Limitations of the Model


The theory of the demand for health
care under conditions of uncertainty has the virtue of explicitly organizing
some of the variables that are central to the decision to engage in activities
that promote health. As presented, however, it has an important limitation.

The reader may find it strange that
the utility function, which is supposed to measure satisfaction, does not
include health. This is indeed a shortcoming of the model, because well-being
can depend on health status as well as wealth. The model looks only at
financial aspects of the situation, in effect assuming that the care fully and
instantly restores health, with no utility implications of either the illness
or the process of getting care. Clearly this is an unrealistic assumption.
Including health status creates a much more complicated model that is more
difficult to apply, and while it is important to understand that we have
abstracted from reality, this should not detract from the value of the model.
The present model has the virtue of focusing on the benefits of risk shifting,
which is an economic good that is distinct from medical care.

Discounting Future Values

Another factor that affects
health-promotion behavior is the individual’s valuation of benefits in
different time periods. Health promotion activities, such as the use of
condoms, smoking cessation, vaccinations, and clean needles (for drug users)
and unhealthy activities, such as smoking, engaging in unsafe sex, and
excessive drug use, generally do not have good or bad impacts on health
immediately. It takes a long time, sometimes years, for individuals to
experience adverse health effects. The timing of health benefits will have an
influence on the demand for health-related activities that promote these

It is generally assumed that $1,000
in current benefits will be worth more to an individual than $1,000 in benefits
one year from now. The value of the preference for earlier rather than later
periods can be expressed in terms of a discount rate, called r. If an
individual is asked how much money he or she would accept at the end of 2001
rather than have $1,000 at the beginning of 2001, the person might take $1,100
at the end of the period. In other words, $1,000 on January 1, 2001, would be
worth as much as $1,100 one year later. The discount rate is .1, and the
discounting equation is be expressed as $1,000 × (1 + .1) = $1,100, or
symbolically as $1,000 × (1 + r) = $1,100. This may be rewritten as
$1,000 = $1,100/(1 + r). This equation says that, in the individual’s
eyes, $1,100 one year hence will be equivalent to $1,100/(1 + r), or
$1,000, now. The discount rate for an individual is derived largely from
introspection—from an acceptance that a given future amount and a lesser
current amount provide the same satisfaction at the present moment.

The same principle holds for
comparisons between December 31, 2001, and December 31, 2002. That is, $1,000
at the end of 2001 is equivalent to $1,100 at the end of 2002 if the
individual’s discount rate is .1. By inference, then, $1,000 at the end of 2002
would be worth $1,000/[(l + r) × (l + r)] on January 1, 2001
(also expressible as $1,000/(l + r)2). Similarly, $1,000 on
December 31, 2003, would be worth $1,000/(l + r)3 at the
start of 2001, and so on. Generally, improved health or added life yields a
stream of benefits. That is, a saved life on January 1, 2001 will yield
benefits in 2001 (valued as of December 31, 2001), 2002 (valued as of December
31, 2002), 2003 (valued as of December 31, 2003), and so on. If the benefits
are $2,000 each year, the present value of future benefits can be
expressed as $2,000 + 2,000/(1 + r) + 2,000/(1 + r)2,
and so on, for as long as benefits last. The letter usually used to symbolize
the annual benefits is B, with subscripts 0, 1, 2, . . . for right now
(0), one year hence (1), two years hence (2), and so on. In our current
example, B0 = B1 = B2,
and the present value of benefits can be expressed symbolically as

If the number of years that benefits
will last is quite large and the value of the benefits for every year is the
same, the present value of the benefits can be expressed as B0/r.
If benefits of $10,000 a year will last forever and if the discount rate is .1,
the present value of these benefits will be 10,000/.1, or $100,000. Benefits
lasting for long periods can be approximated using this formula.

The discount factor can be quite
substantial for benefits that will not be experienced for many years. For example,
hepatitis C may not be recognized for 20 years. If hepatitis C imposes
health-related costs of $1,000 in 20 years, and the discount rate is 10
percent, then the present value of these imposed costs is $148.64

Not everyone will have the same
discount rate. An individual who has a very strong preference for current
satisfaction rather than future benefits will have a high interest rate,
perhaps 15 or 20 percent. On the other hand, a person who places very great
importance on future satisfactions will have a very low discount rate, perhaps
2 percent or even 0 percent. In the latter case, there would be no discount
rate, and present and future values would be the same.

Discounting is usually done with a
hand-held calculator or with present value tables. InTable 4–2
we show a series of discounted values varying according to discount rates (4,
8, and 12 percent) and time periods (one to five years). For example, in Part
A, at a discount rate of 8 percent and a four-year time horizon, the value of
(1 + r)4 is 1.36. The present value of a benefit of $10,000
that occurred in four years, discounted at a rate of 8 percent, would therefore
be $ 7,353.

4–2 Calculation of Present Value of Benefits under Alternative Discount Rates
Part A: Discounting Factors
Discount Rate (1 + r) (1 + r)2 (1 + r)3 (1 + r)4 (1 + r)5
.04 1.04 1.08 1.12 1.17 1.22
.08 1.08 1.16 1.25 1.36 1.41
.12 1.12 1.25 1.41 1.57 1.63
Part B: Discounted Present Value
of Benefits ($10,000)
Discount Rate B1/(1 + r) B2/(1 + r)2 B3/(1 + r)3 (B4/(1 + r)4 B5/(1 + r)5 Present Value (row sum)
.04 8,615 9,233 8,896 8,554 8,196 44,494
.08 9,259 8,620 8,000 7,353 7,092 40,324
.12 8,928 8,000 7,029 6,275 5,602 35,834


Siegal has two alternative activities to help relieve her backache. In the
first, she can visit a physiotherapist. The total time for a physiotherapist
visit, including travel and waiting, is two hours. Mrs. Siegal earns a wage of
$20 an hour. Physiotherapists charge $50 per visit, and Mrs. Siegal does not
have any health insurance. As a second alternative, Mrs. Siegal can take pain
killers. Each pill costs 50 cents, and Mrs. Siegal needs to take 30 pills per
month. The two treatments are not equally effective. The physiotherapy visits
yield 10 additional healthy days per month, while the pills yield 6 healthy

a.If Mrs. Siegal can only
choose one alternative, and if she wants to maximize the most healthy days
per dollar that she gets, which option will she choose?
b.If the price of a pill
increases to $3, which option will she choose?

this and answer exercise #2
5.7.4Hospital Economies of Scale

A large number of studies have investigated the possible existence of
economies of scale in hospitals, with very mixed results (Berki 1972;
Frech and Mobley 1995).
Early studies identified economies of scale but subsequent studies have
uncovered no evidence (Lave and Lave 1984)
or conflicting evidence (Frech and Mobley 1995).
There is an explanation for the differences in findings.

As discussed earlier, the typical hospital is an organization with a complex
case mix and a large number of different services. Each service has its own
cost-output relation, which may exhibit economies of scale. The scope of
services is greater for larger hospitals (Berry 1973),
but these hospitals may have more varied case types, so some services (e.g.,
cobalt therapy) that are devoted to specific case types may be operated at low
capacity and high cost. A multiproduct hospital can be quite large yet have a
number of services with considerable excess capacity (Finkler 1979b).
As a result, it might exhibit a higher average cost than many smaller

One study (Hornbrook and Monheit 1985)
that incorporated both case mix and service scope variables to investigate
economies of scale found no such economies at the hospital level. But a number
of studies of individual services, such as open-heart surgery facilities, CT
scanner units, therapeutic radiology facilities, and hospital laundries, have
found evidence of economies of scale (Finkler 1979a;
Gregory 1976–1977;
McGregor and Pelletier 1978;
Okunade 1993;
Schwartz and Joskow 1980).
This suggests that the economies of scale that do occur in some hospital
departments are offset by diseconomies of scale in others.

5.7.5Nursing Home Costs

A number of studies have been undertaken in the nursing home area with a
view to determining the effect on costs of operating variables such as volume
of operations, product quality, case mix, and organizational characteristics
(e.g., for-profit or nonprofit status and membership in a chain) (Bishop 1980).
The relevant variable for such studies is average cost, which is the most
appropriate variable for a comparison of costs in different facilities. There
is no agreement as to whether total costs (which include fixed costs such as
administrative costs, interest, and depreciation) or only variable costs should
be used. Using just variable costs would be appropriate when focusing on
short-term operations, whereas including capital and other fixed costs would be
appropriate when dealing with long-term issues. For example, one might want to
find out whether a large-scale plant is more efficient than a small-scale
plant. Asking which is the most efficient implies that time would be allowed to
develop a plant of the appropriate size.

Studies that have examined the relationship between average cost and various
causal variables have uncovered some interesting relationships. There is
disagreement as to the relationship between average cost and scale of
operations (Bishop 1980;
McKay 1988).
The fact that a nursing home is a member of a chain does not appear to
influence its costs (Ullman 1986).
On the other hand, for-profit nursing homes have been identified as having a
lower average cost that nonprofit nursing homes (Ullman 1984).

As with all cost studies in the health care area, such studies have had to
deal with difficulties in measuring and netting out the impact of patient case
mix and the level of quality, two factors that influence the level of care and
hence nursing home costs. For example, it has proved extremely hard to identify
patient characteristics associated with specific levels of care. Patients
differ considerably with regard to health status, and their different needs
should translate into differences in the level of care or resource intensity.
Several case mix classifications (for long-term care patients) that try to take
into account resource use differences have been developed. These measures are
far from perfect, but even allowing for their shortcomings, their inclusion in
the cost analysis may not be sufficient to account for differences in average
cost that are related to level-of-care differences. A nursing home that offers
“high-quality” care as measured by resource-intensive processes
(rehabilitation, nursing care) may provide more care to all patients regardless
of their health status. Similarly, in a low-quality nursing home, all patients
may receive fewer services than in the high-quality home, adjusting for health
status. One must therefore find a quality measure that is independent of case
mix or case severity in order to control for the influence of each factor on
cost of care. As will be seen in the following chapter, most measures of case
mix do not adequately distinguish between case mix and severity, and so it has
been very difficult to identify each factor’s specific impact on cost.


Radiology Labs has a fixed amount of radiology equipment. The laboratory can
hire any number of radiology technicians per hour to produce radiographs, which
are displayed on a screen. The relationship between the number of technicians
hired per hour and the number of radiographs produced per hour is shown in the
following table. Show the total and marginal products and indicate at each
level of production whether the production function exhibits increasing,
constant, or diminishing marginal productivity.
Radiograph Technician per Hour Radiograph Produced per Hour
1 10
2 26
3 50
4 74
5 94
6 100

Read this and answer exercise # 4


Representation of the trade-off
between quality and quantity. Based onFigure 6–5,
for any given reimbursement rate, a higher quality level can be achieved only
with a lower quantity of output. The curve shows alternative levels of quantity
and quality that can be achieved at a given reimbursement rate.

An alternative theory of resource
allocation and product supply in nonprofit agencies focuses on the behavior of
the executive or administrator of the organization. The underlying assumption
is that the administrator, even though just an agent of the trustees, has
considerable control over the organization’s resources. This seems a plausible
assumption given that trustees of a nonprofit agency typically can devote only
a small portion of their time to trustee-related activities, whereas the
administrator is usually a full-time employee. As part of this approach, a
comparative analysis can be done that examines how the same administrator would
behave if operating the same agency as a profit-seeking enterprise and as a
nonprofit enterprise. The differences in behavior, which are due solely to the
different incentive structures of the two types of organization, create
differences in the use of the agency’s resources and in the agency’s output.

The theory can be viewed as simply an extension of the basic demand
hypothesis presented in Chapter
3. According to this hypothesis, the lower the direct cost of a commodity
or other benefit to an individual, the more the commodity will be demanded. The
extension of the hypothesis involves identifying the commodities that are
desired by the administrator of an agency as well as their relative prices or costs
under varying institutional circumstances. Since we are focusing on the
administrator’s behavior, we will identify two types of benefits that can be
obtained in the context of the job. First, there are the pecuniary benefits,
especially the administrator’s salary. In addition, if the administrator is a
part or full owner of the agency, the pecuniary benefits will encompass the
profits that accrue. Benefits of the second type, sometimes called on-the-job
benefits, are nonpecuniary. These include high-grade office furniture, a
relaxed work atmosphere, “business” trips to exotic places, and so on. Both
types of benefits are wanted by the administrator, but because their supply is
limited, the administrator cannot have everything he or she would like.

Before developing the hypothesis about how much of each type of benefit will
be demanded, we will look at the implications for resource use of obtaining the
two types. First, when a smaller amount of resources is used to obtain a given
output, an opportunity to increase profits is created. Nonpecuniary benefits
also require the commitment of resources. Better office equipment, more liberal
working conditions, and other on-the-job benefits are obtained from the
expansion of the total resource commitment and result in an increase in costs
and a contraction of profits. In a nonprofit enterprise, this reduction in
profits does not detract from the manager’s pecuniary benefits since he or she
will not be rewarded on the basis of the profits the enterprise earns.

The hypothesis as to how the administrator will behave under these
alternative incentive structures is based on the constraints facing the
administrator in the two different environments. In a nonprofit environment,
since the administrator cannot convert profits into take-home pecuniary
benefits, they must be converted into organizational resources if any benefit
is to be obtained. On the other hand, the use of these extra resources in a
for-profit organization will detract from profits and hence from take-home pecuniary
benefits, assuming these are related. The personal costs of on-the-job benefits
are lower for the administrator of the nonprofit agency, and we thus
hypothesize that more will be demanded.

The implications of this hypothesis for nonprofit resource allocation are
considerable. The hypothesis implies that the nonprofit agency will use more
resources to get a given job done, and so its costs will be higher. The absence
of incentives for efficiency has been the target of investigation, including
its effect on nonprofit agency operating costs, particularly in the case of
nonprofit health insurers (Frech 1976),
nursing homes (Borjas et al. 1983;
Frech 1985),
and dialysis units (Lowrie and Hampers 1981).
Similar analyses comparing nonprofit and for-profit hospital behavior have not
been as conclusive for several reasons. First, to compare operating costs
between nonprofit and for-profit hospitals, variables such as case mix, case
severity, and quality must be adjusted for. Assertions have been made that
nonprofit hospitals have a more complex case mix because for-profit hospitals
engage in “cream skimming” by encouraging the admission of low-cost cases.
Evidence on this score seems mixed (Bays 1977a,
Renn et al. 1985;
Schweitzer and Rafferty 1976).
Even more difficult to determine is whether quality differentials exist by
ownership category. Nonprofit managers do have an incentive to produce quality
care (which will show up in higher costs). The role of quality in pushing costs
higher has yet to be fully explored.

Another difference that has been uncovered when comparing nonprofit and
for-profit hospital behavior lies in the pricing area. Charges are the prices
set by the hospital for its services. Two California studies found that
for-profit hospitals had higher charges (relative to costs) for ancillary (lab,
radiology, pharmacy) services (Eskoz and Peddecord 1985;
Pattison and Katz 1983).
Generally, markups (charge-to-cost ratios) for ancillary services were found to
be higher than basic room charges. For-profit hospitals also provided more
(high-profit) ancillary services per patient than nonprofits in the studies and
were more profitable, although cost levels were similar. One possible
explanation of this finding is that nonprofit managers (or trustees) can gain
nonpecuniary benefits from encouraging the use of hospital services by keeping
patient charges low (which may result in lower profits) as well as by providing
more free care to indigents.

However, relying solely on the incentives identified in the administrator as
agent model to explain cost and price differences between for-profit and
nonprofit hospitals would be a mistake. The incentive differences are but one
factor operating to influence costs (and possible cost differences) in the two
types of organization. The reimbursement system is another major influence on
cost and supply behavior. Indeed, the absence of cost differences between
nonprofit and for-profit hospitals that was uncovered by the investigators in
California may have been partly due to the reimbursement system, which, at the
time of the studies, encouraged cost inflation in all types of hospitals. It is
to this factor that we turn to next, in Chapter


following is a cost function for clinic visits in a small inner city clinic:
Quantity of Visits Total Cost per Week
0 $10
1 15
2 25
3 45
4 75
5 115
6 165

a.Determine the marginal cost
for each level of output.
b.If the price per visit is
given to be $25, at what level of visits will the maximum profit position
be? What are the profits at this level? What is the quantity supplied?
c.If the price per visit
increases to $45, what will be the quantity supplied (assuming maximizing