The Demand for health and
healthcare - Grossman
Model
Dr Emma Frew
Health Economics Unit
Medical School
Learning objectives

How individuals allocate their resources to
produce Health – role of age, wage and education

Cost of Capital and Marginal Efficiency of
Investment (MEI)

Understand how the four-quadrant Grossman
model works
Outline

MEI

Changes in equilibrium due to age, wage
and education

Depiction of integrated Grossman model
Demand for Health Capital (1)

Individuals invest in themselves through education,
training and health. The goal is to increase earnings

Two important concepts: Cost of Capital and MEI

Cost of Capital (C)
C = Opportunity cost (cost of foregone alternatives
i.e. interest rate) + rate at which capital good
depreciates
C = r + δ
Demand for Health Capital (2)

MEI – Rate of return vs amount of resources invested
If rate of return on capital good is greater (less) than
cost of capital, then the good will (not) be purchased.
Capital good will be purchased only up to point where:
Rate of return = Cost of Capital
Relationship of healthy days to Health stock
365 days
Healthy
Days
Hmin
Health Stock
Production of Healthy Days

Health is a productive good which produces healthy
days

Greater health stock leads to more healthy days –
however with diminishing returns

Hmin is health stock minimum – production of
healthy days at this point is zero i.e. death

Natural Maximum of 365 days
Optimal Health Stock
Cost of
Capital
MEI
r + δ0
A
H0
Health
Stock
MEI

If cost of capital is r + δ0 , then the optimal quantity of
capital is H0, A represents the point of equilibrium

An x-ray machine that costs £50,000 and has 20 %
rate of return (£10,000) will only be purchased if
(r + δD) ≤ £10,000

A 2nd machine will only be purchased if its rate of
return ≥ (r + δD)

Diminishing Marginal Returns to investment - The rate
of return of a 2nd machine would probably be less than
the first, therefore MEI is downward
sloping
Practical questions

What effect on optimal health stock or demand for
health inputs do the following have:

Increases in life expectancy?

Getting a higher salary?

Going to college?
Changes in Equilibrium - Age

The rate at which health stock may depreciate may
increase during some periods of life and decline
during others.

As an individual ages the δ rate of health stock is likely
to increase (from δ0 to δ1 and finally to δD) i.e. the
health of older individuals is likely to deteriorate faster
than the health of younger individuals.

Assume that wage and other factors determining MEI
are not substantially altered by aging

Optimal health stock decreases with age (i.e. HO > H1)
Changes in Equilibrium - Age
Cost of
Capital
MEI
B
r + δD
r + δ1
r + δ0
A
Hmin
H1
H0
Health
Stock
Changes in Equilibrium - Wage

Wage change will not affect cost of capital (r + δD is
constant)

Increased wage rate will increase returns obtained
from health days, hence a higher MEI curve i.e.
8 hrs @ £4/hr = £36
8 hrs @ £5/hr = £40

If original MEI curve represents lower-wage case, then
optimal health stock is HO . MEI2 shows MEI for
someone with higher wages, with higher optimal
health stock (H2)

Optimal health stock increases with level of wages
(i.e. H2 > H0). Benefits of being healthy
are greater for higher-wage workers
Changes in Equilibrium - Wage
Cost of
Capital
MEI
MEI2
C
r + δ0
A
H0
H2
Health
Stock
Changes in Equilibrium – Education

Education improves efficiency in production

Higher education level raises marginal product of
direct inputs i.e. less inputs are needed to produce a
given amount of investment. A given investment can
be generated at less cost for an educated person ,
hence higher rate of return to a given stock of health

Higher education level means a higher MEI curve
(similar to effect of increased wage rate).

Optimal health stock increases with level of education
(i.e. H2 > H0). A more educated person will choose a
higher optimal stock of health than the
less educated person.
Changes in Equilibrium – Education
Cost of
Capital
MEI
MEI2
C
r + δ0
A
H0
H2
Health
Stock
The Integrated Grossman Model (1)
In maximising utility subject both to time and money
in a given period, a consumer must:
A. Allocate time between work and leisure
B. Spend remaining leisure time on health and
nonhealth activities
C. Spend income earned on health (medical) and
nonhealth (e.g. baking) resources
D. Produce health capital that may help in future
years
The Integrated Grossman Model (2)
Quadrant 1
 labour-leisure trade-off with respect to allocation of time
to wage-earning activities

Budget constraint (BC-BC) indicates trade-off between
labour and leisure (steeper line indicates higher wages)

Slope of indifference curve (U1) shows consumer’s
subjective trade-off between leisure and earnings

Consumer’s optimal division between market work (TW)
and leisure is equilibrium point A – Assuming no days
are lost to illness (TL), he will work for (365-OT*) days
and earn income G* [to be spent on medical inputs (for
health production) and home good inputs]
The Integrated Grossman Model (3)
Quadrant 2

Trade-off between health investment (I) and home
good (B) given consumer’s income and time

Consumer divides his time and money in producing I
and B based on his preferences & his productivity

The Production Possibility Curve (PPC) shows all
efficient combinations of I and B that can be produced
when all of consumer’s income (G*) and time (OT*)
are used to their full potential
The Integrated Grossman Model (4)
Quadrant 4

Shows production of either I or B based on his
preferences

Width of ‘Edgeworth box’ is amount of time remaining
after allocation of time between work and leisure and
height is income that was earned

Contract curve – shows only combinations that are
efficient for consumer to produce I or B

If he spends no time or money on health, he spends all
of both on B and is at O; if he spends all his money
(G*) and time (TH=nonwork time) on health, he is
spending none on B and is at southeast corner of box
The Integrated Grossman Model (5)
Quadrant 3

Relates medical expenditure (M) to level of health
investment (I)

If he spends TH time and M* amount of money on
producing health, then I* level of health investment will
be made

Note that he will spend (OT*- TH) on, and invest B* in,
the home good

The higher M is, the higher I will be
Income (£)
II
I
BC
Optimal levels of
Health Investment
and the Home Good
PPC
Labour - Leisure
Trade-off
G*
A
B*
U1
Imax
O
Health
Investment
TH
T*
BC
Leisure
I*
contract curve
Medical
Expenditure
and Health
Investment
M*
Production of Health
and the Home Good
Imax
III
IV
Medical expenditures (£)
Equilibrium in the Integrated Grossman
Model

Consumer picks point A in QI, generating income of G*
and has OT* leisure time.

From QII, consumer’s equilibrium is at A1, giving optima
investment in health of I* and in home good of B*

In QIV, TH and M* are spent on health care.

M* is translated through QIII to determine level of
health in investment I*
Income (£)
II
I
BC
PPC
Four-Quadrant
representation of
the Grossman model
G*
A
A1
B*
U1
Imax
O
Health
Investment
TH
T*
BC
Leisure
I*
contract curve
M*
Imax
III
IV
Medical expenditures (£)
Key messages from Grossman Model
To maximise utility, a consumer must:
A. Allocate time between work and leisure
B. Spend remaining leisure time on health and
nonhealth activities
C. Spend income earned on health and nonhealth
resources
D. Produce or invest in health capital for future use
Summary

Optimal health stock will decline as the person
ages if the depreciation rate of health increases as
a person ages

Benefits of good health are greater for high wage
workers so they demand higher optimal health
stock

The more educated people are, the less costly it is
to generate health resulting in a higher optimal
health stock for this group

Individuals will allocate resources in order to
produce health capital.
Conclusions

Grossman model has been influential in health
economics.

Demand for health care inputs is demand derived from
demand for health itself
References
Grossman, M. (1972) On the concept of health capital and the demand for
health, Journal of Political Economy 80: 223-255.
Wagstaff, A. (1993), The demand for health: an empirical reformulation of
the Grossman model, Health Economics 2: 89-198.
McGuire, A., Henderson, J. & Mooney, G. (1988). The Economics of
Health Care. London: Routledge and Kegan Paul
Morris, S., Devlin, N. & Parkin, D. (2007) Economic analysis in health
care. Chichester: John Wiley & Sons
Grossman, M. (1982) The demand for health after a decade, Journal of
Health Economics 1: 1-13
Folland, S., Goodman, A. & Stano, M. (2004). Economics of Health and
Health Care. London: Prentice Hall