1
Grossman's theory of
the demand for health care
For Health Economics, Oslo, Sept 2003
Professor Paul Dolan
Aims of the session
(what I hope to do)
Provide an insight into the Grossman model
Provide guidance on the technical concepts
and graphical representation of the model
Show the implications of the model ­ and
highlight some criticisms
Objectives
(what I hope you are able to do)
Understand the contribution of the Grossman model
to health economics
Assess the application of consumer theory to the
debate on the demand for health and health care
Be able to discuss the role of variables such as age,
income and education on the demand for health care
General background
Health is determined by many factors among which
medical care is only one
These factors include social class, work environment,
employment status, income, housing conditions,
heating, education, diet and lifestyle
The relative importance of inequalities in these types
of resources cannot be determined unless there is an
understanding of the links between resources,
behaviour and health
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Background to Grossman
Grossman (JPE, 1972) was concerned with how
individuals allocate their resources to produce health
The model goes beyond traditional demand analysis
and has been extremely influential in health
economics
It utilises the idea of the individual as a producer of
health (not simply a consumer) by removing the
artificial separation of consumption and production
It also introduces the idea of investing in human
capital (health and education) to improve outcomes
in both the market (work) and non-market
(household) sectors
Key concepts
Demand for health care is derived
from a demand for health (few people want health
care for its own sake)
Demand for health is derived
from the demand for utility (e.g. healthy days in
which to participate in leisure and work)
Individuals are not passive consumers of health
but active producers who spend time and money
on the production of health
Health can be seen as lasting over time periods.
It depreciates (perhaps at a non-constant rate)
and can therefore be analysed as a capital good
Key assumptions
Individuals value health but do not value it above all
else (if they did, they would not over-eat, smoke,
drink too much, or drive too fast)
We have limited incomes with which to finance
health and other activities, and neither is costless
We exert a relatively high degree of control over our
health by virtue of the fact that we can influence our
health-affecting consumption patterns, our health
care utilisation and our environment.
The demand for health
Health demand consists of two elements:
(1) Consumption effects:
health yields direct utility i.e. you feel better when
you are healthier
(2) Investment effects:
health increases the number of days available to
participate in market and non-market activities ­
the novel bit of the model
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Health as a capital good
H Stockt = H Stockt-1 ­ dep'n () + inv. in H (I)
A person is born with initial endowment of H, which
they add to by investment.
The rate of H production will depend on the efficiency
of investment in H.
There will be  in the value of the stock of H through
age, accident, carelessness, sudden disease.
As we are considering U over a life-time we also need
to be aware of the issue of time-preference
The human capital model
The individual is a producer of H (amongst other
things): they buy market inputs (medical care, food,
clothing), and combine them with their own time to
produce services that increase their utility
The analysis is based on human capital theory which
shows how individuals invest in themselves e.g.
through training or education, to increase their
productivity
The optimal amount of investment in human capital is
determined by the relative Cs and Bs: usually the Cs
occur in the short-term whilst the Bs accrue in the
future in the form of enhanced job opportunities
Investing in health
HEALTH
STOCK
HEALTHY
DAYS
PRODUCTION
PROCESSHealth Care
Diet
Exercise
Environment
Income
OUTPUT
Time
INPUTS
And to quote ...
"The only way to keep your health is to eat
what you don't want, drink what you don't
like and do what you'd rather not."
Mark Twain (1835-1910)
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The investment decision
Household production functions:
Health production
I = f(M,TH;E)
Consumption goods
Z =f(X,TC;E)
I = investment in health
M = market health care inputs
TH= time spent on improving health
Z = composite consumption good
X = market produced goods
TC = time spent on composite consumption good
E = education
The investment decision
Analogy with a firm using inputs to produce goods:
decisions made according to production functions ­
relationship between inputs and outputs.
Education plays a crucial role in determining the
efficiency of health capital and also in other
production functions, therefore influences
consumption patterns of households
Assume:
individuals want to maximise their lifetime utility
they have perfect knowledge
and able to allocate time between different activities
Implied choices
Inter-related time choices:
Labour time (income) vs. leisure time vs. ill time
Within leisure time choice:
health producing time (gym) vs. non-health producing time
Resource choices:
Health care inputs vs. other consumption
subject to budget constraint
Optimal choice of investment
Marginal cost (of investing in H) = Marginal benefits
Marginal cost = r + ,
where
r = rate of interest on other investments
 = rate of depreciation of health
i.e. the opportunity cost
Both r and  are exogenous to the model
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Optimal choice of investment
Marginal benefit = rate of return = (W*G)/C
where
W = wage rate,
G = marginal product (rate of return) of health
investment which is subject to diminishing MR (stop
smoking through to Michael Jackson's oxygen tent)
C = direct cost of investment in health
This is the `marginal efficiency of capitaľ (MEC)
Demand for Health Capital
Cost of capital
Health StockH*
r + 
MEC
X
At point X marginal cost = marginal benefit
Diminishing returns between health
investment and health i.e. the production
function is the normal shape - as the level
of health capital increases it is increasingly
difficult to generate health from inputs
The Effect of Ageing
Cost of capital
Health Stock
H*
r + 
MEC
r + 1
Part of this is offset by increasing investment in H so health care demand rises.
H1
Depreciation increases (d to d1) over the life
cycle (not a constant rate), therefore MC
rises, and hence demand for health capital
falls ­ but demand for health care may rise
due to inelastic demand curve for health
And to quote ...
"Biological factors associated with ageing raise the
price of human capital and cause individuals to
substitute away from future health until death is
chosen" (Grossman, 1972)
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Changes in the Wage Rate
Cost of capital
Health Stock
H1
r + 
H2
An increase in W raises the returns on healthy
days. The optimal level of H is thus higher. But
investment in HC also requires an input of time
which increases the costs of such investment.
MEC2
MEC1
Changes in Education
MEC
Health CapitalH1
r + 
H2
Education increases the efficiency of nonmarket
production ­ it increases the MP of
health inputs thereby raising the optimal
health stock. Also better educated may
enjoy exercise etc. more and may be more
able to follow treatments
MEC2
MEC1
Implications
Raise education amongst the poorly educated
Reduce price of health care, especially to the
poor
Increase wages of the low paid
Use policies to affect depreciation
The 4 quadrant diagram
Consumption
Health
Health
Inputs
I (Consumption possibilities)II (Production function)
III (budget constraint)
IV
45°
a
Consumption
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A reduction in income
Consumption
Health
Health
Inputs
I (Consumption possibilities)II (Production function)
III (budget constraint)
IV
45°
a
Consumption
b
Change in prices
A fall in the price of a unit of health inputs results in
the budget line swivelling outwards from the
intercept on the consumption axis
Assuming that the individual did not devote all of her
income to consumption before the price change, she
will employ more health inputs and consequently will
be achieve better health.
This suggests that subsidising the price of health
inputs (for example, milk and heating) will result in
improved health for those receiving such subsidies.
Technical knowledge/education
Advances in medical science or education will cause
an upward shift in the health production function
This means that the individual can reach a higher
level of health for the same level of health inputs
This suggests that a health education programme
may bring about improved health without any
increase in the demand placed on health services and
other health inputs
Application to choice behaviour
If other capital stocks are low an individual will
choose to deplete her health stocks in order to
replenish other stocks
e.g a high wage occupation that causes the stock of
health to decline may be chosen if the stock of
wealth is low
A similar kind of argument might be applied to the
type of recreation activities which are chosen
e.g. an individual with low stocks of wealth relative to
health may smoke since it is a relatively cheap in
terms of wealth and expensive in terms of health
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Policy implications
The model can be used to predict the likely (and
opposite than intended) effects of policy changes
e.g the government may attempt to reduce queuing
time in order to encourage greater utilisation of
health care by the poor
This will increase the MEC of both rich and poor but
since the value of extra time is greater for the rich,
the MEC will shift up further for this group, thus
increasing the inequality
Criticisms of the model
Assumes health care is a constant life time
investment
It ignores insurance markets
Assumes perfect information on the part of
consumers about the MEC of health care, interest
rates, depreciation, etc. ­ for now and the future.
It is deterministic including the choice of when to die!
Summary
Consumers want health not health care per se
Consumers produce health
Health does not depreciate instantly
Demand for health has pure consumption and pure
investment aspects
The cost of holding health is the opportunity costs of
capital plus the depreciation rate
The MEC curve is downward sloping due to MR
Rewards of being healthy are greater for high income
Health can be generated as less cost by educated
Questions
Describe the aspects of health that make it a consumption good and
those aspects that make it an investment good
Give examples of how health might be produced from market and nonmarket
goods
Discuss some of the factors that might increase an individuaľs marginal
efficiency of investment in health capital
Do you think the typical person becomes more or less healthy upon
retirement? What does the Grossman model predict?
Richer people can afford more of all goods (including health care) yet
according to the model will choose a higher health stock. Why?
Provide a critique of the paper by Hey and Patel (JHE, 1993)