Medical Care Production and Costs

1
Medical Care Production and Costs
2
Producing Medical Care

• Production of output as a function of inputs,
  most commonly aggregated into labor and capital
• q f(n,k)

For example, in the case of health care q
hospital services n nurses k medical
equipment, hospital building
3
Producing Medical Care (cont.)

• Short run k is fixed, while n is variable

4
Graphical RepresentationShort run (one
variable input)
Total product q f(n,k)
n1
n2
MPn Dq / Dn
MP is the slope of the TP curve.
5
Graphical Representation
AP q / n
AP is the slope of a ray from the origin to the
TP curve.
C
B
TP
A
6
Numerical Example
7
Substitutability in Production of Medical Care

• There may be more than one way to produce a given
  level of health care.
• Licensed 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 cant prescribe meds in
  most states.

8
Substitutability in Production of Medical Care
(cont.)
We can use different combinations of LPNs and RNs
to produce the same output
LPNs
The location shows that RNs are more productive
than LPNs. Do you see why?
10
5
Q
2
5
RNs
9
Substitutability in Production of Medical Care
(cont.)

• 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.

10
K
K
Q
Q
L
L
No substitutability
Perfect substitutability
11
Substitutability in Production of Medical Care
(cont.)
LPNs
TC/wL
If LPNs are relatively cheap, use more of them.
If LPN wages go up, use fewer LPNs and more RNs
10
TC/wL
wLgt wL and TCgtTC.
Do you see why?
5
Slope of BC wR/wL
Q
2
5
TC/wR
TC/wR
RNs
12
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.

13
Results
Each additional physician generated 6.05 more
admits per year. Nurses by far the most
productive
14
Results (cont.)
Each inputs is a substitute for other in
production process. If wages of nurses rise, can
substitute away by having more hospital beds.
15
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
16
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.

17
Recall

• Given a production function
• q f (n,k)
• q hospital services
• n labor nurse n
• k capital medical equipment, hospital
• building

18
Short-Run Total Cost
19
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).

20
Short-Run Total Cost (cont.)

• Recall Production function initially exhibits
  IRTS
• Total costs rise at decreasing rate up to q0

STC
STC
w n
r k
q0
21
Marginal and Average Costs
?STC ?q
SMC
?(wn rk)/?q
w(?n/?q) w(1/MPn)
w/MPn
The short run marginal cost of nurses depends on
their marginal productivity.
22
Marginal and Average Costs (cont).
STVC q
SAVC
(wn)/q
w(1/APn)
w/APn
The short average variable cost of nurses depends
on their average productivity.
23
Graphing Marginal and Average Costs
SMC
Costs
SMC0
SATC
SAVC
SATC0
SAVC0
0
q
q0
24
Graphing Marginal and Average Costs

• SATC and SAVC are u-shaped curves.
• 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.

25
Relating Product and Cost Curves
MPn APn
Cost
SMC
SAVC
APn
MPn
0
q1
q3
n
q
n1
n3
26
Empirical Evidence on Hospital Costs

• 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.

27
Empirical Evidence (cont.)

• Definition Economies of scope
• Cost of producing 2 outputs lt sum of cost of
  production 2 goods separately.

• Find Diseconomies of scope with respect to ER and
  other services.
• Larger ERs may bring in more complex mix of
  patients to the hospital. OR
• Larger ERs generate operating challenges for
  other services (e.g. communication, staffing
  scheduling).

28
Cost-minimizing input choice

• Example
• - Health care providers choice of nursing staff
  mix.
• RNs care for 6 patients per hour hourly wage
  20
• LPNs 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?
29
Cost Minimizing Input Choice

• Costs are minimized when
• Suppose that instead
• Then the last dollar spent on an LPN generates
  more output than the last dollar spent on a
  registered nurse.

Recall earlier graph
MPRN wRN
MPLPN wLPN

MPLPN wLPN
MPRN wRN
lt
30
Cost Minimization
LPNs
TC/wL
If LPNs are relatively cheap, use more of them.
If LPN wages go up, use fewer LPNs and more RNs
10
wLgt wL and TCgtTC.
TC/wL
Slope of BC wR/wL Slope of Isoquant MPR/MPL
5
Q
2
5
TC/wR
TC/wR
RNs
31
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.
• Cost minimization requires that

32
Are physicians costly to hospitals? (cont.)
If we know wn and both MP then we can solve for
shadow price of doctors, and find that if we
were efficient physician wages would be wdoc
7,012 per year. Physician wages exceed this,
so we have the left hand side is too large MP
of physicians is too low. We use too much
physician services relative to other inputs.
33
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?

34
The Long Run Average Cost Curve
Average Cost of Hospital Services
LATC
q0
q1
q2
of patients
35
Long Run Costs of Production

• Just like the short run cost curve, the long run
  cost curve for a firm is also u-shaped.
• 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.

36
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.

37
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.

38
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).

39
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.

40
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.

41
The Long Run Average Cost Curve
Average Cost of Hospital Services
LATC
q0
q1
q2
of patients
Economies of scale
Diseconomies of scale
42
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 of inputs results in a doubling of
  output.

43
The Long Run Average Cost Curve under Constant
Returns to Scale
Average Cost of Hospital Services
LATC
of patients
44
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 _____

45
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

46
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.

47
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.

48
Graphing Profits
Total dollars
TC
TR
TR0
??
TC0
Quantity of output (q)
q0
?(q0) TR0 TC0
49
Graphing Profits
Total dollars
TC
TR
TR0
??
TC0
q0
Quantity of output (q)
Q0 is where the TR curve is above the TC curve,
and the 2 curves are the furthest apart (in
vertical distance). It is also where the slopes
are equal.
50
Computing Profits (cont.)

• Recall that the slope of the total cost curve
  represents marginal costs.
• MC ?TC/??q
• The slope of the total revenue curve represents
  marginal revenue.
• MR ?TR/??q
• ?A firm maximizes profits where
• MRMC

51
Computing Profits (cont.)

• A firm maximizes profits where MRMC.
• If the firm was instead producing at a point
  where MRgtMC.
• Then additional units of output would generate
  more marginal revenues than marginal costs, and
  profits could be higher.
• If the firm was instead producing at a point
  where MCgtMR.
• Then the last unit of output generates economic
  losses.

52
Graphing Profits
Total dollars
TC
?MCgtMR
TR
MRgtMC
?
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.