Title: PRODUCTION AND COST
1PRODUCTION AND COST
2Substitution 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
3Isoquants and Isocost Curves
- Isoquants
- all combinations of inputs that produce a given
output - marginal rate of technical substitution
- slope of isoquant
- diminishing MRTS
4Isoquants
A
Doctor Hours
x
B
Q3
y
C
Q2
x
D
Q1
z
0
Nurse Hours
5Isocost 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
6Isocost Curves and Input Price Changes
- Change in an input price causes isocost curve to
swivel
Doctor Hours
wn5
wn10
Nurse Hours
0
7Cost 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
8Graphical Model of Cost Minimization/Output
Maximization
Q2
Expansion path
Q1
Doctor Hours
B
A
TC2
TC1
0
Nurse Hours
9Input 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
10Substitution 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
11Elasticity 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
12Physician 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
13Substitution 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
14From 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
15Long Run Total Cost Curve
Long Run Total Cost
I
Cost
H
G
F
C
E
B
D
A
Output
0
16Long Run Total Cost
Cost
D
Output
0
17Long Run Total Cost
I
Cost
H
G
F
C
E
B
D
A
Output
0
18The 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
19Economies 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
20Economies of Scope
- Economies of scope exist when joint production of
different outputs is cheaper than separate
production - Sharing of inputs
21Importance 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!
23Estimating 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
25Survival 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
26Survival Approach Applied to Physician Practices
- Tiny practices (1-2 docs) declining in market
share - Huge practices (100) increasing
27Technical and Allocative Efficiency
- Technical efficiency
- maximizing output for a given combination of
inputs - Allocative efficiency
- using the right input mix
28Illustrations 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
29Technical vs. Allocative Efficiency
Point A -- Technically efficient
Allocatively inefficient Point B -- Technically
efficient Allocatively efficient
Capital
A
B
Q1
0
Labor
30Estimation
- 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