• TABLE OF CONTENTS
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 Front Cover
 Title Page
 Chapter summaries
 Introduction
 Part one: The partial budget
 Part two: Marginal analysis
 Answers to exercises
 Back Cover
 Copyright






Title: Introduction to economic analysis of on-farm experiments draft workbook
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Title: Introduction to economic analysis of on-farm experiments draft workbook
Physical Description: vi, 104 p. : ill., forms ; 28 cm.
Language: English
Creator: CIMMYT Economics Program
Farming Systems Support Project
Publisher: International Maize and Wheat Improvement Center
Place of Publication: Mexico
Publication Date: 1986?
 Subjects
Subject: Agriculture -- Research -- On-farm -- Economic aspects   ( lcsh )
Field experiments -- Economic aspects   ( lcsh )
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General Note: Reproduced by the FSSP for inclusion in the FSSP FSR/E Training Materials Collection.
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Table of Contents
    Front Cover
        Front Cover
    Title Page
        Title Page
    Chapter summaries
        Page i
        Page ii
        Page iii
        Page iv
        Page v
        Page vi
    Introduction
        Page 1
        Page 2
        Page 3
    Part one: The partial budget
        Page 4
        1. Experimental and non-experimental variables
            Page 5
            Page 6
            Page 7
            Page 8
            Page 9
            Page 10
        2. Identifying costs that vary
            Page 11
            Page 12
            Page 13
        3. Calculating costs that vary
            Page 14
            Page 15
            Page 16
            Page 17
            Page 18
            Page 19
            Page 20
        4. Total costs that vary
            Page 21
            Page 22
            Page 23
            Page 24
            Page 25
            Page 26
        5. Average yield
            Page 27
            Page 28
            Page 29
            Page 30
            Page 31
            Page 32
            Page 33
            Page 34
            Page 35
            Page 36
            Page 37
        6. Adjusted yield
            Page 38
            Page 39
            Page 40
            Page 41
        7. Field price of the crop
            Page 42
            Page 43
            Page 44
        8. Gross field benefits
            Page 45
            Page 46
            Page 47
        9. Net benefits
            Page 48
            Page 49
            Page 50
            Page 51
            Page 52
            Page 53
            Page 54
            Page 55
    Part two: Marginal analysis
        Page 56
        10. Dominance analysis
            Page 57
            Page 58
            Page 59
        11. Net benefit curves
            Page 60
            Page 61
            Page 62
            Page 63
            Page 64
        12. Marginal rate of return
            Page 65
            Page 66
            Page 67
            Page 68
            Page 69
            Page 70
            Page 71
            Page 72
        13. Minimum rate of return
            Page 73
            Page 74
            Page 75
            Page 76
        14. Interpreting net benefit curves
            Page 77
            Page 78
            Page 79
            Page 80
            Page 81
            Page 82
            Page 83
            Page 84
            Page 85
            Page 86
            Page 87
            Page 88
            Page 89
            Page 90
            Page 91
        15. Partial budgets and fixed costs
            Page 92
            Page 93
            Page 94
        16. Final exercises
            Page 95
            Page 96
            Page 97
            Page 98
            Page 99
            Page 100
            Page 101
            Page 102
        17. Conclusion
            Page 103
            Page 104
    Answers to exercises
        Page 105
        Page 106
        Page 107
        Page 108
        Page 109
        Page 110
        Page 111
        Page 112
        Page 113
        Page 114
        Page 115
        Page 116
        Page 117
        Page 118
        Page 119
        Page 120
        Page 121
        Page 122
        Page 123
        Page 124
        Page 125
        Page 126
        Page 127
        Page 128
        Page 129
        Page 130
    Back Cover
        Back Cover
    Copyright
        Copyright
Full Text













Introduction to Economic Analysis
of On-Farm Experiments

Draft Workbook

CIMMYT Economics Program
February, 1985


















Introduction to Economic Analysis
of On-Farm Experiments

Draft Workbook

CIMMYT Economics Program
February, 1985










Chapter Summaries


Page 1 Introduction

This workbook provides an introduction to the
economic analysis of agronomic experiments for
on-farm research. This type of analysis is
useful for assessing new technologies that can
be adopted by farmers. The analysis requires
that you develop a partial budget for the
experiment and then carry out a marginal
analysis.



Part One: The Partial Budget




Page 5 1. Experimental and
Non-Experimental Variables



Distinguish the experimental from the non-
experimental variables. The farmer's practice
should be one of the experimental treatments,
so that the economic analysis can compare costs
and benefits of new treatments with those of
the farmer's practice. In order for the
economic analysis to be useful, the
non-experimental variables should be at the
level used by representative farmers.









Page 11 2. Identifying Costs That Vary

Make a list of all the costs that vary for the
experiment. These include all costs of inputs,
labor and equipment rental that are associated
with the experimental variables.



Page 14. 3. Calculating Costs That Vary

Obtain the data necessary for calculating the
costs that vary for each treatment. This will
usually involve conversations with farmers and
visits to the places where they buy their
inputs. For fertilizer experiments the cost of
transportation should be included in the field
price of the fertilizer or nutrient.



Page 21 4. Total Costs That Vary

Calculate the total costs that vary for each
treatment. This is the sum of all the costs
that vary.



Page 27 5. Average Yield

Review diagnostic and experimental evidence
and decide what recommendation domains will be
used for the analysis. Calculate the average
yield for each treatment across the
recommendation domain. Refer to the









statistical analysis of the yield data before
proceeding with the partial budget.

Page 38 6. Adjusted Yield

Look at the characteristics of the experiment
(farmer vs. researcher management, plot size,
harvest date and method) and estimate the
difference between the experimental yield and
what the farmer could expect. Calculate an
adjusted yield for each treatment.



Page 42 7. Field Price of the Crop

Calculate the field price of the crop. This is
the price that the farmer could expect to
receive for the crop, less all costs of
harvesting, transport, marketing and storage
that are proportional to the yield.



Page 45 8. Gross Field Benefits

Calculate the gross field benefits for each
treatment. This is the adjusted yield
multiplied by the field price of the crop.



Page 48 9. Net Benefits

Set up a partial budget for the experiment. The
first line should be the average yield. Next


iii








comes the adjusted yield and then the gross
field benefits. Below this list each cost that
varies, and then the total costs that vary.
The final line is the net benefits, which is
the gross field benefits minus the total costs
that vary.



Part Two: Marginal Analysis




Page 57 10. Dominance Analysis

For each treatment, look at the total costs
that vary and the net benefits, the last two
lines of the partial budget. Arrange the
treatments in order of increasing total costs
that vary, and do a dominance analysis by
eliminating each treatment that has lower net
benefits than a lower cost treatment.



Page 60 11. Net Benefit Curves

Draw a net benefit curve by plotting the net
benefits on the Y-axis and the total costs that
vary on the X-axis. Connect the non-dominated
treatments with straight lines.










Page 64 12. Marginal Rate of Return

Calculate the marginal rate of return between
the lowest cost treatment and the next
treatment. This is calculated by dividing the
difference in net benefits by the difference in
total costs that vary and expressing the ratio
as a percentage. Continue calculating marginal
rates of return for each adjacent pair of
treatments.



Page 72 13. Minimum Rate of Return

Estimate the minimum rate of return for the
recommendation domain. Either official or
unofficial interest rates are often good
estimates of the cost of capital. At least 20%
should be added to this to estimate the cost of
management.



Page 76 14. Interpreting Net Benefit Curves

In order to choose the treatment that is most
economically attractive, for either further
experimentation or recommendation, the marginal
rates of return should be compared to the
minimum rate of return. Compare the marginal









rate of return between each pair of treatments
with the minimum rate of return, and stop when
the marginal rate of return approaches, but
does not fall below, the minimum rate of
return.



Page 91 15. Partial Budgets and Fixed Costs

A marginal analysis of a partial budget gives
the same results as when you include fixed
costs.



Page 94 16. Final Exercises



Page 102 17. Conclusion











Introduction



A. On-Farm Research



This is a workbook on the economic analysis of agronomic
experiments for on-farm research. On-farm research consists
of three major types of activities:


1) Diagnosis and planning. Researchers gather
information about farmers and their circumstances,
identify priority problems that limit farmers'
productivity, and design agronomic experiments
that test possible solutions to these problems.


2) Experimentation. The agronomic experiments are
planted on the fields of representative farmers.


3) Assessment and recommendation. The results of the
on-farm experiments are assessed from the
agronomic standpoint, and they are also subjected
to statistical and economic analysis. This
analysis helps researchers select particular
experimental treatments that merit further
investigation and, when there is sufficient
information, to make recommendations to farmers.


Thus the results of an economic analysis are used both to
help plan the next cycle of on-farm experiments and to
formulate recommendations that will help farmers improve
their productivity.










Diagnosis

Planning

Experimentation

Assessment

Recommendations

The method of economic analysis presented in this workbook
assumes that the farmer's practices are taken as a starting
point for the research. It assumes that relatively small
changes in those practices are proposed during diagnosis and
planning and tested through experimentation. This type of
gradual, step-by-step change is the way that farmers usually
improve their practices.



B. Partial Budgets and Marginal Analysis

The discussion of economic analysis in this workbook is
divided into two major parts.


The first part of the workbook will show you how to set up a
partial budget. A partial budget looks at the costs and
benefits associated with the different treatments in an
experiment.


The second part of the workbook deals with marginal
analysis. A marginal analysis examines the changes in costs
and benefits between treatments, moving step by step from
the farmer's practice to other practices being tested.











C. How To Use This Workbook

Each chapter of the workbook introduces a new concept and
illustrates it with examples and exercises. In order to
make sure that you understand the material you should do
each one of the exercises. Spaces are provided in the
workbook for doing the exercises. It will be much easier,
although not essential, to use a calculator for the
exercises.


The exercises and examples are presented for teaching
purposes only. They are representative of the kind of data
generated by on-farm research, but are not meant to be taken
as models for experimental design nor as recommendations for
particular practices. The use of the names of certain
commercial products does not imply an endorsement. The
symbol $ is used for a monetary unit and is not meant to
refer to any particular country.














Part One:
The Partial Budget










1. Experimental and
Non- Experimental Variables

Before setting up a partial budget for an experiment, you
must be able to answer three questions about the experiment:

- Which are the experimental variables?
- Is the farmer's practice included as a treatment in the
experiment?
- Are the non-experimental variables set at the farmer's
level of management?



A. Experimental Variables

When designing agronomic experiments, researchers select
certain variables to be examined in different treatments,
and other variables that will remain constant across all
treatments. The variables that change according to
treatment are called experimental variables. Variables that
are left constant are called non-experimental variables.

For example, in an experiment that examines three varieties
and two levels of fertilizer, variety and fertilizer are the
experimental variables. If all treatments have the same
weed control, seeding rate and land preparation, then these
are among the non-experimental variables.





























B. The Farmers Practice as a Treatment

The method of economic analysis presented in this workbook
compares the farmer's practice with one or more
alternatives. You should therefore be sure that the
farmer's practice is included as one of the treatments in
the experiment. For example, if you are testing different
types of insect control (insect control is an experimental
variable) you must make sure that the farmer's method of
insect control is one of the treatments. If the farmers use
a particular type of insecticide, this insecticide should be
one of the treatments. If the farmer usually does nothing
to control insects, one treatment should have no control.


This is not to say that all agronomic experiments must
include the farmer's practice. There are certainly cases
where it may be difficult or unnecessary to do so. But in
order to do an economic analysis of the trial results using
the methods illustrated in this workbook, it is necessary to
include the farmer's practice in the experiment.


EXERCISE 1.1

An experiment is planted to determine the response of the
local variety to three levels of nitrogen and two levels of
phosphorus. What are the experimental variables in this
experiment?











EXERCISE 1.2 Exercise 1.2


In one research area, the majority of farmers applied 40
kg/ha of nitrogen to their crop. Researchers felt that it
would be worthwhile to experiment with other levels of
nitrogen. In order to do an economic analysis of the
experiment, which level of nitrogen must be one of the
treatments?


a) 0 kg/ha
b) 40 kg/ha
c) the level used on the experimental station










C. Setting Non-Experimental
Variables at the Farmer's Level

Another factor that must be considered is whether the
non-experimental variables are at the level of current
farmer practice. Researchers are often tempted to set non-
experimental variables at optimum levels in order to
increase the chances of there being observable responses to
the experimental variables. For example, in a variety trial,
researchers may want to use optimum fertilizer levels to
ensure vigorous plant growth so that they can see clear
differences between the varieties. This may be justified in
some cases, but the marginal analysis demonstrated in this
workbook is usually not appropriate for this kind of trial.


Another example may be useful. Assume you want to plant a
fertilizer experiment in an area where insects cause crop
losses. Researchers might say that unless you control
insects, you won't get good results from the fertilizer
experiment. There are three possibilities:

1) Plant the fertilizer experiments with good insect
control. The results will allow you to say what
response to fertilizer applications farmers can expect
if they use good insect control. This may be useful
information to have, but it will not allow you to make
a fertilizer recommendation to farmers. This
experiment cannot be analyzed using the techniques
described in this workbook.


2) Plant the fertilizer experiments with farmer's
current level of insect control. The results may not be
as clear as in case (1), but you will be able to do an
economic analysis to determine what level of fertilizer








is appropriate given the farmer's current insect
control practices.


3) An alternative to (2) would be to include insect
control as an experimental variable, thereby expanding
the experiment to one with two experimental variables,
fertilizer and insect control. Or, if insects cause
serious losses for farmers, it may be best to
concentrate on insect control experiments before doing
fertilizer experiments.












EXERCISE 1.3


For each of the following experiments decide whether it is
designed so that an economic analysis can be carried out.
If it is not, suggest changes in the design so that an
economic analysis could be carried out.


a) A trial in which four levels of nitrogen, including the
level used by the farmer, are tested. The trial is
planted and managed by the farmer.





b) A trial in which 5 levels of nitrogen and 3 levels of
phosphorus are applied to the crop. A (0,0) treatment
is included, which is the farmer's current practice.
Researchers prepare the plot where the experiment will
be planted and use seeding rates, weed control and pest
control methods which they feel are the optimum for the
area.





c) An experiment that examines two new varieties and two
seeding rates (above and below the farmer's usual
rate). The farmer prepares the plot and the researchers
control the weeds and insects in the way that the
farmer normally does.











2. Identifying Costs That Vary

When developing a partial budget for an agronomic
experiment, you must identify the costs that vary. The costs
that vary are those associated with the experimental
variables. In constructing a partial budget, you do not
have to be concerned with the fixed costs that do not vary
across treatments (i.e, costs of the non-experimental
variables).


The costs that vary are those related to:


1) Inputs the cost of any inputs used as
experimental variables, such as fertilizer,
herbicide, insecticide, fungicide, or seed. Also,
the transport costs of bulky inputs, such as
fertilizer, must be included.


2) Labor the cost of labor for performing any
operation that is part of the experimental
variables, such as labor for applying chemicals,
for planting, for land preparation, or for
weeding.


3) Equipment rental the cost of renting equipment
that is part of the experimental variables, such
as tractor or animal-drawn equipment for land
preparation, seeding, or cultivation; or sprayers
or pumps for applying chemicals.


There is another kind of costs that vary that have not been
considered here. These are the costs that vary with the
yield, and are paid around harvest time. These include such
things as the cost of harvesting, transport to point of sale








and storage. Because the farmer pays these costs at harvest
time, they will be included later (see Chapter 7). Farmers
also must pay interest on loans, and this is covered in
marginal analysis (see Chapter 13).



EXAMPLE

Suppose that researchers find that farmers are having
disease problems in their bean crop and wish to test three
different fungicides (A,B, and C) against the farmer's
practice of not using fungicide. The experimental variable
in this case is fungicide treatment, and the costs that vary
that must be obtained are:


1) Cost of fungicide A
2) Cost of fungicide B
3) Cost of fungicide C
4) Cost of labor to apply the fungicide
5) Cost of labor to haul water to mix with the
fungicide
6) Cost of renting a sprayer to apply fungicide











EXERCISE 2.1


For each of the following experiments, make a list of all
the costs that vary associated with the different
treatments.


a) Insect Control Experiment, Maize


Treatment 1:
Treatment 2:
Treatment 3:


Farmer's practice = no insect control
Furadan applied in hole at planting
Orthene (granular) applied at 20 days


b) Nitrogen Experiment, Wheat


Treatment 1: 40 kg N at planting (farmer's practice)
Treatment 2: 20 kg N at planting; 20 kg at 30 days
Treatment 3: 40 kg N at planting; 40 kg at 30 days
Treatment 4: 20 kg N at planting; 60 kg at 30 days





c) Weed Control by Density Experiment, Maize


Treatment 1: 30,000 plants/ha; one hand weeding
Treatment 2: 30,000 plants/ha; Atrazine herbicide at
emergence
Treatment 3: 50,000 plants/ha; one hand-weeding
Treatment 4: 50,000 plants/ha; Atrazine herbicide at
emergence











3. Calculating Costs That Vary

When you have identified the costs that vary for an
experiment you must then obtain the data needed to calculate
the costs that vary. This chapter looks at the calculation
of these costs for inputs, labor, and equipment.



A. Inputs

Data on the costs of inputs should be obtained at the place
where farmers are most likely to make their purchases. For
instance, if farmers buy insecticide at small village shops,
researchers should use the price of insecticide in these
shops, rather than from stores in the city that may have
lower prices but are not accessible to the farmers.
Researchers also want to make sure that they obtain prices
for the exact type and concentration of input that is being
used in the experiment. Conversely, care must be taken when
experimenting with inputs which are not currently available
to farmers. Experiments with such inputs may provide
valuable information but cannot be used for making immediate
recommendations to farmers.

Fertilizer Costs: Fertilizer is a special case when
calculating input costs for two reasons: First, fertilizer
is bulky, so you must make sure to include the cost of
transport in your calculations.

The field price of fertilizer is calculated by adding the
price of the fertilizer and the cost of transporting the
fertilizer from the place of purchase to the farm. The field
price is usually expressed per kilogram.











EXAMPLE

Suppose that a 50 kg bag of "10-30-10" sells for $250 in
town. To get that 50 kg bag of "10-30-10" to the farm, the
farmer must pay $30 in transport charges. The field price
of the fertilizer is:


$250 price of 50 kg "10-30-10"
+ $ 30 price of transporting 50 kg to farm
$280 field price of 50 kg "10-30-10"


$280/50 kg = $5.60/kg, field price of "10-30-10"


The second reason fertilizer may require special care in
calculating costs that vary is that fertilizer experiments
are often designed on the basis of single nutrients, rather
than commercial fertilizer. If the single nutrient
fertilizers are used in the experiment, then it is more
convenient to calculate the field price of nutrients.











EXAMPLE

In one experiment researchers tested 4 levels of nitrogen.
They used urea as the source of nitrogen. This is how they
calculated the field price of nitrogen:

$372 cost of 50 kg urea in town
$ 20 cost of transport of 50 kg to farm
$392 field price of 50 kg urea


$7.84/kg Field price of urea


Because urea is 46% N, to calculate the field price of N (as
urea) you must divide the field price of urea by .46:


$7.84/kg urea = $17.04/kg field price of N
.46 Kg N/kg urea










EXERCISE 3.1

A N x P experiment is planted using ammonium sulfate as the
source of N and triple superphosphate (TSP) as the source of
P. Use the following data to calculate the field price of N
and the field price of P.


Cost of 45 kg ammonium sulfate in shop $ 740
Cost of 45 kg TSP in shop $1620
Cost of transporting a 45 kg bag from
shop to farm $ 95

Ammonium sulfate is 21% N
TSP is 46% P











B. Labor

It is important to estimate the costs of all labor
associated with the experimental variables. Such
calculations usually involve two steps: First, estimating
the amount of time it takes to carry out the operation (e.g.
hand weeding) and second, assigning a cost to that amount of
labor.


For example, in an experiment that compares one hand weeding
to two hand weedings, the researchers must find out from the
farmers how many man-days it takes to hand weed one hectare.
(Often farmers are not familiar with hectares, making
necessary to talk about land measures the farmers know
about, and then convert to hectares). Questions to farmers
must be as specific as possible. For example, the amount of
labor needed for weeding may vary depending on the time of
the year at which the weeding is done.


It is important to estimate all the labor associated with a
particular task. In the case of spraying herbicide, for
example, the labor needed (and perhaps the rental of
animals) to haul water should be included. If the experiment
involves an operation that farmers have never performed
before (such as a new planting method) careful measurements
and observations must be made in order to estimate the
amount of labor required.


In assigning a cost to labor, you should use the local wage
rate. In other words, farmers are either hiring labor, or if
they are using family labor, assume that labor has an
opportunity cost equal to the local wage rate. This means
that if a farmer is using family labor to do weeding family
members are giving up the opportunity to work as laborers








for another farmer and to earn the local wage rate. There
will be cases where the opportunity cost of labor is above
or below the local wage rate, but these will not be covered
in this workbook.





EXERCISE 3.2

In the analysis of a weed control experiment it was found
that it takes five 6-hour days to hand weed one acre (.4 ha)
of a maize-sorghum intercrop. The local wage rate was $35
for a 6 hour day, and the farmer was also expected to
provide the laborer with one meal, valued at about $10.
Calculate the cost of weeding one hectare.











C. Equipment Rental

It is also necessary to estimate the cost of renting
equipment used as part of the experimental treatments. The
concept of opportunity cost is useful here as well. For
instance, if a farmer owns a tractor or oxen, you still
should assign a cost to the use of these, since they could
be rented out instead.


EXERCISE 3.3

Two different types of land preparation were examined in an
experiment.


Treatment 1: One plowing and two harrowings with a
tractor
Treatment 2: Plowing with a horse


Economic data
Tractor plowing $200 per hectare
Tractor harrowing $100 per hectare
Horse plowing $35 per day (horse can plow ha in
f one day)


Calculate the costs of land preparation for Treatment 1
and Treatment 2.











4. Total Costs That Vary

Once you have identified the costs that vary for an
experiment and obtained the data necessary for their
estimation, you are then ready to calculate the total costs
that vary for each treatment of the experiment.



EXAMPLE

Calculate the total costs that vary for the following weed
control by seeding rate experiment:


Treatment
1
2
3


Weed control
No weed control
2,4-D (2 It/ha)
2,4-D (2 It/ha)


Seeding rate
120 kg/ha
120 kg/ha
160 kg/ha


Data:
Seed cost:
2,4-D:
Labor to apply herbicide:
Labor to haul water:
Wage rate:
Sprayer rental:


$40/kg
$350/it
2 man-days/ha
0.5 man-day/ha
$250/man-day
$150/ha


First, calculate the individual costs that vary.


To calculate seed cost:


Treatments 1 and 2: 120 kg/ha x $40/kg = $4,800/ha
Treatment 3: 160 kg/ha x $40/kg = $6,400/ha








To calculate


Treatments 2


To calculate


Treatments 2



To calculate


Treatments 2



To calculate


Treatments 2


herbicide cost:


and 3 2 It/ha X $350/it = $700/ha


labor to apply herbicide:


and 3: 2 man-days/ha X $250/man-day
= $500/ha


labor for hauling water:


and 3: 0.5 man-days/ha X $250/man-day
= $125/ha


sprayer rental:


and 3: $150/ha


Then arrange all of these costs by treatment and add them to
get the total costs that vary.


Treatment 1 Treatment 2 Treatment 3
Cost of seed $4,800 $4,800 $6,400
Cost of herbicide 0 700 700
Labor to apply herbicide 0 500 500
Labor to haul water 0 125 125
Sprayer rental 0 150 150
Total costs that vary $4,800 $6,275 $7,875











EXERCISE 4.1


For each of the following experiments, calculate the total
costs that vary.


a) Insect Control Experiment, Maize


Treatment 1
Treatment 2
Treatment 3


Farmer's practice (no insect control)
10 kg/ha Furadan, applied at planting
8 kg/ha Orthene, applied at 20 days


Data:


Cost of Furadan:
Cost of Orthene:
Labor to apply Furadan
at planting:
Labor to apply Orthene
Cost of labor:


$3.00/kg
$1.20/kg


1.5 man-days/ha
1.0 man-days/ha
$5.00/man-day









Nitrogen Experiment, Wheat


Treatment
1
2


Kg N at planting


Kg N at 30 days
0
20
40
60


Data:


Cost of urea:
Cost of transport of urea:
% N in urea:
Labor to apply fertilizer
at planting:
Labor to apply fertilizer
at 30 days:
Cost of labor:


$21.50/kg
$1.50/kg
46%


0.5 man day/ha


0.5 man-day/ha
$160.00/man-day


b)








c) Weed Control by Density Experiment, Maize


Treatment
1


Density
30,000 plants/ha

30,000 plants/ha

50,000 plants/ha

50,000 plants/ha


Weeding
1 hand weeding


2.5 kg/ha Gesaprim

1 hand weeding

2.5 kg/ha Gesaprim


Data:


Cost of seed:
(1 kg of seed contains 2,500 seeds)
Labor to plant 30,000 plants/ha:
Labor to plant 50,000 plants/ha:
Labor to hand weed:
Cost of Gesaprim:
Labor to apply Gesaprim:
Labor to haul water to mix
with herbicide:
Sprayer rental:
Cost of labor:


$40/kg

2 man-days/ha
3 man-days/ha
12 man-days/ha
$1,000/kg
2 man-days/ha

1 man-days/ha
$300/day
$500/day


I










5. Average Yield

Chapters 1-4 explained how to identify and calculate the
costs that vary of each treatment in an experiment.
Chapters 5-9 will explain how to calculate the benefits
associated with those treatments. The benefits of different
treatments depend, of course, on the yields, and this
chapter is concerned with the concept of average yields.
There are two things to bear in mind in using average yields
in a partial budget: 1) The yields for each treatment should
be the average yield from all experiments in one
recommendation domain. 2) It is necessary that you refer to
the statistical analysis of this yield data before deciding
how to proceed with the partial budget.



A. Pooling Yields for Economic Analysis

When doing an economic analysis of agronomic experiments,
the average responses of the treatments across sites are
used rather than the results at any one site. We therefore
usually average the yields of the treatments across sites in
order to do set up a partial budget.

When averaging yields across sites, you want to make sure
that the sites are similar. Since the purpose of the
experiments is to be able to recommend improvements to a
target group of farmers, the experiments should be designed
to meet the needs and conditions of that target group. A
group of farmers who have similar circumstances, and who
should be eligible for the same recommendation, is called a
recommendation domain. The various treatments of an
experiment for one recommendation domain should be pooled
for economic analysis. The results from several years of









experiments in one recommendation ,domain can also be pooled
for economic analysis.


The average yields are presented on the first line of the
partial budget.


EXERCISE 5.1


A variety by fertilizer experiment was planted in one
research area consisting of two recommendation domains.
Recommendation Domain A was distinguished by very sandy
soils, while Recommendation Domain B consisted of those
farmers who had clay-loam soils.


Yield data from 9 sites are presented below. Find the
average yields for each treatment for each recommendation
domain.


Recarrmen-
dation
Site Domain
1 A
2 A
3 B
4 A
5 B
6 B
7 A
8 B
9 A


Yields (kg/ha)
1 2 3 4
Local Improved Local Improved
Variety, Variety, Variety, Variety,
No No With With
Fertilizer Fertilizer Fertilizer Fertilizer
965 912 1,562 1,381
1,012 624 1,820 1,457
1,825 1,657 2,240 2,926
572 496 987 826
2,274 2,428 2,750 3,308
1,900 1,742 2,196 2,841
822 1,057 1,423 1,526
2,433 2,016 2,745 3,217
895 623 1,482 1,375


(Continued) -













Recommendation Domain A
Treatment 1 Treatment 2 Treatment 3 Treatment
Average yield
(kg/ha)


Recommendation Domain B
Treatment 1 Treatment 2 Treatment 3 Treatment
Average yield
(kg/ha)













B. Partial Budgets and Statistical Analysis

Since the purpose of the partial budget is to compare the
costs and benefits of different treatments, you will need
some assurance that the differences between the treatments
are real differences. In other words, it makes little sense
to calculate the benefits of two different treatments if a
statistical analysis tells you that there is little chance
that the expected yields from the treatments are in fact
different.


It is important to pay particular attention to the
statistical analysis of the pooled results. An economic
analysis should only be done when you feel confident that
yield differences among treatments are real (and when you
understand the nature of the agronomic response). This is
not to say that you only do an economic analysis when there
is a very high statistical significance, such as .01. You
should be flexible in choosing an appropriate significance
level. In many cases it may be .10, .20 or even more. But
you must have some confidence that the trial results
represent real, understandable differences among treatments
before proceeding with a complete partial budget.


i) No statistical difference between treatments
If the results of an experiment show no statistically
significant difference among the yields of different
treatments, then you will normally select the lowest cost
treatment for further research or for recommendation to
farmers.











EXAMPLE

Consider the following experiment with fungicides:


Average Yield
(10 sites)
Treatment 1 Fungicide A, one application 1,625 kg/ha
Treatment 2 Fungicide A, two applications 1,709 kg/ha
Treatment 3 Fungicide B, one application 1,681 kg/ha


Statistical analysis showed no significant differences in
yields.


The following costs that vary were calculated:


Treatment 1 Treatment 2 Treatment 3


Fungicide A $10 $20 0
Fungicide B 0 0 $16
Labor for applying
Fungicide $ 3 $ 6 $ 3
Labor for hauling $ 1 $ 2 $ 1
water
Sprayer rental $ 1 $ 2 $ 1
Total costs that vary $15 $30 $21


Because the results of the experiment show no significant
difference in yields between treatments it is best to choose
Treatment 1 for further attention, because it has the lowest
costs that vary. A comparison of costs that vary is all
that is necessary in this case, and you should not continue
with the partial budget.








ii) Factorial experiments
If an experiment looks at two or more factors, it may be
that one factor is responsible for significant yield
differences, while another factor shows no response. In
this case, you can average the yields of the significant
factor across those of the other factor, and use these
yields in the partial budget.



EXAMPLE

The following is a summary of the results of 8 density by
insecticide experiments in one recommendation domain.


Treatment Density Insecticide Average Yield
1 25,000 A 2500 kg/ha
2 25,000 B 2300 kg/ha
3 50,000 A 2900 kg/ha
4 50,000 B 3100 kg/ha


The statistical analysis shows that the difference between
the two densities is significant at .05, but there is no
significant difference between insecticide A and insecticide
B. Therefore the partial budget should only look at the
average yields of the two density treatments.


Average yield of density 25,000: 2,500 + 2,300 2,400

kg/ha
2
Average yield of density 50,000: 2,900 + 3,100 3,000

kg/ha
2









The first line of the partial budget should look like this:


Average yield (kg/ha)


Dens. 25,000
2,400


Dens. 50,000
3,000


The less expensive of the two insecticides should be chosen
for further research or for recommendation.












EXERCISE 5.2

Examine the results of each of the following experiments and
decide


i) Should you use the average yields to begin a
partial budget, or should you simply choose the
lowest cost treatment for further experimentation
or recommendation?


ii) If you should use the average yields, what is the
first line of the partial budget?



a) Herbicide experiment


Herbicide A
Herbicide B
Herbicide C


Average Yield
3,240 kg/ha
3,110 kg/ha
3,195 kg/ha


Statistical analysis shows no significant differences
between treatments.









b. Nitrogen X phosphorus experiment


Nitrogen
80


Phosphorus


1,600
1,800


1,700


2,000
2,400


2,200


2,200
3,000


2,600


N Sig. at .05
P Sig. at .05
N x P Sig. at .10


Av
1,933
2,400


2,167









c) Nitrogen X phosphorus experiment


Nitrogen
0 40 80
Av
0 2,100 2,750 3,100 2,650
Phosphorus
40 2,200 2,650 3,240 2,700


Av 2,150 2,700 3,170 2,675


N Sig. at .05
P not significant at .30
N x P not significant at .30









d) Nitrogen X phosphorus experiment


Ni
0


Phosphorus


2,400


2,350


N not significant at .30
P not significant at .30
N x P not significant at .30


trogen
40
2,560


2,620


80
2,600


2,450











6. Adjusted Yield

Once you have calculated the average yields for the
different treatments of an experiment across all the sites
in a recommendation domain, you then need to think about
adjusting these yields. You must make yield adjustments if
you believe that the yields from your experiment do not
represent the yield the farmer could get with a particular
treatment on his field.


There are several reasons why the yields from an experiment
may be somewhat higher than the yield the farmer can expect:


1) Management:- Researchers can often be more precise and
timely than farmers in applying a particular treatment,
e.g. plant spacing, timing of planting, fertilizer
application, or weed control.


2) Plot size: Despite efforts to plant experiments on
representative sites, yields estimated from small plots
tend to be higher than yields from an entire field,
which may not be as uniform.


3) Harvest date: Researchers often harvest a crop at
physiological maturity, whereas farmers may let their
crop dry in the field. Thus even when the yields of
both researchers and farmers are adjusted to a constant
moisture content, the researchers' yield may be higher,
because of fewer losses to insects, birds, rodents, ear
rots, or shattering.


4) Form of harvest: At times, farmers' harvest methods
may lead to heavier losses than researchers' harvest
methods. This might occur, for example, if farmers








harvest their fields by machine, while researchers
carry out a more careful manual harvest.


5) Storage losses: If the farmer stores his harvest for
home consumption or later sale, and thereby incurs
insect or rodent damage, his effective production is
less than that predicted by researchers on the basis of
experimental data.


Because of these factors you need to estimate an adjusted
yield before proceeding with a partial budget. Only rarely
is it possible to quantify exactly what the difference is
between experimental yields and the farmers'. Nevertheless,
you should review the factors listed above, consider how
they affect your yields compared to those of the farmer, and
estimate as best as possible a yield adjustment.



EXAMPLE

In a fertilizer experiment on potatoes, researchers decided
that because of their careful application of fertilizer,
yields should be reduced by 5% to estimate the expected
yields from farmers' fertilizer management. They also
estimated that the effect of small plot size warranted
another 5% reduction. Harvesting date and method were the
same as the farmers', and the farmers generally suffered few
storage losses. Thus the experimental yields were adjusted
by 10%.












Site 1
Site 2
Site 3
Average yield


Treatment A
11,500
12,400
9,400
11,100


Yield (Kg/ha)
Treatment B
14,700
16,200
13,800
14,900


Treatment C
18,500
18,400
16,200
17,700


The first two lines of the partial budget are:


Treatment A Treatment B Treatment C
Average yield (kg/ha) 11,100 14,900 17,700
Adjusted yield (kg/ha) 9,990 13,410 15,930












EXERCISE 6.1

Researchers want to analyse the results of some experiments
that include variety and insecticide. The experiments
consist of three treatments, each planted in a single
2
repetition on about 200 m plots.


They decided to reduce the yields of treatments B and C by
5% because of management differences (for insecticide).
Plot size was large enough to not be judged a problem.
Harvest date for the trial was much earlier than the
farmers', who usually left the crop in the field to dry. It
was decided to reduce all yields by 10% because of this
difference.


The three treatments and yield adjustments are:

Yield

Treatment Variety Insect Control Adjustment
A Farmer's None 10%
B Farmer's Insecticide (applied
by researcher) 15%
C Improved Insecticide (applied
by researcher) 15%


Make the yield adjustments for the following data.

Kg/ha
A B C
Average yield 2,200 2,500 3,000
Adjusted yield











7. Field Price of the Crop

Field price is defined as the price the farmer receives (or
can receive) for the crop when he sells it, minus costs
associated with harvest and sale that are proportional to
yield. To calculate the value of the yields that are
obtained from various treatments, you need to obtain the
field price of the crop.


The first thing to consider is the price the farmer receives
for his crop. To estimate this, you must find out from the
farmers exactly how they sell their crop, to whom they sell
it, and under what conditions (time of sale, discounts for
quality, etc.) You must understand what the farmer actually
receives, rather than merely using the official price or
market price of the crop.


The second factor to consider in calculating field price are
the costs associated with harvest and sale that are
proportional to yield. These costs are subtracted from the
price the farmer receives for the crop. They are not
included in costs that vary because the farmer does not have
to pay them until harvest time.


The costs of harvest and marketing that are proportional to
yield include: harvest costs (if the harvest cost depends
upon the amount harvested, not simply on area harvested);
shelling, threshing or winnowing costs; bagging costs;
transport costs to point of sale; storage costs, if the crop
is stored for a period before sale.











EXAMPLE

Suppose that a farmer sells his maize to a trader for
$6.00/kg. It costs the farmer $0.30/kg to harvest the
maize, $0.20/kg to shell it and $0.20/kg to transport it to
the point of sale. The field price of this maize is then
calculated as:

$6.00/kg selling price to trader
.30/kg harvest cost
.20/kg shelling cost
.20/kg transport cost
$5.30/kg field price of maize




EXERCISE 7.1

In a maize-growing region, farmers received $80 per 50 kg
bag of grain in the local market. The cost of transporting
the grain to market averaged $5 per 50 kg bag. Harvesting
took about 8 man-days per hectare. Average yields in the
area were 2,400 kg per hectare. A worker was able to shell
about 400 kg of maize per day. The wage rate was $40 per
day. What is the field price of maize?











EXERCISE 7.2

In another area, wheat farmers harvested their crop with
rented combine harvesters. The combine operators charged
$550 per hectare, regardless of yield. Farmers sold their
wheat at a government warehouse in town, and had to pay
trucking costs of $160 per ton. The official buying price
of the wheat was $2.20 per kilo, but farmers found that they
were usually charged a discount of 5% because of impurities
in their wheat. Average wheat yields in the area were 2
tons/hectare. What is the field price of wheat?











8. Gross Field Benefits

Gross field benefits express the value of the yield of each
treatment, without yet considering the costs that vary
associated with each treatment. Gross field benefits are
calculated by multiplying the adjusted yield (in kg/ha) by
the field price (in $/kg).



EXAMPLE

In the following experiment with rice, the yield adjustment
for all treatments was taken to be 10%.


Average yield
(kg/ha)
Adjusted yield
(kg/ha)


TREATMENT
1 2 3 4 5

2,000 2,400 2,500 2,850 3,000

1,800 2,160 2,250 2,565 2,700


The field price of rice was $8/kg, so gross field benefits
were calculated as follows:


Treatment 1:
Treatment 2:
etc.


1,800 kg/ha X $8/kg = $14,400/ha
2,160 kg/ha X $8/kg = $17,280/ha


The first three lines of the partial budget for the
experiment are shown below:












Average yield
(kg/ha)
Adjusted yield
(kg/ha)
Gross field benefits
($/ha)


1

2,000

1,800

14,400


2

2,400

2,160

17,280


TREATMENT
3 4

2,500 2,850

2,250 2,565

18,000 20,520


5

3,000

2,700

21,600


--------











EXERCISE 8.1

The average yields from a maize experiment are shown below.


TREATMENTS
1 2 3 4
Average yield (kg/ha) 1,740 2,430 1,420 2,790


Because of plot size, differences in management, and time of
harvest researchers decided to adjust all treatment yields
downward by 20%. Maize was sold in town, for $12.00/kg.
Transport costs from farm to town were $0.60/kg and the cost
of harvesting and shelling was $0.80/kg.


Fill in the first 3 lines of the partial budget.


TREATMENTS
1 2 3 4
Average yield (kg/ha)
Adjusted yield (kg/ha)
Gross field benefits
($/ha)











9. Net Benefits

You are now able to calculate gross field benefits and total
costs that vary. The final step in constructing a partial
budget is to calculate the net benefits. The net benefits
are equal to the gross field benefits minus total costs that
vary.


The following example will review the steps in constructing
a partial budget.



EXAMPLE

A nitrogen experiment was planted for maize.


Treatment
A
B
C
D


Kg N/ha
0
40
80
120


Fertilizer
applications
0
1
2
2


The planting date and method, density, variety, weed
control, and all other non-experimental variables were left
at the farmer's level.


The experiment was planted in each of two years, at 5 sites
each year, in the same recommendation domain. Researchers
thus had the results of 10 experiments to analyze.


Step 1:


Calculate the average yields.


The average yields over the 10 sites were as follows:











Average yield (kg/ha)


0 N
2,222


40 N
2,722


80 N
3,028


120 N
3,194


Differences between treatment means were significant at .10.


Step 2: Calculate the adjusted yield.


Researchers decided that all yields should be adjusted
downwards by 10%


0 N 40 N
Average yield (kg/ha) 2,222 2,722
Adjusted yield (kg/ha) 2,000 2,450


Step 3: Calculate the gross field


The field price of maize was calculated u!
data:


Price farmer receives for maize at market
Cost of harvesting maize
Cost of shelling maize
Cost of transport to town
Field price of maize


For treatment 0 N, gross field benefits =
2,000 kg/ha X $0.20/kg = $400/ha


80 N 120 N
3,028 3,194
2,725 2,875


benefits.


sing the following


$0.26/kg
$0.03/kg
$0.01/kg
$0.02/kg
$0.20/kg










0 N 40 N 80 N 120 N
Yield (kg/ha) 2,222 kg 2,722 kg 3,028 kg 3,194 kg
Adjusted Yield 2,000 kg 2,450 kg 2,725 kg 2,875 kg
(kg/ha)
Gross Field Benefit $400 $490 $545 $575
($/ha)


Step 4:


Calculate the total costs that vary.


The costs that vary in this experiment are:
a) The cost of nitrogen (in this experiment,
sodium nitrate (16%N) was used).
b) The cost of labor for applying fertilizer.


a) The cost of nitrogen was calculated with the following
data:


Price of sodium nitrate
Cost of transporting sodium
nitrate to farm
Field price of sodium nitrate


$0.09/kg


$0.01/kg
$0.10/kg


Field price of N = $0.10/kg = $0.625/kg
.16


Treatment
0 N
40 N
80 N
120 N


Cost of Nitrogen
0 X $0.625 = 0
40 X $0.625 = $25/ha
80 X $0.625 = $50/ha
120 X $0.625 = $75/ha


b) The cost of labor was calculated using the following
data:


Labor to apply fertilizer:
Cost of labor:


0.5 man-day/ha
$10/man-day








Treatment
0 N
40 N
80 N
120 N


Number of Applications


Cost of Labor
0
$5
$10
$10


The total costs that vary were:


Cost of nitrogen ($/ha)
Cost of labor ($/ha)
Total costs that vary
($/ha)


Step 5: Subtract total costs
field benefits to get net benefits.
partial budget for the experiment:


Treatment


ON


40 N


that vary from gross
This is the complete


80 N


120 N


Yield
(kg/ha)

Adjusted Yield
(10 /o)
(kg/ha)


2,222 kg


2,000 kg


- Gross Field Benefit $400
(Field Price = $.20/kg)
($/ha)


Cost of Fertilizer
(including transport)
($/ha)

Cost of Labor for
Applying Fertilizer
($/ha)

Total Costs that Vary
($/ha)

Net Benefits
($/ha)


$ 400


2,722 kg


2,450 kg



$490



$ 25



$ 5


$ 30


$ 460


3,028 kg 3,194 kg


2,725 kg



$545



$ 50



$10



$ 60


$ 485


2,875 kg



$575



$ 75



$10



$ 85


$ 490


0 N
0
0


40 N
25
5


80 N
50
10


60


120 N
75
10


85









EXERCISE 9.1

Complete the following partial budget for an insecticide
experiment, using the information found on the following
page:


T R E A T M E N T
TREATMENT
A B C D
Birlane Birlane Birlane
No One Two +
Variable Control Application Applications Furadan
Average Yield
(ka/ha) 2717 2635 2917 3233


Adjusted Yield
(kg/ha)
Gross Field
Benefits ($/ha)
Insecticide Cost
($/ha)
Application Cost
($/ha)
Total Costs that
Vary ($/ha)
Net Benefits
($/ha)


(Continued) -1


I








Data:
Sales price of maize:
Harvesting cost:
Shelling cost:
Transport-field to
sales point:
Cost of labor:
Price of Birlane:
Price of Furadan:
Insecticide application:
Birlane:
Furadan:
Yield adjustment:


Each application of Birlane
application.


An application of Furadan is
at planting.


= $ 0.32/kg
= $ 0.03/kg
= $ 0.02/kg

= $ 0.04/kg
= $ 6.00/day
= $ 1.70/kg
= $ 4.30/kg


= 1 man-day/application
= 0.5 man-day/application
= 20%


is 8 kg per ha, as a foliar



4 kg per ha, placed in the hole


I












EXERCISE 9.2


Construct a partial budget with the following data:


Experimental Data:


Treatment
1


3


Insecticide Fertilizer
0 0
0 50 kg/ha N
6 kg/ha Furadan 50 kg/ha N


Average Yield
(4 Sites)
2,000 kg/ha
2,500 kg/ha
3,000 kg/ha


Economic Data:


Selling price of maize in the city:
Transport of maize from farm to city:
Cost of harvest and shelling (total):
Cost of urea (46%N) in the city:
Cost of transport of fertilizer:
Cost of Furadan:
Cost of labor:
Application of fertilizer:
Application of insecticide:
Yield adjustment:


$ 17.50/kilo
$1.50/kilo
$1.00/kilo
$17.00/kilo
$1.40/kilo
$200.00/kilo
$100.00/day
1 man-day/ha
2 man-days/ha
10%












Part Two:
Marginal Analysis










10. Dominance Analysis

When you have completed the partial budget for an experiment
you can then begin to compare the total costs that vary and
the net benefits for each treatment. This comparison begins
with a dominance analysis.

After completing a partial budget, in which the total
variable costs and the net benefits for each treatment are
presented, the next step is a dominance analysis. In a
dominance analysis the treatments are arranged in order of
variable costs, from lowest to highest. The net benefits
are then compared. If a treatment B has higher variable
costs than treatment A, but lower net benefits, treatment B
is said to be dominated by treatment A, and can be
eliminated from further consideration.



EXAMPLE

Examine the last two lines of this partial budget.

TREATMENTS
1 2 3 4
Total Costs that Vary ($/ha) 476 522 452 607
Net Benefits ($/ha) 988 945 967 1,040

The first step in dominance analysis is to arrange the
treatments in order of total variable costs.









Treatment
3
1
2
4


Total Costs that Vary
$ 452
$ 476
$ 522
$ 607


Net Benefits
$ 967
$ 988
$ 945
$1,040


The next step is to examine the net benefits of each
treatment, beginning with the lowest cost treatment. If any
treatment has higher variable costs but lower net benefits
than any proceeding treatment, it is considered dominated.
In this case, the net benefits of treatment 1 are higher
than those of treatment 3, the net benefits of treatment 2
are lower than those of treatment 1, and the net benefits of
treatment 4 are higher than those of all proceeding
treatments. Therefore, treatment 2 is the only dominated
treatment.


Treatment
3
1
2
4


Total Costs that Vary
$ 452
$ 476
$ 522
$ 607


Net Benefits
$ 967
$ 988
$ 945 D
$1,040











EXERCISE 10.1


Do a dominance analysis on the following data from a partial
budget.


Total Costs that Vary ($/ha)
Net Benefits ($/ha)


Treatments
1 2 3 4
0 80 45 30
240 280 265 270


5 6
65 100
295 290











1 1. Net Benefit Curves

In order to help compare the total costs that vary and the
net benefits of different treatments it is useful to draw a
net benefit curve.

This is done by plotting the net benefits on the Y-axis and
the total costs that vary on the X-axis and drawing a curve
connecting the treatments. Make sure to connect only the
points showing a higher net benefit so that the curve never
has a negative slope. The treatments that remain
below this net benefit curve are the dominated treatments.











EXAMPLE

The following is a net benefit curve using the example from
Chapter 10.


Treatments


Total costs that vary ($/ha)
Net benefits ($/ha)


476
988


2
522
945


3
452
967


4
607
1,040


Net Benefit Curve


1040- i r i 1 i [i T 1 i T-


102C
o
100(

S98C


z
94C


500


550


600


650


Total Costs That Vary ($/ha)




The net benefit curve connects treatments 3, 1, and 4.
Treatment 2, which is dominated, is below the net benefit
curve.


2


460












EXERCISE 11.1


Perform a dominance analysis in the spaces provided and draw
the net benefit curve for each of the following experiments.


a. Nitrogen x Phosphorus Experiment


Dominance Analysis


1.


3.
4.
5.
6.
7.


*N 0 P
N40P 0

N80P 0
N P,
40 O
NO

N40 30

N80P30

N80 60


*Farmer's practice




760-

740-
o
720- -

0t 700

S680

Z ccrn


TCV
0
38
70
83
128
115
160


NB
640
692
722
704
688
735
731


Total Costs That Vary ($/ha)









b. Herbicide Experiment (Maize)


Dominance
Analysis
TCV NB

1. Roundup
(one application) 623 1,188

2. Gramoxone
(one application) 275 1,382

3. Gramoxone
(two applications) 550 1,147

4.*2,4-D
(one application) 124 1,214

5. 2,4-D
(two applications) 248 1,255

* Farmers practice.










Density by Fertilizer Experiment


Treatment Density Fert.

1 I I

2 I F

3 F I

4 F F

F = Farmer's

I = Improved.


TCV

172

35

137

0


Dominance
Analysis


NB

797

812

821

832


C.









12. Marginal Rate of Return
The next step in a marginal analysis is to calculate
marginal rates of return.
Marginal rates of return are calculated by dividing the
difference in net benefits between two treatments by the
difference in costs that vary.


A Net benefits
ACosts that vary


= Marginal rate of return


EXAMPLE

The following is an example using the fertilizer experiment
discussed in Chapter 10.


Treatment


Costs that vary
Net benefits


0 N


$400


40 N


$ 30
$460


80 N


$ 60
$485


120 N


$ 85
$490


Treatment Costs that Vary
ON 0


40 N

80 N

120 N


$ 30

$ 60

$ 85


Net Benefits
$400
$460

$485


$490


Marginal Rate of
Return


I



I


200%
83%

20%


The calculation is done as follows: For the MRR from ON to
40 N

460 400 60
30 0 30 200%
Notice that the marginal rate of return is expressed as a
percent.








Simila' ly, the MRR from 40 N to 80 N is


485 460 25
83%
60 30 30

The MRR from 80 N to 120 N is

490 485 5 2
85 60 20
85 60 25


$480



$460


Net
Net 440
Benefits $4


$ 420



$ 400


0o1 120 N
80 N A NB=$ 5
aCV=$ 25

-ANB=$ 25


ACV=$ 30



o\0
IANB= $ 60






ON ACV=$ 30


$ 40 $ 60
Costs that Vary


For every $ 1
invested, the
farmer receives
$1 +$2


For every $ 1
invested, the
farmer receives
$1 +$0.83


For every $ 1
invested, the
farmer receives
$1 +$0.20


0 $ 2


I








The graph helps you to understand the meaning of the
marginal rate of return.


A marginal rate of return of 200% means that for every $1
the farmer invests, he will get back the $1 (remember that
the costs that vary are already accounted for in the net
benefits) plus $2 more.


In the case of a farmer who is currently applying no
nitrogen, investing in 50 kg N/ha means that, on the
average, the farmer will get back $2 for each $1 invested in
fertilizer and labor.


Similarly, in going from 50 kg N/ha to 100 kg N/ha the
farmer will receive $0.83 for each $1 invested, and in going
from 100 kg N/ha to 150 kg N/ha the farmer will receive
$0.20 for each $1 invested.











EXERCISE 12.1

Refer to the data in Exercise 11.1, and for each experiment
calculate marginal rates of return between the non-dominated
treatments.

a. Nitrogen X Phosphorus Experiment








b. Herbicide Experiment (Maize)


c. Density by Fertilizer Experiment









EXERCISE 12.2


The following are the
50, 100 and 150 kg N/h


a) construct a pa
bh do a donminanrc


results of some fertilizer trials (0,
a.). For recommendation domain #1.


>rtial budget
analvsis


c) draw a net benefit curve
d) calculate marginal rates of return


Recommendation Experiment Yields (Kg/ha)
Domain No. NO N50 N100 N150
1 1 1000 1850 2200 2250
1 2 900 1860 2100 2400
2 3 1900 2400 2500 2600
1 4 1300 2200 2400 2500
2 5 2000 2600 2600 2700
1 6 1100 2100 2400 2500
1 7 1400 2050 2600 2600
2 8 1700 2200 2100 2200
2 9 (abandoned drought)


Data:


Yield adjustment:
Maize sales price:
Shelling cost:
Harvest cost:
Wage:
Urea (46% N):
Transport (urea):
Fertilizer application:
(Fertilizer is applied in a
treatments.)


15%
$6.50/kg
$0.50/kg
$0.75/kg
$150/day
$4.00/kg
$0.30/kg
2 man-days/ha
single application for all











13. Minimum Rate of Return

After calculating marginal rates of return between
treatments the next step is to determine the minimum rate of
return acceptable to the farmer. For example, in the
previous section you saw that if a farmer was applying no
nitrogen to his crop, and invested in the fertilizer and
labor for 40 kg N/ha, he would obtain, on the average, a
200% rate of return on that investment. How do you know if
200% (or 83% or 20%) is acceptable to the farmer?
Calculating the minimum rate of return will help you find
this out.

The minimum rate of return is composed of two elements: the
cost of capital and the cost of management.



A. Cost of Capital

The cost of capital is the cost that the farmer must pay to
obtain cash for investment. It may be that the farmer can
obtain a loan through an official source, such as the local
bank. In this case we must make sure that we use all costs
involved in obtaining the loan to calculate the cost of
capital.



EXAMPLE

Suppose a farmer asks for a loan of $1,000 for 8 months at
an annual interest rate of 18%, that there is a service
charge of $30, and that to obtain the loan the farmer has
personal expenses (transport, etc.) of $70. The cost of
capital is estimated as follows:









$1,000 X .18 = $180 annual interest
$180 X 8 $120 interest for period of loan
12
$120 + $30 + $70 = $220 total costs of the loan
$220 22% cost of capital for the period of the loan
$1000

Notice that the cost of capital is expressed as a percent,
and is calculated for the period of the loan, usually
equivalent to the crop cycle.


Calculating the cost of capital is not always this easy.
Credit is often not available for the majority of farmers in
a region. Credit may be subsidized and available to only a
small proportion of the farmers, or the system is very
bureaucratic and the credit arrives late. In these cases,
farmers may depend on local money lenders, who generally
charge much higher interest rates than the bank.





EXERCISE 13.1

A farmer borrows $3,000 for eight months at an annual
interest rate of 20%. Besides interest, the farmer must pay
a service charge of $60 and has $140 in personal expenses
related to obtaining the loan. There is also a crop
insurance charge of $90. What is the cost of borrowed
capital?
































Opportunity cost of capital If the farmer does not borrow
money for investing in a new technology, you can use an
opportunity cost of capital. If the farmer already has some
cash available, he will be giving up other opportunities for
using that cash when he invests in the new technology.
Hence an opportunity cost of capital must be estimated.
This can often be done by ascertaining local bank rates or
finding out what money lenders are charging, as you did in
Exercises 13.1 and 13.2.





B. Cost of Management

If you estimate that the cost of capital for a farmer is
50%, and if your calculation of the marginal rate of return
for 40 kg N is also 50%, there is little likelihood that the
farmer will be interested. It would mean that for every
$100 the farmer invests he recovers the $100 plus an


EXERCISE 13.2

A farmer borrows $2,000 from the village money lender. He
does not have to pay any service charge, insurance charge or
personal expenses. The money-lender charges 10% per month
interest. If the loan runs for seven months, what is the
cost of borrowed captial?








additional $50. But because the cost of capital is 50%, the
additional $50 goes to the bank or to the money lender and
the farmer is back where he started.


Obviously the minimum rate of return must be above the cost
of capital. So you must add something for the cost of
management, that is, to repay the farmer for the management
of the new technology. As a general rule you can add about
20% onto the cost of capital, but in some cases the cost of
management is much higher than 20%.



EXAMPLE

In the example in the previous section, the cost of capital
on a bank loan was 22%. Using 20% as a cost of management,
the minimum rate of return acceptable to the farmer in this
case would be 42%.



It is important to realize that the estimation of minimum
rates of return cannot be done with great precision. In
cases where there is a well-developed market for capital,
such as in areas where most farmers have access to bank
loans, it may be possible to be fairly precise about a
minimum rate of return. Usually, though, the minimum rate
of return can only be estimated. A minimum rate of return
for a crop cycle of 100%, or even higher, is not uncommon in
many developing countries.









14. Interpreting
Net Benefit Curves

When you have calculated marginal rates of return, and
estimated the minimum rate of return acceptable to farmers,
you are ready to complete the marginal analysis of the
experiment. The experiment may be from the early stages of
research. In this case, the economic analysis will help
select treatments which should be included in future
experiments. Or, the experimental data may come from
several years of on-farm research on a particular topic, and
the economic analysis will help select treatments that can
be recommended to farmers.



A. Graphical Interpretation

How do you identify treatments that are attractive for
further research or for recommendation to farmers? You
should be interested in treatments that provide the highest
net benefits, but still have acceptable marginal rates of
return compared to other alternatives. You can find such
treatments by moving along the net benefit curve towards
increasing net benefits until the marginal rate of return
approaches (but does not fall below) the minimum rate of
return.




EXAMPLE 1

Turn back to the nitrogen experiment introduced in Chapter
9. If this represents results from one recommendation
domain over two years, researchers may feel they are ready








to make a recommendation to farmers. Assume that the
minimum rate of return is 40%.
Treatment TCV NB
0 N $ 0 $400


40 N
80 N

120 N


$30
$60

$85


$460
$485

$490


MRR
200%


80%

20%


In this case, the recommendation should be 80 N.
Moving along the net benefit curve, 80 N is the treatment
with the highest net benefits where the MRR (from the next
lowest cost treatment to this one) is still above the
minimum rate of return (40%).


o 120 N
80 N 20 ANB= $5
$ 480 / ACV=$-25
o\o
S jANB=$ 25

$460- 40 N
ACV=$30

Net
Benefits \$ 440
IANB=$ 60

$ 420-



$ 4004 ^


0 $


Costs that Vary








Notice that the recommendation is not the treatment that has
the highest marginal rate of return compared to the farmer's
practice. If you were to stop at 40 N, you would be
eliminating a possibility for the farmer to earn higher net
benefits.


Notice also that the recommendation is not the treatment
with highest net benefits (120 N). If you skip steps in
calculating the MRR you would find that, compared to 0 N,
120 N has an acceptable rate of return (106%). That is


490 400 90
85 0 106%
85 0 85

Treatment Net Benefits Costs that Vary MRR
ON 400 0 -
200%
40 N 460 30
83%-106%
80 N 485 60
-20%
120 N 490 85


This illustrates the problem with skipping steps in the
marginal analysis. The farmer does not have to choose
between 0 N and 120 N, but can choose any level in between.
It was shown that going from 0 N to 40 N produces an
acceptable rate of return, and going from 40 N to 80 N also
gives an acceptable rate of return on the investment in this
second quantity of fertilizer. If instead 120 N was
recommended, the farmer would need to invest an extra $25
(above his investment in 80 N) to get a return of only $5,
or 20%. The farmer would say that it would be better to
invest in 80 N and then use that extra $25 to invest in
something that will give a better return. This might be
insecticide for his crop, medicine for his animals, or many
other possibilities.









Another Case
If the net benefit curve is not smooth, then extra care is
required for its interpretation. If, as you follow the
curve in the direction of increasing net benefits, the MRR
falls below the minimum rate of return, but a subsequent MRR
is above the minimum rate, then you must take an extra step.
You must calculate the MRR between the last acceptable
treatment and the next treatment associated with a MRR above
the minimum rate of return.




EXAMPLE 2


Insectici
(Min:
Treatment
No insecticide

Insecticide A

Insecticide B

Insecticide C

500





z 450---


4- 0
U)
.)

S400


de Experiment
imum rate of return = 40%)
TCV NB
0 350


35

75

105


420

430

475


MRR

S200%

- 25%
-- 79%
- 50%


Total Costs That Vary ($/ha)








In this case insecticide B would definitely not be the
recommendation. In order to test whether insecticide C
should be the recommendation you must calculate the MRR
between A and C. That is:


475 420 55 79%
105 35 70


Because 79% is above the minimum rate of return (40%), you
can recommend insecticide C to the farmers.










B. Using Residuals to Interpret Net Benefit Curves

Another way of deriving recommendations from a net benefit
curve is the following:


List the non-dominated treatments in order of increasing
variable costs. In the first column place the net benefits,
in the second the variable costs, and in the third column
list the minimum return on the investment acceptable to the
farmer. Figures in the 3rd column are calculated by
multiplying the minimum rate of return by the variable costs
associated with the treatment. The fourth column is the
residual after accounting for the minimum return. This is
calculated by subtracting column (3) from column (1). The
treatment with the highest residual is the recommendation.


This method will be illustrated using the previous two
examples.








EXAMPLE 1

(Nitrogen experiment)


(1) (2) (3) (4)
Minimum return
on investment Residual after
acceptable to accounting for
Net Total Costs farmer minimum return
Treatment Benefits that Vary 40% x (2) (1) (3)
0 N 400 0 0 400
40 N 460 30 12 448
80 N 485 60 24 461 *
120 N 490 85 34 456


The treatment with the highest residual after repaying all
the costs that vary, and the costs of capital and
management, is 80 N, with a residual of $461. This is the
same treatment that was recommended through the graphical
interpretation.


The residuals are useful for helping to understand the two
questions discussed in the graphical interpretation of this
experiment:


i) Why not choose the treatment with the highest
marginal rate of return, compared to the farmer's
treatment? Column 4 shows that the residual for
40 N is lower than for 80 N. By using 40 N, the
farmer is missing an opportunity to earn more
money per hectare.


ii) Why not choose the treatment with the highest net
benefits? Column 4 shows clearly that if the
farmer invests in 120 N, he actually ends up with
$5 less per hectare, after paying the costs of
fertilizer, labor, capital and management, than
when he invests in 80 N.









EXAMPLE 2


(Insecticide experiment)


(1)



Net
Treatment Benefits
No insecti-
cide 350


Insecticide
A

Insecticide
B

Insecticide
C


(2) (3) (4)
Minimum return
on investment Residual after
acceptable to accounting for
Total Costs farmer minimum return
that Vary 40% x (2) (1) (3)

0 0 350


420


430


433 *


In this example, the treatment with the highest residual
after repaying all the costs that vary, and the costs of
capital and management, is insecticide C. Again, this is
the treatment recommended by graphical interpretation.











EXERCISE 14.1

The following are the results of 40 fertilizer trials
planted over 3 years in one recommendation domain.
Statistical analysis shows significant response for both N
and P. Conduct a dominance analysis, draw the net benefit
curve, and use marginal analysis to make a recommendation to
farmers. The minimum rate of return is 40%.


Net Benefit Costs that Vary
Treatment ($/ha) ($/ha)
NO PO* 500 0
NO P40 480 91
N40 PO 610 99
N40 P40 520 178
N80 PO 675 186
N80 P40 580 265
N120 PO 420 273
N120 P40 350 352


* Farmer's practice











EXERCISE 14.2


The following are the results of five N x P experiments
planted in one year in a single recommendation domain.
Statistical analysis shows significant response for both N
and P. Conduct a dominance analysis, draw the net benefit
curve, and use marginal analysis to help decide what levels
of fertilizer researchers should experiment with next year.
The minimum rate of return is 100%


Nitrogen x


Phosphorus Experiment


CV($/ha)
0


Treatment

1.NOP0*


2.N50P 0

3.N100 0
100o*


5.N100P50


6.N100P75


7.N100 100


* Farmer's


100


100


150


175


200


NB($/ha)
800


950


965


945


1065


1075


1040


practice












EXERCISE 14.3


The following are results of 25 trials planted over 2 years
in one recommendation domain. They look at the effects of
improved variety, weed control, and fertilization. If the
minimum rate of return is 100%, what should be recommended
to farmers?


Variety
0


1


Weed
Control
0


0


Fertili-
zation CV($/ha) NB($/ha)
0 0 625 -


685 =


72


79


141


600%


S197%
807 -


782 D I-


907 -


145%


(0 = Farmer's practice 1 = improved practice)




900-
145 %


S800- 3
197 % 04


MO
z c-


50 100 150
Total Cost That Vary ($/ha)












EXERCISE 14.4


In one recommendation domain researchers planted four
insecticide experiments. The response to insecticide was
statistically significant. The results of the partial
budget are shown below. If the minimum rate of return is
100%, what would you recommend that researchers do the
following year?


Treatment
1. No insect control *

2. Furadan (at planting)

3. Orthene (granular)

4. Furadan + Orthene

* Farmer's practice




750-



S740-

0 267
730-
4- 25 %
a)^ -^


CV ($/ha)
0

32

35

67


NB ($/ha)
722
25%
730
73 267%
738
752 50%
752 -


Total Cost That Vary ($/ha)











EXERCISE 14.5


Researchers planted 10 seeding method by fertilizer
experiments in wheat in one recommendation domain. The
results of the marginal analysis are shown below. Minimum
rate of return is 100%. What should they recommend to
farmers?


Fertili-
Seeding Method zation CV($/ha) NB ($/ha)
1. Broadcast 0-0 240 630
172%
2. Drill 60-0 287 711

3. Drill 60-30 319 756 141%

(Farmer's practice = Broadcast; 40-0)




750- 3

141%




710- 2





7O
4-
S6f 72 %
Z 670-1


Total Cost That Vary ($/ha)








15. Partial Budgets
and Fixed Costs

It was pointed out at the beginning of this workbook that
the method of economic analysis presented here was based on
partial budgets. When constructing a partial budget, you do
not have to be concerned about the fixed costs. For
example, in a fertilizer experiment you only have to budget
for the cost of fertilizer and the labor to apply it, rather
than worry as well about cost of seed, land preparation,
weeding, and all of the other fixed costs that do not vary
by treatment. You can do this because in marginal analysis
you are only interested in the differences in costs and
benefits between treatments, not in their absolute values.




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