Economics 387
Lecture 6
Demand for Health Capital
Tianxu Chen
Outline
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The Demand for Health
Labor–Leisure Trade-Offs
The Investment/Consumption Aspects of Health
Investment over Time
The Demand for Health Capital
Changes in Equilibrium: Age, Wage, and
Education
• Empirical Analyses Using Grossman’s Model
• Obesity—The Deterioration of Health Capital
• Conclusions
THE DEMAND FOR HEALTH
Consumer as Health Producer
• Grossman used the theory of human capital
to explain the demand for health and health
care.
• According to human capital theory,
individuals invest in themselves through
education, training, and health to increase
their earnings.
• Four important aspects of health demand:
Consumer as Health Producer
1. It is not medical care as such that
consumers want, but rather health. People
want health; they demand medical care
inputs to produce it.
2. Consumers do not merely purchase health
passively from the market. Instead, they
produce health, combining time devoted to
health-improving efforts with purchased
medical inputs.
Consumer as Health Producer
3. Health lasts for more than one period. It does not
depreciate instantly, and it can be analyzed like a
capital good.
4. Perhaps, most importantly, health can be treated
both as a consumption good and an investment
good. As a consumption good, health is desired
because it makes people feel better. As an
investment good, health is desired because it
increases the number of healthy days available to
work and to earn income.
Health Capital
• Your body is like a “car.”
• Huh ???
• How do we think of the body as a capital
good, and medical care as a health
investment ???
A Schematic
Figure 7-1 Investing in Health Care
A Model for Time Spent Producing
Health
• I = I(M,TH), where I is investment in health, M is
market health inputs and TH is time used in the
production of health
• B = B(X,TB), where B is other goods produced, X
is market purchased goods and TB is time used
producing other goods
• The ultimate resource is time:
T = TH (improving health) + TB (producing other
goods) + TL ( lost to illness) + TW (working)
LABOR–LEISURE TRADE-OFFS
• Suppose now the time spent creating health
investment to be “health-improvement
time” TH and call TB the leisure time.
• Assume TH and TL are fixed (we will relax
this assumption later)
• Time available for work or leisure=365- TH
– TL= TB + TW
• TB is measured toward to the right while TW
is measured toward the left.
LABOR–LEISURE TRADE-OFFS
Labor-Leisure Model
• VS represents the laborleisure trade-off faced
which reflects the wage
rate.
• Given labor-leisure
preferences represented
with indifference curves,
utility is maximized at
income of Y2 and leisure
time A.
Figure 7-2 Labor-Leisure
Trade-Off
Impact of Investments in Health
• Over time investments in
health reduce time lost to
illness, TL’, and thereby
increase leisure time 365 –
TH’ – TL’.
• The labor-leisure tradeoff
line shifts to the right
allowing for a choice with
more income and more
leisure time at E’.
Figure 7-3 Increased Amount
of Healthy Time Due to
Investment
THE INVESTMENT/CONSUMPTION
ASPECTS OF HEALTH
Production of Healthy Days
• This illustrates the
production of healthy days
using a single input, health
stock.
• If health stock falls below
Hmin, it indicates death.
• The shape of the function
indicates diminishing
marginal returns.
Figure 7-4 Relationship of
Healthy Days to Health
Stock
Production of Home and Health Goods
• AECD represents
production possibilities.
• If health is an investment
good only, indifference
curves look like U1. will
not trade any B to get
additional health.
• If health is a
consumption good then
indifference curves look
like U2.
Figure 7-5 Allocation of
Production Between Heath
and Bread
INVESTMENT OVER TIME
The Cost of Capital
• We demand health capital because it helps
us earn more and feel better. What does it
cost? By analogy, a health clinic purchases
thousands of dollars of X-ray equipment.
The return to the X-ray equipment is in the
future earnings that ownership of the
equipment can provide.
The Cost of Capital
• Suppose that an X-ray machine costs
$200,000, and that its price does not change
over time. Suppose that the annual income
attributable to the use of the X-ray machine
is $40,000 for 5 years. Is purchasing the
machine a good investment?
The Cost of Capital
• Consider the alternative: Instead of purchasing the
X-ray machine, the clinic could have put the
$200,000 in a savings account, at 5 percent
interest, yielding the following:
200,000 x 1.05 = 210,000 at the end of Year 1
210,000 x 1.05 = 220,500 at the end of Year 2
220,500 x 1.05 = 231,525 at the end of Year 3
231,525 x 1.05 = 243,101 at the end of Year 4
243,101 x 1.05 = 255,256 at the end of Year 5
The Cost of Capital
• For the investment in an X-ray machine to be
desirable by these criteria, it should provide at least
$55,256 in incremental revenue over the five years.
• The problem is more complicated, however, because
capital goods depreciate over time.
• For an investment in an X-ray machine to be
worthwhile, then, it must not only earn the
competitive 5 percent return each year, but it also
must provide enough return to cover depreciation.
Cost of Capital
• The problem is more complicated, however,
because most capital goods depreciate over time.
• The clinic must earn enough not only to cover the
opportunity cost from the bank, but also to
maintain the value of the machine. For the
investment to be worthwhile, then, it must not
only earn the competitive 5 percent return each
year, but it must also provide enough return to
cover depreciation of the machine.
Cost of capital
This suggests that the cost of holding this
capital good for any one year, as well as
over time, will equal the opportunity cost of
the capital (interest foregone) plus the
depreciation (deterioration of value).
The Demand for Health Capital
• Conventional economic analysis provides a
powerful conceptual apparatus by which to
analyze the demand for a capital good.
• The cost of capital, in terms of foregone resources
(for health capital, both time and money) is a
supply concept.
• The other needed tool is the concept of the
marginal efficiency of investment, the MEI, a
demand concept which relates the return to
investment to the amount of resources invested.
Marginal Efficiency of Investment and
Rate of Return
• MEI is the marginal
efficiency of investment. As
investment in the stock of
health increases, the rate of
return on additional
investment declines.
• If the foregone interest rate
plus depreciation is r + δ0,
then optimal investment is
H0, which represents the
amount of capital at which
the marginal efficiency of
investment just equals the
cost of capital.
Figure 7-6 Optimal
Health Stock
Marginal Efficiency of Investment
• If they considered owning two X-ray machines, they
would discover that the rate of return to the second Xray machine was probably less than the first.
• To understand this, consider that a clinic buying only
one X-ray machine would assign it to the highest
priority uses, those with the highest rate of return. If
they were to add a second X-ray machine, then
logically it could only be assigned to lesser priority
uses (and might be idle on occasion). Thus it would
have a lower rate of return than the first.
• The clinic would then purchase the second X-ray
machine as well, only if its rate of return was still
higher than interest plus depreciation.
CHANGES IN EQUILIBRIUM: AGE,
WAGE, AND EDUCATION
Impact of Age on Investment in Health
• As we age, our health stock
depreciates faster, that is, the
depreciation rate rises from δ0
to δ1 to δD.
• The result of aging in this
model is a continuously falling
optimal level of health stock.
Figure 7-6 Optimal Health
Stock
CHANGES IN EQUILIBRIUM:
AGE, WAGE, AND EDUCATION
Impact of Age on Investment in Health
• Age may also shift the MEI curve to the left,
because the returns from an investment will
last for a shorter period of time.
• This will reinforce the decrease in
investment that occurs due to increased
depreciation.
Wage Rate
• As the wage rate rises,
so does the return
from healthy days and
therefore the MEI
curve shifts to the
right.
• It is now optimal to
increase health stock
from H0 to H2.
Figure 7-6 Optimal
Health Stock
Education
• Education is seen as
improving the
efficiency of
producing health
which shifts the MEI
curve to the right.
• The optimal
investment in health
stock increases from
H0 to H2.
Figure 7-6 Optimal
Health Stock
EMPIRICAL ANALYSES USING
GROSSMAN’S MODEL
Results
• Sickles and Yazbeck (1998) developed and
estimated a structural model of health
production that looks at the demand for leisure
and the demand for consumption for elderly
males. They find that both health care and
leisure consumption tend to improve health.
Results
• Demand for health is estimated by
Gerdtham and Johannesson (1999) and their
results are consistent with the theoretical
predictions and show that the demand for
health increases with income and education
and decreases with age, urbanization, being
overweight, and being single.
OBESITY—THE DETERIORATION OF
HEALTH CAPITAL
Table 7-1 Weight Status Classified by Body Mass Index
Table 7-2 2009 US State Obesity Rates
An Economic Treatment of Obesity
• Yaniv, Rosin, and Tobol (2009) note that
the human body needs energy to function,
with food being the fuel that creates this
energy. Their theory of obesity views
weight gain as the outcome of a rational
choice that reflects willingness to tradeoff
future health for present pleasures of eating
and lower physical activity.
An Economic Treatment of Obesity
Overweight individuals can consume junk-food
meals, F, and healthy meals, H. They may choose
their level of exercise, x. The model defines obesity,
S, as:
where δ and ɛ represent calorie per meal F and H,
respectively, and μ represents calories expended per
instant of physical activity. BMR is the Basal
Metabolic Rate, the largest source of energy
expenditure.
An Economic Treatment of Obesity
People may eat snacks when they are not hungry, so FS
and M denote snacks and hunger-induced meals,
respectively:
When the two equations are combined, we see the
following result:
When junk food is substituted for a healthy option, S
increases by (δ – ɛ).
Economic Effects of Obesity
• Obesity is a bad health investment, leading to higher
medical expenditures and lower earnings. Finkelstein and
colleagues (2009) report that medical spending for the
obese was about 42 percent higher per year when compared
to someone of normal weight.
• Cawley (2004) finds that heavier white females, black
females, Hispanic females, and Hispanic males tend to earn
less, and heavier black males tend to earn more, than their
less heavy counterparts.
Why Has Obesity Increased?
• Cutler, Glaser, and Shapiro (2003) show that there was
increased caloric intake for men and women from the late
1970s to the late 1990s.
Table 7-3
Changes in
Food Consumption,
1977-1978 to 19941996
Why Has Obesity Increased?
• The reductions in the time required to prepare food
reduced the per-calorie cost of food by 29 percent
from 1965 to 1995.
Table 7-4 Time Costs by Demographic Group (minutes)
CONCLUSIONS
• People benefit from health in four important
ways:
- They feel better when well.
- They lose less time to illness, and hence can
work more.
- They are more productive when they work and
can earn more for each hour they work.
- They may live longer.
CONCLUSIONS
• By analyzing the demand for health in this
way, we recognize that the demands for
health care inputs— from physicians’
services, to drugs, to therapy—are demands
that are derived from the demand for health
itself.