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