Download Document

Chapter 7: Medical Care
Production and Costs
Health Economics
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, communication problems,
hospital services
Graphical Representation
Total product = q = f(n,k*)
hospital
services
(q)
TP
n1
marginal
product
n1
n2 Nurses (n)
n2
nurses
MP = Dq / Dn
 MP is the slope of the TP curve.
Graphical Representation
AP = q / n
 AP is the slope of a ray from the origin to the TP
curve.
hospital
services
average
product
C
B
B
TP
A
n3
Numerical Example
# of
nurses
(n)
Amount
of k
Total
output
(q)
AP of n
(q/n)
MP of n
(Dq/Dn)
0
10
0
---
---
1
10
10
2
10
30
3
10
60
Practice Question
People living in Boston are hospitalized about 1.5
times as often as those living in New Haven,
However, the health outcomes of patients in
these 2 cities appear to be identical. Does this
mean that hospital care has no ability to improve
health?
health
outcomes
hospitalizations
Substitutability in Production of
Medical Care

There may be more than one way to produce
a given level of health care.
 Licenced
practical nurses (LPNs) vs
Registered Nurses (RNs) in hospitals.
LPNs have less training.
 Maybe not as productive, but not as costly.


Physician assistants vs physicians at
ambulatory clinics.

But physician assistants can’t prescribe meds in
most states.
Substitutability in Production of
Medical Care (cont.)
 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.

r=0
r=
8

no substitutability.
perfect substitutability.
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
Annual Marginal Products for Admissions
Input
Physicians
Nurses
Other Staff
Beds
MP (at the means)
6.05
20.30
6.97
3.04
 Each additional physician generated 6.05 more
admits per year.
 Nurses by far the most productive
Results (cont.)
Elasticity of Substitution between Inputs
s
Input pair
Physicians with nurses
Physicians with beds
Nurses with beds
0.547
0.175
0.124
 Each inputs is a substitute for other in production
process.
If wages of nurses rise, can substitute away by
having more hospital beds.
8
Ex. for when s =
Medical Care Cost
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
Medical Care Cost (cost.)
Economic Costs
= Accounting Costs
 i.e. opportunity 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
STC( q ) = w n + r k*
w = wage rate for nurses
short run
k fixed
r = rental price of capital
w n = variable cost
r k = fixed cost .
cost
STC
STC
wn
rk
q0
hospital service
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.)
 Recall : Production function initially exhibits IRTS
 Total costs rise at decreasing rate up to q0
cost
STC
STC
wn
rk
q0

After q0, DTRS in production
increasing rate
hospital service
costs rise at
Marginal and Average Costs
DSTC
SMC =
Dq
= D(wn + rk*)/Dq
= w(Dn/Dq) = w(1/MPn)
= w/MPn
The short run marginal cost of nurses depends
on their marginal productivity.
Marginal and Average Costs (cont).
STVC
SAVC =
q
= (wn)/q
= w(1/APn)
= w/APn
The short average variable cost of nurses
depends on their average productivity.
Graphing Marginal and Average Costs
SMC
Costs
SMC0
SATC
SAVC
SATC0
SAVC0
0
q0
q
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
MPn
Cost
SMC
APn
SAVC
APn
MPn
0
n1
n3
n
q1
q3
q
Average and Marginal Co (cont.)
 IRTS followed by DRTS in production leads to U
shaped AC curve.
 Hospital doesn’t necessarily produce at q* (min.
cost).
 Depends on hospital’s objectives.
 Even so, will attempt to stay on the cost curve
(not above it).
Determinants of Short-run Costs
(cont.)
5 different measures of q
ER care
medical/surgical care
pediatric care
maternity care
other inpatient care
Cowing and Holtmann 1981
inputs
nursing labor
auxiliary labor
professional labor
administrative labor
general labor
materials and supplies
Findings
 Found short run economies of scale
 Hospitals operate to left of min. on AVC curve.
i.e Larger hospitals producing at lower costs
than smaller hospitals.
 Best way to reduce aggregate hospital costs?
 Reduce # of hospital beds by a fixed % in all
hospitals.
 Close the smallest hospitals in each region.
Findings (cont.)
 Definition : Economies of scope
 Cost of producing 2 outputs < sum of cost of
production 2 goods separately.
 Found Diseconomies of scope with respect to
ER and other services.
 Larger ER’s may bring in more complex mix of
patients to the hospital. OR
 Larger ER’s generate operating challenges for
other services (e.g. communication, staffing
scheduling).
Cost-minimizing input choice
Example
- Health care providers’ choice of nursing staff mix.

RN’s care for 6 patients per hour; hourly wage = $20

LPN’s care for 4 patients per hour; hourly wage = $10

TC(q0)=20RN + 10LPN
If a hospital needs to hire nurses to care for
growing patient volume, which should be hired?
Cost Minimizing Input Choice

Costs are minimized when:
MPRN
MPLPN
wRN = wLPN

Suppose that instead:
MPLPN
MPRN
< w
wRN
LPN
 Then
the last dollar spent on an LPN generates
more output than the last dollar spent on a
registered nurse.
Are physicians “costly” to
hospitals?
 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.
MPdoc
wdoc
MPn
wn
Are physicians “costly” to
hospitals? (cont.)
 Can solve for “shadow price” of doctors, if other
variables known.
 wdoc = $7,012 per year.
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
Does Higher Quality
Higher Costs?
“ In an increasingly competitive environment,
hospitals must take a critical look at their
product lines… Many institutions must decide
between eliminating or investing in unprofitable
product lines”
Juran Report
e.g. Hospital may have unprofitable, high quality
heart surgery, but kidney surgery may be losing $,
lower quality.
Business opportunities in costs
 Companies which can synthesize complex data
to improve quality and restrain cost will survive.
 Express Scripts Pharmacy Benefit Manager (PBM)
 Manages
prescription claims on behalf of
HMO’s, insurance companies, unions, etc.
 Obtains drug cost savings through drug
utilization review, generic substitution, mail-order
pharmacy, volume discounts from retail
pharmacy.
Business opportunities in costs
 Express ScriptsPractice Pattern Science (PPS)
 An
information service company.
 Offers practice variation analysis and disease
management support service linking healthcare data
from all points of care.
 Complements PBM services
 Be a leader in the development of disease
management, provider profiling and outcomes
assessment technologies.
Business opportunities in costs
 Express ScriptsPractice Pattern Science (PPS) (cont.)
Diagnostic ClusterSM Methodology :
links to a “global” pattern treatment through its patient
treatment episodes (PTETM)

Provider Profiling :
reduce providers practice pattern variation
Diseases Management Support Service :


Gatekeeper of patient case mix.
 Scorekeeper for patterns of treatment.
Pharmaceutical Information :

Benchmark prescription drug patterns
 Track the composition of prescription drugs
 Report the mean and median global treatment cost
Business opportunities in costs
(cont.)
 Practice Pattern Science (PPS) subsidiary.
 Computerized
patient profile database.
 Bars claims if potential dangerous interactions
identified.
 Identifies people over-utilizing drugs by visiting
multiple doctors.
Long Run Costs of Production

In the long run, all inputs are variable.
k is no longer fixed.
 e.g. A hospital can build a new facility or
add extra floors to increase bedsize in the
long run.


If all inputs are variable, what does the
long run average cost curve look like?
The Long Run Average Cost Curve
Average Cost
of Hospital
Services
LATC
q0
q1
q2
# of patients
Long Run Costs of Production

Just like the short run cost curve, the
long run cost curve for a firm is also ushaped.
 However,
the short run cost curve is due to
IRTS, then DRTS relative to a fixed input.
 e.g. In the short run, the only way to
increase the number of patients treated
was to hire more nurses; but the # of beds
(k) was fixed.
 But in the long run, there are no fixed
inputs.
Long Run Costs of Production

The u-shaped long run average cost
curve is due to economies of scale and
diseconomies of scale.

Economies of scale
 Average
cost per unit of output falls as the
firm increases output.
 Due to specialization of labor and capital.
Long Run Costs of Production

Example of specialization and the
resulting economies of scale.
 A large
hospital can purchase a
sophisticated computer system to manage
its inpatient pharmaceutical needs.
 Although the total cost of this system is
more than a small hospital could afford,
these costs can be spread over a larger
number of patients.
The average cost per patient of dispensing
drugs can be lower for the larger facility.
Long Run Costs of Production

Economies of scale arise due to
specialization of labor and/or capital.
 That
is, the long run relationship between
average costs and output reflects the
nature of the production process.
 This is why economies of scale (in costs)
are can also be referred to as increasing
returns to scale (in production).
Long Run Costs of Production

Increasing returns to scale
 An
increase in all inputs results in a more
than proportionate increase in output.
 e.g. If a hospital doubles its number of
nurses and beds, it may be able to triple
the number of patients it cares for.

However, most economists believe that
economies of scale are exhausted, and
diseconomies of scale set in at some
point.
Long Run Costs of Production

Diseconomies of scale arise when a
firm becomes too large.
 e.g.
bureaucratic red tape, or breakdown in
communication flows.
 At this point, the average cost per unit of
output rises, and the LATC takes on an
upward slope.

Diseconomies of scale (in costs) imply
decreasing returns to scale in
production.
The Long Run Average Cost Curve
Average Cost
of Hospital
Services
LATC
q0
q1
q2
# of patients
Economies of scale Diseconomies of scale
Long Run Costs of Production

Decreasing returns to scale
 An
increase in all inputs results in a less
than proportionate increase in output.
 e.g. Doubling the number of patients cared
for in a hospital may require 3 times as
many beds and nurses.

In some cases, the production process
exhibits constant returns to scale.
 A doubling
output.
of inputs results in a doubling of
The Long Run Average Cost Curve
under Constant Returns to Scale
Average Cost
of Hospital
Services
# of patients
Long Run Costs of Production

Like the short run cost curve, a number
of factors can cause the short run cost
curve to shift up or down.
 Input
prices.
 Quality.
 Patient casemix.

e.g. If the hourly wage of nurses
increases, the average cost of caring for
each patient will also rise.
The average cost curve will shift _____
Long Run Costs of Production
Empirical evidence on HMOs and costs.
 See handout.

Computing Profits
Recall that the total costs of production
for a firm are:
TC(q) = wn + rk
 Sum of each input price times the # of
inputs used.


We can express total revenues derived
from producing and selling a given level
of output (q) as:
 TR(q) = output price x q
Computing Profits (cont.)

Thus, we can express profits for the firm
as:
(q) = TR(q) – TC(q)
 = Profits
TR = Total revenue
TC = Total costs

We assume that firms choose a level of
output (q) to maximize profits.
Computing Profits (cont.)
Assume that as output increases, total
revenue rises at a diminishing rate.
 Also, recall the shape of short run total
cost curve derived previously.
 Then we can graph the total revenue
curve and the total cost curve, and use
them to visualize profits.

 Profits
will be the vertical distance between
total revenues and total costs at any given
quantity of output.
Graphing Profits
Total
dollars
TR0
TC0
(q0) = TR0 – TC0
TC

q0
TR
Quantity of output (q)
Graphing Profits
Total
dollars
TC
TR
Quantity of output (q)
At what output level(s) does the firm make profits
equal to 0? At what output levels could the firm make
negative profits ?
Graphing Profits
Total
dollars
TR0
TC0
TC

q0
TR
Quantity of output (q)
Notice that I have plotted q0 where the TR curve is
above the TC curve, and the 2 curves are the furthest
apart (in vertical distance).
Computing Profits (cont.)

I have plotted q0 at the point where the
firm maximizes profits.
 At
this point the difference between total
revenues and total costs is the greatest,
and TR>TC.

Note that this is also the point where the
slopes of the TR curve and the TC
curve are equal.
Computing Profits (cont.)

Recall that the slope of the total cost
curve represents marginal costs.
MC = DTC/ Dq

The slope of the total revenue curve
represents marginal revenue.
MR = DTR/ Dq
A firm maximizes profits where:
MR=MC
Computing Profits (cont.)
A firm maximizes profits where MR=MC.
Why?
 Suppose the firm was instead producing
at a point where MR>MC.



Then additional units of output would
generate more marginal revenues than
marginal costs, and profits could be higher.
Suppose the firm was instead producing
at a point where MC>MR.
 Then
the last unit of output generates
economic losses.
Graphing Profits
Total
dollars
TC
MC>MR
MR>MC
TR

q1
q2
Quantity of output (q)
At q1, the firm should raise output to increase profits.
At q2, the firm should lower output to increase profits.