Fermat's Library | Uncertainty and the Welfare Economics of Medical Care annotated/explained version.

TH1E

AMERICAN

ECONOMIC

REVIEW

VOLUME

LIII

DECEMBER

1963

NUMBER

5

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

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.

942

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

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

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 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

hWighly 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

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

inter-

personal

comparisons are, of

course, value

judgments. The

change,

however, by the

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

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

achieved

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

stressed by I.

M. D.

Little [19, pp.

71-74].

For the

concept of a

"persuasive

definition," see C.

L.

Stevenson [27,

pp. 210-17].

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.2

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.3

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.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

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] .

ARROW:

UNCERTAINTY

AND

MEDICAL CARE

945

Eilther

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

tlle

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

exist-

ing

market

to

provide a

means

whereby the

services

can

be both

of-

fered

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 com-

municable

diseases,

or it

may

be

due

to

social

or

historical

controls,

such

as

those

prohibiting

an

individual

from

selling

himself into slav-

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-

cerned is

that

of

risk-bearing.

The

relevance

of

risk-bearing to

medical

care

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

poorly

developed

or

nonexistent.

Why

this

should be

so is

explained

in

more

detail

in

Section

IV.C

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.

The

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

included

with

other

commodities.6

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

these

"commodities,"

i.e.,

desired

protection

against

many

risks,

are

'The

theory,

in variant

forms,

seems to

have

been

first

worked

out

by

Allais

[2],

Arrow

[5],

and Baudier

[7].

For

further

generalization,

see Debreu

[11]

and

[12,

Ch.

71.

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.7

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.8

That risk

and

uncertainty

are,

in

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.9

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.

948

THE

AMERICAN

ECONOMIC

REVIEW

dictable: the

blind,

dependent

children,

the

medically

indigent.

Thus,

optimality,

in

a

context

which

includes

risk-bearing, includes

much

that

appears

to

be

motivated

by

distributional

value

judgments

when

looked

at

in

a

narrower

context."

This

methodological

background

gives

rise

to

the

following plan

for

this

paper.

Section

II

is a

catalogue

of

stylized

generalizations about

the

medical-care

market

which differentiate

it

from

the usual commod-

ity

markets.

In

Section

III

the

behavior

of

the

market

is

compared

with

that of

the

competitive

model

which

disregards the

fact of uncer-

tainty.

In

Section

IV,

the

medical-care

market is

compared,

both

as

to

behavior

and as to

preconditions,

with

the ideal

competitive

market

that

takes

account of

uncertainty;

an

attempt

will be made to

demon-

strate

that the

characteristics

outlined

in

Section

II

can be

explained

either

as the

result

of

deviations

from

the

competitive

preconditions

or

as

attempts

to

compensate

by

other

institutions

for

these

failures.

The

discussion

is

not

designed

to

be

definitive, but

provocative.

In

particu-

lar,

I

have been

chary about

drawing

policy

inferences;

to

a consider-

able

extent,

they

depend

on

further

research,

for

which

the

present

paper

is

intended to

provide

a

framework.

II. A

Survey

of

the

Special

Characteristics

of

the

Medical-Care

Market'2

This

section

will

list

selectively

some

characteristics

of

medical

care

which

distinguish

it from

the

usual

commodity of

economics

textbooks.

The list

is not

exhaustive,

and

it is

not

claimed

that

the

characteristics

listed are

individually

unique to

this

market.

But,

taken

together,

they

do

establish

a

special

place

for

medical

care

in

economic

analysis.

A.

The

Nature

of Demand

The

most

obvious

distinguishing

characteristics

of

an

individual's

demand for

medical

services

is

that

it

is

not

steady in

origin

as,

for

example,

for

food

or

clothing,

but

irregular

and

unpredictable.

Medi-

cal

services, apart

from

preventive

services,

afford

satisfaction

only

in

the

event

of

illness,

a

departure

from

the

normal

state

of

affairs. It

is

hard,

indeed,

to

think

of

another

commodity

of

significance

in

the

average

budget

of

which this

is

true.

A

portion of

legal

services,

de-

voted to

defense in

criminal

trials

or

to

lawsuits,

might

fall in

this

cate-

gory

but

the

incidence

is

surely

very

much

lower

(and,

of

course,

there

'Since

writing the

above,

I

find

that

Buchanan

and

Tullock

[10,

Ch.

13]

have

argued

that

all

redistribution can be

interpreted as

"income

insurance."

12For

an

illuminating

survey

to

which

I am

much

indebted,

see

S.

Mushkin

[20].

ARROW:

UNCERTAINTY

AND

MEDICAL CARE

949

are,

in

fact,

strong

institutional

similarities

between the

legal

and

medical-care

markets.)'3

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

is

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

Comments