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LIBRARY
Michigan State

UniversitZI-J

 

 

 

This is to certify that the

dissertation entitled
AN ANALYSIS OF THE RELATIVE ECONOMICS OF SELECTED CROP SYSTEMS

ACCOUNTING FOR INTERDEPENDENT CASH FLOWS ARISING FROM
DIFFERENTIAL INTERTEMPORAL SOIL PRODUCTIVITY

presented by

Robert John Procter

has been accepted towards fulfillment
of the requirements for

 

 

Ph.D . degree in Agricultural Economics

Mom '

Major professor

Date December 1, 1987

 

MS U i: an Affirmative Action/Equal Opportunity Institution 0-12771

 

 

 

 

IVIESI_J RETURNING MATERIALS:
Place in book drop to
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AN ANALYSIS OF THE RELATIVE ECONOMICS OF SELECTED CROP SYSTEMS

ACCOUNTING FOR INTERDEPENDENT CASH FLOWS ARISING FROM

DIFFERENTIAL INTERTEMPORAL SOIL PRODUCTIVITY

BY

Robert John Procter

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultural Economics

1988

ABSTRACT

AN ANALYSIS OF THE RELATIVE ECONOMICS OF SELECTED CROP SYSTEMS
ACCOUNTING FOR INTERDEPENDENT CASH FLOWS ARISING FROM
DIFFERENTIAL INTERTEMPORAL SOIL PRODUCTIVITY
BY

Robert John Procter

This research has five inter-related components. First, a
review and critique of existing investment/disinvestment models
will be presented. Second, a review and critique of previously
used modeling approaches is presented. Third, a reformulation of
an existing investment/disinvestment model will be presented.
Finially, a simulation model will be constructed which is
consistent with the underlying analytical model.

The review of existing investment models separates these
models into independent and interdependent cash flow models. It
is argued that the independent cash flow models are not really
applicable to the problem being studied. One interdependent cash
flow model is reviewed and critiqued. Based in part on this
critique, an alternative formulation of this model is presented.

The review of selected modeling approaches separates these
models into two categories: Math Programming and Simulation
models. Generally, the Math Programming models do a better job of

describing the economics of competing production proactices at a

Robert John Procter

point in time. The simulation models tend to do a better Job at
modeling the dynamics of the interaction between alternative rates
of crop system soil loss and system cash flow.

The simulation model formulated in this research makes several
contributions to existing models. First, initial steps at
endogenizing input use are made. Further, this model calculates
relative cash flows by comparing two systems of differential
erosivity, and not requiring one system to be in a steady state.
Third, the model can study the asset switching problem.

The model is then used to study the relative economics of
agternative moldboard and chisel plow crOp systems in two areas of
Michigan. In the area characterized by relatively flat terrain,
and deep fertile soil, no chisel plow system could compete with
the moldboard plow system. In another area of Michigan
characterised by rolling terrain and varying soil depths, some
chisel plow systems are competative with moldbnoard plow systems.
Further, the sooner that the chisel plow system was adapted, the
closer were the profit estimates of the moldboard/chisel plow
combination to that of the comparable chisel plow system, when the

chisel plow was used from the beginning of the analysis.

Copyright by
Robert John Procter

1988

ACKNOWLEDGEMENTS

Larry Libby, J. Roy Black, A. Allan Schmid, and Lester V.
Manderscheid composed my Guidance and Dissertation Committies.
Larry and Roy provided the propulsion to lift this research off
the ground. They all were instrumental in providing several mid -
course corrections which directed the focus of the researcher to a
coherent set of integrable research issues.

Several professionals in the Economic Research Service and in
the Soil Conservation Service of the United States Department of
Agriculture provided invaluable guidance in sorting through some
of the more turbid technical issues of crops, soils, and
production agriculture. Most notable among this group was Dan
Kugler who helped cultivate my understanding of these technical
issues.

My freshman english composition instructor must also be
acknowledged fer he had the "vision" to asset that I would attend
graduate school. Unfortunately, his lessons did not stay with me
as did his vision.

In passing, when one stops and thinks about what has just been
completed, deciding whether or not what you did was good for you
is sort of like the child who has just been administered a good

V

dose of cod liver oil being asked, "now wasn't that good?"

Undoubtedly, one's perceptions mellow with age.

vi

TABLE OF CONTENTS

Page
LIST OF TABLES ....... . ....... . ........ . ......... . ........ .. x
LIST OF PIMES ..... O ........ O O O O O OOOOOOOOOOOOOOOOOOOOOOOOO x1
CHAPTER ONE - FOCUS OF THE RESEARCH
1.1 Introduction ...... ..... .......................... 1
1.2 Problem Statement .......... ...... ......... ....... 1
1.3 Objectives of the Study.......................... 2
1.4 Overview of the Thesis. .......................... 3

CHAPTER TWO ’ REVIEW OF SELECTED INVESTMENT/DISINVESTMENT
MODELS AND EMPIRICAL MODELS OF SOIL LOSS/
CROP SYSTEM ECONOMICS

2 1 IntrwuctionOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO 5
2.2 Independent versus Interdependent
asset caSh Flws O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 5

2.3 Independent Cash Flow Models .......... . ........ .. 8
2.3.1 Myopic Rule ............. ... ...... . ..... ... 8
2.3.2 Comparison of Net Present Values

or Annuitie .................. ...... ....... 9
2.3.3 Perrin‘s Approach ....... .................. 11

2.3.4 Summary of Independent Cash Flow Models... 13
2.4 Interdependent Cash Flow Model -

walker' 3 Method ........................... ....... 13
2.5 Summary of Investment Models ................... . 17
2.6 Review of Selected Empirical Analysis of 8011

Loss and Crop System Economics ........ .......... 18

2.6.1 Math Programming Approaches .............. 19
2.6.2 Simulation Approaches .................... 22
2.7 smry 0.0........OOOOOOOOOOOOOOOOO0.0.0.0000... 24

CHAPTER THREE - MANAGEMENT DECISION MAKING WITH
INTERDEPENDENT CASH FLOWS - A REFORMULATION
3.1 Introduction .............................. . ...... 28

vii

3.2 Intertemporal Statics Approximation of a Dynamic

Process ......................................... 28
3.3 Requirements of an Alternative Approach ......... . 32
3.4 Adjusting for Interdependent Cash Flows ......... 32
3.5 Mathematical Derivation of the Decision Rule .... 33
3.6 Transition Analysis when Multiple Switches

are P0831b1e000.....OOOOOOOOOOOOOOOO......OOOO... 36
3.7 Decision Making for the Owner versus
the TenantOOOOOO.......0.0.........OOOOOOOOOOOOOO 38

3.8 Selection of the Time Horizon ...... .. ....... ..... 40
3.9 Generalizability of the Model ........... ......... 41
3.10 Summary ......................................... 41

CHAPTER FOUR - SIMULATION MODEL FORMULATION

4.1 Introduction ....... ... ........................... 43
4.2 This Models' Contribution to Studying
Soil Loss and Crop System Economics ........... .. 43
4.3 Structure of the Computer Model ............ . ..... 44
4.3.1 Macro Overview of the Model..... ....... ... 45
4.3.2 Structure of Each Sub - Program..... ...... 47
4.3.2.1 Input Prompt Program .................. 47
4. 3. 2. 2 Soil Loss Calculation Program .......... 49
4. 3.2.3 Soil Productivity Program ....... . ...... 49
4. 3.2.4 Input Use Program ............. . ........ 53
4. 3. 2.5 Cash Flow Program ...................... 56
4. 3. 2. 6 Write Program .......................... 56
4.4 Summary ......................................... 58

CHAPTER FIVE - ANALYSIS OF ALTERNATIVES

5.1 Introduction .................................... 59
5.2 Alternative Scenarios ........................... 59
5.3 Saginaw Results ................................. 61
5.4 St. Joseph Results ....... . ...................... 65
5.5 Conclusions ..................................... 68

CHAPTER SIX - SUMMARY AND CONCLUSIONS

6.1Introduction..................................... 69
6. 2 Literature Review ................. ...... . ...... 69
6. 3 mcision Making with Interdependent Cash Flows .. 69
6. 4S Simulation Model Formulation .. ................ . 7O
6. 5 Empirical Analysis ............................... 71
6. 6 Conclusions ..................................... 71

viii

CHAPTER SEVEN - FUTURE RESEARCH DIRECTIONS

7.1 Introduction ..................................... 77
7.2 Model Structure Development .............. ..... ... 77
7.2.1 Incorporating Tax/Financial Structure ...... 78
7.2.2 Expand the Range of Possible Activities..... 78
7.2.3 Endogenize Equipment Selection in
the Productivity Analysis .................. 80
7.2.4 Endogenize Heather ................ ........ . 80
7.3 Data Base Development ............................ 81
7.3.1 Crop Rotation. Tillage Method.
Pesticide - Fertilizer Regime........ ..... .. 81
7.3.2 Crop Rotation. Tillage Method. 5011
Type. Initial Crop Yield.................... 82
7.3.3 Cost. Transition. and Selecting a
Soil Conserving Strategy .................. 82

APPENDIX .................................................. 83

BIBLIOGRAPHY ............................................... 92

ix

5.1

5.2

5.3

A.1

A02

A.3

A.4

A.5

LIST OF TABLES

IQPLE Egg;
Characteristics of Alternative Scenarios .............. 62

Cash Flow and Soil Loss - Saginaw County
scenarioSOOOOOOOOO0.0000000000000000000000000.00.....0 64

Cash Flow and Soil Loss - St. Joseph County
Scenarios ............................................. 67

Factor Product Prices for Inputs/Outputs Whose
Price/Cost are Non-Producer Dependent ........... . ..... 85

Producer Dependent Factor Prices. ............... . ..... 87

Crop Rotations. Acreage Allocation.
Initial Yields ......................... . .............. 88

Herbicide. Fertilizer. and Seed Use By Crop.
Crop Rotation. and Tillage Method ..................... 90

Crop Rotation/Farm Practice. CP. Factors for
Alternative Crop Rotations. Tillage Methods.
and Geographic Locations .............................. 91

LIST OF FIGURES

2192!: Base

2.1 Illustration of Two Assets with Interdependent

Cash Flows...................................... ...... 7
4.1 Macro Flowchart ....................................... 46
4.2 Input Prompt Program Flowchart..... ................... 48
4.3 Soil Loss Ca1cu1ation Flowchart ....................... 50
4.4 Soil Productivity - Yield Calculation

Program Flowchart....................... ....... ....... 51
4.5 Input Use Program Flowchart............. ....... . ...... 54
4.6 Economic Analysis Program Flowchart ............. ...... 55
4.7 Output Program Flowchart .............................. 57

xi

CHAPTER ONE

FOCUS OF THE RESEARCH

1.1 Introduction

Soil loss and soil productivity relationships have long been
a concern to farmers, economists, scientists, and policy
makers. Researchers are continuing to try to improve their
understanding of the relation between soil loss today and
productivity tomorrow. Agricultural economists translate this
physical relation into an issue of resource management by the
producer by studying the relation between producer goals,
alternative management options, and the impact of differential
rates of soil loss on goal attainment by the decision maker.
This research will attempt to advance the thinking of analysts

who pose the issue as does the agricultural economist.

1.2 Problem Statement

Asset adoption/sale decision making models have generally
assumed that the level of net return in a particular year to a
challenger durable good is independent of how long the currently
held asset is kept. Relying on this premise, backward induction
solution techniques are applied to endogenously determine how
long each asset should be kept.

Studying adoption/sale decisions assuming cash flows are

2
interdependent is a more complex problem. Interdependent cash
flows arise when, because of soil loss, today's management
decisions will likely affect tomorrow's cash flows. This
researcher knows of no analytic framework which can study the
asset switch problem using an intertemporal statics framework
which is constructed in such a way as to allow for
interdependent cash flows.

Moving to the empirical analysis, the reader will come to
see that existing one period and multi - period models have not
adequately dealt with the relation between crop systems with
interdependent cash flows and asset decision making. Of
critical importance is capturing the effect of a crop systems'
differential rate of soil loss and net returns to the operator

and/or owner.

1.3 Objectives of the Study

When this research was conceived, the questions raised were
concerned with furthering the understanding of the process of
switching from one machinery complement to a new machinery
complement, either with or without aditional changes in the
farming enterprise. It was thought that how a producer went
about switching machinery complements was probably an important
part of the decision to switch machinery complements.

After some initial investigation, a slightly different but
related set of issues surfaced. One reason for the slight shift
in focus was the observation that there didn't appear to be an

appropriate analytic and empirical framework to apply to study

3

when producers choose to switch machinery complements. From
this observation was derived the overriding objective of this
research. The primary objective is to develop a workable
conceptual and analytic framework for studying investment
decision making when asset cash flows are interdependent.

A related objective is to try to further clarify the
economic roots of the transition problem. How can researchers
begin to formulate the process of switching from one machinery
complement to another machinery complement? Another objective
is to clarify the relationships between soil loss and producer
investment decisionmaking, and the impact of that relationship
on the relative profitability of various courses of action. A
fourth objective is to draw some inferences for erosion control
policy using the information produced by this study. These
inferences will be limited to the farm prodictivity dimension of

selected policies.

1.“ Overview of the Thesis

Chapter two presents a review of selected approaches to the
(1) asset investment disinvestment (ID) problem, and (2)
empirical analysis of the relation between soil loss and net
returns to farm enterprises. Subsequent model deveIOpment is
based, in part, on how the existing literature addresses
critical aspects of the crop system selection] soil loss/
intertemporal productivity problem.

Chapter three reformulates an existing decision rule used to

answer the question of when one asset should be replaced by

u
another, when cash flows are interdependent. First, the
requirements of the new approach are specified. Next, the
approach is formulated for the cases of a single transition
(switch between two different crop systems). Lastly, the
approach is generalized to the problem of more than one
transition within a given time horizon.

Chapter four presents a discussion of the simulation model
which is developed and applied in this research. What
contributions the model makes to the study of (a) the relative
economics of two or more mutually exclusive crop systems, and
(b) the relative economics of combinations of mutually exclusive
crOp systems, and intertemporal productivity are presented.
Lastly, a more detailed discussion of each of the models'
programs which comprise the model.

Chapter five presents the alternative management scenarios
which are analyzed with the model, the results of the analysis,
and a discussion of the results. The empirical analysis is
structured to (1) provide information to the research process on
the relationship between the profitability of alternative
management scenarios and the crop system/physical conditions
assumed in each scenario, and (2) to illustrate how the model
may be applied to the study of the relation between crop system
profitability/ soil loss/ and intertemporal soil productivity.

Chapter six presents a summary of the research and a set of

conclusions. Finally, chapter seven identifies some issues for

future research.

CHAPTER TWO

REVIEW OF SELECTED INVESTMENT/DISINVESTMENT MODELS

EMPIRICAL MODELS OF SOILAEUSS/CROP SYSTEM ECONOMICS
2.1 Introduction

This chapter provides the foundation for the remainder of
this dissertation. Alternative approaches to the
Investment/Disinvestment (ID) problem are first reviewed. Next,
a review of selected empirical models used to study the relative
economics of alternative agricultural practices is presented.

Both independent and interdependent cash flow models are
included in the review of alternative approaches to the ID
problem. Prior to reviewing an interdependent cash flow model,
the concept of interdependence between asset cash flows is
discussed and illustrated. Both Math Programming and Simulation
methods are included in the review of the selected empirical

models.

2.2 Independent versus Interdependent Asset Cash Flows

Analysis of the problem of capital allocation has included a
focus on the problem of when to switch asset holdings.
Generally referred to as the investment/disinvestment problem,
the decision maker is attempting to determine the point in time

when the Opportunity cost of holding the asset for one more

6
period exceeds the Opportunity cost of switching assets during
this period.

Most of the approaches to this problem have assumed that the
level of cash flows in any subsequent year for the challenger
(asset which may be required) are independent of the point in
time when the assets are switched.

Here, interdependent cash flows are assumed to exist when
the level of annual net returns to the challenger in a given
year vary as a function of when the asset trade occurs.1 That
is,

(2.1) dNR(t)/dt. f‘O v t=t*, . . ., r,

Where,
NR(t)=Net returns to the new asset in post trade year,t;
T=Length of analysis.

Figure 2.1 is a representation of both independent and
interdependent cash flows. For purposes of illustration,
assume that the two assets are two machinery complements.
Tillage complement A is more erosive than the alternative
complement, denoted complement B. As the soil depth declines,
yield also declines. Finally, only the change in yield can
affect net returns to complement B, NRb(t), between when
asset B is held from t=O and when asset B is adOpted in a later
time period. While these assumptions are more restrictive than
what one would want to assume, they simplify the analysis and
allow us to focus on the relationship between alternative
transition periods and the annual returns to the new asset.

As Figure 2.1 indicates, the solid line is assumed to

represent the level of net returns to complement A across

 

NR(I)

 

   

Asset A adopted at t=0
------- Asset 3 adopted at t=1
...... Asset B adopted at t=0

 

Figure 2.1

Illustration of Two Assets with Interdependent Cash Flows

8
time. Initially, the net returns to complement B, indicated by
the dotted line, are assumed to lie below those of complement
A. Later, the exact Opposite situation arises. If one conducts
the capital budgeting analysis assuming independent cash flows,
,the transition period is determined using the aformentioned
curves. If, on the other hand, the analysis is conducted
incorporating interdependent cash flows, one needs to consider
the cash flow for complement B indicated by the dashed line.
The sum of the vertical distance between the dotted and dashed
curves, appropriately discounted, from some potential switch
year to the end of the period, represents a component of the
opportunity cost of deciding not to switch from complement A to
complement B at the potential switch year.2 Reiterating, this
sum of discounted differences in annual net returns, when the
annual differences arise from interdependence between when asset
A is traded and the annual net returns to asset B, are omitted
from the analysis if the asset cash flow for the challenger is

assumed to be independent.

2.3 Independent Cash Flow Models
Three independent asset cash flow models will be
reviewed. These are: (l) the Myopic Rule, (2) comparison of Net

Present Values (NPV), and (3) Perrin's Approach.3

2.3.1 Myopic Rule
Harsh, Conner, and Schwab propose an ID rule which is

relatively simple and requires little information to

 

9
implement.” They propose that the maximum annuity of the
challenger be calculated and compared to the discounted value of
the next period's return for the currently held asset.5 When
the maximum annuity of the challenger is at least as large as
next period's discounted returns of the existing asset, it is
time to switch assets. Equation (2.2) depicts this rule,
(2.2) NRC/(1+r)t6 Max [("Rcu(1’/‘1*'”'AF1,1~"

([ unch(t)/(1+r)tJ'Ar ).

2,r

t
...,([ NRch(t)/(l+r) ]'AFT,r)]

Where,
AFt’rzAnnuity factor for asset held for T years,
at interest rate r;
NRc(t):Net returns of currently held asset, in year t;
NRch(t)=Net returns to challenger, in year t.

There are three necessary conditions for this rule to result
in a correct investment decision. First, only one replacement
is being considered.6 Second, the level of NRch(t) V
t=l,...,T is independent of the point in time when the
transition occurs. Third, NRc(t) is a smooth concave function
between [0,T].

2.3.2 Comparison of Net Present Values or Annuities7

Comparing the net present values (NPV's) or annuities of
the challenger(s) with that of the currently held asset marks
the next step in complexity. Equation (2.3) formulates the

problem for the case of NPV's.

rt 1

(2.3) NPV SJCNRa(t)e'

- ‘flL - -
+ e ”Tlgnnbum ”at - 1(1'1) + SVb(T2)e

dt - Ia(0) + SVa(r1)e"T

T'TZ:I

10

Where,
13(0) = Capital cost of asset A, at t = O;

Ib(T1) = Capital cost of asset B, when trade occurs;
NRa(t) : Net returns to asset A, in year t;
NRb(t) = Net returns to asset B, in year t;

SVa(T1) = Salvage value for asset A, in year T1;
SVb(T2) = Salvage value for asset B, in year T2.

The first step in calculating the NPV in equation (2.3)

is to solve for the life of each asset, denoted T1 and

T2. First, the second bracketed term, which denotes the NPV

of some asset B held for T2 years, is differentiated with

respect to T2. When equation (2.A) holds, the Optimal time

to keep asset B has been found.

-rt
(2.“) 0 = d(NPVb)/dT2 = NRb(t)e
-rt
+ (dSVb(T2)/dT2)e -
rSVb(T2)e-rT2.

The last term in equation (2.“) represents the opportunity
cost of keeping B one more period. The entire equation is

part of the opportunity cost Of keeping A one more period.

Now it is possible to solve for T the Optimal life of the

1!
first asset. Substituting equation (2.M) into the brackets

in equation (2.3) and differentiating equation (2.3) by T1,

equation (2.5) is obtained.

(2.5) 0 = d<NPVa)/dr1 = una(t)e'rt .

rT rTl

(dSVa(T1)/dT1)e- 1 - rSVa(T1)e-
- re’rT1[NPVb,T2].
Where,
NPVb,T2=Net present value for asset B, when
asset B is kept for T2 years.
By rearranging equation (2.5), equation (2.6) is obtained

in which the terms on the left side of the equation indicate

11
the discounted marginal net returns from holding asset A one
more period, and the terms on the right side of the equal

sign represent the opportunity cost of keeping asset A one

more period.

(2.6) NRa(t)e'rt + [d(SVa(T1))/drl)]e”T1

rSVa(T1)e'rTl + re'rT

l[NPVb,T2].

Again, the question of what are the necessary conditions
for a decision to switch assets based on equation (2.6) to be
a correct decision must be raised. First, returning to
equation (2.3), it was implicitly assumed that only one

replacement was going to occur. At T the owner

2.
disinvests in asset B, and closes up the shOp.Second, it was
also implicitly assumed that the returns to asset B in year
t, NRb(t), are not dependent on the transition period between
assets A and B. Two results of this analysis are (l) the
existence of a replacement asset shortens the period of time
for which a currently held asset is kept, assuming NPVb,T2
I O, and (2) how long asset A is held depends on the optimal
life of B. This method of solving the problem of how long to

keep each asset is referred to as the method of backward

induction.

2.3.3 Perrin's Approach

Perrin8 wanted to derive analytical solutions to the
problem of when to switch assets. While only one of his
approaches is summarized here, the same general framework

applies to other models he derived. Here, Perrin's model

12
assumes an infinite number of replacements and each asset is
identical to the one it replaced. Using the same terms as
were used in equation (2.3), his approach is represented by
equation (2.7),

'11
(2.7) NPV sjéRa(t)e

"tat - 1(0) + SVa(T1)e-rTl

‘f
+ e'rTl[ NRa(t)e-rtdt - 1(0) +

O
SVa(rl)e”T1]

+ e-rTnE£§%a(t)e-rtdt - 1(0)
+ SVa(Tl)e"T1]
Since each asset was assumed to be identical, equation (2.7)
could be simplified. Equation (2.8) reflects the simplified

version of equation (2.7).

(2.8) npv = (1.e"T1 + ... + e-rTl)[ NRa(t)e-rtdt
a
- x(0) + SVa(Tl)e"T1J.
Assuming n approaches infinity, equation (2.9) is Obtained.

The apprOpriate length of time to hold each asset, denoted

T1, is determined by differentiating equation (2.9) and
finding the T where dNPV/dT = 0.
1 l
-rTl 1i -rt
(2.9) NPV = [1/(1 - e )[ NRa(t)e dt - 1(0)
9’

+ SVa(T1)e'rT1]

Since (1) each asset is assumed to be the same, and (2) the
net returns to any one of the A assets in year t, NRa(t),
is independent of when asset switching occurs, once T is

1

determined for the last asset, you have determined the lives

13
of all the assets.
2.3.“ Summary of Independent Cash Flow Models

All of the above methods have their advantages and
disadvantages. The myopic rule is easy to implement, but one
must be careful when acting on the results of the rule.
Comparing NPV's is an improvement over the Myopic Rule
because more of the cash flow stream for the currently held
asset is included. The comparison of NPV's rule raised two
important questions: (1) how many trades will take place, and
(2) what is the pattern Of net returns to each asset? Perrin
addressed these two questions in his analysis. Perrin's
approach was necessary in the light of his goal to perform
comparative statics analysis.

All of the above models assumed that cash flows are
independent of each other. This assumption may pose serious
problems in the application of ID rules to asset switching in
the soil erosion area. In the next section, Walker's Method
will be presented. This method relaxes the assumption about
the independence between the point in time when assets are

switched and the cash flow pattern of the new asset(s).

2.“ Interdependent Cash Flow Model - Walker's Method

Walker attempted to devise an analytic approach to ID
analysis which could capture the component of opportunity
cost which reflects the change in the discounted value of net
returns to the challenger with changes in the time when

adoption occurs. First, a review of his formulation of the

1A
problem will be presented. Second, his formulation will be
evaluated.

Equation (2.10) to (2.12) comprise the heart of his
analysis. Referring first to equation (2.10), this equation
represents the NPV of using the erosive technology in the
current period and switching to the conserving technology for
all subsequent, T-l, periods. Next,equation (2.11)
represents the NPV of using the conserving technology from
the current period and in all subsequent, T-l, periods.
Equation (2.12) represents the decision rule which is used to
find the point in time when asset switching should occur.
When DIFF(t) 0, asset switching should occur.

(2.10) EPFT =-P*Ye(t,D(t)) - Ce(t,D(t)) +
731
£[(P"Yc(t+i,d(t))
evil. 1:
-C0(t+i,D(t)))/(l+r) 1
(2.11) CPFT = P'Yc(t,D(t-l)) - Cc(t,D(t-l))
:{I(P*Yc(t+i ,D(t-i))
f'gc'IC:(t’.4-:l,D(l’.--l)))/(i-I-r)t]

(2.12) DIFF(t) = EPFT - CPFT

Where,

Cc(t,D(*)) = Variable production cost, including equipment
ownership cost for the conserving technology,
in period t, with soil depth D(*);

Ce(t,D(')) = Variable production cost, including equipment
ownership cost for the erosive technology,
in period t, with soil depth D(');

P = Output price;

'1
ll

Discount rate;

15

Yc(t+i,D(*)) = Yield using the conserving technology, in
period t+i, with soil depth D(*);

Ye(t,D(*)) = Yield using the erosive technology, in
period t, with soil depth D(*).9
Walker presents a generalized version of equation (2.12)
which allows for multiple crops and net changes in soil depth
for the conserving practice is used. This is presented in
equation (2.13).
(2.13) Diff(t) = P'[Yej(t, (t-1)) - ch(t,D(t-1))]
- [Cej(t,D(t-l)) - CcJ(t,D(t-l))]/
-}EP*[ch(t+i,D(t+i-1,t-1) - ch(t+i,D(t+i-1,t))]
JbLEc(t+i,D(t+i-1,t)) - Cc(t+i,D(t+i-1,t-l))]/.

Where,

D(n,m) = Projected top soil depth at the end of year h,
after using the erosive practice for m years;

Number of crops in the rotation;

Crop j.

h
J

A number of comments regarding Walker's method are in
order. First, Walker's approach violates the conditions of a
staged problem by varying the starting and ending dates used in
selecting the set of action choices. Staged problems, Of which
this is one, are solved after the starting and ending conditions
have been specified. Then, if the starting and/or ending
conditions are varied, one can examine how the action choices
vary, in turn. Walker's approach violates this set of
conditions by varying the start and ending dates used in
selecting the Optimum set of action choices.

For example, assume T=20, and t =1980. Here, EPFT and

0
CPFT will be determined using data covering the period

1980-2000. According to his discussion of how to implement his

approach, if the decision is made to keep the erosive asset for

l6
atleast one more period (until atleast 1982), the next analysis
will cover the period 1981-2001. To be consistent with the
formulation of staged problems, the analysis should cover only
1980-2000 and explore this space for the optimal trade year.
Then, the sensitivity of the trade year to alternative time
horizons can be determined. What the decision maker needs is
the present values in 1980 of CPFT and EPFT calculated assuming
various trade years and time horizons, in either nominal or real
dollars. In addition, Walker's approach implies that a farmer
is concerned only with the yearly decision, and not the
cumulative effect on productivity resulting from his/her
decision. A well informed decision on the part of the farmer is
based on the net present value of various future actions, at one
point in time. Walker's approach does not provide that
information.

Second, given the way Walker's approach addresses the asset
trade problem, a decision to switch assets can result in a less
profitable asset being adopted. This is because his analysis
does not include the NPV of holding the more erosive asset until
T-l. In this case, Walker's rule would suggest that a trade
should occur. Since this decision is based on information which
does not include the net returns to the currently held asset
beyond the current period, there is no way of knowing that a
decision to switch is valid. The greater the effect of
increased erosion from the more erosive tillage equipment, on
the net returns to the challenger, and the lower are the net

returns to the erosive asset this year relative to future years,

17
the greater is the chance that a less profitable asset will be
adapted.

Third, Walker defines the various cost functions as
depicting the variable cost of production including e equipment
ownership costs. This cannot be the case. The analysis needs a
term reflecting initial capital cost, or the cost functions must
be redefined as total cost functions, reflecting both the
variable cost of production, and the annualized capital cost,
net of salvage value.

Fourth, it should be assumed that asset salvage value may be
sensitive to when trading occurs. In turn, a discussion of the
relation between asset switching and asset salvage value should
be included in the analysis.

Finally, according to Walker, the correct time to switch is
when DIFF(t) 0.10 This rule implicitly assumes that once the
decision rule is satisfied, the underlying cash flow streams of
the assets are such that no future period exists where a higher
level of NPV is attained for the combination of assets,ts when

the conserving technology is adopted later.

2.5 Summary of Investment Models

Walker's approach relaxed the assumption of independence of
asset cash flows. Perrin's approach made more explicit the
importance of (a) specifying the number of transitions which are
assumed to occur, and (b) the length of time an asset is held.
Making investments based on the NPV, or annuities, of the

competing investments was argued to base decision making on more

18
information than simply using the discounted net return to the
existing asset in the next period. The Myopic Rule was argued
to require the least amount of information of any of the
methods, but requires that the net returns to the existing asset
be a smooth concave function with one maxima over the domain of

the function.

2.6 Review of Selected Empirical Models of
Soil Loss and Crop System Economics

Mathematical Programming and Simulation analysis appear to
be the two predominant approaches used in the study of soil loss
and the economics of alternative cropping systems. The Math
Programming strategies emphasize the economics Of the underlying
production practices, and do not adequately address the dynamics
of the underlying physical process. Simulation models, on the
other hand,have tended to more adequately model the dynamics of
the physical process and pay less attention to the economic
analysis.

More substantive review of both of the above approaches
appears below. First, math programming approaches will be
reviewed, following by a review of selected simulation
approaches. In both cases, only the models' structure and
policy options are discussed. Conclusions were not summarized

because of our concern with problem formulation.

19
2.6.1 Math Programming Approaches

POpe, Arden, Bhide, and Ready11 report on a model they
developed which also forms the basis for several subsequent math
programming studies of alternative crOpping systems. This
particular model is a representative farm linear programming
(LP) model. Eighteen representative farms were constructed
using three criteria: (a) represent the full range of
erosiveness, (b) include the principle soil association areas,
and (c) represent the six major land resource areas in Iowa.
Each farm was defined on the basis of (a) soil resources; and
(b) possible tillage systems, crop rotations, and supporting
practices in Iowa.

The author states that the goal of the analysis is to
maximize before tax net returns to land, management, family
labor, and permanent livestock facilities. Where the soil tax
policy is modeled, the goal is to maximize after tax returns.

The model takes a whole farm perspective. Fifteen crop
rotations, five tillage systems, three supporting practices, and
two livestock activities formed the alternative activities which
could be modeled.Budgets were generated using the Oklahoma State
Budget Generator.

Further, the five year crop rotation was collapsed into one
year by calculating the average input/output coefficient for
each enterprise. The model also implicitly assumes that a
producer is starting out with a new operation today. Since the
LP model they develop is a one period model, changes in
productivity due to erosion cannot be captured by the analysis.

In addition, it must be assumed that the producer does not

20
engage in any other enterprises outside the model, or that they
are separable from the enterprises included in the model.

Banks, Bhide, Pope, and Ready12 report on a study which
explores the relation between tenure arrangements, capital
constraints, and farm size on the relative economics of various
cropping systems in Iowa. This analysis relies on the model
presented above.

Using an objective function of maximum before tax net
returns, in the absence of a soil loss tax, and an after tax
maximum net returns in the presence of a soil loss tax, their
analysis had four objectives. First, they wanted to analyze the
economics of various cropping systems from the perspective of
the (a) tenant, (b) owner - operator, and (c) landlord, under
various tenancy arrangements. Second, they wanted to study the
effect which alternative soil loss restrictions may have on net
returns and the incentives of various groups to pursue soil
conservation strategies. Third, they wanted to study the impact
of capital constraints on practice adoption. Lastly, they
wanted to explore for any relation between farm size and
practice adoption.

There were six alternative scenarios modeled for each of
five ownership/tenancy arrangements. The alternatives included
no restrictions, using a moldboard plow, restricting soil loss
to a pre - specified T level, and a soil loss tax set at
different levels, on a dollar/ton basis.

13

Olsen, Kent, Heady, Chen, and Meister conducted an

analysis of a fertilizer restriction and a ban on selected

21
insecticides on the production, sale, and distribution of
selected crops and livestock activities at the national level.
Using a quadratic programming (QP) approach, with an objective
of maximum net aggregate producer profit, the U.S. was segmented
into 10 producing regions and 103 consuming regions.
Production, transportation, and demand levels for the

various goods modeled in the analysis must conform to all the
standard assumptions of LP, except for one. Here, the use of QP
allows for some non - linearities to be incorporated into the
model. In this analysis, the total revenue functions are
assumed to be non - linear functions of at least the quantities
of own output.

Saygideger, Vocke, and Headylu also conducted an analysis
of the tradeoffs between production efficiency and soil loss
control using a multi - goal LP model. The trade - off was
between the cost of producing the food supply and maintaining a
land base and limits on soil loss. According to the authors,
three alternative approaches were modeled: (1) prior weighting
of the objectives, (2) exploration of the search space, and (3)
goal programming. Weights on the soil loss goal varied from a
low of zero to a high of twenty dollars.

Endogenous crops were barley, corn, corn silage, cotton,
legume, and non - legume hays, grain sorgham, sorgham silage,
soybeans, sugar beets, oats, and wheat in rotation.
Conservation practices were contouring, strip cropping, and
terracing. Lastly, three tillage practices were included:

conventional with residual removed, conventional without the

22

residual removed, and reduced till.

2.6.2 Simulation Approaches

Williams, Dyke, and Jones have developed a simulation model
useful in analyzing the relation between soil erosion and soil
productivity.15 Known as the EPIC model, the model simulates
the interaction of enviornmental and technological factors on
soil erosion, the impact of soil erosion on soil productivity,
the impact of soil productivity on crOp yield, and the economics
of the above process. There are eight components of the EPIC
model: hydrology, weather, erosion, nutrients, plant growth,
soil temperature, tillage, and economics. All calculations are
performed on a per hectar basis, using a daily time step.

Turning to the economics component, crop budgets are
generated using parts of the Oklahoma State budget generator.
Budgets are generated for a year or for the whole period of the
simulation. Inputs are divided into fixed and variable, with
machinery fixed cost being allocated to crops on an hour by hour
basis.

This model is a vast improvement over the LP models in terms
of how the physical system is modeled. The various subroutines
in the model combine to simulate daily plant growth, erosion due
to farming practices and weather, and the resulting economics of
the alternative crop systems.

Pierce et. al.16 have also develOped a soil - erosion

productivity model which can be used to calculate the

intertemporal soil depth - yield curve for a given crop system,

23
on a given soil type, having a particular set of soil
characteristics across horizons. This model operates on a
yearly time step calculating the change in soil depth, change in
soil productivity, change in crop yield, net revenues, and net
present value.

In this model, the rooting zone is assumed to be the
critical factor affecting plant develOpment. The only way that
weather affects yields is through the annual rate of soil loss.
Combining the yield calculation from the model with exogenously
specified annual costs and output prices, the annual net returns
and discounted net returns are calculated. In addition, the
model calculates the level of annual investment a producer can
make if the producer were to shift today from the system being
used to a steady - state system.

Both EPIC and this model are not optimizing models. These
models simply calculate the values of the endogenous variables
for a pre specified system. Like EPIC, this model has a general
structure which, with appropriate data, can be used to model any
given producers' circumstances. Of course, this is constrained
by the limits within the model itself.

Muhtar17

used a simulation approach in constructing a

model to select machinery complements which can perform a
specified set of operations at least cost, for a particular crop
rotation, on a specified soil type, at a specified confidence
level for completing the tasks within an alloted time period.

Three alternative tillage systems can be modeled: moldboard

plow, chisel plow, and no- till.

2A

In part, the model relies on producer provided data to
select an initial machinery complement, which is the smallest
complement able to perform the required Operations within the
number of available hours provided by the user, at the specified
confidence level. Then, the model iterates through alternative
machinery sizes to determine if a larger complement is capable
of performing the specified operations within the alloted time
at a lower total cost than the next smallest complement.

Some of the management and machinery assumptions underlying
the above analysis are:

1. Hours available on a given day for field work were set
based on actual farming practices in the area;

2. Suitable days for field work were grouped into calendar
weeks based on soil type and the probability level
desired by the user;

3. Implements were assigned to power units in the
following manner. Tillage and planting equipment were
assigned to tillage tractors. Other operations like
secondary tillage were assigned to utility tractors;

A. No limits were placed on the number of combines,
tractors, or implements;

5. Row crop machinery had to match one another.18

2.7 Summary

This chapter began with a review of a number of analytic
approaches to the problem of asset investments/disinvestment
decision making. First, several models were presented which
assume that the cash flow streams of competing assets are
independent of each other. Next, a model was presented which
relaxed the assumption of independent cash flows. The

assumptions of the various models were compared, and the

25

advantages and disadvantages of each approach was presented.

Next, several math programming and simulation models were
presented which have as their focus the economic analysis of
alternative crop systems and soil loss. A review of the
structure of each of these models was presented, as well as the
identification of the critical assumptions. From the review of
the analytical and empirical models, two general observations
were made. First, there is room to develOp a simulation model
which does a better job of applying capital theory principles
and accounting for interdependent cash flows in the analysis.
Second, an ID model needs to be developed which addresses the

criticisms leveled at Walker's analysis.

FOOTNOTES

1. This formulation of the problem is consistent with hw the
finance literature formulates the problem of selecting an
investment from among a set of investment from among a set of
investments whose cash flows are interdependent. For example,
see: Lawrence D. Schall and Charles C. Haley, Introduction to
Financial Management, 2nd Edition, (McGraw - Hill, New York,
1980). PP. 365.

2. Referring to Figure 2.1, the curve of annual cash flows
for asset B, when 8 is adopted at the beginning of period two,
does not begin at t=0 because asset A is held, and the decision
maker is confronted by the cash flow stream for asset A.
Further, additional cash flow schedules for asset B may exist if
one is considering switching from asset A to asset B at
different points in time.

3. Why Perrin's analysis is classified as it is will be
discussed below.

A. Their approach to the problem is based on earlier work by
Paris. Paris states that "the optimum time to replace is when
the marginal net revenue from the present enterprise is equal to
the highest amortized present value of anticipated net returns
from the following enterprise." See: J. Edwin Paris "Analytical
Techniques Used in Determining the Optimal Replacement Pattern,"
Journal of Farm Economics (l)l960:755-766.

5. Stephen Harsh, Larry Conner, and Gerald Schwab, Managing
the Farm Business, (Prentice-Hall, Englewood Cliffs, N.J.,
1981), p. 263.

6. Why this condition must be met will become clear when
Perrin's method is reviewed.

7. The approach used in this section has benefited from the
writings of Lindon Robison. For an example, see: Lindon
Robison, ”Investment/Disinvestment and Use of Durables: An
Analytic Framework," pp. hl-56 in Models for Investment and
Disinvestment Decisionmaking under Uncertainity, ed. by L.J.
Robison and M.H. Abkin (Electric Power Research Institute, Palo
Alto, CA), January 1982.

8. R.K. Perrin, "Asset Replacement Principles," American
Journal of Agricultural Economics, 1 (l972):60-65.

9. David J. Walker "A Damage Control Function to Evaluate
Erosion Control Economics,” American Journal of Economics,
1(1982), pp. 692.

10. Ibid., p. 69A.

26

27

11. C. Arden Pope III, Shashanka Bhide, Earl O. Heady, The
Economics of Soil and Water Conservation Principles in Iowa:
Model and Data Documentation, CARD Report 108, SWCP Series I,
(Iowa State University, Ames, Iowa: Center for Agricultural and
Rural Development, August, 1982).

12. Tim N. Banks, Shashanka Bhide, C. Arden Pope III, and
Earl O. Heady, Effects of Tenure Arrangements, Capital
Constraints, and Farm Size on the Economics of Soil and Water
Conservation Practices in Iowa, CARD Report 111, SWCP Series IV,
(Iowa State University, Ames, Iowa: The Center for Agricultural
and Rural Development, April, 1983).

13. Kent D. Olsen, Earl O. Heady, Carl C. Chen, and Anton D.
Meister, Estimated Impacts of Two Enviornmental Alternatives in
Agriculture: A Quadratic Programming Analysis, CARD Report No.
72, (Iowa State University, Ames, Iowa: The Center for
Agricultural and Rural Development, March, 1977)

1a. Orhan Saydeger, Gary P. Vocke, and Earl O. Heady, A
Multi - Goal Linear Programmigg Analysis of Trade - Offs between
Production Efficiency and Soil Loss Control in U.S. AgricultureJ
CARD Report No. 76, (Iowa State University, Ames, Iowa: The
Center for Agricultural and Rural Development, January, 1977).

15. J.R. Williams, P.T. Dyke, and C.A. Jones, "EPIC - A
Model for Assessing the Effects of Erosion on Soil
Productivity," paper presented at the Third International
Conference on State of the Art in Ecological Modeling, Colorado
State University, May 2A-28, 1982).

16. F.J.Pierce, W.E. Larson, R.H. Dowdy, and W.A.P. Grahm,
"Productivity of Soils: Assessing LOng - Term Changes due to
Erosion," Journal of Soil and Water Conservation,
(January-February 1983): 39-uu.

17. H. Muhtar, and C.A. Rotz, "A Multicrop Machinery
Selection Algorithm for Different Tillage Systems," paper
presented at the American Society of Agricultural Engineers
Mettings, University of Wisconsin-Madison, 27-30, 1982.

18. Ibid., p.”.

CHAPTER THREE

MANAGEMENT DECISION MAKING WITH INTERDEPENDENT CASH FLOWS -
A REFORMULATION

3.1 Introduction

In the previous chapter, Walker's model had been introduced
and critiqued. While Walker's attempt to deal with the
interdependent cash flow problem is a step in the right
direction, there were a number of reservations about the
structure of his model. The model presented in this chapter is
partially based on a reSponse to these reservations.

Section Two discusses the intertemporal statics approach to
dynamic processes. Section Three presents the requirements
which a new approach must satasfy. In Section Four, several
concepts from investment theory are applied to formulating the
innterdependent cash flow problem. Section Five generalizes the
model to multiple transitions. Section Six discusses some
differences in decision making for the owner Operator versus
tenant Operator. Section Seven argues that the algorithm may be
applied to any change in a crop system, not just equipment

switches.

3.2 Intertemporal Statics Approximation of a Dynamic Process
This chapter will focus on one approach to modeling dynamic
processes. Here, an intertemporal statics approach will be

developed. Another term for this approach is Hicksian Dynamics.

28

29

Approximating dynamic problems using an intertemporal
statics framework reflects (1) limited data upon which to base
an estimate of the rate equation(s) and objective functional of
optimal control, and (2) the desire to build a model which is
less presumptive of the dynamics of crOp production for a given
Operation. Since the present analysis is concerned with
developing a framework useful for individual Operator decision
making, it must be sufficiently general to allow the use of data
describing the production process of the operator.

Conceptualizing natural resource problems as capital
allocation issues related to determining what decisions lead to
an Optimal resource allocation has developed relatively
recently, but very vigorously. Some examples of how dynamic
approaches have previously been used are provided by Samuelson,
Cummins, Smith, Mc Connell, and Burt.

Cummins1 wanted to explore the analytics of the optimal
extraction rate of a natural resource whose stock is
exhaustable. Samuelson2 was concerned with identifying the
correct way of framing the issue of optimal timber rotation. He
relied heavily on principles of Capital Theory to formulate the
economic problem of combining various inputs across time, and
harvesting various amounts of timber across time, in a way which
maximizes the net return to the owner. As part of his analysis,
he addressed the externality/common property issue.

Smith3

is concerned with applying Control Theory to
analyze the problem of optimal intertemporal capital

allocation. Capital is thought of as renewable or non-renewable

30
resources as well as enviornmental resources. He was concerned
with the technology, production, and consumption of natural
resources in a two-commodity dynamic economic model.
Moving to the soil erosion area, Mc Connell A and Burt5
have both used optimal control approaches to resource allocation
decision making. Mc Connell's article formulates the problem of
soil loss in an optimal control framework. The rate equation,
used to describe the path of a state variable, soil depth,
across stages, has two arguments: ameliorative inputs and
productive inputs. Crop production is a function of soil loss,
soil depth, and an index of variable inputs. The rate equation
expresses the change in soil depth as a function of a tolerance
level and soil loss in that stage.

Burt also used an Optimal control approach. He used two
state variables: soil depth and percent organic matter in the
top six inches of the soil. The objective function was defined
as net returns in dollars/acre as a function of percent of land
planted to wheat, an annual organic matter loss function, and an
annual soil loss fUnction. Burt has to assume that fertilizer
and cultural practices were fixed for a particular rotation,
which reduces the decision variable to rotation choice.

It should be noted that these are only several examples of a
rather extensive literature which couches natural resource
allocation questions in the context of an Optimal control
problem concerned with allocating a capital stock across time.

Usually there is a profit function which is being maximized.

Further, the capital stock at the beginning Of the analysis may

31
or may not be augmentable during the analysis. The goal is to
find that set of values for the policy variable(s) across time
which lead to the constrained optimum of the objective
functional.

An Optimal Control problem is essentially a path selection
problem. A problem, say the Optimal time to switch a machinery
complement, is segmented into stages. One or more rate, or
state-space, equations are specified which indicate the impact
some decision variable(s) have on one or more state
variable(s). These state variables then enter the Objective
functional. The objective functional is a function of a
function. Therefore, one does not solve the problem by finding
the scalar which is the constrained Optimum. Rather, one finds
the function which describes the path across time of the
constrained optimum.

Numerical Integration is an approach used to provide an
approximate solution to systems of difference or differential
equations. Algorithms exist which can solve systems of these
equations where the objective function is non-linear, subject to
non-linear inequality constraints.

A further approximation of the Numerical Integration
approximation is provided by couching the problem in an
intertemporal statics framework. Here, the concern is with
finding the values of a decision variable, or variables, which
have associated with them values for state variable(s) at each
stage which optimize the objective function. External to the

model, a path is selected based on the values of the objective

32
function associated with the prespecified paths analyzed with
the model. No attempt is made to pre-specify the rate
equation(s) which link stages together, and which determine the
value of the state variable(s) entering the objective
functional, in such a way that the model determines the optimal

path.

3.3 Requirements of an Alternative Approach

There are three requirements which a new approach must
meet. First, the approach must not require that each asset be
the same or that any difference between asset cash flows be
restricted to a geometric form. Second, the method must be able
to handle any number of replacements. Third, it must be able to

address the criticisms leveled at Walker's approach.

3.u Adjusting for Interdependent Cash Flows
Schall and Haley present a framework for handling this
problem. First, if any of the future investments have a rate of
return (ror) at most equal to the cost of capital, r, these
projects can be ignored.6 Second, for the remaining
investment opportunities, three steps are followed:
1. Form all possible combinations of mutually exclusive
investment Options;
2. Determine the net present value (NPV), required
investment, and after tax cash flows of each

combination; and,

3. Adopt the combination with the greatest NPV.7

In this analysis, the investment options are the

 

33

alternative machinery complements between which the producer may

choose.8 Two mutually exclusive investment options may also

be differenciated by differences in the switch years between

machinery complements. Mutually exclusive investment Options,

which will be referred to as management options, are composed of

various sequences of the machinery complements being evaluated.

One example of two mutually exclusive

management options is:

Option One: Practice conventional tillage until the
end of the analysis, in year T;

Option Two : Practice conventional tillage until some
year T-t', where t'! is a potential

switch year, and practice conservation tillage
from t. to T.

 

3.5 Mathematical Derivation of the Decision Rule

Using continuous discounting, the following three equations

represent management options one, two, and three, respectively.

-rt -rT
(3.1) NPVa =JLNRa(t)e dt - 18(0) + SVa(T)e
-rt
(3.2) vabo = .nabo(t)e dt - Ib0(0) +
“home-3""T
1:
-rt
(3.3) NPVa’bi {:Raflzk dt - ram) .14:
sv (t)e-rt + e-rtE‘NR (t)e-rt
a o bi(T t)
...r ..
- Ibi(0) + SVb1(T-t)e ]
Where,

13(0) = Capital cost of A;
Ib1(0) = Capital cost of B, at the beginning of year i;
NRa(t) = Gross returns minus variable cost for asset
A in each period;
NRb1(t) = Gross returns minus variable cost for asset B
in each period, when E is adopted at the
beginning of period 1;
SVa(T) = Salvage value of asset A at the end of period
T;

3“
SVbi(T) = Salvage value of asset B at the end of period
T when E is adopted at the beginning of
period 1

Equation (3.1) will calculate the NPV corresponding to
holding the erosive asset until T. Equation (3.3) is a
reformulation of the equation used by Walker to calculate EPFT.
It has been reformulated in order to allow the analyst to search
for a trade year which will maximize NPV, given a pre-specified
beginning year and ending year. Equation (3.2) calculates the
NPV corresponding to using the chisel plow from the beginning of
the analysis.

Referring to equation (3.3), if t is first equal one and
then equal to two, the analysis boils down to addressing the
question: should I switch from asset A to asset B at the end of
period one or wait at least one more period? Mathematically,
this appears as,

(3.u) v2 = [NP a,b2] - [NPVa’b1].

Substituting the terms from equation (3.3) into (3.“), and
simplifying, equation (3.5) is obtained.

1.
(3.5) v2 = [( NR (t)e"tdt - I (0) + sv (2)e'2’)
.Wf' a a

rt

({NR (t)e'
0'3 ‘f t
- [e-rErNRb1(t)e-r dt - I

rT

dt - 13(0) + SVa(l)e-r)]

l(0)

-2r -rt
) - e ( NPb2(t)e

+

SVb1(T)e
-fT
- Ib2(0) + SVb2(T)e )1

The general form of equation (3.5) is,

35

h
-rt -rh
(3.6) Vh : [( ::a(t)e dt - Ia(0) + SVa(h)e )
- ( NR (t)e-rt - I (0) + sv (h-j)e'r(h’3))]
.8 T.“ a t a
-r(h) -r
-[e ( 2Rb(T-h)(t)e dt
-r(T-h)
' Ib(T-h)(o).;H:;b(T-h)(T-h)e )
- e”‘“‘3)( Rbt(t)r-rtdt - 1bt(0)
C
+ SVbt(T-h-j)e'r(T-h-j)].

What is the interpretation of equation (3.6)? The first
bracketed term is the change in the NPV from holding asset A
between h-j and h, where j is set so that h-j equals the
beginning of the period when asset A could have last been
traded. The second bracketed term is the change in the NPV of
asset B which arises from the decision to postpone adoption of
asset B from year h—j to atleast year h.

Equation (3.6) provides a stopping rule to use in searching
for the correct time to switch from asset A to asset B. When
Dhe 0, the correct transition period may have been found.
Caution is used because Vh=0 is a necessary but not a
sufficient condition for the identification of the appropriate
transition period. When trading can occur at any point in time
between 0 and T, there may be more than one point where Dh=0.
In practice, it may not be possible to find a point where Dh=0
because asset trades can occur at discrete points in time. In
addition, when trading can only occur at discrete points in
time, there may more than one period within which Dh changes

sign. The following section details a solution procedure which

circumvents these problems.

36

Therefore, the new approach must (1) be flexible in both the
number of replacements assumed and the pattern of net returns to
all replacements, (2) be consistent with how staged problems are
formulated, (3) include the net returns to the erosive asset
assuming it is held until the end of the analysis, (“) be
analytically correct in how the cost functions are formulated,
(5) include salvage value as an explicit argument in the asset
switch decision, and (6) be implemented in such a way that the
probability that the local optimum corresponding to a
recommended switch also is a global optimum. Alternative
management options can be arrived at via alternative
combinations of crOp systems, the number of transitions assumed
to occur between crop systems, and the points in time when a
switch can occur. All of this analysis is conducted assuming
the planning period is held constant. Further, the planning
period is the total length of time over which the producer makes
asset switching decisions. A difference exists between the £153
horizon and the planning period for the case of the owner
operator who should consider changes in the salvage value of

land when making crOp system decisions.

3.6 Transition Analysis when Multiple Switches are Possible
Studying the problem of asset switching when one switch is
assumed to occur is the problem raised by Walker. The analysis
was structured to be consistent with the assumption that only
one switch will occur. As the reader observed in chapter two,

this is a very restrictive assumption. Perrin dealt with this

37
problem by assuming that an infinite number of replacements will
occur and that either (a) each subsequent asset is identical to
the one it replaced, or (b) that each subsequent asset is
technologically improved in a geometric fashion. Due to the
definition of interdependent cash flows used in this analysis,
backward induction cannot be used to solve for the life of the
asset held last and working back to determine the optimal life
of the asset held first.

When one allows for more than one replacement to occur,
there does not appear to be any general form for a first order
condition, within the structure of the current framework.
Borrowing from Schall & Haley's approach, one solution to this
problem is simply to specify all the alternative management
Options,ca1culate the NPV for each, and then select that option
which maximizes NPV. Equation (3.7) is the general form of the
equation used to form the alternative investment options.

‘5 rt
ifNRl(t)e ac - 11(0) .
o -rle

(3.7) NPVi

13)e

1;;
+ e-rTlJ[(SéR2(t)e-rtdt - 12(0)
-rT2j
2j 13! )

-rT2j -rt
dt -

+ e [(LNR3(t)e 13(0)
-rT3J)

SV1(T

+ SV(T )e

+ SV(T3 )8

J

11WU)

+ e"T((N‘1)3)[( NRN(t)e'rtdt -

0
J)e"'”"”)1...11

Equation (3.7) is analyzed for all management Options 1,

- IN(O) + SVNU'N

38

i=1,...,M. Interpreting equation (3.7), the first line
represents the discounted net returns to pursuing crop system
one for a period of le years. Line two represents the
discounted net returns to crop system two, when this system is
followed for a period of T23 years. The last line represents
the discounted net returns to crop system N, when N is followed
for TNJ years. Equation (3.7) accounts for interdependent
cash flows because the net returns to subsequent crop systems
will, in part, reflect the use of prior crop systems on the
state of the system in future periods. Changing the sequence of
crop systems and/or the trading period between two crop systems
will be reflected in the level of NPV for that management
option. In turn, after calculating the NPV for the various
options selected for analysis, the correct Option can be

selected based on maximum NPV.

3.7 Decision Making for the Owner versus the Tenant

While capital is assumed to be the constraining factor to
which returns are maximized for both the owner and tenant, there
is a difference between the capital to which returns are
maximized for the owner versus for the tenant. Owners do, or
should, make ID decisions with respect to their impact on
returns to the investment in land and machinery. Therefore,
both machinery salvage value and land salvage value must both be
included. Whether or not a switch between crOp systems entails
switching machinery complements, the salvage values for both

land and machinery should reflect any change in their value

39

arising from a decision to not switch complements this period.
Referring back to equation (3.7), an additional term must be
added to reflect the value of land at the point in time when
disinvestment occurs.

Within the bounds of the current analysis, an estimate of
the discounted value of future land prices is provided by the
Basic Capital Budgeting equation presented in equation (3.8).

Where,
NR = Net returns to the asset in any year;
r = Discount rate;
VL = Present value of future returns to land.

This model is derived from equation (3.9),

(3.9) upv = NR(t)/(l+r)t.

In this model, net returns are assumed to be constant across
time, no inflation or taxes exist, the asset does not
depreciate, the asset is held for an infinite length of time,
and the alternative investment earns a return of r.10 The
value of VL is discounted by the discount factor corresponding
to the time when disinvestment is assumed to occur, and this
value is added to equation (3.7).

Tenancy arrangements affect capital budgeting in several
ways While the complete discussion of tenancy arrangements
requires that the issue of risk spreading and decision making be
discussed, there are several observations which can be made even
in a deterministic model.

First, the tenant is assumed to attempt to maximize returns

to the investment in equipment. Here, the tenant is assumed to

“0
provide the machinery and labor input. Second, the major
difference between cash versus share rentals arises in the
distribution of revenue and cost between the owner and the
tenant. Third, in analyzing ID decisions, the time horizon used
is determined by the tenant. Fourth, as with the owner,
machinery salvage value is included in the analysis, as well as
the change in machinery salvage value from postponing

disinvestment. Returns to land are not part of the analysis.

3.8 Selection of the Time Horizon

All the analysis in this chapter assumed that the time
horizon was finite and determined exogenously. In chapter two,
the models which were analyzed had as one of their goals the
endogenous determination of the economic life of the asset. Due
to the fact that the annual cash flow of each future asset
depends on when the transition occurs, it is not possible to use
the method of backward induction to solve for the Optimal life
of each asset. While more sophisticated algorithms can solve
for the optimal life of each asset endogenously, even when
interdependent cash flows exist, the present analysis must
circumvent this problem by exogenously specifying the time
horizon. Sensitivity analysis can be performed to identify the
rate of change in the value of the objective function to
variations in the time horizon. Then, the option whose asset
lives maximizes NPV, ceteris paribus, is the appproiate option

to select.

“l

3.9 Generalizability of the Model

While most of the analysis in this chapter was couched in
terms of switching assets, the framework can be used to assess
the impact of other changes in a crop system on the farmers'
profit. For example, changes in crop rotations and/or tillage
practices can also be evaluated. In this case, the alternative
crop systems comprising one management option are differenciated
atleast by the crop rotation used. Then, the appropriate set of
crop systems, (ie: the appropriate management option), is
selected by finding the management option which results in a
global extremum (which one depends on the objective function) of

the objective function.

3.10 Summary

Chapter three began by identifying the requirements which
any new approach must satisfy. These requirements were
identified based on (a) Perrin's analysis, (b) Schall and
Haley's method for selecting an investment from among a set of
investments whose cash flows are interdependent, (c)
requirements of a new approach presented earlier,and (d) the
criticisms of Walker's approach.

Based on the criticisms of Walker 3 approach to ID decision
making when one transition is considered, the approach to this
problem was reformulated. Equation (3.5) depicts the general
form for the first order condition (FOC) used to search for the
optimal transition period, when one transition occurs.

Going beyond the one transition problem, a model was

“2
formulated with which to analyze a multiple transition problem.
Here, it was argued that a FOC probably does not exist, given
the approach used in this analysis. Equation (3.7) is the
general form used to determine the NPV for each management
option. This equation captures the interdependent cash flow
aspect of the problem.

While most of the discussion of existing ID models, as well
as the derivation of the models in this chapter, were couched in
terms Of investment analysis, the framework can be generalized
to other dimensions of management decision making. Relying on
the definition of a crOp system as being completely defined when
the (a) crop rotation, (b) tillage method, and (c) tillage
practice are specified, the model developed in this chapter can
be applied to a change in any one Of these three dimensions of a

crop system.

CHAPTER FOUR

SIMULATION MODEL FORMULATION

“.1 Introduction

This chapter presents the empirical model used for the
analysis. The next section discusses what this model
contributes to the study of soil erosion. Section three
presents five assumptions which affect either the calculation of
net returns for each case studied, or affect the interpretation

and extension of the results to other cases studies outside the

model. Section four presents the components of the model.

“.2 This Models' Contribution to Studying
Soil Loss and Crop System Economics

First, this model provides the broad outline of how future
model building should progress in the area of producer decision
making and soil loss control. Before this model can be used for
producer decision making, more assumptions will have to be
relaxed; but, the general approach is consistent with a focus on
producer decision making.

Second, unlike existing empirical models, this model is
derived from an explicit focus on interdependent cash flows from
competing crop systems. Any model in this subject matter area
which purports to be useful for producer decision making should

address the issue of interdependent cash flows.

43

““

Third, this model determines the profitability of competing
combinations of crop systems given a planning period. In turn,
unlike the Pierce-Larson model, the amount which a producer can
invest in a soil conserving machinery complement is determined
using the NPV of two competing options, not one realistic
complement and one in a hypothetical steady-state.

Fourth, numerous management Options can be studied. For
example, the asset switch problem can be studied using this
model. In addition, two competing management Options can be
defined as including the same two crop systems with the only
difference being when a switch between systems is assumed to
occur. The conceptual basis for this empirical model includes
allowing for changes in other dimensions of a crop system other
than the machinery mix. This is only reasonable considering the
fact that there are a range of management decisions which impact
on soil loss.

Fifth, this empirical model begins to relax the assumption
that input use is invariant to changes in yields as soil depth
changes. Pesticide, fertilizer, potassium, phosphate, and seed

demand vary as a function of output.

“.3 Structure of the Computer Model
This section will look at the model's overall structure.
This is followed by a more detailed look at the various sub -

programs of the model.

“5

“.3.1 Macro Overview of the Model

As Figure “.1 indicates, there are seven programs which
together form the framework used in the analysis. Each program
is called from the main program, EASL, which stands for Economic
Analysis of Soil Loss. When a program is called, computation is
shifted from EASL to that program, and when the computations are
completed, computing shifts back to EASL.

First, INP is called which prompts the user to input user
provided data. These data are then saved in a file created by
the program. Next, USLE is called and the annual average rate
of soil loss is calculated for each respective crOp system,
using the Universal Soil Loss Equation. After a number of
control variables are initialized, DYNSDSP is called. This
model is a modified version of the Pierce Larson et. al. model
used to calculate the productivity of a specified soil, in a
given year, by relying on selected soil characteristics and the
annual rate of soil loss. After the productivity calculations
are performed, the yield of a given crop is determined, for a
given year in the time horizon. Once the yield is determined,
programming moves to the input use calculation program, IU,
which calculates the use, and cost, of pesticides, fertilizer,
potassium, phosphate, and seed. Next, computation is
transferred to the ACCT program which calculates the cash flow
for each option. When all "J" components for all "K" Options
have been analyzed, computing shifts to the WRITE program which
prints selected information. When all Options have been
analyzed, computing ends.

It should be noted that the model is structured to be

“6

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“7
consistent with equation (3.7) developed in the previous
chapter. In the simulation model, X represents the number of
alternative management options, and NT(K) represents the number
of changes in some component of the crop system which is assumed
to occur within a decision maker's time horizon. For example,
if Farmer Jones faces the following alternatives:

(1) Continue to use his moldboard plow and then retire;

(2) Use the moldboard plow for 5 years and then switch to a

chisel plow and then retire; or,

(3) Switch to a chisel plow now and then retire.

Farmer Jones has three management Options, and management
option two contains two crop systems. Whereas, options one and
three each contain one crop system. Each management Option is
composed of one or more cropping systems over a pre - specified
planning period, T. For example, Farmer Jones' planning period
is today until retirement. His planning period may be any
length of time he sees as relevant. The user can specify both

the planning period of the decision maker, T, and the length of

time for which each crop system is practiced, T(J,K).

“.3.2 Structure of each Sub - Program

There are six sub - programs. These are: Input Prompt (INP),
Soil Loss Calculation (SOIL), Soil Productivity (DYNSDSP), Input
Use (10), Economic Analysis (ACCT), and the Output Program

(WRITE).

“.3.2.l Input Prompt Program
Figure “.2 is the macro flowchart for the input prompt

program. Each block in the flowchart indicates the type of

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“9
information which the user must provide. The user is
automatically prompted for the necessary data. When the user
has responded to the prompts, the data are saved in a separate
program for later use. After all the data are entered,

computing‘returns‘to-EASL.

“.3.2.2 Soil Loss Calculation-Program

This program is depicted in Figure “.3. First, to assure
subsequent calculations are performed using the correct annual
rate of soil loss, the rates of soil loss for each crop system
are set equal to zero. Next, using the USLE, the average annual
rate of soil loss is calculated For each crop system. These
calculations are saved for later use. When a particular
management Option contains more than-one crop system, each crop
system will have a corresponding annual rate of soil loss. The
form of the USLE used in the subroutine determines the average
annual rate of soil loss under the specified climatic
conditions, topography, andsmanagement practices. As a result,

soil erosion attributable to sevens storm events is not captured.

“.3.2.3 Soil Productivity Program

DYNSDSP is the acronym for Dynamic Soil Depletion and Soil
Productivity. As was stated earlier, this program is a modified
version of the Pierce - Larson et. a1. model.

Referring to Figure “.“, the reader will note that the model
first calculates the weighting factors for each centimeter

within a 100 cm rooting zone. These factors are used in the

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52
calculation of the weighted productivity for a given soil depth
in the root zone. After the weighting factors are determined,
the sufficiency of bulk density, sufficiency of soil reaction,
and the sufficiency of available water in the horizon being
studied are determined. These parameters are determined by
comparing selected SOILS - 5 information to various critical
values contained in DYNSDSP. The product of these terms
determines the unweighted productivity by horizon.

Next, the weighted productivity is determined for the
horizon(s) within which tillage and rooting are occurring. When
soil inversion occurs, the model determines the horizon(s)
contained within the 15cm plow depth, and adjusts the weighted
productivity if more than one horizon is involved. Once the
weighted productivity is known, the slope of the productivity
curve is determined for the horizon being studied. This is, in
part, dependent on the number of years it would take to deplete
the horizon given the annual rate of soil loss and initial soil
depth. In principle, the productivity curve is a piecewise
linear function in yield - time space. As soil erosion occurs,
the model shifts the 100cm rooting zone down into lower
horizons. Therefore, the productivity of a given horizon at a
point of time is partly a function of past soil loss.

DYNSDSP has memory in two ways. First, if the current year
happens to also be (1) the last year for which a particular crOp
system is practiced, and (2) a new crOp system will be adopted
next year, and (3) the yields for each crop in the crop sequence

differed under the two crop systems, the model adjusts the

53
initial yields for each crop to reflect the soil loss which has
occurred from t=0 to the beginning of the current period. If
the initial yields are identical, the model simply starts with
the yield at the end Of the previous period. Another way in
which the model has memory is in the determination of soil
loss. In any given year, the variable which indicates soil loss
actually indicates the cumulative loss which has occurred. When
a transition occurs between systems, the amount of soil lost up
to that point in time is saved and added to the annual soil loss
which occurs under the new crop system. When all the above

calculations are performed for a given year, computing returns

to EASL.

“.3.2.“ Input Use Program

Figure “.5 depicts the input use (IU) program. Within this
program, the annual use, and cost, of pesticides, fertilizer,
seed, potassium, and phosphate are calculated. Labor and
maintenance inputs are determined in the machinery model which
determines the machinery complements.

These inputs whose use is dependant on a crops' yield are
modeled as a constant times yield. This constant returns to
size assumption may need modification. Both the quantity and
total variable cost of these inputs are determined by combining
(a) yield, (b) cost per unit for each input, (c) application
rate for each input, and (d) percent of each acre planted to
each crop. Appendix A presents and discusses how the

application rates were determined.

 

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M.3.2.5 Cash Flow Program
Since the decision maker is assumed to select an option based
on maximum profit, there must be some way to calculate the
profit of each option and compare it to the profit of any
competing Option(s). Figure ".6, which illustrates the ACCT
program, performs this function.

Both annual returns and total costs are calculated by crop
within the crop sequence, for each year in the time horizon.
Annual total cost is the sum of annualized per acre fixed cost
for the machinery complement, annualized machinery dependent
variable cost for labor, fuel, and maintenance, and the annual
cost for the variable inputs calculated in the 10 program.
These costs are all on a per acre basis.

After the net return for a given year is determined, it is
discounted using the corresponding discount factor, using
continuous discounting. The discounted annual returns are then
summed for each crop system within each management option. When
new equipment will be used next period, or when the end of the
planning horizon is reached, equipment salvage value is
calculated and added to NPV. Also, if the decision maker is an
owner - operator, the future value of land is estimated,
discounted, and added to NPV. When all calculations have been

performed, computing returns to EASL .

u.3.2.6 Write Program

The WRITE program, depicted in Figure N.7, is called after

all the crop systems for a given management Option have been

57

 

 

 

 

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58
evaluated. First, user provided data which are independent of
any particular crop system or management option are printed.
Next, crop system specific data, which are user provided, and
selected endogenously calculated data are printed. At this
point, the annual (1) crop yield(s), soil loss, productivity,
gross revenue, total cost, and discounted net returns are
printed for each year in the manager's time horizon. The last
value to be printed is the NPV of the options which were

analyzed.

”.4 Summary

 

First, the contributions which this empirical model makes to
the study of the on farm economics of selected methods to
control soil loss were discussed. Contributions were made to
the study of inter-dependent cash flow problems, comparing
systems not in a steady state, endogenizing the use of selected
variable inputs, the ability to study ID problems under
alternative ownership structures, and including returns to land
in crop system decision making.

Second, a macro overview of the simulation model was
presented. Part of the overview included a discussion of the
relation between the structure of the simulation model and the
analytic model developed in Chapter Three. Each of the
individual programs was discussed in general terms and a
flowchart was presented for each program, and program sequencing

was discussed.

CHAPTER FIVE

ANALYSIS OF ALTERNATIVES

5.1 Introduction

This chapter will first present the alternative scenarios
which are analyzed. Part of this discussion will focus on why
these scenarios were selected. Next, the results of the

analysis will be presented.

5.2 Alternative Scenarios

Two areas in Michigan were selected for analysis. One area
is in the Southeast part of the lower peninsula, and is often
referred to as the "Thumb Area." In this area, the land tends
to be fairly flat, with deep, fertile, soils. Soil loss
attributable to water run-off is not much of a problem in this
area. The other area studied, St. Joseph's County in Southwest
Michigan, contains much more rolling terrain, with varying soil
depths, and a higher erosion potential. These two areas are
assumed to represent a range of erosiveness and soil depths.

Table 5.1 lists the characteristics of the scenarios which
were studied. A scenario is comprised of (a) crop rotation; (b)
machinery, denoted either by conventional (moldboard) or
conservation (chisel plow); (c) tillage method, either straight
up/down the field, or contouring; (d) CP factor, which is a
parameter in the calculation of soil loss, and is a function of

59

60
the type of tillage equipment, crop rotation, when plowing
occurs, and how much residue is left; (f) the number of
components, where a component was previously defined as one crop
system; (g) the planning period of the decision maker; (h) the
length of time a particular component is held; and, (i) the
discount rate of the decision maker.

Two crop rotations were analyzed for each area. They were
selected to represent rotations common in each area. As was
indicated in the previous chapter, the machinery complement was
developed using Muhtar's machinery complement model. His model
selects a moldboard plow for the conventional complement, and a
chisel plow for the conservation complement.

Two tillage practices are included. Either up/down or
contour plowing may be selected. The up/down plowing
alternative was included to obtain some information on how a
crop systems' profitability changes with a move to contour
plowing. This will allow separation of profitability changes
attributable to the type of plow used and the type of tilling
pursued.

Chemical usage for each crop rotation - machinery mix
combination are presented in Appendix A. The chemical regimes
were developed with the assistance of Agronomists and
Entomologists at Michigan State University.

The results can only be used to compare the profitability of
one scenario. No significance is to be attributed to the

absolute amount of profit for any one scenario.

61
5- 3 Saginaw Results

Referring to Table 5.1, scenarios one through eight
represent analysis conducted in the Saginaw Bay area. Table 5.2
presents net present values (NPV) for these cases. Recall that
the NPV's represent the discounted net return per acre from the
beginning of the analysis to infinity, and that significance can
only be attributed to their relative magnitudes.

As the results in Table 5.2 indicate, in all the cases
evaluated, the conventional tillage system results in a greater
per acre net return than all comparable conservation systems.
Muhtar's study of the relative economics of conventional and
conservation systems in the Saginaw area indicate that the
conservation system had higher net returns than the conventional
system. Two important differences between his analysis and the
present analysis are (1) his model could not capture the
intertemporal soil productivity relation, and (2) in his
analysis the herbicide programs were assumed to remain constant.

The latter point turns out to be particularly critical in
the cases evaluated. Referring to cases one and two, the reader
will note, referring to Table A.2, that the capital cost of the
conventional system was $1.25 per acre cheaper than the
corresponding conventional system. In addition, the erl,
labor, and timliness costs were $5.fl5 less for the conservation
system than they were for the corresponding conventional
system. Comparing the herbicide program for the two systems,
the per acre cost for both corn and navy beans is greater under

conservation tillage than the conventional system.

62

Table 5.1

Characteristics of Alternative Scenarios

 

 

 

Option Crop Machinery Till CP Disct. No. Yrs.
Rot. Comp. Method Factor Rate Comp Held

1 C/NBJ- CVTd UP/DOWN .119 8 . 125 1 253

2 C/NB CON UP/DOWN .32 8.125 1 25

3 C/NB CVT CONTOUR .u9 8.125 1 25

u C/NB CON CONTOUR .32 8.125 1 25

5 C/NB CVT UP/DOWN .52 8.125 1 25

6 C/NB CON UP/DOWN .32 8.125 1 25

7 C/NB/SGB CVT CONTOUR .su 8.125 1 2S

8 C/NB/SGB CON CONTOUR .uu 8.125 l 25

9 C/C/SYB CVT CONTOUR .37 8.125 1 25

10 C/C/SYB CON CONTOUR .26 8.125 1 25

ll C/C/SYB CVT/CON CONTOUR .37/.26 8.125 2 10/15

12 C/C/SYB CVT/CON CONTOUR .37/.26 8.125 2 5/20

13 C/C/SYB CVT/CON CONTOUR .37/.26 8.125 2 15/10

1n C/C CVT CONTOUR .3 8.125 1 25

15 C/C CON CONTOUR .17 8.125 1 25

16 C/C CVT/CON CONTOUR .3/.l7 8.125 2 lO/lS

l7 C/C CVT/CON CONTOUR .3/.17 8.125 2 15/10

 

 

Notes: l/C=Corn, NB:Navy Beans, SGB:Sugar Beets,
SYB:Soybeans.
2/ CVT=Moldboard Plow, Con=Chisel Plow.
appears, this indicates that the type of plow used is
switched during the 25 year planning horizon.
3/This indicates the number of years each component of a
management option is held for.

When a slash

63
This cost differential more than overcomes the conservation
systems' lower cost for fuel, labor, and timliness. It still
could be the case that the conservation system would result in a
greater NPV than the conventional system, but for this to occur,
the intertemporal yield differentials must be great enough to
overcome the per acre cost disadvantage of the conservation
system. Since yields do not fall fast enough under the
conventional system vis-a-vis the conservation system, the end
result is a higher level of profit for the conventional system.
This same analysis can be applied to a comparison of the results
of options three with four, five with six, and seven with eight.

These results also indicate that there is no Justification
for finding the year in which a producer would shift from a
conventional to a conservation system. The producer can do no
better than he/she does by using the conventional system from
the beginning, under the cases studied.

One question which is reasonable to ask is how sensitive
might the results be to a greater difference in potential
erosion between systems? Comparing scenarios five with six, you
can see from Table 5.1 that the CP factor, which is a function
of tillage system, and cr0p rotation, and is used in the USLE
calculation of soil loss, for these alternatives are .52 and
.32, respectively. This is an increase in erosion differential
between the conventional and conservation systems of about 50
percent, when compared to alternatives one and two. For the
alternatives analyzed, this is probably the most erosive set of

conditions. As Table 5.2 indicates, even here the NPV of the

6H
Table 5.2

Cash Flow and Soil Loss - Saginaw Scenarios

 

 

 

Option Soil Loss NPV
(Tons/Acre/Year) (S/acre/year)
1 3.06 us7u.07
2 2.18 “386.80
3 1.53 “600.03
M 1.09 “352.69
5 3.2“ “568.18
6 1.uu uu02.18
7 3.37 7651.1u
8 2.75 7584.91

 

 

conventional system, $M568.18, is greater than the conservation
system, Shu02.18.

Changes in the discount rate, either higher or lower should
not have any effect on the relative positions of the options
which were studied. This prediction follows from the
observation that the yield differential across systems across
time is not significant enough to result in annual net return
patterns which are different enough to allow the discount rate
to affect option rank. This prediction may not hold when tax
based subsidies are provided to encourage adoption of chisel
plow systems.

Lastly, one might ask how sensitive the results might be to
the herbicide program. Here, in fact, is where one might

expect that the ranks might change given different assumptions

 

65
about the herbicide programs. For example, the greatest
difference between NPV values occurs when one compares the NPV
of Options three with four, a differential of $217.3N. In this
case, these systems would have the same NPV if annual
conservation system costs, were $17.66/acre lower.

It should be noted that the analysis assumes that
transition costs are zero. If there are any costs of moving
from conventional to conservation plowing, either because costs
of the latter system being higher than assumed or yields are

lower, the conservation system will be even less attractive.

5.4 St. Joseph's Results

Turning to the results for the St. Joseph's area, one
should expect to observe the effects of differential soil
depletion across systems exerting more effect of options rank.
Since the soils in this area are more erosive than those in the
Saginaw area, a switch from a more to a less erosive crop
system should exert a greater influence of system cash flows,
ceteris paribus. Therefore, the relatively higher chemical
costs for the conservation system should be able to be more
easily counteracted by the higher productivity of the
conservation system than was the case in the Saginaw area where
the soil was not very erosive.

Turning back to Table 5.1, scenarios 9 through 17 represent
cases analyzed in the St.Joseph's area. Profit and soil loss
results are presented in Table 5.3.

One striking result, indicated in Table 5.3, is the

 

66
comparison between the NPV of the conventional system in
scenario 9 ($28u3.u5), with that in scenario lO, ($3188.u2).
What this result suggests is that it is at least worth
conducting an analysis of when to switch systems, since the NPV
Of the conservation system excedes that Of the conventional
system.

Looking at scenarios ll - 13, the period Of switch from the
conventional to the conservation system is varied from year 5,
to year 10, to year 15, respectively. The earlier that the
switch occurs, the closer is the level Of NPV to that for
Option 10, which corresponds with holding the conservation
system from the beginning Of year one. What these results tend
to suggest is that the earlier that the trade occurs, the more
profitable it will be.

One way to look at the results in Table 5.2 is to compare
the profitability of alternative crop systems for a given type
of tillage. For example, comparing the profitability of
scenarios 9 with 1“, we see that a shift from a
corn-corn-soybean rotation to a continuous corn rotation
reduces soil erosion by 3.36 tons/acre/year, and increases
profit by $11k.5u/acre, which corresponds to an annual average
increase Of $9.31/acre/year. e closer together, ceteris
paribus.

Referring back to scenarios 9 and 10 again, one issue that
the relative NPV's raises pertains to the magnitude Of any
transition costs. Calculating the difference in the NPV of

these twO scenarios, and analyzing this figure, one notes that

 

67
Table 5.3

Cash Flow and Soil Loss - St. Joseph Scenarios

 

 

 

Option Soil Loss NPV

(Tons/Acre/Year) (Slacre/year)
9 17.76 28H3.H5
10 12.u8 3188.u2
ll 17.76/12.M8 3122.32
12 17.76/12.fl8 3060.97
13 17.76/12.h8 302fl.26
1H lA.HO 2957.99
15 9.12 3107.80
16 1u.u/9.12 3192.68
17 1u.u/9.12 3171.03

 

 

break - even is attained if the NPV of scenario 10 declines
by an annual average amount of $ 28.04/acre. This difference
could arise in a number Of ways. Considering the fact that
conservation systems require a higher level of management
skill, it could be the case that the potential yields
generated by the model overestimate actual yields due to a
learning curve effect. Also, there may be other Opportunity
costs associated with switching management practices.
Comparing the NPV's for scenarios 9 and 1a, at $ 28u3.&5
and $ 2957.99, respectively, it could be argued that this is
the value of using a less erosive crop rotation, keeping the
tillage method and practice constant. Shifting to continuous
corn from orn - corn - soybeans reduced the annual erosion

by 3.36 tons/acre/year. The profit increased by

_ rib-E,

 

68
$llu.5u/acre, or an annual average Of $9.31/acre/year.5.h
5.5 Conclusions

First, given the assumptions Of this analysis, there
appears to be little reason for farmers in the Thumb area to
consider adopting a chisel plow system, if the decision is
based solely on relative profitability. In the Options
studied, no chisel plow system had a higher level Of profit
than the corresponding moldboard plow system.

Second, given the assumptions Of this analysis, the
chisel plow system is more profitable than the corresponding
moldboard plow system in the St. Joseph's area. It was also
the case that the sooner the chisel plow system was adopted,
the higher was the level of profit.

Third, while the analysis.(a) was before taxes, and (b)
assumed hat all costs and prices were constant in relative
terms, the relative pattern of results should be invariant to
relaxation of these assumptions, except for the introduction
of subsidies for the use of chisel plow systems. Again,
while the estimates of NPV were interpreted as profit
estimates, they are not to be interpreted as returns to land
in either the Saginaw or St. Joseph's areas. Taxes were not
included, the discount rate used may be different than a
potential investors weighted average cost of capital, and the
NPV figure includes other returns to the current owner which
would not be included in a prospective purchaser's bid price

calculation.

CHAPTER SIX

SUMMARY AND CONCLUSIONS

6.1 Introduction

First, the literature review will be summarized. Next,

the reformulation Of interdependent cash flow models will be
summarized. Following this will be a review Of the
simulation model. Finally, the empirical results will be

summarized.

6.2 Literature Review

Chapter two presents a review Of both selected
disciplinary principles which address the issue Of how to
decide when to trade assets and empirical studies Of the
relation between soil loss and returns to the farm
enterprises. It was argued that most of the analytic
frameworks which address the problem of asset cash flows are
independent Of one another. One model was presented which
was implicitly designed to include in ID decision making an

additional component Of Opportunity.

6.5 Decision Making with Interdependent Cash Flows
An existing decision making model, develOped by Walker,
was reformulated in order to correct for several flaws in his

model. First, the one transition problem was addressed, and

69

70
then the multiple crop system switch problem was addressed.
It was argued that the same framework can be used to study
crop system switching from either the owner Operator or
tenant's perspective. Finally, it was argued that the
framework used to determine when to switch tillage
complements could also be used to study other changes in a
crop system which will affect the pattern Of intertemporal

cash flows.

6.4 Simulation Model Formulation

A modified version of a simulation model develOped by
Pierce - Larson et. al. was further modified for use in this
analysis. Using the parts of the model which calculate
annual crop yield, a modified set of economic calculations
was added tO the model. This new model (a) calculates the
use Of some inputs based on yield, (b) can address the
question Of when tO switch crop systems, and (c) selects a
system or sequence Of systems based on the relative economics
Of competing systems as Opposed to comparing the economics of
a soil depleting system to one assumed to be in a steady
state.

It was noted that the model is written in ADVANCED BASIC,
and is composed Of four sub-programs. These sub-programs
calculate (1) amount Of selected variable inputs used, (2)
annual soil loss, (3) annual crop yield, (4) annual cash
flow, and selected discounted values. An input data and

output program is also included.

71
6.5 Empirical Analysis

Chapter 5 noted that two areas were selected for study.
One area, Saginaw County, contained less erosive soils, and
the other area, St. Joseph County, contained more rolling,
erosive, soils. Two tillage systems were modeled, a
moldboard and a chisel plow system. Two crop rotations for
each area, representing crop rotations could in that area,
were assumed in the analysis.

In all cases studied for Saginaw County, the moldboard
plow systems resulted in a higher net present value (NPV)
than any comparable chisel plow system. Turning to St.
Joseph County, there were some cases where the NPV for the
chisel plow system exceeded the NPV for the comparable
moldboard plow system. For these cases, the NPV Of the
combination increased the earlier a switch occured. Finally,
the results suggest that correct specification Of the
pesticide-herbicide regime was particularly important to the

relative economics Of moldboard versus chisel plow systems.

6.6 Conclusions

While the empirical analysis in the previous chapter is
not very exhaustive, it does convey some information about
the relative profitability Of competing crOp systems under a
range Of soil erosion conditions. One result Of that
analysis is that even after accounting for intertemporal
productivity and differences in recommended

pesticide/fertilizer regimes, the change in capital costs

72
between the conventional system and conservation system must
be sufficiently different in order for the crOp system using
conservation tillage to be profitable in low erosion
potential areas. In low erosion potential areas, the gain in
discounted revenues arising from using a less erosive
machinery complement is at least partially Offset by the
higher variable costs associated with increased
pesticide/fertilizer applications. When positive transition
costs are included, the less erosive machinery complement
will appear even less attractive, from a profit maximizing
perspective.

In low erosion areas, target subsidies may have their
greatest impact on changing an investor's gO-no go decision.
It is also the case that a given subsidy will likely "buy"
less soil loss reduction here than in‘a more erosive area.

In more erosive areas, a subsidy may be (1) a rent to the
potential investor, and/or (2) an inducement to adOpt at an
earlier point in time. Further, the subsidy can also be
viewed as compensation for the investor's lack Of information
about the economic success of a conservation tillage
machinery complement. Clearly, there is ample grist here for
anyone's political mill.

One question for policy is whether to Offer subsidies to
farmers where the economic incentive to adopt conservation
tillage may not exist, or to Offer subsidies where soil loss
reductions may be greater, but where farmers may already have

an incentive to adopt conservation tillage. Current

73
discussions on targeting focus on allocating cost share funds

to areas with the greatest soil loss. These are also the

situations where farmers have the greatest incentive for
voluntary adOption, ceteris paribus. This leaves three
alternative justifications: to induce earlier adOption, to
compensate for any perceived increased riskiness Of
conservation versus conventional tillage, and to serve as a
proxy for the value Of mitigating Off-site impacts. A
related policy issue pertains to determining whether or not
any soil savings are of sufficient value to society to
compensate for any rents conferred on farmers.

Analysis in Chapter Five also suggests that conservation
tillage does not always pay. While soil loss is lower, and
therefore, discounted gross revenues are higher, pesticide
and fertilizer expenditures also tend to be higher. The
question then becomes whether or not the present value of
revenues minus Operating costs is greater than the sum Of (1)
any increased capital cost Of the conservation system, (2)
any transition costs, and (3) the farmer's risk premium
associated with moving to a management system which may be
perceived as being riskier. Since this research assumes away
the latter two costs, which in reality are probably positive,
the issue is whether or not the present value Of revenues
minus Operating costs compensates for the higher capital cost
of the conservation tillage system. In the cases analyzed,
the answer was no in the area Of low soil erosion potential.

Unless there is some paticularly unique aspects Of the

74
off-farm enviornment it would be relatively more difficult to
justify subsidies as a bribe to farmers, in these areas, to
reduce their rates of soil loss.

Another Observation from results in Chapter Five is that
when the value of increased future soil productivity
attributable to lower current erosion is included in the
analysis, some farmers have an incentive to act in a manner
consistent with reducing off-site impacts Of soil loss. That
is, there is a limit to which the farmer's interests are
served by mining the soil. This limit will tend to increase
with increases in net returns, to the less erosive crop
system. In turn, this would tend to suggest that the
allocation Of cost share funds should perhaps also be
affected by income level.

The analysis conducted in this research does not provide
information for such a global question as: what is the
correct government policy? What this research does represent
is a further step towards a more complete formulation of the
investment problem from the individual investors' view. In a
world of voluntary adoption, this is the relevant unit Of
analysis.

Finally, there are some specific conclusions from the
analytical model and analysis. These are presented below.

First, concerning the develOpment of the analytic model,
it is important to distinguish between the one trade problem
and the multiple switch problem, at this level of

sOphistication. With the one trade problem, a piecewise

 

75
linear solution algorithm can be used to solve the problem
which does not require exhaustive enumeration, as does the
multiple switch problem.

Second, given the simplicity of the algorithm used in
this model to solve the problem Of which set of crop systems
to use, the analyst must pay particular attention to the set
Of management Options which are selected for consideration.
Taking into consideration that one management Option can be
differentiated from another by (a) number Of crop systems,
(b) differences in switch years, (c) types of crop rotations,
and (d) types of tillage equipment, how good a selection is
made depends, in part, on how good the set Of management
Options is from within which one is choosing.

Third, in Saginaw County, the moldboard plow systems had
higher NPV's than their comparable chisel plow systems.

Since the capital cost Of the moldboard and chisel plow
systems were nearly identical, it was the relative yields and
the pesticide-herbicide regimes which exerted the greatest
effect on the relative profitability of competing systems.
Fourth, for St. Joseph County, some crOp systems using the
chisel plow had a higher NPV than the comparable crop system
using the moldboard plow. For these cases, the joint profit
of a moldboard-chisel plow combination approached the profit
level of the system using the chisel plow from t=to, the
sooner the chisel plow system was adOpted. Therefore, it was
always better to use the chisel plow system from the

beginning, rather than switching to it later.

 

76

Fifth, the model developed in this research, and the
existing version of the Pierce et. a1. model used by ERS, are
not adequate for policy analysis where accurate profit
estimates for a particular system are required. This is
because (a) both the model used in this research and
ERS'model omit many financial and tax parameters important to
a financial analysis of competing crop systems; (b) this
analysis assumed that real prices would remain constant in
relative terms; and (c) ERS' model calculates the maximum
amount that a farmer can invest in a chisel plow system by
comparing the cash flows for a moldboard plow system and a

hypothetical system assumed to be in a steady state.

CHAPTER SEVEN

FUTURE RESEARCH DIRECTIONS

7.1 Introduction

Based on the prior six chapters, what suggestions can be
made regarding issues for future research? Referring back to
chapter one, one goal Of this analysis was to identify a set Of
issues which could comprise a research agenda in this subject
matter area.

For purposes of discussion, future research directions are
segmented into: (1) model structure and development, and (2)
data base develOpment. Further, model structure issues are
limited to advancing the sOphistication of simulation

approaches.

7.2 Model Structure Development

Four research areas are: (l) incorporating tax/financial
structure in the model, (2) expanding the range of activities a
producer may pursue, (3) inbedding equipment selection in the
productivity analysis, and (4) including weather in the
analysis to a greater extent than is currently the case. Each

of these points will be discussed below.

77

78

7.2.1 Incorporating Tax/Financial Structure

This may be the most important extension which could be
made to the modeling of this problem. Issues of capital
availability, after tax cash flow, after tax profit,
depreciation,and other financial parameters are important to
the decision making process. In turn, policy analysis is
improved when based on after tax profit because of the relation

between after tax profit and the ability to invest. Even if
the relative profitability of any two or more alternatives
remain the same after tax as before tax, shifting to an after
tax analysis may be important for policy analysis when
policies, such as subsidy levels, are being considered. If the
relative magnitudes change after tax as compared tO before tax,

there is an even greater need to use an after tax analysis.

7.2.2 Expand the Range of Possible Activities

At present, the various simulation models have implicitly
assumed either that (a) the producer does not engage in any
other activities, or (2) the producer's cash flow from other
activities is separable from the investment and returns from
the cropping activities being studied. At the very least, this
limits the applicability Of the simulation approaches to
producers who are not vertically integrated forward or backward.

One possible extension would be to explicitly allow for
interdependent cash flows between Operations. For example,
this would allow the analyst to endogenize a livestock

enterprise and study the relation between changes in the crOp

79
enterprise and the livestock enterprise. Some of the existing
LP models which were reviewed in chapter two already have dealt
with this issue.

Another extension Of this analysis would be to allow for
stochastic cash flows and to study the problem Of asset
investment/disinvestment in a portfolio theory context. One
contribution Of this type Of extension would be to characterize
the capital allocation process Of the decision maker in a
broader context.

One additional extension would be to allow for a broader
range of enterprises in the farm Operation. While the current
analysis includes some horizontal integration, producing corn
and soybeans for feed, for example, vertical forward
integration into storage, transportation, and livestock
activities would be some possibilities.

Extending the analysis in this way may be important for
several reasons. First, the issue of capital allocation in a
portfolio theory context, as was discussed above, may lead to
different results concerning partial allocation. Second, to
the extent that alternative crop rotations are affected by
livestock Operations, a shift in machinery and/or crop
sequences which would be desirable from the view towards soil
loss are separable cash flows, may in fact not be desirable
from the expanded whole farm perspective.

Third, the present model cannot be used to anaLyze the
relative economics of switches in crOp rotations during the

time horizon the decision maker. While the model has been

 

80
constructed to address this possibility, the data are not
available as to how the machinery complement may change.
Currently, studying switches in crOp rotations also requires
that the machinery complement be traded. This arises because
MACHSEL generates different machinery complements for the crop
sequences studied, ceteris paribus. Information needs to be
compiled on how the machinery complement may change, given a

change in crop rotation.

7.2.3 Endogenize Equipment Selection in the Productivity
Analysis

One limit to all the simulation modeling approaches is
handling the machinery complement. Selecting the appropriate
mix and size Of machines is an input to the model which
performs the productivity analysis. Then, the selection of a
machinery complement occurs via the selection of the most
profitable crop system, based in part on the productivity
model. It is not necessarily the case that the type and/Or
size of the machinery mix which corresponds to the Optimal crop
system, as it is presently selected, is the same as would be
selected based on net cash flows derived based on the
productivity model. There doesn't appear to be any way to say,

apriori, how the equipment sizing/selection may change.

7.2.4 Endogenize Weather
Setting aside both the EPIC model and Muhtar's model, in

both the ERS model and the model developed by this author,

81
weather is deterministic. Weather is accounted for only
through the use of long run rainfall parameters in calculating
soil loss. Including weather is important for the impact it
can have on actual crop yields as this is affected by the soil

type. machinery complement. and crop residue.

7.3 Data Base Development

Three areas where data can be improved are: (1) the
relation between crop rotation/ tillage method/ and pesticide -
fertilizer regime. (2) the relation between crop rotation/
tillage method/ soil type and initial yield. and (3) the cost,
process, and decision making involved in the decision to adopt
some soil conserving practice. Each of these points will be

discussed below.

7.3.1 Crop Rotation. Tillage Method. Pesticide - Fertilizer
Regime

Based on this authors' research. the pesticide - fertilizer
regime assumed to be used with various crop systems can be a
very important determinant of the relative economics of
conventional versus conserving systems. There appears to be
controversy among various researchers in this area concerning
what pesticide - fertilizer regime to assume under a given set
of circumstances. This should be explored not only to arrive
at some consensus among researchers. but to reconcile theory

with practice.

82

7.3.2 Crop Rotation. Tillage Method. Soil Type. Initial Crop
Yield

Again. there appears to be a lack Of consensus as to the
relation among crop rotation. tillage method. soil type. and
initial crop yield. It is particularly important to determine
the extent to which conservation systems have higher or lower
yields than a conventional system. ceteris paribus. TO the
extent that more pesticides and fertilizer are used with a
conservation system. relative yields. become more important.
As the discount rate decreases. this Observation attains even

more importance.

7.3.3 Cost. Transition. and Selecting a Soil Conserving Strategy
Not much is known concerning the transition process
producers go through when adopting a less erosive crop system
and/or structural improvement. Referring to the machinery
complement. to what extent is the Old equipment kept versus
sold? What does the learning curve look like pertaining to

achieving potential yields under the adopted system?

APPENDIX

APPENDIX

DATA

Economic analysis of alternative crOpping systems which
attempts to endogenize intertemporal soil productivity under a
given management system requires that the analyst compile data
on both the relevant economic, management, and physical
parameters. One possible taxonomy of the data is the following:

1. Economic - non producer dependent;
2. Economic - producer dependent:

3. Management system; and,
4. Physical system.

The data used in this analysis, and the sources of the data are

the subjects of this appendix.

Economic - Non Producer Dependent

Both the prices of selected inputs to production and
outputs from production are assumed to be independent of the
actions of any one producer. Table A.l lists the input and
output prices assumed in this analysis. Other inputs to the
production process which are producer dependent will be

discussed in the following section.

Economic - Producer Dependent
The remaining economic parameters are (1) the discount
rate; (2) annualized machinery cost; and (3) timliness, fuel,

83

84
and labor cost. The reader should note that if the analysis
was extended to after tax from before tax, there would be
additional producer dependent costs reflecting the producer's
tax bracket, tax rates for all the relevant taxes, depreciation
rates, and so forth.

Table A.2 lists the values of the previously mentioned
parameters. As is indicated in the table, the machinery costs
used in this analysis represent the annualized cost on a per
acre basis. These costs are calculated by an engineering
model, MACHSEL, develOped in the Agricultural Engineering
department at Michigan State University. As was discussed in
chapter two, MACHSEL is a heuristic simulation model which
searches for the approximately Optimal machinery complement
which minimizes the annualized cost Of performing a specified
set Of farming practices, for a particular crop rotation,
subject to a constraint on time. When a particular complement
is not able to perform the Operations within the time
constraint, a penalty, in the form Of an Opportunity cost, is
assessed. Adding discounted maintenance costs, discounted
owner labor charges, and discounted fuel costs together, the
total machine complement dependent variable cost is Obtained.
Dividing discounted machinery fixed cost and machine dependent
variable cost, by the appropriate annuity factor and farm size,
one Obtains annualized fixed and machine dependent variable
cost, on a per hectar basis. Since MACHSEL assumed a 200
hectar farm when generating the equipment complements, the

value in the table assumes a farm size which is the acre

c/

85
Table A.1

Factor-Product Prices for Inputs/Outputs whose
Price/Cost are Non-Producer Dependent

 

 

Factor - Product33 Price ($)
Amiben 8
Atrazene 2.37
Basagran 21.05
Betamix 44.07
Blazer 37.50
CrOp Oil 4.0/gal.
Dual 5.96
Eptan 2.92
Lasso 5.02
Lexone 23.90
Nortron 35.50
Pyramin 13.25
Treflan 7.0
H 273 9.74
2,4 - D 2.0
NitrOgen .15
Phosporous .23
Potassium .lO
Corn seedb 1.25
Navy bean seed .50
Soybean seed .28
Sugar beet seed 10.0
Cornc 2.78 bu.
Navy bean 22.38 cwt.
Soybeans 6.54 bu.
Sugar beets 35.47 ton

 

 

Notes:

a/All herbicide prices are adjusted to reflect the cost per
pound of active ingredient. The prices were develOped by
David Tschirley and Gerald Schwab, Department Of Agricultural
Economics, Michigan State University. August 1984.

b/ Seed prices are per pound. Source:Sherril Nott, Gerald
Schwab, Mike Kelsey, Jim Hilker, and Al Shapley,Estimated
Crop and Livestock Budgets for 1984, Agricultural Economics
Report 446, Michigan State University,February, 1984.
Product prices were Obtained from: Economic Research
Service, USDA, Normalized Prices,Washington, D.C., October
24. 1983.

 

86
equivalent Of the 200 hectar farm.
Management System Data
All of required data describe characteristics of the crOp

system(s) which are studied. For the purposes of this
discussion, the croP system is completely described when
information on the following three characteristics are provided:

1. Crop rotation;

2. Tillage method (machinery complement); and,

3. Tillage practice.

The machinery model used to calculate the machinery
complement assumes that the farm's acreage is equally divided
between the crOps in the rotation. Since the
depletion/productivity model is structured on a per acre basis,
for modeling purposes, each acre is assumed to be divided
between the various crops in the same fraction as is the entire
farm's acreage. Table A.3 lists the various crop rotations,
fraction Of an acre planted to each crOp, and yields. Table
A.4 lists the herbicide, pesticide, and fertilizer usage by
crop rotation and machinery complement. Table A.5 lists the
machinery complements and tillage practices used in the
analysis.

The crop rotations,machinery complements, and soil series
were selected in response to the following guidelines:

1. Select crop rotations which are representative
of rotations used in each study area;

2. Secect one machinery complement which uses a moldboard
plow, and one which uses a chisel plow;

3. Select a soil series which is representative Of the
soil characteristics found in the study area;

 

87

Table A.2
Producer Dependent Factor Prices

 

Equipment Dependent Costsc

 

Conventional Conservation

---------- Machinery Costs --
C/NBd 76.57 75.23
C/NB/SGB 96.00 92.96
0/0 77.98 72.28
C/C/SB 66.89 66.98

--------- Fuel, Labor, Timliness-------
C/NB 23.34 17.79
C/NB/SGB 27.60 23.98
C/C 20.49 17.60
C/C/SB 26.22 24.95

 

Notes: a/ Equipment dependent costs are Obtained from a
Tillage report prepared by the Department of Agricultural

Economics and Agricultural Engineering, Michigan State
University, Summer 1984.

b/ Rate used to evaluate public projects, published by the
Water Resources Council.

c/ All cost are annualized cost on a $/acre basis.
d/ C=Corn, NB=Navy Beans, SYB=Soybeans, SGB*Sugar Beets.

C/NB denotes a corn-navy bean rotation. All other
rotations can be similarly interpreted.

4. Make sure that there is compatibility between the
selection made in response to the above four points;

5. Be sure that the selections above can be analyzed,
which requires that there exist the necessary infor-
matio on the soil, on soil erosion, on yield, and
on input use for those inputs listed in Table A.4.
Physical Systems Data

Since the relative economics Of alternative management
practices depend in part on the nature Of the underlying
physical system, it is important tO be specific about what
is being assumed about that system. Some Of this

information is contained within the computer model and is

invariant to the selection of a crop system. Other pieces

 

88
Table A.3

Crop Rotations, Acerage Allocation, Initial Yields

 

Saginaw County
Rotation Percent Ac. 08 NB SIB SGB
(bu) (cwt) (bu) (ton)

Conventional
C/NB 50/50 115 13 - -
C/NB/SGB 33/33/33 115 13 - 21
Conservation
C/NB 50/50 115 13 - -
C/NB/SGB 33/33/33 115 13 - 21

St. Joseph County

 

Conventional
0/0 50/50 105/100b - - -
C/C/SYB 33/33/33 115/105 - 38 -
Conservation
C/C 50/50 100/100 - - -
C/C/SIB 33/33/33 115/100 - 38 -

 

Source: Data compiled by Davidechirley in conjunction with Don
Christianson. Departments Of Agricultural Economics and

Crops and Soil Science, respectively. August 1984.

Notes: a/C=Corn, NBeNavy Beans, SYBFSOybeans, SGBBSugar Beets

b/ A/B: A - yield of corn in first year; B - yield of

corn in the second year for corn.

Of information are dependent on either the crop system and/or

soil being studied. Two blocks Of information must be user
supplied:
1. Physical system and crOp system parameters used
to calculate soil loss:

2. Selected characteristics of each horizon in the soil
profile of the soil series being studied.

The second block of information is used in calculating the

productivity index Of each horizon in the soil profile, and the

89

annual rate of soil loss. Data which are required to calculate
the annual rate Of soil loss correspond to the parameters of

the Universal Soil Loss Equation. These parameters are:
R - Rainfall factor;
CF - CrOp rotation/Farm practice composite factor;
LS - Field slope/SlOpe length composite factor;
TP 8 Tillage practice factor.

Several of the parameters need explanation. First, the Cp

 

factor is a function of (a) crop rotation: (b) tillage method: !
(c) when tillage occurs using a mold board plow, (d) whether :
residue is removed or not, and (e) the amount Of residue 4
(lb/ac) left on the field when chisel plow is used. Table 1.5 i
presents the assumptions underlying the CP factors used in the t

analysis.

Second, the LS factor is read Off a graph which correlates
lepe length and percent slope and indicates a particular LS
factor. The percent lepe which is used corresponds to the
mean of the range Of possible lepe for the predominant slope
range for the particular soil being used in the area being
studied.

Third, the TP factor is a weighting factor whose value
depends on what type of plowing occurs (eg: whether straight
up/down plowing is pursued, or contour plowing is used).
Up/down plowing has a factor of 1.0.

Data which are used to calculate soil productivity which
are situation specific are Obtained from the SOILS - 5 record
for the particular soil series being used. These data are: (l)
depth of each horizon in the soil profile, (2) permeability Of

each horizon, (3) Ph for each horizon, and (4) available water

90

Table A.4

Herbicide, Fertilizer and Seed Use
by Crop, Crop Rotation, and Tillage Method

 

 

Conventional Conservation
Herbicides
Corn, except preceding sugar beets
Lasso - 2.0 Lasso - 2.5
Atrezene - .5 Atrezene - .75
Bladex - 1.0 Bladex - 1.0
Corn, preceding sugar beets
Lasso - 2.0 Lasso - 2.5
Bladex - 1.5 Bladex - 1.5
Navy Beans
Eptan - 2.25
Treflan - .5 Amiben - 2.0
Amiben - 2.0 Basagran - .75
Crop 011 - 1 qt./ac
Soybeans
Treflan - .75 Lasso - 2.5
Lexone - .38 Lexone - .38

Basagran - 1.5

Blazer - .25

Crop Oil - 1 pt./ac.

Sugar Beets

Pyramin - 3.0
Nortron - 2.0
Antor - 2.0 Same
H 273 - .5
Betamix - 1.0

Seed application rates1

Corn 15 1b/ac
Navy beans 40 1b/ac
Soybeans 45 lb/ac
Sugar beets 1 1b/ac

Phosphatel Fertilizerl Potassiuml

Corn (lb/bu) .35 1.25 .27
Navy beans (lb/cwt) .83 3.13 .83
Soybeans (lb/bu) .9 O 1.4
Sugar beets(lb/ton) 1.3 5 3.3

 

‘SOurceszl/Data compiled by David Tschirley and Ted Jenne with
assistance from Drs. Don Christianson and John Kells,
Departments Of Agricultural Economics and Agronomy,
respectively, Michigan State University, August 1984.

CrOp Rotation/Farm Practice, CP, Factors

91

Table A.5

for Alternative Crop Rotations, Tillage Methods,

and Geographic Locations

 

Rotation
C/NB
C/NB/SGB

C/NB
C/NB/SGB

--------------------- St. Joseph County ---------------------

C/C
C/C/SYB

C/C
C/C/SYB

- -- Saginaw County -

Conventional

Conservation

Conventional

Conservation

 

CP Factor
.49/ . '52a

.54 A

.32
.44

 

.30 j
.37

.17
.26

 

Note:a/ The first figure assumes up/down plowing and the second

assumes contour

plowing.

capacity. Except for depth, the number used in the analysis

corresponds to the mean Of the range Of possible values for

each parameter for each horizon.

 

BI BLIOGRAPHY

 

l.

8.

9.

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