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American Economic Association

Uncertainty and the Welfare Economics of Medical Care

Author(s): Kenneth J. Arrow

Source: The American Economic Review, Vol. 53, No. 5 (Dec., 1963), pp. 941-

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TH1E AMERICAN

ECONOMIC

REVIEW

VOLUME LIII DECEMBER 1963 NUMBER 5

UNCERTAINTY AND THE WELFARE

ECONOMICS OF MEDICAL CARE

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 characteris-

tics 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 dis-

ease 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 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 Stanford University. He wishes to express his

thanks for useful comments to F. Bator,

R. Dorfman, V. Fuchs, Dr. S. Gilson, R. Kessel,

S. Mushkin,

and C. R. Rorem. This paper was prepared under the sponsorship of the Ford

Foundation

as part

of a series of papers on the economics of health, education, and welfare.

ARROW: UNCERTAINTY AND MEDICAL CARE 943

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-

plied.

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 dis-

tribution 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 neces-

sarily optimal; and any optimal state is a competitive equilibrium cor-

responding 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 ap-

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 income.

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

2The separation between allocation and distribution even under the above assumptions

has 4osSed over problems in the execution of any desired redistribution policy; in practice,

it is virtually impossible to find a set of taxes and subsidies that will not have an ad-

verse effect on the achievement of an optimal state. But this discussion would take us

even further afield

than we have already gone.

'The basic theorems of welfare economics alluded to so briefly above have been the

subject of voluminous literature, but no thoroughly satisfactory statement covering both

the theorems themselves and the significance of exceptions to them exists. The positive

assertions of welfare economics and their relation to the theory of competitive equilibrium

are admirably covered in Koopmans [181.

The best summary of the various ways in

which the theorems can fail to hold is probably Bator's [6].

944 THE AMERICAN ECONOMIC REVIEW

comparison between the actual market and the competitive model. The

methodology of this comparison has been a recurrent subject of con-

troversy 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.

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 equiva-

lence of competitive equilibria and optimal states. The major competi-

tive 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 retiurns. 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

imply the existence of a competitive equilibrium, i., 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-

sated; 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 [18, pp. 50-551.

5 For a more precise statement of the existence conditions, see Koopmans [18, pp. 56-60]

or Debreu [12, Ch. 5].

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-

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

disutility as well as money.) But the demand for information is diffi-

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 bouight from most physi-

cians, and, indeed, from most professionals. The elusive character of

information as a commodity suggests that it departs considerably from

the usual marketability assumptions about commodities.

That risk and uncertainty are,

fact,

significant elements in medi-

cal care hardly needs argument. I will hold that virtually all the special

features of this industry, in fact, stem from the prevalence of uncer-

tainty.

The nonexistence of markets for the bearing of some risks in the first

instance 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 profit-

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

other markets.

It should also be remarked that in the presence of uncertainty, indivisibilities that are

sufficiently small to create little difficulty for the existence and viability of competitive

equilibrium may nevertheless give rise to a considerable range of increasing returns be-

cause of the operation of the law of large numbers. Since most objects of insurance (lives,

fire hazards, etc.) have some element of indivisibility, insurance companies have to be

above a certain size. But it is not clear that this effect is sufficiently great to create serious

obstacles to the existence and viability

of competitive equilibrium in practice.

8 One form of production of information is research. Not only does the product have

unconventional aspects as a commodity,

but it is also subject to increasing returns in use,

since new ideas, once developed,

can be used over and over without being consumed, and

to difficulties of market control,

since the cost of reproduction is usually much less than

that of production. Hence,

it is not surprising that a free enterprise economy will tend

to underinvest in research; see Nelson [211 and Arrow [4].

ARROW: UNCERTAINTY AND MEDICAL CARE 947

The failure of one or more of the competitive preconditions has as

its most immediate and obvious consequence a

reduction in welfare

below that obtainable

from existing resources and technology,

in the

sense of a failure to reach an optimal state in the sense of Pareto. But

more can be said. I propose here the view that, when the market fails

to achieve an optimal state, society will, to some extent at least, recog-

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

face achieve a desirable goal may have less obvious consequences

particularly 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 in

its 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.'0 I am arguing here that in some circum-

stances other social institutions will step into the optimality gap, and

that the medical-care industry, with its variety of special institutions,

some ancient, some modern, exemplifies this tendency.

It may be useful to remark here that a good part of the preference

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-

'An important current situation in which normal market relations have had to be

greatly modified in the presence of great risks is the production and procurement of

modern weapons; see Peck and Scherer [23, pp. 581-82] (I am indebted for this refer-

ence to V. Fuchs) and [1, pp. 71-75].

0For an explicit statement of this view, see Baumol [8]. But I believe this position

is implicit in most discussions of the functions of government.

ARROW: UNCERTAINTY AND MEDICAL CARE 949

are, in fact, strong institutional similarities between the legal and

medical-care markets.)'

In addition, the demand for medical services is associated, with a

considerable probability, with an assault on personal integrity.

There is

some 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

also 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

from the cost of medical care.

B. Expected Behavior of the Physician

It is clear from everyday observation that the behavior expected of

sellers of medical care is different from that of business men in gen-

eral. These expectations are relevant because medical care belongs to

the category of commodities for which the product and the activity

production are identical. In all such cases,

the customer cannot test the

product before consuming it, and there is an element of trust in the

relation.' But the ethically understood restrictions on the activities of

a physician are much more severe than on those of, say, a barber. His

behavior is supposed to be governed by a concern for the customer's

welfare which would not be expected of a salesman. In Talcott Par-

sons's 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.'

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

"In governmental demand, military power is an example of a service used only

irregularly and unpredictably. Here too, special institutional and professional relations

have emerged, though the precise social structure is different for reasons that are not hard

to analyze.

Even with material commodities, testing is never so adequate that all elements of

implicit trust can be eliminated. Of course,

over the long run, experience with the quality

of product of a given seller provides a check on the possibility of trust.

15See [22, p. 463]. The whole of [22,

Ch. 101 is a most illuminating analysis of the

social role of medical practice; though Parsons' interest lies in different areas from mine,

I must acknowledge here my indebtedness to

his work.

16 I am indebted to Herbert Klarman of Johns Hopkins University for some of the

points discussed in this and the following paragraph.

950 THE AMERICAN ECONOMIC REVIEW

divorced from self-interest. (3) It is at least claimed that treatment is

dictated by the objective needs of the case and not limited by financial

considerations."7 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

certifying to the existence of illnesses and injuries for variouslegal and

other purposes. It is socially expected that his concern for the correct

conveying of information will, when appropriate, outweigh his desire

to please his customers."g

Departure from the profit motive is strikingly manifested by the

overwhelming predominance of nonprofit

over proprietary hospitals.

The hospital per se offers services not too different from those of

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

side 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

institutions.

Either explanation implies

a preference

on the part of some

group, whether

donors or patients, against the profit motive in the

supply of hospital services'

1T The belief that the ethics of medicine demands treatment independent of the patient's

ability to pay is strongly ingrained. Such a perceptive observer as Rene Dubos has made

the remark that the high cost of anticoagulants restricts their use and may contradict

classical medical ethics, as though this were an unprecedented phenomenon. See [13, p.

"A time may come when medical ethics will have to be considered in the harsh

light of economics" (emphasis added). Of course, this expectation amounts to ignoring

the scarcity of medical resources; one has only to have been poor to realize the error.

We may confidently assume that price and income do have some consequences for

medical expenditures.

18A needed piece of research is a study of the exact nature of the variations of medical

care received and medical care paid for as income rises. (The relevant income concept

also needs study.) For this purpose, some disaggregation is needed; differences in hospital

care which are essentially matters of comfort should, in the above view, be much more

responsive to income than, e., drugs.

"9 This role is enhanced in a socialist society, where the state itself is actively concerned

with illness in relation to work; see Field [14,

Ch. 91.

About 3 per cent of beds were in proprietary hospitals in 1958, against 30 per cent in

voluntary nonprofit, and the remainder in federal, state, and local hospitals;

see [26,

Chart 4-2, p. 601.

C. R. Rorem has pointed out to me some further factors in this analysis. (1)

Given

the

social intention of helping

all patients

without regard

to immediate ability

to pay,

economies

of scale would dictate a predominance

of community-sponsored hospitals. (2)

952 THE AMERICAN ECONOMIC REVIEW

have as good or nearly as good an understanding of the utility of the

product as the producer.

D. Supply Conditions

In competitive theory, the supply of a commodity is governed by the

net return from its production compared with the return derivable

from the use of the same resources elsewhere. There are several sig-

nificant departures from this theory in the case of medical care.

Most obviouisly, entry to the profession is restricted by licensing.

Licensing, of course, restricts supply and therefore increases the cost of

medical care. It is defended as guaranteeing a minimum of quality.

Restriction of entry by licensing occurs in most professions, including

barbering and undertaking.

A second feature is perhaps even more remarkable. The cost of

medical education today is high and, according to the usual figures, is

borne only to a minor extent by the student. Thus, the private benefits

to the entering student considerably exceed the costs. (It is, however,

possible that research costs, not properly chargeable to education,

swell the apparent difference.) This subsidy should, in principle, cause

a fall in the price of medical services, which, however, is offset by ra-

tioning through limited entry to schools and through elimination of

students during the medical-school career. These restrictions basically

render superfluous the licensing, except in regard to graduates of for-

eign

schools.

The special role

of educational institutions

in simultaneously sub-

sidizing and rationing entry is common to all professions requiring

advanced training It is a striking and insufficiently remarked phe-

nomenon that such an important part of resource allocation should be

performed by nonprofit-oriented agencies.

Since this last phenomenon goes

well beyond

the purely medical

aspect,

we will not dwell on it longer

here except

to note that the

anomaly

is most striking

in the medical field. Educational costs tend to

be far higher there than

in any

other branch of professional training.

While tuition is the same,

or only slightly higher, so that the subsidy is

much greater, at the same time the earnings of physicians rank high-

est among professional groups, so there would not at first blush seem

to be any necessity for special inducements to enter the profession.

Even if we grant that, for reasons unexamined here, there is a social

interest in subsidized professional education,

it is not clear why the

rate of subsidization should differ among professions. One might ex-

23The degree

of subsidy in different branches of professional education is worthy of a

major research effort.

ARROW: UNCERTAINTY AND MEDICAL CARE 953

pect that the tuition of medical students would be higher than that of

other students.

The high cost of medical education in the United States is itself a

reflection of the quality standards imposed by the American Medical

Association since the Flexner Report, and it is, I believe, only since

then that the subsidy element in medical education has become signifi-

cant. Previously, many medical schools paid their way

or even yielded

a profit.

Another interesting feature of limitation

on entry to subsidized edu-

cation is the extent of individual preferences concerning the social

welfare, as manifested by contributions to private universities. But

whether support is public or private, the important point is that both

the quality and the quantity of the supply of medical care are being

strongly influenced by social nonmarket forces'

One striking consequence of the control of quality is the restriction

on the range offered. If many qualities of a commodity are possible, it

would usually happen in a competitive market that many qualities will

be offered on the market, at suitably varying prices, to appeal to dif-

ierent tastes and incomes. Both the licensing laws and the standards of

medical-school training have limited the possibilities of alternative

qualities of medical care. The declining ratio of physicians to total

employees in the medical-care industry shows that substitution of less

trained personnel, technicians, and the like, is not prevented com-

pletely, but the central role of the highly trained physician is not af-

fected at all.

E. Pricing Practices

The unusual pricing practices and attitudes of the medical profes-

sion are well known: extensive price discrimination by income (with an

extreme of zero prices for sufficiently indigent patients) and, formerly,

a strong insistence on fee for services as against such alternatives as

prepayment.

'Strictly speaking, there are four variables in the market for physicians: price, quality

of entering students, quality of education, and quantity. The basic market forces, demand

for medical services and supply of entering students, determine two relations among the

four variables. Hence, if the nonmarket forces determine the last two, market forces will

determine price and quality of entrants.

'The suipply of Ph.'s is similarly governed, but there are other conditions in the

market which are much different, especially on the demand side.

'Today oinly the Soviet Union offers an alternative lower level of medical personnel,

the feldshers, who practice primarily in the rural districts (the institution dates back

to the 18th century). According to Field [14, pp. 98-100, 132-33], there is clear evidence

of strain in the relations between physicians and feldshers, but it is not certain that the

feldshers will gradually disappear as physicians grow in numbers.

ARROW: UNCERTAINTY AND MEDICAL CARE 955

B. Increasing Returns

Problems associated with increasing returns play some role in allo-

cation of resources in the medical field, particularly in areas of low

density or low income. Hospitals show increasing returns up to a point;

specialists and some medical equipment constitute significant indivisi-

bilities. In many parts of the world the individual physician may be a

large unit relative to demand. In such cases it can be socially desirable

to subsidize the appropriate medical-care unit. The appropriate mode

of analysis is much the same as for water-resource projects. Increasing

returns are hardly apt to be a significant problem in general practice in

large cities in the United States, and improved transportation to some

extent reduces their importance elsewhere.

C. Entry

The most striking departure from competitive behavior is restriction

on entry to the field, as discussed in II above. Friedman and Kuz-

nets, in a detailed examination of the pre-World War II data, have

argued that the higher income of physicians could be attributed to this

restriction.

There is some evidence that the demand for admission to medical

school has dropped (as indicated by the number of applicants per

place and the quality of those admitted), so that the number of medi-

cal-school places is not

as significant a barrier to entry as in the early

1950's [28, pp. 14-15]. But it certainly has operated over the past and

it is still operating to a considerable extent today. It has, of course,

constituted a direct and unsubtle restriction on the supply of medical

care.

There are several considerations that must be added to help evaluate

the importance of entry restrictions: (1) Additional entrants would be,

in general, of lower quality; hence, the addition to the supply of medi-

cal care, properly adjusted

for quality, is less than purely quantitative

calculations would show. (2) To achieve genuinely competitive con-

ditions,

it would be necessary not only to remove numerical restrictions

on entry but

also to remove the subsidy in medical education. Like any

other producer, the physician should bear all the costs of production,

See [16, pp. 118-37]. The calculations involve many assumptions and must be re-

garded as tenuous; see the comments by C. Reinold Noyes in [16, pp. 407-10].

'It might be argued that the existence of racial discrimination in entrance has meant

that some of the rejected applicants are superior to some accepted. However, there is

no necessary connection between an increase in the number of entrants and a reduction

in racial discrimination; so long as there is excess demand

for entry, discrimination can

continue unabated and new entrants will be inferior to those previously accepted.

956 THE AMERICAN ECONOMIC REVIEW

including, in this case, education' It is not so clear that this change

would not keep even unrestricted entry down below the present level.

(3) To some extent, the effect of making tuition carry the full cost of

education will be to create too few entrants, rather than too many.

Given the imperfections of the capital market,

loans for this purpose to

those who do not have the cash are difficult to obtain. The

lender really

has no security. The obvious answer is some form of insured loans, as

has frequently been argued; not too much ingenuity would be needed

to create a credit system for medical (and other branches of higher)

education. Under these conditions the cost would still constitute a de-

terrent, but one to be compared with the high future incomes to be

obtained.

If entry were governed by ideal competitive conditions, it may be

that the quantity on balance would be increased, though this conclu-

sion is not obvious. The average quality would probably fall, even

under an ideal credit system, since subsidy plus selected entry draw

some highly qualified individuals who would otherwise get into other

fields. The decline in quality is not an over-all social loss, since it is

accompanied by increase in quality in other fields of endeavor; indeed,

if demands accurately reflected utilities, there would be a net social

gain through a switch to competitive entry.

There is a second aspect of entry in which the contrast with com-

petitive behavior is, in many respects, even sharper. It is the exclusion

of many imperfect substitutes for physicians. The licensing laws,

though they do not effectively limit the number of physicians, do ex-

clude all others from engaging

in any one of the activities known as

medical practice. As a result, costly physician time may be employed

at speCific tasks for which only a small fraction of their training is

needed, and which could be performed by others less well trained and

therefore less expensive. One might expect immunization centers, pri-

vately operated, but not necessarily requiring the services of doctors.

In the competitive model without uncertainty, consumers are pre-

siumed to be able to distinguish qualities of the commodities they buy.

Under this hypothesis, licensing would be, at best, superfluous and

exclude those from whom consumers would not buy anyway; but it

might exclude too many.

D. Pricing

The pricing practices of the medical industry (see II above) de-

One problem here

is that the tax laws do not permit depreciation of professional

education,

so that there

is a discrimination against this form of investment.

To anticipate later discussion, this condition is not necessarily fulfilled. When it

comes to quality choices, the market may be inaccurate.

958 THE AMERICAN ECONOMIC REVIEW

only effect of a change in price will be the redistribution of income as

between the medical profession and the group with the zero elasticity

of demand. With low elasticities of demand, the gain will be small. To

illustrate, suppose the price of medical care to the rich is double that to

the poor,

the medical expenditures by the rich are 20 per cent of those

by the poor, and the elasticity of demand for both classes is .5; then

the net social gain due to the abolition of discrimination is slightly over

1 per cent of previous medical expenditures.

The issues involved in the opposition to prepayment, the other major

anomaly in medical pricing, are not meaningful in the world of cer-

tainty and will be discussed below.

IV. Comparison with the Ideal Competitive Model under Uncertainty

A. Introduction

In this section we will compare the operations of the actual medical-

care market with those

of an ideal system in which not only the usual

commodities and services but also insurance policies against all con-

ceivable risks are available Departures consist for the most part of

3It is assumed that there are two classes, rich and poor; the price of medical services

to the rich is twice that to the poor, medical expenditures by the rich are 20 per cent

of those by the poor, and the elasticity of demand for medical services is .5 for both

classes. Let us choose our quantity and monetary units so that the quantity of medical

services consumed by the poor and the price they pay are both 1. Then the rich pur-

chase .1 units of medical services at a price of 2. Given the assumption about the

elasticities of demand,

the demand function of the rich is DR(p)

.14 p--5 and that of

the poor is Dp(p) = p`.

The supply of miiedical services is assumed fixed and therefore

must equal 1. If price discrimination were abolished, the equilibrium price, p, must

satisfy the relation,

DR(P)

Dp(p) 1,

and therefore p

= 1. The quantities of medical care purchased by the rich and poor,

respectively, would beDR(7p) =. and Dp(75)

= .965.

The inverse demand functions, the priCe to be paid corresponding to any given quantity

are djv(q) = .02/q2, and dp(q)

= l/q'. Therefore, the consumers' surplus to the rich

generated by the change is:

135

(1) J (.02/q2)dq - 7(.135 -

.1),

and similarly the loss in consumers' surplus by the poor is:

(2)

f

(l/q2)dq

.965)

If (2) is subtracted from (1), the second terms cancel, and the aggregate increase in

consumers' surplus is .0156, or a little over 1 per cent of the initial expenditures.

'A striking illustration of the desire for security in medical care is provided by the

expressed preferences of etmigr&s from the Soviet Union as between Soviet medical prac-

tice and German or American practice; see Field [14, Ch. 12]. Those in Germany pre-

ferred the German system to the Soviet, but those in the United States preferred (in a

ratio of 3 to 1) the Soviet system. The reasons given boil down to the certainty of

medical care, independent of income or health fluctuations.

ARROW: UNCERTAINTY AND MEDICAL CARE 959

insurance policies that might conceivably be written, but are

in fact

not. Whether these potential commodities are nonmarketable, or,

merely because of some imperfection in the market, are not actually

marketed, is a somewhat fine point.

To recall what has already been said in Section I,

there are two

kinds of risks involved in medical care: the risk of becoming ill,

and

the risk of total or incomplete or delayed recovery.

The loss due to

illness is only partially the cost of medical care. It

also consists of dis-

comfort and loss of productive time during illness, and,

in mole serious

cases, death or prolonged deprivation of normal function. From the

point of view of the welfare economics of uncertainty, both losses are

risks against which individuals would like to insure. The nonexistence

of suitable insurance policies for either risk implies a loss of welfare.

B. The Theory of Ideal Insuran cc

In this section, the basic principles of an optimal regime for risk-

bearing will be presented. For illustration, reference will usually

made to the case of insurance against cost in medical care. The princi-

ples are equally applicable to any of the risks.

There is no single

source to which the reader can be easily referred, though I think the

principles are at least reasonably well understood.

As a basis for the analysis, the assumption is made that each individ-

ual acts so as to maximize the expected value of a utility function. If

we think of utility as attached to income, then the costs of medical

care act as a random deduction from this income, and it is the expected

value of the utility of income after medical costs that we are concerned

with. (Income after mnedical costs is the ability

to spend money on

other objects which give satisfaction. We presuppose that illness is not

a source of satisfaction in itself; to the extent that it is a source of

dissatisfaction,

the illness should

enter into the utility function as a

separate variable.) The expected-utility hypothesis, due originally to

Daniel Bernoulli (1738), is plausible and is the most analytically man-

ageable of all hypotheses that have been proposed to explain behavior

under uncertainty.

In any case, the results to follow probably would

not be significantly affected by moving to another mode of analysis.

It is further assumed that individuals are normally risk-averters. In

utility terms, this means that they have a diminishing marginal utility

of income. This assumption may reasonably be taken to hold for most

of the sKgnificant

affairs of life for a majority of people, but the pres-

ence of gamibling provides some difficulty in the full application of this

view. It follows from the assumption of risk aversion that if an indi-

vidual is given a choice between a probability distribution of income,

with a given

mean n, and the certainty of the income m, he would prefer

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