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Microeconomics ­ECO402
VU
Lesson 17
Production with Two Variable Inputs
There is a relationship between production and productivity.
Long-run production K& L are variable.
Isoquants analyze and compare the different combinations of K & L and output
The Shape of Isoquants
Capital
per year
E
5
In the long run both
4
labor and capital are
variable and both
experience diminishing
3
returns.
A
B
C
2
Q3 = 90
D
Q2 = 75
1
Q1 = 55
1
2
3
4
5
Labor per year
Diminishing Marginal Rate of Substitution
­ Reading the Isoquant Model
1) Assume capital is 3 and labor increases from 0 to 1 to 2 to 3.
­ Notice output increases at a decreasing rate (55, 20, 15) illustrating diminishing
returns from labor in the short-run and long-run.
2)  Assume labor is 3 and capital increases from 0 to 1 to 2 to 3.
­ Output also increases at a decreasing rate (55, 20, 15) due to diminishing returns
from capital.
Substituting Among Inputs
­ Managers want to determine what combination if inputs to use.
­ They must deal with the trade-off between inputs.
­ The slope of each isoquant gives the trade-off between two inputs while keeping output
constant.
­ The marginal rate of technical substitution equals:
MRTS = - Changein capital/Change in labor input
MRTS = - ΔK
(for a fixed level of Q)
ΔL
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Microeconomics ­ECO402
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Marginal Rate of Technical Substitution
Capital
5
per year
Isoquants are downward
sloping and convex
2
like indifference
4
curves.
1
3
1
1
2
Q3 =90
2/
1
1/
Q2 =75
1
1
Q1 =55
5 Labor per month
3
4
2
1
Observations:
1. Increasing labor in one unit increments from 1 to 5 results in a decreasing MRTS from
1 to 1/2.
2. Diminishing MRTS occurs because of diminishing returns and implies isoquants are
convex.
MRTS and Marginal Productivity
· The change in output from a change in labor equals:
(MP L )( Δ L)
·  The change in output from a change in capital equals:
)( Δ K)
(MP
K
· If output is constant and labor is increased, then:
(MP L )( Δ L) + (MP K )( Δ K) = 0
(MP L )(MP K ) = - ( Δ K/ Δ L) = MRTS
Isoquants When Inputs are perfectly substitutable
A
B
C
Q1
Q2
Q3
Labor per month
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Microeconomics ­ECO402
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Perfect Substitute
Observations when inputs are perfectly substitutable:
1) The MRTS is constant at all points on the isoquant.
2) For a given output, any combination of inputs can be chosen (A, B, or C) to
generate the same level of output (e.g. toll booths & musical instruments).
Fixed-Proportions Production Function
Capital
per
month
Q3
C
Q2
B
Q1
K1
A
Labor
per month
L1
Fixed-Proportions Production Function
­ Observations when inputs must be in a fixed-proportion:
1) No substitution is possible. Each output requires a specific amount of each input
(e.g. labor and jackhammers).
2)To increase output requires more labor and capital (i.e. moving from A to B to C
which is technically efficient).
A Production Function for Wheat
Farmers must choose between a capital intensive or labor intensive technique of
production.
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Microeconomics ­ECO402
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Isoquant Describing the Production of Wheat
Capital
(Machine
Point A is more
hour per
capital-intensive, and
120
year)
B is more labor-intensive.
A
100
B
ĆK = -10
90
ĆL = 260
80
Output = 13,800 bushels
per year
40
Labor
250
500
760
1000
(hours per year)
Observations:
1) Operating at A:
·
L = 500 hours and K = 100 machine hours.
2) Operating at B
·  Increase L to 760 and decrease K to 90 the MRTS < 1:
MRTS = -ΔK
= -(10 / 260) = 0.04
ΔL
3) MRTS < 1, therefore the cost of labor must be less than capital in order for the
farmer substitute labor for capital.
4) If labor is expensive, the farmer would use more capital (e.g. U.S.).
5) If labor is inexpensive, the farmer would use more labor (e.g. India).
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Microeconomics ­ECO402
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Returns to Scale
Measuring the relationship between the scale (size) of a firm and output
1. Increasing returns to scale: output more than doubles when all inputs are doubled
­ Larger output associated with lower cost (autos)
­ One firm is more efficient than many (utilities)
­ The isoquants get closer together
Increasing Returns:
Capital
A
The isoquants move closer
(machine
together
hours)
4
30
20
2
10
Labor (hours)
0
5
10
2. Constant returns to scale: output doubles when all inputs are doubled.
· Size does not affect productivity
· May have a large number of producers
· Isoquants are equidistant apart
Capital
(machine
hours)
A
Decreasing returns to scale: output less than doubles when all inputs are doubled
6
30
Constant Returns:
4
Isoquants are
20 equally spaced
2
10
Labor (hours)
0
5
10
15
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Microeconomics ­ECO402
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3. Decreasing returns to scale: output less than doubles when all inputs are doubled
· Decreasing efficiency with large size
· Reduction of entrepreneurial abilities
· Isoquants become farther apart
A
Capital
(machine
hours)
Decreasing Returns:
Isoquants get further
apart
4
30
2
20
10
Labor (hours)
0
5
10
Returns to Scale in the Carpet Industry
The carpet industry has grown from a small industry to a large industry with some very large
firms.
Question
­ Can the growth be explained by the presence of economies to scale?
The U.S. Carpet Industry
Carpet Shipments, 1996
(Millions of Dollars per Year)
1. Shaw Industries
$3,202
6. World Carpets
$475
2. Mohawk Industries
1,795
7. Burlington Industries
450
3. Beaulieu of America
1,006
8. Collins & Aikman
418
4. Interface Flooring
820
9. Masland Industries
380
5. Queen Carpet
775
10. Dixied Yarns
280
Are there economies of scale?
­ Costs (percent of cost)
·  Capital -- 77%
·  Labor -- 23%
Large Manufacturers
­ Increased in machinery & labor
­ Doubling inputs has more than doubled output
­ Economies of scale exist for large producers
Small Manufacturers
­ Small increases in scale have little or no impact on output
­ Proportional increases in inputs increase output proportionally
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Microeconomics ­ECO402
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­ Constant returns to scale for small producers
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