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