclues fewe hysicias i its etwo by ayig lowe eimbusemets to cotol costs. 8
To see how the mix of atiets isue by the MO chages whe the istibutio of heath iss chages, iffeetiate Euatio 46 with esect to. Taig also the exessio fo eimbusemet fom Euatio 43 ito accout we get Fom Euatio 39 we have: [ ] [ ]. 88. 89 Substitutig Euatio 89 i Euatio 88 yiels [ ] [ ] >. 9 The eivative i Euatio 9 is ositive because the uality a umbe of octos ovie by MO is lowe tha that ovie by the alteative la. The MO fis it ofitable to attact some highe is iiviuals because fewe iiviuals with low is emai. To etemie how the isuace emium chage by the MO chages, ewite Euatio 5 as. 9 Totally iffeetiatig Euatio 9 with esect to we get. 9 ecause >, <, a < it must be that <. Hece, the isuace emium also eceases. 9
3 oof of oositio 5 To show that the ecetage eceases i uality, eimbusemet, a umbe of octos i MO s etwo ue to iceases i oulatio health is ae geate whe the exteality is geate, iffeetiate the absolute value of the eceases i Euatio 87 with esect to [ ] >. 93 Similaly, oe ca show that the ecetage eceases ae geate whe - iiviuals cae moe about the uality of health cae sevice [ ] > 94 - the elasticity of the suly of octos with esect to eimbusemets is highe [ ] > 95 [ ] > 96 - the cocetatio of high health iss i the oulatio is smalle to stat with <. 97 To show that the ecetage eceases i uality, eimbusemet, a umbe of octos i MO s etwo ue to iceases i the magial cost of oviig uality ae geate whe the
3 exteality is geate, iffeetiate the absolute value of the eceases i Euatios 8, 8, a 83 with esect to [ ] >. 98 Similaly, oe ca show that the ecetage eceases ae geate whe - iiviuals cae moe about the uality of health cae sevice [ ] > 99 - the elasticity of the suly of octos with esect to eimbusemets is highe [ ] > [ ] >. oof of oositio 6 Diffeetiatig Euatios 43 though 47 with esect to yiels > > 3 > 4
3 >. 5 oof of oositio 7 Diffeetiatig Euatios 43 though 47 with esect to yiels < 6 < 7 < 8 <. 9 The MO efes to euce uality a the umbe of octos i its efee etwo to estai costs, eve though this meas it has to chage a lowe emium.
Table. Effect of icease i aametes o the MO s eimbusemet, uality, umbe of octos, magial health is, a isuace emium aametes Vaiables of iteest Reimbusemet Quality umbe of octos utoff obability Isuace emium ocetatio of health iss i the oulatio - - - - Imotace of uality fo olicyholes - /- Iiect exteality aamete Imotace of umbe of octos fo olicyholes Elasticity of suly of octos with esect to eimbusemet - /- /- /- /- - /- Magial cost of uality - - - - - Doctos maximum teatmet cost e atiet - - - - - umbe of octos i the maet REFEREES ltma, D., utle, D. M., a R. J. Zechause, 3. Eollee Mix, Teatmet Itesity, a ost i ometig Iemity a HMO las. Joual of Health Ecoomics, 3-45. mstog, M., 6. ometitio i Two-Sie Maets. Ra Joual of Ecoomics 373, 668-69. ow, K. J., 963. The Welfae Ecoomics of Meical ae. meica Ecoomic Review 53, 94-973. aey, D. a Rochet, J-., 6. ometitio mog Health las: a Two-Sie Maet oach. vailable olie at htt://ecoomia.uiaes.eu.co/es/cotet/owloa/9/459/file/aey.f. haa,., a. olla-wexle, 8. Meges i Two-Sie Maets: licatio to the aaia ewsae Iusty. vailable olie at htt://ages.ste.yu.eu/~acolla/meges%i%two-sie%maets.f. Deb,., a. K. Tivei, 6. Secificatio a Simulate Lielihoo Estimatio of a o- omal Teatmet-Outcome Moel with Selectio: licatio to Health ae utilizatio. Ecoometics Joual 9, 37-33. 33
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