ARROW (1963): UNCERTAINTY AND THE WELFARE ECONOMICS OF MEDICAL CARE
BY KENNETH J. ARROW*
I. INTRODUCTION: SCOPE AND METHOD
This paper is an exploratory and tentative study of the specific differentia of medical care as the object of normative economics. It is contended here, on the basis of comparison of obvious characteristics of the medical-care industry with the norms of welfare economics, that the special economic problems of medical care can be explained as adaptations to the existence of uncertainty in the incidence of disease and in the efficacy of treatment.
It should be noted that the subject is the medical-care industry, not 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 be 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 operation of the 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 economist usually uses for the purposes of such comparisons is the operation of a competitive model, that is, the flows of services that would be 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 prices were such that the amounts of services which were available equalled the total amounts which other individuals were willing to purchase, with no imposed restrictions on supply or demand.
The interest in the competitive model stems partly from its presumed descriptive power and partly from its implications for economic efficiency. In particular, we can state the following well-known proposition (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 in the 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 favorable connotations, it is clear that we are really trying to be persuasive; we are implicitly recommending the achievement of optimal states.1 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 allocation which is optimal in the Pareto sense, we should not change to any other. 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 interpersonal 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 sense here used.
However, a value judgment on the desirability of each possible new distribution of benefits and costs corresponding to each possible reallocation 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 achieved depends in good measure on the initial distribution of purchasing power, which consists of ownership of assets and skills that command a price on the market. A transfer of assets among individuals 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 supplied.
With this in mind, the following statement can be made (Second Optimality Theorem): If there are no increasing returns in production, and if certain other minor conditions are satisfied, then every optimal state is a competitive equilibrium corresponding to some initial distribution of purchasing power. Operationally, the significance of this proposition is that if the conditions of the two optimality theorems are satisfied, 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 market will, under the assumptions made, achieve a competitive equilibrium which is necessarily optimal; and any optimal state is a competitive equilibrium corresponding to some distribution of purchasing power, so that any desired optimal state can be achieved.
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 ex post judge the distribution of satisfactions and, if deemed unsatisfactory, take steps to correct it by subsequent transfers. Thus, by successive approximations, a most preferred social state can be achieved, with resource allocation being handled by the market and public policy confined to the redistribution of money income.2
If, on the contrary, the actual market differs significantly from the competitive model, or if the assumptions of the two optimality theorems are not fulfilled, the separation of allocative and distributional procedures becomes, in most cases, impossible.3
The first step then in the analysis of the medical-care market is the comparison between the actual market and the competitive model. The methodology of this comparison has been a recurrent subject of controversy 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 relevant 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 argument against its value. But the price-quantity implications of the competitive model for pricing are not easy to derive without major—and, in many cases, impossible—econometric efforts.
In this paper, the institutional organization and the observable mores of the medical profession are included among the data to be used in assessing the competitiveness of the medical-care market. I shall also examine the presence or absence of the preconditions for the equivalence of competitive equilibria and optimal states. The major competitive preconditions, in the sense used here, are three: the existence of competitive equilibrium, the marketability of 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 optimal; the third insures that every optimal state is the competitive equilibrium corresponding to some distribution of income.4 The first and third conditions are interrelated; indeed, nonincreasing returns plus some additional conditions not restrictive in a modern economy imply the existence of a competitive equilibrium, i.e., imply that there will be some set of prices which will clear all markets.5
The concept of marketability is somewhat broader than the traditional 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 procedure, 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 endangered, a price sufficiently high so that the others would feel compensated; or, alternatively, there would be a price which would be paid to him by others to induce him to undergo the immunization procedure. 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, technologically possible, and capable of influencing some individual’s welfare, for better or for worse, is meant here the failure of the existing market to provide a means whereby the services can be both offered and demanded upon payment of a price. Nonmarketability may be due to intrinsic technological characteristics of the product which prevent a suitable price from being enforced, as in the case of communicable diseases, or it may be due to s...