medical insurance, technological change, and welfare

MEDICAL INSURANCE, TECHNOLOGICAL CHANGE, AND WELFARE

JOHN H. GODDEERIS*

Concerns have been expressed about the welfare effects of expensive innovations in medical care financed largely through medical insurance. This paper develops a model which considers such issues. It is shown that even if insurance is purchased optimally (subject to a plausible constraint on the form of the contract), innovations may be adopted that have the effect of reducing expected welfare. The question of how the benefits of medical innovations ought to be measured in the presence of insurance is also explored.

Economists have for some time been aware of the conflict between risk-spreading and appropriate incentives involved in medical insurance (Pauly, 1968; Zeckhauser, 1970). Some have contended that the rapid growth in medical expenditures experi- enced in the U.S. is primarily a result of “overinsurance” (Feldstein, 1973; Feldstein and Friedman, 1977). But analyses of the distorting effects of insurance have been carried out in models in which the state of technology is presumed to be fixed. Little or no attention has been paid to the interaction of medical insurance and technological change. In fact, medical knowledge is advancing rapidly; indeed, some argue that technological change, not the growth of insurance, is the driving force behind medical expenditure increases (Altman and Blendon, 1979). The path of technological change can be supposed to be influenced by the manner in which medical care is financed. Hence analysis of models that incorporate both insurance and technological change seems warranted. This paper explores the welfare economics of changes in medical knowledge, taking account of the existence of insurance. It is shown that some innovations may be adopted which have the effect of reducing welfare in a well-defined sense, even if insurance is itself purchased optimally. The question of how the benefits of innovations ought to be evaluated in the presence of insurance is then pursued. The paper concludes with some comments on distributional consider- ations and on the general economic principles explored here.

I. WELFARE-REDUCING TECHNOLOGICAL CHRNGE

The notion that technological progress could reduce welfare may strike economists as rather strange. Since economists are accustomed to thinking in terms of rational consumers and producers, it seems impossible that something that expands productive capabilities could reduce welfare. After all, any advances that do not increase welfare may simply be ignored; they do not have to be adopted. Yet in the area of medical care, the idea that technological advance is an unmixed blessing has increasingly been called into question (U.S. Congress, Office of Technology Assess- ment, 1978; Russell, 1979). There appears to be a widespread feeling that the benefits we are getting from some recent advances may not justify the accompanying costs.

‘Michigan State University. I wish to thank Burton Weisbrod, Charles Wilson, Arthur Goldberger, Ronald Fisher, Mary Winicker, and an anonymous referee for helpful comments on earlier drafts.

56

GODDEERIS: MEDICAL INSURANCE AND TECHNOLOGICAL CHANGE 57

The realities of the market for medical care are, of course, far removed from the economist’s textbook competitive model. Hence, given the actual imperfections in the market, an attempt to establish the possibility of welfare-reducing technological change may proceed along several plausible lines. If, for example, physicians always choose the treatment believed to be most medically beneficial (with no regard for cost), and consumers simply accept physicians’ judgments, then it is obviously possible for technological advances to yield marginal benefits at such high cost as to reduce welfare. Alternatively, a new treatment - adopted before its effects are fully understood - may in retrospect prove to be even medically harmful. The task in this section is to show that such changes are possible in a model of well-informed actors, in which medical insurance is purchased optimally. The market imperfection accounting for this result is a plausible constraint on the type of insurance contract offered.

A. TheModel We begin with a model of medical insurance similar to those developed by Zeck-

hauser (1970) and Arrow (1976), modified to permit consideration of technological change. The typical individual seeks to maximize an expected utility function of the form1

where i indexes the state of illness, a random variable, and p, denotes the probability of state i. Once in a particular state, the individual’s utility is given by ui(x,, h, (mi)), where x, is consumption (other than medical care) and m, is expenditure on medical care. The u functions are assumed twice differentiable, increasing, and jointly concave in x and h. The functions h(m), referred to as “health production functions,” are introduced to facilitate discussion of technological change. A particular h, (mi) denotes the relationship between medical expenditure and improvements in health, given that illness i occurs. Its form depends on the state of technology. A technological advance is defined as a shift from some h:(m,) to some h:(mi), such that h:(mi) 2 hf(m,) for all m, , with the strict inequality holding for at least some m, .2

Insurance in this model takes the form of a contract purchased ex unte - before the state of illness becomes known - which consists of a premium ?r and a co- insurance rate z. The individual pays the premium ex ante, and in return the frac- tion (1 - z) of his medical expenditures are covered by the insurer. The set of available (a, z) combinations is constrained by the condition that for each contract the premium must equal expected benefits per individual. Medical expenditures are made ex post - after the insurance contract is purchased and the state has become known

1. We assume for simplicity that individuals have identical utility functions and endowments and face the same (exogenous) probability distribution of illness states. Each gets an independent drawing from that distribution, however, which creates the possibility for risk-pooling.

2. An innovation may apply to more than one illness state, but the weak inequality must hold every- where for all i .

58 ECONOMIC INQUIRY

- so as to maximize utility given the insurance policy held. Notice that R is treated as a parameter at the time the expenditure decision is made, but that in equilibrium it must be a function of expected medical expendit~re.~

The form of the insurance contract requires further comment. The linearity assumption (that benefits are a fixed proportion of medical expenditure), though used frequently by economists in theoretical and empirical work, is clearly a simpli- fication. In practice medical insurance is more complicated than that. Linearity per se is not crucial to the analysis. More important is the fact that benefits are an increasing function of medical expenditure, rather than being strictly determined by the actual state of the world (state of illness). It is well-known that insurance of this type creates a problem of moral hazard by distorting the choice between medical care and other consumption for the ill individual (Pauly, 1968). The possibility of welfare-reducing change is a manifestation of this moral hazard problem.

For a given state of technology, the choice of z (and its associated ?r) determines V; so that the consumer’s problem ex ante may be described as choosing the optimal co-insurance rate. For a given state of technology there is thus an optimized V; denoted V*, where V* = max V(z).

We may now define welfare-reducing technological change. If we denote V* before the change as v, and afterward as V,*, a welfare-reducing change is one such that V,* < %*. Expected utility is higher before the advance than after. Put another way, if an individual could be presented with the choice ex ante between a world with or without this advance, he would choose the world without it. Notice that this definition does not rule out the possibility that, ex post, an individual in a health state to which the advance applies might end up better off with the advance than without it. Such a change could still satisfy the definition if the effects on utility in the other states (through the effect on the premium, for example) were such as to reduce V*. This notion of a welfare-reducing advance seems a reasonable one. By taking the ex ante perspective, it takes account of the fact that with insurance the costs of expensive technologies may be borne largely by people who will never use them.

B. Some Examples

a series of examples.

and i = 2 denotes “ill,” and p is the probability of illness. Let

The possibility of welfare-reducing technological change is easily shown through

1. For simplicity, consider a two-state world, in which i = 1 denotes “healthy”

3. This is a crucial (and seemingly reasonable) feature of the model. See the discussion in Zeckhauser (1970, p. 12).


Suppose that endowment income, x,, is the same in both states of the world, so that

x, = xo - K - z m , and

T = p ( 1 - z ) m , ,

medical care being purchased only if illness occurs. Let

p = . 1 and x, = 10.

Suppose that the original technology is such that

-10, if m2 < 5

-4, if m, r 5 (5) h,(m,) =

Heuristically, illness creates a utility loss that can be partially restored through expenditure on medical care. In this case it is optimal to fully insure (z = 0), which leads to m, = 5 , K = .5, and V; = -.000476 (the subscript b denotes “before innovation”).

Now suppose that an innovation is developed that offers additional health benefits, but only at a high level of medical expenditure. The h function becomes

-10, if m, < 5

-4, if 5 5 m, < 15

-3, if m, I 15. (6) h,(m,) =

At z = 0, this innovation is adopted since it offers some benefit at no marginal cost to the insured con~umer.~ But the higher level of medical expenditure implies a larger premium. Simple calculation shows that with m = 15 and K = 1.5, V,(z = 0) = -.000592 < v,* (a denotes “after innovation”). The presence of the innovation leads to a reduction in expected utility.

The true cost of this innovation is so large relative to its benefits that its use is demanded only because the co-insurance rate is so low. If the rate is adjusted upward to z 2 . 1, the additional benefit is too expensive to the ill individual and he chooses m = 5. But, as it happens, the larger added expenditures in the ill state leads to an even greater reduction in expected utility. A zero co-insurance rate remains optimal after the innovation. Thus v,* < vd”, and the innovation - which clearly expands productive capabilities and is in fact adopted - is welfare-reducing by our ~ t a n d a r d . ~

4. Note again that the premium is taken as a parameter at the time the medical expenditure decision is made. A seeming difficulty in our example is that with z = 0, m, appears to be indeterminate. We can remove the indeterminacy, however, by assuming that - taking z and r as parameters - the ill individual chooses the smallest m at which utility is maximized.

5. Another way to look at the welfareloss is to ask how much of his endowment would a consumer be willing to give up in order to live in a world without this innovation. In this case the answer is about .2, two percent of the endowment.

60 ECONOMIC INQUIRY

How is this result possible? Why can this innovation not simply be ignored so that no welfare loss occurs? It is because of the nature of the insurance contract and the fact that the individual acts ex post as though his expenditure decisions have no effect on the insurance premium. Since individuals act this way, an ill person facing a low co-insurance rate will make use of the innovation if it is available. Moreover, this use must be reflected in the premium. Hence, after the innovation becomes available, the individual can no longer purchase an insurance contract with a very low co- insurance rate at the same premium as before. The premium must be higher to reflect the higher level of expected medical expenditure. In this sense the innovation cannot simply be ignored; its very presence affects the set of insurance contracts available. Suppose alternatively that individuals could purchase contracts arrang- ing actuarially fair lump-sum transfers across states of the world. For example, if illness has probability p and health probability (1 - p) , an individual could arrange to receive one dollar if illness occurs in return for a payment of p / ( 1 - p ) dollars if he remains healthy. Such contracts might be called "perfect insurance,"since they permit risk-spreading without distorting relative prices. The welfare-reducing result could not occur if perfect insurance were available; in that case the development of an innovation does not change the set of available contracts.6 In practice, however, medical insurance seems not to take this form. Since each type of illness and degree of severity is in principle a different state of the world, such contracts would evi- dently be very difficult and costly to set up and enforce. The obvious problems include simply enumerating the different possible states, as well as determining which one has o ~ c u r r e d . ~

The welfare reduction would also not occur if the consumer could purchase the same contract as before the innovation, with the provision that the innovation would not be covered. Then that technology would be effectively ignored. To assume automatically that such a contract would be written, however, is to assume away all information and transaction costs. A modification of the example will give a further indication of why such contracts may not emerge.

2. Let us change the example somewhat by adding a second illness state, so that

where p = p z + p 3 . The function u' and u2 are given by (3) and (4), and

~3 (x3, h3) = -e%eh3.

6. The availability of actuarially fair transfers across states - what is called perfect insurance here - is sufficient to mure a Pareto optimum in this model. This is essentially a special case of Arrow's (1964) optimality result (Malinvaud, 1972).

7. It is interesting to ask whether the provision of insurance through health maintenance organiza- tions (HMOs) might solve the problem discussed here. A possible model with HMOs is the following. The consumer pays only a premium (no co-insurance) and delegates the medical care decision to the HMO. With identical individuals choosing (a ante) among HMOs, the only plans to survive in equilibrium will be those that offer r, m, t = 1, . . . , I) combinations that maximize Ei-, p , d(r, - r, h'(m,)) subject to T = C: -, p,m,. This f& short of perfect insurance (the endowment is not freely transferred across states at actuarial rates), but it does eliminate the possibility of welfare reducing change, since an innovation will only be adopted if it makes the plon more attractive to consumers. To presume that HMOs act in this way, however, ignores all information problems. The contract just described amounts to an ex ante determination of what medical expenditure would be in all possible states of the world. This seems unrealistic for the same reasoIls perfect insurance does. Whether HMOs do in fact use expensive technologies differently from conventional insurance plans is an interesting empirical question.


We continue to assume that endowment income is the same in all states, so that

x, = xo - R - z m i , i = 1,2 ,3 , and

where mi is medical expenditure if state i occurs. Let

P = - 1 , pz = .095, p, = .005, andx, = 10.

Suppose that, as before, h,(m,) before the innovation is given by (5) , and that

-2, if m3 < 5

-3, if m3 1 5 . h3(m3) =

It is again optimal to choose z = 0. Consider now a single innovation (a new machine, for example) that shifts both m functions. Let h,(m,) again shift to (6), and now

-2, if m3 < 5

-.8, if 5 5 m3 < 15 I 0, if m3 2 15. hdmd =

Simple calculations reveal that z = 0 remains optimal in this case after the innovation and that the innovation is welf are-reducing. This example differs from the previous one in that the innovation does provide substantial benefits for those in state 3. If its use could be restricted to state 3 individuals, it would indeed increase expected utility. But to achieve this increase in welfare, the insurance contract must contain more than just a provision stating whether this particular innovation is covered. Rather, the contract must specify precisely under what conditions it is covered.

The problem illustrated here may have relevance far beyond this simple model. This result may be restated in less technical terms. A technology is introduced that, though costly in use, appears to offer important benefits for a few. Therefore, there is a demand for insurance to cover its costs. But once it is covered by insurance, use of the innovation is demanded by a larger group, a group for whom the benefits are less substantial, for whom the innovation is in an important sense not worth its costs. The result is an increase in expected medical expenditures (and insurance pre- miums), which partially offsets the benefit offered by the advance, or in the extreme case, outweighs the benefit. This story might well apply to many of the most widely known recent technological changes in medicine. The coronary bypass operation, radiation therapy for cancer, electronic fetal monitoring, intensive care, and renal dialysis are all possible candidates8

8. See U.S. Congress, Office of Technology Assessment (1978) and Russell (1979) for discussions of a number of recent innovations in medical care, including estimates of costs and evidence on benefits.

62 ECONOMIC INQUIRY

3. In the health production functions used in the first two examples, health does not improve smoothly with increased medical expenditure; rather certain levels of expenditure are associated with discrete improvements in health. It seems clear that expensive medical treatments often involve such indivisibilities. To see, however, that this condition is not necessary for the result and to gain additional insight, consider the following example. In a two-state case, suppose that h(m) in the ill state is smooth and concave, like h"(m) in figure 1. A technology can be constructed that is "less advanced than K(m) which allows the consumer to attain a higher level of expected utility.

FIGURE 1

AWelfare-Reducing Change

Note first that when insurance is chosen optimally in this model, the V* attained is in general less than could be achieved if perfect insurance were available. Now find the point on h" (m) that would be chosen if perfect insurance were available and purchased optimally. Label it (mo, h") .g The constructed technology follows h"(m) up to (m", h") and then becomes horizontal (or nearly so), like hb(m). Facing hb(m), the consumer chooses (approximately) m' if ill, regardless of the co-insurance rate. Thus the co-insurance rate may be adjusted so as to reach the same level of expected utility as could be achieved with perfect insurance. lo It follows that if hb (m) were the original technology and an innovation shifted it to h"(m), that innovation would be welfare-reducing.

9. At this point, h = u, lu, in the perfect insurance case, since the price of a unit of m is perceived as one unit of x. With co-insurance ratez, m is chosen so that h = z (u, /u2), since here a unit of m is perceived as costing only z units of r. Hence, we expect that the level of m chosen along hb(m) with imperfect insurance is greater than mo. If u, /u, is independent of r this is guaranteed to be true.

10. In some cases, there may be no co-insurance rate between zero and one that leads to the same transfer of income across states as could be achieved with perfect insurance.


This example illustrates the essence of the problem. Insurance against the costs of ill health can only be achieved (in this model) by subsidizing the purchase of medical care. Because of the subsidy, a technique need only provide benefits equal to a frac- tion of its costs in order to be demanded.

II. WELFARE EFFECTS OF INNOVATIONS

As already mentioned, one possible response to the problem of welfare-reducing technological change is to write very specific insurance contracts that exclude particular technologies from coverage. To the same effect, government might simply prohibit the use of certain technologies. Current governmental interest in technology assessment with regard to medical innovations suggests perhaps some interest in the latter approach. But to propose such a strategy rasies another question: by what operational criterion is it possible to judge whether an innovation is welfare- reducing? The economist's instinctive answer to that question is that one must com- pare benefits - that is, willingness-to-pay - with costs. It is not immediately obvious, however, what concepts of benefit and cost are appropriate. Should willingness-to-pay, for example, include or exclude the portion covered by insurance? Within the context of this model an appropriate criterion for assessing the effect on welfare of a given innovation can be developed.

Consider first the case of an innovation that applies to one state j . Assume that all income effects on the demand for medical care are negligible. The only possibly relevant income effects on the demand for care in what follows would result from the effect of the innovation on the insurance premium, and it seems reasonable to assume that these are quite small. We also assume (though we did not in the examples above) that the optimal co-insurance rate before the innovation, denoted Z, remains optimal afterward. This does not seem terribly unreasonable, since if many states are possible and the probability of each one is quite small, no single state would be expected to contribute much to the choice of the co-insurance rate.

Prior to the innovation there is a set of net incomes and health levels in the various states of illness associated with co-insurance rate 2 . Denote these by x, and h, , i = 1, . . . , I. Let Ah be the increase in health in state j resulting from the innovation and Am be the increase in medical expenditure. We want an expression for the change in expected utility due to this innovation. Since the utility effects in all states except i come only through the change in premium, we can simplify notation by aggregating these other states and treating expected utility in this combined state as a function of the insurance premium. That is, we express expected utility before the innovation as

I

%* = C p , ~ ' ( x , , h,) = p 1 ~ ' ( x , , h, ) + (1 - P , ) v (r,). i = l

(7)

Notice that v' = av/d?r, is the negative of the weighted average of marginal utilities of income in all states other than i . The change in ?r associated with the innovation is p i (1 - Z ) Am, while Z Am is the change in out-of-pocket medical expenditure in state i . Expected utility after the innovation is then

v,* = p i u' (x, - pi (1 - X) Am - Z Am, hi + Ah)

+ (1 - p i ) 0 (rb + p i (1 - Z ) Am).

64 ECONOMIC INQUIRY

To further simplify notation we suppress the index j. The change in expected utility associated with this innovation is then

AV = v,*-v,* = p [ u ( x - p ( 1 - Z ) A m - Z A m , h + Ah)-u(x ,h) ]

+ ( l - p ) [ o ( n b + p(1-Z)Am)-V(Tb)] . (9)

Now define e such that u(x, h) = u(x - e, h + Ah). When faced with the choice between technologies that yield health levels h and h + Ah, e is the maximum additional amount that the ill consumer would be willing to pay (out-of-pocket) for the use of the technology yielding h + Ah. In the consumer surplus terminology, e is a compensating variation. Then we may rewrite (9) as

AV = p [ u ( x - p ( 1 - Z ) A m - Z A m , h + A h ) - u ( x - e , h + Ah)] (10)

+ ( l - p ) [ v ( n b + p ( 1 - Z ) A m ) - ~ ( n , ) ] .

Using the mean value theorem, (10) may be rewritten as

( 1 1 ) AV = p ( e - p ( 1 - Z ) A m - Z A m ) GI + ( 1 - p ) p ( l - Z ) A m E ' ,

where GI is u1 evaluated at h + Ah and some level of net income between x - e and x - p ( l - Z)Am - ZAm, and Z' is v' evaluated somewhere between nb and nb + p ( 1 - Z)Am. Our interest is in the sign of this expression, which is unchanged if we divide by pGl to get

(12) e - Z Am + ( 1 - z ) Am [ p - ( 1 - p ) (E1 /z l ) ] .

Expression (12) makes the conditions under which a technological change is welfare-reducing more transparent. We can see immediately that a necessary condition is that it increases medical expenditure. An innovation will not be adopted unless e - ZAm 2 0 - the additional out-of-pocket cost must not exceed willingness- to-pay - so that the first part of (12) is non-negative. The full expression could only be negative if the other term - capturing the effect on expected utility through the premium - were sufficiently negative, which requires that Am be positive.ll

One might have suspected that any innovation that is welfare-increasing would be adopted even if the full additional expense had to be paid out-of-pocket, that is, that e - Am > 0 is a necessary condition for an innovation to be welfare-increasing. As expression (12) makes clear, however, e - Am > 0 is neither necessary nor sufficient in general for the change in expected utility to be positive. The relationship between GI and - E' is important. If GI = - E' , then e - Am > 0 is necessary and sufficient for AV > 0. If GI > - E ' , the condition is sufficient but not necessary; if GI < - E ' , it is necessary but not sufficient. These are sensible results. The rela-

11. We can extend this result slightly to the case in which z may be adjusted in response to an innovation. It is conceivable that a welfare-reducing innovation may reduce medical expenditure by inducing an increase in theco-insurance rate. But since any innovation that reduces V' must reduce V(Z), where Z was formerly optimal, it follows from the argument in the text that Am at Z must be positive.


tionship between U , and - 5' indicates whether an additional dollar is worth more in this particular state than it would be on average in the others. The marginal utility of income may be relatively high in some high medical expenditure states (perhaps because net income after medical expenditure is low). It may then increase expected utility to purchase through insurance some innovations that would not (or could not) be paid for out-of-pocket. On the other hand, if the marginal utility of income when ill is low, some innovations that would be paid for out-of-pocket may nonetheless reduce welfare. This can happen because with insurance these innovations are financed in part out of consumption in states in which income is more highly valued.

The question of the operational meaning of these concepts remains. Expression (12) does provide an operational criterion in the following sense. We can design a set of questions about preferences among commodity bundles (and lotteries) that, if answered truthfully, would provide us the information necessary to determine the direction of the change in expected utility resulting from the adoption of an innovation. Whether the required information could somehow be inferred from market data is less clear.

What kinds of information would be required to evaluate the direction of change in expected utility? The term e, as defined previously, is the maximum amount the ill consumer is willing to pay out-of-pocket in order to use the innovation rather than the original technology. This value is in principle observable; we can imagine offer- ing individuals the use of the innovation at different prices, and finding that price at which it is just demanded. But such experiments may not be a practical possibility, and whether or not a reasonable estimate could be obtained by some other means is worthy of further research.

The other piece of information needed to apply the criterion of expression (12) (in addition to p and Am, which ought to be relatively straightforward to estimate), is the relationship between Z , and -F'. This relationship is observable in much the same sense that a von Neumann-Morgenstern utility index is measurable. An individual could be asked ex ante - with the innovation available and an insurance policy with co-insurance rate Z - to choose between pairs of lottery tickets. In each pair, one ticket would offer a particular sum if state i occurs and the other would offer a different sum if it does not occur. The aim would be to find the ratio between the two sums at which the individual is indifferent between lottery tickets. With p known, knowledge of this ratio would provide information on the ratio

Extending this approach to innovations that apply to more than one illness state is (at least conceptually) straightforward. There are two cases. If it is thought feasible to restrict the use of the innovation to particular applications, one may simply carry out the analysis as described above, treating the application of the innovation to each different state as a different innovation. It may be politically difficult, however, to allow some people to use a particular treatment technique while denying it to others who would like to use it. Or it may simply be considered too costly to

of z, to - 7 . 1 2

12. The marginal rate of substitution of income in all other states for income in state j is p times the marginal utility of income in state i divided by (1 - p ) times the average marginal utility of income across all other states. This average marginal utility across all other states may reasonably be considered equiva- lent to - G'. But i7, is not the marginal utility of income in state j . Rather it is the average utility per dollar over what may be a broad range of income (if e - ZAm is large), It would, therefore, also be useful if possible to get information on willingness to trade income from the other states to state j if e dollars were taken from income in state j beforehand.

66 ECONOMIC INQUIRY

distinguish among the different states for which use of the innovation is or is not to be permitted. The relevant choice may be to approve the use of the innovation whenever it is demanded or to ban it entirely. In that case one may, by appropriately aggregating those states in which the innovation is demanded, arrive at a criterion similar in form to expression (12). The expression contains an additional term if, as is possible, the changes in medical expenditure (Am’s) would be different in different states in which the innovation would be used.

Ill. CONCLUDING COMMENTS

This paper addresses a difficult social issue that seems likely to confront us with increasing frequency in the future: What should policy be toward medical advances that provide some benefit at very high cost, when the cost is borne primarily by persons other than the direct beneficiaries? That question has received relatively little attention from economists, and our efforts to deal with it here must be viewed in that context. We have obviously sidestepped distributional issues throughout the paper by assuming that individuals are identical ex ante. Further analysis in which that assumption is relaxed seems warranted. It is interesting to ask, however, whether the criterion of social welfare employed here - the expected utility of the typical individual - is necessarily appropriate even in this context. Welfare is not, after all, equalized ex post; maximization of expected utility may result in a highly unequal final distribution. Is it not possible, then, that as a matter of social policy these individuals would choose to place greater emphasis (than that implied by expected utility maximization) on the welfare of those who will ultimately prove least fortunate? More concretely, might they not rationally choose to adopt a medical advance which provides some comfort to the cancer sufferer, even if that benefit comes at so high a cost as to reduce everyone’s utility in the ex ante sense?

In answering that question, it seems useful to distinguish two motives for favor- ing redistributional policies. One motive - purely self-interested - is that at the time policies are set the individual may be uncertain as to which slot he will ultimately occupy in society. Redistributional measures may then be favored as a kind of insurance policy. But if that is the only motivation present, each individual would, in the situation envisioned here, opt for policies that place the same relative weights on the marginal utilities of individuals in different health states as he places on those states in his personal expected utility calculations. The expected utility function would be accepted as an appropriate social welfare function. The second motive for redistribution is more purely altruistic. If ex post utilities are interdepen- dent - if individuals truly care about the welfare of others - a complication is added to the analysis. To measure the benefits derived from any particular innovation, it becomes necessary to add some appropriately weighted measure of the willingness-to-pay of all other individuals to that of the direct beneficiaries. An analysis of that case is beyond the scope of the present paper.

Finally, let us consider briefly the general economic principles explored here. Broadly interpreted, the analysis has focused on a dynamic aspect of the moral hazard problem that has apparently received little attention. Moral hazard might be thought of in general as arising whenever some mutually beneficial activity - here the spreading of risk - can be achieved only (or most efficiently) with the by- product of distorted incentives. Optimal resource allocation in such cases generally involves accepting some level of distortion. (As has frequently been pointed out, the


problem of optimal taxation is formally very similar), What we have emphasized here is that since incentives are distorted at the optimum - since someone faces the “wrong” prices - it may be privately profitable to search for new production possi- bilities that, by increasing the cost of distortion, ultimately reduce social welfare. In addition to our medical insurance context, the problem might arise whenever, as is frequently the case in government programs, output is difficult to measure and the provider’s compensation is based instead on some imperfect operational measure of performance. The choice of the operational measure may initially be optimal - based on the existing technological relationship between the operational measure and the true output. But once a measure is chosen, it creates incentives to develop new ways of maximizing that measure as cheaply as possible, perhaps at the expense of the desired output. The upshot is that due to incentives created by the original optimal contract, that contract may after a time no longer be optimal, and conceiv- ably the level of welfare attainable under any contract may be reduced.

REFERENCES

Altman, Stuart, and Blendon, Robert, editors, Medical Technoiogy: The Culprit Behind Health Care Cosb?, Washington, Government Printing Office, 1979.

Arrow, Kenneth, “Welfare Analysis of Changes in Health Coinsurance Rates,” in The Role of Health Insurance in the Health Seruices Sector, Richard Rosett, editor, New York, National Bureau of Economic Research, 1976.

, “The Role of Securities in the Optimal Allocation of Risk-Bearing,’’ Review of Economic Studies, April 1964,31,91-96.

Feldstein, Martin, “The Welfare Loss of Excess Health Insurance,” Journal of Political Economy, March/ April 1973,81,251-80.

, and Friedman, Bernard, “Tax Subsidies, the Rational Demand for Insurance, and the

Malinvaud, Edmund, “The Allocation of Individual Risks in Large Markets,” Iournal of Economic

Pauly, Mark, “The Economics of Moral Hazard: Comment,” American Economic Aeoiew, March 1968,

Russell, Louise, Technology in Hospitals: Medical Adoances and Their Diffusion, Washington, Brookings,

U.S. Congress, Office of Technology Assessment, Assessing the Efficacy and Safety of Medical Tech-

Zeckhauser, Richard, “Medical Insurance: A Case Study of the Trade-off Between Risk Spreading and

Health Care Crisis,” Journal of PubZic Economics, April 1977, 7, 155-78.

T h e o q April 1972,4,312-28.

58, 531-37.

1979.

nologies, Washington, Government Printing Office, 1978.

Appropriate Incentives,” Journal of Economic Theory, March 1970,2, 10-26.

medical insurance, technological change, and welfare

Documents