1 Chapter 4 Health Insurance Healthcare demand .docx

1
Chapter 4 Health Insurance
Healthcare demand is inextricably associated with insurance
demand due, fundamentally,
to individual risk aversion that reflects willingness to pay for
reducing the financial risk
one faces. Since the financial burden of an episode of illness is
often large with respect to
most individuals’ incomes and the illness itself unpredictable,
individuals demand
insurance, i.e. they want to spread and smooth out such random
variations in their wealth.
Moreover, since this illness-related financial burden is mostly
invariant to one’s income1,
health insurance is regularly provided publicly as part of social
insurance in a large
number of countries. Public health insurance is also motivated
by the fact that, by
increasing coverage and hence producing a positive impact on
the workforce, it may
boost earning power. Ironically, as higher incomes positively
affect health, there exists a
simultaneity (Lynch [2004]). Yet, in many countries that build
universal coverage health
insurance systems, coverage is neither uniform nor publicly
provided.
This chapter includes a simple but rigorous presentation of
individual demand for

insurance while deferring the details of healthcare provision as
social insurance to the
part on healthcare system analysis. Both aspects of healthcare
insurance were first
rigorously analyzed in Arrow [1963]. Whereas personal demand
for insurance arises from
individuals’ concern for sharp variations in their wealth, social
insurance is a social
solidarity phenomenon. Although there may be economic
efficiency reasons, such as a
healthier workforce (Deaton [2002]) and economies of scale in
administration, favouring
social insurance (Hussey & Anderson [2003]), the insurance
affordability prevails as the
main reason for public provision (Besley & Gouveia [1994]).
Many countries have
developed differing institutional arrangements and varying
amounts of coverage in the
provision of health insurance.
a. Demand for insurance
Risk-averse individuals facing risky prospects demand
insurance. We will first break
down this loaded statement into its four components. Firstly, a
risky prospect is simply
the possibility that a decision-maker will face mutually
exclusive future financial states of
the world, i.e. any one of those states may turn out to be the
case. These may be, for
example, a state where one continues to possess his car as is and
another where the car is
stolen or subject to an accident as a result of which the owner
incurs a financial loss. A
loss state implies a significantly different financial state than

the one in which the owner
continues to possess his car. In the case of health, a serious but
curable illness possibility
implies different financial prospects as the unhealthy individual
will have to pay for
medical care and his financial situation is significantly worse
than in a healthy state.
Secondly, in both cases, the difference in financial outcomes
implies that the individual
would have enjoyed different levels of wealth in the two states
and, correspondingly,
different marginal utilities of wealth, higher with lower wealth
and vice versa. If neither
state can be ruled out ex ante, i.e. neither is assigned zero
probability, then the
1 There exists, however, some evidence that there is an “income
gradient”, i.e. higher income means better
health (see Deaton [2002], Lynch et al. [2004]).
2
individual’s expected utility2 will be higher if some wealth can
be transferred from the
high to low wealth state. This happens because the marginal
utility of low wealth is
higher than that of high wealth (see Figure 4.1). If a dollar is
transferred from a high to
low wealth state, the marginal utility lost from the former
exceeds that gained from the
latter. This, then, is a net increase in the individual’s total
utility. Thus, thirdly, the risk-
averse3 individual would be willing to pay for a transfer of

wealth across states because
the transfer increases her total utility. This transfer requires
contracting with a third party
that could assure the individual that, in return for a sure fee (i.e.
a fee paid regardless of
the state), compensation will be available in case of financial
loss. The availability of
such a contract turns the demand for insurance into a market
insurance contract. Finally,
there is evidently a strong link between demands for healthcare
and for healthcare
insurance (Dusansky & Koc [2006]), i.e. those who are to
demand healthcare (and that
would be all of us) do demand health insurance beyond the pure
insurance motivations.
As we saw in the previous chapter, the health stock is desirable
in itself as well as it
enables one’s earning capacity. Combined with the inherent
unpredictability of healthcare
expenses, not only demand for healthcare influences
individuals’ healthcare insurance
contract choices but also a feedback phenomenon exists in the
form of the terms of
insurance contracts and affects the demand for healthcare.
It goes without saying that the availability (that insurers are
willing to offer contracts) and
affordability (that insurance is available at prices lower than the
price at which demand is
choked) of insurance also depends on the supply side. Since
insurance is a transfer of risk
from insuree to insurer, insurers’ profitability will determine
the existence of market
provision to which we will return below.
We now consider Figure 4.1, below, where the utility function

reflects decreasing
marginal utility by its concavity. As explained below, this
property of individuals’ utility
functions will yield risk aversion and, hence, demand for
insurance. The wealth levels
wB0 = W – L and wG0 = W are, respectively, the individual’s
wealth in loss and no-loss
states of the world. Correspondingly, she would derive utilities
u(wB0) and u(wG0) in the
respective states. However, none of these states are to occur
with certainty when, ex ante,
the individual is making an insurance decision. Of course, ex
post, the individual is in one
of the two mutually exclusive states. The likelihoods of the ex
post states, whether
computed objectively or subjectively4, are p for the loss state
and (1 – p) for the no-loss
state. The loss is given by L = wG0 – wB0 whereas we = pwB0
+ (1 – p)wG0 is the expected
wealth and w0 the certainty equivalent of the risky prospect
because u(w0) = pu(wB0) + (1
2 The expected utility consists of the weighted average of her
utilities in the two states. Since the insurance
decision precedes the knowledge of the exact state of the world,
economic analysis typically postulates that
individuals maximize their expected utility, the weights
representing the likelihood of a state’s occurrence.
These weights may be endogenous (or at least partially
determined by the decision-maker) or exogenous,
and objective or subjective. See any microeconomics textbook
for a discussion of the expected utility
hypothesis.
3 A risk-averse individual strictly prefers the expected value of
a risky prospect to the risk. In the current

case for health insurance, it amounts to u(we) > pu(wB
0) + (1 – p)u(wG
0) in Figure 4.1.
4 The objective determination of these probabilities is simply
based on count data on past group
occurrences. Insurers use this information in designing and
supplying contracts. Individuals, on the other
hand, form their own subjective evaluations of the states’
occurrences when forming their demands for
insurance contracts.
3
–p)u(wG0), the utility provided by w0 is equal to the expected
utility from the risky
prospect. In fact, the difference (we – w0) is called the risk
premium.
u
u(wG0)
u(w)
EU0 EU0 =
pu(wB0) + (1 – p)u(wG0)
u(wB0)

wB0 w0 we
wG0 w
we = pwB0 + (1 – p)wG0
wG
wG0
w0 EU(wB,wG;p)
= u(w0) = EU0
slope = –
p
p
−1

450
wB0 w0
wB
Figure 4.1 Derivation of state-space indifference
curves
4
Figure 4.1 graphically displays the concept of risk aversion.
Those individuals who
exhibit a positive risk aversion have positive demands for
insurance. They are willing to
pay to transfer the financial risk onto others. In fact, such a
transfer would be acceptable
if the contract premium is low enough that the individual attains
at least the expected
utility EU0 she would have had on her own, facing the risky
prospect. This means that the
choking price for coverage L would be exactly equal to (wG0 –
W) because, for a higher
premium, she would do better on her own. Thus any premium
lower than (wG0 – W)
combined with the full coverage L would leave the individual
better off with insurance.
The economic analysis of insurance is best represented
graphically in a state-space
diagram that allows the explicit representation of the demand

and supply prices5 of
insurance or, in other words, of indifference curves and a
budget constraint. Moreover,
the analysis of informational problems of adverse selection, ex
ante and ex post moral
hazard finds intuitive representations in state-space diagrams.
Figure 4.1 explains the transition from the introductory
explanation, above, of risk-
aversion and demand for insurance to a state-space diagram.
The individual’s initial
bundle or endowment is (wB0,wG0). The slope of the
indifference curve passing through
this bundle is evidently very steep as the marginal utility of
wB0 far exceeds that of wG0.
Note how wG0 in the bottom panel is derived from the top by
using the 450 line as the
reflector. The slope of the indifference curve when it crosses
the 450 line is equal to –
p/(1 – p) (as explained in Appendix 4A) and of course much
flatter than at (wB0,wG0).
This graphically yields the convexity of the indifference curves
towards the origin.
Intuitively, the convexity of the indifference curves corresponds
to risk aversion. Since a
risky prospect in the current context is where wealth is
significantly different in the two
states, the marginal utilities will likewise be different, a high
marginal utility for low
wealth in the loss state and a low marginal utility for high
wealth in the no-loss state. The
high marginal utility in the bad state with low wealth (the
numerator of the slope) will
quickly fall whereas the marginal utility in the good state with
high wealth (the

denominator of the slope) will slowly increase when the gap
closes towards full
insurance. These opposite changes in marginal utilities indicate
that the slope becomes
flatter and converges to – p/(1 – p) along the 450 line where
wealth is equalized across
states or, in other words, no risk exists any longer. In Figure 4.2
below, two full coverage
contracts are shown, w0 and w1. The former yields as much
utility as the individual would
have enjoyed without insurance at the initial situation whereas
the latter strictly increases
her utility above the initial level.
An individual’s demand price6 for an extra dollar of coverage is
then simply the slope of
his indifference curve as the slope represents the maximum
amount the individual is
willing to sacrifice in the no-loss state in order to buy the one-
dollar coverage in the loss
5 Keeping with conventions, the price of insurance, as different
from the contract premium, is defined as the
unit price for insurance, i.e. the amount payable per dollar of
coverage.
6 The demand price is the maximum unit price that a potential
buyer is willing to pay for a given quantity of
a good. The willingness to pay is also constrained by the ability
to pay. The collection of demand prices, as
a schedule, constitutes a demand curve.
5
state. Consistent with standard demand curves, the convexity of

the indifference curve
towards the origin ensures a decreasing demand price or
marginal willingness to pay for
extra coverage.
wG
w0
wG0 •
Complete
coverage
wFI
slope = –
p
p
−1
π = 0
U(wB,wG) = U0
450

wB0 wFI
wG0 wB
Figure 4.2 Complete coverage insurance contract
The budget constraint in Figure 4.2, originating at the
individual’s initial endowment and
with slope – p/(1 – p), is called a fair odds line and represents
an actuarially fair transfer
of funds from the good to the bad state. It reflects competitive
insurance provision under
the rather strong assumption that insurance companies face no
administrative costs.
Competitive insurance provision implies that any demanded
contract will be supplied by
some company provided it makes a non-negative profit. In such
an environment, an
insurance company’s expected profit can be formulated as a
function of the loss
probability, the premium R7 and the coverage Q as
πe = p(R – Q) + (1 – p)R.
7 The premium can always be expressed as a fraction r of the
chosen coverage Q without affecting the
derivation.
6
Noting that (Q – R) = dwB and (– R) = dwG and, also, under

perfect competition,
expected profits will be driven down to zero8, one obtains
πe = – pdwB – (1 – p)dwG = 0
and the slope of the budget constraint is thus obtained as
B
G
dw
dw
= –
)1( p
p
−
.
Given that the initial endowment point is part of the budget set,
the budget line is hence
obtained. Returning to Figure 4.2, facing such a budget
constraint, the individual will
choose Q = L, i.e. full coverage and the corresponding premium
R1 will be equal to the
actuarially fair cost of the coverage, i.e. R1 = pL = wG0 – w1.
This corresponds to a
premium of p per dollar covered. Note that, if the full coverage
contract happened to be
w0, then the premium would have been equal to R0 = pL + (w1

– W) = wG0 – W. As seen
in Figure 4.2, this latter contract leaves the individual
indifferent between remaining
uninsured at {W – L, W} and purchasing full coverage at w0,
with the high premium R0.
The last incremental step towards the demand curve for
insurance is the addition of
loading costs, i.e. the costs of actually running the insurance
firm. Although theoretically
simple, loading costs constitute a significant proportion of
premia in general9. In case
loading costs are proportional to coverage, the actuarially fair
premium per dollar of
coverage is just augmented by the unit loading cost r = p + t.
We note that, as above, [Q – R] = dwB and [– R] = dwG.
Thence, the slope of the budget
line, as developed in Appendix 4B and shown in Figure 4.3
below, is steeper and
individuals will purchase incomplete coverage and the loading
cost imposes a lower
utility on insurees.
The zero expected profits requirement for the existence of
insurance10 implies that the
addition of loading cost t reduces the demand for insurance as
individuals facing a
premium exceeding the actuarially fair rate choose less than
complete coverage.
The intuition for the incomplete coverage solution hinges on the
individual’s willingness
to pay for extra coverage or, simply, her demand price for
insurance. As the supply price
of insurance is higher with loading costs added (i.e. p+t rather

than just p), the
individual’s demand price falls to p+t faster in terms of
coverage demanded. In other
words, the demand price falls below the supply price well
before full coverage Q = L.
8 If any insurance contract is expected to yield strictly positive
profits, it will be offered. And, of course,
loss contracts will be withdrawn.
9 American private insurance loading costs have been estimated
at 24 cents in the dollar. See Wolf [2007].
10 See Appendix 4B. The dissipation of expected profits is,
however, to be qualified because, in reality,
insurance firms are also risk-averse and they would build risk
premia into their pricing. However, for a first
approximation, the expository and pedagogical gain to assuming
zero expected profits outweighs the lack
of realism therein.
7
wG
w0
wG0
Incomplete
coverage

wGINC
slope = –
p
p
−1
π < 0
450 slope = –
tp
tp
−−
+
)1(
and π = 0
wB0 wBINC
wB
Figure 4.3 Loading cost and incomplete coverage

Insurer loading costs consist of overheads and other
administrative costs. It must be noted
that insurees incur loading costs averaged over the number of
insurees rather than their
individual coverage. Consequently, if the loading cost
component of an individual’s
premium is taken as constant, it provides some incentive for the
individual to spread it
over a larger coverage.
The demand for insurance is thus defined as the coverage
required in response to the
market premium that is the price for dollar of coverage. Tracing
the amount of coverage
demanded in response to changes in premia thus yields the
demand curve for insurance,
as drawn in Figure 4.4 below.
There is graphic congruence between this case and the two other
reasons why insurance
demand may fall short of complete coverage. The
incompleteness of coverage also arises
of informational problems in insurance markets. The budget
constraint introduced above
will be key to understanding the two informational problems of
adverse selection and
moral hazard that we now turn to.
8
wG

wG0
EU(wB,wG;pL) = EU(wB0,wG0;pL)
Complete
coverage
wFull
slope = –
L
L
p
p
−1
π(pH) = 0
π(pL) = 0
450
wB0 wFull
wG0 wB

a
pH
pL
QD
QFI Q
Figure 4.4 Insurance coverage demand
9
b. Insurance markets and information problems
The economics of information has found perhaps its most fertile
application in insurance
because, plainly, insurance markets are inextricably grounded in
elicitation and
integration of information into contract design. The information
in question relates to the
identification of different pools of insurees with similar

characteristics and, once in the
pools and covered, to their behaviour that is costly to observe.
Insurers’ two fundamental
concerns are the matching of contracts to potential insurees and
the design of contract
incentives so as to affect insuree behaviour upon being covered.
The first concern is the
self-selection (or adverse selection) problem and the second the
moral hazard problem. In
turn, the moral hazard problem has the ex ante and the ex post
components. The first
refers to the insuree’s effect on the likelihood of a loss covered
under the contract and the
second on the size of the loss.
As an example of adverse selection, consider the case of the
chronically ill11. The self-
selection problem would arise if insurers offered premia based
on averages whereas
policies are purchased only by chronically ill who are normally
expected to make
frequent and large claims, if not for treatment but for
medications. Thus, insurers would
earn negative profits if a larger percentage of such people
purchased policies than
anticipated by insurers. Provided all buy the average contract,
the insurers would not lose.
However, if not, the marketplace would force insurers to try to
segment the general pool
of potential insurees into more homogeneous pools by designing
profitable contracts that
are relatively more attractive and specific to each pool. If any
pool supports profitable
contracts then the insurance market ought to work properly,
matching a particular pool of
insurees with corresponding insurance contracts. If not, a

market failure12 will arise due
to this first type of information problem.
The adverse selection problem thus arises when there is a
mismatch between the type of
insuree, not necessarily known to the insurer, and the contract
designed with a particular
insuree in mind. Surprisingly, this may occur as a result of ex
ante mismatch in which
wrong people joining a particular insurance plan or, simply, a
plan retaining only the
wrong people (Altman et al. [1998]).
To understand the problem, let us consider Figure 4.5a below
and assume, temporarily,
that the insurer has complete information on potential insurees,
i.e. the insurer knows
their risk types. To simplify the exposition, we will henceforth
consider two risk types
represented by illness probabilities pL and pH corresponding,
respectively, to low-risk and
high-risk insurees. As in Figure 4.4, these two homogeneous
groups, whose members
11 This is an interesting category because, quietly, most types
of cancer joined the chronic illness category
where the ill carry the illness at bay for the long term.
12 A market failure is a market outcome that is an equilibrium
but a suboptimal one in that the market
allocation can be improved upon had it not been for reasons
impeding the proper functioning of markets.
These reasons typically include non-competitive behaviour
arising from such sources as market entry and
exit restrictions that induce market power, lack and/or
asymmetry of information on tastes and technology

of market participants, ill-defined property rights leading to
public goods and externalities, transactions
costs that prevent a market’s functioning and, finally,
technologies that induce large scale economies.
10
being perfectly known to the insurer, are offered the complete
coverage contracts
{wL,wL} and {wH,wH} with respective premia rL = wG0 – wL
and
rH = wG0 – wH such that rH > rL simply because pH > pL.
Thus the riskier class members
pay a higher premium. We note that both complete coverage
contracts yield zero
expected profits, an outcome consistent with perfect
competition.
If insurer information is incomplete, i.e. the insurer no longer is
able to identify members
of a risk group, the high-risk group members adversely self-
select into purchasing the
contract {wL,wL}, the one designed for the low-risk group and
that would break even
only if low-risk members purchased it. Understandably, the
threat of negative profits
from high-risk members purchasing low-risk type contracts
would have insurers
anticipate this adverse selection phenomenon and respond.
While we will return to the
impossibility of pooling (or blending) contracts below in Figure
4.5b, we now consider
an attempt at separating risk groups. In Figure 4.5a, {wH,wH}

and {wBL,wGL} allow
separation, the first weakly preferred by high-risk types and the
second strongly preferred
by low-risk types. We note that the market fails due to
incomplete information (as the
insurer has less information than individual risk group members
on their own risk
categories) in that the overall welfare is lower than in the case
of complete information.
Although the high-risk group members do not suffer a welfare
loss, their presence
imposes negative externalities on the low-risk members whose
loss of utility is equal to
(UL1 – UL2).
wG
UL2 UL1
(wB0,wG0) •
wGL
πL = 0 and
slope = –
L
L
p
p

−1
UH1
UHADVERSE
slope = –
H
H
p
p
−1
450 and πH =
0
wBL wH wL
wB
Figure 4.5a Adverse selection and incomplete coverage
11
A set of uniform-premium contracts or a pooling one (identical
for all) for all will not
arise under competitive market conditions because cream-

skimming insurers will break
ranks and pry away healthy individuals with lower premia in
return for accepting some
risk. Consider Figure 4.5b below with uniform-premium case
illustrated, {wH1,wH1}
chosen by high risks as more than complete coverage will not be
available and
{wBL1,wGL1} for low risks. The wedge-shaped area enclosed
by the two individuals’
indifference curves and the fair premium budget line for low
risks includes profitable
contracts that attract only low risks. Thus the market will be
segmented and the emerging
equilibrium can only be of a separating type where low and high
risks pay different
premia13.
wG
UH Cream-
skimming contracts
UL
(wB0,wG0) •
wGL
wH
slopeL = –
L
L

p
p
−1
UH
and πL = 0
slopeAVERAGE
and πAVERAGE = 0
slopeH =
–
H
H
p
p
−1
450 and πH =
0
wBL wH
wB
Figure 4.5b Adverse selection and community rates
We can now proceed to analyze the case of incentives in health

insurance. As an example
of ex ante moral hazard, consider the behaviour of an insuree
vis-à-vis lowering the
12 A separating equilibrium may not exist if the proportion of
low risk types is so large that separation may
break down due to insurers offering a pooling contract that
would trade off low risks’ low premium for
lower risk in such a way to make them better off pooling with
high-risk types. Thus, in Figure 4.5a, the
pooling budget line would be closer to that for low risks’ and
allow them an increase in utility.
12
likelihood of ill health by improving one’s diet and physical
activity (AAFP [2007]).
Eating well necessarily imposes a constraint thus requires some
effort and physical
activity not only requires effort but also is typically costly. In
the absence of positive
incentives (or strong inner motivation) lowering the cost of
taking these preventive
measures, individuals would normally choose suboptimal levels.
The failure therein of an
individual to undertake these preventive measures upon
purchasing insurance that would
mitigate some of the harmful consequences through medical
care leads to the ex ante
moral hazard problem. In other words, complete coverage over
the consequences of one’s
actions tends to impel complacency, in particular if one is
predisposed to have an

inadequate diet and lead a sedentary lifestyle14. The very
existence of health insurance
coverage generates, ironically, a disincentive for conditions
conducive to good health
(see Osterkamp [2003] for incentives under public insurance).
This, in turn, increases the
cost of insurance on the average as illness becomes more likely.
Law of the unintended
consequences at work!
Figure 4.6 below depicts the ex ante moral hazard problem with
the potential insuree
facing the initial allocation {wB0,wG0} in which case, on her
own, she would have chosen
a high level of effort as we will see from the following
reasoning. The insurer lacks
information on the potential insuree’s health-enhancing effort
choice, either plain
impossible or too costly to observe. The consequence of this
asymmetry in information is
that complete coverage would simply induce a suboptimal
allocation because the insuree
would choose a lower than optimal level of effort. To see this,
first consider the complete
coverage contract w1. Clearly, this contract would give a higher
utility to the low effort
choice by virtue of the fact that a low effort costs less whereas,
in terms of benefit
consequences, no difference exists because the contract is one
of complete coverage at
{w1,w1}. Thus, adopting the simpler notation U(wB,wG) =
p(e)u(wB) + (1 – p(e))u(wG),
UL1 = U(w1,w1) – v(eH) < U(w1,w1) – v(eL) = UH1
simply because low effort is less costly whereas the benefits are

equal due to complete
coverage. Since high effort is desired and the uninsured
individual would have chosen a
high level of effort, a movement along the budget line with
slope equal to slopeL from
{w1,w1} towards the original non-insured allocation
{wB0,wG0} makes high effort more
and more attractive over low effort because such a movement
corresponds to increasing
risk via incomplete insurance. Thus a higher effort starts
dominating the low effort when
incompleteness reaches a certain level where the incremental
cost of high effort is more
than compensated by its beneficial effect in reducing the
likelihood of illness. That point
is {wB2,wG2} in Figure 4.6 below. As for the insurer, it can
afford to offer that allocation
as a zero-profit and incomplete coverage contract with premium
equal to (wG0 – wG2),
which corresponds to a premium rate of pL/(1 – pL), and a
deductible of (wG2 – wB2) or a
14 Regular exercise is well known to bring about numerous
health benefits. It lowers high blood pressure,
reduces obesity and abates the risk of heart disease,
osteoporosis and diabetes. It keeps joints, tendons and
ligaments flexible so it is easier to move around. It contributes
to your mental well-being and helps treat
depression, and helps relieve stress and anxiety. It improves
sleep. It boosts one’s metabolism (the rate of
of burning calories) and thus helps maintaining a normal
weight. It reduces some of the effects of aging. It
increases endurance and the energy level. (AAFP [2007]) In
short, all consequences of regular exercise
lower the probability of ill health.

13
co-insurance rate of (wG2 – wB2)/L0 = (wG2 – wB2)/(wG0 –
wB0).
wG UL2 = UH2
(wB0,wG0)
wG0 • UL1 < UH1
wG2
w1 w1
slope = – pL /(1 – pL)
slope = – pH
/(1 – pH)
450

wB0 wB2 w1 wG2
wB
Figure 4.6 Ex ante moral hazard and incomplete coverage
With ex ante moral hazard, the behavioural incentives are
combined with the partially
endogenous risk. Consequently, the insuree’s health status is
not entirely determined by
her behaviour but some randomness as well. Despite the fact
that nobody would desire
bad health, the presence of insurance, desirable in its own right
against risk and lumpy
expenditure upon illness, may induce a change in behaviour for
the worse resulting in a
higher probability of a poor health outcome. Contrastingly, the
ex post moral hazard
concerns the ex post behaviour in seeking treatments whose
marginal costs may exceed
their marginal benefits or, in other words, seeking unnecessary
treatments. Thus the ex
post moral hazard problem arises in succession to a partial
resolution of the uncertainty
surrounding the health status of the insuree. For example, when
the insuree is ill, the
illness vs. health dichotomy is resolved. However, if completely
covered, she has an
incentive to consume all medical services with positive benefits
whether her net benefits
are positive or not. This behaviour generates the ex post moral
hazard with hidden
knowledge as the seriousness of the illness is not precisely
known to the insurer (Koc

14
[2005]). The presence of this information asymmetry causes the
moral hazard problem
and the resulting sub-optimality.
Technically, this case can be understood with the exact tools we
used to explain adverse
selection. Under complete coverage, the insuree has no
incentive to economize on
medical resources. This can be thought of as, whereas an
insuree with a heavy illness
need not economize, the presence of one with a light case who
would mimic the heavy
case would then engender the moral hazard with hidden
information15, formally akin to
adverse selection. The insurer, however, possesses less
information on the insuree’s ex
post health status (i.e. the severity of illness once the insuree is
ill)16. The behavioural
problem is to get the insuree to choose the treatment
corresponding to her illness level
rather than having a light case choosing the treatment
corresponding to a heavy case or,
in other words, exaggerating the required treatment. The light
and heavy cases require
treatments costing mL and mH as in Figure 4.7 below. As
higher treatment expenditure is
better and higher coinsurance rate worse, the two types’ utilities
increase in the southeast
direction.
If the insurer possesses complete information on the claimant’s
illness status then the

allocation is optimal in the sense that light and heavy cases
receive the proper treatments.
What distinguishes the two cases is that, whereas the light-case
insuree wouldn’t benefit
much from extra treatment and hence wouldn’t be willing to pay
in terms of coinsurance,
the heavy case would benefit and hence be willing to pay more.
Graphically, the marginal
willingness to pay (or the subjective price of insuree for extra
coverage) is given by the
slope of the indifference curves in Figure 4.7. In the complete
information case, (mL,0)
and (mH,0) are, respectively, the optimal allocations for the
light and heavy cases. These
allocations yield Yet, if the insurer is asymmetrically informed
and can’t distinguish
between types, the light-case insuree will benefit by declaring
he is a heavy case and,
correspondingly, choosing the treatment mH. This is
misallocation of resources and
suboptimality.
Though the misallocation problem may be resolved through
coinsurance, suboptimality
will remain due to information asymmetry. Since coinsurance is
costlier to the light-case
insurees, the imposition of the rate c0 deters them from taking
up mH. Thus, their utility
remains at uL*. However, their presence costs the heavy-case
insurees in terms of utility
as the bundle (mH,c0) yields them uH1, a lower level of utility
than under complete
information.
Related to ex post moral hazard, there are three issues
remaining to be discussed. First,

insurance contracts typically provide incomplete coverage,
whether to solve the adverse
selection and the moral hazard of the ex ante variety or the ex
post moral hazard.
15 Moral hazard with hidden information arises when,
originally endowed with symmetric information
under uncertainty, one of the parties to the contract gains an
informational advantage upon the resolution of
uncertainty. This is certainly the case in the present problem as,
when the insuree is ill, he alone knows
whether the illness is light. In this latter case, the insuree has an
incentive to pretend to be a heavy case.
16 A related case of ex post moral hazard in which ex ante
behaviour has an alleviating effect on ex post
damages would be handled by inducing the insuree to commit to
ex ante preventive measures that would,
should the illness state arise, result in lower damages. These
preventive measures are typically verifiable
thus contract enforcement would be easy.
15
Deductibles and/or coinsurance appear as insurers’ standard
tools for reducing coverage
for purposes of sharing risk with insurees and providing
incentives to reduce moral
hazard. The choice between the two types of risk-sharing tools
is crucial depending on
the nature and the interactions of the problems (The Economist
[1995]). An eminent
c uH1

uH*
uL*
uL0
c0
mL mH
m
Figure 7 Ex post moral hazard and incomplete coverage
feature of healthcare is the progressive nature of many known
illnesses and, hence, the
importance of early detection and intervention. Since early
intervention is significantly
less costly, contractual disincentives to contact one’s physician
(such as a copayment or
user fee17) may be counterproductive when the patient chooses
to delay reporting the
symptoms and the illness progresses to a level where substantial
intervention becomes
necessary. Moreover, the determination of contractual coverage

with incentive
considerations also depends on whether the insuree is able to
affect the likelihood of an
illness and the costs of treatment should she develop it.
As opposed to adverse selection and ex ante moral hazard, the
existence of an ex post
moral hazard problem is essentially questionable. Once an
insuree with an average
understanding of medicine enters the health care system with
some symptoms and
channeled by the primary care physician, he then is under the
care of physicians.
Therefore, the choice set before the patient is characteristically
defined by medical
norms18 with little patient leeway although the patient selects
options from choice sets
along the way. That the patient is restricted reduces the
relevance of ex post moral hazard
17 As opposed to a deductible, a user fee is a fixed amount per
use whereas the deductible is a fixed amount
for use of insurance benefits per contract period.
18 One must bear in mind the “small area variations”, an
awkward term to translate the idea that medical
norms are not uniform spatially and that different treatments
may be the preferred choice of the local
medical profession in response to same symptoms and
diagnostics.
16
but, in turn, increases the importance of physician agency
problems, in the first as

patient’s agent and in the second as the payer’s agent.19 Thus,
the alleviation of the ex
post moral hazard problem is more intimately related to the
physician’s role as agent than
the patient herself. As such, the institutions and incentives
surrounding the physician will
have to be the primary focus of analysis.
Second, when the insurer designs insurance contracts, three ex
ante states of nature are
consistent with the above discussion of asymmetric information
problems. However,
when the first uncertainty unfolds, the insuree is either healthy
or unhealthy. If she is
unhealthy the seriousness of illness becomes a matter of
information asymmetry and
generates a problem of moral hazard with hidden knowledge.
Methodologically, the
insurance contract design will take as given the coinsurance
necessary to solve this ex
post moral hazard problem and then choose the risk-sharing and
incentives to address the
ex ante problems. Thus the contract design proceeds backwards
whereas parties to the
contract are forward-looking. We note that risk-sharing and
contract incentives influence
insurees’ healthcare demands in various ways. First, the initial
self-selection induced
through a menu of contracts aims at alleviating adverse
selection. Second, the premium
and coverage in each contract target stronger preventive effort
on the part of insurees thus
targeting the ex ante moral hazard problem. Finally, the
coinsurance rate20 provides a
strong incentive for the insuree, if ill, to self-select into the
correct illness pool thus

zeroes in on the ex post moral hazard problem.
Finally, ex post moral hazard is intimately connected to social
considerations. If
healthcare insurance is unaffordable to an individual in the
absence of social insurance
and he accesses healthcare in its presence, technically speaking
he is generating ex post
moral hazard. Thus the presence of insurance changes his
behaviour in such a way that
his consumption of healthcare rises above the uninsured level.
This is, of course, an
expected response to changing incentives. Since insurance
works by lowering the price of
insured services by transferring funds from non-claimants (or
insured but healthy) to
claimants (insured but ill), the affordability of such services
increases. To claim that this
is a net welfare loss is to ignore the increase in benefits the
extra service consumption
provides and that would not have been available to the
uninsured, who would be willing
to pay but cannot21. This case is an example of second-best
welfare analysis where
departures from what would have been the first-best do not
necessarily worsen social
welfare. In fact, as claimed in Nyman [2004], the net welfare
gain of social insurance, by
increasing the number of insured, may be positive.
c. Social insurance and public provision of insurance
The healthcare insurance issue reveals to be deeper and more
controversial than the fairly
technical individual health insurance framework presented

above. For, the powerful and
justifiable social solidarity consideration retains the issue of
universal healthcare
insurance in policy agendas, if not for its introduction always
for various modifications to
19 These agency problems are analyzed in the next two
chapters.
20 See Zeckhauser [1995] for a discussion of copayments and
coinsurance.
21 Economic theory has been largely quiet on this till recently
(see Nyman [2004]) yet the problem was first
identified by Pauly [1983]. Bundorf & Pauly [2006] revisits the
issue.
17
existing structures. This section will thus end the chapter with
an introduction to social
insurance that will be examined in detail in the later chapter on
alternative organizations
of healthcare systems.
The bumpy history of social healthcare insurance descends to
19th century German
unification under Bismarck22. The corporatist system
established by the 1883 legislation
in Germany was rooted in Illness Funds established along
vocational boundaries.
Workers in a trade became mandatory members of these
insurance funds based on cost
sharing by workers and employers. This structure continued, by
and large, till 1990s
when, in order to induce both horizontal and vertical

competition, mandatory
membership in one’s vocational fund was relaxed in favour of
mobility across funds. This
modification to the German health insurance system introduced
both horizontal and
vertical competition. It has relaxed the inefficient spatial and
vocational locks. Moreover,
it allows vertical competition in quality.
As part of the social insurance framework but at a wider scale
of universality, the newly
elected Labour government introduced the national health
insurance (and the NHS23) in
1948, based on the well-known Beveridge24 report of 1942
(Musgrove [2000]). As
opposed to the German system with regulated insurance markets
(Files & Murray
[1995]), the British system exhibits the government as the
primary insurer as well as a
small but significant private parallel insurance system
(Colombo & Tapay [2003], Tapay
& Colombo [2004]) for those who opt out (i.e. who want to
complement or supplement)
and even for those who ride the fence for rainy days when they
might need the swiftness
of private delivery. Until recently, NHS was a unitary system
with public funding and
public provision. Whereas public funding continues, NHS
recently started purchasing
services from the private sector providers (Csaba & Fenn
[1997]).
The Bismarck vs. Beveridge is important in the evolution of
healthcare systems as
historical benchmarks in the evolution of healthcare systems
with substantial regulation

and universal coverage of the population. However, the set of
real healthcare systems is
significantly richer as they combine public and private
provisions of insurance and
healthcare services to varying combinations (Besley & Gouveia
[1994]). Ironically, as the
recent NHS experiment demonstrates, a public system can even
relax the monopoly in
provision of services by introducing internal markets, i.e.
competition amongst providers
within the public system. A further dimension along which
healthcare systems can be
differentiated is the degree of incompleteness of the universal
public insurance coverage.
22 Otto von Bismarck (1815-1898), chancellor of Germany for a
long time, 1867 to 1890, introduced
components of the modern welfare state. The decentralized
health insurance was introduced in 1883 and it
worked locally through participation of employers and workers
in its administration and with cost sharing
by employers and, mostly, by workers themselves. This latter
phenomenon conferred majority
representation in insurance boards for workers with the
consequential political advantage accruing to
German Social Democrats and, eventually, setting an example to
other social democratic parties elsewhere.
23 The National Health Service (NHS) is a publicly funded
unitary provider of comprehensive healthcare
services.
24 William Beveridge (1879-1963) served as consultant to the
Liberal government (1906-1914) on old age
pensions and national insurance. After serving as the director of
LSE from 1919 to 1937, the wartime
Conservative government commissioned him, in 1941, to

produce a report on postwar social
reconstruction. He reported to parliament, in 1942, on social
insurance part of which was the new
comprehensive health insurance scheme.
18
This incompleteness may transpire in two forms, first services
that are simply not covered
and second the lack of complete insurance coverage for covered
services. The first
incompleteness potentially creates a complementary coverage
market and the second the
supplementary coverage market. For example, there is a
surprising and remarkable
resemblance between the essentially public French system with
its supplementary
coverage markets (Buchmueller & Couffinhal [2004]) and the
Medigap insurance market
in the US (Browne & Doerpinghaus [1994]) providing not only
complementary but also
supplementary coverage to essentially public Medicare
insurance system. For the rest of
US population above the official poverty level, private
insurance markets in different
markets cover a high percentage of the population with wildly
different baskets but leave
about 45 million without basic coverage (Vanness & Wolfe
[2002], Woolhandler &
Himmelstein [2002]). Whereas supplementary insurance is not
legal in Canada with
public insurance covering a substantial basket of healthcare
services25, complementary
insurance markets are reasonably thick (Emery & Gerrits

[2006], Gordon [1998]).
References
AAFP (American Academy of Family Physicians) [2007],
“Benefits of regular exercise”,
http://familydoctor.org/online/famdocen/home/healthy/physical/
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selection and adverse
retention”, American Econ. Rev., Papers and Proceedings 88(2),
122-126
Arrow, K. [1963], "Uncertainty and the Welfare Economics of
Medical Care",
American Econ. Review 53(5), 941-973
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care provision”,
Econ. Policy October, 200-258
Browne, M.J. & H. Doerpinghaus [1994], “Asymmetric
information and the demand for
medigap insurance”, Inquiry 31, 445-450
Buchmueller, T.C. & A. Couffinhal [2004], “Private health
insurance in France”, OECD
Health Working Papers No. 12
Bundorf, M.K. & M.V. Pauly [2006], “Is health insurance
affordable for the uninsured”,
J. Health Econ. 25(4), 650-673
Csaba, L. & P. Fenn [1997], “Contractual choice in the managed
health care market: An
empirical analysis”, J. Health Econ. 16, 579-588

Colombo, F. & N. Tapay [2004], “Private health insurance in
OECD countries: The
benefits and costs for individuals and health systems”, OECD
Health Working
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Australia: A case study”,
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health and wealth”, Health
Affairs 21, 13-30
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contract choice effect”,
Econ. Inquiry 44(1), 121-127
(The) Economist [1995], “Economics focus: An insurer’s worst
nightmare”, July, 70
25 This structure grants the insurer a monopsonistic purchasing
power over providers (Herndon [2002]). Of
course, the extent of the basket of services covered will in turn
affect the complementary insurance markets
(Stabile & Ward [2006]).
http://familydoctor.org/online/famdocen/home/healthy/physical/
basics/059.html
19
Emery, J.C.H. & K. Gerrits [2006], “The demand for private
health insurance in
Alberta in the presence of a public alternative”, in Beach et al.
[2006]
Files, A. & M. Murray [1995], ''German risk structure

compensation: Enhancing
equity and effectiveness'', Inquiry 32, 300-309
Gordon, M. et al. [1998], ''Funding Canada's health care system:
a tax-based alternative
to privatization'', CMAJ 159(5), 493-496 (plus discussion, 497-
501)
Herndon, J.B. [2002], “Health insurer monopsony power: The
all-or-none model”,
J. Health Econ. 21, 197-206
Hussey, P. & G.F. Anderson [2003], “A comparison of single-
and multi-payer health
insurance systems and options for reform”, Health Policy 66,
215-228
Koc, C. [2005], “Health-Specific Moral Hazard Effects,"
Southern Econ. J. 72(1), 98-118
Lynch, J. et al. [2004], “Is income a determinant of population
health? Part 1”, Milbank
Quarterly 82, 5-99
Musgrove, P. [2000], “Health insurance: The influence of the
Beveridge Report”,
Bulletin of the World Health Organization 78(6), 845-855
Nyman, J.A. [2004], “Is ‘moral hazard’ inefficient? The policy
implications of a new
theory”, Health Affairs 23(5), 194-199
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allocative improvements
through differentiated copayment rates”, European J. Health
Econ. 4, 79-84
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2(1), 81-85

Stabile, M. & C. Ward [2006], “The effects of delisting publicly
funded health-care
services”, in Beach et al. [2006]
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the Netherlands: A case
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employer-sponsored
health insurance: Who is still not covered?”, Int. J. Health Care
Finance and Econ.
2(2), 99-135
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Legislative Policy Forum
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national health insurance –
And not getting it”, Health Affairs 21(4), 88-98
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papers on Risk and
Insurance Theory 20(2), 157-175
Discussion questions
1. Why do societies include healthcare with social insurance?
2. Does the public provision of health insurance pose
institutional difficulties compared
to market provision?
3. Are there incentive and information problems specific to
public health insurance?
4. What is adverse selection in health insurance?

5. Does the fact that public insurance generates a single pool
really solve the adverse
selection problem?
6. What are the advantages and the disadvantages of public
over private health
insurance?
20
7. “Even if there were no informational problems in insurance
markets, complete
coverage would still be unavailable.” Why?
8. Are the social insurance concepts of Beveridge and Bismarck
different?
9. What is moral hazard in health insurance?
10. Distinguish between the concepts of ex ante and ex post
moral hazard.
11. Define and explain user fees, co-payments, deductibles and
co-insurance.
12. When should co-insurance replace deductibles?
13. Is there a friction between social insurance and incomplete
coverage insurance?
14. Does the fact that a household doesn’t buy health insurance
constitute market failure?
Problems
1. Show that the demand for insurance increases with the
illness probability or the cost
of treatment.
2. Does an insuree’s demand for insurance increase when he
becomes more risk-averse?

3. Explain why an insurance contract ought to include a
deductible.
4. Explain risk-pooling, one of the principles on which
insurance is based, in the case of
just two individuals.
5. Explain why the presence of loading costs rules out complete
coverage.
6. Show that total welfare is decreased when, in a competitive
insurance market, the
presence of adverse selection prevents insurers offering
complete coverage.
7. Show that total welfare is decreased when, in a competitive
insurance market, the
presence of moral hazard prevents insurers offering
complete coverage.
8. Under what circumstances deductibles would dominate co-
insurance?
9. How would the co-insurance rate vary with the insurer’s
perception of the
composition of the insurees pool under ex post moral
hazard?
10. Is it possible that a deductible may generate perverse
incentives for moral hazard?
11. How would incompleteness of coverage reduce ex ante
moral hazard?
12. Carefully explain the relationship between coverage
incompleteness and the second-
best solutions to adverse selection and ex ante moral
hazard.
13. Why can’t insurers offer as many contracts as the number of
types of potential
insurees?
14. How does an increase in the co-insurance rate affect the
demand for healthcare?
15. Does incomplete coverage due to loading costs depend on
insurer size?

Appendix 4A Slope of the indifference curves in state-space
diagrams
The slope of an individual’s indifference curves in a state-space
diagram is the subjective
(or demand) price for insurance as the slope yields what the
individual is willing to pay in
the good state for an extra dollar of coverage in the bad state.
The individual’s expected
utility function is given as
21
EU = pu(wB) + (1 – p)u(wG).
The derivation simply consists of taking the total derivative,
noting that utility is constant
along an indifference curve and obtaining the slope expression
on the right-hand-side of
the resulting equation. First, we take the total derivative and
equate it to zero:
dEU = pu’(wB)dwB + (1-p)u’(wG)dwG = 0
and solve for the slope:

B
G
dw
dw
= –
)(')1(
)('
G
B
wup
wpu
−
.
An important property of indifference curves in state-space
diagrams is that their slope
when they cross the 450 line is always equal to the slope of
fair-odds line
–
)1( p
p
−

.
This use of the property will prove crucial in the analysis of the
basic insurance problems
of adverse selection and moral hazard.
Appendix 4B Competitive premia and loading costs
Incorporating a loading cost T > 0 and rewriting a competitive
insurer’s expected profit
becomes
πe = p[R – T – Q] + (1 – p) [R – T]
and, assuming linear premia and loading costs,
= p[rQ – tQ – Q] + (1 – p) [rQ – tQ]
= [r – t – p]Q
which yields, due to profit dissipation (i.e. expected profits
reduced to zero) under perfect
competition, r = p + t. This implies that the potential insuree’s
budget line is now steeper.
To see this, consider the individual’s payoffs in the two states
of the world.
wG = W – rQ
wB = W – rQ + Q – L.

22
Isolating Q in the second, substituting it into the first and
rearranging the resulting
equation yields the budget line
BG wr
r
LW
r
r
Ww
−
−
−
+=
1
)(
1
for wB ≥ W – L

that is represented in Figure 4.3 with the slope r/(1 – r) steeper
than p/(1 – p), the slope pf
the fair odds line at which the individual would have purchased
complete coverage, i.e.
Q = L. To see this, consider the individual’s expected utility
maximization problem
)()1()(max
}{
rQWupLQrQWpuU
Q
−−+−+−=
where W – rQ + Q – L = wB and W – rQ = wG. The first-order
condition for this
maximization is given as
0)(')1()1)((' =−−− rwuprwpu GB
which, rearranged, yields
p
p
r
r
wup
wpu
dw

dw
G
B
B
G
−
>
−
=
−
−=
11)(')1(
)('
.
This inequality implies
1
)('
)('
>
G
B

wu
wu
which, in turn, yields wB < wG. Thus, as shown in Figure 4.3,
the individual chooses
incomplete coverage.
Appendix 4C Moral hazard and health-enhancement costs
In the presence of moral hazard, as explained in the text,
individuals’ control over the
likelihood of healthy outcomes has to be explicitly treated, with
its benefits and its costs.
Individuals’ health-enhancing activities (from better eating
habits to good sleep to
physical exertion) are typically costly, not only in terms of time
allocated but also in
terms of the purchased inputs (from gym time to quality food)
into activities. The
benefits accrue as healthy time that can be used for work or
leisure, or simply enjoyed as
health. The utility function introduced in Appendix 4A can be
augmented to incorporate
these benefits and costs as follows.
EU = p(e)u(wB) + (1 – p(e))u(wG) – v(e).
23

The first part of this utility function, p(e)u(wB) + (1 –
p(e))u(wG), is as above except that
the probabilities are now determined by the individual’s costly
effort e. An increase in
this effort increases the probability of the healthy state G (i.e. 1
– p(e)) but, of course, this
increase is slower than the increase in the effort. The second
and new part v(e) is the cost
of effort and it is increasing in effort. Consistent with typical
cost functions, the cost
increases faster than the effort.
For notational simplicity, we can interchangeably use
U(wB1,wG1;eL) = UL1 = p(eL)u(wB1) + (1 – p(eL))u(wG1) –
v(eL).
Of course, given the assumed structures, the individual would
choose an optimal
prevention level in the absence of insurance so as to maximize
his expected utility.
Appendix 4D Ex post moral hazard
Since the ex post moral hazard problem arises when and if the
insuree turns into a patient,
the health vs. illness dichotomy ceases to exist and illness turns
into shades of illness.
The informational problem is one of moral hazard with hidden
knowledge where the
patient, knowing her illness better than the insurer may choose
to exaggerate the level of
her illness by consuming medical care services with negative
net benefits.

Under symmetric information, the heavy-case and light-case
patients receive treatments
mH and mL respectively as in Figure 4.7. However, if the
insurer is unable to distinguish
cases, the light-case patient prefers the heavy-case treatment in
the absence of a screening
mechanism, as follows
uL* = uL(mL,w – R) < uL(mH,w – R) = uL0.
If a screening mechanism in the form of a coinsurance payment
c0 is chosen so as to
minimize the cost of separation of light and heavy cases,
separation would occur if the
light case prefers the treatment level corresponding to her
illness. Separation then
requires
uH(mH,w – R – c0mH) ≥ uH(mL,w – R – c0mH)
uL(mL,w – R) ≥ uL(mH,w – R – c0mH).
As shown in Figure 4.7, if the contract specifies a coinsurance
c0 applied to the heavy-
case treatment level, then proper separation takes place. In fact,
since the coinsurance
aims at forcing the light case to separate, the coinsurance rate is
solely determined by the
light-case patient’s willingness to pay for treatment.
Of course, this is just a demonstration that tools are available to
improve allocation. On a
separate note, note the negative externality imposed on the
heavy-case by the mere
presence of the light case as the heavy-case is worse off in

comparison to the symmetric
information case.
24
Discussion questionsProblems
1
Chapter 3
Demand for healthcare
3.1 Introduction
As we have already seen in chapter 1, to most of us healthcare
means visiting our family
doctor and taking medications, going for medical diagnostic
tests like blood-work or a
magnetic resonance imaging (MRI) session, and having to check
into the hospital for a
minor procedure or a serious operation. These components of
healthcare require the
efforts of doctors, nurses, various technologists and all other
inputs required to operate
the family doctor’s practice, the hospital and the diagnostic
clinic. Briefly, healthcare
includes services supplied by the medical profession or, in other
words, the medical care.

However, healthcare also includes health-enhancing activities,
from exercise and vitamin
intake to good sleep to eating well. These self-initiated
activities may also need market
services such as a gym and goods such as a good bed and
healthy food. Thus, as
healthcare requires the purchase of various goods and services,
economic analysis
classifies the purchasing need as demand for healthcare.
The demand for healthcare does not originate from primitive
preferences but, rather, it is
a demand derived from the more primitive demand for health.
However, it also differs
from most inputs in production where the output is also a flow.
Individuals directly
demand health1, a stock variable or the level of one’s health at
a given moment in time,
whereas the demand for healthcare is a flow or a certain amount
of healthcare over a
given time period. The healthcare demand is rather similar to a
worker’s demand for
human capital where training, education and on-the-job learning
are all flow inputs
combined with one’s time and effort to produce human capital.
Similarly, human capital
enhances the individual’s earning potential by boosting one’s
wages or salaries whereas
the health stock increases one’s healthy time available for work
and leisure. Taken in the
long run context, sustained periods of health positively affect
the individual’s earnings
both in terms of wages and his ability to work. Where the health
stock and human capital
differ is the direct demand for health stock. While human
capital may not be a

prerequisite for leisure activities, health stock necessarily is.
Since being healthy is a desired state by individuals under all
circumstances, work or
leisure, such a desire generates the first reason for the demand
for health stock. The
second reason is that, normally, individuals have to work for a
living and work is better
performed if the individual in question is healthy. Therefore,
the first reason is health
stock as consumption good whereas the second as an investment
good2.
Healthcare, as a produced good, exhibits the following
properties. First, as discussed
above, healthcare demand is a derived demand, i.e. health is
demanded and healthcare is
1 Or the flow of daily good health as is modeled in Grossman
[1972, 2000].
2 See Grossman [2000] for a technical analysis of these two
distinct cases.
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2
demanded because it produces health. Second, health is
produced by using various inputs,
one of them being healthcare in the larger sense and medical
care in the narrow. Finally,

the replenishment of the health stock introduces a dynamic
relationship between the
health stock and healthcare. The combination of healthcare and
other health inputs
produces the health investment. The individual’s health profile
over time can then be
represented as a stock adjustment model where the stock of
health varies for the better if
the individual positively contributes to his health over a given
period whereas reckless
behaviour lowers the stock. This relationship between one’s
stock of health and the flow
of health investment yields a simplified version of the health
stock model of healthcare
demand originally developed by Grossman [1972]. A graphic
summary of the model is
given in figure 3.1 below.
Individuals consume various goods and services by purchasing
them and allocating their
valuable time to consume them. Going to the movies as well as
jogging involve
substantial amounts of leisure time as well as purchased inputs
like movie tickets,
transport, and running shoes. The model lumps such goods and
services into home goods
represented by B and health investment goods by I. B is
consumed by combining one’s
time TB with the purchased inputs X and I by combining time
TI with inputs M. The
consumption of goods exhibits properties of production
functions in that the time and
purchased inputs are combined to yield the consumption. The
two production functions in
the simple model are B(X,TB;E) and I(M,TI;E) where E denotes
environmental variables,

such as noise and pollution that would, respectively, spoil the
production of home goods
B and health investment I. At the centre of figure 3.1 lies the
link between health
investments and the state of one’s health. The genetically
programmed erosion of human
health over time is represented by δH, i.e. humans lose a
varying fraction of their health
stock H over a given period of time. However, health
investment I contributes to the
stock. Therefore, the sum I - δH yields the rate of change of the
health stock. The health
stock is not only good in itself. The healthier the person, the
more healthy time is
available either for work or for leisurely activities B and I, the
latter being the critical
contributor to health stock. TH can thus be split between work
time TW and the time
allocated to the consumption of home goods and health
investment, respectively TB and
TI. We note that TW generates the income used to purchase
inputs X and M. Finally, since
individuals value their consumption of goods and services B as
well as their state of
health H, they allocate their resources between B and I, towards
B because it yields
utility, towards I because it contributes to the health stock. Now
that the Grossman model
has been intuitively introduced, the purchased inputs M can be
interpreted loosely as
healthcare.

3
Figure 3.1 Health stock model of healthcare demand
schematically summarized
However, an important distinction must be drawn between
medical care and the more
comprehensive concept of healthcare. Often used
interchangeably, both are gross
investments into one’s health. Medical care is the collection of
health-restoring, health-
preserving and health-enhancing services provided by applied
medicine. As such,
medical care consists of the available medical technology,
running typically from
symptoms to diagnosis to treatments, but also including
preventive technologies. Thus it
can be preventive3 or curative. Healthcare, however, beyond
medical care involve layers
of individual choices over work, consumption and leisure. For
example, choices of
workplace, vocation, work tempo, consumption of healthy food
and the allocation of

3 Contrary to popular belief prevention is not uniformly less
costly and less invasive than treatment
(Laupacis [1996], Marshall [1996]).
Health stock
accumulation
HI
dt
dH δ−=
Individual preferences
over B and H
U(B,H)
Healthcare
investment
production
I = I(M,TI;E)
Consumption
production
B = B(X,TB;E)
T0 - TL = TH = TW + (TB + TI)
TW generates income
wTW = C = pMM + pXX
TB TI

TW
X M
4
leisure time to health investment all fall into the healthcare
category without being
medical interventions. Moreover, these choices tend to be
overwhelmingly preventive
rather than the mostly curative modern medicine. Thus, whereas
all choices enhancing
one’s health constitute healthcare, a subset of services mostly
provided by medicine
constitute the medical care.
The second section of this chapter will progressively develop
the health stock model of
demand for healthcare. As summarized in figure 3.1, the model
internalizes the ability of
individuals to choose their health profile as well as the inherent
dynamics of one’s health
stock. The section will thus examine individuals’ preferences
for health as well as their
allocations of time and money towards healthy activities and
medical care in order to
derive their demand for healthcare and medical care. The third
section considers
examples. The effects of non-monetary and monetary factors on
the demand for
healthcare will be examined. For instance, the response of

healthcare demand to changing
preferences and rising wages will be analyzed. The fourth
section traces the effects of
user fees, a demand management tool. The conclusions section
reemphasizes the
fundamentals covered in the chapter and provides links to the
demand for healthcare
insurance covered in chapter four. .
3.2 The health stock model of healthcare
Individual’s preferences
When individuals enjoy various goods and services, this
enjoyment is normally translated
into a demand to purchase and consume. However, this
enjoyment is stronger, the better
the individual’s health. Technically speaking, demands for
goods and services are health-
state dependent. Thus, there exists some complementarity
between an individual’s state
of health and her consumption of goods and services through
this state-dependency. This
complementarity relationship does strongly suggest that health,
in itself, is desirable and,
hence, individuals would be prepared to allocate resources to
enhance health.
Yet, there definitely exists some substitutability between health
and consumption through
tradeoffs between health-enhancing goods vs. the rest. For
instance, over-exertion and
stress in pursuit of higher income frequently appear at the
expense of health or, simply, as
lower levels of health investment. This substitutability may

involve both dimensions of
health, as purely a consumption good as well as investment into
income-generating health
capital. For expositional purposes, we will henceforth refer to
health as a consumption
good entering an individual’s utility function alongside other
goods and services without
conditioning individuals’ utility functions by health status.
Thus, an individual’s utility function U(B,H) is defined over
ordinary goods and services
B (henceforth home-goods, consistent with Grossman [1972]
terminology) and health H4,
with utility increasing in both B and H and the utility function
yielding convex towards
4 We’ll simplify the Grossman [1972] notation that enters
health stock services, rather than the health stock
itself, into the utility function.
5
the origin indifference curves representing diminishing
marginal rate of substitution
between B and H. Referring back to figure 3.1, this tradeoff
represents individuals’
preferences both current and intertemporal. Currently, enjoying
a certain level of income,
individuals can choose to marginally sacrifice health investment
goods (e.g. less sleep

causing short-term drop in alertness) for an increase in home-
goods. However, this is not
the full opportunity cost of the increase in home-goods because
current lower investment
in health would induce a long-term drop in the health stock with
the reduced healthy time
consequence. The present discounted value of the reduced
healthy time decrease in the
future combined with the current loss of health constitute the
opportunity cost of an
increase in home-goods consumption. Since individuals thus
decide over intertemporal
allocations, the modeling must intrinsically be intertemporal.
The dynamics (or the time profile) of the health stock requires
that the single-period
individual utility function U(B,H) be modified so as to reflect
individuals’ intertemporal
tradeoffs and their discounting of future utilities. Two other
intertemporal channels, in the
general optimization problem, beyond individuals’ valuation of
the future are the
depreciation of the health stock and the possibility of
countering such ultimately
inevitable depreciation through health investments. Health as
stock can be accumulated
or rather decumulated over time and health as consumption
good5 can be consumed at
different points in time; individuals characteristically take
account of their future health
for both these reasons. Health as consumption good then
necessitates all future
consumptions be taken into account and health as investment
good generates healthy time
required for work and hence income. The individual’s lifetime
utility can then be

modeled as the present discounted value of future utilities6 (as
the continuous version of
Ried [1998])
∫
−T t dtHBUe
0
),(θ
(3.1)
where t is the instantaneous time unit (or the moment in time), θ
is the time discount rate,
e-θt the discount factor (or, simply, the individual’s subjective
weight attached to every
moment in the future) and T the individual’s residual life
expectancy. The utility function
U(B,H) in equation 3.1 must be interpreted as the instantaneous
utility of the individual
and the whole expression then is the weighted sum of utilities
over the residual lifetime.
The weights decline over time, signifying that today’s
enjoyment is more valuable than in
a future period. Hence, the individual’s choice of current levels
of consumption and
health investment are, therefore, not independent of their future
expected values. For
instance, a lower health investment today may increase current
consumption without
lowering current health but its opportunity cost is a fall in the
future stream of health
stock in turn lowering not only the future consumption but also
the individual’s future
earning capacity and hence his future consumption. These

tradeoffs are moderated by the
discount weights e-θt that assign higher utility weights to
today’s health and consumption.
Thus, the maximand in equation 3.1 is fairly straightforward
except for the time horizon
T. There are two issues regarding T. The first is whether there
is an optimal length of
5 The health as consumption good in Grossman [1972] is
modeled as flow of services from stock.
6 Grossman [1972, 2000] uses a discrete time framework for the
individual lifetime problem.
6
horizon. For example, euthanasia is an endogenous choice of
end-of-life whereas a
terminal illness is a relatively randomly-timed exogenous end to
life. Most individuals
choose their health investments considering a normal or average
residual life expectancy.
This optimality question links the time profile of the
depreciation rate to the individual’s
willingness to invest in health so as to aim at a health stock
perhaps well above the
survival minimum beyond a certain advanced age. Alternatively,
de-investment in the
form of harmful addictions or negligence today boost the health
depreciation rate (Becker
& Murphy [1988]). The second issue related to residual life

expectancy T involves a
modeling technicality. Whereas the time profile of the
depreciation rate is not
deterministic in so far as we scientifically know, the question
remains as to whether it
should be analyzed as such as. A random evolution of the
depreciation rate would add
considerable modeling complexity yet, with advances in
genetics, some of sources of
randomness are becoming predictable. We will return to the
discussion of the
depreciation rate below in the section entitled Health stock
profile and health investment.
Allocation of time and income
Every individual is endowed with the same amount of time T0
regardless of the unit of
time chosen for analysis. Though, for the sake of realism, T0
must be long enough to
allow days of morbidity as, typically, days can be characterized
as healthy or unhealthy.
A longer period chosen would then yield meaningful periods of
illness versus wellbeing.
The total time endowment will now be broken down into
components as
)(0 IBWL TTTTT +++=
(3.2)
where TL is the ill days time, TW the work time, TB the time
allocated to produce the
home good B and the time TI allocated to produce the health
investment good I. The
home good B can be produced by a combination of TB and of

market-purchased inputs X
thus obeying the production function
);,( ETXBB B= .
(3.3)
Similarly, for health investment I, the production function is
given as
);,( ETMII I=
(3.4)
where M is the set of market-purchased inputs, including
medical care. In both equations
3.3 and 3.4, E represents the exogenous factors such as the
individual’s genetic
inheritance and environmental context. As such, changes in any
component of E will
induce shifts in the production function. For example, for the
same input levels, the
quantity of health investment produced will be lower in an
unhealthy environment, e.g. a
polluted environment, than in a healthy one. Both production
functions should normally
exhibit decreasing returns to scale. Although easily
understandable for home-goods,
decreasing returns to scale in the production of health
investment must be related to the
human body’s capacity to absorb one’s health-enhancing
activities. For instance, while

7
moderate to medium levels of exercise go a long way, medium
to high levels of exercise
do not enhance the health stock as much. The convex-towards-
the-origin shape of the
production possibility frontier (PPF) in figure 4(b) easily
follows from the decreasing
returns to scale property of the production functions. The shape
of the PPF corresponds to
the increasing opportunity cost for either the home-goods or the
health-investment.
Individuals face time and income constraints. The time
constraint was introduced above
in equation 3.2 whereas the income constraint is given by
wTW = pMM + pXX
(3.5)
where w, pM and pX are, respectively, the wage rate, the price
of medical care (or health-
enhancing goods at large) and the price of other goods and
services. The constraint means
that the individual cannot spend more than her earned income
wTW on purchased inputs
M and X. The two constraints are not independent. First, time
and income allocated to
healthy activities may reduce time lost to illness and boost time
available for work.
Moreover, in the longer term, it may enhance productivity
through improvements in
health stock and thus increase wages. Finally, while it will be
ignored here, the
intertemporal planning of time and income allocations allows

further interactions
between the two constraints over time.
Individuals strive to allocate their income and time resources
efficiently between the
production of these health-enhancing and other goods as
presented in figure 3.2 below.
The rectangular box, representing the time and money resources
given a distribution of
one’s time between work (hence money income) and leisure, is
called the Edgeworth
box. This box shows the feasible distribution of resources
towards the production of B
and I. Times allocated to production plus and time allocated to
work for income add up to
TH, healthy time available. And the time allocated to work
yields the total income
available to purchase the two inputs M and X anywhere in the
box. Moreover, to simplify
the exposition, the input prices are normalized to unity (i.e. pM
= pX = 1) by adjusting the
units of M and X. This simplification allows us to identify
every quantity M or X with the
expenditure on that input. Furthermore, whereas the horizontal
dimension of the
Edgeworth box being the total leisure time TLE = TB + TI, the
vertical dimension is equal
to the total expenditure on those inputs. Concisely, every point
in the box is an allocation
of time and money. Of course, one the ultimate objective being
efficient production
levels for B and I, inefficient input allocations must be ruled
out.
One such inefficient allocation is the bundle (M0,TI

0) in figure 3.2 below. Given this
bundle, the individual can produce (B0,I0) as given by the
isoquants passing through the
bundle. However, since marginal rates of substitution at the
bundle are not equal, a
reallocation of more time but less money to B production along
the broken arrow induces
higher levels of both B and I. In fact, the bundle (M* ,TI
*) allows the production of ILOW >
I0 whereas at the same bundle (X* ,TB
* ) allows BHIGH > B0. The initial bundle as well as
the final bundle are feasible and use all the available inputs,
except that the
{(M *,TI
*),(X* ,TB
* )} bundle allows a higher production level of both goods. We
note that,
at this latter bundle, the isoquants BHIGH and ILOW are
tangent, i.e. the marginal rates of
8
technical substitution are equal. In other words, any departure
from this bundle will lead
to a decrease in one output or the other along the diagonal curve
(or possibly both if one
moves off the curve) whereas from {(M0,TI

0),(X0,TB
0)} to {(M *,TI
*),(X* ,TB
*)} both
outputs increased. We conclude that {(M*,TI
* ),(X*,TB
*)} is an efficient bundle. In fact, all
bundles along the diagonal curve are efficient. This diagonal
curve in the Edgeworth box
is then called the contract curve and it consists of those input
bundles that are efficient.
I = 0
X
{(M0,TI
0),(X0,TB
0)} TI
(B,I)-inefficient
■
BVERY HIGH •
BHIGH {(M* ,TI
*),(X0,TB
0)}
B0

I LOW
I0 Locus of efficient (B,I)
X + M = C
BLOW
IHIGH
•
(B,I)-inefficient ■
TB
B = 0
M
TB + TI
Figure 3.2 Efficient choices of B-I production
Intuitively, at any allocation off the contract curve, such as
{(M0,TI
0),(X0,TB
0)}, a

reallocation of time from the production of, say, B to I requires
a smaller increase in X to
9
preserve the B production than the release of M to preserve the
I production. Thence,
either B or I can be increased without the other being decreased
or, as we saw above,
both can be increased along the broken arrow. This move is a
Pareto improvement, i.e.
more of each output can be produced with the same total
resources but by redistributing
them. Thus, the individual would never choose a bundle off the
contract curve. Note that
movements along the contract curve aren’t Pareto-improving
because an increase in one
comes at the expense of decreasing the other. As such, their
relative evaluation depends
on the individual’s preferences over (B,I) bundles.
An example can illustrate the efficiency along the contract
curve. Suppose I is an
individual’s fitness activity in a gym and B a home
entertainment activity like hosting
friends. Let the initial bundle off the contract curve be {(M0,TI
0),(X0,TB
0)}. Given

(M0,TI
0) this individual reaches I0 = I(M0,TI
0), a sufficient level of fitness. We note that if
she spends less time in the gym by reducing TI while
purchasing the services of a
personal fitness advisor by increasing M, she can preserve the
same fitness level if the
substitution time for money towards B is realized along the
isoquant I0. The individual
then reaches the bundle where the two isoquants BVERY HIGH
and I0 are tangent along the
contract curve. The significant increase in B derives from input
substitutions. Along I0,
little increase in money is required to compensate decreases in
time because the
individual is already spending too much time in the gym. Yet,
the production of B steeply
increases with time rather than money because, at (X0,TB
0), an extra unit of time is very
valuable. Overall then, the individual realizes that she is
spending too much time rather
than guidance in the gym and rectifies the situation by releasing
time towards the home-
good that dearly requires more time. The final bundle yields as
much fitness I0 as before
but much more in B at BVERY HIGH, surely a Pareto
improvement.
A remark concerning the size of the Edgeworth box is now in
order. Since individuals are
endowed with TH = (T0 - TL) of healthy time, they can allocate
it between work time TW
and leisure time TLE = TB + TI. This time allocation problem
will be further studied in the

following section as well as in Appendix A as a movement
along the contract curve may
have second-round effects. A change in preferences inducing,
say, an increase in I, will
induce not only a first-round change in the bundle (B,I) but,
also, via the effect of I on the
health stock H and subsequently on TH. And, of course, if the
health stock increases, so
do the healthy time and the dimensions of the Edgeworth box.
Health stock profile and health investment
Humans, like all living beings, have a generic lifecycle. In the
absence of major illnesses
and medical interventions, we are born, get healthier and
stronger to our mid-twenties
and then decline towards the natural death through a net loss of
various cells in our
bodies. Where healthcare essentially intervenes is when illness
sets in or when our health
stock can be improved with the consequential retardation of cell
death. In technical terms,
human health stock typically accumulates at first and
decumulates later, with the eventual
demise of the body. This health stock profile is neither
completely exogenous, nor
completely endogenous. The function of health investment as
introduced above is to
boost this profile and, assumed away in the model under
consideration, is the effect of the

10
individual’s activities on the depreciation rate.7 This latter
effect can lower the rate or
retard its inevitable increase.
In order to understand the basics of healthcare demand, we
would be justified in
significantly simplifying the framework used. Thus, the health
stock profile can be
represented by the following equation of motion of the health
stock H over time
.HI
dt
dH
δ−=
(3.5)
Equation 3.5 yields the time rate of change of health stock or
the net investment as the
difference between the gross investment in health stock, I, and
the total stock
depreciation δH where δ, a fraction, denotes the current rate of
stock depreciation. The
rate of depreciation of the health stock is not time independent,
being typically low early
in life and getting larger later. Three observations on δ are in
order. First, biological
reality makes it so that, towards the end of life, no matter how
high investments may have
been, the health stock will eventually fall below a threshold
level signifying death. Thus,

when the gross investment I required for preventing negative
net investment becomes
prohibitively costly or simply impossible, the individual starts
approaching the end of
life. Second, though the depreciation rate δ is fundamentally
determined by genetic
makeup, it will also be influenced by cumulative health
investments and the environment
in which the individual in question lives. Finally, δ may even be
negative early in life as
the person becomes stronger, acquires immunities and,
significantly, learns to produce
health investment more efficiently.
The solution to equation 3.5, as part of the individual’s overall
problem set up below in
equation 3.7 and explained in Appendix B, yields the health
stock profile. This trajectory
starts at birth with an initial health stock for a particular
individual, typically rises over
time towards mid-twenties, more or less follows a plateau till
late middle ages, then starts
a steady decline and, finally, takes a tumble late in life. Of
course, various relatively
random events, from catastrophic illnesses and accidents, may
cut one’s life short.
Throughout individual’s life, the health stock is the major
determinant of morbidity as
represented by ill time TL and, hence, time available for work
TW. A higher health stock
translates into a longer healthy time TH
through a healthy time production function
TH = T(H) . Not only is there an upper limit to one’s time
available but also health stock
improvements exhibit diminishing returns in that increases in

the health stock reduce
morbidity slower or, on other words, increase healthy time
slower. This relationship is
illustrated in figure 3.3 below.
7 Chang [1996].
11
TH
365
T(H)

Hmin
H
Figure 3.3 Healthy days production function
Figure 3.3, by linking the health stock and healthy time, does in
fact link the income and
time constraints because a higher health stock enables one to
earn more and relax the
income constraint. Moreover, Tmin in the diagram is the end of
life threshold although
one’s health could deteriorate as a result of catastrophic illness
or accident and not just
old age.
Now, in order to concentrate on the fundamentals of
individuals’ decisions concerning
health, we will restrict our attention to snapshots of reality
called steady states where a
given health stock prevails. This simplifies the exposition and
allows the use of simple
diagrams. Every snapshot corresponds to a particular steady
state where, given a steady
rate of depreciation, health stock is momentarily constant, that
is dH/dt = I – δH = 0 or,
simply, I = δH. This is a reasonable approximation to reality in
that, barring random
occurrences of serious illness, most individuals’ working lives
are characterized by
steady yet diverse levels of health. As health investment is kept

equal to total health
depreciation, the derivation of the demand for healthcare can be
graphically derived.
(Appendix B presents the simplified but still dynamic health
stock model.)
Since health investment equals the health stock replacement δH,
the health stock variable
H can simply be replaced by I/δ in the individual maximand
U(B,H). As a result, any
exogenous changes, from prices to tastes, will simply induce
changes in health
investment I and H instantaneously to a new level instead of H
adjusting over time. Since
12
the intertemporality of the problem is thus suppressed, the
individual’s current
preferences can then be represented by
)/,(),( δIBUIBV = .
(3.6)
The individual enjoys increasing utilities from higher levels of
home-goods and health
investment given that health investment boosts health stock, this
latter being the
ultimately desired consumption and investment good for the
individual. The indifference
curves generated by V(B,I) are illustrated below in figures

3.4(b) and 3.5(b).
This simplification is, just to reiterate, used for expositional
purposes only. However, the
constancy of the health stock in the absence of major illnesses
is not far from reality. As
exemplified by the difficulties of lowering one’s weight or
cholesterol levels over short
periods of time, this constancy constitutes a fairly realistic
approximation over the short
term. Moreover, high levels of investment may prove infeasible
simply due to the time
constraint and the limitation induced by income-earning
potential. On the other hand, de-
investment in health is clearly feasible and self-destruction can
bring the health stock
down fairly easily not only in individual cases but also at
community level as recently
exemplified in 1990s’ turmoil in Russia. Within a few years,
Russian life expectancy fell
by about six years due to deterioration in diet and obesity, to
increased addiction to
alcohol and harmful substances and stress as well as a lack of
medical care (Brainerd
[2005]). What happened in Russia can be easily put into context
with the help of equation
3.5 above. Falling incomes did not allow Russians to invest in
health as current
consumption needs took precedence. Moreover, the health
depreciation rate increased,
even in such a short term, as a result of dreadful social and
economic circumstances.
Thus, both I falling and δ rising, the health stock took a tumble,
lowering life expectancy
drastically.

Before we look at the full problem of the individual it is worth
noting that another
simplification is the dropping of the possibility of intertemporal
income transfers keeping
with our earlier simplification of the dynamics of the problem.
Individuals can and do, in
general, save and borrow with an eye to the ultimate evening
out of their marginal
utilities over time (see Grossman [1972, 2000], Ried [1998]).
Just like in simple
consumption problems where the consumer reallocates his
marginal dollar from a lower
utility generating consumption to a higher one, health care
would require reallocation of
that dollar from a healthy state where the return is low to an
unhealthy state where the
extra dollar would generate a high utility return by enabling
purchase of healthcare.
Similarly, one might want to transfer the extra dollar from his
youth when illness is
unlikely to occur to old age when it is more likely. This
intertemporal behaviour
corresponds to a lifetime utility maximization over various
goods and services. The
simple and most pervasive examples being a house mortgage,
retirement savings and
health insurance, though this latter is not only against old age
ailments but also for
income-smoothing against lumpy and unexpected healthcare
expenses for random and
serious illnesses.

13
Given the steady-state assumption simplifying equation 3.5 and
hence the individual’s
maximand as in equation 3.6, the individual’s full but now
static problem of utility
maximization can be written as follows
max V(B,I)
{X,M,TB,TI}
s.t. B = B(X,TB;E)
(3.7)
I = I(M,TI;E)
T0 = TL + TW + TLE
wTW = pMM + pXX
TLE = TB + TI.
The first two constraints are the production functions for home-
goods and health
investment. The inputs for the production functions, i.e. time
and purchased goods or
money, have to satisfy the availability constraints, the first
being the overall time
constraint and the second the budget constraint. Finally, the last
constraint limits the time
available for the production of B and I to the leisure time, after
subtracting the ill and
work times from total time available to the individual. The
variable E in the production
functions acts as a shift variable, depending on given genetic
and environmental
backgrounds. The problem is illustrated in figure 3.4 below.
Two remarks will relate this simplified version of the model to

the original. First, as
health stock is kept constant, time ill TL is also constant. As a
result, healthy time TH is
given. When the individual allocates it between work and other
activities, it suffices to
choose TB + TI in order to determine work time or vice versa.
Second, complementing the first remark, the opportunity cost of
time spent in the
production of B or I must be equal to the wage rate. In figure
3.4(a), the slopes of
isoquants are equal at {(M*,TI
*),(X* ,TB
* )} therefore the last hour spent in either activity is
worth an equal value. If, however, the opportunity cost of time
spent in B (or, equally, in
I) in terms of purchased goods exceeded the wage rate, the
individual would work less
and consume more. From figure 3.4(a), the marginal rates of
substitution in production
are equalized and the value of marginal time spent in leisure
activities is equal to
consumption goods sacrificed at the margin. This marginal
willingness to pay is then
equal to the wage rate, as seen in figure 3.4(c) where the
indifference curves shown are
induced preferences, i.e. they are derived from V(B,I). Since
individuals choose efficient
combinations (B,I), any bundle chosen necessitates a
corresponding bundle of leisure
time and income. A corresponding apportionment of the
available healthy time would
yield this latter bundle of leisure time and income.

Figure 3.4(a) below illustrates the efficient production choices
made by the individual.
Given the availability of time TLE
* = TB
* + TI
* (from panel (c)) the individual splits it
between the productions of B and I (from panels (a) and (b)),
combining the time inputs
with the allocation of available income wTW
* to purchase, respectively, the inputs X* and
M* into the two lines of production. Panel (b) exhibits the
production possibilities
boundary (PPF) derived from the Edgeworth box in panel (a).
Given decreasing returns to
14
scale technologies in the productions of B and I, the PPF is
concave towards the origin.
The individual then picks the utility-maximizing bundle (B*,I* )
along the PPF. This
choice simultaneously determines first the health stock H* and,
secondly, the allocation of

15
B = 0 T*B M
TB I
I* IMAX
X* M*
(B*,I*)
B*
V(B,I) = V*
TI T
*
I I = 0
B

MAX B
X
(a) Efficient allocation of time and inputs (b) Utility
maximized over
individual PPF
C
C* = X* + M*
V*
T* B T
*
B + T
*
I TH T0

TW T
*
W
(c) Leisure-work allocation of time
Figure 3.4 Individual demand M* for healthcare
16
one’s time between work TW
* and leisure TLE
* as well as the purchased inputs M* and X* .
We note that, given the parameters of the model, M* is the
quantity demanded of
healthcare (medical care) if M is interpreted to be healthcare
(medical care).
A simple comparative statics exercise will be used to illustrate
(see figure 3.5 below) the
functioning of choices in response to changes in the individual’s
environment. What
happens when, say, preferences change? Since preferences are
exogenously specified,
this initial change will first trigger a complex process of
reallocations. Time endowment
is the individual’s fundamental resource in that time is a

primary input into the
production of B and I as well as being the marketable labour
resource that enables one to
work and purchase X and M.
As shown in panel (b), the individual’s marginal rate of
substitution in consumption (i.e.
her marginal willingness to pay for B in terms of I) has
increased. This induces the lower
level of health investment I2 and hence the lower health stock
H2 (not shown on the
diagram). However, from healthy days production function in
figure 3.3, TH falls from
TH
1 to TH
2 thus inducing the smaller Edgeworth box as in panel (a). We
note that this
Edgeworth box is smaller both in terms of time and
expenditures as the individual prefers
to reduce leisure time considerably from TLE
1 to TLE
2 as well as work time slightly from
TW
1 = T1H - T
1
LE to TW
2 = T2H - T
2
LE rather than, say, reducing work considerably and

leisure slightly in panel (c). Returning to panel (a), we also note
that the individual’s final
preferences reveal that she is indifferent between the original
bundle (B1,I1) and the final
bundle (B2,I2). However, if the PPF had not shrunk, the
individual could have been better
off at his new bundle (B2,I2) with his new indifference curves
than with the old bundle
(B1,I1). This process of adjustment will later be used (in
section 3.3 below) to analyze
exogenous (e.g. pollution) and endogenous (e.g. addiction)
harmful consumption
activities.
Here is an example to gain further insight into this adjustment
process. Considering our
mundane attitudes to emerging health information, our recent
experience with the Atkins
diet may be easily understood to illustrate the Grossman model
adjustments. The low-
carbohydrate Atkins diet, upon proving as an effective short-
term weight loss tool,
became a fad in the early part of this decade but then fizzled
away as serious health
concerns with the diet ensued. Of course, when the diet became
popular, consumers were
not yet aware of the negative health consequences. The Atkins
Company went bankrupt
in 2005. At the diet’s heyday, food manufacturers flooded the
markets with low-
carbohydrate food items upon consumers’ increasing demand
following their change of
preferences relative to weight-loss products and services. If we
maintain the current
wisdom that the Atkins diet may, overall, be a consumption
good B rather than a health

investment good I, the consumers’ initial shift to the Atkins diet
may be seen as an
increase in their marginal willingness to pay for the diet in
terms of health investment
goods forgone as in figure 3.5(b). However, the negative effects
of the diet would have
shrunk the PPF thus eventually yielding a level of utility no
higher than the original.
This section introduced the concept of health care demanded as
a demand for input, an
input into the production of desirable health investment goods.
In fact, individuals
17
B = 0 pM M
TB I
Vinitial (B,I)
I1
Vfinal (B,I)
B1
(B1,I1)
I2

B2
(B2,I2)
TI I = 0
B
pXX
(a) Efficient reallocation of time and inputs (b)
Utility maximized over
smaller individual PPF
C
Wfinal
C1
C2
Winitial
Slope = - w
TLE

2 TLE
1 TH
2 TH
1 T0
(c) Leisure-work reallocation of time
Figure 3.5 Changes in preferences
18
demand consumption goods and health, this latter also being
demanded as it enables one
to earn income. We can therefore derive the healthcare demand
function from this same
framework by varying the price of healthcare.
Demand for healthcare
Demand for healthcare in the health stock model is demand for
purchased inputs into
healthy activities, ranging from medical care to jogging.8 We
will now derive the demand
curve for healthcare by simply defining M as healthcare9. A fall
in the price pM of

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