Farm Management
Chapter 7
Economic Principles
Choosing Production Levels
Chapter Outline
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•
•
•
•
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Marginalism
The Production Function
How Much Input to Use
How Much Output to Produce
Applying the Marginal Principles
Equal Marginal Principle
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Chapter Objectives
1. To explain the concept of marginalism
2. To show the relation between a variable input and
an output by use of a production function
3. To describe the calculation of average and marginal
physical products
4. To illustrate the law of diminishing returns
5. To find the profit-maximizing point using the
concepts of marginal value product and marginal
input cost
6. To find the profit-maximizing point using the
concepts of marginal revenue and marginal cost
7. To explain the use of the equal marginal principal
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Marginalism
The term marginal refers to incremental
changes, either increases or decreases,
that occur at the edge or at the “margin.”
It may help to mentally substitute “extra”
or “additional” whenever the word marginally
is used. But keep in mind that the “extra”
can be negative.
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The Production Function
The production function is a systematic
way of showing the relation between
different amounts of a resource or
input that can be used to produce a
product and the corresponding output.
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Table 7-1
Production Function in Tabular Form
Input
level
Total
physical
product
(TPP)
Average
physical
product
(APP)
Marginal
physical
product
(MPP)
0
1
2
3
4
5
6
7
8
9
10
0
12
30
44
54
62
68
72
74
72
68
12.0
15.0
14.7
13.5
12.4
11.3
10.3
9.3
8.0
6.8
12.0
18.0
14.0
10.0
8.0
6.0
4.0
2.0
-2.0
-4.0
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Total Physical Product
Total physical product (TPP) is the
amount of production expected from
using each input level. Output or
yield is often called total physical
product.
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Average Physical Product
Average physical product (APP) is the
average amount of output produced
per unit of input used.
TPP
APP =
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input level
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Marginal Physical Product
Marginal physical product (MPP) is the
additional TPP produced by using an
additional unit of input.
TPP
MPP =
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 input level
9
Figure 7-1
Graphical illustration of a production function
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Stages of Production
• Stage I:
APP increasing, MPP>APP,
TPP increasing
• Stage II: APP decreasing, MPP<APP,
TPP increasing
• Stage III: TPP decreasing, MPP<0
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Law of Diminishing Marginal Returns
As additional units of a variable input
are used in combination with one or
more fixed inputs, marginal physical
product will eventually begin to decline.
Diminishing returns may start with the
first unit of input used, or may start
later after a period of increasing returns.
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How Much Input to Use
• Do not produce in Stage III, because more
output can be produced with less input.
• Do not normally produce in Stage I
because the average productivity of the
inputs continues to rise in this stage.
• Stage II is the “rational stage” of
production.
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Marginal Value Product
 total value product
MVP =
 input level
TVP = TPP × product selling price
If output price is constant:
MVP = MPP × product selling price
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Marginal Input Cost
 total input cost
MIC =
 input level
TIC = amount of input × input price
If input price is constant:
MIC = input selling price
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Table 7-2
Marginal Value Product, Marginal Input Cost
and the Optimum Input Level
Input
level
Total
physical
product
(TPP)
0
1
2
3
4
5
6
7
8
9
10
0
12
30
44
54
62
68
72
74
72
68
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Marginal
physical
product
(MPP)
Total
value
product
(TVP) $
Marginal
value
product
(MVP) $
Marginal
input
cost
(MIC) $
12.0
18.0
14.0
10.0
8.0
6.0
4.0
2.0
-2.0
-4.0
0
24
60
88
108
124
136
144
148
144
136
24
36
28
20
16
12
8
4
-4
-8
12
12
12
12
12
12
12
12
12
12
input price = $12; output price = $2
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The Decision Rule
MVP = MIC
If MVP > MIC, additional profit
can be made by using more input.
If MIC > MVP, less input should
be used.
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How Much Output to Produce
An alternative way to find the
profit-maximizing point is to
find directly the amount of
output that maximizes profit.
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Marginal Revenue
 total revenue
MR =
 total physical product
Total revenue = Total value product
If output price is constant:
MR = output selling price
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Marginal Cost
 total input cost
MC =
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 total physical product
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The Decision Rule
MR=MC
The decision rule, MR=MC, leads to
the same point as the decision rule
MVP=MIC.
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Table 7-3
Marginal Revenue, Marginal Cost and the
Optimum Output Level
Input
level
Total
physical
product
(TPP)
0
1
2
3
4
5
6
7
8
9
10
0
12
30
44
54
62
68
72
74
72
68
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Marginal
physical
product
(MPP)
12.0
18.0
14.0
10.0
8.0
6.0
4.0
2.0
-2.0
-4.0
Total
revenue
(TR) $
Total
input
cost
(TIC) $
Marginal
revenue
(MR) $
Marginal
cost
(MC) $
0
24
60
88
108
124
136
144
148
144
136
0
12
24
36
48
60
72
84
96
108
120
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
1
0.67
0.86
1.20
1.50
2.00
3.00
6.00
input price = $12; output price = $2
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Applying the Marginal Principles
Given prices for irrigation water and
for corn, the principles from the last
two sections can be used to determine
the amount of water and the corresponding
amount of corn that will maximize profit.
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Table 7-4
Determining the Profit-Maximizing Irrigation
Level for Corn Production
Irrigation
water
(acre-inch)
Corn yield
per acre
(bu)
Marginal
physical
product
(MPP)
10
12
14
16
18
20
22
24
26
104.0
116.8
128.6
138.2
144.8
149.0
151.8
153.6
154.2
6.4
5.9
4.8
3.3
2.1
1.4
0.9
0.3
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Margianl
value
product
(MVP)
Marginal
input
cost
(MIC)
Marginal
revenue
(MR)
Marginal
cost
(MC)
16.00
14.75
12.00
8.25
5.25
3.50
2.25
0.75
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
0.47
0.51
0.63
0.91
1.43
2.14
3.33
10.00
water at $3.00/acre-inch, corn at $2.50/bu
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Equal Marginal Principal
In some situations an input may be
limited so that the profit-maximizing
point cannot be reached for all
possible uses. A limited input should
be allocated among competing uses in
such a way that the marginal value
products of the last unit used on each
alternative are equal.
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Table 7-5
Application of the Equal Marginal Principle to
the Allocation of Irrigation Water
Irrigation
water
(acre-inch)
0
4
8
12
16
20
Marginal value products ($)
Grain
Wheat
Sorghum
Cotton
(100 acres)
(100 acres) (100 acres)
1,200
800
600
300
50
1,600
1,200
800
500
200
1,800
1,500
1,200
800
400
Each application of 4 acre-inches on a crop is a total use
of 400 acre-inches (4 acre-inches times 100 acres)
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Figure 7-2
Illustration of the equal marginal system
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Summary
Economic principles using the concept
of marginality provide useful guidelines
for decision making. MVP and MIC are
equated to find the profit-maximizing input
level. MR and MC are equated to find
the profit-maximizing output level. The
equal marginal principle is used when a
limited input must be allocated among
competing uses.
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