TH1E AMERICAN ECONOMIC REVIEW VOLUME LIII DECEMBER 1963 NUMBER 5 UNCERTAINTY AND THE WELFARE ECONOMICS OF MEDICAL CARE By KENNETH J. ARROW* I. Introduction:Scope and Method This paper is an exploratoryand tentativestudy of the specific differentiaof medical care as the object of normativeeconomics. It is contendedhere, on the basis of comparisonof obviouscharacteris- tics of the medical-careindustry with the normsof welfareeconomics, that the special economicproblems of medicalcare can be explained as adaptationsto the existenceof uncertaintyin the incidenceof dis- ease and in theefficacy of treatment. It shouldbe notedthat the subjectis the medical-careindustry, not health.The causal factorsin health are many,and the provisionof medical care is only one. Particularlyat low levels of income,other commoditiessuch as nutrition,shelter, clothing, and sanitationmay be much more significant.It is the complexof servicesthat center about the physician,private and grouppractice, hospitals, and public health,which I proposeto discuss. The focus of discussionwill be on the way the operationof the medical-careindustry and the efficacywith which it satisfiesthe needs of societydiffer from a norm,if at all. The "norm"that the econo- mistusually uses forthe purposes of such comparisonsis theoperation of a competitivemodel, that is, the flowsof servicesthat would be * The author is professorof economicsat StanfordUniversity. He wishes to expresshis thanks for useful commentsto F. Bator, R. Dorfman,V. Fuchs, Dr. S. Gilson, R. Kessel, S. Mushkin,and C. R. Rorem. This paper was preparedunder the sponsorshipof the Ford Foundation as part of a seriesof papers on the economicsof health,education, and welfare. 942 THE AMERICAN ECONOMIC REVIEW offeredand purchasedand the pricesthat would be paid forthem if each individualin themarket offered or purchasedservices at thegoing prices as if his decisionshad no influenceover them,and the going prices were such that the amountsof serviceswhich were available equalled the total amountswhich other individualswere willingto purchase,with no imposedrestrictions on supplyor demand. The interestin the competitivemodel stemspartly from its pre- sumeddescriptive power and partlyfrom its implicationsfor economic efficiency.In particular,we can state the followingwell-known prop- osition (First OptimalityTheorem). If a competitiveequilibrium existsat all, and if all commoditiesrelevant to costs or utilitiesare in factpriced in the market,then the equilibriumis necessarilyoptimal in the followingprecise sense (due to V. Pareto): There is no other allocationof resourcesto serviceswhich will make all participantsin themarket better off. Both the conditionsof thisoptimality theorem and the definitionof optimalitycall forcomment. A definitionis just a definition,but when the definiendumis a wordalready in commonuse withhWighly favor- able connotations,it is clear thatwe are reallytrying to be persuasive; we are implicitlyrecommending the achievementof optimalstates.' It is reasonableenough to assertthat a changein allocationwhich makes all participantsbetter off is one thatcertainly should be made; thisis a value judgment,not a descriptiveproposition, but it is a veryweak one. From thisit followsthat it is not desirableto put up witha non- optimalallocation. But it does not followthat if we are at an alloca- tionwhich is optimalin the Paretosense, we shouldnot changeto any other.We cannotindeed make a changethat does not hurtsomeone; but we can still desire to changeto anotherallocation if the change makesenough participants better off and by so muchthat we feelthat the injuryto othersis not enoughto offsetthe benefits.Such inter- personal comparisonsare, of course,value judgments.The change, however,by the previousargument ought to be an optimalstate; of coursethere are manypossible states, each of whichis optimalin the sensehere used. However,a value judgmenton the desirabilityof each possiblenew distributionof benefitsand costs correspondingto each possible re- allocationof resourcesis not,in general,necessary. Judgments about the distributioncan be made separately,in one sense,from those about allocationif certainconditions are fulfilled.Before stating the relevant proposition,it is necessaryto remarkthat the competitiveequilibrium achieveddepends in good measureon the initialdistribution of pur- chasingpower, which consists of ownershipof assets and skills that 'This point has been stressedby I. M. D. Little [19, pp. 71-74]. For the concept of a "persuasivedefinition," see C. L. Stevenson [27, pp. 210-17]. ARROW: UNCERTAINTY AND MEDICAL CARE 943 commanda price on the market.A transferof assets amongindivid- uals will, in general,change the finalsupplies of goods and services and the prices paid for them.Thus, a transferof purchasingpower fromthe well to the ill will increasethe demandfor medical services. This will manifestitself in the shortrun in an increasein theprice of medicalservices and in the long runin an increasein theamount sup- plied. With this in mind,the followingstatement can be made (Second OptimalityTheorem): If thereare no increasingreturns in production, and if certainother minor conditions are satisfied,then every optimal state is a competitiveequilibrium corresponding to some initialdis- tributionof purchasingpower. Operationally, the significanceof this propositionis thatif the conditionsof the twooptimality theorems are satisfied,and if theallocation mechanism in thereal worldsatisfies the conditionsfor a competitivemodel, then social policycan confineitself to steps taken to alter the distributionof purchasingpower. For any given distributionof purchasingpower, the marketwill, under the assumptionsmade, achieve a competitiveequilibrium which is neces- sarilyoptimal; and any optimalstate is a competitiveequilibrium cor- respondingto some distributionof purchasingpower, so that any desiredoptimal state can be achieved. The redistributionof purchasingpower among individualsmost simplytakes the formof money:taxes and subsidies.The implications of such a transferfor individualsatisfactions are, in general,not knownin advance. But we can assumethat society can ex post judge the distributionof satisfactionsand, if deemedunsatisfactory, take steps to correctit by subsequenttransfers. Thus, by successiveap- proximations,a mostpreferred social state can be achieved,with re- sourceallocation being handled by the marketand publicpolicy con- finedto the redistributionof moneyincome.2 If, on the contrary,the actual marketdiffers significantly from the competitivemodel, or if the assumptionsof the two optimalitythe- oremsare not fulfilled,the separationof allocativeand distributional proceduresbecomes, in most cases, impossible.3 The firststep thenin the analysisof the medical-caremarket is the 2The separationbetween allocation and distributioneven under the above assumptions has 4osSed over problemsin the executionof any desiredredistribution policy; in practice, it is virtuallyimpossible to find a set of taxes and subsidies that will not have an ad- verse effecton the achievementof an optimal state. But this discussion would take us even furtherafield than we have already gone. 'The basic theoremsof welfare economics alluded to so brieflyabove have been the subject of voluminous literature,but no thoroughlysatisfactory statement covering both the theoremsthemselves and the significanceof exceptionsto them exists. The positive assertionsof welfareeconomics and theirrelation to the theoryof competitiveequilibrium are admirably covered in Koopmans [181. The best summary of the various ways in which the theoremscan fail to hold is probablyBator's [6]. 944 THE AMERICAN ECONOMIC REVIEW comparisonbetween the actual marketand thecompetitive model. The methodologyof thiscomparison has been a recurrentsubject of con- troversyin economicsfor over a century.Recently, M. Friedman[15] has vigorouslyargued that the competitiveor any othermodel should be testedsolely by its abilityto predict.In the contextof competition, he comesclose to arguingthat prices and quantitiesare the onlyrele- vant data. This point of view is valuable in stressingthat a certain amountof lack of realismin the assumptionsof a model is no argu- mentagainst its value. But theprice-quantity implications of thecom- petitivemodel for pricing are noteasy to derivewithout major--and, in manycases, impossible-econometricefforts. In thispaper, the institutional organization and theobservable mores of the medicalprofession are includedamong the data to be used in assessingthe competitivenessof the medical-caremarket. I shall also examinethe presenceor absence of the preconditionsfor the equiva- lence of competitiveequilibria and optimalstates. The major competi- tive preconditions,in the sense used here,are three: the existenceof competitiveequilibrium, the marketabilityof all goods and services relevantto costsand utilities,and nonincreasingretiurns. The firsttwo, as we have seen,insure that competitive equilibrium is necessarilyop- timal; the thirdinsures that everyoptimal state is the competitive equilibriumcorresponding to some distributionof income.4The first and thirdconditions are interrelated;indeed, nonincreasing returns plus some additionalconditions not restrictivein a moderneconomy implythe existenceof a competitiveequilibrium, i.e., implythat there will be someset of priceswhich will clear all markets.5 The conceptof marketabilityis somewhatbroader than the tradi- tional divergencebetween private and social costs and benefits.The latterconcept