PINDYCK PHALL-82241 CHAPTER 06
page 4 of 12
FIGURE 6.1 Production with One Variable Input
Output
per
month
D
112
C
Total Product
B
60
A
0
1
2
3
4
5
6
7
8
9
10
Labor per Month
(a)
30
Output
per
worker 20
per
month
E
Average Product
10
Marginal Product
0
1
2
3
4
5
6
(b)
7
8
9
Labor per month
The total product curve in (a) shows the output produced for different amounts of labor
input. The average and marginal products in (b) can be obtained (using the data in
Table 6.1) from the total product curve. At point A in (a), the marginal product is 20
because the tangent to the total product curve has a slope of 20. At point B in (a) the
average product of labor is 20, which is the slope of the line from the origin to B. The
average product of labor at point C in (a) is given by the slope of the line 0C. To the left
of point E in (b), the marginal product is above the average product and the average is
increasing; to the right of E, the marginal product is below the average product and the
average is decreasing. As a result, E represents the point at which the average and
marginal products are equal, when the average product reaches its maximum.
Fig 06-01.EPS
10
PHALL-82241 PINDYCK CHAPTER 06
page 5 of 12
FIGURE 6.2 The Effect of Technological Improvement
Output
per
time
period
C
O3
100
B
A
O2
50
O1
0
1
2
3
4
5
6
7
8
9
10
Labor per time period
Labor productivity (output per unit of labor) can increase if there are improvements
in technology, even though any given production process exhibits diminishing
returns to labor. As we move from point A on curve O1 to B on curve O2 to C on curve
O3 over time, labor productivity increases.
Fig 06-02.EPS
PHALL-82241 PINDYCK CHAPTER 06
page 6 of 12
FIGURE 6.3 Cereal Yields and the World Price of Food
350
3.6
3.4
Food price index (1990 = 100)
3.2
Cereal Yield
3
250
2.8
200
2.6
2.4
150
Food Price Index
2.2
2
100
1.8
50
1.6
1970
1975
1980
1985
1990
1995
2000
2005
Cereal yields have increased. The average world price of food increased temporarily in the early
1970s but has declined since.
Fig 06-03.EPS
Cereal yields (metric tons per hectare)
300
PHALL-82241 PINDYCK CHAPTER 06
page 7 of 12
FIGURE 6.4 Production with Two Variable Inputs
Capital
per
year
E
5
4
3
A
B
C
q3 90
2
q2 75
D
1
q1 55
1
2
3
4
5
Labor per year
Production isoquants show the various combinations of inputs necessary for the firm to
produce a given output. Aset of isoquants, or isoquant map, describes the firms production
function. Output increases as we move from isoquant q1 (at which 55 units per year
are produced at points such as A and D), to isoquant q2 (75 units per year at points such
as and B) to isoquant q3 (90 units per year at points such as C and E).
Fig 06-04.EPS
PHALL-82241 PINDYCK CHAPTER 06
page 8 of 12
FIGURE 6.5 Marginal Rate of Technical Substitution
Capital
per
year
5
K = 2
4
L = 1
3
K = 1
K = 2 3
2
L = 1
L = 1
q3 = 90
1
K = 3
1
q2 = 75
L = 1
q1 = 55
0
1
2
3
4
5
Labor per year
Like indifference curves, isoquants are downward sloping and convex. The slope of
the isoquant at any point measures the marginal rate of technical substitution-the
ability of the firm to replace capital with labor while maintaining the same level of
output. On isoquant q2, the MRTS falls from 2 to 1 to 2/3 to 1/3.
Fig 06-05.EPS
PHALL-82241 PINDYCK CHAPTER 06
page 9 of 12
FIGURE 6.6 Isoquants When Inputs Are Perfect Substitutes
Capital
per
year
A
B
C
q1
q2
q3
Labor per year
When the isoquants are straight lines, the MRTS is constant. Thus the rate at which
capital and labor can be substituted for each other is the same no matter what level of
inputs is being used. Points A, B, and C represent three different capital-labor combinations
that generate the same output q3.
Fig 06-06.EPS
PHALL-82241 PINDYCK CHAPTER 06
page 10 of 12
FIGURE 6.7 Fixed-Proportions Production Function
Capital
per
year
q3
C
q2
B
K1
A
L1
q1
Labor per year
When the isoquants are L-shaped, only one combination of labor and capital can be
used to produce a given output (as at point A on isoquant q1, point B on isoquant q2,
and point C on isoquant q3). Adding more labor alone does not increase output, nor
does adding more capital alone.
Fig 06-07.EPS
PHALL-82241 PINDYCK CHAPTER 06
page 11 of 12
FIGURE 6.8 Isoquant Describing the Production of Wheat
Capital
(machine
hours per
year)
120
A
100
K = 10
90
B
80
Output = 13,800 Bushels
per Year
L = 260
40
250
500
760
1000
Labor (hours per year)
A wheat output of 13,800 bushels per year can be produced with different combinations
of labor and capital. The more capital-intensive production process is shown as
point A, the more labor-intensive process as point B. The marginal rate of technical
substitution between A and B is 10/260 = 0.04.
Fig 06-08.EPS
PHALL-82241 PINDYCK CHAPTER 06
page 12 of 12
FIGURE 6.9 Returns to Scale
Capital
(machine
hours)
Capital
(machine
hours)
A
A
6
30
4
20
4
2
30
2
20
10
0
5
10
(a)
10
15
Labor (hours)
0
5
10
Labor (hours)
(b)
When a firms production process exhibits constant returns to scale as shown by a movement
along line 0A in part (a), the isoquants are equally spaced as output increases proportionally.
However, when there are increasing returns to scale as shown in (b), the isoquants move closer
together as inputs are increased along the line.
Fig 06-09.EPS