PRODUCTION AND COST

1
PRODUCTION AND COST
2
Substitution and Efficiency

• How substitutable are health care inputs?
• What is the optimal size for hospitals and
  physician practices?
• How efficient are health care providers?
• technical efficiency
• allocative efficiency

3
Isoquants and Isocost Curves

• Isoquants
• all combinations of inputs that produce a given
  output
• marginal rate of technical substitution
• slope of isoquant
• diminishing MRTS

4
Isoquants
A
Doctor Hours
x
B
Q3
y
C
Q2
x
D
Q1
z
0
Nurse Hours
5
Isocost Curves

• Combinations of inputs that cost the same

TC D.wd N.wn where TC Total cost
D Doctor hours N Nurse
hours wd Doctor wage
wn Nurse wage Rearrange terms to get
D TC/wd wn/wd .N
Doctor Hours
TC2
TC1
intercept
slope
0
Nurse Hours
6
Isocost Curves and Input Price Changes

• Change in an input price causes isocost curve to
  swivel

Doctor Hours
wn5
wn10
Nurse Hours
0
7
Cost Minimization/Output Maximization

• For given output, firm locates on point on
  isoquant which minimizes cost
• For given cost, firm locates on point on isocost
  that maximizes output

8
Graphical Model of Cost Minimization/Output
Maximization
Q2
Expansion path
Q1
Doctor Hours
B
A
TC2
TC1
0
Nurse Hours
9
Input Substitution

• Flexibility in substituting between inputs
• labor versus capital
• one type of labor versus another type of labor
• Monotechnic view
• only one right way to treat an illness

10
Substitution Flexibility
Monotechnic View
Flexible Substitutability
B
Doctor Hours
B
C
Doctor Hours
Q2
A
Q2
Q1
Q1
A
2o
Nurse Hours
Nurse Hours
0
0
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Elasticity of Substitution

• Ratio of percentage change in input ratio to
  percentage change in input price ratio
• Zero elasticity means no responsiveness to input
  price changes
• The higher the elasticity, the greater the
  responsiveness

12
Physician Extenders

• Physician assistants and nurse practitioners
• Studies indicate that one physician extender
  could substitute for 25 to 50 of a physicians
  time
• Physicians are not using the efficient number

13
Substitution by Hospitals

• One study finds considerable elasticity of
  substitution between nurses and capital
• Low elasticity between physicians and capital
• High elasticity between nurses and residents
• Moderate elasticity between physicians and
  residents

14
From the Expansion Path to Total Cost to Average
Cost
Capital
Q3
Expansion path
NOTE Long run Capital is variable
Q2
C
Q1
B
A
TC2
TC3
TC1
Labor
0
15
Long Run Total Cost Curve
Long Run Total Cost

I
Cost
H
G
F
C
E
B
D
A
Output
0
16

Long Run Total Cost
Cost
D
Output
0
17
Long Run Total Cost

I
Cost
H
G
F
C
E
B
D
A
Output
0
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The Long Run Average Cost Curve and Economies of
Scale

A
LRAC
Average Cost
B
H
C
G
D
F
E
Economies of scale
Diseconomies of scale
Constant costs
0
Output
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Economies of Scale

• Long run concept
• What happens as plant size (output capacity)
  increases?
• If increasing plant size causes average cost to
  fall, the firm is experiencing economies of scale
• If costs rise, firm is experiencing diseconomies

20
Economies of Scope

• Economies of scope exist when joint production of
  different outputs is cheaper than separate
  production
• Sharing of inputs

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Importance of Economies of Scale and Scope

• Efficiency requires minimization of costs
• minimum average cost (efficient plant size or
  maximum economies of scale)
• outputs be produced using least costly technology
  (maximum economies of scope)

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• Under ideal conditions, perfect competition
  squeezes out all possible economies
• The health care industry is not perfectly
  competitive!

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Estimating Economies of Scale for Hospitals

• Estimation problems
• distinguishing between long and short run
• the case-mix problem
• hospitals are multi-product firms
• quality differences
• general versus tertiary hospitals
• must include physician input prices

24

• Some evidence of economies up to 250 beds but
  evidence weak because problems hard to overcome

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Survival Approach

• What happens over time to hospitals of different
  size?
• Indirect evidence of economies of scale
• Bays (1986) finds small hospitals (lt100 beds) are
  losing market share

26
Survival Approach Applied to Physician Practices

• Tiny practices (1-2 docs) declining in market
  share
• Huge practices (100) increasing

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Technical and Allocative Efficiency

• Technical efficiency
• maximizing output for a given combination of
  inputs
• Allocative efficiency
• using the right input mix

28
Illustrations of Technical Efficiency
Production Function
Isoquant
Q
Capital
Output
8
3
9
6
4
1
5
2
10
7
Q1
Firms 2, 4, and 5 are inefficient
Firms 8, 9, and 10 are inefficient
Labor
0
0
Labor
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Technical vs. Allocative Efficiency
Point A -- Technically efficient
Allocatively inefficient Point B -- Technically
efficient Allocatively efficient
Capital
A
B
Q1
0
Labor
30
Estimation

• Data envelopment method
• sensitive to exogenous shocks showing up as
  inefficiency
• Stochastic frontier method
• controls for exogenous shocks but sensitive to
  case-mix problem
• technique still being refined

31

• Estimates of about 10 to 20 inefficiency in
  hospitals
• same for non- and for-profits