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PRODUCTION AND COST

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What is the optimal size for hospitals and physician practices? ... Bays (1986) finds small hospitals ( 100 beds) are losing market share ... – PowerPoint PPT presentation

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Title: 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
11
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
18
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
19
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

21
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)

22
  • Under ideal conditions, perfect competition
    squeezes out all possible economies
  • The health care industry is not perfectly
    competitive!

23
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

25
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

27
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
29
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
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