PRODUCTION OF MEDICAL CARE and
PRODUCTION COST
OUTLINE
• PRODUCTION OF HEALTH
• APPLICATION OF LAW OF DIMINISHING RETURNS ON HEALTH CARE INSTITUTIONS
• APPLICATION OF LAW OF DIMINISHING MARGINAL UTILITY ON PATIENTS
Assessing the Productivity of Medical Firms
Economists often describe production of output
as a function of labor and capital :
q = f(n,k)
In the case of health care :
q = hospital services
n = nurses
k = medical equipment, hospital building
Assessing the Productivity of Medical Firms (cont.)
Short run : k is fixed, while n is variable
a) At low level of n, k is abundant. Each in nurses
when combined with capital greater in services.
- potential synergy effect because nurses can
work in teams.
b) Further in nurses service, but a decreasing
rate - law of diminishing marginal productivity.
c) “Too many “ nurses can cause congestion, com-
munication problems, hospital services
Graphical Representation
Total product = q = f(n,k*)
hospital
services
(q)
Nurses (n)
marginal
product
nurses
MP = Dq / Dn
MP is the slope of the TP curve.
n1 n2
TP
n2n1
Graphical Representation
hospital
services
AP = q / n
AP is the slope of a ray from the origin to the TP
curve.
average
productB
n3
TPB
C
A
Production Function for Hospital Admissions
Jensen and Morrisey (1986) Sample : 3,450 non-teaching hospitals in 1983.
q = hospital admissions
inputs : physicians, nurses, other staff, hospital beds.
q = a0 + a1physicians + a2nurses + …. + e
Coefficients in regression are MPs.
Results
Each additional physician generated 6.05 more
admits per year.
Nurses by far the most productive
Annual Marginal Products for Admissions
Physicians 6.05
Nurses 20.30
Other Staff 6.97
Beds 3.04
Input MP (at the means)
Medical Care Cost
Economic Costs = Accounting Costs
Explicit costs of doing
business.
e.g. staff payroll, utility
bills, medical supply costs.
Necessary for :
Comparing performance
evaluation across
providers/depts.
Taxes
Government
reimbursement/rate setting
Accounting Costs
e.g. opportunity cost of a facility
being used as an outpatient
clinic = rent it could earn
otherwise
Necessary for :
optimal business planning.
allows one to consider
highest returns to assets
anywhere, not just vs.
direct competitors, or w/in
health care industry.
Recall
Given a production function :
q = f (n,k)
q = hospital services
n = labor = nurse = n
k = capital = medical equipment, hospital
building
Short-Run Total Cost
cost
hospital service
STC( q ) = w n + r k*
w = wage rate for nurses r = rental price of capital
short run k fixed w n = variable cost
r k = fixed cost .
q0
STC
STC
w n
r k
Short-Run Total Cost (cont.)
STC( q ) = w n + r k*
• In the short run, k is fixed.
rk* is the same, regardless of the amount of
hospital services (q) produced.
•As q rises, increases in STC are only due to
increases in the number of nurses needed (n).
Short-Run Total Cost (cont.)
cost
hospital service
Recall : Production function initially exhibits IRTS
Total costs rise at decreasing rate up to q0
q0
STC
STC
w n
r k
After q0, DTRS in production costs rise at
increasing rate
Graphing Marginal and Average Costs
• SATC and SAVC are u-shaped curves.
– Increasing returns to scale followed by decreasing returns to scale.
• SMC passes through the minimum of both SATC and SAVC.
– If marginal cost is greater than average cost, then the cost of one additional unit of output must cause the average to rise.
Relating Product and Cost Curves
n q
MPn
APn
Cost
n1 n30
MPn
APn
SMC
SAVC
q1 q3
Determinants of Short-run Costs
5 different measures of q inputs
ER care nursing labor
medical/surgical care auxiliary labor
pediatric care professional labor
maternity care administrative labor
other inpatient care general labor
materials and supplies
Physicians
Cowing and Holtmann 1981
Cost Minimizing Solutions
• SUBSTITUTION
• Health care providers’ choice of nursing staff mix. <RNs and LPN) If a hospital needs to hire nurses to care for growing patient volume, which should be hired?
Review price paid to doctors
Physicians bill insurers or their patients for care.
In most cases, physician not paid a wage by a hospital.
However, physicians generate other hospital costs.
Review and process physician’s application.
Monitor physician’s performance.
Examining rooms and other supplies.
Substitutability in Production of Medical Care (cont.)
r = 0 no substitutability.
r = perfect substitutability.8
Potential for substitutability If price of 1 input
increases, can minimize impact on total costs by
substituting away.
Elasticity of substitution :
r = [D(I1/I2)/I1/I2] : [D(MP2/MP1)/MP2/MP1]
% change in input ratio, divided by % change in
ratio of inputs’ MPs.
Results
Each inputs is a substitute for other in production
process.
If wages of nurses rise, can substitute away by
having more hospital beds.
Elasticity of Substitution between Inputs
Physicians with nurses 0.547
Physicians with beds 0.175
Nurses with beds 0.124
Input pair s
Ex. for when s =
8
Does Higher Quality Higher Costs?
Reducing costs without sacrificing quality.
Improved production line.
bedside access to computerized treatment guidelines.
computerized patient charts.
Motivated work force.
involving nurses in case management
reimburse physicians based on performance evaluations
Health Production Functions
Outline
• Measures of Health
• Concepts:– Health Production Function
– Marginal Product of Health
• Health Production Functions– Contributions of health care
– Lifestyle & Environment (Pollution)
– Education
Measures of Health Status
A measure of the population’s health status, that captures those aspects of health that are meaningful, and can be measured with accuracy (i.e., quantifiable).
• Two main types mortality and morbidity.
Health Production Functions(Determinants of Health)
Health Production Function: overall effects of medical care utilization on the health status of population
• Where output is usual some measure of health status (HS).
• HS=F(inputs to health)
• What could the inputs be?
• HS=F(health care, environment, education, lifestyle, genetic factors, income)
Measures of Health Status:Mortality Measures
• Popular measures because is easy to quantify
– know when someone dies and is regularly recorded information
• Crude death rate
– number of deaths per 100,000 population
– for some time period—usually a year
Infant mortality rate:
Number of death of
children < age 1 per
1000 live births
Adjust for age, sex,
and race to make
more meaningful
Not necessary
accurate in low-
income and war-torn
places
Under-five mortality rate
Mortality rate for elderly
Measures of HealthMorbidity
• Morbidity: A statement about the extent of disability a person suffers as a consequence of a disease over time.
• Need to measure the disability which could be physical, mental, functional, or social.
• Some sources of these types of data are:
– Hospital inpatient discharge records.
– Hospital outpatient discharge records / outpatient records.
– Survey data: self health assessments, days lost from work.
Health Production Functions
Health Care
Inputs (HI)
Health Status
(HS)
1 2 43 5 6
A
B
A>B : as you increase the
number of health care
inputs, the effects on total
health status decrease.
Does it make sense
the curve flattens
out, should it bend
downwards again?
Marginal Product of Health Care
HS HS
HI HI
D
D
Health Care
Inputs
Marginal Product of Health
Care
21 3 4 5
A
B
Marginal Product: Is the increment
in health status caused by one
extra unit of Health Care, holding
all other inputs constant?
MP is diminishing in size,
demonstrating the law of
diminishing marginal returns.
Marginal Product of Health Care
• Marginal product that is relevant for policy makers:
– They want to know if I add one billion dollars to health care, how much will the health status of the population improve.
• The marginal product might be different for different types of groups, such as young, elderly, or poor.
Why has mortality declined?• Big medicine theory
– Antibiotics for infectious diseases
– High-tech treatments for cardiovascular disease
• Economic growth theory – Nutrition allows one to withstand disease
• Public health theory – Better sewers, cleaner water and air
• The long reach of early life factors– Maternal nutrition in utero and fetal development
– What looks like big medicine now could be long-term effects of better nutrition, public health in the past
0
10
02
00
30
0
De
ath
s p
er
10
0,0
00
1900 1920 1940 1960 1980 2000year
Influenza and Pneumonia Deaths per 100,000
Big Medicine:Antiobiotics
The development of
antibiotics helped, but it
came very late in the
process.
Why has health improved?
1. Economic development/nutrition
• Most important before c. 1880
2. Public health/germ theory
• Most important c. 1880-1960
3. Improved medical care (Big Medicine)
• Most important since 1960
Economic Growth Explanation
• This was a time of exploration and many new foods were introduced into people diets.
• Agriculture was advancing, new crops, crop rotation, seed production ….
• Standards of living were increasing as a result of trade so people had the money to buy more food.
• Better nutrition results in stronger immune system
Public Health Explanation• Preston and Deaton response to Fogel:
– Fogel presents evidence on nutritional status not availability
• Economic growth not only factor in nutrition
• Interaction between disease and caloric intake
– Relationship between income and health changing• Example: China is about as rich as the US in 1900, but
has life expectancy fairly close to US today and far above US in 1900
• Quality of the food matters
The Public Health Revolution• Modern health practices date from the early
20th century (post germ theory)
– Macro public health: sanitation; clean water; pasteurized milk
– Micro public health: bathing and hand washing
• Epidemiological studies: specific public health interventions improve health
• Gap in child mortality by class emerges after public health information is available
– Upper classes had more information?
• END