Arrow a Uncertainty and the welfare Economics of Medical Care 851 THE AMERICAN ECONOMIC REVIEW VOLUME LIII DECEMBER 1963 UNCERTAINTY AND THE WELFARE ECONOMICS OF MEDICAL CARE By KENNETH J. ARROW* I. Introduction: Scope and Method This paper is an explorator and tentative study of the specfc is contended here, on the basis of comparison of obvious characteris- tics of the medical-care industry with the norms of welfare economics as adaptations to the existence of uncertainty in the incidence of dis- ease and in the efficacy of treatmen It should be noted that the subject is the medical-care industr health. The causal factors in health are many, and the provision of medical care is only one. Particularly at low levels of income, other commodities such as nutrition, shelter, clothing, and sanitation may e much more significant. It is the complex of services that center about the physician, private and group practice, hospitals, and public health, which I propose to discuss The focus of discussion will be on the way the operati of th medical-care industry and the efficacy with which it satisfies the needs of society differ from a norm, if at all The "norm"that the econo- mist usually uses for the purposes of such comparisons is the operation of a competitive model, that is, the flows of services that would be The author is professor of economics at Mushkin, and C. R. Rorem. This paper Foundation as part of a series of papers on the
852 Journal of Health Politics, Policy and Law THE AMERICAN ECONOMIC REVIEW offered and purchased and the prices that would be paid for them if each individual in the market offered or purchased services at the going prices as if his decisions had no influence over them, and the going equilibrium prices were such that the amounts of services which were available alled the total amounts which other individuals were willing to urchase, with no imposed restrictions on supply or demand a The interest in the competitive model stems partly from its pre- sumed descriptive power and partly from its implications for economic efficiency. In particular, we can state the following well-known prop osition(First Optimality Theorem). If a competitive equilibrium exists at all. and if all commodities relevant to costs or utilities are in fact priced in the market, then the equilibrium is necessarily optimal in the following precise sense (due to V. Pareto) There is no other allocation of resources to services which will make all participants iD he market better off Both the conditions of this optimality theorem and the definition of optimality call for comment. a definition is just a definition, but when the definiendum is a word already in common use with highly favor- able connotations, it is clear that we are really trying to be persuasive we are implicitly recommending the achievement of optimal states. It is reasonable enough to assert that a change in allocation which makes all participants better off is one that certainly should be made; this is a value judgment, not a descriptive proposition, but it is a very weak one. From this it follows that it is not desirable to put up with a non- optimal allocation but it does not follow that if we are at an alloca tion which is optimal in the Pareto sense, we should not change to any ther. We cannot indeed make a change that does not hurt someone but we can still desire to change to another allocation if the change makes enough participants better off and by so much that we feel that the injury to others is not enough to offset the benefits. Such inter- personal comparisons are, of course, value judgments. The change, however, by the previous argument ought to be an optimal state; of course there are many possible states, each of which is optimal in the ense here used However, a value judgment on the desirability of each possible distribution of benefits and costs corresponding to each possible re- allocation of resources is not, in general, necessary. Judgments about the distribution can be made separately, in one sense from those about allocation if certain conditions are fulfilled. Before stating the relevant proposition, it is necessary to remark that the competitive equilibrium chieved depends in good measure on the initial distribution of pur chasing power, which consists of ownership of assets and skills that This point has been y I. M. D. Little [19, 74]. For the concept of a persuasive definition, se
Arrow m Uncertainty and the Welfare Economics of Medical Care 853 ARROW: UNCERTAINTY AND MEDICAL CARE command a price on the market. a transfer of assets among individ uals will, in general, change the final supplies of goods and services and the prices paid for them. Thus, a transfer of purchasing power from the well to the ill will increase the demand for medical services. This will manifest itself in the short run in an increase in the price of medical services and in the long run in an increase in the amount sup With this in mind, the following statement can be made(Second Optimality Theorem ): If there are no increasing returns and if certain other minor conditions are satisfied then every optimal state is a competitive equilibrium corresponding to some initial dis- tribution of purchasing power. Operationally, the significance of proposition is that if the conditions of the two optimality theorems are tisfied and if the allocation mechanism in the real world satisfies the conditions for a competitive model, then social policy can confine itself to steps taken to alter the distribution of purchasing power. For any given distribution of purchasing power, the ,ma kat wl, ainier the assumptions made, achieve a competitive equilibrium which is neces sarily optimal; and any optimal state is a competitive equilibrium cor responding to some distribution of purchasing power, so that any The redistribution of purchasing power among individuals most simply takes the form of money: taxes and subsidies. The implications of such a transfer for individual satisfactions are in general, not known in advance. But we can assume that society can er post judge the distribution of satisfactions and, if deemed unsatisfactory take steps to correct it by subsequent transfers. Thus, by successive proximations, a most preferred social state can be achieved with re- source allocation being handled by the market and public policy con fined to the redistribution of money If, on the contrary, the actual market differs significantly from the competitive model, or if the assumptions of the two optimality the- orems are not fulfilled, the separation of allocative and distributional procedures becomes, in most cases, impossible. The first step then in the analysis of the medical-care market is the a The separation bet ween allocation and distribution subsidise further afield than we have already gone. The basic theorems of welfare economics alluded to so briefly above have been the admirably covere omies and their relation to teptions to them exists. The ing ot Koopmans [18]. The best summary of the various ways in which the theorems can fail to hold is probably Bator's [6
854 Journal of Health Politics, Policy and Law THE AMERICAN ECONOMIC REVIEW omparison between the actual market and the competitive model. Th methodology of this comparison has been a recurrent subject of con oversy in economics for over a century. Recently, M. Friedman [15] has vigorously argued that the competitive or any other model should be tested solely by its ability to predict. In the context of competition he comes close to arguing that prices and quantities are the only rele- vant data. This point of view is valuable in stressing that a certain amount of lack of realism in the assumptions of a model is no argu ment against its value. But the price-quantity implications of the com- petitive model for pricing are not easy to derive without major--and, in many cases, impossible--econometric efforts Hammer In this paper, the institutional organization and the observable mores (institutions of the medical profession are included among the data to be used in economic data) assessing the competitiveness of the medical-care market I shall also examine the presence or absence of the preconditions for the equiva lence of competitive equilibria and optimal states. The major competi- tive preconditions, in the sense used here are three: the existence of competitive equil all goods and services relevant to costs and utilities, and nonincreasing returns. The first two as we have seen, insure that competitive equilibrium is necessarily op- timal; the third insures that every optimal state is the competitive equilibrium corresponding to some distribution of income. The first and third conditions are interrelated indeed nonincreasing returns plus some additional conditions not restrictive in a modern economy mply the existence of a competitive equilibrium, i. e, imply that there will be some set of prices which will clear all markets. The concept of marketability is somewhat broader than the tradi tional divergence between private and social costs and benefits. The latter concept refers to cases in which the organization of the market does not require an individual to pay for costs that he imposes on others as the result of his actions or does not permit him to receive compensation for benefits he confers. In the medical field, the obvious example is the spread of communicable diseases. An individual who fails to be immunized not only risks his own health, a disutility which presumably he has weighed against the utility of avoiding the proce- dure but also that of others. In an ideal price system, there would be a price which he would have to pay to anyone whose health is endan gered a price sufficiently high so that the others would feel compen ated; or, alternatively, there would be a price which would be paid to him by others to induce him to undergo the immunization procedure. There are further minor conditions, for which see Koopmans [1, pp 50-5 For a more prec se statement of the existence conditions, see Koopmans [18, pp. 56-60] or Debreu【12,Ch.5l
Arrow a Uncertainty and the welfare Economics of Medical Care 855 ARROW: UNCERTAINTY AND MEDICAL CARE Either system would lead to an optimal state, though the distributional implications would be different. It is, of course, not hard to see that such price systems could not, in fact, be practical; to approximate an optimal state it would be necessary to have collective intervention in the form of subsidy or tax or compulsion. By the absence of marketability for an action which is identifiable, Chernew technologically possible and capable of influencing some individual's (marketability welfare. for better or for worse is meant here the failure of the exist- ng market to provide a means whereby the services can be both of fered and demanded upon payment of a price. Nonmarketability may e due to intrinsic technological characteristics of the product which prevent a suitable price from being enforced as in the case of com- es, or it may be due to social or historical such as those prohibiting an individual from selling himself into slay ery. This distinction is, in fact, difficult to make precise, though it is obviously of importance for policy; for the present purposes, it will be sufficient to identify nonmarketability with the observed absence of markets The instance of nonmarketability with which we shall be most con- erned is that of risk-bearing The relevance of risk-bearing to medical are seems obvious; illness is to a considerable extent an unpredictable phenomenon. The ability to shift the risks of illness to others is worth a price which many are willing to pay. Because of pooling and of supe- rior willingness and ability, others are willing to bear the risks. Never- theless, as we shall see in greater detail, a great many risks are not covered, and indeed the markets for the services of risk -coverage are borly developed or nonexistent. Why this should be so is explained in more detail in Section IVC below; briefly, it is impossible to draw up insurance policies which will sufficiently distinguish among risks, par- ticularly since observation of the results will be incapable of distin guishing between avoidable and unavoidable risks so that incentives to avoid losses are diluted he optimality theorems discussed above are usually presented in the literature as referring only to conditions of certainty, but there is no difficulty in extending them to the case of risks, provided the addi tional services of risk-bearing are inchuded with other commodities. However, the variety of possible risks in the world is really stagger ing. The relevant commodities include, in effect, bets on all possible occurrences in the world which impinge upon utilities. In fact, many of hese"commodities, ' i.e., desired protection against many risks, a
856 Journal of Health Politics, Policy and Law 946 THE AMERICAN ECONOMIC REVIEW simply not available. Thus, a wide class of commodities is nonmarket able, and a basic competitive precondition is not satisfied. There is a still more subtle consequence of the introduction of risk- Robinson bearing considerations. When there is uncertainty, information or knowledge becomes a commodity. Like other commodities, it has a cost of production and a cost of transmission, and so it is naturally not spread out over the entire population but concentrated among those who can profit most from it. (These costs may be measured in time or cult to discuss in the rational terms usually employed. The value of information is frequently not known in any meaningful sense to the buyer; if, indeed, he knew enough to measure the value of informa tion, he would know the information itself. But information, in the form of skilled care, is precisely what is being bought from most physi- cians, and, indeed, from most professionals. The elusive character of information as a commodity suggests that it departs considerably from he usual marketability assumptions about commodities, That risk and uncertainty are, in fact, il care hardly needs argument. I will hold that virt features of this industry, in fact, stem from the pi The nonexistence of markets for the bearing of some risks in the first reduces welfare for those who wish to transfer those risks to others for a certain price, as well as for those who would find it proft able to take on the risk at such prices. But it also reduces the desire to render or consume services which have risky consequences; in techni cal language, these commodities are complementary to risk-bearing Conversely, the production and consumption of commodities and serv ices with little risk attached act as substitutes for risk-bearing and are encouraged by market failure there with respect to risk-bearing. Thus the observed commodity pattern will be affected by the nonexistence of m tion of the law of large numbers Since most objects of insu ear that this effect is sufficiently great to create serious y of co (R&D and nat of production. Hence, it is not surprising that a free enterprise economy will ten to underinvest in research; see Nelson [211 and Arrow [41
Arrow a Uncertainty and the Welfare Economics of Medical Care 857 UNCERTAINTY AND MEDICAL CAR The failure of one or more of the competitive preconditions has as bloche, its most immediate and obvious consequence a reduction in welfare chernew below that obtainable from existing resources and technology, in the Glied, Hammer more can be said. I propose here the view that, when the market fails (nonmarket to achieve an optimal state society will, to some extent at least, recog- institutions) nize the gap, and nonmarket social institutions will arise attempting to bridge it. Certainly this process is not necessarily conscious; nor is it uniformly successful in approaching more closely to optimality when the entire range of consequences is considered. It has always been a favorite activity of economists to point out that actions which on their ace achieve a desirable goal may have less obvious consequences, articularly over time, which more than offset the original gains But it is contended here that the special structural characteristics of the medical-care market are largely attempts to overcome the lack of optimality due to the nonmarketability of the bearing of suitable risks and the imperfect marketability of information. These compensatory institutional changes, with some reinforcement from usual profit mo- tives, largely explain the observed noncompetitive behavior of the medical-care market, behavior which, in itself, interferes with opti- mality. The social adjustment towards optimality thus puts obstacles ts own path The doctrine that society will seek to achieve optimality by non market means if it cannot achieve them in the market is not novel Certainly, the government, at least in its economic activities, is usually implicitly or explicitly held to function as the agency which substitutes for the market's failure. I am arguing here that in some circum- that the medical-care industry, with its variety of speciality gap some ancient, some modern, exemplifies this tendency. It may be useful to remark here that a good part of the preference reinhardt for redistribution expressed in government taxation and expenditure policies and private charity can be reinterpreted as desire for insur- ance. It is noteworthy that virtually nowhere is there a system of sub sidies that has as its aim simply an equalization of income. The sub sidies or other governmental help go to those who are disadvantaged in life by events the incidence of which is popularly regarded as unpre- ns have had to eck and Scherer [23, pp. 581 ence to V. Fuchs)and [1, pp. 71-751 or an explicit statement of this view, see Baumol (81. But I believe this position is implicit in most discussions of the functions of governmen
858 Journal of Health Politics, Policy and Lay THE AMERICAN ECONOMIC REVIEW dictable: the blind dependent children, the medically optimality, in a context which includes risk-bearing hat appears to be motivated by distributional value looked at in a narrower context. 1 his paper. Section II is a catalogue of stylized generalizations about the medical-care market which differentiate it from the usual commod ity markets. In Section III the behavior of the market is compared with that of the competitive model which disregards the fact of uncer- tainty. In Section IV, the medical-care market is compared, both as to behavior and as to preconditions, with the ideal competitive market that takes account of uncertainty an attempt will be made to demon strate that the characteristics outlined in Section II can be explained either as the result of deviations from the competitive preconditions or as attempts to compensate by other institutions for these failures. The discussion is not designed to be definitive, but provocative. In particu- lar, I have been chary about drawing policy inferences; to a consider- able extent, they depend on further research, for which the present paper is intended to provide a framework IL. A Survey of the Special Characteristics of the Medical-Care Market This section will list selectively some characteristics of medical care which distinguish it from the usual commodity of economics textbook The list is not exhaustive, and it is not claimed that the characteristics listed are individually unique to this market. But, taken together they do establish a special place for medical care in economic analy A. The Nature of demand Sloan (role of the demand for medical services is that it is not steady in origin as, for example, for food or clothing, but irregular and unpredictable. Medi cal services, apart from preventive services, afford satisfaction only the event of illness, a departure from the normal state of affairs. It is ard, indeed, to think of another commodity of significance in the average budget of which this is true. a portion of legal ser oted to defense in criminal trials or to lawsuits, might fall in gory but the incidence is surely very much lower(and, of course, there that all redistribution can be interpreted as"inco a For an illuminating survey to which I am much indebted see S. Mushkin [201
Arrow a Uncertainty and the Welfare Economics of Medical Care 859 ARROW: UNCERTAINTY AND MEDICAL CARE are, in fact, strong institutional similarities between the legal andSage medical-care markets. )13 In addition, the demand for medical services is associated, with a of medicine) considerable probability, with an assault on personal integrity. There is ome risk of death and a more considerable risk of impairment of full functioning. In particular, there is a major potential for loss or reduc tion of earning ability. The risks are not by themselves unique; food is lso a necessity but avoidance of deprivation of food can be guaranteed with sufficient income where the same cannot be said of avoidance of illness. Illness is, thus, not only risky but a costly risk in itself, apart om the cost of medical care B. Expected Behavior of the Physician It is clear from everyday observation that the behavior expected of Bloche, sellers of medical care is different from that of business men in gen- hal eral. These expectations are relevant because medical care belongs to Millenson che category of commodities for which the product and the activity of production are identical. In all such cases, the customer cannot test the Peterson product before consuming it, and there is an element of trust in the (expected relation. But the ethically understood restrictions on the activities of behavior of a physician are much more severe than on those of, say, a barber. His physicians behavior is supposed to be governed by a concern for the customers welfare which would not be expected of a salesman. In Talcott Par- sonss terms, there is a" collectivity-orientation, " which distinguishes medicine and other professions from business, where self-interest on the part of participants is the accepted norm. s A few illustrations will indicate the degree of difference between the behavior expected of physicians and that expected of the typical busi nessman. (1) Advertising and overt price competition are virtually eliminated among physicians. (2)Advice given by physicians as to further treatment by himself or others is supposed to be completely governmental demand, military power is an example o nerged, though the precise social structure is different f not hard run, experience with the quality See [22, p. 463]. The whole of [22, Ch. 10] is a most illuminating analysis of the acknowledge here my indebt I am indebted to Herbert Klarman of Johns Hopkins University for some of the points discussed in this and the following paragraph
860 Journal of Health Politics, Policy and Law THE AMERICAN ECONOMIC REVIEW Kronick divorced from self-interest. (3) It is at least claimed that treatment is harity) dictated by the objective needs of the case and not limited by financial considerations, While the ethical compulsion is surely not as absolute in fact as it is in theory, we can hardly suppose that it has no influence over resource allocation in this area. Charity treatment in one form or another does exist because of this tradition about human rights to ade- quate medical care. 8(4) The physician is relied on as an expert in (lawyerization certifying to the existence of illnesses and injuries for various legal and other purposes. It is socially expected that his concern for the correct conveying of information will, when appropriate, outweigh his desire Needleman Departure from the profit motive is strikingly manifested by the (nonprofits) overwhelming predominance of nonprofit over proprietary hospitals. 20 The hospital per se offers services not too different from those of a hotel, and it is certainly not obvious that the profit motive will not lead to a more efficient supply. The explanation may lie either on the supply ide or on that of demand. The simplest explanation is that public and private subsidies decrease the cost to the patient in nonprofit hospitals. A second possibility is that the association of profit-making with the supply of medical services arouses suspicion and antagonism on the part of patients and referring physicians, so they do prefer nonprofit tions. Either explanation implies a preference on the part of some whether donors or patients, against the profit motive in the bility to pay is strongly ingrained. Such a perceptive observer as Rene dubos has medical ethics, as though this unp ical resources: one has only to have been poor to realize the error. research is a study of the exact nature of the va ved and medical care paid This roie is enhanced in a socialist society, where the state itself is actively concerned th illness in relation to work; see Field [14, Ch 9 About 3 per cent of beds were in proprietary hospitals in 1958, against 30 per cent in Chart 4-2, p. 60] "C.R. Rorem has pointed out to me some further factors in this analysis. (1)Given onomies of scale would dictate a predominance of comnunity-sponsored hospitals,(2)
