Transcript Farm Management Chapter 7 Economic Principles— Choosing Production Levels © Mcgraw-Hill Companies, 2008 Chapter Outline • • • • • • The Production Function Marginal Analysis Law of Diminishing Marginal Returns How Much Input.

Farm Management
Chapter 7
Economic Principles—
Choosing Production Levels
© Mcgraw-Hill Companies, 2008
Chapter Outline
•
•
•
•
•
•
The Production Function
Marginal Analysis
Law of Diminishing Marginal Returns
How Much Input to Use
Using Marginal Concepts
Marginal Value Product and Marginal Input
Cost
• Equal Marginal Principle
© Mcgraw-Hill Companies, 2008
Chapter Objectives
1. Explain the concept of marginalism
2. Show the relation between a variable input
and output by use of a production function
3. Describe the concepts of average and
marginal physical products
4. Illustrate the law of diminishing returns
5. Find the profit-maximizing point using
marginal concepts
6. Explain the use of the equal marginal
principal
© Mcgraw-Hill Companies, 2008
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
Nitrogen
applied
(lbs.)
Yield
(bu.)
Total
physical
product
(TPP)
0
1
2
3
4
5
6
7
8
0
25
50
75
100
125
150
175
200
130
148
162
170
177
180
182
183
183
0
18
32
40
47
50
52
53
53
Average
physical
product
(APP)
Marginal
physical
product
(MPP)
-18.00
16.00
13.33
11.75
10.00
8.67
7.57
6.63
-18
14
8
7
3
2
1
0
Note that TPP is the portion of yield attributed to
nitrogen use.
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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 =
input level
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Marginal Analysis
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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Marginal Physical Product
Marginal physical product (MPP) is the
additional TPP produced by using an
additional unit of input.
TPP
MPP =
 input level
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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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Figure 7-2
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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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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Total Cost and Total Revenue
• Multiply the amount of a variable input by
its price per unit to get the variable cost for
that input.
• Add the variable cost(s) for the input(s) to
the fixed costs to get Total Cost (TC).
• To find Total Revenue (TR), multiply the
output level by the output price per unit.
• The accounting profit is the difference
between TR and TC.
© Mcgraw-Hill Companies, 2008
Table 7-2
Total Cost, Total Revenue, and Profit
Input
level
Nitrogen
applied
(lbs.)
0
1
2
3
4
5
6
7
8
0
25
50
75
100
125
150
175
200
Yield
(bu.)
Total
cost
(TC) $
Total
revenue
(TR) $
Profit ($)
(TR-TC)
130
148
162
170
177
180
182
183
183
400.00
406.25
412.50
418.75
425.00
431.25
437.50
443.75
450.00
325.00
370.00
405.00
425.00
442.50
450.00
455.00
457.50
457.50
(75.00)
(36.25)
(7.50)
6.25
17.50
18.75
17.50
13.75
7.50
nitrogen price = $.25; corn price = $2.50
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Using Marginal Concepts
• Profit-maximizing level of input can be
found by examining marginal changes in
costs and revenues
• Marginal revenue is the change in total
revenue from selling one more unit of
output
• Marginal cost is the additional cost of
producing that additional unit of output
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Marginal Revenue
 total revenue
MR =
 total physical product
If output price is constant:
MR = output selling price
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Marginal Cost
 total cost
MC =
 total physical product
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The Decision Rule
MR=MC
The decision rule, MR=MC, leads to the
profit-maximizing point.
If data in a table is such that this point
can’t be found exactly, use the closest
point, without letting MR fall below MC.
© Mcgraw-Hill Companies, 2008
Table 7-3
Marginal Revenue, Marginal Cost
and the Optimum Output
Input
level
Nitrogen
applied
(lbs.)
0
0
Yield
(bu.)
1
3
0
Margnal
physical
product
(MPP)
-
Total
revenue
(TR) $
Total
cost
(TC) $
-
3
2
5
.
0
0
4
0
0
.
0
0
Marginal
revenue
(MR) ($)
(ΔTR/ΔTPP)
-
Marginal
cost
(MC) ($)
(
Δ
T
C
Δ
/
-
-
T
-
1
2
5
1
4
8
1
8
3
7
0
.
0
0
4
0
6
.
2
5
2
.
5
>
0
.
3
5
2
5
0
1
6
2
3
2
4
0
5
.
0
0
4
1
2
.
5
0
2
.
5
>
0
.
4
5
3
7
5
1
7
0
4
0
4
2
5
.
0
0
4
1
8
.
7
5
2
.
5
>
0
.
7
8
1
7
7
4
7
4
4
2
.
5
0
4
2
5
.
0
0
2
.
5
>
0
.
8
9
>
<
<
2.08
3.13
6.25
4
1
0
0
5
6
7
8
125
150
175
200
180
182
183
183
50
52
53
53
450.00
455.00
457.50
457.50
431.25
437.50
443.75
450.00
2.5
2.5
2.5
nitrogen price = $.25; corn price = $2.50
© Mcgraw-Hill Companies, 2008
P
P
)
Table 7-4
Marginal Revenue and Marginal Cost
Under Varying Prices
Input
level
Nitrogen
applied
(lbs.)
0
1
2
3
4
5
6
7
8
0
25
50
75
100
125
150
175
200
Yield
(bu.)
Total
revenue
(TR) $
Total
cost
(TC) $
130
148
162
170
177
180
182
183
183
325.00
370.00
405.00
425.00
442.50
450.00
455.00
457.50
457.50
400.00
412.50
425.00
437.50
450.00
462.50
475.00
487.50
500.00
Marginal
revenue
(MR) ($)
Marginal
cost
(MC) ($)
Marginal
revenue
(MR) ($)
Marginal
cost
(MC) ($)
(corn price =$2.50)
(N price = $.50))
(corn price =$3.50)
(N price =$.25)
-2.50
2.50
2.50
2.50
2.50
2.50
2.50
-0.69
0.89
1.56
1.79
4.17
6.25
12.50
-3.50
3.50
3.50
3.50
3.50
3.50
3.50
-0.35
0.45
0.78
0.89
2.08
3.13
6.25
>
>
>
>
<
<
<
© Mcgraw-Hill Companies, 2008
>
>
>
>
>
>
<
Price Ratios and Profit Maximization
If output and input prices are constant,
then the rule MR=MC is equivalent to
Pi
____
MPP =
Po
where Pi is the input price and Po is
the output price
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Marginal Value Product and
Marginal Input Cost
• Marginal Value Product (MVP) is the
change in revenue associated with
increasing input use by one unit
• Marginal Input Cost is the cost of buying
one more unit of input (which will equal the
input price if it doesn’t change as
additional input is purchased)
• The decision rule is MVP=MIC
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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
4th
1,600
1,200
800
500
200
2nd
5th
Each application of 4 acre-inches
is a total use of 400 acre inches.
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1,800
1,500
1,200
800
400
1st
3rd
6th
Figure 7-3
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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