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LIBRARY

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University

 

 

 

This is to certify that the

dissertation entitled

Designing Production Contracts to Reduce
Agricultural Nonpoint Source Pollution

presented by

Me i-Chin Chu

has been accepted towards fulﬁllment
of the requirements for

Ph.D. Agricultural Economics

degree in

Major progessor

 

 

Date August 6 , 1997

 

MS U is an Afﬁrmative Action/Equal Opportunity Institution 0-1277!

 

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DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU ioAn Ni'irrnotivo Action/Equal Opportunity inotltmon
m

Ina-9.1

DESIGNING PRODUCTION CONTRACTS TO REDUCE
AGRICULTURAL NONPOINT SOURCE POLLUTION

By

Mei-Chin Chu

A DISSERTATION
Submitted to
Michigan State University

in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultural Economics

1997

ABSTRACT

DESIGNING PRODUCTION CONTRACTS TO REDUCE
AGRICULTURAL NONPOINT SOURCE POLLUTION

By

Mei-Chin Chu

The restructuring of US. agriculture toward more contract arrangements
between the agribusiness ﬁrm and the producer could provide new opportunities to
control nonpoint source pollution (NPSP). This research addressed two issues: Can a
production contract be used as a means to reduce NPSP? If yes, what incentives can be
incorporated to induce the contracted producers to achieve voluntary NPSP abatement?
A seed corn contract in St. Joseph County, Michigan, is employed as a case study to
explore contract speciﬁcations that can reduce nitrate leaching. Seed corn is widely
grown in St. Joseph County, where signiﬁcant nitrate levels have been found in
groundwater.

The analysis shows that certain contract speciﬁcations, such as a high price
premium on marginal gains in seed corn yield and grower concern over risk of contract
loss, could be directly related to high nitrogen application rates. These rates, in turn,
could result in excessive nitrate leaching. Other agronomic practices, such as crop
rotation, also affect nitrate leaching outcomes.

Four categories of alternative contract designs are discussed. They are: a)

restricting agronomic practices or nitrate leaching, b) charging a fee on nitrate leaching

or nitrogen use, c) reducing the variable payment, and (1) providing appropriate
agronomic information for nitrate reduction. These contract designs are evaluated with
respect to nitrate leaching and proﬁtability for a representative seed corn processing
ﬁrm and contracted-grower within a principal-agent model. These evaluations are
implemented using a grower whole-farm optimization model, based on 42 years of
simulated yield and nitrate leaching data. Two forms of dominance analysis, contract
acceptability dominance and cost effectiveness dominance, are used to evaluate the
feasibility and efﬁciency of alternative contracts.

The results show that contracts can be redesigned to reduce nonpoint source
pollution. Contract designs that targeted nitrate leaching directly or agronomic
practices both succeeded in reducing expected nitrate leaching. These contract designs
can be mutually acceptable to both the processor and the contracted grower; however,
the choice of the leaching threshold level as well as incidence of cost hearing are
crucial.

The results also indicate that targeting only a single contracted crop does not
necessarily reduce whole-farm leaching levels. Enforceability is a key issue in
determining the feasibility of alternative contract designs to reduce NPSP voluntarily.
Given that low cost techniques to monitor NPSP are not available, targeting observable

agronomic practices such as crop rotation was the preferred contract design.

K913219315; production contract, seed corn, nitrate leaching, whole-farm model,

principal-agent theory, safety-ﬁrst programming, quadratic programming

Dedicated to my beloved parents Fu Chu and Ming Wu

ACKNOWLEDGMENT

Life is a voyage of discovery and I have been fortunate enough to have
discovered many people at Michigan State University who have made my stay here a
wonderful journey.

First and foremost, I would like to thank Dr. Sandra Batie, my major professor,
and Dr. Scott Swinton, my thesis supervisor, for their encouragement and patience, not
only in my research but also in my professional career. Their inputs in my dissertation
are tremendous.

I would also like to thank the other members of my guidance committee, Dr.
Steve Harsh who helped me with my empirical analysis. Dr. John Hoehn who taught
me how to communicate efﬁciently in this profession; and, lastly to Dr. Jack Meyer
whose inputs in the ﬁnalization of my theoretical model were very valuable.

The ﬁnancial support from National Research Initiative (N RI), supported by
USDA, and dissertation completion fellowship from Associate Dean Rick Brandenburg
are highly appreciated. I am also very grateful for the support from the NR1 project
research, especially to Dr. Joe Ritchie and Mr. Brian Baer from the Department of
Crop and Soil Science who have helped with the simulation data. I also beneﬁted from
the help of Dr. Otto Doering, Dr. Craig Dobbins, and Miss Becky Pfeifer. Rod King,

extension director in St. Joseph County, Gary Brinkman, Adorée Miron, and Steve

Lupkes from Pioneer, and the others from extension ofﬁce.

I wish to also acknowledge the support from the department. My sincere
appreciation for the support and the tremendous help of Dr. Eric Crawford, Dr. Linden
Robison, and Dr. Steve Hanson. Special thanks to secretaries Pat Eisele, Pat Neuman,
Ann Robinson, and Sherry Rich; librarians, Marty Duarte and Judith Dow; computer
staffs, Elizabeth Bartilson, Carol Graysmith, and Chris Wolf. Not only did they
provide the most efﬁcient way to meet my requests, but also extended their friendship
and personal support during my graduate career.

Many thanks go to my department peers and graduate students: Mubariq
Ahmad, Oggie Arcenas, Kim Aldridge, Sam Asuming-Brempong, Gregg Hadley,
Daniel Karanja, Anwar N aseem, Brian Radke, Tom Moen, Lorie Srivastava, Matt
Schaefer, David Yanggen ...... Thank you for helping me with my writing, and for the
spiritual support and encouragement. Your company has made my life here a very
joyful experience.

I would also thank my friends from home for the encouragement especially
when I was down. Special thanks go to my sweet roommate Meng-Li Yang whose
continuous encouragement and cooking skills have helped me go through low
movements in my student life. The friendships from Su-Hao Tu, Ching-Ju Lin, and
Ishien Li have made my life here full of surprises and more colorful.

I would like to thank my friends here. I owe a special debt of gratitude to my
host family, Celia and Frank Marxer. I am very grateful to them for making me a

member of their home. I am going to miss their turtles, garden, birds, ﬂowers,

vi

vegetables, and pleasant company. Special thanks to Stacey and Tom Bieler from
University Reform Church for friendship and helping my writing.

Finally, I would like to thank my parents, Fu Chu and Ming Wu, for giving me
the opportunity to pursue my dreams. It is the best gift that I have ever had, and one
that has changed my life. Thanks for your unconditional love. To my brothers, Da-
Yu, Yin-Chi, and Da-Jiang, and sister, Mei-Hui, thank you too for helping me in many

ways that are not apparent to you.

vii

TABLE OF CONTENTS

LIST OF TABLES .......................................... xii
LIST OF FIGURES .......................................... xiv
CHAPTER 1
INTRODUCTION ....................................... 1
1.1 The Problems of Agricultural N onpoint Source Pollution ......... l
1.2 Signiﬁcance of Production Contractual Arrangements ........... 4
1.3 Signiﬁcance of Nitrate Leaching ......................... 8
1.4 Research Objectives ................................. 9
1.5 Organization of the Dissertation ........................ 10
CHAPTER 2
ISSUES FOR DESIGNING PRODUCTION CONTRACTS TO REDUCE
AGRICULTURAL N ONPOINT SOURCE POLLUTION ............ 13
2.1 Problems of Agricultural NPSP ......................... 13
2.1.1 Sources of Variation in Outcomes .................. 15
2.1.2 Imperfect Monitoring and Measurement .............. 17
2.2 Elements in Modeling NPSP Abatement ................... 19
2.3 NPSP Abatement in a Contractual Production Relationship ....... 22
2.3.1 Issues Related to Nitrate Leaching Reduction ........... 23
2.3.2 Strategies for Nitrate Leaching Reduction ............. 25
2.3.3 Evaluation for Alternative NPSP Strategies ............ 28
2.3.4 Lessons from Regulatory Policy Designs .............. 32
2.4 Summary ....................................... 34
CHAPTER 3
CONTRACTUAL PRODUCTION:
A SEED CORN CONTRACT IN ST. JOSEPH COUNTY, MICHIGAN . . 36
3.1 Contractual Production .............................. 36
3.1.1 Categories of Production Contracts ................. 39
3.1.2 Compensation Methods ......................... 40
3 .2 Contractual Seed Corn Production ....................... 42
3.2.1 Seed Corn Industry in the United States .............. 42
3.2.2 Seed Corn Production Management ................. 43
3.3 Geographic Characteristics of St. Joseph County ............. 45
3.4 A “Tournament” Seed Corn Contract in St. Joseph County ....... 47
3.4.1 A “Tournament” Seed Corn Contract ................ 48
3.4.2 Key Environmental Issues: Nitrate Leaching ........... 49
3 .5 Summary ....................................... 51

viii

CHAPTER 4
THEORETICAL FRAMEWORK FOR CONTRACT DESIGNS:

A PRINCIPAL-AGENT MODEL ............................ 52
4.1 Review on Contract Design Literature .................... 52
4.2 Conceptual Framework for A Seed Corn Contract ............. 57
4.2.1 Objective of the Processor and Contracted-Grower ....... 58
4.2.2 Seed Corn Production and Leaching Functions .......... 59
4.2.3 Participation Constraint and Incentive Compatibility
Constraint .................................. 62
4.2.4 Optimization Without Environmental Constraint ......... 62
4.3 Alternative “Green” Contract Designs ..................... 64
4.3.1 Imposing 3 Restriction within Contracts .............. 65
4.3.2 Specifying Financial "Punishment" within Contracts ...... 68
4.3.3 Reducing the Incentive Payment Schemes ............. 69
4.3.4 Providing Information within Contracts ............... 71
4.4 Summary ....................................... 72
CHAPTER 5

SIMULATION OF ALTERNATIVE CROP MANAGEMENT SCENARIOS
.................................................. 74
5.1 Review on the Crop Growth Simulation Model -- DSSAT 3.0 ..... 74

5.2 Analytical Methods to Simulate Crop Yield and Nitrate Leaching . . . 76
5.2.1 Methods for Crop Growth and Nitrate Leaching Simulation . 78

5.2.2 Adjustment to the Original Model .................. 80
5.3 Simulation Yield and Nitrate Leaching Data from DSSAT 3.0 ..... 82
5.3.1 Nitrogen Application and Seed Corn Yield ............ 85
5.3.2 Nitrogen Application and Nitrate Leaching ............ 86

5.3.3 Relationship between Seed corn Yield and Nitrate Leaching . 86
5.3.4 Yield and Nitrate Leaching Distributions under Three

Nitrogen Treatments ........................... 89

5.4 Yield and Nitrate Leaching Data for All Enterprises ........... 91
5 .5 Summary ....................................... 97

CHAPTER 6

AN EMPIRICAL PRINCIPAL-AGENT MODEL ................. 98
6.1 Mathematical Programming Model for Optimal Contract Designs . . 98
6.2 Welfare Measurement for the Seed Corn Contract ............ 100
6.3 A Linear Programming Model ........................ 103
6.3.1 Assumptions of a Linear Programming Model ......... 104

6.3.2 Purdue Crop/Livestock Linear Programming .......... 106

6.4 Description of the Seed Corn Farm Based Model ............ 107
6.4.1 Resource Constraints .......................... 107

6.4.2 Crop Enterprises ............................ 109

6.4.3 Yield Adjustment and Moisture Content ............. 112

ix

6.4.4 Tillage Practices ............................. 114
6.4.5 Commodity Prices and Input Costs ................. 115

6.5 Optimization of the Representative Risk-Neutral Whole-Farm Model
............................................ 1 16
6.5.1 Shadow Prices .............................. 119
6.5.2 Sensitivity Tests ............................. 120
6.5.3 Other Commodity Price Scenarios ................. 123
6.6 Analysis of Alternative Contract Designs ................. 125
6.6.1 Justiﬁcations of Alternative Contract Designs .......... 126
6.6.2 Impacts on Nitrate Leaching Reduction from Alternative
Contract Designs ............................ 128
6.6.3 Impacts on Gross Margin from Alternative Contract Designs
........................................ 132
6.6.4 Contract Acceptability Dominance ................. 135
6.6.5 Cost Efﬁciency Dominance ..................... 138
6.7 Summary ...................................... 141
CHAPTER 7
CHANCE CONSTRAINTS IN DESIGNING SEED CORN CONTRACTS
TO REDUCE N ITRATE LEACHING ....................... 144
7.1 Issues in Designing Seed Corn Contracts to Reduce Nitrate Leaching
............................................ 145
7.1.1 Risk of Seed Corn Contract Loss .................. 145
7.1.2 A Probabilistic Nitrate Leaching Reduction Strategy ..... 146
7.2 Safety-First Rule: A Probabilistic Chance Constraint .......... 148
7.2.1 Modeling Contract Loss Risk Avoidance ............. 148
7.2.2 Modeling a Probabilistic Leaching Control ........... 150
7.2.3 Modeling the Whole-Farm Decision Rule ............ 151
7.3 Whole-Farm Optimization with a Chance Constraint on Contract
Loss ......................................... 155
7.4 Speciﬁcation of a Chance Constraint on Nitrate Leaching ...... 160
7.4.1 Probabilistic Chance Constraint on Nitrate Leaching
Threshold 35 lb/ac ........................... 161
7.4.2 Probabilistic Chance Constraint on Nitrate Leaching
Threshold 40 1b/ac ........................... 166
7.4.3 Comparisons Between Nitrate Threshold at 35 lb/ac and
40 lb/ac within a Leaching Chance Constraint ......... 169
7.5 Summary ...................................... 170
CHAPTER 8
AN EMPIRICAL PRINCIPAL-AGENT MODEL WITH RISK AVERSION
................................................. 172
8.1 Sources of Ordinary Business Risk ..................... 172
8.2 Mean-Variance Objective Function ..................... 173

8.3 Growers Optimization under Different Levels of Risk Preference . . 176
8.4 Alternative Contract Designs with Risk Aversion ............ 180
8.5 Efﬁciency under Two Dominance Criteria ................. 188
8.5.1 Contract Acceptability Dominance ................. 188
8.5.2 Cost Efﬁciency Dominance .................... 190
8.5.3 Evaluation Under Both Efﬁciency Criteria ............ 192
8.6 Enforcement of Contract Speciﬁcations ................... 193
8.7 Summary ...................................... 194
CHAPTER 9
CONCLUSIONS AND IMPLICATIONS ...................... 196
9.1 Review of Research Objectives ........................ 196
9.2 Conclusions .................................... 203
9.3 Policy Implications ................................ 205
9.4 Limitations and Suggestions for Future Research ............ 207
APPENDICES ............................................ 210
A. PARAMETERS USED IN CROP GROWTH SIMULATION MODEL
DSSAT 3 .0 .......................................... 211
B. WEATHER INPUT FOR DSSAT 3.0 ........................ 212
C. COEFFICIENTS IN THE WHOLE-FARM PROGRAMMING MODEL . 213
D. OPTIMAL CROP ENTERPRISES FROM EXPECTED UTILITY
MAXIMIZATION ..................................... 220
E. PROOF THE EQUIVALENT CONDITION OF A CHANCE
CONSTRAINT ....................................... 222
F. GAMS VERSION OF PC-LP WHOLE-FARM PROGRAMMING
MODEL ........................................... 224
REFERENCES ............................................ 238

xi

 

I s

Table 2.1:
Table 5.1:

Table 5.2:

Table 5.3:

Table 6.1:

Table 6.2:

Table 6.3:

Table 6.4:
Table 6.5:

Table 6.6:

Table 6.7:

Table 7.1:

Table 7.2:

Table 7.3:

Table 7.4:

Table 7.5:

Table 7.6:

Table 7.7:

Table 7.8:

LIST OF TABLES

Evaluation of nonpoint source pollution abatement strategies ...... 30
Average simulated seed corn yield and nitrate leaching from

DSSAT 3.0 for St. Joseph County, Michigan, 1951-92 ......... 83
Mean simulated yields of four crops from DSSAT 3.0 for St. Joseph
County, Michigan, 1951-92 ........................... 94
Mean simulated nitrate leaching of four crops from DSSAT 3.0

for St. Joseph County, Michigan, 1951-92 ................. 95
Mean yield and nitrate leaching under enterprises included in the
whole-farrn programming model ....................... 110
Crop prices and cash production expenses (excluding nitrogen cost)

of each crop .................................... 116
Summary of optimization results for a representative grower in the

base scenario model ............................... 117
Alternative seed corn contract designs ................... 125
Mean yield and nitrate leaching for a proﬁt-maximizing grower

Under different contract designs ....................... 129
Nitrate leaching, principal’s and agent’s gross margins under

various contracts ................................. 133

Nitrate leaching, principal’s and agent’s gross margins, and unit

cost of leaching reduction from seed corn production under various
contracts ...................................... 138
Seed corn mean yield and nitrate leaching from growing seed corn
(ASNL) and from the whole farm (ANL) under different regional

yield and permissible probability levels of a contract loss chance
constraint ...................................... 156
Gross margins of the grower and the processor under different

regional yield and permissible probability levels of a contract loss

chance constraint ................................. 156
Acreage of seed corn enterprise under different regional yield and
permissible probability levels of a contract loss chance constraint . . 157
Summary of seed corn yields from DSSAT 3.0 using different agronomic

practices under 10 states of nature ...................... 159
Summary of nitrate leaching, proﬁts, and unit cost of leaching
reduction under a probabilistic constraint Prob (SNL235): 1/h* . . . 161

Shadow prices of land and contracts, and crop enterprise mix from
the grower’s proﬁt optimization under a probabilistic constraint

Prob(SNL235)_< I/h’ ............................... 162
Summary of nitrate leaching, proﬁts, and unit cost of leaching
reduction under a probabilistic constraint Prob (SNL240): 1/h* . . . 166

Shadow prices of land and contracts, and crop enterprises for a
proﬁt-maximizing grower under a probabilistic constraint
Prob (SNLz40)s 1/h* .............................. 167

xii

Table 8.1:

Table 8.2:
Table 8.3:

Table 8.4:

Table 8.5:

Table 9.1:
Table B.1:
Table C.1:
Table C.2:
Table C.3:
Table C .4:
Table C.5:
Table C.6:
Table C.7:
Table D.1:

Summary of the grower’s expected-utility maximization results under

three risk preference levels ........................... 176
Optimal crop enterprise mix under three risk preference levels . . . 176
Summary of the results from various alternative contract designs for

the growers with different risk preference levels ............. 182
Contracts that are undominated under contract acceptability

dominance under various levels of grower risk aversion ........ 189
Contracts that are not dominated under cost efﬁciency dominance

under various levels of grower risk aversion ............... 191
Evaluation of alternative contract designs under various criteria . . . 204
Mean average weather data during 1951-1992 .............. 212
Machinery working rates ............................ 213
Time periods and suitable days for ﬁeld work .............. 214
Yield adjustment and moisture level sets .................. 215
Tillage practices for seed corn ........................ 217
Tillage practices for commercial corn .................... 218
Tillage practices for soybeans ......................... 219
Tillage practices for potatoes ......................... 219

Optimal mixed of crop enterprises from expected utility maximization for
alternative contract designs under three levels of risk-aversion . . . . 220

xiii

Fi

Pi

Figure 2.1:
Figure 2.2:
Figure 5.1:
Figure 5.2:
Figure 5.3:
Figure 5.4:
Figure 5.5:
Figure 5.6:

Figure 6.1:
Figure 6.2:

Figure 6.3:
Figure 6.4:

Figure 7.1:

Figure 7.2:

Figure 7.3:
Figure 7.4:
Figure 8.1:

Figure 8.2:

Figure 8.3:
Figure 8.4:
Figure 8.5:

Figure 8.6:

LIST OF FIGURES

Sources of randomness in pollution relationships ............. 14
Distribution of ambient pollution level under two abatement levels . . 16
Seed corn yield under various nitrogen treatments ............. 85
Nitrate leaching from seed corn production under various nitrogen

treatments ....................................... 86

Relationship between mean nitrate leaching and seed corn yield under

various nitrogen treatments ........................... 87
Probability distribution of seed corn yield under three nitrogen
treatments ....................................... 89
Probability distribution of Nitrate Leaching under Three Nitrogen
Treatments ...................................... 90
Relationship between nitrate leaching and seed corn yield under

different rotation practices ............................ 92
Crop mix in the base scenario ......................... 118
Mean nitrate leaching from seed corn production (ASN L) and from

the whole farm (AN L) under alternative contract designs ....... 130
Cost efﬁciency dominance analysis ..................... 139
Cost efﬁciency dominance analysis of the processing ﬁrm’s and
contracted grower’s cost for per pound of leaching reduction . . . . 140

Average nitrate leaching from seed corn production (ASNL) and

from whole farm (ANL) under different permissible probability of
exceeding 35 lb/ac ................................ 163
Unit cost of leaching reduction under different permissible

probability of mean leaching from seed corn (ASNL) exceeding the
threshold level 35 lb/ac ............................. 165
Mean nitrate leaching from seed corn production (ASNL) and the
whole-farm (AN L) under various permissible probability levels . . . 167
Changes in the gross margins under different permissible probability

of nitrate leaching from seed corn production exceeding 40 lb/ac . . 169
Growers’ expected utility and proﬁt under various risk preferences

............................................ 177
Average nitrate leaching from whole-farm (AN L) and from seed
corn production (ASN L) under different levels of constant absolute
risk aversion .................................... 178
Shadow values of seed corn contract and land under various risk aversion
coefﬁcients ..................................... 179
Mean nitrate leaching from growing seed corn (ASNL) under
alternative contract design with three risk-aversion levels ....... 181
Mean nitrate leaching from the whole farm (ANL) under alternative
contract designs with three risk preference levels ............ 184
Grower’s expected utility from alternative contract design under
different risk preference levels ........................ 186

xiv

Figure 8.7: Processor’s gross margins from alternative contract designs under
three levels of risk preference ......................... 187

XV

CHAPTER 1

INTRODUCTION

Within the last two decades, the share of US. agricultural output produced
under contract has increased dramatically (Drabenstott, 1994). At the same time, the
public has a growing concern about agro-environmental problems. The structural
change of increased contracting provides an opportunity to use contract speciﬁcations to
achieve agricultural nonpoint source pollution control.

The objective of this research is to explore whether and how to use agricultural
production contracts as a means to reduce nonpoint source pollution. This dissertation
examines the problems associated with agricultural nonpoint source pollution, and then
explores the signiﬁcance of contractual production in the US. agriculture, how
contracts may be related to nonpoint source pollution, and how contracts can be

redesigned to achieve nonpoint source pollution abatement.

l. 1 The Problems of Agricultural Nonpoint Source Pollution

Agricultural nonpoint source pollution is now widely recognized as a serious
source of water quality problems in the United States. Pesticides and nitrates have been
found in both ground and surface water (Hallberg, 1989; US. Environmental

Protection Agency, 1990; Kellogg et a1., 1992), as have animal fecal contaminants and

2

sediments (National Research Council, 1993). Such pollution imperils both human and
animal health, and may also affect ecosystem functions.

In response to the concerns about water pollution, many state and national
policies have been developed to address these issues (Fox et a1. , 1991). For instance,
the 1972 “Clean Water Act” as well as the 1974 “Safe Drinking Water Act” address
national surface and groundwater contamination issues. Also, as of 1997, forty-four
states had implemented state groundwater protection strategies (EPA, 1997). These
concerns are also embodied in governmental farm programs. The Conservation
Compliance and Conservation Reserve Program, initiated in the 1985 farm bill, was
designed as a “carrot and stick approach” to curtail agricultural nonpoint source
pollution. In addition, the Federal Insecticide, Fungicide and Rodenticide Act (FIFRA)
and the Food Quality Protection Act (FQPA) of 1996 require a rigorous pesticide
registration process (Swinton et al., 1997; Benbrook et al., 1996; Marshall, 1988).

Agricultural nonpoint source pollution (NPSP) is an unintended side effect of
agricultural production. It is produced by many polluters without easily identiﬁed
discharge sites, and the concentration of pollutants is affected by random factors, such
as weather. Within the economics discipline, NPSP is characterized as a “non-
exclusive” and “non-rival” good. It is impossible or costly to exclude or to separate
each individual’s contribution of pollution.

In order to implement successfully policies to control NPSP, information on the
physical and economic dimensions of NPSP is required. Physical dimensions include

production technologies, pollution-generating processes and environmental fate.

SC

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199

SM;

3

Economic dimensions include proﬁt from production and damages caused by nonpoint
source pollutants. These data are difﬁcult to obtain because of the high transaction
costs to collect information on the characteristics of the locations affected as well as on
individual agronomic practices. Furthermore, determining the extent and the sources of
pollution is difﬁcult. Due to these heterogeneous characteristics, results generalized
from small area studies might not be suitable for other locations. These difﬁculties
have made environmental quality regulation costly and administratively problematic
(Russell and Shogren, 1993; Tomasi et al., 1994).

Applied economic research to date has focused on public policy remedies to
control NPSP. This approach stems from a welfare economics perspective that
identiﬁes NPSP as an externality which results when the private cost of a given action
is less than the social cost. Standard remedies that have received recent empirical
examination include input taxes and bans, efﬂuent taxes, efﬂuent standards, tradeable
pollution permits, and subsidies for pollution-reducing practices (Crutchﬁeld et al. ,
1992; Hrubovcak et al., 1990; Johnson et al., 1991; Ribaudo and Bouzaher, 1994;
Swinton and Clark, 1994; and Taylor et al., 1992). However, these NPSP control
policies are difﬁcult to enforce in many circumstances due to asymmetric information
between regulators and polluters, where the latter hold more information than the
former (Segerson, 1988; Tomasi et al. , 1994). The high cost of obtaining appropriate
monitoring information makes these standard environmental policies impractical to
enforce (Braden and Segerson, 1993; Xepapadeas, 1991 and 1992).

This research introduces an alternative approach to control NPSP via contracts

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between private parties. It explores whether agricultural production contracts can be
redesigned to induce contracted farmers voluntarily to reduce agricultural nonpoint
source pollution. As contractual production becomes more important in U.S.

agriculture, this approach deserves examination.

1.2 Significance of Production Contractual Arrangements

Using production contracts to control N PSP was ﬁrst proposed by the National
Research Council in 1993. The Council recognized that, when agricultural production
takes place under contracts, there may be little incentive for producers to adopt less
polluting practices even when the technology is readily available. They further
recognized that contractual arrangements could potentially be used to prevent or to
control agricultural NPSP (National Research Council, 1993).

The rapid growth of contractual production is driven by advanced technology,
the changes of consumer preferences for “branded” or “identity preserved” products, as
well as the pursuit of lower costs of production (Urban, 1991). This trend has caused a
“quiet revolution”, industrializing the U.S. agribusiness and food systems (Schertz and
Daft, 1994). Contracts are used most commonly in broilers, processing vegetables,
hogs, and specialty crops, such as seed corn (Drabenstott, 1994). Contractual
arrangements account for 25 percent of farm operator household income in the U.S.
(ERS/USDA, 1993).

Vertical coordination under production contracts provides control across

segments of a production! marketing system in the agriculture sector (Schertz and Draft,

5

1994; Barkema et al., 1991; Boehlje, 1996). The production contract has two
characteristics: 1) it links the processor to production activities; and 2) it reduces the
needed number of processing ﬁrms while increasing the operation size of each ﬁrm to
capture the economies of scale in production. A contract often requires contractor-
farmers either to adopt certain speciﬁc production practices or to use some speciﬁc
inputs to meet the quantity , quality, and timing requirements of the operation. The
processing ﬁrm keeps close supervision on the contracted grower in order to ensure that
the requirements are met. Consequently, processors often have detailed information
about production processes. For the processors, this arrangement can minimize risks
by ensuring predictable supplies and consistent quality. For the producers, the
arrangement can offer price stability and access to specialized expertise, information,
and inputs (Hamilton, 1995).

In a certain circumstances, contracted farming can pose a risk to environmental
quality (Ervin and Smith, 1994). First of all, industrialization often leads to more
geographically concentrated operations which can concentrate agricultural pollutants,
such as pesticides or livestock wastes. Second, if farmers’ environmental stewardship
is closely tied to their autonomy (and majority ownership of capital assets), their loss of
power through vertical coordination within a contract may undermine farm-level actions
to conserve natural resources or enhance environmental quality. Third, the ﬁnancial
incentive provided by the processing ﬁrm to meet output speciﬁcations may undermine
the incentives offered by voluntary agro-environmental programs under existing

abatement policies. When production practices are partially dictated by the processing

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ﬁrms, contracted-growers may lack the ﬂexibility to make substantial changes to meet
the environmental goals.

One example is that the agricultural production contracts provide contracted
farmers high price premiums on high output. This encourages the contracted farmers to
use inputs intensively in order to achieve high output goals. The heavy use of some
inputs, such as fertilizers and pesticides, can cause NPSP, thus degrading
environmental quality. For instance, contracted seed corn production in southwestern
Michigan has been linked with nitrate contamination of the groundwater (Peterson and
Corak, 1994).

There are two potential reasons for agricultural processors to consider the
environmental impacts of contracted production processes (Batie, 1997). The ﬁrst is to
avoid future governmental regulations that might be developed to curtail pollution.
Processors face the risk that more stringent governmental regulations, or liability rules
could be extended to cover contracting processor ﬁrms as well as growers through
legislative vehicles such as the Clean Water Act or the Comprehensive Environmental
Response, Liability, and Compensation Act (CERLCA) (Segerson, 1994). The second
reason is to appeal to changing consumer preferences. As consumer demand for
environmentally benign products increases, more businesses are seeking to build a
“green” reputation, including food and agricultural ﬁrms (Porter and van der Linde,
1995).

If regulations or voluntary incentives can target the processing ﬁrms, making

them responsible for pollution, the governmental cost for monitoring each individual

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ﬁrm to meet NPSP standards will be reduced. The number of processing ﬁrms under
an industrialized sector is much less than the number of farmers (Ervin and Smith,
1994), making it easier to track environmental performance of each ﬁrm. These
processing ﬁrms tend to have more information than regulatory agencies on contracted-
growers’ activities (NRC, 1993). Studies from some sectors suggest that large
processing ﬁrms adopt proﬁtable new technologies earlier and at a faster pace than
traditional farm businesses (Porter and van der Linde, 1995). Furthermore, when
policies target the ambient environmental quality, processors in the same area can
engage in cooperative pollution control at lower transaction costs than individual
farmers because the number of processors are smaller.

Using contracts as a means to control or prevent NPSP implies the need to
change the contract speciﬁcations. Each type of contract requires different analysis,
depending on the principal pollutants and the production process. In hog or dairy
production, the focal pollutant would be manure; for vegetable and fruit production, it
would more likely be excessive nutrients and pesticides.

This research explores contractual speciﬁcations to reduce nitrate leaching into
groundwater that is associated with seed corn production. It is developed as a
representative case study in St. Joseph County, Michigan, where seed corn is widely
grown and where signiﬁcant nitrate levels have been found in groundwater. Seed corn
production is an important case because seed corn has the largest revenue share in U.S.
seed industry ($1.6 billion; Grooms, 1993) and all seed corn is produced from

contractual arrangements.

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1.3 Signiﬁcance of Nitrate Leaching

Nitrate (N03) is the most common agricultural nonpoint source water pollutants
in the United States (Kellogg et al. 1992; CAST, 1985). Surveys from the U.S.
Combelt show that nitrate concentration in groundwater has increased over time since
the 1960s (Keeney, 1986; Hallberg, 1986). Nitrate is soluble and highly mobile,
converted from nitrogen in the soil environment. It can be leached through the crop
root zone and eventually into the groundwater.

Nitrate concentrations can affect both surface water and groundwater. The
major health risk from excess nitrate in drinking water is clinical infant
methemoglobinemia or “blue baby syndrome”. Nitrate consumed by infants reduces
blood oxygen levels. Other potential impacts, yet unproven, are cancer and inhibited
reproduction in humans and other animal species (Fan et al., 1987; CAST, 1985;
Keeney, 1986). In order to avoid damage, the U.S. Environmental Protection Agency
(EPA) has set the safe drinking water standard of nitrate at 10 ppm.

Numerous sources of nitrogen in the soil, including crop residue, manure,
buried organic matter, septic systems and geologic sources, can contribute nitrate to
ambient groundwater nitrates. However, agricultural activities, such as nitrogen
fertilizer applications in crop production and animal manures in livestock production,
are increasingly being held responsible for contributing excess nitrate to groundwater
(Follett et al., 1991). Particularly, the increase in nitrogen fertilizer applications have
been highlighted as a major source of groundwater nitrate in the United States

(Hallberg, 1986; Kellogg et al., 1992). The Combelt states, Texas and California

 

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accounted for two-thirds of the nitrogen fertilizer consumption in 1984. Among all

crops, 43 percent of the fertilizer was applied to corn land (Vroomen, 1987). These
data indirectly suggest that high-fertilizer nitrogen application to corn in these areas

may be a major source of groundwater nitrates (Hallberg, 1986).

Concerns about nitrate leaching has grown recently in Michigan’s St. Joseph
County, with evidence of rising groundwater nitrate levels that frequently exceed
permissible maximum contaminant levels (Martin, 1992; Weight, 1996). The problem
appears linked to intense agricultural production that is practiced on a sandy soil over a
shallow groundwater aquifer (Loudon, 1988). Although livestock production and other
crops play a role, seed corn production has been identiﬁed as major part of the problem

(Martin, 1992).

1.4 Research Objectives
The general objective of this research is to design and evaluate alternative

contracts that can induce production contracted-growers voluntarily to reduce

agricultural nonpoint source pollution. The NPSP to be analyzed is the nitrate leaching
from contractual seed corn production. The speciﬁc sub—objectives include:

1. To identify the relationships among contract speciﬁcations, input use, output,
and nonpoint source pollution. Speciﬁcally, this research will examine the
relationships among contract terms, nitrogen use, yield, and nitrate leaching in
the case of seed corn production.

2. To identify production practices that will reduce nonpoint source pollution and

 

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major obstacles to adopt these practices within a contractual relationship.

To identify possible contractual terms that can be modiﬁed to reduce nonpoint
source pollution.

To structure a set of alternative contracts that could potentially reduce nonpoint
source pollution. The speciﬁc model employed will focus on fertilizer
management and nitrate leaching, especially for seed corn production.

To develop an empirical principal-agent model to analyze and evaluate the
economic impacts of alternative contractual speciﬁcations. The impact on the
welfare changes of a representative seed corn processor and seed corn

contracted-grower will be examined.

Organization of the Dissertation

Chapter 2 reviews the characteristics inherent in NPSP and related policy issues,

since these elements are essential in designing an effective contract that reduces NPSP.

Possible N PSP abatement strategies are identiﬁed. Several evaluation criteria have

been used in the literature to rank these strategies. A conceptual structure that

illustrates a general relationship between the processor and contracted-growers is

outlined to examine how this relationship can be used to control NPSP. Possible

changes in contractual speciﬁcations for more effective NPSP abatement are reviewed.

Nitrate in groundwater is discussed as an example, including related environmental

impacts, agronomic practices that reduce nitrate leaching, obstacles to the adoption of

less nitrate leaching practices, and suggested institutional arrangements to reduce nitrate

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leaching are examined as well.

Chapter 3 presents information on geographic characteristics of the research
area, current seed corn contracts in St. Joseph County, Michigan, and related seed corn
production practices. The relationship between current contract speciﬁcations and
nitrate leaching will be explored as well.

The principal-agent framework for alternative contract design is outlined in
Chapter 4. Four types of contract designs are examined: restricting agronomic
practices, imposing a user fee on agronomic practices, adjusting incentive payment
schemes, and providing information on nitrogen use.

In order to evaluate the impacts of alternative contracts, the physical-economic
relationships are examined in an empirical principal-agent model that is developed in
Chapters 5, 6, 7, 8 and 9. Three components are included: a crop growth simulation
model, a deterministic whole-farm planning model, and risk programming model.

Chapter 5 illustrates the use of the crop growth simulation model—DSSAT 3.0--
to examine yield and nitrate leaching relationships under different nitrogen treatments.
The main features and validation of this model are reviewed. The impacts on crop
yields and nitrate leaching, resulting from the use of rotations, are also simulated in this
model. All of these data are subsequently incorporated into a math programming model
in order to evaluate the physical impacts from alternative contract designs.

Chapter 6 outlines a way to use a principal-agent model. A whole-farm
mathematical model (PC-LP) is used to examine the behavior of a representative proﬁt-

maxirnizing grower. The grower’s behavior is examined under alternative “green”

12

contract designs. Data collection, model parameters, model structure, and results from
various contract speciﬁcations will also be examined. The impacts under various
contract speciﬁcations for both the processor and the grower are examined.

Chapter 7 uses a safety-ﬁrst programming (in GAMS) to incorporate two major
contract risk concerns into an empirical principal-agent framework. Growers are
concerned about risk of losing seed corn contracts when their yields fall below a norm
established by the processing company. The second concern stems from stochastic
characteristics of nitrate leaching reduction. The leaching reduction goal can be to
restrict the probability that nitrate leaching exceeds a certain public safety threshold.
Both concerns are modeled using probabilistic safety-ﬁrst constraints.

Income risk is another important component for contract design. Risk-attitudes
of both processors and contractors will affect optimal decisions as well as risk-sharing.
Chapter 8 examines the case where the contractor-grower is risk-averse. How to
incorporate risk components in a mathematical programming model is ﬁrst reviewed,
and one particular risk model —- mean-variance analysis -- is selected for use in a
quadratic programming analysis. Results for the alternative contract designs are
examined based on acceptability and cost efﬁciency criteria.

Finally, Chapter 9 summarizes the major ﬁndings of this study. The
conclusions, implications, and suggested future research are drawn as a guideline for

using contract designs to control agricultural nonpoint source pollution.

CHAPTER 2

ISSUES FOR DESIGNING PRODUCTION CONTRACTS TO REDUCE
AGRICULTURAL NONPOINT SOURCE POLLUTION

In order to explore and evaluate available contract speciﬁcations to control
NPSP, the managerial issues associated with NPSP have to be identiﬁed. This chapter
ﬁrst outlines the special characteristics inherent in N PSP control in order to understand
the key regulatory difﬁculties. A conceptual processor-grower relationship is examined
to discuss modeling issues and the information needed in designing incentives to control
NPSP within a contractual arrangement. Several alternative ways to inﬂuence
contracted-growers’ behavior and ultimately improve environmental quality are
reviewed. This chapter uses nitrate leaching as an example to discuss available nitrate

leaching reduction strategies that can be incorporated into a production contract.

2.1 Problems of Agricultural NPSP

This section reviews some characteristics inherent in N PSP. Figure 2.1 outlines
a general framework that includes detailed information on the sources and the ultimate
impacts of pollutants within a pollution-generating process under a contractual
relationship. A pollution-generating process includes the initial input or technology

choice that results in production, emissions, ambient pollution, and ultimate

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environmental or health damages. Emissions can consist of different types (such as
nutrients and pesticides) from multiple sources, which may affect several environmental
media (such as surface and ground water). The combined emissions determine the
ambient pollution level and ultimately may cause health and environmental damages.
The pollution-generating process of one farm (Farm 1) might affect another farm’s
production process (Farm 2) (dotted line). Exposure to contamination beyond the
susceptible level of humans, animals, or the ecosystem leads to damages.

The relationship in Figure 2.1 also illustrates the physical uncertainty within
NPSP, stemming from climatic and topographic conditions as well as mechanical
operations. A particular abatement practice and discharge level may result in different
ambient outcomes under different locations and at different times. Therefore, a range
of possible ambient levels will be associated with any given abatement practice and
discharge level at any given time. From the processor’s perspective, the-observable
outcomes are output and, possibly, ambient pollution levels as well as environmental
and health damages (shadowed areas). It is difﬁcult to know the input and abatement

effort made by each individual farm from the processor’s viewpoint.

2.1.1 Sources of Variation in Outcomes

Pollution processes are affected by various natural sources of variability. These
include weather, mechanical malfunctions, and susceptibility to damages (Braden and
Segerson, 1993). Due to this natural variability, each discharge level or abatement

practice tends to generate a range of possible ambient levels. This range can be

16

 

Probability Tolerance Level

         

    

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Distributt With abatement 3

 

 

 

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Figure 2.2: Distribution of ambient pollution level under two abatement levels
(Source: Segerson, 1988)

represented by the probability density function in Figure 2.2, which gives the
probability of the ambient pollutant levels at a speciﬁc time.

In Figure 2.2, two ambient pollution distributions are affected by level of
abatement. The distribution with low mean loading represents the probability
distribution of ambient level with abatement, while high mean loading represents the
distribution without abatement. This ﬁgure shows that the probability of the ambient
level exceeding the tolerance level without abatement is greater than that with
abatement (Segerson, 1988).

Another type of variation relates to spatial differences, including locations and
soil structures. Local circumstances and enduring variation over time affect the relative
curvatures of beneﬁt as well as cost of abatement, and then determine the efﬁciency of
the NPSP reduction strategies.

Timing is also an important element in controlling NPSP. There is a time lag

 

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between when decisions are made and when actual NPSP occurs, making instant
monitoring impractical. For instance, corn growers in high rainfall regions tend to
apply nitrogen fertilizers in the early spring while most of nitrate leaching occurs in the
winter. A leaching reduction strategy should consider this time lag between nitrogen

applied (action) and leaching occurred (outcome).

2.1.2 Imperfect Monitoring and Measurement

In the context of agricultural NPSP, imperfect monitoring arises from the
unobservability of emissions. Because emissions are diffused, monitoring of NPSP
emissions from an entire ﬁeld tends to be impractical. The associated monitoring costs
are prohibitively expensive and the inability to observe emissions impedes the use of
emission standards, emission taxes, and the application of liability (Miceli and
Segerson, 1991). These reasons also reduce the abatement incentives from each
individual.

Two information issues related to NPSP control have been identiﬁed in the
literature. They are moral hazard and adverse selection (Tomasi et al. , 1994). Moral
hazard results when a contracted-grower makes management choices that advance
his/her interests rather than those of the processor. Adverse selection refers to the case
when the processor cannot observe farm types, where some of them have low
abatement costs while others have high abatement costs. In both cases, farmers have
more information than processors about the production process of the commodity as

well as the abatement. In economics, this situation is known as “asymmetric

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information”. Under this situation, the actions taken by the contracted-grower may not
result in the outcomes that are preferred by the processor.

A suggested approach to resolve these information problems is to design an
incentive scheme to induce the grower to undertake the actions that are preferred by the
processor. In designing a production contract to control NPSP, moral hazard may be
the only issue raised because the processor tends to have information on the contracted-
grower’s managerial ability.

Due to natural variability as well as imperfect monitoring and measurement,
effectively controlling NPSP is a complicated issue to policy makers. Some studies
have suggested that one way to account for variation in pollution outcomes is to have
regulatory policies set a threshold level on the ambient environmental quality plus a
safety margin. This objective is expressed as a maximum acceptable frequency above
the ambient threshold (Lichtenberg and Zilberman, 1988; Braden et al., 1991) such

that:
Prob(W2W)_< w 0-”

where W is measured environmental contamination; W is the environmental threshold
level; and w is the permissible cumulated probability of environmental contamination W
exceeding the threshold W. This strategy is designed to account for not only the mean
realizations of abatement (threshold level), but also the deviation of the pollution above
the threshold level.

Other studies proposed indirect NPSP abatement strategies that target output

19

level, input use (with state policies, such as taxes or subsidies on pesticide use), or
ambient pollution levels (down-line policies) (Braden and Segerson, 1993; Dosi and
Moretto, 1993). The reason is that emissions could be partially correlated with some
other observable part of the production or pollution process, such as output levels,
input uses, technology or ambient quality (Nichols, 1984). In order to examine how to
incorporate these strategies within a contract design, NPSP abatement modeling needs

to be explored.

2.2 Elements in Modeling NPSP Abatement

Most N PSP literature models abatement issues from a regulatory perspective.
However, the same concepts can be applied in a processor-grower relationship. A
principal-agent model is commonly proposed as an analytical framework to resolve the
asymmetric information problem occurred in NPSP abatement. A regulator (or
processor) is considered as the principal and polluters (or growers) are the agents. The
objective of the principal is to reduce NPSP, which is a side—effect from production
processes generated by several agents (Segerson, 1988; Meran and Schwalbe, 1987;
Xepapadeas, 1992; Peterson & Boisvert, 1995; Wu and Babcock, 1995; Wetzstein and
Ahouissoussi; 1996; Bystrom and Bromley, 1996). Within the principal-agent model,
the principal designs an incentive scheme, such as a fee or a direct payment, to induce
the agent to undertake N PSP abatement. The incentive scheme could be within an
individual contract (Segerson, 1988; Xepapadeas, 1992) or a group contract (Bystrom

and Bromley, 1996; Devuyst, 1997).

20

Several elements need to be included when modeling the relationship between
the regulator and polluters in a NPSP context. The ﬁrst element to be considered is the
physical-economic dimension of a nonpoint source pollutant. This physical dimension
includes the relationship between environmental/health damages and input uses,
technology, emissions, as well as ambient levels. Crop growth simulation models, like
DSSAT (T suji et al., 1994), are often used to estimate the agri—chemical components of
pollution, such as the relationship among input uses, yields, and nitrate leaching
(emission). These emissions will determine the ambient pollution level according to
their environmental fate (Mapp et al. , 1994). These data are then incorporated into an
economic model to predict the relationships between NPSP and farm proﬁtability. A
representative farm linear (or nonlinear) programming model can be used as an
economic model to examine the tradeoff between environmental quality and farm
proﬁtability (Thomas and Boisvert, 1995; House et al., 1995 and1996; Devuyst, 1997).

The second element concerns the number of polluters. An ambient level of
agricultural NPSP at a given location is often contributed to by many farms. The
existence of multiple and heterogeneous polluters raises a number of regulatory
difﬁculties. As the number of farms increases, it becomes more costly to trace the
source and extent of the pollution, because it is impossible to separate activities from
each individual farm from ambient pollution level (Tomasi et al. , 1994). Insufﬁcient
information creates potential for “free-riding” because it is difﬁcult to identify and
penalize non-compliant polluters. In addition, each farm tends to perceive its own

pollution contribution to be small relative to the group (Batie, 1983). Therefore, a

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large number of farms reduces the likelihood of cooperation among farms to reduce
ambient pollution levels.

The third element is the spatial heterogeneity among farms. The extent of the
damage is site-speciﬁc, depending on variables such as soil structure, animal and plant
population density, and the technology used. The abatement costs for polluters across
different locations are different.

Technological differences, including production technologies and abatement
technologies, are the fourth element that needs to be considered. Such differences stem
from climate, soil type, slope, depth of groundwater and intervening geologic structure.
Although there is some correlation between production and pollution levels, this
correlation differs under different technology. A uniform and mandatory required
management practice or emission standard for a certain pollutant will have different
cost impacts on each farm and will not lead to equating marginal costs across farms.

Both spatial and technological differences are also related to stochastic
inﬂuences. Weather is the most important stochastic element that inﬂuences crop
production and environmental effects. Other stochastic elements include input and
output prices, which affect farmers’ choices of input use and pollution outcomes.

Other elements in modeling NPSP abatement include dynamic perspectives:
carryover effects and accumulated experiences. Environmental quality is affected by
the accumulation of pollutant (“stock”) that is carried—over from previous periods and
are accumulated over time. In addition to carryover effects, the NPSP reduction

process is also inﬂuenced by accumulated learning experience in terms of abatement

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cooperation and technological advance. Such experience affects transaction costs from
negotiation among parties and administrative efforts (Tomasi et al., 1994).

In conclusion, modeling NPSP issues within a contractual framework should
consider many perspectives. It is important to recognize physical dimensions starting
from input use to pollutant concentration and the number of polluters contributing to
ambient pollution at a given location and potential contribution of each farm.
Additional factors include site-speciﬁcation, technological heterogeneity across farms,
the role of stochastic inﬂuences in determining ambient pollution as well as production,

and long-term dynamic elements.

2.3 NPSP Abatement in a Contractual Production Relationship

Figure 2.1 illustrates a general conceptual framework of a processor-grower
relationship, where a processor contracts with two farms. In a scenario where the
processor is concerned with future liability or his or her “green” image, the processor
will include product output and environmental quality in his or her objectives (Batie,
1997). The levels of both output and environmental quality depend upon the decisions
made by contracted-growers. The processor observes individual output levels from
each farm and a combined ambient pollution level from the emissions from both farms.
The individual inputs, technology, and emission may not be observable from the
processor’s perspective. Therefore, a contract design needs to specify an incentive
scheme based on observable outcomes to achieve preferable results.

The ambient level of nonpoint source pollution depends upon a grower’s

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production decisions. These decisions are primarily determined by a grower’s
objectives, though also affected by other factors such as input and output prices, site
characteristics, degree of risk aversion, governmental programs, and contract terms. A
grower’s objective(s) can include expected utility from proﬁts, preference over
environmental quality, ﬁnancial punishment, and stewardship. These decisions are also
constrained by feasible technology, other grower’s decision, and available information
on input use.

The processor, however, can inﬂuence the contracted-growers’ behavior
through contract term speciﬁcations. For instance, a contract with high price premiums
on yields will encourage a contracted-grower to use inputs intensively in order to
achieve high yield goals. The environmental problems and production practices
associated with NPSP abatement depend on the nature of pollutants. Therefore, NPSP
abatement strategies and their corresponding enforceability vary. The next section uses
an example to explore the potential alternatives of a processor to design a lower

leaching contract.

2.3.1 Issues Related to Nitrate Leaching Reduction

Excessive nitrogen applications are the most direct factor contributing to nitrate
leaching. Other factors include weather (rainfall, temperature, solar radiation, etc.),
soil dynamics (such as soil texture), timing of application, and various agronomic
practices, including nitrogen application schedules, irrigation schedules, tillage

systems, rotation carryover, form of nitrogen fertilizer, and cover crops. These factors

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intertwine to determine the extent of nitrate leaching.

Management strategies for nitrate NPSP recommended for areas which are
vulnerable to nitrate leaching are available for farmers (Loudon, 1988). The strategies
involve setting realistic yield goals based upon previous crop histories for a speciﬁc
ﬁeld; crediting all nitrogen sources, including soil organic matter content, crop residue,
manure applications, nitrogen in irrigation water, as well as fertilizer nitrogen in
determining the total amount which will be available to the crop; using appropriate
application methods; and incorporating nitrogen into soil to prevent volatilization and
surface runoff.

Several factors inﬂuence the adoption of these nitrogen management strategies
(Supalla et al. , 1995). These factors include information in the recommended nitrogen
application rate, knowledge of irrigation scheduling and water quality, available
nitrogen application technology, institutional arrangement, and other demographic
factors (such as years of schooling and farming experience).

Recommendation for fertilizer application levels based on experimental results
have been provided to farmers by extension agents and consultants. There are several
drawbacks related to using these fertilizer recommendations. First, the recommended
fertilizer application lacks the representativeness of the experimental response
(SriRamaratnam et al., 1987; Perrin, 1976). Variations in soil type, soil fertility levels,
and the level of management and technological advances in crop yield potential are not
considered in extension recommendations in some cases. Second, reconciling results

from different sites and different years may not adequately estimate a nitrogen-yield

25

relationship for a speciﬁc area (Anderson, 1974). Third, farmers might set an
unrealistic yield goal that results in over-application (Babcock and Blackrner, 1994).
Farmers tend to use high nitrogen fertilizer rates to ensure an adequate supply of
nutrients in case the growing season turns out to be favorable (Babcock and Blackrner,
1994; Babcock, 1992). As a result, farmers may “over-apply” nitrogen fertilizer
relative to needs for an average year.

The Supalla et al. study (1995) also indicates that institutional arrangements are
potentially responsible for providing incentives to set high yield goals. Examples were
the governmental deﬁciency payment that tied payment with yield levels, and high price
premiums paid to the contracted-grower who produces higher yield levels within a

contractual arrangement (Swinton and Clark, 1994; Batie, 1994).

2.3.2 Strategies for Nitrate Leaching Reduction

This section explores potential strategies that can be incorporated into a “green”
contract design to reduce nitrate leaching. Most NPSP reduction strategies in the
literature are conceived from a regulator’s perspective, because it is assumed that only
the government will undertake NPSP control due to its externality property. Five
general approaches are discussed in the NPSP or leaching reduction literature. They
are: A) emission control strategies; B) output-based strategies; C) strategies based on
purchased inputs or management; D) ambient- or performance-based strategies; and E)

legal liability for damages (common or statutory law).

CC

26

A. Emission-Based Strategies

The standard textbook remedies for an externality are based on efﬂuent
emissions. In the case of reducing nitrate leaching, this strategy could be to charge an
emissions tax (Pigouvian tax), or to specify a permissible amount of nitrate leaching.
Another strategy is to design an incentive payment to induce the polluter to achieve a

nitrate leaching reduction goal.

B. Output-Based Strategies

A strategy designed to target agricultural output levels presupposes that NPSP is
correlated with output levels. For example, it is typically assumed that high nitrate
leaching is correlated with crop yields. High levels of nitrate leaching could result
from institutional arrangements that encourage intensive fertilizer use. Two common
examples are governmental farm programs and contractual crop production. Both
examples provide subsidies or premiums for achieving high yield goals, which is likely
also to increase NPSP. Therefore, one way to reduce NPSP is to reduce price

premiums on per unit output (Supalla et al., 1995; and Swinton and Clark, 1994).

C. Purchased Input- or Management-Based Strategies

Controlling inputs to reduce NPSP was proposed by Grifﬁn and Bromley (1982)
and Shortle and Dunn (1986). This approach suggests that a “user fee” or standard on
the input use could serve as a substitute for an emission fee. This instrument of

controlling input use assumes that input use is highly correlated with pollution

far

27

emissions and input consumption is more easily observed. Management-oriented
instruments, including requiring different cropping patterns, have been suggested to
reduce agricultural pollution (Drake, 1993; Fleischer et al., 1989). This strategy
includes charging a fee or imposing a restriction on either nitrogen fertilizer use or
agronomic practices such as rotation, spring nitrogen application only, split application,
and the planting of winter crops. Another strategy is to design a “green” payment that
is directly related to environmental friendly practices, such as the use of best

management practices (BMP).

D. Nitrate Concentration-Based Strategies

This strategy involves specifying a ﬁnancial punishment (or incentive) based on
the ambient nitrate concentration in the groundwater when it exceeds a certain threshold
level (such as 10 ppm). Segerson (1988) and Xepapadeas (1991 and 1992) theoretically
show that this approach can provide the correct incentives for individual polluters
within a group to undertake socially efﬁcient abatement measures. In this case, the
variation among individual polluters is not important, if and only if, the ambient level

does not exceed the targeted threshold level.

E. Liability-Based Strategies
A liability-based strategy makes polluters liable for damages caused by NPSP
(Segerson, 1988; Meran and Schwalbe, 1987; and Xepapadeas, 1992). In this case,

farmers in the same region might share the same liability for any health or

28

environmental damage caused by nitrate contamination.

All the strategies mentioned above can potentially reduce nitrate leaching.
Enforcement is key to the design of an effective water-quality improvement strategy
that is site- and time-speciﬁc. The monitoring and measurement depend on the
availability of appropriate technology. Crop yield can be easily measured.
Technologies to measure crop nitrogen need could justify fertilizer application with
good nutrient uptake. The available techniques include soil nitrate test, plant tissue,
and remote tests (such as leaf reﬂectance, canopy reﬂectance, aerial photography)
(Silva, 1996). Well sampling can provide a measure of ambient water nitrate levels.
However, all of these measures cannot accurately measure the exact amount of
leaching.

Since each of the above strategies has its own strength in dealing with NPSP, a

set of criteria is needed to evaluate the efﬁciency of these strategies.

2.3.3 Evaluation for Alternative NPSP Strategies

Braden and Segerson (1993) have identiﬁed three criteria to evaluate the
effectiveness of NPSP abatement strategies: A) ability to target; B) ability to enforce;
and C) correlation with improved environmental quality. All three are applicable to

nitrate leaching.

A. Ability to Target

NPSP is inherently variable, so the impacts of pollution-related decisions will

29
vary over both time and space. In general, efﬁciency is increased by a strategy that can
be targeted to sensitive areas or times. Here, a strategy that can induce site- or time-

speciﬁc responses is preferred to one that induces uniform responses.

B. Ability to Enforce

Enforcement requires both detection and the ability to sanction noncompliance.
The administration and monitoring costs are also critical in determining enforceability.
The inability to perfectly monitor pollution-related decisions suggests the need to design
alternative strategies that are based on other observable targets, such as input uses or

agronomic practices.

C. Correlation with Environmental Quality

The strategies should ultimately improve environmental quality, reducing
pollution-related damages. For instance, if nitrogen fertilizer is employed as a
reference of likely pollution, randomness (weather) and substitution effects (other
sources of nitrogen) in the production process are two factors that might affect its
relationship with environmental quality. The correlation between policy tools and
environmental quality needs to be considered.

Table 2.1 summarizes the effectiveness of ﬁve leaching reduction approaches
from a regulatory perspective based on the ﬁrst three criteria: A) ability to target, B)
ability to enforce, and C) correlation with environmental quality (Segerson et al. , 1993;

Segerson, 1990).

30

Table 2. 1: Evaluation of nonpoint source pollution abatement strategies

 

 

 

 

 

 

 

 

ll Rating with respect to: I
. . 4 Correlation
Fee/Payment/Restriction on Ability to Target Ability to enforce with Water
Quality

1) Output Product L H L

2) Purchased Inputs L (charges) H (charges)

ll M (regulations) M (regulations)

3) Emissions/Manage- H M M
ment Practices

4) Ambient H L (charges) H
Concentration M (payments)

“5) Use of Liability H L H

 

 

 

 

 

, -
Note: L: low; H: high; and M: medium (Source: Braden and Segerson, 1993, p16)

Output-based or yield-based strategies are relatively easy to enforce given
current marketing systems. However, this approach cannot be easily targeted to
sensitive areas or times. Furthermore, water quality problems may not stem from the
output level per se, but also from the way or place in which the output is produced. In
addition, output-based strategies might induce output-substitution without inducing
input-substitution. If this happens, the water quality may not be improved.

Nitrogen fertilizer inputs can directly contribute to water quality degradation.
However, it will not necessarily cause excessive nitrate leaching if farmers follow
proper agronomic practices. A strategy based on a particular input use could diminish
efﬁciency by biasing the selection of inputs or by failing to account for differences in
emissions from different agronomic practices or from different locations. Without

careful monitoring, taxation or regulation of easily observable inputs may only distort

31

the chosen input mix and induce inappropriate substitutions.

Ambient nitrate levels are relatively easy to measure, but inferring emissions
from a given ambient level for a particular source is difﬁcult due to natural randomness
and inﬂuence of other neighboring polluters. Ambient standards ensure targeting and
consider site-speciﬁc differences in making pollution-reduction decisions to meet water
quality goals. However, the effectiveness of this strategy also depends on individual
farmers perceiving their own contribution toward achieving the standard (Batie, 1983),
yet by the nature of NPSP, this is unlikely. A charge-based approach may be difﬁcult
because it is impossible to measure each individual’s performance. Alternatively,
subsidies for compliance with the standard will reduce enforcement difﬁculties because
farmers will voluntarily provide information in order to obtain payments.

Legal liability might result from polluting activities, thus avoiding the risk of
liability might induce polluters to consider site- and time- speciﬁc NPSP damages.
However, it may be difﬁcult to identify a responsible party for the damages.
Moreover, because agricultural inputs are approved for use by federal agencies and are
part of "normal” farming practices in U.S. agriculture, farmers have been granted
exemptions from general liability requirements under Comprehensive Environmental
Response, Compensation, and Liability Act (CERCLA) and some state laws
(Mill,1992; Segerson, 1995). These exemptions make the liability rule approach
difﬁcult to enforce in agricultural production.

Table 2.1 suggests that no single strategy instrument is likely to yield efﬁcient

pollution abatement decisions. Those strategies that rank highest in ability to target

32

linkage with water quality tend to be the most difﬁcult to enforce. Strategies that are
easy to enforce cannot be easily targeted, nor directly related to water quality. Because
of these tradeoffs, multiple instrument approaches have been proposed as alternative
strategies by past studies (Miltz et al, 1988; Segerson, 1988; Xepapadeas, 1991, 1992;
Braden and Segerson, 1993). For instance, Segerson (1988) examined combinations of
liability rules and taxes to reduce nonpoint source pollution, and Xepapadeas (1991)
proposed an environmental policy that combined ﬁnes and subsidies to overcome moral
hazard issues under imperfect information.

An alternative approach is to provide incentives to induce farmers to reduce
NPSP voluntarily. This approach has been adopted in the current governmental
programs, such as the “green” payment scheme or the Conservation Reserve Program.
This strategy makes an incentive payment to a farmer who can prove his or her
“compliance”. Incentive payments can reduce the transaction costs of monitoring
NPSP, making the target more enforceable (Batie, 1994; Wu and Babcock, 1995;
Peterson and Boisvert, 1995), since farmers hold the information about the production

practices. However, this policy may trigger large governmental expenditures.

2.3.4 Lessons from Regulatory Policy Designs

The above discussions on NPSP abatement are mainly based on regulatory
literature; however, several lessons can be learned for private production contract
designs. First, a principal-agent framework proposed in the literature can be used to

design incentive schemes to induce the polluters (growers) to reduce NPSP. This

33

approach can be employed to design a production contract. Second, the NPSP
abatement schemes used in a regulatory literature can be applied to provide contract
designs.

Using the processor-grower relationship outlined in Figure 2.1 has several
strengths to potentially reduce administration cost. First of all, the processor needs
less data because it might need only examine the particular good and pollutant produced
by the contracted producer. Second, the information is easier for the processor to
monitor than for a regulator, because the processor already monitors the contracted-
grower’s production process. The marginal cost of additional monitoring for the
processor is less than for a regulatory agency.

Apart from the three effectiveness evaluation criteria listed in section 2.3.3, the
magnitude as well as distribution of abatement cost between grower and processor
needs to be considered in designing alternative contracts to induce voluntary nitrate
leaching reduction. This cost, including abatement cost as well as monitoring cost,
determines the acceptability of alternative contracts. If either cost is too high, then it is
difﬁcult to design contracts that are acceptable to both contracted parties.

Each strategy tends to have different impacts on the processor and the grower .
A charge on nitrate leaching, for example, could increase growers’ production costs
while increasing the processor’s revenue, although the processor would bear the costs
of monitoring. An incentive payment could increases farmer revenue at the expense of
the processor; in this case, the grower would provide information in order to receive

payments. In regulatory context, who bears the abatement as well as monitoring costs

34
depends upon the ownership assigned by the institution‘. For instance, if the strategy is
to pay growers for leaching reduction, growers implicitly “own” environmental quality.
That is, they have a right to pollute and must be compensated if forced to control
pollution. Who should bear abatement and monitoring costs becomes an important
equity issue in designing NPSP control strategies. Organization of Economic
Cooperation and Development (OECD), for instance, has proposed a polluter-pay-
principle criteria as an equity criterion. It requires polluters to pay for damages caused

by their pollutants or for abatement costs.

2.4 Summary

This chapter reviewed the literature on NPSP abatement. Asymmetric
information between regulators and polluters is due to nature variability as well as
imperfect monitoring and measurement. A principal-agent model can be used to design
an incentive scheme to induce polluters to undertake NPSP abatement under an
asymmetric information situation. In addition to the objectives of regulators and
polluters, a NPSP abatement model needs to consider the physical dimensions of
pollutants, number of farmers, spatial heterogeneity, technological feasibility, and
stochastic inﬂuences. A bio-economic (or physical-economic) model is often employed
in analyzing the relationship between the environmental quality and proﬁtability.

The speciﬁcation of a “green” contract design depends on the type of pollutant.

 

l“Institution” is deﬁned as collective actions, including laws, customs, contracts, and
other social norms (Schmid, 1987).

35

Several strategical tools can be employed to reduce nitrate leaching. They target
outputs, input uses, management practices, emission levels, ambient concentration in
the groundwater, or make farmers liable for damages caused by NPSP contaminations.

The effectiveness of these policies depends upon their ability to target, their
enforceability and their correlation with environmental quality. The magnitude and
distribution of abatement costs are also important in determining the acceptability of
redesigning contract to reduce NPSP. The rest of this research will use a seed corn
contract as a means to examine how to structure production contract incentives in order

to induce growers to reduce nitrate leaching voluntarily.

CHAPTER 3

CONTRACTUAL PRODUCTION:
A SEED CORN CONTRACT IN ST. JOSEPH COUNTY, MICHIGAN

In order to explore how production contracts can be designed to control
nonpoint source pollution, information on contractual production practices and contract
speciﬁcations is important. This chapter ﬁrst reviews the role of production contracts
in U.S. agriculture. Categories and compensation schemes commonly used in
production contracts are examined as background information. Contracts are important
in seed corn production due to the concern over genetic security. The seed corn
industry and seed corn production are examined in order to identify the market
structure, which affects the negotiation power between the processor and the grower.

A leading seed corn production contract in St. Joseph County, Michigan, is analyzed as
a case study that outlines the linkage between nitrate leaching (agricultural nonpoint

source pollution) and contract designs within a production process.

3.1 Contractual Production
Contract production has rapidly increased in U.S. agriculture during the last
four decades (O’Brien, 1994; Manchester, 1994). Contracts have long been used in the

seed, vegetables and horticultural crops, as well as poultry industries. They are now

36

37
spreading into other commodities, including swine and traditional grains (Drabenstott,
1994; Hurt, 1994).
Hamilton (1995) deﬁned an agricultural production contract as:

“... a legally binding agreement of a ﬁxed term, entered

before production begins, under which a producer either:

agrees to sell or deliver all of a speciﬁcally designated

crop raised on identiﬁed acres in a manner set in the

agreement to the contractor, and is paid according to a

price or payment method, and at a time, determined in

advance; or agrees to feed and care for livestock or

poultry owned by the contractor until such time as the

animals are removed, in exchange for a payment based on

the performance of the animals...” (Hamilton, 1995, p3)
This statement deﬁnes a main feature of a production contract; it locks in marketing
commitments between a buyer (processing ﬁrm) and a seller (grower) before or during
the production process. There are two major reasons for contractual production
(Hamilton, 1994 and 1995; Barkema, 1994). One is risk management; contracting
provides an attractive way to reduce and manage ﬁnancial risks for both parties.
Another reason is because of new marketing opportunities, such as growing demands
for “identity-preserved” or “value-added” crops, and the availability of new bio- and
information-technology that makes such crops possible (Horstrneier, 1993; Phillips,
1994; Urban, 1991).

From a contracted-grower’s perspective, production contracts provide a form of

risk management, including reducing ﬁnancial risk and stabilizing income. Contracts
often provide higher output prices for raising new crops or for using certain production

methods. Production contracts also offer opportunities for contracted-growers to access

capital, new technology, and new markets.

38

From a processing ﬁrm’s viewpoint, contracts have several advantages over
non-contracted production processes. First, a production contract provides control
over production methods, and thus helps to ensure the uniformity and quality of the
commodity. Second, contracts offer a mechanism to control quantities and the way
crops are marketed to processors and consumers, thus assuring adequate supply.
Contracts allow the company to lock in a guaranteed supply to meet potential demand.
Third, contracts promote adoption of marketing-related technologies or production
methods, thereby providing opportunities for economic linkages (such as “packages” of
seeds, chemicals, and marketing). Fourth, in seed corn production, contracts give the
company control over the specialized crop genetics that create the added-value trait,
allowing the contract to serve as a form of intellectual-property protection. Other
advantages of contractual production include marketing protection, pricing
conﬁdentiality, the reduction of risks and higher proﬁts.

The advantages listed above make contract farming an attractive alternative
compared with traditional marketing approaches. The processing ﬁrm often requires
the contracted-grower to adopt certain management practices within a contract in order
to obtain high quality products. The management requirements vary across ﬁrms
depending on commodities and production methods.

Based on the ﬂexibility of management practices, production contracts can be
categorized into three groups: marketing contracts, production management contracts,
and resource providing contracts (Mighell and Jones, 1963). The processing ﬁrm and

its contracted-grower bear different degrees of risk under each type of contract.

39

3.1.1 Categories of Production Contracts

A market speciﬁcation contract provides the contracted grower with an assured
buyer for a speciﬁc product at a given price, quantity, and quality before it is produced.
Under this type of contract, a contracted-grower retains most production decisions
while being assured of a market for his or her product. However, a contracted grower
still bears risk associated with production, although the price risk is reduced (Mighell
and Jones, 1963; Eide, 1997).

A production management contract gives the contracting company direct control
over farm production practices. This type of contract is often used to guarantee
“identity preservation” (Hamilton, 1995). In this case, a contracted grower is required
to adopt certain management practices as well as inputs. Meanwhile, the processing
ﬁrm usually maintains close supervision of the production practices in order to
guarantee output quality. Price premiums are provided as a compensation for required
production costs, as well as an incentive mechanism to motivate the grower for superior
performance. Production risk is shared between the processing ﬁrm and the contracted
grower under a production management contract.

A resource-providing contract gives the processing ﬁrm greater control over the
whole production process. It is often used when the production of a commodity
requires special inputs, technology information, or special investment. Under this
contract, the processing ﬁrm supplies all or most of the inputs, as well as technology
information and certain custom services. The ownership of the commodity belongs to

the processing ﬁrm. A contracted-grower, therefore, has less ﬂexibility over the

40
production processes. The processing ﬁrm is responsible for most of the risk
associated with production of this commodity (Eide, 1997).
The processing ﬁrm has different control over production processes, depending
on the type of contract. These three types of contracts can be combined in a production
contract design. A processing ﬁrm tends to tailor its contract based on the product

characteristics and speciﬁc production information requirements.

3.1.2 Compensation Methods

A contracted-grower receives a payment from the processing fu'm through
different compensation schemes, including ﬁxed price (cash-rent), piece-rate, and
competitive compensation schemes. The payment scheme serves as an incentive
mechanism to induce the contracted-grower to undertake the action preferred by the
processing ﬁrm as well as a way to provide risk-sharing between these two parties.

Under a ﬁxed payment compensation (rent), the processing ﬁrm pays a ﬁxed,
predetermined fee to the grower, regardless of the grower’s performance. A
contracted-grower’s income is ensured under this compensation scheme. A ﬁxed
payment scheme might not provide the contracted-grower with adequate incentive to
achieve the goal preferred by the processing ﬁrm. For instance, moral hazard can arise
when the processing company cannot perfectly monitor the grower’s actual behavior
and the performance outcome is greatly inﬂuenced by random elements.

A piece-rate compensation scheme makes payments to a contracted grower

based on actual performance outcomes. A contract grower earns a speciﬁed per-unit

41

output payment. Under this payment, the grower bears a large proportion of risk
(Knoeber, 1989). This result may not be efﬁcient under an optimal risk-sharing rule,
which requires risk to be shared between two parties according to the degrees of risk-
aversion.

Both ﬁxed payment and piece-rate compensation methods compensate the
contract-grower’s performance based on an absolute standard. They may fail either to
provide incentives to avoid moral hazard under imperfect monitoring, or to consider
risk-sharing. When these two elements occur, a third compensation scheme has
evolved. It is a competitive compensation scheme, based on the contracted-grower’s
relative performance (Knoeber, 1989; Knoeber and Thurman, 1994; Martin, 1995).

A competitive compensation scheme, or relative performance payment scheme,
compares the contracted-grower’s performance to the performance of other growers or
to a ﬁxed standard. This compensation method makes payment either through
“tournaments” or linear relative performance measures (Knoeber, 1989; Knoeber and
Thurman, 1994). Tournament contracts base compensation on a predetermined scale
such as x cents per pound for ﬁrst place, y cents per pound for second place, and so
forth. For instance, linear relative performance measures base a contracted grower’s
reward on a linear function of the difference between his or her performance and other
growers’ (Martin, 1995). Therefore, the payment received by a grower is not
predetermined, but instead, depends on the performance of other growers.

Competitive compensation has an advantage over ﬁxed payment and piece-rate

compensation schemes in that moral hazard becomes less important. All growers in the

42

same area face the same shocks inherent in a production process, therefore, the
information on other growers’ performance enables the processing ﬁrm to differentiate
and screen producers of varying managerial ability (Nalebuff and Stiglitz, 1983;
Knoeber, 1989). For this reason, competitive compensation schemes are the most
widely used method in designing agricultural contracts, particularly where weather has
a great inﬂuence on output and the grower’s efforts are difﬁcult to observe.

A compensation method along with speciﬁc management requirements within a
production contract could generate undesirable environmental impacts (Martin and
Zering, 1997). To illustrate this point, a seed corn production contract is used in the
next section as a case study to examine potential linkages between contract production

and environmental quality.

3.2 Contractual Seed Corn Production

Plant genetics play an important role in keeping commodity grain production
costs competitive and high quality. Production contracts have traditionally been used in
the seed industry to ensure genetic purity and protect genetic security. Use of contracts
to control grain production is part of a larger trend of agricultural industrialization in

the United States. (Hamilton, 1994).

3.2.1 Seed Corn Industry in the United States
The seed industry is deﬁned as that industry which sells seed to farmers, dealers

and distributors. U.S. seed revenues for major seed segments were estimated to be

43
about $4.9 billion in 1992. Seed corn is the largest crop segment in the seed industry
(Grooms, 1993).

The size of seed corn companies varies greatly. Many are small, local, family—
owned and operated businesses. The largest seed corn company, Pioneer Hi-Bred
International Co. , accounted for 38.7 percent of the 1992 U.S. seed corn market share.
The compensation to seed corn contracted-growers is the single largest production
expense for U.S. seed corn companies. It is estimated that the seed corn industry
injects over $600 million into primarily rural economies, thus, seed corn production
becomes an important source of farm income. Given that U.S. corn production
accounted for 46.3 percent of world corn production in 1994-1995 and 77.9 percent of
world corn exports, the seed corn industry plays an important role in the

competitiveness of U.S. agriculture (USDA, cited by Urban, 1995).

3.2.2 Seed Corn Production Management

Seed corn production requires producing seed of the desired purity, quality and
quantity by hybrid type. Seed corn production requires speciﬁc practices, such as
delay-planting, male-row removal, female-row detasseling, and particular pesticide
practices (Martin, 1992; Shaw et al. , 1989). The production processes are closely
supervised by the seed corn processing ﬁrm in order to protect the genetic security and
purity. More than 99 percent of seed corn is produced by contracting directly with
farmer-growers to produce the seed.

Seed corn production is different from commercial corn production in a number

44

of ways. Commercial hybrid corn seed is produced by crossing two parent genetic
lines called inbred varieties. The process typically entails planting one row of male
inbred for every four rows of female inbreds. Because maturity time may differ
between male- and female inbred varieties, seed corn inbreds may require planting at
two different dates for the same ﬁeld. After planting, the major ﬁeld operation in the
seed corn ﬁeld is the detasseling of the female plants. This operation is done prior to
silk emergence and pollen shed on the female plants. Male rows are removed after they
have tasseled and fertilized the female rows (Martin, 1992; Shaw et al., 1989).

Seed corn growers are required to isolate their seed corn ﬁelds from other
commercial corn ﬁelds in order to prevent fertilization from unwanted genetic lines.
Contracted-growers are typically compensated for the reduced yields due to the lower
yield capacity of the inbreds and the loss of the male rows.

Because seed corn is a high value crop and the availability of seed corn contracts
is restricted, growers are competing with each other in order to obtain seed corn
contracts. Contracted-growers are selected by the seed corn company depending on the
historical yields, grower cooperativeness, and availability of an isolated seed corn ﬁeld.

In general, seed corn production requires more labor and pesticides than
commercial corn. Except for those noticed above, most of the crop production
activities are similar to commercial corn. Pest management is important to seed corn
production. Some strict restrictions are imposed on the timing and the use of
herbicides, insecticides and fungicides because seed corn is very sensitive to these

chemicals. The company sends out a group of scouts and agronomists frequently to

45

examine the seed corn ﬁelds and provide contracted-growers with information on how
to manage pest problems. Therefore, the company has considerable information about
each individual grower’s agronomic practices. The company also keeps a complete
record of growers’ chemical use (Miron, 1995).

Nutrient management is another important element in seed corn production.
Growers apply fertilizers, including lime, phosphorus and potash, on the seed corn
ﬁeld. Most seed corn growers apply nitrogen twice on their ﬁeld: pre-planting and
side-dress. Studies have shown that inbred corn requires less nitrogen than hybrids.
These differences are due to less biomass and grain yield, detasseling and removing

male rows (Balko and Russel, 1980; Martin, 1992; and Peterson and Corak, 1994).

3.3 Geographic Characteristics of St. Joseph County

Most U.S. seed corn production is concentrated in the Midwest. Among these
areas, St. Joseph County in Michigan is one of the most important regions. Over ten
seed corn companies operate within this region. Many of the companies have similar
payment schemes that provide a high premium to encourage contracted-growers to
produce high yields. Therefore, this research will mainly focus on the type of contract
used by the leading seed corn company in the region.

St. Joseph County is located in the southwestern Michigan. The soils are
dominated by sandy loams. A signiﬁcant proportion of the cropland is irrigated. The
groundwater is associated with an unconﬁned shallow glacial drift aquifer in St. Joseph

County (Weight, 1996). These three factors combined to raise the risk that heavy

46

nitrogen application will cause nitrate leaching. Thus, it is not surprising that this
county is one of the three areas in Michigan that have high nitrate concentrations in the
groundwater (Kittleson, 1987; Weight, 1996). The local public is pressing the growers
to reduce nitrate leaching (King, 1989; Martin, 1992). For example, the
Environmental Protection Agency (EPA) found that the nitrate level in several wells
exceeded the EPA threshold of 10 ppm maximum contaminate level (MCL) -- permitted
under the Safe Drinking Water Act (Martin, 1992; Weight, 1996). The EPA required
the town of Constantine, in the center of the seed corn production area, to install a $1.2
million de-ionizer in their water system to reduce the nitrate levels below the 10 ppm
MCL.

St. Joseph County is a major producer of agricultural products in Michigan,
with gross farm receipts of over $65 million. Total cropped acres are 190,000, with
80-85,000 (45 percent) acres of irrigated cropland. Agriculture in St. Joseph County is
diversiﬁed. The primary crops grown in this area include commercial com (29 percent
of all cropped acreage) and soybeans (21 percent), seed com (24 percent) and some
horticultural crops (11 percent, including tomatoes, cucumbers, carrots and potatoes)
(King, 1994). Conventional crops are usually grown as cash crops, while specialty
crops such as seed corn and horticultural crops are based mostly on contract production
in St. Joseph County.

The production contracts can be classiﬁed into two main categories according to

management requirementsz. The ﬁrst category, representing the majority of contracts,

 

2Other contract types are also used in this area (Eide, 1997) but rarely.

47

requires intensive on-farm labor from contracted-growers. To grow seed corn, for
example, contracted-growers use their own equipment and do most of the needed ﬁeld
work. All of the seed corn is grown on irrigated land, and it accounts for more than
one half of irrigated cropland in this area.

The second category of contracts is closer to a cash-rent agreement.
Contracted-growers do part of the tillage at the pre-planting stage and might be required
only to run irrigation systems while the contracting company does the remainder of the
ﬁeld work. These contracts include potatoes, snap beans, carrots and tomatoes, are
grown under different contract speciﬁcations. Among seed corn producers, potatoes
are regarded as the second most proﬁtable crop after seed corn. Although potatoes
were introduced to this region after 1993 , an increasing amount of land was devoted to

potatoes during 1993-96 (King, 1994).

3.4 A “Tournament” Seed Corn Contract in St. Joseph County

Seed corn contracts have the characteristics of marketing, production
management, and resource-provision base contracts. In addition to general agronomic
practices mentioned in section 3 .2.2, the seed corn contract also speciﬁes a premium
paid to the growers, based on per bushel seed corn yield. This premium provides an
incentive mechanism to induce the grower to produce high yields. In one common type
of seed corn contract, the seed corn conditioning company offers a “tournament”

contract, where the payment is based on the grower’s relative performance.

48

3.4.1 A “Tournament” Seed Corn Contract
The case examined in this research is a contract where a seed corn grower is
rewarded by producing yield above the average regional yield, and penalized otherwise.

This payment can be expressed in a general form (Shaw et al., 1989):

50’) = ﬁlm-yaHQPPA (3.1)

where S denotes total payment from the seed processor to the contracted grower; y,
grower yield per acre of seed corn from female inbred rows; yo, average regional yield
per acre; Q, base crop yield (or per acre average regional commercial corn yield); P,
price of commercial corn per bushel; A, gross acres of the seed corn variety; a, a
coefﬁcient that transforms seed corn yield to commercial corn equivalent; ﬂ, a price
premium adjustment coefﬁcient. Because the inbred lines have lower yields than
commercial hybrids, the value of a is always greater than one. The costs associated
with contract production are compensated through a price premium adjustment
coefﬁcient, ,3, which also is greater than one.

The ﬁxed portion, Q multiplied by EPA, ensures the seed corn grower is
compensated for the expected opportunity cost of not raising an alternative crop such as
commercial corn. The payment above regional yield, [city-yon multiplied by ﬂPA, is
the premium that rewards (or penalizes) the grower whose seed corn yield is higher
(lower) than the average regional yield (yo). This contract’s ﬁnal payment is
conditional on each grower' 5 relative performance which creates competition among

contracted-growers.

49

The advantage of this tournament contract design for the processing ﬁrm is the
cost-effectiveness. There is a high transaction cost associated with per acre seed corn
production, including monitoring and scouting costs. Other costs include seed,
pesticides, and detasseling costs. The processor’s cost can be reduced, if the
contracted grower produces a high level of seed corn yield. A tournament contract is
designed for this purpose.

Two factors motivate contracted—growers to achieve high yield goals. First, a
high premium (or penalty) is associated with seed corn yield above (or below) the
average regional yield. Second, competition exists due to limited contract availability.
Because seed corn companies tend to offer contract renewals based on the contracted-
growers' historical yield performance, growers perceive a risk of losing the contract
associated with low yields. Therefore, contracted-growers interviewed believed that
achieving high yields is important for maintaining existing seed corn contracts and
obtaining new ones (Dobbins and Swinton, 1995; Batie and Swinton, 1995).

One common way to attempt to achieve high yields is to increase the amount of
nitrogen fertilizer applied. Though this can be done at relatively low cost, high

nitrogen fertilizer applications can lead to leaching.

3.4.2 Key Environmental Issues: Nitrate Leaching
Swd corn is a high-value crop because the grower net incomes from producing
seed under current contract is higher than if they produced commercial corn or other

crops. The economic return for one additional bushel of seed corn is high. Though

50

nitrogen is one of the most effective inputs to achieve high yield goals its uptake is
constrained by plant capacity and it is inﬂuenced by weather conditions (Martin, 1992;
Ritchie, 1993). For example, plants are able to take up more nitrogen fertilizer under
excellent weather conditions than in normal or poor weather. Because weather
conditions are difﬁcult to predict, growers tend to apply high nitrogen rates in order to
maximize corn yields in hopes of excellent weather conditions (Babcock, 1992). In
normal or poor weather conditions, excessive nitrogen application causes more nitrate
leaching to groundwater. In addition, because seed corn is a specialty crop that is not
widely grown nationally, research-based optimal nitrogen fertilizer recommendations
for seed corn growers are not widely available. There is no restrictions on the amount
of nitrogen used within seed corn contracts. Hence, seed corn growers tend to apply
nitrogen fertilizer to ensure maximum yield under optimal weather conditions (Wych,
1988).

In addition to nitrogen applications, other agronomic practices can affect nitrate
leaching as well. Examples include nitrate carryover from previous crops, tillage
practices, and irrigation and fertilization timing (Martin, 1992). In order to design an
optimal “green” contract, relationships between nitrogen use, nitrate leaching,

proﬁtability and agronomic managements have to be considered.

3.5 Summary
This chapter has reviewed the importance of contractual production in U.S.

agriculture. Production contracts are especially important in the seed corn industry in

51

order to ensure genetic purity and protect genetic security. A speciﬁc seed corn
contract from St. Joseph County, Michigan, is used to illustrate how nitrate leaching
could be related to existing contract designs. Nitrate leaching comes from excessive
nitrogen application, although it can be affected by other agronomic management
practices as well. If a processing ﬁrm is concerned the environmental quality,
production contracts can be used as a tool to control agricultural NPSP. The principles

of contract design to accomplish this goal will be explored in the next chapter.

CHAPTER 4
THEORETICAL FRAMEWORK FOR CONTRACT DESIGNS:
A PRINCIPAL-AGENT MODEL
This chapter develops a theoretical principal-agent framework to examine the
relationship between a representative agricultural processor (the principal) and a
representative contracted-grower (the agent). This model is extended to examine the
design of contracts where environmental quality outcomes supplement the agricultural

products and services.

4. 1 Review on Contract Design Literature

Contract theory is a subﬁeld of information economics that is usually treated in
the context of principal-agent problems. A central issue is the information asymmetries
between principal (the processor) and agent (the contracted-grower), which makes it
impossible or costly for the principal to observe actions taken by the agent. Such
situations present the potential for moral hazard--instances in which the agent can
beneﬁt through actions that the principal cannot observe, but which may be contrary to
the principal's welfare. Thus, if the principal wants the agent to take an action
favorable to the principal but costly for the agent, an incentive scheme must be
designed to inﬂuence the agent’s decision rule (Baron, 1987; Demski and Sappington,

1984; Hirshleifer and Riley, 1992; Kreps, 1990; Milgrom and Roberts, 1992;

52

53

Sappington, 1991; Varian, 1992).

A general conceptual framework for a principal-agent model is described below.
This model can be used to describe the relationship between a seed corn processing
ﬁrm (the principal), and a contracted-grower (the agent). This framework outlines the
key elements that need to be identiﬁed in designing an optimal contract. Let A be the
set of actions (which includes the levels of nitrogen fertilizer input, labor, etc.)
available to the agent. 5 is assumed to be a state of nature drawn from a probability
density function g. The action taken by the contracted-grower (denoted by a, where
aEA) and the state of nature jointly determine an observable outcome y=y(a, e) as well
as the monetary payoff 7:: Ida, e) for the principal. y can be a vector, such as yield of
seed corn and nitrate-leaching (a by-product), and 7: is the revenue of the seed corn
processor. The utility functions of both the processor and the contracted grower
increase with the monetary payoff. The agent receives a payment s(y), based on the
observable outcome. The agent also incurs a cost for taking action a, which is denoted
c(a). The objective function of the representative contracted-grower (agent) can be

written:

u(w)=u(S(v)-C(a)) (4.1)

That is, the monetary payoff (w) to the contracted-grower is a function of the payment
received minus the cost of complying with the contract.
The processor's problem is to design an incentive scheme s(.) that will induce

the contracted-grower to take the action that maximizes the processor's objective

54
function, denoted by v(7r-s(y)), over all states of nature. Through the payment scheme
s(y) that transforms outcomes into payments for the agent, the processor can indirectly
control the contracted-grower's action. Mirrlees (1974, 1976), Holstrom (1979), and
Hart and Holstrom (1987) proposed a method to re-specify parameters of the
distribution to solve this problem. Revenue (It) is assumed to be a function of y. They
argued, by the choice of a, the agent effectively chooses a distribution over y and n,
which can be derived from g via the technology y(. ). This derived probability
distribution is denoted by f(y;a). The principal's problem therefore becomes:
Max / V(7r-S(v))f(y;a)dy

subject Zia / u(s(y)-c(a))f(y;a)dy 2 u” (4.2)

/ u(S(y)-c(a))ftv;a)dy 2 / u(stv)-C(a‘)lf(v;a‘)dy (4.3)

where u“ is the agent's reservation utility, and d“ is an agent's alternative action.

This model illustrates the two key components of the principal's problem. The
participation constraint in equation (4.2) ensures that the agent elects to engage in the
principal's enterprise. The intuition behind this constraint is that participation yields
utility at least equal to what the agent might obtain from some alternative feasible
enterprise. The incentive compatibility constraint in equation (4.3) ensures that the
optimizing agent will choose those actions preferred by the principal (a) over
alternative feasible actions (a‘).

The processor chooses incentive payments to induce the grower's action a,

which satisﬁes both constraints. The Lagrangian function yields the optimal risk-

55

sharing rule:

__v’(y-s(y)) = u+g(1 _ﬂy___;a 41)) (for s)

u ’60)) 1W) “'4’

where v and g are Lagrangian multipliers corresponding to the participation constraint
and the incentive compatibility constraint.

If the action preferred by the principal has either a lower cost to the agent than
other alternative action, or is easy to monitor, the ﬁrst-best risk-sharing rule will be
satisﬁed automatically. That is, the principal's marginal utility in terms of the agent's
marginal utility is equal to the agent's reservation price of taking this contract (i.e.,
incentive compatibility constraint is not binding, thus (=0). If the agent's action is
impossible, or costly to observe, the incentive compatibility constraint will be binding
(i.e. ;> 0).

Equation (4.4) thus states that penalties or bonuses should be paid in proportion
to the ratio f(y;a‘)/f(y;a), referred to as a likelihood ratio (Holrnstrom, 1979). It
measures the ratio of the likelihood of observing y given that the agent chooses d‘ to the
likelihood of observing y given that the agent chooses a. A high value of the likelihood
ratio is evidence in favor of the view that the agent chose the action (1', while a low
value of the likelihood ratio suggests that the agent chose the action a (Milgrom, 1981;
Varian, 1992). The Monotone Likelihood Ratio Property is a commonly used condition
that requires this likelihood ratio f0;a‘)[f(v;a) to decrease monotonically in output y.
Consequently, the payment s(y) will be a monotonically increasing function of output.

That is, the payment increases when the observed output increases.

56

Contractual production was ﬁrst examined by Coase in his seminal study, The
Nature of the Firm. He emphasized that transaction costs of production can be
minimized through vertical coordination (Coase, 1937). Such vertical coordination is
especially important when risk is very high, information is scarce, or when asset-
speciﬁcity exists in a production process (Williamson, 1979). Contract production is
one form of vertical coordination that can reduce risks, resolve the issue from
asymmetric information, and avoid a big investment of the ﬁrm.

Three elements affect contract speciﬁcation: the structure of markets faced by
both principal and agent, the risk preferences and production sets of both principal and
agent; and the principal’s ability to observe the agent’s actions (Holmstrom, 1979 and
1982; Krep, 1990; Varian, 1992). The market structure will determine the bargaining
power with respect to contract speciﬁcations. For instance, when the principal is in a
monopsony-type ﬁrm while the agent is a competitive ﬁrm, the agent can only get its
reservation price under a contract. Risk attitudes determine the risk-sharing between
the principal and the agent. If the agent's action can be directly observed (the third
element mentioned above) without signiﬁcant cost, a “ﬁrst best” risk-sharing rule will
be reached. Otherwise, there is a trade-off between observability and risk-sharing
(Hart and Holmstrom, 1987; Rees, 1987; and Sappington, 1991).

The literature on contract theory provides the theoretical framework to
formulate the relationship between the principal and agent; however, empirical work
consistent with this framework is rare. Incentive schemes are usually discussed in the

literature in terms of taxes or penalties to control nonpoint source pollution; thus, they

57

represent a regulatory perspective. This research will take an empirical approach to
contract speciﬁcation focusing on voluntary pollution control. The principal-agent
framework is modiﬁed to represent a speciﬁc seed corn contract, which has a linear
incentive payment. A general form of a linear payment includes a ﬁxed amount and a

variable payment proportional to seed corn yield.

4.2 Conceptual Framework for A Seed Corn Contract

The model presented here assumes that the processor (the principal) is a
monopsonist, while the contracted-grower is a competitive farmer. The assumption is
based on the evidence that farmers compete to obtain seed corn contracts because they
provide higher return and lower risks than other contracts or other crops. Therefore,
the principal has more negotiation power than do the growers. As indicated in Chapter
3 , the current seed corn contract puts a high premium on those yield increments above
the average regional yield, creating an incentive for growers to apply nitrogen fertilizer
generously.

The relationship between nitrogen use and the incentive payment can be shown
in equation 4.5. With the price of seed corn normalized to 1, the per-acre payment to
the seed corn grower becomes:

30’) = [m-yOHQIﬂP’

= ﬂP’(Q-a)’") +aﬂP’y (4.5)
= K + by

where P’ is the price ratio of commercial corn to seed com. This payment s(y) can be

58

written in a linear form consisting of two parts: a ﬁxed payment (x=,6P’(Q-ay’)) and a
variable payment (b= aﬂP’), based on actual seed corn yield. Coefﬁcients K and b on
the ﬁxed and variable payments become the seed corn processing ﬁrm's choice
variables to design an incentive payment. This linear payment form has two
advantages. Not only does it provide a convenient basis for analysis, but more
importantly, a linear form has shown to be optimal for the principal to induce desired

agent actions (Diamond, 1995).

4.2. 1 Objective of the Processor and Contracted-Grower

In order to illustrate the optimal contract design, the objectives for both
processor and contracted-grower need be identiﬁed. Assume that the processor is risk-
neutral3, and that he (or she) will specify K, a ﬁxed payment, as well as b, a variable
payment, to induce the agent's action to maximize expected proﬁts. In this case, the
nitrogen fertilization rate, n, and other inputs, 2, are the agent’s control variables to
grow seed corn. The processor’s objective function is to maximize his or her gross

margin, calculated by seed corn yield minus the payment made to the grower. That is:

Max ELy - s(y)] = (1-b)y - x (4.6)

 

3The seed corn processor examined in this model is a large ﬁrm. A large ﬁrm often
has insurance against losses, and has the ability to spread out risks through equity as
well as other investments, therefore, it is reasonable to assume risk-neutral behavior
(Diamond, 1995).

59

This research uses a representative seed corn contracted-grower to evaluate the
economic impacts from alternative contract designs. Let the grower-agent's risk
preferences be characterized by a mean-variance utility function with constant absolute
risk aversion (Freund, 1956), where the risk aversion coefﬁcient is denoted 11. (The
criteria for selecting the empirical risk model will be discussed in Chapter 7.) The
grower's expected utility function per acre from growing seed becomes:

Eu(w) = Eu[s(v)-c(n,z)]
= [(Q-WWP’I + dﬂP’y -pn - z - (4/2)(dﬂP’)’0’
= x + by - (1/2)b’o’ -pn - z (4.7)
Equation 4.7 states that the grower’s expected utility equals the expected proﬁt (x + by
- pn - 2) minus the variance of income (b’a’) weighted by his or her risk preference
(/l/2). Equation 4.7 assumes that yield is the only random variable faced by the
grower, and that nitrogen use and other inputs do not affect the probability distribution

of yields.

4.2.2 Seed Corn Production and Leaching Functions
The seed corn production function is assumed to be:
y = f (n. z)+ 8. (4.8.a)
8"(0, 0’)
where n is the amount of nitrogen fertilizer applied, 2 is the vector of other inputs, and

e is a random variable. Nitrogen fertilizer is assumed to increase yield at a diminishing

60
rate (y, > 0, y," < 0, where y,, = oy/o’n, and y,“ = c7y/o'h2 )4.

The use of nitrogen generates a by-product--nitrate leaching, L. The leaching

function from seed corn production is assumed to be:
L=g(n,z, y(n))+ r) (4.8.b)
7) ”(0, 6 ’).
leaching is affected by nitrogen application and other inputs, such as irrigation. It is
also affected by seed corn yield. In a good weather condition, plants might be able to
uptake more nitrogen and produce higher yield, resulting in less nitrate leaching, than
they would in a normal weather condition. In general, the amount of nitrate leaching
increases with respect to nitrogen use (i.e., L. > 0, where L,=o’g/o‘n +(ag/oyxoy/az).
In many cases, nitrate leaching is ignored by the grower because of its externality
characteristic, that is, the social cost of nitrate leaching is ignored.

For simplicity, the random variables, 8 and r], are assumed to be distributed
independent of the nitrogen application level. Other inputs, 2. might affect nitrate
leaching as well. Examples that reduce leaching include planting cover crops in the
winter, controlling irrigation properly, and using minimum tillage (Martin, 1992). For
analytical convenience, this research will focus on the impacts from nitrogen
application control, assuming that other inputs are held constant at 2" and do not

contribute to the level of nitrate leaching.

 

" This assumption mirrors reality for many but not all circumstances. Evidence
exists for instances where yield may plateau or actually decline with supplemental
nitrogen (Peterson and Corak, 1994). Plant response depends heavily on existing soil
nitrate levels, climate, and biological activity.

61

Based on the functional form in equation (4.7), the decision rule of nitrogen
application for the representative grower becomes:

Maxm EU(W) = [(Q-ay‘WP’l + My -Im - Z" - (Ii/2)(aﬂP’)’0’

= K + by - (Ii/2)sz -pn - z” (4.9)
Equation 4.9 implies that the grower chooses a nitrogen level to maximize his or her
proﬁt, which equals the payment received from the processor minus nitrogen costs and
the expenses for other inputs.

Since nitrate leaching is incorporated neither in the current contract nor the
grower’s objective function, a proﬁt-motivated contracted-grower will use nitrogen at
the level where aﬂP’ ,, = p or by, = p. That is, he or she will use nitrogen according
to the marginal beneﬁt (by,) equal to its margin cost (p). As the variable payment
increases, or the price of nitrogen decreases, the application of nitrogen fertilizer will
increase. This decision rule implies that the social damage cost (or externality) from
nitrate leaching is ignored in the production process. As a result, the grower uses too
much nitrogen fertilizer from the social perspective. This result is coincident with the
evidence of excessive nitrate concentration in the groundwater for some seed corn
production regions (King, 1994).

For purposes of avoiding future regulation or negative public relations, a
processor may wish to reduce nitrate leaching on the farms of contracted growers. If
the processor cares about the contract' 5 indirect inﬂuence on environmental quality,

then the processor should design contracts that do not put too much weight on the

62

variable payment due to its tendency to induce high nitrate-leaching’.

4.2.3 Participation Constraint and Incentive Compatibility Constraint
In order to ensure that the contracted-grower can earn at least up to his or her

reservation utility level, the participation constraint should be satisﬁed. That is:

Eu(w) = K + by - (’1/2)b’02 -pn - z” 2 u" (4.10)

where u“ is the opportunity cost for growing seed com; a" can represent the retum from
growing cash crops, or taking other contracts.
The corresponding incentive compatibility constraint for the contracted-grower

is denoted by byn = p, where the grower's expected utility is always maximized.

4.2.4 Optimization Without Environmental Constraint
Without considering nitrate leaching, an optimal incentive scheme for the
processor is to choose a combination of the ﬁxed payment, K, and the variable

payment, b, to induce the contracted grower to undertake the action, It. That is,

 

3 While reducing fertilizer use can result in “win-win” situations where proﬁtability and
environmental quality are both served, the high value of many contracted commodities -
seed corn in particular -- makes a “win-win” outcome less likely than in the instance of
lower-value agronomic commodity production.

Eqi
Pal

\‘ari

63

Max (1 -b) y -K
K,b,n

subject to (4.11)
x+by-—:—b202-pn—z° 2 u0

by. =p

The corresponding non-comer solution will be:

b. : y,,(v,,-p)
(-y,,,,) 102

K: = uo-b y+pn+§ b2 02 (4.12)
where i, i, 92 <0
(3A 602 6p

Equation 4.12 states the optimal variable payment as well as ﬁxed payment. This
payment scheme deﬁnes an optimal risk-sharing rule. The equation shows that the
variable payment (b) decreases with increases in the contracted-grower's level of risk
aversion (21), in the level of yield risk (0’), and in the price of nitrogen (p). These
results have implications. Intuitively, equation 4.12 states that the variable payment
should be less if the grower is highly risk-averse (’1 is high), so that this risk-neutral
principal will share more risk in order to meet an optimal risk-sharing rule. If the
objective of the grower is characterized by decreasing or increasing absolute risk
aversion, the level of wealth might affect the optimal results. Furthermore, if the yield
variation is high, the variable payment should be small under this optimal risk-sharing

rule.

64

4.3 Alternative “Green” Contract Designs

Since penalties for nitrate leaching are not incorporated in the current contract,
and because leaching possesses the characteristic of a negative externality, a proﬁt-
motivated contracted-grower may use higher nitrogen levels than is socially optimal.
The processing ﬁrm may be concerned with maintaining its “green” reputation as well
as fearing potential future government regulations for nitrate leaching caused by seed
corn production. The assumption is that the company wants to reduce nitrate leaching
from the production of its contracted-grower, providing there is not too large a tradeoff
with seed corn production or proﬁts. The research issue to be addressed is how to
design a seed corn contract that will encourage contracted-growers to voluntarily reduce
nitrate leaching while still maintaining high yields and proﬁtability, i.e., being “green
and competitive” (Porter and van der Linde, 1995).

Using a contract for pollution control is discussed by Segerson and Tietenberg
(1992), Cabe and Herriges (1992) and Segerson (1994). They recognize that due to the
contractual (principal-agent) relationship between the employer and the employee, the
buyer and the seller, or the owner and the lender, there is a possibility of cost shifting
between the two parties. For example, if the government imposes a liability rule on the
processing ﬁrm for the environmental damage caused by its contracted—producer, the
ﬁrm can shift some of the associated costs to its farmer producers through decreases in
compensation, or increased monitoring efforts and input prices. The effectiveness of
this liability shifting (transfer) will depend on the lags between the time contamination

occurs and the time cleanup is required, as well as information about the extent of the

65

contamination. In order to model this relationship, the principal may design an
incentive scheme, based on his or her preference with respect to proﬁt and potential
liability as well as the agent's constraint, that is, the need to induce the agent to
undertake the activity that is preferred by the principal (Segerson, 1994). In order to
obtain the optimal incentive payment, the relationship and terms in contract theory need
to be explored.

As identiﬁed in Chapter 2, a number of contract designs are capable of
achieving N PSP control. These strategies can be employed to reduce NPSP, based on
outputs, inputs, managements, emissions, ambient levels, and damage liability. These
strategies are modiﬁed and used to induce contracted-growers to reduce nitrate
leaching. Four potential approaches are: 1) restricting nitrate leaching outcomes or
agronomic practices within contracts; 2) specifying ﬁnancial “punishment” within
contracts; 3) rearranging the incentive payment schemes; and 4) providing information

within contracts.

4.3.1 Imposing a Restriction within Contracts

The most common textbook approach to reduce nitrate leaching is for the
contract to restrict outcomes or permissible production practices directly. Such
restrictions might include the expected level of nitrate leaching in groundwater”, or

restrict permissible agronomic practices, such as the amount of nitrogen fertilizer

 

6The ambient level can be measured by sampling underground water from the region,
or simulated from a crop growth model, such as DSSAT 3.0. However, the enforcement
costs Md to be considered. Such enforcement issues will be discussed in the Chapter 8.

66

applied (It), timing of nitrogen fertilization and irrigation, choice of crop rotation, or
planting of winter crops (Harwood, Ritchie, Vitosh, 1996).

Assume that nitrate leaching has a non-random relationship with nitrogen
fertilizers, and it can be easily observed or simulated with high reliability; the processor
can impose on the contracted-grower a constraint for the permissible level of nitrogen
fertilizer (n‘), where the consequence of failing to comply is loss of the seed corn
contract, or some other penalty. The contracted-grower' s optimization problem
becomes:

Max Eu(v) = K + by - (zl/2)b’o2 -pn - 2‘"

Subject to n s n” (4.13)
Equation 4.13 states that in order to grow seed corn, the amount of nitrogen applied has

to be lower than the permissible level (11"). Optimization yields the following decision

rule:
by" = p + # (4.14)

where ,u (the Lagrangian multiplier on the constraint) takes the value zero if the
constraint is not binding, or represents the shadow price of the additional constraint if
the constraint is binding. A positive value of # means that the use of nitrogen fertilizer
will decrease due to diminishing margin product of nitrogen. Depending on the value
of the seed corn contract to the contracted-grower, this constraint could be a strong
incentive to comply with the nitrogen fertilizer standard.

Another form of restriction is to specify a permissible probability on the ambient

67

nitrate level above the water threshold levels (Segerson, 1988). That is, the objective
can be designed to meet the following chance restriction if the strategy targets nitrate

level from growing seed corn.
B(L;E) =Prob(L 2531/}; ‘ (4.15)

where B(. ) is the cumulative distribution function of nitrate leaching above the
threshold level (L); and Nb" is the permissible probability for nitrate leaching (L)

exceeding the threshold level (L_). In this case, the optimal nitrogen use is:
by, = p + a’BLLn (4.16)

where BL (= 68/01.) and L, are greater than zero, that is, higher nitrate application
increases the probability of nitrate leaching above the threshold level. A positive value
of u’BLL, means that the use of nitrogen fertilizer will decrease.

From a contract-design standpoint, much depends on the value of the contract.
For a contracted-grower who values the seed corn contract only slightly more than an
alternative enterprise, the value of the contract will be close to zero and therefore the
incentive to comply with the fertilizer constraint will be small. Nevertheless, to the
extent that such marginal contracted-growers fail to comply and lose their contracts, the
processor will violate the participation constraint in equation (4.10), so the incentive
payment, s(y)=x+ by, must be enhanced.

Such restrictions can be imposed on other agronomic management practices as

well. One example of such a restriction would be to forbid seed corn in rotation with

68

high leaching crops such as potatoes.

4.3.2 Specifying Financial "Punishmen " within Contracts

One alternative to a rigid restriction is a ﬁnancial penalty associated with
exceeding a speciﬁed threshold level of nitrate leaching. For example, if nitrate
leaching from each ﬁeld can be measured or simulated, a Pigouvian fee can be imposed
on the amount exceeding a certain level, perhaps the safe drinking water standard of 10
ppm MCL. A ﬂat-rate penalty on any ﬁeld exceeding the permissible level would be
simpler to apply. Alternatively, such a ﬁnancial punishment can be imposed on
nitrogen fertilizer uses to induce growers to cut nitrogen application, and subsequently
reduce nitrate leaching.

For example, if nitrogen applied can be directly observed, the processor might
impose a fee (or simply transfer the user charge fee), r, on the contracted-grower for
nitrogen use above the permissible nitrogen level, n”. Moreover, assume that the
amount of nitrate leaching is affected by weather and it can only be measured ex post.
A ﬁxed penalty 2' can be imposed on this excessive nitrate leaching outcome. Again,
B(L ;L-) = Prob(L 2 L_) represents the cumulated distribution function of nitrate leaching
(L) above the threshold level (L). The optimization for the contracted-grower thus
becomes:

Max Eu(v) = K + by - (1/2)b’o’ -p n - z“ - r max(0,n-n") - E(T),

n
where E(T) = rB(L;L) (4.17)

69

Equation 4.17 outlines two kinds of ﬁnancial penalties: on nitrogen use or on nitrate
leaching. Nitrogen user fee (r) is directly imposed on the amount of nitrogen use.
E( T) is the expected penalty when the ambient nitrate leaching level exceeds the
threshold L”. This expected penalty depends on B(. ), the cumulative distribution
function for nitrate leaching above the threshold level, and r is a ﬂat rate for this
violation. B(.) depends on the speciﬁcation of threshold level as well as the actual
amount of nitrate generated. When the threshold level is high, the possibility of
receiving a penalty would be low, i.e. , é’B/o‘L"< 0. On the other hand, when the
amount of nitrate leaching increases, a penalty is more likely, that is, 03/01» 0. Since
the use of nitrogen fertilizer increases the amount of nitrate leaching, it also increases
the probability of a penalty, that is,o"B/c5h =BLL, > 0.

Optimization yields the following decision rule:

by, = p+r+ rBLL, if n > n" (4.18)

by, = p+ rBLL, otherwise
This result shows that imposing a ﬁnancial punishment, r or 2', increases the marginal
cost of using nitrogen fertilizer. When this penalty is large, or when the use of nitrate
increases the probability of incurring the penalty, the amount of nitrogen applied will
be reduced compared to the scenario without the penalty. This result is due to its

diminishing marginal physical product of nitrogen fertilizer (i.e., y,, <0).

4.3.3 Reducing the Incentive Payment Schemes

If the principal internalizes the social cost of nitrate leaching into the incentive

70

payment, the resulting variable payment will be less than what would result if the
negative externality is ignored. One form in which environmental concern could enter
the processor's objective function is as a per-unit leaching penalty on nitrate leaching
when leaching (L(n)) exceeds some threshold (L‘). As equation 4.8 showed, nitrate
leaching is assumed to be L(n)=g(n,z”)+ r), where r)’(0, 6"). Such a ”penalty" could be
interpreted as a weighting placed by the processor ﬁrm on the risk of future regulation
resulting from perceived groundwater contamination that is tied to the company's
activities. If nitrate leaching is linear with respect to nitrogen fertilizer use, then the

processor's problem becomes:

Max (1 -b)y -K -t(L —L°)
K,b,n

subject to (4. 19)
0

K +by-gbzo2 -pn -z " 2 u
by, =p
where the processor’s objective is affected by the amount of nitrate leaching. If nitrate

leaching exceeds the threshold level, L", such that the tax takes effect, the optimal

variable payment that solves the processor's problem is

 

 

9 h — <0 0
(“ya")YOZ) w ere at (4 20)

b. = \J ynon-th-p). ab
Equation (4.20) suggests several interesting results for design of an optimal variable
payment (b). As expected, the variable payment, b, declines with increases in the

leaching "penalty", t.

71

While this contract design avoids the moral hazard (enforceability) problem
inherent in the nitrogen use constraint contract, the processor bears all costs of leaching
reduction. The reduced incentive payment (b) would force the ﬁxed payment (It) to
increase by a corresponding amount in order to respect the participation constraint. In
terms of proﬁtability, since expected seed corn yield would decline, the processor
would be worse off by the value of the yield decline plus the change in the ﬁxed
payment minus the weighted value of the variable payment. The contracted-grower will
be no worse off than before.

The above contracts, however, vary in the required measures as well as
economic impacts on the principal and the agent. Imposing a restriction or charging a
ﬁnancial fee on nitrate leaching or nitrogen use requires monitoring the amount of
nitrate leaching or nitrogen application rate. On the other hand, modifying the
incentive payment requires the observation of yield output. An empirical analysis is
required to evaluate the economic impacts. Both issues will be examined in the

following chapters.

4.3.4 Providing Information within Contracts

The processor-principal could provide information to contracted-growers as a
supplement to any contract design. The principal may be well-positioned to support
applied research on low-cost methods of reducing nitrate NPSP, and diffusing the
results to contracted-growers. Many processing ﬁrms either have developed their own

research projects, or have joint projects with other researchers such as those within

72

universities. Research is frequently directed at discovering practices which reduce
nitrate leaching. The information offered by the processor-principal might include
adequate amount of nitrogen, appropriate timing for nitrogen fertilization and
irrigation, less leaching crop rotation practices, and winter crop planting. Such
information could be delivered through a required grower training program,
information packet, or ﬁeld visits, and could be certiﬁed through a stewardship test.
Providing information to growers might avoid setting an unrealistic yield goal
from the grower’s subjective perception on nitrogen uses (Supalla et al. , 1995).
Because the information about nitrogen uptake for seed corn is not widely available,
such information is more valuable to develop a “win-win” strategy. From personal
interviews with several current growers, the results indicated that some growers apply
the same amount of nitrogen on seed corn as that on commercial corn (Batie and
Swinton; Dobbins and Swinton, 1995). Since some reduction from commercial corn
fertilization rates is possible without reducing yields, even in excellent weather, there

appears to be considerable potential for an information program.

4.4 Summary

This chapter identiﬁes the structure, and the main components of an optimal
seed corn production contract. A principal-agent model is adopted to examine
alternative “green” contract designs from the perspective of a risk-neutral seed corn
monopsonist and a risk-averse grower. Four categories of alternative contract designs

were illustrated: a) restricting outcomes or practices within contracts; b) specifying

73

ﬁnancial “punishment” within contracts; c) rearranging the incentive payment schemes;
and (1) providing information within contracts.

These contracts, however, vary in economic impacts on the principal and the
agent as well as in enforceability. In order to evaluate the effectiveness of these
alternative contracts, an empirical analysis is required. Chapters 5, 6, 7, and 8, will
present an empirical method that incorporates the biophysical production and
environmental impacts of seed corn production to evaluate and compare the
performance of these alternative contract designs. Contract enforceability will be

examined as well.

CHAPTER 5

SINIULATION OF ALTERNATIVE CROP MANAGEMENT SCENARIOS

In order to successfully design contracts that can control NPSP, knowledge of
the biological and economic dimensions of the pollution generation processes are
essential. This research uses a crop growth simulation model «DSSAT 3.0-- to
examine the relationships between nitrogen use, yield, and nitrate leaching. These data
are subsequently incorporated into whole-farm planning models in Chapters 6, 7 and 8
to calculate the economic impacts on the contracted-grower and the processor from

alternative contract designs.

5.1 Review on the Crop Growth Simulation Model - DSSAT 3.0

The Decision Support System for Agrotechnology Transfer (DSSAT 3.0; Tsuji,
Uehara, and Ballas, 1994) that contains a set of crop growth simulation models were
used in this research. DSSAT 3.0 is supported by International Benchmark Sites
Network for Agrotechnology Transfer (IBSNAT). The CERES models are used to
simulate cereal crops, including maize, wheat, sorghum, and rice (Jones and Kiniry,
1986). The CROPGRO models are used for legume crops, including soybeans,
peanuts, and dry beans (Wilkerson et al., 1983). Other models are used for rootcrops

and other vegetable crops. Three crop growth simulation models will be used in this

74

75

research; CERES-MAIZE for both commercial corn and seed corn (Jones and Kiniry,
1986; Martin, 1992), SOYGRO for soybeans (Wilkerson et al., 1983), and SUBSTOR
for potatoes (Ritchie et al. , 1996).

DSSAT 3.0 simulates plant growth and development on a daily basis by
integrating the interactions of genetic type, daily weather, soil, and soil nitrogen, as
well as management practices. DSSAT 3.0 has two advantages over other crop growth
simulation models. First, it provides a more detailed accounting of phenological
development and stresses encountered in each phenological stage than other models
(Kiniry, 1991; Jones et al., 1991; Krause, 1992). This advantage enables more
accurate prediction of variation in crop yields from year to year under different planting
dates. - Second, DSSAT 3.0 requires only moderate amounts of input data, compared
with other simulation models (Krause, 1992). These two advantages have made
DSSAT an attractive tool to researchers.

DSSAT has undergone considerable testing and use by researchers (Algoxin et
al., 1988; Boggess and Ritchie, 1988; Hodges and Evans, 1990; and Martin, 1992).
For instance, Kovacs et al. (1995) showed that CERES-MAIZE accurately projected
regional yields in Hungary during a twenty year period test. DSSAT explicitly tracks
nitrogen sources and fates, including nitrogen application, grain nitrogen, soil nitrate,
and nitrate leaching. Thus, DSSAT is well suited to developing nitrogen fertilizer
management alternatives. The amount of yield, and the cumulative nitrate leaching
have been validated by several studies in different locations (Jones and Kiniry, 1986;

Martin, 1992; Ritchie et al., 1993; Kovacs et al., 1995).

76

The soybean model within DASSAT 3.0 -- SOYGRO -- was developed and
improved by Wilkerson et al. (1983) and Jones et al (1987). Tests were conducted in
Gainesville, Florida, to evaluate the accuracy of the model at various locations (Jones
and Mishoe, 1991). These tests showed that the model predicted well for different
cultivars and locations. The potato model--SUBSTOR--was originally developed by
Grifﬁn, Johnson, and Ritchie (1993). The potato growth, development, and yield were
tested in Michigan by Ritchie et al. (1996).

Its versatility, wide validity, and limited data demands have led researchers to
use the DSSAT models for simulating such different management strategies, as varying
the planting populations (Piper and Weiss, 1990), light interception (Hodges and Evans,
1990), irrigation strategies (Algozin et al., 1988; Boggess and Ritchie, 1988; Worman
et a., 1988), and tillage systems (Krause, 1992). These ongoing research projects have

greatly improved the ﬂexibility of DSSAT model.

5.2 Analytical Methods to Simulate Crop Yield and Nitrate Leaching
Each crop growth simulation model in DSSAT 3.0 shares the same basic
structure and input data requirements (Krause, 1992; Martin, 1992; Jones and Kiniry,
1986; and Wilkerson et al., 1983). The basic structure includes:
1. Planting is done on a speciﬁc date. Soil characteristics, plant genetic
coefﬁcients, nitrogen treatments, irrigation treatments, and climatic data need to
be speciﬁed.

2. The model simulates the growth process based on daily increments.

10.

77
Temperature, photoperiod, and genetic parameters regulate the phenological
development of the plant.
Phenological stages determine how biomass production through photosynthesis
is partitioned among plant organs.
Solar radiation and plant leaf area determine biomass production.
Various stresses (including soil moisture, nitrogen or other nutrient deﬁciencies,
temperature, soil bulk density and soil pH), reduce the plant’s capacity to
produce biomass and partition it for maximum yield.
The timing of these stresses relative to the phenological stage has important
effects on crop yield.
Temperature, photoperiod, and/ or genetic parameters determine the maturity
date.
Grain yield is determined by genetic parameters and by how much biomass has
been partitioned to the grain.
Soil moisture and nitrogen dynamics are determined by various processes
throughout the simulation period (e.g. evaporation, transpiration, drainage, N

uptake, mineralization, denitriﬁcation, leaching.)

The required input data for each simulation include:

1.

Various soil characteristics, such as soil moisture, initial soil nitrogen levels,
and soil temperature.
Meteorological data, including daily maximum and minimum temeratures, daily

solar radiation, and daily precipitation.

78

3. Dates for the start of the simulation, planting, and irrigation treatments.

4. Planting depth and plant spacing (plant population).

5. Crop-speciﬁc genetic parameters.

6. Residue amounts from the previous crop, depth of incorporation, and the carbon
to nitrogen ratio for those residues.

7. Dates, amounts, formulations, and depths of nitrogen fertilizer applications.

For the purposes of this study, the location and soil structure are speciﬁed to reﬂect the
typical characteristics in St. Joseph County, Michigan. Appendix A lists the key
parameters used in the simulation model, including genotypes, soil type, initial soil
conditions, planting and harvesting details, irrigation, as well as water management,

and fertilization management.

5.2.1 Methods for Crop Growth and Nitrate Leaching Simulation

Forty-two years of yield and nitrate leaching were simulated for common
Michigan seed corn, commercial corn, soybean, and potato genotypes using 1951-1992
actual daily weather data. Rainfall, temperature, and precipitation daily data are from
the case study area, Three Rivers, Michigan, and solar radiation data are from nearby
Ft. Wayne, Indiana (National Weather Service, provided by Andresen, 1996). These
locations are the nearest weather stations to the study area with complete records for the
study period. Annual average minimum temperature, average maximum temperature,

total rainfall, and average solar radiation used in this simulation model are listed in the

79
Appendix B.

Twenty-one nitrogen treatments were simulated in continuous seed corn
production, starting from 0 kg/ha and increasing in 10 kg/ha intervals to 200 kg/ha, in
order to estimate the variations of seed corn yield, as well as nitrate leaching with
respect to different nitrogen application rates. Seed corn yield represents the
productivity and nitrate leaching represents the extemalities (by-products) of nitrogen
use in this case.

The simulation of seed corn yield and nitrate leaching involves two stages. The
genotypes used for male rows and female rows in seed corn production were different,
therefore, these two gene types were designed in separate DSSAT 3.0 ﬁles. Because
one row of male inbred is planted for every four rows of female inbred in seed corn
production and since no yield is obtained from the male com, the simulation data for
female-row yield was multiplied by 0.8 to obtain actual per acre yields. In order to
estimate total nitrate leaching from seed corn production, female rows and male rows
are simulated separately and then adjusted by their acre proportions, where a coefﬁcient
on nitrate leaching of 0.8 is used for female rows and 0.2 is used for male rows.

In principle, the amount of nitrate leaching from seed corn production is the
summation of leaching from both male and female rows. However, this estimation is
subject to bias — that is, some of the nitrate released from the cutting of male rows
after pollination will be absorbed by the female rows. Thus, it is difﬁcult to simulate
accurately the total amount of nitrate leaching for seed corn production when male- and

female-rows are run in separate models. For simplicity, because the proportion of

80

female rows is greater than the proportion of male rows, this study assumed that there
was a ﬁxed proportional relationship in nitrate leaching between male rows and female
rows across all rotation practices in seed corn production, and this relationship could be
estimated from continuous seed corn production (Ritchie, 1996). The estimated total
amount of nitrate leaching was obtained from the model in two steps. In the ﬁrst step,
the relationship between nitrate leaching from female rows and from male rows was
estimated by a regression, using the amount of nitrate leaching from female rows as the
independent variable and nitrate leaching from the male rows as the dependent variable.
The regression result is then used to estimate the total amount of nitrate leaching from
seed corn production by adjusting simulated leaching from female rows.

Each crop in different rotation patterns is also simulated for the 42 year period.
These patterns include continuous seed corn, seed corn in rotation with soybeans or
potatoes, continuous commercial corn, and commercial corn in rotation with soybeans
and with potatoes. Soybeans do not require any nitrogen application because they ﬁx
nitrogen. The nitrogen fertilization for potatoes is set at 265 kg/ha, an average nitrogen

fertilization rate for Michigan potato production (Ritchie, 1989).

5.2.2 Adjustment to the Original Model

The previous validations for DSSAT were based on discrete data from one
particular year, not from sequential years. Some biases existed in data simulated from
the Sequential Analysis program of DSSAT 3.0, therefore, adjustments were made to

the original DSSAT 3.0 model.

81

First, there was only a slight yield response to nitrogen applications from the
original model. The output ﬁle indicated that the amount of organic matter in the
model was decreasing over time, where organic matter was one source of plant-
available nitrogen. The released decomposition of organic matter was absorbed by crop
plants in the model. As a result, yields were over-estimated, compared with an actual
situation. The parameter for organic matter in the soil was adjusted from coefﬁcient
1.00 to coefﬁcient 0.68 within the model. This adjustment keeps the soil organic
matter pool at a constant level over time for continuous commercial corn with 120
kg/ha of nitrogen application rate (Ritchie, 1996). The organic matter for the
treatments above 120 kg/ha will accumulate over time while those below 120 kg/ha will
decline over time.

Second, several studies have indicated that the decay rate of fresh organic matter
speciﬁed in DSSAT 3.0 was over-estimated by 10 times (Gabrielle and Kengni, 1996;
Vigil et al., 1991). Therefore, the decay rate is adjusted to the correct level, that is, 10
times less than the original level.

The third bias occurs as an estimation error. Some of the yield data in one
given treatment appear to be 10 percent higher than the yield from the treatment with
10 kg/ha more, and 10 kg/ha less nitrogen fertilizer in the same year. In this case,
adjustment is made by taking the average of yield data from the treatments with 10
kg/ha more and 10 kg/ha less nitrogen fertilizer (Ritchie, 1996).

The DSSAT 3.0 model assumes perfect conditions for crop growth except

weather and other user speciﬁed agronomic practices. Other risk sources, such as pest

82

problems and mechanic failures, are not included. As a result, the yield data simulated
from DSSAT 3.0 tended to over-estimate compared to actual ﬁeld conditions, especially
for continuous corn and seed corn (Ritchie, 1996). It was estimated that a 5-8 percent
yield reduction in continuous corn and seed corn due to rootworm damage could occur
in actual conditions (V itosh, 1996; Miron, 1996; Stute and Posner, 1993). In potato
and corn/seed-com rotation, a 2-3 percent yield reduction might be expected because of
some constraints on post-emergence herbicide use. However, because these data have
considerable variation across farms, as well as across states of nature and because these
are relatively small reductions, this research assumes that seed corn growers are able to
control these risks by using pesticides so that any yield reduction is ignored in this

study.

5.3 Simulation Yield and Nitrate Leaching Data from DSSAT 3.0

The average yield and nitrate leaching data simulated from DSSAT 3.0 under
different nitrogen applications for continuous seed corn are listed in Table 5.1. Split
applications were speciﬁed in the simulation model, where 30 kg/ha was applied as the
starter. In order to be consistent with conventional U.S. farm data, these numbers were
converted to Imperial units: acres (ac), pounds (lb), and bushels (bu). The moisture
level of seed corn yield in Table 5.1 is at 15.5 percent, a standard moisture content for

corn grain.

83

Table 5.1: Average simulated seed corn yield and nitrate leaching from DSSAT
3.0 for St. Joseph County, Michigan, 1951-92

 

 

 

Nitrogen Fertilizer Average Seed Corn Yield Average Nitrate Leaching
No. (A) (B) (C) (D) (E) (F)
(kg/ha) (lb/ac) (kg/La) ath’ust.(bt_1_lac) (kg/ha) adjust. (lb/ac)
1 0 0.0 750 9.56 13.6 19.5
2 10 8.9 1189 15.17 13.6 19.5
3 20 17.9 1705 21.75 14.5 20.4
4 30 26.8 2294 29.27 15.5 21.5
5 40 35.7 3063 39.07 15.9 21.9
6 50 44.6 3690 47.07 16.5 22.5
7 60 53.6 4168 53.17 17.1 23.2
8 70 62.5 4630 59.06 18.0 24.1
9 80 71.4 5101 65.07 18.8 24.9
10 90 80.4 5541 70.69 19.5 25.7
11 100 89.3 5805 74.05 20.2 26.5
12 110 98.2 6001 76.55 21.4 27.7
13 120 107.1 6047 77.14 23.2 29.6
14 130 116.1 6100 77.82 25.9 32.4
15 140 125.0 6119 78.05 29.4 36.1
16 150 133.9 6129 78.19 34.3 41.2
17 160 142.9 6133 78.24 41.1 48.3
18 170 151.8 6135 78.26 48.6 56.2
19 180 160.7 6136 78.28 56.7 64.8
20 190 169.6 6137 78.28 65.1 73.6
21 200 178.6 6137 78.28 74.4 83.3

 

Column A indicates the amount of nitrogen application in terms of kilograms per
hectare, and it is divided by coefﬁcient 1.12 to convert to pounds per acre (column B).
Column C lists the average seed corn yield in terms of kilogram per hectare, which are
directly obtained from the female rows in DSSAT 3.0. These yield data were adjusted
by multiplying by a coefﬁcient of 0.8 to convert the simulated yield of the inbred
female variety to the grower’s actual seed corn yield. Yield data in kg/ha were then
divided by 62.71 to convert them into bushels per acre (or bu/ac) units. The adjusted

yield data are listed in column D. Columns E and F list the average amount of nitrate

84

leaching of female—rows simulated from DSSAT 3.0 and adjusted average total nitrate
leaching from seed corn production, respectively. Column F combines the amount of
nitrate leaching from female rows and male rows from seed corn production. Twenty-
one nitrogen treatments using forty-two years of weather data (882 observations) were
used to estimate the nitrate leaching relationship between female rows and male rows.

The result from the regression is shown below.

L.

29.12 + 1.87 L, (5.1)
(t-statisitic) (24.29) (60. 79)

Adjusted R’ = 0. 77

where L, is per acre nitrate leaching from the male row and l,r is per acre nitrate
leaching from the female row. Using the result from equation 5.1, the total amount of
nitrate leaching from seed corn production in terms of pounds per acre is calculated by:

Total nitrate leaching (lb/ac) = (0.8'“ L, +0.2'“ L,I )/1.12 (5.2)
= 5.20+1.05 L,

where 1/1.12 is the coefﬁcient that converts kg/ha to lb/ac.

Two observations can be made from Table 5.1. First, seed corn yield increases
at a diminishing rate with nitrogen fertilization. However, the nitrate leaching
increases at an increasing rate as nitrogen application increases. Therefore, when the
grower intends to increase yield by increasing nitrogen fertilization rate, more nitrate

leaching will be expected. That is, there is a tradeoff relationship between yield and

85

the reduction of nitrate leaching.

5.3.1 Nitrogen Application and Seed Corn Yield

Figure 5.1 describes the average seed corn yield response with respect to the

amount of nitrogen application from the simulation model.

 

I Yields vs Nitrogen Rates

as
O

. ..

(bu/ac)
(##me
00000

N
0

Seed Corn Yield

H
O

 

O

0 3O 60 90 120 150 180
Nitrogen Application Rate (lb/ac)

 

 

Figure 5.1: Seed corn yield under various nitrogen application rates

This yield curve shows a von Liebig (i.e. , plateau) production function (Peterson and
Corak, 1994). This curve displays three stages of seed corn production. When
nitrogen use is less than 80 lb/ac, seed corn yield increases linearly with the amount of
nitrogen use; when nitrogen use is between 80 Mac to 120 Mac, there is only a slight
increase in seed corn yield; and there is no yield response when nitrogen application is
more than 120 lb/ ac. The optimal nitrogen application rate will depend upon the

marginal beneﬁt and marginal cost of nitrogen fertilizer, which are discussed in

Chapter 6.

 

86

5.3.2 Nitrogen Application and Nitrate Leaching

In order to control nitrate leaching, its relationship with nitrogen use needs to be
explored. Figure 5.2 graphs the average amount of nitrate leaching with respect to
nitrogen applications (Table 5 . 1, column F), based on the simulation result from

DSSAT 3.0.

 

Nitrate Leaching vs Nitrogen Rates

\lmw
COO

 

O

(lb/ac)
K31» e tn m
(3 o c: o

litrato Leaching
p
O

 

O

0 20 40 60 80 100 120 140 160 180
Nitrogen Application Rete- (lb/ac)

 

Figure 5.2: Nitrate leaching from seed corn production under various nitrogen
treatments

The amount of nitrate leaching increases slightly with the nitrogen application rate
when nitrogen application rate is less then 100 lb/ac. However, beyond 100 lb/ac, the

nitrate leaching increases geometrically.

5.3.3 Relationship between Seed corn Yield and Nitrate Leaching
In order to design a “green” contract, the relationship between seed corn yield
and nitrate leaching must ﬁrst be identiﬁed. Figure 5.3 shows this relationship based

on simulation of continuous seed corn production from DSSAT 3 .0.

87

 

Seed Com Yleld (bu/ac)

 

 

l o 15 30 45 60 75 90
l Nitrate Leaching (lblec)

 

 

Figure 5.3: Relationship between mean nitrate leaching and seed corn yield under
various nitrogen treatments

The graph shows that as yield increases, so does the amount of nitrate leaching.
However, the rate of increase in nitrate leaching is slow before point L (with 30-90
kg/ha, or 27-80 lb/ac, N-application rate, where 30 kg/ha (27 lb/ac) and 90 kg/ha (80
lb/ac) were applied as starter and sidedress fertilizers, respectively). After this point,
the amount of nitrate leaching increases geometrically, but seed corn yield does not
signiﬁcantly increase. Therefore, the opportunity cost for the processor should be
small to reduce the nitrate leaching level to 30 lb/ ac in continuous seed corn. This
conclusion, however, ignores rotational practices that might increase nitrate leaching.
In conclusion, there is a positive relationship between seed corn yield and
nitrogen application rate when the amount of nitrogen applied is less than 107 lbs per
acre (or 120kg/ha). Beyond this level, there is only a slight yield response to additional

nitrogen applied. Secondly, nitrate leaching increases with nitrogen fertilizer

88

application rate, and the trend increases geometrically about 30—90 kg/ha (27-80 bu/ac)
of N-application.

Field interviews in southwest Michigan indicated that some farmers applied
nitrogen fertilizer up to 180 lb/acre (Dobbins and Swinton, 1995; Batie and Swinton,
1995). Two factors might explain this result: lack of information and/or aversion to
risk. Because seed corn is a specialty crop, and a relatively new crop to many growers,
growers may lack sufﬁcient information about nitrogen application. Furthermore,
farmers apply nitrogen use as an ex-ante decision, which is based on their expectation
of weather conditions. As Chapter 3 indicated, some farmers apply more nitrogen
fertilizer than average plant uptake capacity in order to avoid any nitrogen shortage in
good weather years (Babcock, 1992). This explanation is also related to the third
explanation, the grower’s risk attitude. The growers might be concerned with yield
distribution as well as its variation. Since this research assumes full information, only
the third explanation was examined.

In order to understand how yield distributions (or variations) under different
nitrogen treatments affect the grower’s decision-making, the relationship between
nitrogen application rates and the grower’s proﬁtability needs to be explored. The
choice of nitrogen application is assumed to be a discrete choice because the data
simulated from DSSAT 3.0 is also discrete. For simplicity, only three nitrogen
treatments for seed corn production are selected and incorporated into a whole-farm
programming model. The medium level (M with 107 lb/ac nitrogen use) shows the

optimal fertilization rate for the programming model to be presented in Chapter 6; high

89
level (denoted by H with nitrogen rate 116 lb/ac) and low level (L with 98 lb/ac
nitrogen use) indicates 10 kg/ha increase and decrease, respectively, from the medium
level. These three levels illustrate a tradeoff relationship between yield and nitrate
leaching reduction. They are closely clustered because the whole-farm model in
Chapter 6 shows proﬁt-maximizing results to be closely linked to yield response in this

range.

5.3.4 Yield and Nitrate Leaching Distributions under Three Nitrogen Treatments
If the processor’s objectives are to ensure stable seed corn production, and to
minimize the possibility of exceeding nitrate leaching thresholds overtime, the
distributions (or the variation) of yield and resulting nitrate leaching under different
nitrogen fertilizer rates are important in any contract design. The yield distributions of

three different nitrogen treatments are shown in Figure 5.4.

; 0.25 ' Tim's“??? MT‘ ‘
| .Medlum-N
l BLOW-N
l
l

 

    

Probability

55-60

3

Seed Corn Yield (bu/ac)

65-70
70-75

E

N

95-100

 

Figure 5.4: Probability distribution of seed corn yield under three nitrogen
treatments

90

From Figure 5.4, high nitrogen treatments tend to have distributions more
skewed toward higher yield than do low nitrogen treatments. The mean yield of the
low nitrogen treatment is 77.2 bu/ac, and it is 77.9 bu/ac in the high nitrogen
treatment. The probability of obtaining at least 75 bu/ac of seed corn yield (or, the
cumulative probability of yield above 75 bu/ac) is 62.5 percent from the low nitrogen
treatment, 67.5 percent from the medium nitrogen treatment, and 70 percent from the
high nitrogen treatment. If the goal is set at 85 bu/ac of sad corn yield, the probability
to achieve this goal is 25 percent with low nitrogen, 27.5 percent with medium
nitrogen, and 30 percent with high nitrogen treatment.

The corresponding nitrate leaching levels from the three nitrogen treatment are

shown in Figure 5.5.

 

1 0.3 _
.Medlum-N
0-25 DLow-N
E 0.2
I .3; 0.15
E
l 0.1

0.05

 

l O
l s
K (0

40-45
45-50
50-55

no 0 In 0 n
v- N O" m (o
5 u") o 11‘) o
.0 ‘— N N n
C
3

I Nitrate Leaching from Seed Corn Production (lb/ac)

Figure 5.5: Probability distribution of Nitrate Leaching under Three Nitrogen
Treatments

From Figure 5.5, the distributions between high nitrogen treatment and low nitrogen

treatment are quite different. The low nitrogen treatment has a mean of 30 lb/ac while

91

the high nitrogen treatment has a mean of 36 lb/ac. If the threshold of nitrate leaching
is set at 50 lb/ac, the probability of exceeding such a threshold under low, medium, and
high nitrogen treatments are 7.5 percent, 10 percent, and 27.5 percent. If the threshold
for nitrate leaching is set at 40 lb/ac, the probability of exceeding such a threshold
under low, medium, and high nitrogen treatments are 27.5 percent, 45 percent, and 60
percent. Thus, at a 40 lb/ac nitrate leaching threshold, the high level of nitrogen
application is more than twice as likely to exceed the threshold as the low nitrogen

application level.

5.4 Yield and Nitrate Leaching Data for All Enterprises

Rotation is another element that affects the amount of nitrate leaching from both
seed corn production, and the whole-farm. Nitrogen applications need to be adjusted
by incorporating nitrate carryover from previous crops. For instance, soybeans ﬁx
nitrogen that is available for following crops. The amount of nitrogen subsequently
applied can be reduced as a result. The average yield and nitrate leaching from seed

corn production under three rotation practices are illustrated in Figure 5.6.

92

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79
7a - . ﬂ - 3011;101:3111;
77 icontin. SSBd corn ‘é‘ [seed corn/soybean 1 30/130 kg/he l
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‘5 76 E 3050 kg/he
I -( , . , 1
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v - A
s 75 t - . .
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S 74 t I .. , ~
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E 73 . 3 : .. .
: l
72 ~1 : T",
' 1
. i
0 30/60 kglha
70 , e T . Y . r
0 10 20 30 40 50 80 70 80
Nitrate Leaching (iblec)

 

 

Figure 5.6: Relationship between nitrate leaching and seed corn yield under

different rotation practices

 

Figure 5 .6 shows three rotation practices for seed corn production: continuous
seed corn, seed corn/potato, and seed corn/ soybean. Each rotation practice has eight
nitrogen treatments, ranging from 90 kg/ha to 160 kg/ha with a 10 kg/ha increment in
both the continuous seed corn and seed corn/potato rotations, and from 80 kg/ha to 150
kg/ha in the seed corn/ soybean rotation. Among these three rotation practices, the data
from continuous seed corn show the lowest average nitrate leaching. These nitrate
leaching data are likely to be underestimated because DSSAT 3 .0 does not account for
pest damages which cause yield reductions and subsequently increase in nitrate

leaching. Nitrate leaching from rotations of seed corn after potatoes has the highest
leaching rate; large amounts of nitrate carryover occurs from potato production which

receives 237 lb/ac of nitrogen fertilizer. The seed corn/soybean rotation has the highest

93

seed corn yield potential among these three rotation practices. The seed corn/potato
rotation and continuous seed corn have similar yield responses under the same nitrogen
treatment.

Four crops -- corn, seed corn, soybeans, and potatoes -- are considered in this
study. The mean yield and nitrate leaching data 3.0 during 1951-1992 simulated from
DSSAT with respect to different crops, rotations, crop enterprise names used in a
programming model, and nitrogen application rates are shown in Table 5 .2 and Table
5.3, respectively.

Because seed corn has a higher unit value than commercial com, the tradeoff
between nitrate leaching reduction and proﬁtability might be greater with seed corn
than with commercial corn. Therefore, the interval between each nitrogen treatment is
set at 10 kg/ha for seed corn production and 20 kg/ha for commercial corn to indicate
the incremental changes in yield and nitrate leaching with respect to nitrogen
application rates.

Several conclusions can be drawn from Table 5.2. First, there is a critical point
where seed corn or commercial corn becomes less responsive to nitrogen fertilizer.
This point occurs when the nitrogen application rate is 120 kg/ha for continuous seed
corn or seed corn after potatoes; it occurs at 90 kg/ha for seed corn after soybeans. It
is 170 kg/ha in both continuous corn and commercial corn after potatoes, and 130 kg/ha
in commercial corn after soybeans. Second, there is not much difference in soybean
mean yield between seed corn/ soybean and commercial corn! soybean rotation from the

simulation. The yield is about 46.6 bu/ac in the model.

94

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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96

One similarity is shown in the amount of nitrate leaching among crops under
various rotation practices. There is a point where the amount of nitrate leaching with
respect to nitrogen applications increases substantially for both seed corn and
commercial com. This point occurs at 110 kg/ha nitrogen application rate in seed corn
production, and at 150 kg/ha in corn production.

As Table 5 .3 has shown, the seed corn crop, which is susceptible to contract
design manipulation, is not the crop responsible for most nitrate leaching. Potatoes
cause more leaching than seed corn, as do commercial corn and soybeans under some
scenarios. The results also show that there is little yield response with nitrogen
application beyond the medium level in seed corn production across all rotation
practices.

Within seed corn or corn production, rotation practices also have a different
impact on the amount of nitrate leaching. When seed corn or corn is grown in rotation
with potatoes, the average level of nitrate leaching generated is about 20-30 pounds per
acre higher, compared with continuous seed corn or seed corn in rotation with
soybeans.

In general, seed corn production generates more nitrate leaching than corn
production. Among all corn rotation practices, growing commercial corn after corn
tends to have the lowest mean nitrate leaching than of the practices simulated. Both
seed corn and corn generate higher nitrate leaching when they are grown after potato
crops. This results because of substantial nitrate carryover from potato production

within the simulation model DSSAT 3.0.

97

5.5 Summary

The data simulated from crop simulation model -- DSSAT 3.0 -- provide
information on the relationship between yield, nitrogen application rate, and nitrate
leaching. These data show that there is a three-stage relationship between yield and
nitrate leaching. In the ﬁrst stage, where nitrogen application rates are low, an increase
in yield does not cause much increase in the amount of nitrate leaching. In the second
stage, a tradeoff exists between yield and nitrate leaching. However, the amount of
nitrate leaching increases rapidly after the yield reaches the capacity of the crop in the
third stage.

The yield and nitrate leaching variations under three nitrogen treatments were
also examined in this chapter. The result shows a slight difference in yield distributions
but with a large variation in the nitrate leaching distribution across these three nitrogen
treatments. This chapter also compares the amount of nitrate leaching from seed corn,
commercial corn, soybeans, and potatoes by incorporating various rotation practices.
The data show that seed corn is not the crop with the highest nitrate leaching potential.
Potatoes incur more leaching. Thus, seed corn production will have more nitrate
leaching when in rotation with potatoes. The data from DSSAT 3.0 provides
information on physical dimensions of NPSP, but not abatement cost and economic

opportunity cost of NPSP abatement.

CHAPTER 6

AN EMPIRICAL PRINCIPAL-AGENT MODEL

Chapter 4 showed that, theoretically, various alternative contract designs are
able to reduce nitrate leaching. Such “green” contract speciﬁcations, however, might
unacceptably impose higher product costs on the contracted grower or reduce the
processor’s proﬁt due to yield reduction. In order to examine how alternative contract
designs affect the processor and the contracted-grower, this chapter presents an
empirical principal-agent framework based on a mathematical programming model of
the agent’s behavior. Using this framework, the tradeoff between nitrate leaching and
proﬁtability under various nitrogen treatments for both processor and contractor-grower
can be predicted under different contract speciﬁcations.

Various alternative contract designs that can reduce nitrate leaching are
identiﬁed in the case of seed corn contracts. In order to rank these alternative contract
designs, this chapter outlines the criteria that can elicit preferable contractual designs

from both processor’s and seed corn grower’s perspectives.

6. 1 Mathematical Programming Model for Optimal Contract Designs
A mathematical programming (MP) model is a common tool to obtain

optimization solutions. In an ideal empirical principal-agent model, the agent's

98

99

optimization problem needs to be nested inside the principal's optimization problem.
Both participation and incentive compatibility constraints are identiﬁed in the
principal’s decision-making process. On the other hand, the agent’s optimization is
affected by the incentive scheme, given technology and resource availability
constraints.

The general structure of a principal-agent model adapted to the seed corn

processor-grower context can be outlined as follows (Candler and Townley, 1982):

Max E{Gb’-S(v)]},
s
subject to
E{U[S(Y),nl} 2 U" (6.1)
n 6 argmax E{U[s(y), n’]} (6.2)
n, n’ EN

where the processor chooses an incentive payment, s(v), based on observable seed corn
yield, y, which induces the grower to choose a nitrogen application rate, n, conditioned
on two constraints: participation (equation 6.1) and incentive compatibility (equation
6.2). The participation constraint states that participation must yield utility at least
equal to what the agent might obtain from some alternative feasible enterprise, that is,
reaching his or her reservation utility level, 0’. The incentive compatibility constraint
guarantees that the agent will choose those actions preferred by the principal over
alternative feasible nitrogen use, It”. The processor’s and the agent’s objective
functions are G(.) and U(.), respectively.

In theory, a principal-agent model can be solved empirically using two-level

mathematical programming (Bard and Moore, 1990; Candler et al., 1981; Candler and

100

Townley, 1982; Komai and Liptak, 1965). However, two practical barriers impede all
but the simplest attempts to use two-level mathematical programming. First, due to the
model’s inherent non-convexity, convergence to the global optimum is not guaranteed
(Candler, et al., 1981; Bard and Moore, 1990). Second, due to the complexity of
stating interdependent objective functions, applications must be limited to small
matrices.

To overcome these barriers, this study decomposes the general principal-agent
model into two steps. Because any constrained optimization must ﬁrst satisfy its
constraints, the ﬁrst step begins by modeling the behavior of the representative seed
corn contracted-grower. A representative whole-farm model veriﬁes whether the
principal’s incentive-compatibility and participation constraints are met when the
grower’s objective function is maximized. In the second step, this research evaluates
the impacts of different contract speciﬁcations for both processor-principal and grower-
agent. This paper then identiﬁes the preferred contract designs for each party,

including which of these might be potentially acceptable to both parties.

6.2 Welfare Measurement for the Seed Corn Contract

The ﬁrst stage in structuring a principal-agent model is to characterize the
objective functions for both the processor and the representative grower. These
objective functions will dictate the decision-making processes and welfare
measurements for each party. The choice of a particular objective function is based on

an analysis of previous literature.

101

In this research, the processor is assumed to be risk-neutral. This assumption is
justiﬁable for a large company that has insurance against losses and has the ability to
spread risks through equity investments. Many studies have provided evidence that
supports the assumption of decreasing absolute risk aversion as wealth increases
(Chavas and Holt, 1990; Lins et al., 1981; Saha et al., 1994). A large ﬁrm tends
toward risk—neutral behavior when its income is high (Diamond, 1995).

In order to estimate the impacts of different contract speciﬁcations on the
processor, the welfare change for the processor will be measured by gross margins, the
difference between gross income and total variable costs. An enterprise’s gross margin
is its contribution to ﬁxed investments and proﬁt after speciﬁed variable costs have
been paid.

The processor’s gross margin per acre over speciﬁed production and marketing

costs is constructed by subtracting the grower payment from marginal revenue,

SCMC

Processor Gross Margin = (1 -
TR

 

0)) * P... - 50’) (6.3)

where P, is the wholesale price of corn seed per 80,000-kernels bag (weighing 47
7 , SCMC . . . . .

pounds , or 0.84 bushel), TM 13 the proportlon of seed condtttomng plus

marketing costs (SCM C) to total seed corn operating income (TR); and SO) is the

payment to the grower.

The base scenario is the case where the wholesale price of conditioned seed corn

 

7The price of corn seed varies by the number of seeds. Weights for each bag varies,
depending on the size of corn seed. The number, 47 pounds per bag, is the average
weight for medium size seed.

102

is $71.50 per bag, a typical wholesaler price for one bag of medium-quality hybrid corn
seed in 1996. The conditioning and marketing costs are assumed to be 40 percent of
the total value (Brinkman, 1996). Therefore, the gross margin for the processor is $51
per bushel.

A representative whole farm model is used to predict the grower’s behavior
under different seed corn production contract speciﬁcations, including outcomes for
nitrate leaching and gross margins. The use of a representative farm assumes that
growers are somewhat homogeneous in objective functions, production practices, and
resource constraints. This assumption is based on the observation that the growers
typically use similar operational practices in seed corn production. The representative
farm approach provides insights into the relationships among factors affecting the
predicted responses to alternative technologies, policies, or pricing mechanisms (such
as contracts). Although not constructed on a statistically representative basis, this
model was developed based on interviews and expert opinion of conditions typical of
full-time seed corn farms in Southwest Michigan (Batie and Swinton; Dobbins and
Swinton; King, 1995).

In order to examine the impacts of alternative contract designs on a
representative grower, a whole-farm planning model will be used. Whole-farm
planning is widely used to determine the optimal size and enterprise mix of the farm
operation (Harsh et al. , 1981). One commonly used analytical technique is
mathematical programming, which maximizes or minimizes an objective function

subject to technology and resource constraints. The whole farm programming model

103

can analyze how a grower’s objective function (gross margin or expected utility), yield,
and nitrate leaching differ between the current contract and alternative contract designs.
Using the results on nitrate leaching and yield from a whole-farm model, the principal
then can choose the preferable contract designs that have higher proﬁtability and/or

lower nitrate leaching.

6.3 A Linear Programming Model

The ﬁrst case to be examined is optimization by a risk-neutral contracted-
grower. A linear programming (LP) model can be used to model the behavior of a
risk-neutral grower, where the grower is assumed to maximize expected proﬁt from the
whole farm operation. In this research, the grower’s proﬁt is calculated using gross
margins (GM), that is, cash income minus all variable costs. Therefore, the grower’s
gross margin represents the return to ﬁxed invesunent and unpaid family labor and
management.

The mathematical programming structure of a whole-farm linear model is:

Max 2 (.71 x].
1
subject to E onyx]. s bm (6,4)
1
x12 0 Vj

where
xi: the level of f“ farm activity (e.g. crop enterprises and inputs); j indicates
the number of activities;

cj: expected net return of one unit of the 1‘" activity, e.g. , price for each

104

crop or marketed input as well as the payment received from seed corn

contract production;

ail-z the technological coefﬁcient, i.e. , the amount of the ni“ resource
required to produce one unit of the 1'” activity; and
b,: the amount of the mLh resource available, including available stocks of

owned land, rental land, family labor, seed corn contract land, and
timeliness restrictions on attainable yield; m indicates the number of
resource, as well as institutional constraints, such as contract restrictions
on nitrogen use.

The grower’s objective is to ﬁnd the farm plan which generates the largest net return

subject to the resources and institutional constraints.

6.3.1 Assumptions of a Linear Programming Model
Linear programming (LP) is based on several assumptions (Hazell and Norton,
1986):
1. Linearity: both the objective function and the constraints are linear;
2. Optimization: the objective function is either maximized or minimized;
3. Finiteness: only a ﬁnite number of activities and constraints are considered in
order to ensure that an optimal solution is obtainable;
4. Fixedness: At least one constraint has a non-zero right-hand side coefﬁcient;
5. Continuity: resources can be used and activities produced in quantities that are

fractional units;

105

6. The coefﬁcients of the objective function, those of the constraints, and the right
hand sides are non-random;

7. Additivity: activities are additive, i.e., the total result of two or more activities
is the sum of their individual results.

8. Homogeneity: all units of the same resource or activity are identical; and

9. Proportionality: the net return and resource requirements per unit of activity are
constant regardless of the level of activity used. This assumption implies a
perfectly elastic demand curve for the product, perfectly elastic supplies of

variable inputs, and a Leontief production function.

The assumption of linearity implies that the aggregate whole farm production function
exhibits constant returns to scale. One advantage of linear programming is that it
allows users to test a wide range of alternative adjustments, and to analyze their impacts
with minimum effort (Beneke and Winterboer, 1973). In this study, LP makes it
possible to evaluate both the proﬁtability and the nitrate leaching reduction associated
with different seed corn contract designs in St. Joseph County, Michigan.

The marginal productivity value of the limiting resources (or shadow prices)
indicate how much the net revenue would be changed through relaxing the resource
constraint by one unit. A comparison of the shadow price with the cost of acquiring
one additional unit of the resource will show whether such an adjustment in resource
use is proﬁtable. LP also lists the inventory of surplus resources which are not

completely used in the model. This inventory can be used as a guide, together with the

106

binding constraints, in planning for long-run adjustments within the farm.

6.3.2 Purdue Crop/Livestock Linear Programming

The primary analytical tool used here for risk-neutral whole-farm modeling is
the PC-LP computer software package (Purdue Crop/Livestock Linear Programming,
Dobbins et al., 1994), a whole-farm planning model developed in the early 1990s by
agricultural economists at Purdue University. PC-LP assists farmers in achieving more
efﬁcient farm management, including planning cropping patterns, machinery
acquisitions, or other farm decisions.

PC-LP examines a farm plan by maximizing the expected proﬁt (or gross
margin) from farm operation during one year. PC-LP includes crop alternatives
(rotation, governmental programs, and types of cultural practices), crop activities (land
preparation, planting and post-planting activities, harvesting activities, labor hiring
activities, and drying and storage activities), and constraints (acreage, machinery
timing, labor time, ﬁeld-accessible time, storage availability, and sequencing
constraints). PC-LP can be designed to incorporate speciﬁcally yield penalties and
machinery, and ﬁeld time constraints under different management practices. Using PC-
LP, the key whole-farm constraints, such as the time of year that labor or equipment
are most constraining, can be identiﬁed as well. These features make PC-LP a

convenient tool to analyze the impact of alternative contract designs.

107

6.4 Description of the Seed Corn Farm Based Model

The representative farm is assumed to own 1200 tillable acres with irrigation
and to have the option to rent up to 500 additional acres. It is operated by one full-time
adult with a typical machinery complement and has the option to hire supplementary
labor. This farm represents a typical seed corn grower in St. Joseph County as
identiﬁed by the county’s Cooperative Extension Director Rod King (1995). The
details of resources, crop enterprises, tillage practices, prices, and other miscellamous

data are listed as follows.

6.4.1 Resource Constraints
The resources used in the whole-farm programming model include land,

machinery, labor, and seed corn contract availability.

A. Land

The soil type of this representative farm is sandy loam, which is well suited to
center, pivot irrigation but has a high propensity for leaching when large amounts of
nitrogen fertilizer are applied. This contracted-grower may rent up to 500 additional
irrigated acres at $165/acre, the typical rental price for irrigated land in this area in

1997 (King, 1997).

B. Machinery

Within the model, the grower is assumed to own two tractors and various tillage

108

equipment. The tillage machinery used on this farm can be divided into ﬁve categories
according to different purposes: ﬁeld preparation, pre-tillage, planting, post-tillage, and
harvesting. The various equipment used, the working hours per day, labor required,
tractor working rate (acres per hour), and cost per acre are listed in Appendix C
(Lazarus, 1996).

Machinery operations require both labor and tractor time. Fertilizer application
is assumed to be done by the grower with rented equipment. Therefore, the cost is
based on custom-hired rates without labor cost. Both equipment for insecticide and
herbicide spraying are also based on custom work (Schwab and Siles, 1994). Within
this model, the seed corn grower is assumed to hire labor to remove the male row after
pollination has ﬁnished. This task is done as piece work at a cost of $5 per acre. It is
assumed that the representative farm does not have drying, processing, or storage

facilities.

C. Labor

The labor force includes one full-time worker (1 person), and two part-time (or
hired) workers in this case study. The wage rate is assumed to be $7.50 per hour. No
off-farm income is included in the model.

For labor constraints, labor activities are divided into 23 periods according to
different tasks and weather conditions. The number of suitable days for ﬁeld work
depends on both soil and weather conditions. Estimates of the suitable days for ﬁeld

work are mainly based on previous publications (Rosenberg et al., 1982; Doster et al.,

109

1994). The details are listed in Appendix C.

D. Seed Corn Contract Availability
Due to high competition in obtaining seed corn contracts among farmers, the
maximum seed corn contract available to this representative grower is restricted to 500

acres in the study.

6.4.2 Crop Enterprises

Crop enterprises include seed corn, commercial corn, soybeans, and potatoes.
The crop alternatives, nitrogen use, and their respective mean yield and nitrate leaching
levels are listed in Table 6.1. Three nitrogen treatrnents--high (H), medium (M), and
low (L)-- are examined in seed corn and commercial corn production.

In the crop enterprise names, the ﬁrst letter indicates previous crops, where S is
seed corn; C, corn; B, soybeans; and P, potatoes. The rest of these names stand for
crops planted this year, where SEED is seed corn; CORN, corn; BEAN, soybeans; and
POTATO, potatoes. In terms of nitrogen application, H indicates high levels of
nitrogen use; M, medium level; and, L, low level. The median level of nitrate leaching
from seed corn production is 35 pounds per acre, and 23 pounds per acre from corn

production.

110

Table 6. 1: Mean yield and nitrate leaching under enterprises included in the whole-
farm programming model

 

 

 

 

 

 

 

 

_
Nitrogen
Crops and rotation Enterprise Name ‘ Yield Leaching
ikg/ha lb/ac bu/ac lb/ec

Commercialm

continuous com CCORN(H) 190 170 189 21
CCORN(M) 170 152 188 19
CCORN(L) 150 134 185 17

com after soybeans BCORN(H) 150 134 189 24
BCORN(M) 130 1 16 188 23
BCORN(L) 1 10 98 187 22

com after potatoes PCORNa-l) 190 170 189 51
PCORN(M) 170 152 188 49
PCORN(L) 150 134 185 47

Scedfmn

continuous seed corn SSEED(H) 140 125 78.1 35
SSEED(M) 130 l 16 77.8 32
SSEED(L) 120 107 77.1 29

seed corn after BSEED(H) 100 89 77 .9 36

soybeans BSEED(M) 90 80 77.6 34
BSEED(L) 80 71 77. 1 34
PSEED(H) 140 125 78.0 58

seed corn after potatoes PSEED(M) 130 116 77.7 56
PSEED(L) 120 107 77 .42 55

Spartans

after seed corn SBEAN 0 0 47 23

after comm. corn CBEAN 0 0 47 22

Rotators

after seed corn SPOTATO 265 237 NA 136

after comm. corn CPOTATO 265 237 NA 121-

 

 

 

 

 

 

 

Source: DSSAT 3.0 simulation.

As Table 6.1 shows, growing seed corn following potatoes incurs a substantial
amount of nitrate leaching, compared to other rotation practices. This result reﬂects
that there is a high level of nitrate carryover from potato production. In reality, the
proﬁt-maximizing grower would reduce nitrogen application rates to account for such
nitrate carryover in the soil. However, the data simulated from DSSAT 3.0 do not

reﬂect such a nitrate carryover advantage. As shown in Chapter 5, seed corn yield

111

responses to nitrogen use is the same as continuous seed corn. This result implies that
nitrogen use in the model from simulation model DSSAT 3.0 might be overestimated.

Both corn and soybeans are cash crops. Seed corn is grown by contracting with
a seed corn processing company and paid according to the relative performance of yield
(i.e. , grower’s yield relative to the regional average). Potato production is based on
cash rent agreements, where potato growers pay a lump-sum rent per acre and require
lime application, spring chisel plowing and periodic irrigations during the summer
season. Although potato production is not undertaken on a large scale in this area, it
serves to represent other specialty crops, such as carrots, cucumbers, and tomatoes.

Commercial corn and seed corn are grown either continuously, or in rotation
with soybeans or potatoes. Due to serious pest problems in continuous cropping,
soybeans and potatoes are only allowed to be grown in two-year rotations. In general,
corn or seed corn in rotation with other crops has several advantages (Harwood, King,
Ritchie, and Vitosh, 1995):

1. Corn or seed corn in rotation with soybeans can increase yields and save costs.
Corn crops can obtain a nitrogen credit of up to 30 lb/ac from soybean crops
and can reduce insecticide use by about $10.75/ac for seed corn production and
$13.05/ac for corn production due to reduced probability of incurring rootworm
problems with rotations.

2. Corn or seed corn in rotation with potatoes can increase yields and save costs.
When corn crops are in rotation with potatoes, potash application can be

reduced by $7.80/ac for commercial corn and by $7.34/ac for seed corn

112

production due to high potash residuals when com is planted after potatoes.
Insecticide use can be reduced by $10.75/ac for seed corn production and
$13.05/ac for corn production due to less pest problems when seed corn or corn
rotates with potatoes.
These two advantages make crop rotation more attractive in terms of cost savings.
However, the whole-farm planning also depends on other elements, such as labor
availability, resource constraints, and economic incentives, including prices and price

premiums .

6.4.3 Yield Adjustment and Moisture Content
Within the model, crop yields and moisture contents vary by planting dates and

harvesting dates (Appendix C).

A. Timeliness and Yield Adjustments

Planting and harvest dates affect crop yields for several reasons. First of all, the
longer the growing season, the higher the probable yield. Second, due to the possible
damages from fall-frost in Michigan, the yield levels of corn and soybeans are likely to
decline when harvesting occurs after late October. Early planting, therefore, can
ensure early harvest, and thus avoids such damage. Although early planting has this
advantage, it also means that during late April and May many activities must be
completed; thus, the farmer might need to sacriﬁce some yield by late planting due to

labor and machine constraints.

113

In general, the highest commercial corn yields are obtained for planting during
April 26 - May 2, and harvesting during October 11 - October 31 (King, and Black,
1995). Planting or harvesting in other periods tend to lead to yield reductions of
varying magnitude.

By contrast, seed corn suffers little yield loss under different planting and
harvesting periods because its growing season is shorter, and because both planting and
harvesting are controlled by the processing company. Planting occurs during late
April and May, and harvest during late August and early October.

Late planting reduces yields in soybean production. However, late planting of
soybeans impacts yield less than it does in corn production. Both potato planting and
harvesting are controlled by the renters of the land, so potato yield variation due to

planting and harvesting dates is not examined in this research.

B. Moisture Content

Delaying corn harvest tends to reduce grain moisture content, which saves
drying costs. The standard moisture level required for corn storage is 15.5 percent. In
this study, the grower is assumed to send his or her crop to an elevator for drying and
storage. The cost to dry one percent of moisture is assumed to be 2.5 cents per bushel.

The moisture content for storing soybeans is 13 percent. It is assumed that no
drying is required in soybean production. Seed corn can be harvested at a relatively
high moisture level of 40 percent. The processing company dries the corn seed to 15.5

percent, so the grower does not need to pay for the drying expense.

114

6.4.4 Tillage Practices

Tillage practices used within the model are based on practices identiﬁed through
interviews with several experts, including agricultural economists (Harsh and Schwab),
agronomists (Harwood, Miron, Lupkes, Ritchie, and Vitosh, 1995), and extension
agents (King, Kennedy, and Warnhoff, 1995). The tillage practices incorporated within
the model can be divided into ﬁve categories: ﬁeld preparation, pre-planting tillage,
planting, post-planting tillage and harvesting (Appendix C). Field preparation is
usually done in the fall to save time in spring. It includes plowing and spreading
phosphate (PZOS), and potash (K10) fertilizers. A V-ripper is used to loosen the soil
after potato harvest.

During December to March, there are no ﬁeld activities, but the grower repairs
and maintains machinery. In the spring, the grower has to cultivate the ﬁeld before
planting. When the soil is hard, a tandem disk is often used to break up the soil. For a
typical grower, tandem disking is done every other year.

Planting commercial corn during the end of April and middle of May, and
planting soybeans and potatoes during mid-late May, generates high yield outcomes.
However, due to the tight time schedule, a grower might need to allocate his or her
time among different crops by delaying some of the planting. All planting, except

potatoes, are done by the grower”. No planting is required in potato contracts.

 

8Different seed corn varieties require different planting practices. Single or double
delay planting, ﬂaming, and male cutting might be required for some varieties in order
to get better pollen production. The variety used in this model covered the highest
percentage of seed corn acreage planted in St. Joseph County in 1995. It requires
single delay planting. Male rows are planted one week after female rows are planted.
The grower is compensated by the company for any delay planting requirement.

115

Standard post-planting tillage includes rotary hoe, ﬁeld cultivation, insecticide
and herbicide spraying, irrigation, and the side-dressing of nitrogen fertilizers. In the
case of seed com, the contracted-grower is responsible for weed control while the
processing company will take care of insect and fungus problems. In the case of
continuous corn or seed com, the farmer will apply insecticides for rootworm at a cost

of approximately $16.30 per acre.

6.4.5 Commodity Prices and Input Costs

Commodity prices tend to ﬂuctuate every year. The price ratio of corn to
soybeans is approximately 1:2.5 (Krause, 1992). During the last several years, the
price for corn was about $2.40/bu. Therefore, the price of soybeans is set at $6.00/bu
in the model. Inputs are based on several studies, where nitrogen fertilizer costs 25
cents per pound (Nott et al. 1995; King, 1993 and 1996). The prices of commodities

and all input expenses except nitrogen fertilizer are listed in Table 6.2.

116

Table 6.2: Crop prices and cash production expenses (excluding nitrogen cost) of

 

 

 

 

 

 

 

 

 

 

 

 

 

 

each crop
Crops Seed Corn Corn Soybeans Potatoes
Commodity Price Fix: $150/acl
Var:$5.28/bu $2.40/bu $6.00/bu $235/ac
Expenses (excluding nitrogen cost)
Seeds $20.00 $26.88 $13.20 -
Fertilizer (total) 29.04 33.10 16.50 $10.00
Phosphate(P205)@250/lb $ 4.50 $ 7.50 - -
Potash (K,O)@13CIlb 14.69 15.60 $ 5.50 -
Limestone @$20/ton 10.00 10.00 10.00 $10.00
Insecticide 10.752 16.302 - -
Herbicide 20.35 20.35 26.63 -
Irrigation 24.00 24.00 - 28.00
Machinery operating costs 32.42 39.49 26.16 4.32
Total Cash Exjenses $136.56 $160.12 $82.49 $42.32
Note:

"The payment of seed corn contract is conv_erted for the following calculation:
Payment per acre = (03y)a+Q)ﬂP
where y is the grower’s seed corn yield; y is the grower’s and average regional seed corn yield (assumed
to be 66.56 bu/acre); Q is the average regional commercial corn (assumed to be 190 bu/acre); and P is
the price of commercial com. a is assumed to be 2 and ,6 is 1.1 in the model.

 

 

2 This cost is based on continuous corn production. In rotation with soybeans or potatoes, this cost will
be $3.25 for commercial corn and zero for seed corn.

6.5

Optimization of the Representative Risk-Neutral Whole-Farm Model

In order to estimate the impact of alternative contract designs, this analysis ﬁrst

examines a base scenario: maximization of expected net revenue for a representative

whole-farm model under no environmental restriction in his or her production process.

Using the data listed above, the optimal solution for the proﬁt-maximizing

representative grower is summarized in Table 6.3.

117

Table 6.3: Summary of optimization results for a representative grower in the

base scenario model

 

 

 

—
Category Results

1. Net revenue (or Gross margin) $357,830/yr
2. Average seed corn yield (bu/ac) 77.7 (bu/ac)
3. Nitrate leaching from the whole-farm (lb/ac) 80.2 (lb/ac)
4. Nitrate leaching from seed corn ﬁeld (lb/ac) 63.9 (lb/ac)
5. Shadow prices: ($/acre)

Land $199.18/ac

Seed corn contracts $193.41/ac
6- Cr0p mixz (acre) IndindnaLasm
Lawson

SSEED (acre) 0

BSEED (acre) 0

PSEED(M) (acre) 500
mm

CCORN (acre) 0

BCORN (L) (acre) 104

PCORN(M) (acre) 246
cm

SBEAN (acre) 0

CBEAN (acre) 104
(Limits:

SPOTATO (acre) 500

CPOTATO (acre) 246

 

 

 

The expected net revenue for the grower is $357,830 per year under the base

scenario. This return represents the gross margin after paying variable costs, therefore,

it is the return to ﬁxed costs and family labor. The total amount of nitrate leaching

from the whole farm is 136,250 pounds (80.2 lb/ac on average).

Should a seed corn processing ﬁrm care about leaching when the analysis shows

that potatoes contribute the majority of leaching from the whole farm .7 Since potatoes

have been introduced into this area only for a few years and before that, nitrate leaching

118

was a major concern in this area, the seed corn processing ﬁrm then needs to consider
this environmental impact from seed corn production.

In the base scenario, the

 

total cropped acreage is 1,700

‘ CBEAN
PSEED(M) 6% 89201110

acres, including 500 acres of ' 30% '
rented land. Seed corn covers the 1 e 9"

P00 ) ‘ CPOTATO
. 14% BCORN(L
contract. These 500 acres are 1n I a.,, l 14%

 

full 500 acres available under l

 

 

 

rotation with potatoes with medium l l
Figure 6.1: Crop mix in the base scenario
nitrogen application rate. For
commercial com, 246 acres (14 percent of total are grown in rotation with potatoes,
and the remaining 104 acres in rotation with soybeans in the base scenario. Figure 6.1
shows the percentage of each crop under a proﬁt-maximizing whole-farm plan.
Potatoes, accounting for 44 percent of 1,700 acres, have the highest percentage of
acres among all crops. Seed corn production is 30 percent of the whole-farm acreage.
Soybeans are only 6 percent of the whole-farm operation.

Comparing these optimization results with crop acreage distribution in St.
Joseph County, the acreage of potatoes seems much higher than the actual potato
acreage. Recall that potato crops are used as a representative for all specialty crops,
which accounts for 11 percent of all cropped acreage in this area. The whole-farm

model examined here does not impose a restriction on the availability of potato

contracts. Another reason to explain this difference is the constraint from governmental

119

policies. Before 1996, farmers were required to keep a corn base in order to receive
deﬁcit payment from government. As a result, little acreage is used in two-year
rotations.

In terms of its contribution to nitrate leaching, seed corn production generates
relatively less nitrate leaching than the whole farm average. The mean nitrate leaching
level from seed corn production (63.9 lb/ac) is below the average nitrate leaching level
from the whole farm (80.2 lb/ ac). More nitrate leaching occurs from potato production
(120 lb/ac on average). Within seed corn production, the seed corn/potato rotation
generates more nitrate leaching (64 lb/ ac on average) than the seed corn/ soybean

rotation (34 lb/ac on average).

6.5.1 Shadow Prices

A shadow price indicates the increased net return obtained by relaxing the
constraint by one unit of the relevant resource. The two most restricted resources in
the base scenario are land and contract availability. The shadow price of land is
$199.18/ac. The shadow price implies that if the grower could have one more acre of
land, his or her expected return would increase by $199.18. Given that the rental rate
for one acre of land is $165/ac, if the grower could rent more land, the proﬁt could be
increased by $34.18 per acre (i.e., $199.18-$165), which is also the shadow price on
the land rental constraint. The 500-acre limit on land contract for seed corn production
generates the shadow price $193.41, so if the grower could increase seed corn

contracted acreage by one acre, the expected returns would increase by $193.41.

120

6.5.2 Sensitivity Tests

Sensitivity tests examine how optimal behavior responds to changes in key
parameters (including prices, costs, technical coefﬁcients, available resources, etc).
For the purpose of this study, sensitivity tests will focus on how changes in nitrogen
prices and contractual arrangements affect optimal nitrogen application and resulting

nitrate leaching.

A. Nitrogen cost

The optimal solution is sensitive to nitrogen costs. Nitrogen prices in 1996
were 25 cents per pound, which was about 30 percent above prices in 1995. When the
nitrogen price is 19 cents per pound, the representative proﬁt-maximizing grower will
not change the nitrogen application rate in seed corn production, but will switch 103
acres of commercial corn from rotation with soybeans using 98 Mac nitrogen to
rotation with potatoes with 152 lb/ ac nitrogen application rate. The mean nitrate
leaching from the whole farm will increase from 80.2 lb/ac (base scenario) to 87.8
lb/ac. This result is because the grower uses higher nitrogen fertilizer and more nitrate
carryover in a potato/com rotation than in a soybean/potato rotation. The mean nitrate
leaching from seed corn average does not change. In terms of the proﬁt from whole-
farrn operation, the gross margin increases to $364,370, an increase of $6,540 per year.

On the other hand, if the price of nitrogen increases from 25¢llb to 35 ¢/lb, the
amount of nitrate leaching will reduce dramatically from 80.2 1b/ac to 54 lb/ac in the

whole farm, and from 63.9 lb/ac to 56.7 Mac in seed corn production by increasing the

121

acreage in rotation with soybeans. This result is because planting corn after soybeans
requires less nitrogen fertilizers, and then has less leaching. The gross margin also
declines from the whole farm operation, from $357,830 to $348,880 per year.

Interestingly, the result shows that both nitrogen application and nitrate leaching
are very sensitive to an increase in nitrogen cost. This result contradicts the literature
which indicates that nitrogen use on commercial corn is insensitive to an increase in
nitrogen cost (House et al. , 1996; Carriker, 1993). The difference lies on the
substitutability of other crops. In this case, the beneﬁt from soybean rotations is
similar to that from potato rotation, while the former requires much less nitrogen
application. Thus, a slight increase in nitrogen cost will result in a switch from potato
rotations to soybean rotations, resulting in a reduction in nitrate leaching.

This result implies both nitrogen application and the grower’s gross margin can
be sensitive to nitrogen cost. When nitrogen fertilizer is cheap, the proﬁt-maximizing
grower will increase the rate of nitrogen fertilizer in order to increase gross margins,
which results in higher nitrate leaching levels. Therefore, an increase in nitrogen cost

could potentially be used as a means to reduce nitrate leaching.

B. Contract availability

Seed corn contract availability indicates the seed corn acreage available to the
representative grower. In the case where no constraint is imposed on contract
availability, the optimal seed corn acreage for the proﬁt-maximizing grower will be 727

acres. All of this seed corn acreage would be in rotation with potatoes. Although the

122

mean nitrate leaching from seed corn production remains the same as the base scenario,
nitrate leaching from the whole farm operation slightly decreases, from 80.2 lb/ac to 80
lb/ac. The decrease of the amount of nitrate leaching results from the additional
commercial corn acreage being planted in rotation with soybeans (from 104 acres to
123 acres), which generates lower nitrate leaching than the base scenario. This switch
is due to the equipment constraint during planting seasons. The increase in seed corn
availability would increase the contracted-grower’s gross margin from $357,830 to

$400,080 per year.

C. Relative performance

The incentive scheme within the current contract includes 4 parameters: average
regional yield (yo), base crop yield (Q), a coefﬁcient that transforms seed corn yield to
commercial corn equivalent (a), and a price premium adjustment coefﬁcient (,6) (Shaw

et al., 1989). In the LP model of this research, the per acre incentive payment is:

SCv)=(a(v-y")+Q)ﬂP (6.5)

The change either in average regional yield, or in base crop yield only alters the ﬁxed
payment of the incentive structure. Therefore, any reduction in either parameter does
not affect the grower’s decision on nitrogen application rate, but only reduces net
revenue and the shadow price of the seed corn contract.

On the other hand, any change in the coefﬁcient a or 13 might affect the amount

of variable payment. For instance, if the coefﬁcient that transforms seed corn yield to

123

commercial corn equivalent (on) changes from 2 (used in the current contract) to l, the
variable payment becomes $2.64 lbu. This change results in a reduction of nitrogen
use, from a medium level (116 lb/ac), to a low level (107 Mac) in potato/seed corn.
As a result, nitrate leaching subsequently declines by 1 Wm from seed corn
production, for a 0.3 lb/ac reduction from the whole-farm operation. The gross margin
of the grower declines to $343,520.

Reducing the price premium adjustment coefﬁcient (,6) from 1.1 to 1, however,
does not change the optimal solution. It is difﬁcult to use the price premium ﬂ
individually to change the contracted-grower’s behavior because a change in ,6 will
greatly affect the revenue received by both processor and contracted-grower. Thus, it
is more likely t1.) be unacceptable to either party.

The minimum total payment for a proﬁt-maximizing grower to grow seed corn
is $365/ac. Below this payment, the optimal seed corn acreage in the solution is less
than 500 acres. This level can be interpreted as the participation constraint for seed

corn contracts .

6.5.3 Other Commodity Price Scenarios

Different commodity prices were used in the model in order to compare how
changes in relative prices affect crop mix as well as the amount of nitrate leaching. For
instance, assume the price of conventional corn is $2.40/bu, soybeans are $5.70/bu and
a potato contract is $235 per acre (1995 commodity prices). If the cost of nitrogen

fertilizer is 25 cents per pound, then the grower will grow commercial corn and seed

124

corn in rotation with potatoes with a medium nitrogen application rate. The average
amount of nitrate leaching is 88.67 lb/acre from the whole farm, and 63.56 lb/acre
from seed corn average. Compared to the base scenario, the mean nitrate leaching
from the whole farm increases because of the switch from a corn/soybean rotation to
corn/potato rotation. In this case, the contracted-grower’s gross margin is reduced,
from $357,830/year to $357,700/year.

If the price of corn is $2.70/bu, soybeans are $6.75/bu, potato contracts are
$235 per acre, and nitrogen is priced at 25 cents per pound (1996 commodity prices),
the grower would cultivate commercial corn in rotation with soybeans (579 acres),
continuous seed com (457 acres), and 43 acres of seed corn in rotation with soybeans.
All corn and seed corn production use medium nitrogen application rates in this case.
Because potatoes are not in the solution, the amount of nitrate leaching is 24.9 lb/ acre
from the whole farm, and 31.6 lb/acre from seed corn average. This result implies that
the relatively high prices of less-nitrate-leaching crops create incentives for the proﬁt-
maxirnizing contracted—grower to reduce nitrate leaching through selection of these
crops. In this case, the grower’s gross margin increases to $438,780 ($357,830 in the
base scenario).

From the sensitivity tests, as well as different price scenarios, the amount of
nitrate leaching is sensitive to price changes and other resource constraints. Therefore,

in order to reduce nitrate leaching, these elements should be considered.

6.6

125

Analysis of Alternative Contract Designs

As shown in Chapter 2 and 4, several strategies can be employed to reduce

nitrate leaching. Three categories of alternative contract designs are evaluated in the

PC-LP model”. They are: A) imposing restrictions on the amount of permissible nitrate

leaching, nitrogen use, or other agronomic practices, B) charging a fee on the amount

of nitrate leaching or nitrogen use that is above a speciﬁed level, and C) reducing

incentive payments. The details are outlined in Table 6.4.

Table 6.4: Alternative seed corn contract designs

 

A.

a.1

a.2

a.3

b.1

b.2

c.1

c.2

Imposing restrictions on agronomic practices

Restrictions on ambient level of nitrate leaching (NL) to 45 lb/acrel
a.1.l Restrict NL to 35 lb/ac on the whole farm

a. 1.2 Restrict N L to 35 lbs/ac on each seed corn ﬁeld

Restrict maximum nitrogen fertilizer to 107 lb/ac

No rotation with potatoes

Charging “fees” on agronomic practices

Charge a 30 C/lb efﬂuent fee on nitrate leaching above 30 lb/ac
Charge an input fee of 15 C/lb on nitrogen fertilizer above 90 lb/ac
Adjusting incentive payment structure

$253/ac ﬁxed payment with $ 3.96/bu variable payment

$230/ac ﬁxed payment with $ 3.96/bu variable payment

 

 

9 The model assumes that the representative grower has full information, so that a
fourth alternative contract design speciﬁed in Chapter 4, providing information within
contracts, will not be discussed here.

126

6.6.1 Justifications of Alternative Contract Designs

The ﬁrst category (A) imposes restrictions on permissible nitrate leaching,
nitrogen use, or agronomic practices. Under strategy al. the maximum permissible
nitrate leaching level in a seed corn ﬁeld is set at 35 lb/ac per growing season. This
rate is the medium nitrate leaching level of those modeled for seed corn production.
The restriction on permissible nitrogen use on seed corn ﬁeld (a.2) is set at a mean of
107 lb/ac, the lowest nitrogen treatment for continuous seed corn in the model. Below
this level, seed corn yield begins to decline on a larger scale, which is unlikely to be
acceptable to both processor and grower. Because potatoes result in leaching in swd
corn production via nitrate carryover, forbidding seed corn/potato rotations (a. 3)
becomes an instrument to reduce nitrate leaching.

Charging a fee on the amount of nitrate leaching above 30 lb/ac, or for nitrogen
fertilizer above 90 lb/ac (category B), raises the marginal cost of nitrogen use for most
crop enterprises. Charging 10 cents per pound on nitrate leaching above the 30 lb/ac
level will cause the grower to begin to lower nitrogen rates, resulting in reduced nitrate
leaching compared to the base scenario. The 15 cents per pound fee on nitrogen
applications over 90 lb/ acre is the minimum fee required to induce substitution of the
base model seed corn enterprise with one that uses less nitrogen.

The third category (category C) of incentive schemes decreases the variable
payment paid to the grower by the processor. The base scenario incentive payment
includes a ﬁxed payment of $150 /ac plus a variable payment of $5.28 fbu for seed corn

yield. One alternative (c.1) increases the ﬁxed payment to $397/ac and lowers the

127

variable payment to $3.96/bu, 75 percent of the original variable payment. This
redesigned contract is intended to induce a risk-neutral grower to lower the nitrogen
rate, while retaining the same income level he/she earns in the base scenario. This
variable payment is the level that a grower will switch nitrogen application rates from a
medium level to a low level. When the variable payment is between $0 and $3.96/bu,
the decision of the contracted-grower is the same as the decision when the variable
payment is $3 .96/bu in this model. Therefore, the model will use the variable payment
$3 .96/bu in the model to represent the change in the payment scheme.

The second alternative (c. 2) retains the variable payment at $3 .96/bu, while
reducing the ﬁxed payment to $230/ac, the ﬁxed payment that will keep the gross
margin of the processing ﬁrm the same as the base scenario. The design of alternative
contracts c.1 and c.2 shows that the incidence of who bears the costs of leaching
reduction has a linear relationship. The amount of cost borne by each party can be
adjusted simply by changing the ﬁxed payment.

The strategy of imposing a leaching restriction on the whole farm (a.1.1) is used
as a method to identify growers with low whole farm nitrate leaching. This strategy
requires measures of nitrate leaching from the whole farm. Those growers who fail to
reduce whole-farm leaching to this 35 lb/ac threshold level will lose seed corn
contracts. Imposing a leaching restriction on the average seed corn ﬁeld (strategy
a.1.2) allows some ﬂexibility in adjusting different nitrate leaching on seed corn ﬁelds.
That is, ifa grower uses higher nitrate leaching practices on some acres, and low

nitrate leaching practices on other acres, the average nitrate leaching for all seed corn

128

production can be maintained at the restricted level. Imposing a restriction on nitrogen
fertilizer rates (a.2) is based on evidence that nitrogen fertilizer use is the most
important and direct element affecting the amount of nitrate leaching (Ritchie, 1996).
Imposing a restriction on rotation with potatoes (a.3) is also a method to reduce nitrate
leaching, since this rotation incurs more nitrate leaching than does other rotation
practice.

Imposing a restriction and charging a fee on the amount of nitrogen or nitrate
leaching will potentially increase the marginal cost of nitrogen use, making the grower
bear an additional cost from using nitrogen fertilizer. Reducing variable payments, on
the other hand, will reduce the value of the marginal product for nitrogen use and

subsequently reduce nitrate leaching as well.

6.6.2 Impacts on Nitrate Leaching Reduction from Alternative Contract Designs
The changes in seed corn yield, average whole-farm nitrate leaching, and
average seed corn ﬁeld nitrate leaching from various contract designs are listed in Table

6.5. The corresponding crop mixes are listed in Appendix D.

Table 6.5: Mean yield and nitrate leaching for a proﬁt-maximizing grower under

129

 

 

different contract designs
Mean seed corn Mean leaching Mean whole-
yield (bu/acre) from seed corn farm leaching
Alternative Contract Designs (lb/ac) (lb/ac)
Unrestricted base scenario 77.71 63.92 80.15
a.1.1 Restrict ANL to 35 lb/ac (whole-farm) 77.66 41.51 35.00
a.1.2 Restrict ASNL to 35 Mac (seed ﬁeld) 77.64 35.00 52.99
a.2 Restrict N fert. to 107 lb/ac 77.15 62.95 79.86
a.3 No rotation with potatoes 77.64 33.97 51.76
b.1 Charge 10 Cllb on ASNL> 30 lb/ac 77.65 36.56 54.87
. b.2 Charge 15 Cllb on N fert. >80 lb/ac 77.60 ' 36.47 54.84
c.1 varpay:$3.96/bu; ﬁxpay:$253/ac 77.15 62.95 79.86
c.2 varpay:$3.96/bu; ﬁxpay:$230/ac 77.15 62.95 79.86

 

Note: AN L: average nitrate leaching from the whole farm;
ASNL: average nitrate leaching from seed com production
Fixpay: ﬁxed components of seed corn contract payment (Slacre);
Varpay: variable components of seed corn contract payment ($lbushel).

From Table 6.5, the alternative contract designs reduce seed corn yield. Under
these contract designs, the contracted grower will switch either from medium to low
nitrogen applications, or from seed corn/potato rotation over to a seed corn/ soybean
rotation, which results in lower seed corn yield and lower nitrate leaching than in the
base scenario. This result implies a trade-off relationship between yield and nitrate
leaching abatement. There are two ways to capture the cost of leaching reduction on
the processor. One is to calculate the opportunity cost forgone under alternative
contract designs. This opportunity cost reﬂects on the gross margin reduction from the
same seed corn acreage.

Another way to calculate the cost is to calculate the cost to achieve the same
yield goal. As mentioned in Chapter 3, one of the main purposes of contracting

production is to maintain a stable supply. The principal’s objective could be to

130
maintain the same yield level as in the base scenario. Therefore, the principal might
need to increase the seed corn acreage. An increase in the seed corn acreage will
increase the processor’s cost, including higher cost for more seed for additional acres,
monitoring cost, detasseling cost, and pesticide cost.

This analysis uses the ﬁrst approach, that is, seed corn acreage changes are not
considered due to several reasons. First, the yield difference between alternative
contract designs and the base scenario is not signiﬁcant, ranging 0.07 bu/ac to 0.56
bu/ac. Second, all alternative contract designs have lower nitrate leaching per unit of
seed corn yield. Therefore, an increase in the seed corn acreage in order to maintain
yield the same as the base scenario still has less nitrate leaching than the base scenario.
The third reason is that it is difﬁcult to formulate a stable yield supply as the objective
function because yield is not a choice variable, but instead it is a random variable. The
fourth reason is due to the difﬁculty in obtaining the additional costs that a processor
incur from alternative contract designs.

The average amount of nitrate leaching from seed corn acreage (ASNL) as well

as from the whole farm (ANL) is described in ﬁgure 6.2.

 

100 ‘H-VANLﬂ

    

 

 

 

Mean Nitrate Leaching
(lb/ac)

Base a.1.1 a.1.2 a.2 a.3 b.1 b.2 c.1

model Alternative Contract Deelgne 6'2

 

 

 

Figure 6.2: Mean nitrate leaching from seed corn production (ASNL) and from the
whole farm (ANL) under alternative contract designs

131

The contract design that forbids seed corn/potato rotation (a. 3) will result in the
lowest nitrate leaching level from seed corn production among all alternative contract
designs. This contract design reduces nitrate leaching by 301b/ac per growing season
by substituting a seed corn/ soybean rotation with medium nitrogen application. The
next most effective nitrate leaching reduction contract designs are restricting nitrate
leaching from seed corn production to 35 lb/ac (a.1.2), charging a fee of 15 C/lb on
nitrogen fertilizer above 901b/ac (b.2), and charging a fee of 10 C/lb on nitrate leaching
above 30 lb/ ac (b.1). These three strategies induce the contracted-grower to switch
most of the 500 acres from seed corn/ potato rotation to seed corn/ soybean rotation,
which reduces nitrate leaching by 29-27 .5 lb/ac per season. A contract design that
restricts the nitrate leaching level from the whole farm (a.1.1) is able to reduce nitrate
leaching by 23 lb/ac per season by switching 374 of the seed corn acres from a rotation
with potatoes to a rotation with soybeans. Restricting nitrogen fertilizer (a.2), and
adjusting contract payment schemes by reducing the variable payment to $3.96 /bu (c.1
and c. 2), reduce nitrate leaching by only 1 lb/ac via reducing nitrogen application to
low levels in a seed corn/potato rotation. Both strategies have only small impacts in
terms of reducing nitrate leaching from seed corn production.

Figure 6.2 also shows the changes of the whole-farm nitrate leaching level under
the alternative contract designs. Interestingly, the average amount of nitrate leaching
from the whole farm is greater than the average nitrate leaching from seed corn ﬁelds,
except in the case that restricts the average whole farm nitrate leaching (a.1.1). The

major source of the whole-farm nitrate leaching is potato production. Seed corn

132

production is not the major nitrate leaching source if the farm is operated on a proﬁt-
maximizing basis.

All of the alternative contract designs are able to reduce whole-farm nitrate
leaching from the base scenario level. If the company can identify growers who
generate low nitrate leaching from the whole farm (a.1.1), then the grower needs to
reduce nitrate leaching to show his or her environmental stewardship in order to obtain
seed corn contracts. As a result, the average amount of nitrate leaching from the whole
farm will be substantially reduced (35 lb/ac per growing season). Other contract
designs that restrict nitrate leaching from growing seed corn (a.1.2), forbid seed
corn/potato rotation (a. 3), or charge a fee on either nitrate leaching (b.1) or nitrogen
use (b.2), can reduce nitrate leaching levels by 25 to 30 lb/ac per growing season.
Such nitrate leaching reduction comes from the switch from seed corn/potato rotations
to seed corn/soybean rotations. Contract designs that restrict nitrogen application to
107 lb/ac (a.2), or reduce the variable payment (c.1 & c.2) only reduce the whole farm

nitrate leaching by 0.3 lb/ac.

6.6.3 Impacts on Gross Margin from Alternative Contract Designs

Increased ﬁnancial returns represent the other objective of the contracting
parties, apart from reduced nitrate leaching. These returns are represented in Table 6.6
as the whole-farm gross margin (GM) over variable costs. For the contracted grower,
this gross margin represents the optimal solution to the LP problem. For the seed corn

processor, GM is calculated as the value of seed corn yield minus payments made to

133

growers plus revenues from fees charged to growers (e.g. , for excessive nitrate

leaching or nitrogen fertilizer application).

Table 6.6: Nitrate leaching, principal’s and agent’s gross margins under various

 

 

contracts
TSNU‘ ASNL‘ Grower’s GM Firm’s GM

Alternative Contract Desigg (lbs) (lb/ac) ($lyeg) ($lyear)
Unrestricted base model 31960 63.92 357830 1386600
a.1.1 Restrict whole-farm NL to 35 lb/ac 20754 41.51 355790 1385700
a.1.2 Restrict seed corn NL to 35 lb/ac 17500 35.00 357140 1385400
a.2 Restrict N fert. tolO7 lb/ac 31474 62.95 357500 1376100
a.3 No rotation with potato 16985 33.97 357030 1385400
b.1 Charge 106/1b on NL > 30 lb/ac 18278 36.56 356960 1385800
b.2 Charge 15¢llb on N fert. >90 lb/ac 18236 36.47 357150 1384700
c.l Fixpay':$253/ac; varpay':$3.96/bu 31474 62.95 357830 1375790
c.2 Fixpay':$230/ac; varpay':$3.96/bu 31474 62.95 347020 1386600

 

Note: TSNL: the total nitrate leaching from seed corn production;
ASNL: the average nitrate leaching from seed corn production;
GM: gross margin; .
Fixpay: ﬁxed components of seed corn contract payment ($/acre);
Varpay: variable components of seed corn contract payment ($/bushel).

From the grower’s viewpoint, decreasing the variable payment to 75 percent of
the original payment ($3.96/bu) and increasing the ﬁxed payment ($253/ac) to maintain
the same revenue as the base scenario (c.1), gives the grower the same gross margin as
the base scenario, which is the highest grower’s margin among all alternative contracts.
Other contract designs decrease the grower’s gross margin from as little as $330
(restricting nitrogen application to 107 lb/ac, a.2) to as much as $10,810 per growing
season (decreasing the variable payment to $3.96/bu with the ﬁx payment $230/ac,
c.2).

From the processing ﬁrm’s viewpoint, all alternative contract designs, except

decreasing the variable payment to $3.96/bu with the ﬁxed payment $230/ac (c.2),

134

decrease the processing ﬁrm’s gross margin. Contract design c.2 maintains the
processor’s grOss margin at the level of the base scenario. Charging a fee on nitrate
leaching above 30 lb/ac (b.1) costs the least to the processing ﬁrm ($800 per growing
season in total) among the contract designs. Restricting the permissible whole farm
nitrate leaching level to 35 lb/ac (a.1.1) reduces the processing ﬁrm’s gross margin by
$900; and restricting the permissible nitrate leaching level from seed corn production to
35 lb/ac (a.1.2), or forbidding the seed corn/potato rotation (a. 3) reduces the
processing ﬁrm’s gross margin by $1,200. Charging a fee on nitrogen fertilizer use
above 90 lb/ac costs the processing ﬁrm $1,900; and restricting nitrogen use to 107
lb/ac costs the processing ﬁrm $10,500. The contract design that involves decreasing
the variable payment to $3.96/bu plus the ﬁxed payment of $253/ac (c.1) maintains the
same gross margin of the grower, but it is the most costly contract design to the
processing ﬁrm. It reduces the processing ﬁrm’s gross margin by $10,810 per year.

A contract design that charges a fee of 15 C/lb on nitrogen application above 90
lb/ac can achieve similar leaching reduction as a contract that charges a fee of 10 ¢/lb
on nitrate leaching above 30 lb/ac, given that the costs to the grower are similar
($356,960 versus $357,150). However, the former costs the processor $1,100 more
than the latter. Under both contract designs, the grower will grow 457 acres of seed
corn in rotation with soybeans with medium levels of nitrogen application. The other
43 acres is in rotation with potatoes. Charging a fee on nitrate leaching will induce the
grower to use medium levels of nitrogen application, while charging a fee on nitrogen

application will result in low levels of nitrogen application. This result is because

135

charging a fee on nitrogen will induce the grower to reduce nitrogen application rates,
based on the tradeoff between nitrogen cost and reduced proﬁt from yield reduction,
although it might not signiﬁcantly reduce nitrate leaching. Charging a fee on leaching
will induce the grower to undertake the practice that incurs less nitrate leaching, based
on the tradeoff between leaching cost and reduced proﬁt from yield reduction. In this
case, the nitrogen cost is greater than the beneﬁt from medium nitrogen fertilization
levels. Therefore, the grower will use low nitrogen application rates to grow seed corn
in rotation with potatoes. On the other hand, the leaching cost is less than the beneﬁt
from medium nitrogen fertilization levels. The grower will use medium nitrogen
application rates to grow seed corn in rotation with potatoes. As a result, the yield and
the processor’s gross margin are reduced under a contract charging a fee on nitrogen
more than they are under a contract charging a fee on leaching.

In order to identify contract designs which are preferable to both the processor
and contracted grower, two criteria can be used. The ﬁrst criterion requires that the
contract design should be acceptable to both parties. The second criterion is that the
contract design should be cost-effective. Based on these two criteria, two deﬁnitions of
dominance analysis will be introduced to evaluate contract designs from both grower’s
and processor’s perspectives. They are acceptability to each contracting party and

eﬁiciency at achieving reduction in nitrate leaching.

6.6.4 Contract Acceptability Dominance

Proﬁtability and environmental quality are the most important elements in

136

designing a “green” contract from the processor’s perspective. A contract with higher
proﬁtability and lower environmental damage is assumed to be preferred from the
processor’s viewpoint. The contract design also needs to be acceptable to the grower,
that is, it must satisfy the grower’s participation constraint. In this case, an acceptable
contract design for the grower is deﬁned as the contract that will reduce the grower’s
gross margin by less than a certain level. A dominant contract is one that is acceptable
to both processor and grower‘o.

Based on these assumed preferences, we deﬁne contract acceptability dominance
in terms of mean nitrate leaching (lower levels preferred) versus mean gross margins
(higher levels preferred) from the processing ﬁrm’s viewpoint. It is deﬁned such that
strategy A dominates strategy B, if and only if, either (ASNL, < ASNL, and GM, 2
GM B) or (ASNL, SASNL, and GM A > GM 5), where ASNL is the average amount of
nitrate leaching from seed corn production and GM is the gross margin. The above
deﬁnition is based on the assumption that the processing ﬁrm desires both proﬁtability
and environmental quality (the latter based on the ﬁrm’s “green” image or avoiding
future regulation). The contract is assumed to be acceptable to the grower if it reduces
expected net return by less than 1 percent.

All contract designs satisfy acceptability dominance from the grower’s

 

‘0 Other circumstances might extend to examine the case where the grower also
desires environmental quality from the whole-farm operation. For instance, if the
grower relies on groundwater from his or her farm for drinking water, the grower will
have the incentive to produce less nitrate leaching. In this situation, game theory can
be used to include the cooperative or non-cooperative behavior in the negotiation
process between processor and contracted growers. For simplicity, this research only
examines the case where only the processor desires nitrate leaching reduction.

137

perspective, except reducing the variable payment to $3.96/bu and increasing the ﬁxed
payment to $230/ac (c.2). From the processor’s viewpoint, some contract designs are
dominated by others. For instance, charging 10 ¢/lb on nitrate leaching above 301b/ac
(b.1) generates a higher gross margin and lower nitrate leaching than strategy al.],
which restricts the permissible nitrate leaching from the whole farm, a.2, which
restricts nitrogen use below 107 lb/ac, or c.2, which reduces the variable payment to
$3.96 with a ﬁxed payment of $230/ac. Therefore, strategy b.1 is the dominant
contract design. In another example, strategies a.2, c.1, and c.2 all result in the same
amount of nitrate leaching from seed corn production, however, reducing the variable
payment to $3 .96/bu, and increasing the ﬁxed payment (c. 2), has the highest gross
margin to the processing ﬁrm. Based on this information, a.3, b.1, and c.2 are
efﬁcient in terms of contract acceptability dominance from the processor’s perspective.

By the deﬁnition of contract acceptability dominance, the efﬁcient strategies that
are undominated from the processor’s (principal’s) and the grower’s (agent’s)
perspective are contracts which forbid seed corn/potato rotation practices (a. 3), or
charge 10 cents per pound on nitrate leaching above 30 lb/ac (b.1).

In additional to aggregate efﬁciency, the cost of reaching the environmental
quality objective of reduced leaching should be considered. In order to account for the
cost for nitrate leaching reduction, another criterion should be used to evaluate contract

alternatives.

138

6.6.4 Cost Efficiency Dominance

One way to measure the cost per pound of reducing nitrate leaching from seed
corn production is to measure the reduction in gross margins, as shown in the last two
columns of Table 6.7.

Table 6.7: Nitrate leaching, principal’s and agent’s gross margins, and unit cost of
leaching reduction from seed corn production under various contracts

 

TSNL ASNL Grower’s Principal’s AGM(G) AGM(P)

 

 

Alternative Contract Designs (lbs) (lb/ac) GM GM $Ilb $l1b

Unrestricted base model 31960 63.92 357830 1386600 NA NA

a. 1.1 Restrict whole-farm NL to 20754 41.51 355790 1385700 0.18 0.08
35 lb/ac

a. 1.2 Restrict seed corn NL to 35 17500 35.00 357140 1385400 0.05 0.08
lb/ac

a.2 Restrict N fert. to 107 lb/ac 31474 62.95 357500 1376100 0.68 21.60

a.3 N o rotation with potatoes 16985 33.97 357030 1385400 0.05 0.08

b.1 Charge 10¢llb on NL> 30 18278 36.56 356960 1385800 0.06 0.06
lb/ac

b.2 Charge 15¢/lb on N fert. > 18236 36.47 357150 1384700 0.05 0.14
90 Wu

C. 1 Fixpay':$253/ac; 31474 62.95 357830 1375790 0.00 22.24
varpay':$3.96/bu

c.2 Fixpay':$230/ac; 31474 62.95 347020 1386600 22.24 000
varpay':$3.96/bu

Note: TSNLand ASNL: the total and the mean nitrate leaching from seed corn production;

AGM(G)I reduction in the grower’s gross margin (GM) for per unit leaching reduction;
AGM(P): reduction in the processor’s gross margin (GM) for per unit leaching reduction;
Fixpay: ﬁxed components of seed corn contract payment ($lacre);

Varpay: variable components of seed corn contract payment ($lbushel).

The 46M and aTSNL ﬁgures are calculated as the differences in gross margins
and total nitrate leaching from seed corn production between the base model levels and
those in each alternative scenario. The aGM/a TSNL ratios can also be evaluated by

dominance analysis. In this instance, strategy A dominates strategy B if it reduces

139

leaching at lower unit cost for the grower without increasing unit costs for the
processor or vice-versa. Algebraically, strategy A dominates strategy B if and only if
[(AGM/AASNL): 2 (aGM/aASNLX,’ and (aGM/AASNLﬁ > (aGM/aASNLﬁ] or
[(aGM/aASNLX,’ > (aGM/aASNLX,’ and (aGM/AASNLX,’ 2 (aGM/AASNLﬁ], where

superscripts G and P indicate the grower and the processor, respectively. This concept

is illustrated in ﬁgure 6.3.

 

In ﬁgure 6.3, A, B, C, D,
D’ and D”are different strategies. Fl
A, B and C are cost-efﬁciency
dominant strategies over all
strategies labeled by D, D’, and

D”. For instance, strategy A has a

Processor’s a GM/aASNL

lower cost than strategies 0’ per

 

 

 

 

one unit of nitrate leaching, Contracted Grower ’s aGM/aASNL
Figure 6.3: Cost efficiency dominance analysis

 

therefore, strategy A is cost
efﬁcient compared to D’. Compared with strategies A and B, however, one cannot
decide which one is more cost efﬁcient because strategy A has a lower per unit cost for
the processor while it has a higher per unit cost for the grower under strategy B.
Therefore, strategies A and B are not dominated by each other. Although this analysis
cannot rank all of the alternative contracts, it does rule out the contract designs with
higher costs to both parties.

By this deﬁnition, the cost—efﬁciency dominance criterion eliminates four

140
inefﬁcient contract designs, a.1.1, a.2, and b.2. The contract designs that fall into
efﬁcient set are the contracts restricting nitrate leaching from seed corn production
(a.1.2), restricting rotation (a.3), and charging for nitrate leaching above 40 lb/ac

(b.1). This result is also shown in Figure 6.4.

 

Processing Flrm's GMIASNL ($Ilb)

 

 

0.00 0.05 0.10 0.15 0.20

, Contracted Grower'sGMIASNL($/Ib)
l

 

 

1
Figure 6.4: Cost efﬁciency dominance analysis of the processing firm’s and
contracted grower’s cost for per pound of leaching reduction

In Figure 6.4, the line indicates a cost efﬁciency frontier. Every strategy on this line
cannot be dominated by another strategy. In terms of the overall cost (combining the
grower’s and the processing ﬁrm’s cost) for per unit nitrate leaching reduction, the
strategy that charges 10 cents per pound for nitrate leaching above 30 lb/ac has the
lowest unit cost, 12 C/lb in total. Strategies a.1.2 and a.3 cost 13 cents per pound of

nitrate leaching reduction.

141

There are two contracts-- restricting seed corn/potato rotation (a. 3), and
charging 10 cents per pound on nitrate leaching above 30 lb/ac (b.1)--that satisfy both
contract acceptability dominance and cost efﬁciency dominance. These contract designs
can be interpreted as the “ﬁrst-best” policy when the grower is risk-neutral. Under the
situation where they are observable or measurable, these two contract designs can
achieve both efﬁciency criteria.

The above analysis has outlined a means to structure empirically a processor-
grower relationship within a principal-agent framework. Several important elements
are not discussed in this deterministic framework. They are: 1) the stochastic
characteristics of nitrate leaching, 2) grower risk of contract loss, 3) the grower’s risk
attitude, and 4) enforceability. The stochastic characteristics of nitrate leaching and
grower risk of contract loss is discussed in Chapter 7, and the grower’s risk-attitude is
examined in Chapter 8. Enforceability is another important issue in contract designs, in
addition to contract acceptability dominance and cost ejﬁciency dominance criteria.

The enforcement issues will be discussed in the following chapters.

6.7 Summary

This chapter has outlined an empirical framework to solve the principal-agent
model. Although two-level mathematical programming methods have been proposed in
the literature, none have proved implementable because of practical complexities. As
an alternative, this research decomposed the principal-agent problem into two stages.

In the ﬁrst stage, whole-farm mathematical programming is applied to model

142
optimizing behavior of the representative grower-agent. The impacts on the processing
ﬁrm (principal) are calculated in the second stage.

The results from the base scenario show that the shadow price of the seed corn
contract ($193/ac) is relatively high. From sensitivity tests, higher nitrogen costs, a
lower variable contract payment, and relatively higher soybean prices can all potentially
reduce nitrate leaching.

The results also show that the mean nitrate leaching from the whole farm is
greater than that from growing seed com. This result indicates that seed corn is not
necessarily the major crop responsible for nitrate leaching, particularly if potato
rotations are included. However, even though seed corn production generates
relatively low nitrate leaching, this analysis shows that the nitrate leaching both from
the whole farm and from seed corn production can be reduced through various
alternative seed corn contract designs.

Three categories of contract speciﬁcations have been examined: imposing a
restriction (on the permissible nitrate leaching, nitrogen application, or agronomic
practice), charging a fee (on the permissible nitrate leaching, nitrogen application), and
adjusting the contract payment formula (by reducing the variable payment). The model
results show that nitrate leaching from growing seed corn can be effectively reduced by
contract designs that impose a restriction on nitrate leaching, forbid rotation with
potatoes, or charge a fee on nitrate leaching or nitrogen use. These contract designs
can reduce nitrate leaching from the whole farm as well.

Two dominance criteria are introduced and used to rank these alternative

143

contract designs: contract acceptability dominance and cost efﬁciency dominance.
Based on this analysis, contracts forbidding rotations with potatoes (a.3) and contracts
charging 10 C/lb for nitrate leaching above 30 lbs (b.1) are the only two contract

designs undominated under either criterion.

CHAPTER 7

CHANCE CONSTRAINTS IN DESIGNING SEED CORN CONTRACTS TO
REDUCE NITRATE LEACHING

Chapter 6 outlined a basic framework that can empirically model the contractual
relationship, and that can evaluate the impacts on the processor as well as the grower
under various alternative contract designs. Two additional concerns need to be
considered in designing a seed contract to reduce nitrate leaching. One is the grower’s
concern over risk of seed corn contract loss, as mentioned in Chapter 4. This concern
has been cited as a major reason for over-fertilization. The other concern is the
stochastic nature of nitrate leaching and its abatement due to unpredictable weather and
water inﬂuences. This is problematic, since the damage caused by NPSP is often
related to exceeding a speciﬁed threshold level.

The objective of this chapter is to incorporate these two concerns into the model
of the grower’s decision-making process. The impacts on nitrate leaching as well as the
grower’s and the processor’s gross margins are estimated in an empirical principal-
agent model. This chapter ﬁrst clariﬁes the probabilistic nature of contract loss risk
and nitrate leaching abatement. The second section subsequently reviews the literature
on how to model these two issues. How these two concerns affect the representative

grower’s decisions as well as the processor’s welfare within a contract are examined.

144

145

Then implications for alternative contract designs are discussed.

7. 1 Issues in Designing Seed Corn Contracts to Reduce Nitrate Leaching
Seed corn contract loss risk and the probabilistic nature of a nitrate leaching
reduction strategy inﬂuence the grower’s response to various seed corn contract

designs. Additional analysis is required to evaluate their impacts.

7.1.1 Risk of Seed Corn Contract Loss

Although several risks are associated with growing seed com, the primary risk
involves losing the seed corn contract'l (Batie, 1994). In some instances, a company
may allocate grower allotments by calculating a grower evaluation index, based on
objective criteria known to the growers such as isolation block requirements and yield
history, and subjective criteria unknown to the grower such as grower cooperativeness
(Doering, 1996). Growers risk losing their contracts if their performance is poor over
time. Some growers believe that such an evaluation index puts heavy weight on yield
history (Dobbins and Swinton; Batie and Swinton, 1995).

Because the availability of seed corn contracts is limited and the proﬁtability of
growing seed corn is high, the seed corn grower has an incentive to maintain or to
increase his or her seed corn acreage (Dobbins and Swinton, 1995). Growers perceive

that they are likely to lose their seed corn contracts if their seed corn yields fall below

 

“This is a subset of the broader category of unpredictable policies by the
processing company, such as reducing grower acreage, changing to new varieties, or
requiring more costly management practices.

146

the average regional yield too frequently, such as, say, two out of ﬁve years (or 40
percent). The concern over risk of seed corn contract loss accentuates the importance
of achieving high yields that is already inherent in the tournament contract payment
scheme.

Preckel et al. (1997) used dynamic programming to model this contract loss
risk. By examining the impacts from the grower’s perspective in a continuous seed
corn cropping, their analysis demonstrated that the contracted-grower will use a
relatively high nitrogen application rate when he or she is concerned with the risk of
contract loss. High fertilization, however, results in excessive nitrate leaching. Their
model, however, considered neither the participation constraint (the opportunity of
growing other crops) nor the impacts on the processor.

Because experimentation with new practices to reduce nitrate leaching might
imperil high yields, the concern over contract loss could become an obstacle to grower
adoption of such practices. This research examines the impacts of contract loss risk
within a principal-agent framework, by incorporating other crop enterprises in the
whole-farm model to represent the opportunity cost from growing seed corn. The

impacts on the contracted-grower and the processor are examined as well.

7. 1.2 A Probabilistic Nitrate Leaching Reduction Strategy
The health risks associated with nitrates in drinking water are linked to nitrate
concentrations. As noted in Chapter 2, EPA has established 10 ppm of nitrate as the

maximum contaminant level (MCL) for nitrates in water judged safe for drinking.

147

Exceeding this threshold could pose health risks to a farm household, or pose
regulatory liability or reputation risks to a processing ﬁrm contracting for the
agricultural product responsible for the contamination.

Nitrate leaching control is subject to a considerable randomness, stemming from
natural variability of weather, soils and plants, imperfect monitoring and measurement;
and time-lags between nitrogen applications and actual leaching. Each abatement
strategy generates a probability distribution of outcomes instead of one single outcome.
‘ In order to manage the risk of exceeding a NPSP threshold, a leaching control strategy
should be designed to take probabilities into account, rather than realization of
abatement efforts. A method to implement probabilistic risk management is proposed
by Lichtenberg and Zilberman (1988), Braden et al. (1991), and Teague et al. (1995).
They suggested a NPSP abatement strategy to prevent bad outcomes by setting a
threshold standard as to ambient environmental quality that includes a safety margin.
Specifying an acceptable frequency (or probability) of achieving the environmental
standard is more practical than specifying a mean nitrate leaching level (Lichtenberg
and Zilberman, 1988; Braden et al., 1991). After all, it is difﬁcult to ensure that a
nitrate leaching standard is always met at different time periods and different locations.
The probabilistic approach is to require the grower to meet the safe drinking water
standard with a minimum probability, for example, in a two out of every ﬁve years.

Both the concerns of seed corn contract loss and exceeding a nitrate leaching
threshold are based on the probability of achieving a target level. This can be modeled

using safety-ﬁrst decision rules.

148

7 .2 Safety-First Rule: A Probabilistic Chance Constraint

Both contract loss risk and risk of exceeding an NPSP threshold are cases where
serious, nonmarginal losses ensue from a bad outcome. This characteristic makes them
amenable to modeling with “safety-ﬁrst” rules. The safety-ﬁrst rule is a model in which
the decision maker is concerned with the probability of failing to achieve his or her
goals. It is often used when the consequence of catastrophe is large (such as
bankruptcy), or when the decision-maker’s decision is subject to a threshold level.
Below this threshold level, there is a discontinuous drop in welfare. In a typical safety-
ﬁrst framework, over-achievement of the goal might not necessarily increase total
utility, but an inﬁnite disutility is associated with under-achievement (Roy, 1952; Pyle '
and Tumovsky, 1970; Telser, 1955; and Kataoka, 1963; and Robison and Barry,
1987). Safety-ﬁrst decision rules can be adopted in this research where the grower is
concerned about the risk of losing contracts, while the processor is concerned about the

risks of nitrate leaching exceeding a threshold level.

7 .2.1 Modeling Contract Loss Risk Avoidance

In order to avoid losing the contract, the grower is assumed to avoid the
probability that his or her own annual seed corn yields fall below the average regional
yield 0'"), exceeding some acceptable probability level, 1/g“. This concern can be

expressed mathematically as follows:

Prob(y s y”) 5 I/g' (7.1)

149

In order to model the contract loss assumption in a whole-farm model and for
simplicity, this research uses a one period analysis. Several techniques can be used to
formulate the equation 7.1 probabilistic constraint in a mathematical programming
framework. One technique is to use the Chebychev inequality that uses mean and
standard deviation to form a boundary for equation 7.1 (Telser, 1955; Anderson et a1. ,
1977). The second alternative is to use a lower partial moment method where negative
deviations from a speciﬁed goal are used to formulate a condition sufﬁcient to meet this
probabilistic constraint (Atwood, 1985; Atwood et al. , 1988). When income is
normally distributed, the deﬁnition in equation 7.1 can be modiﬁed and analyzed within
a mean-variance model (Pyle and Turnovsky, 1970; Hazel] and Norton, 1986). Among
these techniques, the lower partial moment approach has a relatively wide range of
applications because it does not require a parametric distribution (Atwood et al. , 1988).

The lower partial moment technique, suggested by Fishbum (1977) and Atwood
(1985), is employed to derive an equivalent condition for a chance constraint. It
measures the deviations below a speciﬁc target level, weighted by the corresponding

probability level and the inverse of a permissible safe margin (equation 7.2), that is,

t-g‘ Z) (W) (1.2% (7.2)

y,st

where t is an endogenously selected target level; I/g‘ is the permissible probability
level; y, is seed corn yield in state i; q, is the probability associated with state i; and y,

is the average regional seed corn yield. The yields below the target level (t - y) is the

150

main concern in equation 7.2. This equation is sufﬁcient to guarantee that the chance
constraint of avoiding contract loss (equation 7.1) is met. The proof is shown in

Appendix E.

7 .2.2 Modeling a Probabilistic Leaching Control

The same chance constraint approach can be applied to the risk that measurable
NPSP exceeds some benchmark. In this instance, the chance constraint would be
imposed to comply with the processor’s interest in avoiding signiﬁcant nitrate leaching.
If the grower is required to ensure that the probability of nitrate leaching (L) surpassing

a threshold level ( L) may not exceed some permissible probability level I/h', that is:
Prob(L 2 L ) s I/h' (7.3)

The sufﬁcient condition to ensure equation 7.3 becomes (Atwood et al., 1988; proof
shown in Appendix E) :
L‘ - h' )3 (LI. -L')p,. 2 o (7.4)
L 3.1?
where L‘ is the reference level of target nitrate leaching; l1 and pg. the level of nitrate
leaching and its corresponding probability in state i; L , the target level of nitrate
leaching (per acre) and U2 L; and,1/h’, allowed probability for nitrate leaching
exceeding L.
The speciﬁcation in equation 7 .4 accounts for leaching exceeding the threshold

level (L,- - L), weighted by corresponding probability and the inverse of the permissible

151

\

probability level. This lower partial moment approach can ensure the leaching chance
constraint in equation 7.3 is met. The main objective is to restrict the occurrence of
undesirable outcomes. Any deviation from the threshold level is undesirable to the

processor.

7 .2.3 Modeling the Whole-Farm Decision Rule

In this research, the objective of the contracted-grower is assumed to be the
maximization of the gross margin from the whole-farm operation, and that he or 'she
will avoid the risk of contract loss if and only if the contract is proﬁtable.

Mathematically, the whole-farm framework of the grower can be expressed as:

Marx] E(M) = 561.19.) (7. 5)
subject to 2:} (aw. xj ) s b”,

t-g‘2(t-y.)q.2y°

y,st
L‘ - [1‘2 (Li-Bpizo
L,2[
xi 2 0 bj

where M: the expected income;

3]: expected income (=price*expected yield);

xi: farm activity j, such as crop acreage and input use;

q, : probability of yield below the target level in state i;

p, : probability of nitrate leaching exceeding the threshold level in state i;

Z} (a.,, x, ) S b,: resource availability constraints (including contract acreage);
where amj is the technical coefﬁcient, representing the amount of

resource m needed in producing xj, b, is the availability of resource m.

152

y,- : the seed corn yield in state i;

y”: the average regional seed corn yield (per acre);

t : reference target seed corn yield, where tzf (per acre);

1/g': maximum allowed probability for seed corn yield falling below f.
L, : level of nitrate leaching in state i;

L: nitrate leaching threshold;

L‘: reference level of target nitrate leaching, where L‘zL;

1/h': allowed probability for nitrate leaching exceeding L'

This whole-farm programming model, as represented in equation 7.5, includes several
components: (1) the states of nature, (2) the possible outcomes, (3) the probabilities of
outcomes, (4) the set of alternative choices, and (5) the decision rule for ordering
choices (Boisvert and McCarl, 1990; Hirshleifer and Riley, 1992; Robison and Barry,
1987). The decision rule of the representative grower is assumed to allow choice of
various farm activities to maximize the expected gross margin, subject to several
constraints: resource availability (or technology feasibility), a leaching chance
constraint, the risk of contract loss, and non-negativity constraints.

For illustration purposes, ten states of nature were constructed for the
mathematical programming model in order to represent the probability distribution of
crop yields and nitrate leaching outcomes. Each state of nature is assumed to have
equal 0.1 probability. The alternative choices include crop enterprises (seed corn,
corn, soybeans, and potatoes), nitrogen fertilization rates in growing seed corn and
corn, and production practices (such as planting date and harvesting date).

Yield and nitrate leaching data are simulated from DSSAT 3.0 using 1951-1992

153

weather input data (as discussed in Chapter 5). The data from the ﬁrst two years were
truncated to remove starting point carryover bias, where yield and nitrate leaching are
highly affected by initial soil conditions in the model. The remaining 40 years of data
were sorted according to the yield of continuous seed corn with 116 lb/ac (or 130
kg/ha; medium level) nitrogen fertilization. The sorted data were then divided into ten
sets of four years each in order to represent “good” states of nature versus “poor” states
of nature. Finally, each four-year set of data was averaged to construct ten “states of
nature”.

In order to include the chance constraints into a whole-farm model, PC-LP is
simpliﬁed and translated into a GAMS (General Algebraic Modeling System; Brooke et
al. , 1988) formulation (Dobbins et al., 1996). This translation is necessary because
PC-LP cannot model risk programming. The optimization results from the GAMS
version of PC-LP have been tested and shown to be almost identical to the original PC-
LP model (Etyang, 1994).

Because the contract loss risk is based on the grower’s relative performance in
the region, data on the long-term grower’s yield and regional yields are required in
order to calculate yield variability. The average regional yield data are affected by the
variations of soil structure, agronomic techniques, and pest control. Because the range
of these variations is large across the region, and because DSSAT 3.0 is a deterministic
simulation model, it is difﬁcult to account for yield variability for one particular year.
DSSAT 3.0 assumes perfect conditions for yield growth-no pests and machinery

failures--so the simulated yield data tend to out-perform the real situation. The only

154

source of yield variation in DSSAT 3.0 comes from different weather conditions, given
nutrient, water treatments, and certain tillage practices. Because of the lack of data on
regional yield variations, the empirical analysis of this study chooses four yield levels
to represent the levels of average regional yield. From these four levels, this research
discusses how the chance constraint of avoiding yield falling below the average regional
level affects the grower’s nitrogen application rate and resulting nitrate leaching.
Leaching data from different states of nature are required to construct the nitrate
leaching chance constraint. In principle, the selection of the threshold level and
permissible probability level should be related to the processor’s objective. It might be
related to how the processor values his or her “green image” as well as potential future
penalties, resulting from nitrate leaching damages. Contamination data requirements to
estimate the potential degree of damage caused by nitrate leaching under seed corn
include the bio-physical fate and transport of fertilizer nitrogen, such as the amount of
nitrogen application, nitrogen uptake by the plant, water table indicators, leaching
potential, nitrate concentration, and environmental susceptibility. Nitrate leaching is
used to represent the environmental quality in this research because that is the
environmental outcome that DSSAT 3 .0 can simulate. The speciﬁcations of the
threshold level, as well as the permissible probability of exceeding this level of nitrate
leaching are crucial in designing a leaching chance constraint. This research employs
two leaching threshold levels, each with ﬁve permissible probability levels, in order to
examine how different speciﬁcations of these two parameters affect nitrate leaching as
well as how they affect the processor’s and the grower’s gross margins. It does so by

examining two leaching threshold levels, each with ﬁve permissible levels.

155

The results of whole-farm optimization with these two sets of chance constraints
will be presented separately in order to consider the impacts from each model
speciﬁcation. The two issues examined are: 1) how the concern of the seed corn
contract loss affects nitrate leaching; and, 2) how a probabilistic nitrate leaching chance
constraint can be used in reducing nitrate leaching. These results will be discussed

subsequently.

7 .3 Whole-Farm Optimization with a Chance Constraint on Contract Loss

The whole-farm model from Chapter 6 was adjusted to incorporate the chance
constraint (equation 7.1), where the grower avoids the risk that seed corn yield (y) falls
below the average regional yield 0'") more than I/g' proportion of the time, in order to
manage the risk of contract loss.

This section examines optimal grower choices under four different average
regional yield levels (yo): 60 bu/ac, 65 bu/ac, 7O bu/ac, and 75 bu/ac and four chance
constraint levels. These four average regional yield levels represent the lowest four
yield levels from ten states of nature. These levels are chosen for the consideration of
avoiding bad yield outcomes. The results from the whole-farm planning are
summarized in Table 7.1- 7.3. There is a particular probability associated with each
average regional yield level that will motivate the grower to use more nitrogen

fertilization. For convenience, the results are shown using four intervals.

156

Table 7 .1: Seed corn mean yield and nitrate leaching from growing seed corn
(ASNL) and from the whole farm (ANL) under different regional yield and
permissible probability levels of a contract loss chance constraint

 

[Chance Constraint:

Mean Nitrate Leaching and Seed Corn Yield from Prob(y: y"): I/g“ ‘

 

interval
0 % ~20 %

interval
20%-40%

interval
40 % -60 %

interval
6096-8096

 

ASNL 65.231b/ac

ANL 80.54 lb/ac

Yield 77.89 bu/ac
(11.5%)

ASNL 63.92 lb/ac
ANL 80.151b/ac
Yield 77.71bu/ac

ASNL 63.921b/ac
ANL 80.151b/ac
Yield 77.71 bu/ac

ASNL 63.921b/ac
ANL 80.151b/ac
Yield 77.71 bu/ac

 

ANL 51.17 lb/ac

ASNL 65.08 lb/ac

ANL 80.49 lb/ac

Yield 77.86 bu/ac
(26%)

ASNL 63.921b/ac
ANL 80.151b/ac
Yield 77.71 bu/ac

ASNL 63.921b/ac
ANL 80.151b/ac
Yield 77.71bu/ac

 

ANL 51.17 lb/ac

ANL 51.17 lb/ac

ASNL 65.851b/ac

ANL 80.721b/ac

Yield 77.97 bu/ac
(48%)

ASNL 63.921b/ac
ANL 80.151b/ac
Yield 77.71 bu/ao

 

Prob(y: y”): I/g“

Average Regional Yield:
bu/ac

y” = 60 bu/ac

y" = 65 bu/ac

y" = 70 bu/ac

y" = 75 bu/ac

 

ANL 51.17 lb/ac

 

ANL 51 . 17 lb/ac

 

ANL 51.17 lb/ac

 

ASNL 64.651b/ac
ANL 80.36 lb/ac
Yield 77.81 bu/ac

 

(80%)

 

Note: (.) indicates the point estimation of actual probability level used for the acreage shown. These acreage
in fact vary over the range of l/g‘ values indicated in the column label.

Table 7 .2: Gross margins of the grower and the processor under different regional
yield and permissible probability levels of a contract loss chance constraint

 

 

 

 

 

 

 

 

 

 

[Chance Constraint: Gross Margin of the Grower (GM(G)) and the Processor (GM(P))
Prob(y: y”): 1/g* from Prob(y: y”): I/g"
Average Regional Yield: interval interval interval interval
0 bu/ac 0%-20% 20%-40% 4096—6096 6096-8096
yo = 60 bu/ac GM(G) 357620 GM(G) 357830FGM(G) 357830 GM(G) 357830
GM(P) 13899001GM(P) 1386600 GM(P) 1386600 GM(P) 1386600
(1 1.5 %)
yo = 65 bu/ac IGM(G) 255330 GM(G) 357650IGM(G) 357830 GM(G) 357830
GM(P) 1389500 GM(P) 1386600 GM(P) 1386600
(26%)
yo = 70 bu/ac GM(G) 255330 GM(G) 255330 GM(G) 357520 GM(G) 357830
GM(P) 1391500 GM(P) 1386600
(48%)

y” = 75 bu/ac 'GM(G) 25533OHGM(G) 255330 GM(G) 255330 GM(G) 357710
GM(P) 1388500

(80%)

 

 

 

 

 

 

 

Note: (.) indicates the point estimation of actual probability level used for the acreage shown. These
acreage in fact vary over the range of 1/g' values indicated in the column label.

 

157

Table 7 .3: Acreage of seed corn enterprise under different regional yield and
permissible probability levels of a contract loss chance constraint

 

Chance Constraint:

Seed Corn Acreage Under Probability: 1/g"I

 

 

 

 

 

 

 

 

 

 

 

Prob(y: y”): I/g: (acres)
Average Regional Yield: interval interval interval interval
bu/ac 0%-20% 20%-40% 40%-60% 60%-80%
y” = 60 bu/ac PSEED(M) 198 PSEED(M) 500 PSEED(M) 500 PSEED(M) 500
PSEED(H) 302
(11.5%)
y” = 65 bu/ac 0 PSEED(M) 234 PSEED(M) 500 PSEED(M) 500
PSEED(H) 266
(26%)
y” = 70 bu/ac 0 0 PSEED(M) 56 PSEED(M) 500
PSEED(H) 444
(48%)
y” = 75 bu/ac 0 0 0 PSEED(M) 331
PSEED(H) 169
l(80%)

 

Note: (.) indicates the point estimation of actual probability level used for the acreage shown. These
acreage in fact vary over the range of l/g' values indicated in the column label.

As these three tables show, for each hypothesized average regional yield level, there is

a probability12 (diagonal part of the tables) that will make the proﬁt-maximizing grower

use high nitrogen applications on part of his or her seed corn acreage. Beyond this

probability level (upper part of the tables), the optimizing grower would use a medium

nitrogen application rate, the same rate as estimated in the base scenario. On the other

hand, if the yield level falls below this probability level (lower part of the tables), the

grower perceives that he or she will lose the seed corn contract. That is, the seed corn

acreage is either nil when the constraint is not met, or 500 acres in rotation with

potatoes when the constraint is not binding.

For example, if the grower expects that the average regional yield is 65 bu/ac,

 

12This permissible probability level of each speciﬁed average regional yield level is
obtained by a trial-and-error process. This process shows that the range of the
permissible level that can alter the optimal solution is small, 1 or 2 percent in general.

158

and the permissible probability of falling below this level is 26 percent, the optimal
solution is for seed corn in rotation with potatoes using a high nitrogen fertilization rate
in 266 acres and a medium level in the other 234 acres (Table 7.3). In order to satisfy
this constraint, the mean yield increases from 77.71 bu/ac to 77.86 bu/ac. Meanwhile,
this increase in nitrogen use also causes more leaching from both seed corn production
(from 63.9 lb/ac to 65.1 lb/ac) and the whole farm (from 80.2 lb/ac to 80.5 lb/ac)
(Table 7.1). By doing this, the grower’s gross margin slightly decreases ($l80/year,
from $357,830 to $357,650), but the grower perceives that he or she is ensured to have
the contract for next year. If the grower fails to achieve this constraint, he or she
perceives that there is a dramatic income loss (from $357,830 to $255,330 per year) by
losing seed corn contracts. When the permissible probability is above 26 percent, the
grower will use the same nitrogen level as the base scenario. On the other hand, when
the permissible probability is below 26 percent, the chance constraint of contract loss is
too restricted. As a result, the grower will no longer “qualify” to grow seed corn, if the
processor indeed uses this criterion to allocate seed corn contracts.

This result implies that concern over risk of losing a seed contract may foster
high nitrogen application rates. However, this concern of losing the contract does not
cause a total switch from medium to high nitrogen fertilization use, because the yield
distributions between these two nitrogen application levels do not different from each
other very much (Table 7.4).

As Table 7.4 shows, all practices except seed corn following soybeans with low
nitrogen fertilization have the same probability of achieving the target yields 60, 65,

70, and 75 bu/ac.

159

Table 7 .4: Summary of seed corn yields from DSSAT 3.0 using different agronomic
practices under 10 states of nature

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Seed Corn Yields Under Different Agronomic Practices (bu/ac)

Continuous Seed Corn Seed Corn after Soybeans Seed Corn after Potatoes
States

H M L H M L H M L
1 58.9 58.8 58.4 58.7 58.9 58.4 59.0 58.9 58.4
2 67.1 66.7 66.0 67.0 66.7 66.2 67.0 66.6 66.0
3 72.5 72.0 70.3 72.3 71.8 71.3 72.3 71.8 70.3
4 75.8 75.5 74.3 75.6 75.2 74.3 76.0 75.6 75.1
5 77.4 77.3 76.9 77.3 77.1 76.8 77.3 77.1 76.8
6 80.8 80.5 79.9 80.9 80.5 80.0 80.9 80.5 80.0
7 83.5 83.3 83.0 83.3 83.1 82.9 83.3 83.2 82.9
8 86.0 85.7 85.2 85.7 85.3 84.7 85.7 85.4 84.9
9 87.3 87.2 86.7 87.1 86.9 86.4 87.1 86.8 86.2
10 91.4 91.1 90.6 91.3 91.0 90.5 91.3 91.1 90.7

Note: H represents high nitrogen fertilization; M, high nitrogen fertilization; and L, low nitrogen

fertilization. Ten states of nature are presented in the order from poor-yield to good-yield

 

states .

There are some potential limitations of this approach. First, the simulated yield
distributions may not be the same as the grower’s expectation before harvest. As
shown in Chapter 2, the grower tends to use nitrogen fertilizer based on expectations of
a good-yield year. As a result, excessive nitrogen may be used if normal or poor
weather occurs. One implication is that the provision of accurate information on yield
or weather distribution may be one strategy to prevent excessive nitrogen applications.

If the actual yield distributions of the medium and high nitrogen treatments are
different, and if the grower because there is a risk of losing contracts for low yield

outcomes, he or she may be motivated to use more nitrogen. Therefore, one direct

160

strategy to reduce nitrate leaching is to “decouple” the relationship between relative
yield performance and seed corn contract assignment, that is, to have less or no penalty

for a poor relative yield performance.

7.4 Specification of a Chance Constraint on Nitrate Leaching

Because leaching outcomes are inﬂuenced by natural variability, perfect
monitoring is impractical, and damage from leaching tends to be associated with a
threshold level ( L ), an alternative strategy for leaching reduction is to impose a

leaching chance constraint on this speciﬁed threshold level. Adapting equation 7.3,
Prob(SNL, 2 L ) 5 I/h' (7.3a)

Equation 7.3a requires that the probability of the nitrate leaching from growing seed
corn (SNL,) in state i exceeds the threshold level must be less than the permissible

, probability level (I/h'). This strategy involves the speciﬁcations of two terms: the
threshold level on nitrate leaching, L , and the permissible probability, I/h'.

In order to estimate the impacts from the speciﬁcation of a threshold as well as a
permissible probability level, different scenarios are examined in this study. Two
nitrate leaching threshold levels are selected as the processor’s objective: 35 lb/ac and
40 lb/ac per growing season. The level of 35 lb/ac per growing season is the medium
level of nitrate leaching from seed corn production in the model. Another threshold
level, 40 lb/ac per growing season, was chosen as an alternative scenario because it will
generate results that are similar to a contract that imposes a deterministic nitrate

leaching level on 35 lb/ac. Five permissible probabilities for each threshold level are

161

speciﬁed. All of these scenarios are modeled and compared in order to examine how

parameter speciﬁcations affect the effectiveness as well as the cost of leaching

reduction.

7.4.1 Probabilistic Chance Constraint on Nitrate Leaching Threshold 35 lb/ac

Table 7.5 and 7.6 summarize the main results for a proﬁt—maximizing grower

under a leaching chance constraint with different permissible probability levels for

nitrate leaching from seed corn production exceeding 35 lb/ac per growing season. For

convenience, this constraint can be written as: Prob (SNLz35 ) 51 /h*.

Table 7 .5 : Summary of nitrate leaching, profits, and unit cost of leaching
reduction under a probabilistic constraint Prob(SNL 235): I/h"

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(1) (2) (3) (4) (5) (6)

Chance Constraint: ASNL ANL GM(G) GM(P) MGM(G) MGM(P)
Prob(SNL235)s 1/h' (lb/ac) (lb/ac) ($lyear) ($/year) ($llb) ($llb)
Unrestricted base scenario 63.92 80.15 357830 1386600 na

a.1.2 Restrict ASNL=35 lb/ac 35.00 52.99 357140 1385400 0.05 0.08]
Restrict Prob(SNL235)s 1/2 32.34 55.45 356010 1375900 0.12 0.681
Restrict Prob(SNL235)s 113 31.48 58.37 355070 1375900 0.17 0.66
Restrict Prob(SNL235)s 1/4 31.08 58.63 354480 1375900 0.20 0.65
Restrict Prob(SNL235)s 1/5 30.88 58.33 354150 1375900 0.22 0.65
Restrict Prob(SNL235)s l/lO 30.52 58.21 353190 1375900 0.28 0.64

 

 

 

where ASNL, AN L: average nitrate leaching from seed corn production and from the whole farm
SNL: nitrate leaching from seed corn production in different states of nature
GM(G), GM(P): grower’s and processor’s gross margin
MGM(G), MGM(P): grower’s and processor’s gross margin change for per unit leaching

reduction

162

Table 7 .6: Shadow prices of land and contracts, and crop enterprise mix from the
grower’s profit optimization under a probabilistic constraint Prob(SNL 235): I/h'

 

 

 

a.1.2iestrict P—rolgbilithevel: I/h' for P—rob(S11LL235)s I/h'

 

 

Results: ASNL=35 1 / 2 1/3 1/4 1/5 1/10
MW
Land 198.42 198.42 193.07 192.61 192.61 192.61
Contract 186.04 187.15 194.18 192.65 192.00 190.87
We!!! 38822 38569 38569 38570 38570 38570
W
PCORN(M) 350 407.5 451 457 454 454
BCORN(L) 0 0 0 14 28 46
SSEED(L) 0 1 15 202 242 263 299
BSEED(M) 483 0 0 0 0 0
BSEED(L) 0 385 298 258 237 201
PSEED(M) 17 0 0 0 0 0
SBEAN 483 385 298 258 237 201
CBEAN 0 0 0 14 28 46
SPOTATO 17 0 0 0 0 0
CPOTATO 350 4075 451—W

 

A. Nitrate Leaching from Seed Corn Production and the Whole Farm

From Table 7 .5, the mean nitrate leaching from seed corn production (ASNL)
declines as the permissible probability (I/h *) of nitrate leaching exceeding 35 lb/ac
becomes more restricted (that is, smaller). When this permissible probability equals
1/10, the mean nitrate level from seed corn production falls to the lowest level, 30.5
lb/ac (compared with 64 lb/ac in the base scenario). This change on the mean nitrate
leaching from seed corn production (ASNL) under each permissible probability level is

shown in Figure 7.1.

163

 

 

 

 

Average Nltrato Leaching
(lb/ac)

 

1/10

1/2 1l3 1l4 1l5
Permlulblo Probablllty of Loachlng Excoodlng I
the Threshold Level 35 lblac .ANL

I
l
’ ASNL=35

 

Figure 7.1: Average nitrate leaching from seed corn production (ASNL) and from
whole farm (ANL) under different permissible probability of exceeding 35 lb/ac

Imposing a probability constraint, Prob(SNLz35): 1/h*, on seed corn nitrate
leaching (SNL) above 35 lb/ac results in a reduction of nitrate leaching from swd corn
production (ASNL) by 32—33 lb/ac, compared to 64 lb/ac in the base scenario. This
leaching reduction is mainly from switching from a seed/com potato rotation with a
medium nitrogen treatment to a seed corn/soybean rotation and continuous seed corn
with low nitrogen use. Nitrate leaching from seed corn reaches the lowest level
modeled in continuous seed corn production. Therefore, the contracted-grower will
grow seed corn continuously with low nitrogen fertilization rate under a strict
restriction on nitrate leaching levels.

Figure 7.1 also shows the changes in mean nitrate leaching from the whole farm
(ANL). On average, mean whole-farm nitrate leaching is reduced by 22-25 lb/ac from
80 lb/ac in the base scenario. In contrast to the nitrate leaching results from seed corn
(ASNL), imposing a very strict chance constraint (e.g. , 1/ 10) does not necessarily
reduce whole-farm nitrate leaching (ANL), because more potato acreage will be grown
in rotation with commercial com. This result implies that a contract which targets only

one leaching source will not necessarily reduce the ambient leaching level.

 

164

There are some differences between a contract that imposes a deterministic
restriction on the mean nitrate leaching from seed corn production (ASNL) to 35 lb/ac,
and a contract that imposes a probabilistic chance constraint on Prob(SNL235). The
leaching chance constraint reduces nitrate leaching by 3-5 lb/ac more from seed corn
production (Table 7.5). This result implies that if the processor is concerned about the
deviation from a threshold (35 lb/ac in this case), only targeting mean leaching levels is
not enough. A relatively conservative mean target level needs to be speciﬁed. Another
difference is that mean nitrate leaching from the whole farm (ANL) is higher when
imposing a probabilistic chance constraint on Prob(SNL235) than when imposing a

deterministic restriction on the mean nitrate leaching on 35 lb/ac.

B. Cost of Leaching Reduction

The economic cost of leaching reduction is calculated by the reduction in the
gross margins from the grower and the processor. Table 7.5 shows that the probability
level (I/h’) in the chance constraint affects these two parties differently. The grower’s
gross margin decreases when the permissible probability becomes smaller. On the
other hand, the processor’s gross margin is insensitive to the various levels of
permissible probabilities applied within a probabilistic chance constraint, although the
resulting gross margin is less than in the base scenario. The reason for this outcome is
that the yield difference is small between seed corn in rotation with soybeans and
continuous seed corn practices, thus resulting a similar revenue level for the processor.

The cost borne by the grower and the processor per unit nitrate leaching

reduction is listed in Column (5) and (6) in Table 7.5 is shown in Figure 7.2 .

 

0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00

Reduction (Sllb)

Unit Cost of Leaching

 

ASNL=35 1/2 1/3 1l4 1l5 1l10

Pennleelble Probability of Nltrete Leechlng from Seed Corn Production Exceeding . rower
35 lblec .Proceeeor

 

 

Figure 7 .2: Unit cost of leaching reduction under different permissible probability
of mean leaching from seed corn (ASNL) exceeding the threshold level 35 lb/ac

As the permissible probability of ASNL exceeding 35 lb/ac becomes smaller, the cost
per pound of nitrate leaching reduction increases for the grower, but slightly decreases
for the processor (Figure 7.2). The chance constraints under different permissible
probability levels cost the grower $012-$028, and cost the processor $064—$068 for
per pound of leaching reduction.

The combined cost per pound of nitrate leaching increases from $0.80/lb to
$0.92/lb as the permissible probability of exceeding the 35 lb/ac leaching threshold
decreases from ‘72 to 1/10 (Figure 7.2). This overall unit cost of leaching reduction
from imposing a leaching chance constraint is much higher than the cost of imposing a
deterministic restriction on seed corn nitrate leaching to 35 lb/ac per growing season.
Indeed, it is about 6-7 times higher ($0.13/lb versus $0.80-0.92/lb). The result is
because of large reductions in seed corn yields due to the switch from medium to low
nitrogen application levels when a leaching chance constraint is imposed using 35 lb/ac
per growing season as a threshold level.

In summary, a chance constraint of 35 lb/ac on seed corn leaching reduces

166

nitrate leaching from growing seed corn production (ASNL) by 3-5 lb/ac more than
imposing a deterministic restriction at the same level. However, the unit cost for
leaching reduction from the former is 6-7 times higher than from the latter.

In order to examine the sensitivity of cost to a threshold speciﬁcation, a
threshold speciﬁcation of 40 lb/ac was examined as an alternative scenario to the 35

lb/ac.

7.4.2 Probabilistic Chance Constraint on Nitrate Leaching Threshold 40 lb/ac
Given a leaching chance constraint with a threshold level of 40 lb/ac, the

optimal solutions from the ﬁve different permissible probability levels show sharply

different results than those at the 35 lb/ac threshold (Table 7.7 and 7.8).

Table 7 .7: Summary of nitrate leaching, proﬁts, and unit cost of leaching

reduction under a probabilistic constraint Prob(SNL 240): Nb"

(1) (2) (3) (4) (5) (5)
Constraint: ASNL ANL GM(G) GM(P) MGM(G) MGM(P)
s l/h' ac ac

base scenario 63.92 80.15 357830 1
1.2 Restrict ASNL=35 lb/ac 35.00 52.99 357140 1385400 0.05

s 1/2 36.61 54.93 357290 1 0.04
3 1/3 36.12 54.34 0.04
5 1/4 35.90 54.07 0.04
5 US 35.79 53.94 357210 0.04

 

where ASN L, ANL: average nitrate leaching from seed corn production and from the whole farm
SNL: nitrate leaching from seed corn production in different states of nature
GM(G): grower’s and processor’s gross margin
MGM(G), MGM(P): grower’s and processor’s marginal gross margin for per unit leaching
reduction

167

Table 7 .8: Shadow prices of land and contracts, and crop enterprises for a profit-
maximizing grower under a probabilistic constraint Prob(SNL240)s I/h“

 

 

 

a.1.2 Probabil—ity level: 1/h* for Prob(SNL240)s l/h
Restrict
Results: ASNL=35 1 /2 1/3 1/4 1/5 1/10
ALShadmmiceMcl
Land 198.42 198.42 198.42 198.42 198.42 198.42
Contract 186.04 189.73 186.27 186.22 186.20 186.15
' 38822 38824 38823 38823 38823 38823
PCORN(M) 350 350 350 350 350 350
SSEED(L) 0 O 0 0 0 0
BSEED(M) 483 456 464 468 470 474
PSEED(M) 17 44 36 32 30 26
SBEAN 483 456 464 468 470 474
SPOTATO 17 44 36 32 30 26
CPOTATO 350 350 359 33) 3Q 3Q

 

A. Nitrate Leaching from Seed Corn Production and the Whole Farm

Columns (1) and (2) in Table 7.7 list the mean nitrate leaching from seed corn
production (ASNL) and from the whole farm (ANL), when the nitrate threshold level of
a leaching chance constraint is 40 lb/ac per growing season. The differences between
these two nitrate leaching levels under different permissible probabilities are shown in

Figure 7.3.

 

 

i ‘5‘

i E

z e

l ‘6

I .5

s a

' 2

t .1

* i

L z

' E

‘ i

i ASNL=35 1l2 1/3 1l4 1l5 1/10

E Permissible Probability of Nitrate Leaching from Seed Corn Production THU
1 Exceeding 40 Iblac .ANL ‘
1 '41

 

Figure 7 .3: Mean nitrate leaching from seed corn production (ASNL) and the
whole-farm (ANL) under various permissible probability levels

168

As Figure 7.3 illustrates, the smaller the permissible probability of nitrate leaching
exceeding 40 lb/ac per growing season, the lower the nitrate leaching from both seed
corn production and whole-farm operation. This result is because the acreage planted

in seed corn/potato rotations declines as the probability level decreases.

B. Cost of Leaching Reduction

At the 40 lb/ac leaching threshold, the probability constraint affects the grower’s
gross margin but only has a small impact on the processor’s gross margin. The smaller
the permissible probability (I/h‘), the lower the grower’s gross margin, although the
decline is slight (Table 7.7). The grower’s gross margin reduction comes from a
decrease of seed corn/potato rotation acreage, although it is accompanied by an equal
acreage increase in seed corn/soybean rotation. However, the yield difference between
these two rotation practices are not signiﬁcantly different from each other. The
processor’s gross margin, therefore, remains at the same level.

The unit cost of seed corn leaching reduction does not vary substantially across
all permissible probability levels (Table 7.8). From the grower’s viewpoint, the unit
cost of leaching reduction is 4 or 5 C/lb under all these permissible probability levels
(Figure 7.4). The unit cost of leaching reduction for the processor under the chance
leaching constraint ranges 8-9 C/lb across various permissible probability levels. The

overall cost from both parties is 12-13 C/lb.

169

 

 

 

 

 

 

Mean Nitrate Leaching

 

ASNL=35 1/2 1/3 1/4 1/5 1/10

Permissible Probability of Nitrate Leaching From Seed Corn Production rower
Exceeding 40 Iblac , =Proceaeor

 

 

Figure 7 .4: Changes in the gross margins under different permissible probability of
nitrate leaching from seed corn production exceeding 401b/ac

In general, a contract imposing a chance constraint on a 40 lb/ac leaching
threshold level results in similar mean nitrate leaching and unit cost of leaching

reduction to a contract imposing a deterministic restriction on a 35 lb/ac leaching level.

7 .4.3 Comparisons Between Nitrate Threshold at 35 lb/ac and 40 lb/ac within a
Leaching Chance Constraint

There are some differences between the two contracts with different leaching
threshold speciﬁcations. In terms of controlling nitrate leaching from seed corn
production, a chance constraint with a 35 lb/ac leaching threshold generates 5 lb/ac less
leaching than a chance constraint with a 40 lb/ac leaching threshold. However, the
threshold level 35 lb/ac does not necessarily reduce more nitrate leaching from the
whole farm (ANL) than the threshold level 40 lb/ac. This result implies that a strict
threshold only on seed corn production does not necessarily improve overall water
quality, which is correlated with whole—farm nitrate leaching. Other crop enterprises
are also important in determining nitrate leaching from the whole farm. In order to

meet the low (35 lb/ac) threshold nitrate leaching level, more seed corn acreage is

170

grown continuously, resulting in an increase in potato/commercial corn rotation acreage
with high nitrate leaching levels. Under the 40 lb/ac threshold level, the grower
switches from seed corn/potato rotations to seed corn/soybean rotations, resulting in
less nitrate leaching.

The result also indicates that there is a large difference in the unit cost of
reducing leaching using these two nitrate leaching threshold speciﬁcations. When the
leaching threshold level is set at 35 lb/ac, the overall cost from both grower and
processing ﬁrm for one pound of nitrate reduction ranges between 80-92 C/lb, while it
is 12-13 ¢/lb when the leaching threshold level is set at 40 lb/ac. This result implies
that the cost of reducing leaching is strongly affected by the choice of the nitrate
leaching threshold level and the crop enterprises that can feasiblely comply. If a
leaching reduction contract is to be voluntarily adopted, it is important to choose a
threshold level that is not costly to both parties under alternative contract designs.

In order to examine the efﬁciency of the contract with a leaching chance
constraint, Chapter 8 evaluates this contract design with other alternative contract
designs speciﬁed in Chapter 6 by serval criteria. Furthermore, the analysis is extended

to examine cases where the contracted-growers have different risk preference levels.

7 .5 Summary

This chapter used lower partial moment approaches to include the risks of seed
corn contract loss and unacceptable nitrate leaching chance into the whole-farm
programming model. One result showed that grower concern over contract loss risk

may foster a higher nitrogen application rate, depending on the average regional yield,

171

the target probability level speciﬁed, and the yield distributions of different nitrogen
treatments. Random assignment of seed contracts can remove this incentive. Also, if
there is a perception gap between actual and expected yield distributions, providing
accurate information on yield distributions and weather conditions can reduce nitrogen
application rates.

This analysis also demonstrates that a leaching chance constraint can be
employed as an alternative contract design when the strategic objective is to avoid
exceeding a threshold level. This strategy is designed to account only for the deviations
exceeding the speciﬁed threshold level. A low threshold level (L) or permissible
probability (1 /h‘) will reduce nitrate leaching from growing seed corn (ASNL), but it
does not necessarily reduce nitrate leaching from the whole farm (ANL), compared with
other strategies. If the objective is to improve the overall water quality, targeting
nitrate leaching from growing seed corn is not enough. The impact on leaching from
other product and input substitutions needs to be considered as well.

The magnitude and incidence of abatement costs are crucial elements in
designing a “green” contract to induce voluntary leaching reduction. Within a leaching
chance constraint, the permissible probability level (I/h‘) and the threshold level (L)
are important in determining the magnitude as well as the incidence of leaching
abatement costs. In this representative farm model, the overall cost from the processor
and the grower at the threshold level 35 lb/ac was 7 times higher than that at the
threshold level 40 lb/ac. Both the grower and the processor would hear much higher

leaching reduction cost in the 35 lb/ac threshold level than the 40 lb/ac threshold level.

CHAPTER 8

AN EMPIRICAL PRINCIPAL-AGENT MODEL WITH RISK AVERSION

Risk is an important consideration in designing agricultural contracts to control
nonpoint source pollution (NPSP). Contract outcomes are highly inﬂuenced by
unobservable stochastic inﬂuences. As shown in Chapter 4, risk preferences will
determine an optimal contractual risk-sharing rule between principal and agent.
Therefore, risk preferences may affect the effectiveness of using contract designs to
reduce NPSP. The objective of this chapter is to explore contract designs that can
induce growers who are averse to production risk to reduce nitrate leaching. Three
levels of risk preferences are used within a whole-farm risk programming model in
order to identify how risk aversion affects the grower’s decision as well as the
processor’s welfare. The level of nitrate leaching as well as the proﬁt of the processor
and the grower under alternative contract designs are evaluated in a principal-agent

framework.

8.1 Sources of Ordinary Business Risk
Agricultural production processes are inﬂuenced by stochastic factors such as
weather, machinery failure, pest populations, and input prices. Two major classes of

ordinary business risks are production risk and marketing risk. Production risk

172

173

includes yield loss due to poor weather, and other sources of yield damage, such as
uncontrolled pest problems or machinery failure. Marketing risk is related to price
ﬂuctuations in commodity markets. These ordinary business risks can affect a grower’s
decisions on enterprise combinations and input uses (Sandmo, 1971).

The grower’s risk preference inﬂuences not only farm-level decision-making
processes, but also plays a role in determining the level of associated NPSP. Some
studies have empirically demonstrated that farmers typically behave in risk-averse ways
(e. g. Binswanger, 1980; Dillon and Scandizzo, 1978). The purpose of this chapter is to
examine optimal “green” contract designs for growers with different levels of risk
aversion. This research thus focuses only on production risk because reduction of
nitrate leaching by reducing nitrogen use or changing rotation will affect the probability
distribution (e. g. , mean and variance) of seed corn yield levels, affecting the associated
production risk. Commodity prices are assumed to be known, deterministic, and
exogenously determined by the market.

This research is designed to examine the potential behavior of representative
growers exhibiting different levels of risk preference under alternative contract designs.
Both yield and nitrate leaching outcomes are random variables, greatly inﬂuenced by
weather conditions, but also affected by grower choices of crops, nitrogen levels, and
crop rotation. The next section discusses a particular expected utility function as the

grower’s objective function.

8.2 Mean-Variance Objective Function

Mean-variance (EV) analysis has been widely used and empirically tested. In

174

general, EV models have several advantages over other risk models (Robison and
Hanson, 1996). EV models are theoretically consistent with the Expected Utility
Method (EUM) under conditions such as those discussed below. EV models have
produced theoretical results that correspond with our intuition in many cases (Robison
and Barry, 1987). The results derived from EV analysis can be described in two
dimensional space for analytical convenience. EV produces more tractable analytical
results than the EUM in the case of multiple sources of risk because of its
computational convenience (Duncan, 1994).

EV analysis assumes that the utility function is expressed over two dimensions -
mean and variance (Freund, 1956; Meyer, 1987; Robison and Barry, 1987). It is
consistent with expected utility theory when one of the following conditions is met: 1)
the utility function is quadratic (Tobin, 1958); 2) the risky income variable has a
normal distribution (Freund, 1956 ); or, 3) the location and scale condition is satisﬁed
(Sinn, 1983; Meyer, 1987). The location and scale condition requires that the expected
return is linearly related to the random variables. For instance, if expected return is a
function of price (deterministic variable) times quantity (random variable) [scale shifter]
plus some ﬁxed payment [location shifter], the location and scale condition is satisﬁed.

In the case of seed corn production, the linear payment scheme commonly used
in contracts satisﬁes the location and scale condition. When an individual's utility can
be represented by the exponential function U(M)=l—e'1‘M and income has a normal
distribution, the maximization of expected utility function is equivalent to a quadratic

form (Freund, 1956):

175
Max EU(M) = E(M) - (1AM. V(M) (8.1)
= 21 (51.xj ) -(%) ijxkxjxkojk
subject to £1- am, xj s bm (m=1,..., E)

sz0 Vj

where E(M) is the expected income; V(M) is variance-covariance matrix of income;
and the parameter A is the coefﬁcient of absolute risk aversion, representing an
individual's risk attitude.

The risk-aversion coefﬁcient A can be obtained by several methods. This ﬁrst
approach is to assume that the expected utility has an exponential functional form, and
to estimate A from empirical data. Pratt (1964) showed that the risk coefﬁcient A could
be approximated by a second-order Taylor expansion. In addition to a linear EV
expression, Robison and Barry (1987) and Meyer and Robison (1988) developed a
nonlinear EV model. Their studies allow EV models to characterize decreasing
absolute risk aversion (DARA) and increasing absolute risk aversion (IARA)
coefﬁcients, where income has impacts on risk-attitude, thus enhancing the ﬂexibility
concerning different risk attitude speciﬁcations.

The EV objective function requires data on income and income variance, which
can be calculated from commodity prices, yields, and input costs. Using this
framework, the effect of grower risk aversion in reducing nitrate leaching and the cost

incidence under alternative contract designs can be examined.

176

8.3 Growers Optimization under Different Levels of Risk Preference

Three levels of risk preferences, characterized by the coefﬁcient of absolute risk

aversion II, are examined here. They are 0 (risk-neutral), 10 5 (mildly risk-averse), and

10" (highly risk-averse). The optimal solutions under these three risk preferences are

summarized in Table 8.1. These results include the grower’s expected utility and

expected proﬁts, the processor’s gross margin, nitrate leaching from the whole farm

and from growing seed corn, and the shadow prices of contracts and land. The acreage

from expected utility maximization under these three scenarios is listed in Table 8.2.

These results are illustrated graphically and discussed in the following subsections.

Table 8. 1: Summary of the grower’s expected-utility maximization results under

 

 

 

      

 

 

 

 

 

three risk preference levels
ﬂ . . .
Grower’s Expected Processor’s Nitrate Leachmg (lb/ac) Shadow Price (Slac)
Risk Gross
Preference Net Mar gm Whole-farm Seed corn
Utility revenue (5) (5 y” (ANL) (ASNL) Contract Land
A = 0 357,830 357,830 1,386,600 80.15 63.92 193.41 199.18
A = 10‘5 346,480 357,700 1,386,600 87.79 63.92 199.71 185.09 [I
A = 104 289,600 340,040 1,386,600 88.85 63.92 210.86 110.53 E

 

 

 

 

 

 

 

 

 

Table 8.2: Optimal crop enterprise mix under three risk preference levels

 

Acres under Various Risk Preferences (acres)

4:

 

 

 

POTATO

 

 

A=10" I

A=0 1:10"
BCORN(L) 103 PCORN(M) 350 PCORN(L)
PSEED(M) 500 PSEED(M) 500 PSEED(M)
PCORN(M) 246
SOYBEAN 103
746

 

 

177

A. Grower’s Expected Utility and Processor’s Gross Margin

From Table 8.1, the scenarios for risk-averse growers have lower expected
utility as well as lower expected proﬁts than for the risk-neutral grower. The
difference between expected utility and expected proﬁt is the insurance premium, which
measures the grower’s willingness to pay in order to ensure a certain income level.
The grower’s expected utility and expected proﬁt of these three risk preferences are
graphed in Figure 8.1. As shown in equation 8.1, the expected utility for a risk-averse
grower as estimated from an EV model weights the variance from income negatively.
Therefore, the risk-averse grower might select an enterprise that has less mean income

if it has less income variation.

 

 

 

 

 

 

 

i ;;_’Exeieeteﬁnmt7*
400000 ._____..____ +Expected Proﬁt
5 t
b
2. 350000l .
. s
i h
i E. 300000
| 5
; D
g 3 250000.
f o
| a
K
I“ 200000 -
0 0.00001 0.0001
Riait Preferences

 

 

Figure 8.1: Growers’ expected utility and proﬁt under various risk preferences

In this model, as the level of risk-aversion increases, the contracted-grower will
grow more potatoes (Table 8.2). Because cash-renting land to a potato grower is less
risky than growing other crops, it generates a higher level of expected utility for a risk-
averse grower. When the grower is highly risk-averse (the coefﬁcient of absolute risk

aversion A=10‘), he or she will only cultivate 1200 acres of crops, rather than the 1700

178

acres in the other two cases where 500 acres were rented (Table 8.2). Renting land
from other farmers is no longer attractive because the disutility from increased income
variation outweighs the utility from increased mean income.

Table 8.1 shows that the processor’s gross margin remains the same
($1 ,386,600/year) across different grower risk preference levels. This outcome is
unchanging because three modeled growers produce seed corn in a seed corn/potato

rotation using medium nitrogen levels (Table 8.2).

B. Nitrate Leaching from Growing Seed Corn and from the Whole Farm
Figure 8.2 shows how the grower risk aversion affect the mean nitrate leaching

from growing seed corn and from the whole farm.

 

3779 no.6:

90

 

 

 

mm Leaching (Iblac)

 

 

|
|
|
i
i
i
i
1
1

0 0.00001 0.0001 'EAW

i

i

I

i

i

‘ CoefficientotRlaitAversion l-ASNL
, .

1

Figure 8.2: Average nitrate leaching from whole-farm (ANL) and from seed corn
production (ASNL) under different levels of constant absolute risk aversion

 

Because growers with three risk preference levels all grow 500 acres of seed
corn in the same way, mean nitrate leaching from seed corn production (ASNL)
remains the same, 64 lb/ac (Table 8.2). In contrast, the mean level of nitrate leaching

from the whole farm (ANL) is higher for a risk—averse grower than for a risk-neutral

179

grower. This result is due to the switch from a commercial corn! soybean rotation to a
commercial corn/potato rotation. Since potatoes have high nitrate leaching potential,

this implies higher levels of nitrate leaching (88-89 lb/ac) from the whole farm.

C. Shadow Prices of Contracts and Land
The last two columns in Table 8.1 indicate how the shadow prices of seed corn
contracts and land are affected by the grower’s risk aversion. Both shadow values

under three grower risk aversion coefﬁcients are shown in Figure 8.3.

 

250

20° . .

150 ; .Contract

100 " ‘ ‘ " ‘
50
0

, .Lend

 

Shadow Value (Slec)

0 0.00001 0.0001
Coefficient of Risk Aversion

 

 

Figure 8.3: Shadow values of seed corn contract and land under various risk
aversion coefﬁcients

As shown in Figure 8.3, the shadow value of the contract is higher for risk-
averse growers than risk-neutral growers. This result follows from the fact that a seed
corn contract provides not only an income stream but also a mechanism to reduce farm
income risk.

On the other hand, the shadow value of land decreases with the level of risk
aversion. Figure 8.3 shows that the shadow price of land is less for the highly risk-
averse grower than for the risk-neutral grower. This occurs because additional land

cultivation increases income variation. For the highly risk-averse contracted-grower

 

180

(A=10"), the shadow price of land is $110.53/ac, which is less than the rental price for
one acre of land ($165/ac). Therefore, this grower will not rent any land.

From the above discussion, risk preferences affect the grower’s expected utility
and gross margin, nitrate leaching from the whole farm, and the shadow values of
contracts and land. As a result, risk preferences could affect NPSP outcomes and cost

incidence of alternative contract designs.

8.4 Alternative Contract Designs with Risk Aversion

This section examines the impacts of alternative contract designs under various
grower risk preference levels. These alternative contract designs include the categories
listed in Chapter 6 and contracts with four different leaching chance constraints from
Chapter 7. The contract designs are restricting nitrate leaching (a.1.1 and a.1.2) or
nitrogen use (a.2), forbidding rotation with potatoes (a. 3), charging a fee on nitrate
leaching (b.1.1) or nitrogen use (b.2), reducing the variable payment (c.1 and c.2), and
imposing one of four leaching chance constraints. For simplicity, only two permissible
probability levels from two leaching threshold levels are chosen and incorporated into the
principal-agent framework. These chance constraints include two permissible
probability levels, 1/2 and 1/10, under two threshold levels, 35 lb/ac per growing
season (r.1.1 and 721.2) and 401b/ac per growing season (712.1 and 722.2). For
convenience, the contracts imposing a leaching chance constraint are speciﬁed as follows:
Prob(SNL 235) 51/2 as r. 1.1; Prob(SNL 235) 51/10, r. 1.2; Prob(SNL 240) sI/Z, r.2.1; and
Prob(SNL 240) 51/10, r.2.2. These contract designs are compared based on their ability

to reduce nitrate leaching, and cost magnitude and incidence for leaching reduction.

181

The optimization results for the three grower risk-aversion levels under the
twelve alternative contract designs are summarized in Table 8.3. These results include
mean nitrate leaching from growing seed corn and from the whole farm (ASNL and
ANL), the grower’s expected utility and the processor’s gross margin (EU(G) and

GM(P)), and unit cost of leaching reduction (MU(G) and MGM(P)).

A. Reducing Nitrate Leaching

As seen in Table 8.3, several contract designs can reduce nitrate leaching from
seed corn production and from the whole farm across three risk preference levels. The
mean nitrate leaching from growing seed corn (ASNL) under alternative contract

designs across the three risk preferences is shown in Figure 8.4.

 

\i
O

 

 

Old)
00

 

&
O

 

AM
DO

 

 

 

Nitrate Leaching from Seed Corn
Field(lblac)
(A
O

 

 

r.1.2 r.1.1 3.3 3.1.2 r.2.2 b.2 b.1 r.2.1 a.1.1 a.2 c.1 c.2 base

iris k- neutral
Alternative Contract Designs .muwmrw“.
1...? highly m k- averse

O

 

 

Figure 8.4: Mean nitrate leaching from growing seed corn (ASNL) under
alternative contract design with three risk-aversion levels

182

Table 8.3: Summary of the results from various alternative contract designs for the
growers with different risk preference levels

 

 

 

Coefﬁcient of (l) (2) (3) (4) (5) (6)
absolute risk-aversion (A) ASNL ANL EU(G) GM(P) MU(G) MGM(P)
(lb/ac) (lb/ac) (5) (5) ($llb) ($llb)
Risk-aversion coefficient A=0
Base model 63.92 80.15 357830 1386600 na na
a. 1 . 1 Restrict ANLs 35 lb/ac 41.51 35.00 355790 1385700 0.18 0.08
a. 1 .2 Restrict ASNLs 35 lblac 35.00 52.99 357140 1385400 0.05 0.08
a.2 Restrict N_<.107 lblac 62.95 79.86 357500 1376100 0.68 21.60
a.3 No rotation w/ potato 33.97 51.76 357030 1385400 0.05 0.08
b.1 Charge lOCIlb NL> 30|b/ac 36.56 54.87 356960 1385800 0.06 0.06
b.2 Charge 15C/lb on N > 9OIb/ac 36.47 54.84 357150 1384700 0.05 0.14
c.1 Payment: $253/ac+$3.96/bu 62.95 79.86 357830 1375790 0.00 22.24
c.2 Payment: $230/ac+$3.96/bu 62.95 79.86 347020 1386600 22.24 0.00
r. l .1 Restrict Prob(SNLz 35) s 1/2 32.34 55.45 356010 1375900 0.12 0.68
r. 1 .2 Restrict Prob(SNLz 35)s1/10 30.52 58.21 353190 1375900 0.28 0.64
r.2.1 Restrict Prob(SNLz 40)s 1/2 36.61 54.93 357290 1385500 0.04 0.08
r.2.2 Restrict Prob(SNL240)s 1/10 35.51 53.61 357190 1385400 0.05 0.08
Risk-aversion coefficient A= 104
Base model 63.92 87 .79 346480 1386600 na an
a. 1.1 Restrict ANLs 35 lblac 41 .51 35.00 343060 1385700 0.57 0.08
a. 1 .2 Restrict ASNLs 35 ib/ac 35.00 52.59 343270 1385400 0.22 0.08
a.2 Restrict N s 107 lblac 62.95 87.51 346060 1376100 0.86 21.60
3.3 No rotation w/ potato 33.97 51.35 343060 1385400 0.23 0.08
b.1 Charge 106/lb NL> 30|blac 63.92 87.79 344790 1388300 - -
b.2 Charge 15¢llb on N >901b/ac 62.95 87.51 344770 1377400 3.52 18.93

c.1 Payment: $253/ac + $3 .96/bu 63 .92 87 .79 349280 1386590 -- —
c.2 Payment: $230/ac + $3.96/bu 63.92 87.79 338470 1397400 -
r. 1.1 Restrict Prob(SNLz 35)s 1/2 32.34 54.98 340790 1375900 0.36 0.68

 

r. 1.2 Restrict Prob(SNLz 35):. 1/ 10 30.52 61.02 336260 1375900 0.61 0.64
r.2.1 Restrict Prob(SNL240).<.1/2 36.61 54.53 343590 1385500 0.21 0.08
r.2.2 Restrict Prob(SNLz 40)s 1/10 36.00 43.94 343430 1382300 0.22 0.31
Risk-aversion coefﬁcient A= 10"

Base model 63.92 88.85 289600 1386600 na na
a. 1.1 Restrict ANLs35 lblac 33.97 35 .00 269410 1385400 1.35 0.08
3.1.2 Restrict ASNLs 35 lb/ac 35.00 40.16 271960 1376400 1.22 0.71
a.2 Restrict N310? lb/ac 62.95 88.44 288540 1376100 2.18 21.60
a.3 No rotation w/ potato 33.97 37.79 271030 1385400 1.24 0.08

b.1 Charge lOC/lb NL> 301b/ac 63.92 88.85 287900 1388300 -- -
b.2 Charge 156/lb on N > 901b/ac 63.92 88.85 287640 1388500 -- -
c.1 Payment: $253/ac+$3.96/bu 63.92 88.85 308070 1386590 -- -
c.2 Payment: $230/ac+$3.96/bu 63.92 88.85 297260 1397400 -
r.1.1 Restrict Prob(SNLz 35):. 1/2 32.34 42.93 261660 1375900 1.77 0.68

 

 

r. 1 .2 Restrict Prob(SNLz 35)s 1/ 10 30.52 51.49 245300 1375900 2.65 0.64
r.2.1 Restrict Prob(SNLz 40): 1/2 36.96 43.45 273410 1377100 1.20 0.70
r.2.2 Restrict Prob(SNLz 40) s 1/10 36.20 42.30 272870 1375900 1.21 0.77

 

where ASNL, ANL: average nitrate leaching from seed corn production and from whole-farm operation
SNL: nitrate leaching from seed corn production in different states of nature
EU(G): grower's expected utility; MU(G): grower’s marginal expected utility
GM(P): processor’s expected gross margin; MGM(P): processor’s expected marginal gross margin;
-: undeﬁned number because of no nitrate leaching reduction.

183

Several conclusions can be drawn. First, any contract design that imposes a
restriction can induce reduced leaching. Imposing a leaching chance constraint on 35
or 40 lb/ac per growing season as a threshold level (r.1.1, r.1.2, r.2.1, and r.2.2),
restricting the permissible nitrate leaching (a.1.1 and a.1.2), or forbiding rotation with
potatoes (a.3) can effectively reduce seed corn nitrate leaching by 23-34 lb/ac across
three growers’ risk preference levels (Column 1). These outcomes are because the
restrictions have to be met in order to grow seed corn. There is no ﬂexibility to adjust
the amount of nitrate leaching even under different risk preferences.

However, among the restriction strategies, the contract that restricts nitrogen
use on seed corn (a. 2) is least effective at reducing nitrate leaching. It only reduces
seed corn nitrate leaching by 1 1b/ ac. This result follows because restricting nitrogen
use cannot target the most nitrate sensitive practices-rotation with potatoes.

Because seed corn/potato rotation generates much higher nitrate leaching than
other seed corn rotation practices, the effective leaching reduction strategies are those
that induce the grower to avoid rotation with potatoes, rather than just use less nitrogen
on seed corn. Imposing restrictions on nitrate leaching or rotation can thus directly
reduce nitrate leaching.

The second conclusion is that contract speciﬁcations that use ﬁnancial
disincentives cannot effectively reduce nitrate leaching from seed corn production when
the grower is risk-averse (A > 0). These strategies include charging a fee on nitrogen
use or nitrate leaching (b.1 and b. 2), or reducing the variable payment (c.1 and c.2).
Such ﬁnancial penalty schemes provide the grower ﬂexibility to make his or her

decision based on the marginal beneﬁt versus the marginal cost of reducing leaching.

184

Since the risk-averse grower is concerned about both mean income and income
variance, the ﬁnancial disincentives from charging a fee on nitrate leaching or nitrogen,
or reducing the variable payment (b.1, b.2, c.1, and c.2) may be less than the risk
reduction advantage from a seed corn/potato rotation. In such a case, the risk-averse
grower would rather pay a penalty than reduce nitrate leaching. Contract designs that
charge a ﬁnancial fee on nitrate leaching or nitrogen (b.1 and b.2) can reduce nitrate
leaching for a risk-neutral grower, but they may not be effective strategies for a risk-
averse grower.

Similar observations can be made concerning nitrate leaching from the whole

farm (ANL; Column 2 from Table 8.3 and Figure 8.5).

 

 

 

 

10- _

 

 

 

Nitrate Leaching From the Whole
Farm(lblec)
b OI a \l m o
O O O O O O
I-

” —
III-II.-
III-IIII!
-—-‘—_-n-

r.1.2 r.1.1 a.3 8.1.2 7.2.2 b.2 b.1 r.2.1 a.1.1 a. c.1 c.2 base

Alternative Contract Deelgn ‘I'rirt-neunni
smildly 711 it- averse

iighly risk-averse

 

Figure 8.5: Mean nitrate leaching from the whole farm (ANL) under alternative
contract designs with three risk preference levels

In this case, imposing a permissible nitrate leaching on the whole-farm (a.1.1) is
the most effective contract design for reducing whole-farm nitrate leaching (ANL). It
can reduce whole-farm nitrate leaching by 45-54 lb/ac per growing season. Other
contract designs that impose a restriction on seed corn nitrate leaching (r.1.1, r.1.2,

r.2.1, r.2.2, a.1.2), or no rotation with potatoes (a.3) are also able to reduce whole

185

farm nitrate leaching by more than 20 lb/ac. This leaching reduction comes from
reduced potato acres.

There is one similarity between nitrate leaching from growing seed corn (ASNL;
Figure 8.4) and nitrate leaching from the whole farm (ANL; Figure 8.5) under
alternative contract designs. Contract designs that impose restrictions on nitrate
leaching or forbid rotation with potatoes can reduce nitrate leaching across all grower
risk preferences shown, while using ﬁnancial incentives cannot lower nitrate leaching
when the grower is risk-averse. The reason is that the beneﬁt from seed corn/potato
rotations is greater than the ﬁnancial disincentive to reduce leaching from seed corn
production.

However, there is also a difference between these two leaching levels from
alternative contract designs. All contract designs, except a.1.1 (restricting the whole
farm leaching) and b.1 or b.2 (charging a fee on nitrate leaching and nitrogen use),
generate similar results on seed corn nitrate leaching across three risk preferences
because the growers with different risk-aversion preferences use the same practices in
seed corn production. On the other hand, these contract designs generate different
whole-farm nitrate leaching when the grower is highly risk-averse. When a restriction
on all agronomic practices (except on the whole-farm nitrate leaching a.1.1), the highly
risk—averse grower will switch using medium levels of nitrogen treatments on
commercial corn to a low level, resulting in less whole-farm nitrate leaching. As in the
unrestricted base scenario, contracts restricting nitrogen use (a.2) and reducing the
variable payment (c.1 and 0.2) have higher mean whole-farm nitrate leaching for the

risk-averse grower than for the risk-neutral grower. This result is due to reduction in

186

the percentage of corn acreage (a potentially low leaching crop).

B. Cost of Leaching Reduction

Both the processor and the grower incur some added costs due to alternative
contract designs in many cases. As noted previously, the magnitude of leaching
reduction cost is measured by the reductions in the grower’s expected utility as well as
in the processor’s gross margin, (Table 8.3 Column 3 and 4).

The magnitude of leaching reduction cost under alternative contract designs

varies by the grower’s risk preference level as shown in Figure 8.6.

 

"51 I

 

.-
'II
I'I
II
II
.I

base a.1.1 a.1.2 a.2 a.3 b.1 b.2 c.1 c.2 r.1. r.1.2 r.2.1 r.2.2
’lrisk-neutrd

Alternative Contract Designs 1 Im‘ldlyrisk-OIUSB 1

i . D iigHy relic/use 1

 

Figure 8.6: Grower’s expected utility from alternative contract design under
different risk preference levels

In general, the risk-averse grower has higher costs than the risk-neutral grower
from complying with the restrictions from the alternative contract designs. All contract
designs that can effectively reduce nitrate leaching will substantially reduce the highly
risk-averse grower’s expected utility. For example, a contract forbidding rotation with

potatoes (a.3) causes a 0.2 percent expected utility reduction for a risk-neutral grower,

 

187

while causing more than 6 percent of expected utility reduction for a highly risk-averse
grower (A=10‘) . In terms of unit cost of nitrate leaching reduction, this strategy costs
$0.05/lb for a risk-neutral grower, $0.23/1b for a mildly risk-averse grower (A=105),
and $1.24/lb for a highly risk-averse grower (A=10") (Column 5, Table 8.3). This
result comes from the increase income variance which occurs from the switch from a
seed corn/potato rotation to a seed corn/soybean rotation.

Among all alternative contract designs, imposing a leaching chance constraint of
35 lblac per growing season threshold level with 1/10 probability (r.1.2) always
reduces the grower’s expected utility to the lowest level across all risk preference
levels. By contrast, reducing the variable payment plus increasing the ﬁxed payment
(c.1 or c.2) increases the grower’s expected utility, since it reduces income variability.

Grower risk preferences also affect the processor’s gross margin. The impacts
of alternative contract designs under different grower risk preferences on the

processor’s gross margin are illustrated in Figure 8.7.

 

 

 

  
  

 

 

 

    

 

 

 

 

 

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1 g 1.395.000 .
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‘3 l I I III I
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‘ Alternative Contract Reigns ‘ lrlsk—rﬁivd ‘
1 Inildyrisk-olase 1
, VUNgi-iyvlsk-oase I

 

 

Figure 8.7: Processor’s gross margins from alternative contract designs under
three levels of risk preference

188

The processor’s gross margin is reduced substantially under the contracts that
impose restrictions on nitrate leaching (a.1.2, r.2.1, and r.2.2) when the grower is
highly risk-averse. In contrast, the processor has a higher gross margin under the
contracts that use ﬁnancial incentives to reduce nitrate leaching (b. 1, b.2, c.1, and c.2)
when the grower is highly risk-averse than when the grower is risk-neutral or mildly
risk-averse. As shown before, contracts using ﬁnancial incentives do not necessarily
reduce leaching.

From the above discussion, grower’s risk preference is critical in determining
the effectiveness of nitrate leaching reduction for non-restriction alternative contract
designs. Imposing a strict restriction reduces nitrate leaching under all grower levels of
risk aversion. However, reducing nitrate leaching may impose added costs on the

processor and the grower.

8.5 Efﬁciency under Two Dominance Criteria
Due to the potential tradeoffs between nitrate leaching and proﬁtability, two
efﬁciency criteria are used for evaluation of the alternative contracts designs. They

are: a) contract acceptability dominance, and b) cost efﬁciency dominance.

8.5.1 Contract Acceptability Dominance

The first criterion to be examined is contract acceptability dominance. This
criterion identiﬁes a contract as acceptable to the grower if it will reduce expected
utility by less than 1 percent. For the processor, the criterion states that strategy A

dominates strategy B if and only if either (ASNLA < ASNL, and GM, 2 6MB) or

189

(ASNL), SASNLB and GM .4 > 6MB), where ASNL is the mean nitrate leaching from

seed corn production and GM is the processor’s gross margin.

The contract designs that are

not unacceptable under contract acceptability

dominance across three grower’s risk preference levels are summarized in Table 8.4.

Table 8.4: Contracts that are undominated under contract acceptability
dominance under various levels of grower risk aversion

 

 

 

 

 

 

[Coefﬁcient of Risk-
Aversion (A) Undominated Contract Designs
A =0 (risk-neutral) .3 No rotation with potatoes;
.1 Charge lOC/lb ASNL> 301b/ac;
c.2 Payment: $230/ac+$3. 96/bu;
.1.1 Restrict Prob (SNLz35) 51/2.
A=10‘5 (mildly risk- .1.1 Restrict ANLs 35 lblac;
Inverse) .3 No rotation with potatoes;
c.2 Payment: $230/ac+$3. 96/bu;
. 1. 1 Restrict Prob (SNL235) sI/Z;
r. 2.1 Restrict Prob(SNL240)s 1/2.
A=104 (highly risk- .1.1 Restrict ANLs 35 lblac;
verse) a.3 No rotation with potatoes;
'3 c.2 Payment: $230/ac+$3. 96/bu;
r. 1. 1___rt__ob SNLz35 51/2 --

 

 

Note: Italics represents the contracts that are undominated under three levels of grower

risk aversion

Three contracts are undominated under this dominance defmition across all three

grower risk preference levels. They

are “no rotation with potatoes” (a. 3), reducing the

variable payment to $3.96/bu with the ﬁxed payment raised to $230/ac (c.2), and

imposing a leaching chance constraint Prob(SNL235)51/2 (r.1.1).

From the grower’s perspective, a contract design (r.1.2) that imposes a leaching

chance constraint on Prob(SNL235):1/10 is not acceptable using the contract

acceptability dominance criteria because it reduces the grower’s expected utility by

 

190

more than one percent across all risk preference levels.

Other contracts designs are undominated only for certain risk preference levels.
Contract designs restricting the permissible whole-farm nitrate leaching to 35 lblac per
growing season (a.1.1) are not dominated when the grower is risk-averse (A=10‘ or
10‘s). Contracts charging a fee on nitrate leaching (b.1) are undominated only when the
grower is risk-neutral. Imposing a leaching chance constraint Prob(SNL240)51/2
(r.2.1) is undominated only for a mildly risk-averse grower (A=105).

Contract acceptability dominance does not capture the degree of NPSP reduction
or the unit cost of abatement achieved. In order to capture another efﬁciency criterion-

cost efﬁciency dominance-needs to be examined as well.

8.5.2 Cost Efﬁciency Dominance

Cost efﬁciency dominance is deﬁned such that strategy A dominates strategy B if
it reduces leaching at lower unit cost for the grower without increasing unit cost for the
processor or vice-versa. Unit cost is measured by the reduction in the grower’s
expected utility or in the processor’s gross margin for per pound of leaching reduction.

The contracts that are undominated under this criterion are listed in Table 8.5.

191

Table 8.5: Contracts that are not dominated under cost efﬁciency dominance
under various levels of grower risk aversion

 

  
  
    
    
  
      
      

Coefﬁcient of Risk-Aversion (A) Undominated Contract Designs

A =0 (risk-neutral) b.1 Charge 10¢/ 1b NL > 301b/ac;
c.1 Payment: $253/ac+$3.96/bu;
c.2 Payment: $230/ac+$3.96/bu;
.2.1 Restrict Prob (SNL240) s1 /2 ;
.1.2' Restrict ANL_<.35 lblac;
.3' No rotation w/ potato;

 

 

 

 

 

  
 

   

.2.2' Restrict Prob(ASNL240)s 1/10.
A=10‘5 (mildly risk-averse) r.2.1 Restrict Prob (SNL240) 51/2;
.3' No rotation w/ potato.
.3 No rotation w/ potato;
* indicates that the unit cost of leaching reduction is less than 2 cents, compared
with contracts that are undominated in this analysis. Italics represents the

.1.2' Restrict ANL535 lblac;
“:0“ (highly risk-averse)
r. 2.1 Restrict Prob SNL240 $1 /2.

contracts that are undominated under three levels of grower risk aversion

As Table 8.5 shows, the only contract design that is undominated across all
grower risk preference levels is the one that imposes a leaching chance constraint on
nitrate leaching from growing seed corn (SNL) exceeding 40 lblac with probability 1/2
(r.2.1). From the grower’s perspective, this design is the least costly per pound of
leaching reduction among the twelve alternative contract designs. It costs 8 ¢/lb for
the processor when the grower is risk-neutral or mildly risk-averse. When the grower
is highly risk-averse(A=10"), the unit cost of leaching reduction escalates from 8 C/lb
to 70 C/lb. As noted above, this result is due to the reduction in seed corn/potato
rotation acreage and the switch from the medium to the low nitrogen treatment in a seed
corn/soybean rotation. Both reasons reduce seed corn yield by 253 bushels from the

base scenario, and subsequently reduce the processor’s gross margin.

Using this cost efﬁciency criterion, three contract designs using ﬁnancial

192

incentives are undominated when the grower is risk-neutral. They are contract designs
charging a fee on nitrate leaching (b.1), or reducing the variable payment (c.1 and 6.2).
However, as discussed previously these contract designs fail to reduce nitrate leaching
when the grower is risk-averse.

Contracts that forbid the seed corn/potato rotation (a. 3) are not dominated only
when the grower is highly risk-averse. They are dominated by contracts with a
leaching chance constraint Prob(SNL 240) 51/2 (r. 2. 1) when the grower is risk-neutral
or mildly risk-averse. Nevertheless, the unit cost from “no rotation with potatoes (a.3)"

is only 1-2 C/lb more than imposing a leaching chance constraintProb(SNL240)sI/2.

8.5.3 Evaluation Under Both Efﬁciency Criteria

There is no contract design that is undominated across all risk preference levels
under both contract acceptability dominance and cost efﬁciency dominance. Contract
designs that impose a chance constraint on nitrate leaching above the threshold 40 lb/ac
with probability in (r.2.1), or that restrict seed corn/potato rotations (a.3) are
undominated in most cases under the two efﬁciency criteria.

A contract design that imposes a chance constraint on nitrate leaching above the
40 lblac threshold level with probability 1/2 (r.2.1) is undominated across all risk
preference levels under cost efﬁciency dominance while it is only undominated for the
mildly risk-averse grower under contract acceptability dominance. This contract fails
to achieve contract acceptability dominance because it is relatively costly for the
processor to reduce nitrate leaching compared to a) contracts charging a fee on nitrate

leaching (b.1) when the grower is risk-neutral, and b) contracts restricting the whole-

193

farm nitrate leaching or forbidding rotation with potatoes (a.1.1 and a.3) when the
grower is highly risk-averse.

Contract designs forbidding seed corn/potato rotations (a. 3) are undominated
under contract acceptability dominance at every risk preference level, but they are
undominated only when the grower is highly risk-averse under cost efﬁciency
dominance. This contract design is dominated by the one with a chance constraint on
nitrate leaching above the 40 lb/ac threshold level with probability 1/2 (r.2.1) under cost
eﬁiciency dominance for the risk-neutral or mildly risk-averse grower. However, it
only costs 1 to 2 c more per pound of leaching reduction than strategy r.2.1. Given the
same cost (8 C/lb) for the processing ﬁrm across all risk preference levels, forbidding
rotation with potatoes costs the processor 62 C less for per pound of leaching reduction
than does a contract with a leaching chance constraint. This contract forbidding
rotation with potatoes would be the most preferable contract design, if cost transfer
were possible.

In addition to efﬁciency criteria, contract enforceability is another essential

element to be considered in contract designs.

8.6 Enforcement of Contract Speciﬁcations

All the above discussions come from a hypothetical efﬁciency perspective;
however, a contract that is unenforceable is unlikely to be efﬁcient. Well sampling is the
primary current means to monitor groundwater nitrate levels. But there is typically no
way to identify the source or individual contribution level of nitrates. Indirect methods to

assess crop nitrogen needs include soil testing and plant tissue testing (such as grains,

194

stalks, leaves, etc.) (Silva, 1996). These tests, however, can be costly and do not directly
measure nitrate leaching. More reliable methods, such as lysimeter sampling, are
prohibitively expensive. Without a low-cost veriﬁcation technique to detect and measure
nitrate leaching, it is difﬁcult to prevent cheating on contracts that restrict or charge an
eﬁluent fee on nitrate leaching.

By contrast, a contract that targets observable agronomic practices is relatively
easy to enforce. Hence, when enforceability is added to the two dominance evaluation
criteria, the contract forbidding seed corn rotation with potatoes comes up as the most

promising one for reducing nitrate leaching under varying levels of grower risk aversion.

8.7 Summary

Ordinary business risk is an important element in designing contracts to control
NPSP. This chapter illustrates a principal-agent framework that uses a mean-variance
(EV) objective function to model contracted-growers with different levels of risk
aversion. In the unrestricted base scenario, all growers at all three levels would grow
seed corn in rotation with potatoes with medium nitrogen treatments because this
practice generates the highest expected income and has lowest yield risk among all seed
corn rotations. However, this rotation generates higher nitrate leaching than other
rotation practices. In terms of nitrate leaching from the whole farm, the more risk-
averse the grower is, the higher the nitrate leaching. The risk averse grower solutions
included a cash-rent potato contract which ensures income stability but causes serious
nitrate leaching.

This analysis showed that risk attitude is crucial in determining the effectiveness

 

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195

of alternative contract designs to reduce nitrate leaching from seed corn production.
Imposing restrictions through contract speciﬁcations on emission (nitrate leaching) or
agronomic practices (rotations) are the most effective ways to reduce nitrate leaching.
Restricting nitrogen input use is not necessarily an effective strategy. Using ﬁnancial
incentives (user fees, variable payment) does not necessarily reduce nitrate leaching
when the grower is risk-averse. In this model, the effectiveness of a contract design to
reduce nitrate leaching comes from its ability to induce the grower to switch from a
seed corn/potato rotation to a seed corn/ soybean rotation.

Some contract designs targeted at seed corn ﬁelds can only effectively reduce
nitrate leaching from seed corn production, but they do not successfully reduce leaching
from the whole farm. Apparently, targeting only one crop does not necessarily abate
whole farm NPSP.

Contract acceptability dominance and cost eﬂiciency dominance criteria are used
to evaluate the efﬁciency of alternative contract designs. There is no contract design
that is undominated across all risk preference levels. The two contract designs that
impose a chance constraint on nitrate leaching above the threshold 40 lb/ac with
probability in (r.2.1), and that forbid seed corn/potato rotation (a.3) are undominanted
in most cases. When enforceability is also considered, forbidding seed corn in rotation
with potatoes is the only strategy that succeeds under all criteria--reduction of nitrate

leaching, mutual acceptability to both the processor and the grower, and enforceability.

CHAPTER 9

CONCLUSIONS AND IMPLICATIONS

This study has examined how to redesign contracts to reduce nonpoint source
pollution. Conclusions and policies implications are made based on these results.

Suggestions for future research are advanced as well.

9.1 Review of Research Objectives

Nonpoint source pollution (NPSP) abatement is a regulatory challenge. Due to
natural variability of NPSP as well as imperfect monitoring and/or measurement,
standard public policy remedies tend to incur high transaction costs. However, the
restructuring of U.S. agriculture toward more contractual arrangements between the
processor and the producer brings new opportunities for the creative design of contracts
to reduce NPSP voluntarily.

Within a production contract, the processing ﬁrm often speciﬁes details such as
production practices and speciﬁc inputs in order to ensure product quality. This
vertical coordination of processors with contracted growers has transferred substantial
inﬂuence over the management of crop and livestock enterprise to agricultural
processors. Some of these contracts incorporate production incentives that may cause

environmental damage due to high rates of agrochemical use.

196

197

There are at least two potential rationales for an agribusiness ﬁrm to seek
voluntarily to reduce N PSP. One is fear of future environmental regulation. A
processing ﬁrm may wish to pre—empt environmental liability by addressing a potential
problem before it receives regulatory scrutiny. The other factor is consumer demand
for improved environmental quality. Because brand reputation becomes increasingly
important in agriculture, a processing ﬁrm may want to pursue and protect a “green”
image. Thus a ﬁrm may wish to design contracts that offer incentives not only for the
pursuit of traditional proﬁt and product quality goals, but also for the pursuit of
environmental goals.

The research issue addressed in this study is the design of a contract that is
acceptable to both the processor and the contracted-grower, and that can eventually
induce contracted growers voluntarily to reduce agricultural nonpoint source pollution.
In order to design and evaluate alternative “green” contracts, this research examined the
potential use of seed corn production contracts to reduce nitrate leaching. The research
on seed corn contracts was focused on St. Joseph County of Michigan where large
acreage of seed corn is grown under production contracts on sandy, irrigated soil and
where there is signiﬁcant nitrate concentration in the groundwater.

Five speciﬁc objectives were identiﬁed in this research. The ﬁrst objective was
to identify the relationships among contract speciﬁcations, nitrogen use, yield and
nitrate leaching. The relationships between nitrogen use, yield, and nitrate leaching
from seed corn production were estimated using a crop growth simulation model.

These data showed that as nitrogen fertilizer rates increased, seed corn yields reached a

198

plateau, whereas nitrate leaching from growing seed corn increases geometrically. Two
interrelated institutional arrangements could encourage the grower to use high nitrogen
fertilizer rates, resulting in excessive nitrate leaching. One is contract speciﬁcations
which place a high premium on seed corn yields, and the other is assignment of
contracts based directly on yield performance.

The second objective was to identify production practices that can reduce nitrate
leaching. Crop rotation turned out to be an important element in addition to nitrogen
use in determining nitrate leaching since certain crops rotated with seed corn receiving
heavy fertilization caused substantial nitrate leaching. Therefore, appropriate nitrogen
application rates and elimination of rotations with potatoes generated the least nitrate
leaching. As discussed in chapters 2 and 3, knowledge of nitrogen fertilizer response
can also inﬂuence the adoption of improved agronomic practices.

The third objective was to identify contractual terms that could result in reduced
nitrate leaching. Chapter 2 summarized several instruments that could reduce nitrate
leaching from seed corn production. The potential instruments included fees, “green”
payments (or incentive payments), and penalties. The instruments were based on: a)
output levels, by using seed corn yields as an index; b) purchased nitrogen fertilizer
inputs; c) production practices such as an appropriate nitrogen application rate or other
agronomic practices; (1) nitrate leaching (emission) levels; e) the ambient nitrate
concentration in the ground water; and t) liability risk due to potential health and
environmental damages caused by nitrate leaching.

The fourth objective was to structure a theoretical framework to analyze

199

alternative “green” contract designs. A principal-agent model was used to examine the
relationship between the processor and a representative contracted-grower. The
essential elements in designing a “green” contract within a principal-agent model
included participation constraint, incentive compatibility constraint, and risk attitude.
This research illustrated four kinds of potential contract designs that would incorporate
environmental concerns into agricultural production contracts. They were a) restricting
ambient nitrate leaching levels or nitrogen application rates, or forbidding rotation with
potatoes; b) charging the contracted-grower a fee on nitrate leaching levels, or nitrogen
applications; c) reducing the variable payment per bushel of seed corn output; and d)
incorporating relevant nitrogen management information within a contract or as a
grower educational program.

The ﬁfth objective of this research was to formulate an empirical principal-agent
analysis to examine and evaluate the impacts from alternative contractual speciﬁcations.
Only the ﬁrst three alternative contract categories were incorporated into a whole-farm
math programming model, because the fourth scenario, incorporating relevant
information, was not compatible with the mathematical programming approach.
Modeling the feasibility of alternative contract designs to reduce nitrate leaching was
done in two steps. First, the seed corn grower’s decisions were modeled within a
whole-farm math programming framework. This modeling was intended to specify the
grower’s participation constraint in terms of the opportunity cost of forgone income
from growing other crops if the grower chose to grow seed corn. Second, the net

revenue to the processing ﬁrm was modeled as the residual after subtracting contract

200

payments from the gross revenue estimated from seed corn sales. The incentive
compatibility constraint was examined using dominance criteria that evaluated whether
the processor or the grower would suffer unduly under the terms of the contract
compared with the baseline contract.

Three criteria were used to evaluate the efﬁciency of alternative contract
designs. These are the ability to reduce nitrate leaching from growing seed corn
(targetability) and from the whole farm (correlation with water quality), and the
magnitude as well as incidence of abatement costs. Two forms of dominance analysis
were used to compare relative efﬁciency among all alternative “green” contract designs
from the perspectives of targetability and cost efﬁciency. The ﬁrst, contract
acceptability dominance, evaluates each pair of contracts separately for the grower
(based on expected utility from mean-variance analysis) and for the processor (based on
mean gross margin and mean nitrate leaching from seed corn ﬁelds). The second, cast
eﬁ‘iciency dominance, evaluates each pair of contracts based on the unit cost of nitrate
leaching reduction for the grower and for the processor. Nitrate leaching from the
whole farm is used as a proxy to examine the correlation with water quality among all
alternative contracts.

Several major ﬁndings emerged. First, crop growth and nitrogen fate
simulations demonstrated that seed corn might be responsible for much less nitrate
leaching than certain other crops such as potatoes.

Second, relative prices among nitrogen fertilizer, corn, soybeans, and potatoes

are important in determining nitrate leaching levels. If the price of corn increases or

201

the price of nitrogen decreases, the contractor-grower may be motivated to use more
nitrogen than in the cases examined in this study. The sensitivity tests also show that if
the relative price of soybeans (a low-nitrate-leaching crop) rises compared with the
price of potatoes (a high-nitrate-leaching crop), this price change could shift seed corn
acreage away from rotation with potatoes into rotation with soybeans, resulting in less
leaching.

Third, contracts restricting nitrate leaching and rotation can effectively reduce
nitrate leaching under various grower risk preference levels. Restricting nitrogen use
in only seed corn contracts may not be effective in reducing nitrate leaching, especially
when the more severe leaching results from a rotation crop.

Fourth, charging fees on nitrate leaching or nitrogen fertilizergwas shown to be
effective in reducing nitrate leaching only when the grower is risk-neutral. Charging a
fee on nitrate leaching gives the risk-neutral grower enough incentive to adopt reduced
leaching practices, such as a seed corn/soybean rotation. Placing a fee on nitrogen
fertilizers could reduce nitrate leaching by causing a risk-neutral grower to switch to an
agronomic practice (seed corn/ soybean) that requires lower fertilization rates.
However, such charging strategies did not reduce nitrate leaching under the risk-averse
grower scenarios modeled. This conclusion was because potatoes had no income risk
in this model (as in the real situation), therefore, the risk-averse grower would not
change his or her seed corn production practices and nitrate leaching would not be
reduced.

Fifth, rearranging the contract compensation scheme by reducing the yield-based

202

variable payment is not necessarily an effective way to reduce nitrate leaching. Other
agronomic practices are also important in determining nitrate leaching. In this analysis,
the beneﬁts from a seed corn/potato rotation exceeded the disincentive from reducing
variable payments. This design could only induce the risk-neutral grower to apply
lower levels of nitrogen application, but was not effective in reducing leaching.

Sixth, nitrate leaching reduction could reduce the processor’s gross margins and
the grower’s expected utility. The magnitude and the incidence of costs from
alternative contract designs depended on the speciﬁcation of nitrate leaching threshold
levels and the grower’s risk preference. The risk—averse growers modeled bore more
cost from leaching reductions than the risk-neutral grower.

Seventh, the analysis indicated that contracts targeting nitrate leaching only from
seed corn production do not necessarily reduce nitrate leaching from the whole farm. If
the ultimate target is to improve the water quality, then targeting only seed corn
production is not sufﬁcient.

Enforceability as well as efﬁciency is the key to effective contract designs.
Unfortunately, it is difﬁcult to come up with a low-cost way of enforcing contract
designs that are based on nitrogen use or nitrate leaching. Without enforcement,
contract redesigns may not be acceptable to both the processor and the grower.
However, targeting observable agronomic practices is a feasible alternative to design

“green" contracts.

203

9.2 Conclusions

The results demonstrate that seed corn contracts can be redesigned to reduce
nonpoint source pollution. Such contracts can be mutually acceptable to both the
processor and the grower at reasonable costs; but enforcement is a key issue. A
principal-agent model is a workable approach in modeling and evaluating nitrate
leaching reduction strategies in a contractual relationship. Several strategies can be
employed as a means to control nitrate leaching. The effectiveness of these alternative
contract designs depends on three factors: the risk of losing contracts, alternative crop
selection, and risk preference of the contracted grower.

The grower concern over risk of contract loss could induce a high nitrogen
application rate, resulting in excessive nitrate leaching. If high yields are a primary
basis for a processing ﬁrm to allocate production contracts then risk of contract loss
will be a serious obstacle inhibiting growers to accept alternative contract designs that
may reduce NPSP at the expense of maximum crop yield. Model results indicated that
alternative crop enterprises are very important to contract design, not only for the
participation constraint, but also for the environmental consequences from alternative
contract designs. The grower risk attitude mattered in reducing nitrate leaching as well
as the incidence of who bore the cost of leaching reduction.

A contract based on seed corn yield can be easily enforced, but it cannot
effectively reduce NPSP as well as improve water quality, especially when the
relationship between output and emission is also affected by other managerial practices.

Although a contract based on input use may be monitored through some indirect

204

techniques, input and N PSP may be inﬂuenced by agronomic practices in addition to
natural variability. Targeting certain agronomic practices is a feasible way to control
NPSP because it is relatively easy to monitor, and it is correlated with water quality.
Nitrate leaching, on the other hand, is difﬁcult to measure although it is related to water
quality. In theory, targeting whole-farm nitrate leaching is a way to induce growers to
use improved practices to improve water quality. However, enforcement can be a
problem.

Using three criteria proposed by Braden and Segerson (1993), the evaluation of

alternative contract designs to reduce nitrate leaching is summarized in Table 8.1.

Table 9.1: Evaluation of alternative contract designs under various criteria

 

 

 

 

 

 

 

 

 

 

 

 

Correlation w/
Instruments for Alternative Contract Designs Targetability Enforceability Water Quality
1) Seed corn yield output:
c. l&c.2: Reduce the variable payment L H L
2) Purchased nitrogen fertilizers:
a.2 Restrict nitrogen use L M L
b.2 Charge a fee on nitrogen use M* L M“
3) Agronomic (rotation) practices:
a.3 No rotation with potatoes H” H
4) Nitrate leaching from seed corn (ASNL):
a. 1 .2 Restrict ASNL H L M
b.2 Charge a fee on ASNL M* L
r.1.1, r.1.2, r.2.1, r.2.2 impose a H M
leaching chance constraint
5) Nitrate leaching from the whole farm (ANL)
a. 1.1 Restrict ANL (screen) M L H
Note: H : high performance; M: medium performance; L: low performance;
* : indicate that this level depends on the grower’s risk-attitude;
**: indicate that this contract designs can effectively reduce nitrate leaching from seed corn

production in this analysis; however, this result does not consider other substitute
practices, which might indeed increase nitrate leaching. Examples are the switch from
a seed corn/potato rotation to a seed corn/tomato rotation. In this case, nitrate leaching
might not be reduced.

As Table 9.1 indicates contracts can be redesigned to to encourage “green”

205

production practices. However, enforcement is the key to determining the feasibility of
alternative contract designs. These “green” contract designs may affect the stability of
earnings and their impacts will depend on grower risk aversion. It is possible to shift
the NPSP abatement cost between the processor and the grower through the contract
payment; however, it will depend on their relative bargaining power. If the current
contract payment is just meeting the participation constraint, the processor may have to
absorb the full cost to induce the growers to change practices. However, if the
payment is higher than the participation constraint, the processor and the grower can

share the NPSP abatement costs.

9.3 Policy Implications

Contract farming provides a new way of production in U.S. agriculture. This
trend is expected to intensify for three reasons. First, consumers increasingly demand
“identity-preserved” products (including ones produced in environmentally friendly
fashion). A second reason is the increase in proprietary technologies, especially,
genetic engineering. The third reason is due to the new change in the U.S. farm policy.
“Freedom to Farm” in the 1996 Farm Bill is a cornerstone for changes in the U.S.
governmental farm programs. This policy indicates that less subsidies as well as
restrictions will be made by the government in the future. As a result, contract farming
will become an attractive way for agricultural production because it provides a means
of risk management as well as attractive income. Improving environmental quality

through appropriate design of contractual production or arrangement becomes a

206

promising alternative.

Evidences have shown that agribusiness has begun business-led self-regulation
(Batie, 1997). If processing ﬁrms are willing to undertake voluntary nonpoint source
pollution reduction, one issue to be addressed is how to achieve socially optimal
abatement. Appropriate information on social beneﬁts (or social damage costs) has to
be provided to the processing ﬁrms. Such information can be obtained through various
nonmarket valuation methods, such as contingent valuation and hedonic prices.

Looking beyond grain crops, a much broader set of contract design potentials
emerge. The applicability of the concept to redesign contracts goes beyond merely

managing nitrate leaching. What is the role for government? Several possibilities

include:

1. To develop and promote less environmentally harmful practices and whole-farm
systems.

2. To provide more information on identifying pollutant thresholds that are socially
optimal.

3. To develop reliable and low cost monitoring techniques to verify the grower’s

pollution-generating actions. Enforceability is a key issue in designing a
workable contract design that will induce a contracted-grower voluntarily to
reduce nonpoint source pollution.

4. To provide cost-sharing to processing ﬁrms to enhance their environmental
stewardship.

5. To provide clear signals as to future liability if serious NPSP persists.

207

9.4 Limitations and Suggestions for Future Research

Although the results of the principal-agent approach were successful in meeting
the research objectives in this case study, there are limitations to this research. First,
the use of nitrate leaching data simulated from DSSAT 3.0 as a proxy for the real
nitrate leaching data ignores the variations across different locations, soils, slopes, and
aquifers. The public is concerned with environmental and health damages, not leaching
per se. The relationship between nitrate leaching, nitrate concentration, and exposure
as well as dose-response resulting in actual damages has to be considered.

Second, although this one-period representative whole-farm approach
demonstrates how alternative contract designs inﬂuence the representative farmer’s
behavior, variations in farm locations, socio—demographic characteristics, management
practices, and technological differences are not incorporated in this analysis. In both
NPSP control and contract design contexts, the dynamic relationship between the
processor and among growers is important. For instance, contracted growers can
negotiate to abate N PSP, or can collude with the processors. If negotiation is feasible,
a high abatement grower can “bribe” a low abatement-cost grower to reduce leaching.
This problem could potentially be modeled in the context of game theory to examine the
dynamics among multiple players, though it was not modeled in the analysis.

Third, the agronomic practices examined in this analysis are limited to four
crops and three nitrogen treatments (that is, high, medium, and low). Although
forbidding rotation with potatoes grants a promising way to reduce nitrate leaching

from seed corn production, this conclusion ignores the possibility for alternative

208

substitute crops, such as cucumbers and carrots, which require high levels of nitrogen
fertilizer and could result in high nitrate leaching as well.

Fourth, high product quality is one of the main objectives of production under
contract. How input use is related to product quality is not examined in this analysis,
since grain quality is not a major factor in seed corn contracts. However, reducing
nitrogen use in horticultural crops may lead to product quality reduction, with
concomitant reduction in the prices received. This result implies that product price
itself can become an indirect function of nitrogen fertilizer or other input use.

The ﬁfth limitation is related to the assumption that growers are not concerned
about direct environmental beneﬁts. In fact, there is evidence to the contrary. A
grower’s health might be associated with water quality, especially when growers
directly use groundwater near their farms. If growers do care for environmental
quality, they could reduce nitrogen use voluntarily (Swinton et al., 1997), as some have
already in St. Joseph County (Hesterman et al., 1993; MASA, 1997).

Although this research has shown the feasibility of designing a “green” contract,
three areas deserve further research. First, if the processor is motivated to reduce
nitrate leaching and expects the contracted grower to bear the attendant costs, the
prevention of cheating is quite important. If enforcement mechanisms are available and
effective, the range of feasible alternative contracts expands. Thus, the development of
accurate, low-cost veriﬁcation techniques that can easily be applied to detect and
measure compliance is an important research priority. The development of accurate

monitoring techniques also can lead to better nitrogen management. For instance, one

209

potential approach is to incorporate a nitrogen use efﬁciency ratio into the contract
design (Ritchie, 1997). The ratio is calculated by nitrogen removed by harvested mass
divided by nitrogen fertilizer input and growers are penalized if their ratios fall below a
certain level. Nitrogen fertilizer is ultimately leached if not used by the plant in a
sandy loam soil. Through this method, the amount of nitrate leaching can be
effectively controlled. .

The second area is to incorporate the dynamics of multiple heterogeneous
polluters in a nonpoint source pollution abatement model. An NPSP contract design
needs to consider each polluter’s characteristics (location and technology) and potential
behavior (cooperation or cheating). A nonpoint source pollutant may involve multiple
environmental media (surface- and ground- water) and multiple processors.
Furthermore, the interactions among these factors need further exploration.

The third area is the exploration of other new means for nonpoint source
pollution control. Using contract designs is only one approach for voluntary NPSP
reduction. There are other approaches, such as green codes and ecolabeling.

Voluntary nonpoint source pollution reduction is a growing phenomenon.

APPENDICES

211

APPENDIX A

PARAMETERS USED IN CROP GROWTH SIMULATION MODEL DSSAT 3.0

CULTIVARS: GENOTYPE

1 Soybean: 990002 M GROUP 2
2 Seed corn: IB0070 P38

3 Commercial corn: PIO 3475

4 Potato: Russet burbank

FIELDS

Specify ﬁeld location (St. Joseph County). weather data (Three Rivers and Ft. Wayne),
and soil data (sandy loamy).

SOIL PROFILE INITIAL CONDITIONS
Specify water content, soil ammonium, soil nitrate, and soil pH all by layer.

PLANTING DETAILS .
Specify the planting data (5/16/51 in this case), plant population, and planting depth.

IRRIGATION AND WATER MANAGEMENT
Assume to be automatically managed, i.e., when water is needed, the system will turn
on irrigation.

FERTILIZERS MANAGEMENT DATA (INORGANIC)
Specify fertilizer application date, type of nitrogen fertilizer, total amount applied,
depth of application.

RESIDUES AND OTHER ORGANIC MATERIALS

HARVEST DETAILS
Specify the harvest date.

SIMULATION CONTROLS
Specify starting date of the simulation, date of measuring, and years.

212

APPENDIX B
WEATHER INPUT FOR DSSAT 3.0

Table B.l: Mean average weather data during 1951-1992

 

 

Total Average Average Average
Year rainfalll max. temp.1 min. temp.l sol. rad.2
(mm) (0C) (0C)
1951 1152.9 15.55 3.69 13.40
1952 978.9 16.43 4.17 17.37
1953 792.9 17.43 4.73 14.53
1954 1317.6 16.09 4.33 14.05
1955 913.5 16.38 3.87 14.83
1956 807.4 15.76 3.31 14.23
1957 1038.4 15.44 3.92 13.60
1958 910.8 14.93 2.84 14.21
1959 943.1 15.95 4.26 14.12
1960 786.2 14.97 3.66 14.01
1961 918.4 15.37 3.55 13.95
1962 674.8 15.47 3.55 14.40
1963 612.4 16.07 2.85 14.91
1964 703.1 16.43 3.99 14.39
1965 1022.2 15.46 4.09 14.11
1966 771.3 15.00 3.34 14.65
1967 909.2 14.00 3.26 13.85
1968 1011.3 14.66 3.86 14.22
1969 834.3 14.35 3.49 13.80
1970 905.2 14.85 3.85 13.74
1971 631.2 15.95 3.99 14.58
1972 979.7 14.68 3.80 13.50
1973 962.8 16.40 5.37 13.45
1974 859.6 15.68 3.90 13.99
1975 959.0 15.80 4.27 14.02
1976 977.8 15.05 1.92 15.11
1977 957.6 16.31 3.83 14.16
1978 966.7 14.78 2.87 14.52
1979 1065.6 14.73 3.30 13.56
1980 1037.4 14.96 3.62 13.80
1981 1137.0 15.32 4.04 13.59
1982 1052.5 15.58 4.10 13.86
1983 951.2 16.33 4.40 14.05
1984 997.0 15.58 4.34 13.82
1985 1094.6 16.03 4.50 14.27
1986 1072.7 16.02 4.84 13.75
1987 963.6 16.97 5.24 14.32
1988 940.1 15.42 3.01 15.13
1989 958.5 14.12 2.44 14.36
1990 1248.5 15.47 4.04 13.90
1991 849.6 15.71 5.00 14.55
1992 922.9 14.01 3.22 13.58

 

(Source: national weather station from lThree Rivers, Michigan and 2Fort Wayne, Indiana)

213

APPENDIX C

COEFFICIENTS IN THE WHOLE-FARM PROGRAMMING MODEL

Table C. 1: Machinery working rates

 

 

Total Resource Required

Hours/ Machineﬂm Working Rate
M chin N d A /H

a e ame ay Tractor hrs Labor hrs ( cre r)

11 1' E E' HE .
P&K spreader 12 1.00 1.00 20.00
Chisel plow 18 ft 12 1.00 1.00 10.47
V-ripper 30" DC. 17ft 12 1.00 1.00 10.51
1 I l . E E _ 1 .
Finish tmd disk 33ft 12 1.00 1.00 17.00
Comb ﬂd cul incorp 33ft 12 1.00 1.00 23.80
1 1 1 . E l .
Min-til planter 16-30 11 1.00 1.50 12.73
1 I 1 . E E -E1 .
Rotary hoe 12 1.00 1.00 37.09
Cultivator 12 1 .00 1 .00 15 .40
Anhydrous 30ft 12 1.00 1.00 12.73
Center pivot irrigation 24 0.00 mm (all)
1 l 1 . E H .
Combine 10 1.00 2.50 5.09

 

(Source: Doane’s Agricultural Report, 1996)

214

Table C.2: Time periods and suitable days for field work

 

 

 

Suitable Days
No. Description Total Days for ﬁeld work
1 Apr 15-Apr 21 7 3.0
2 Apr 22-Apr 25 4 1.7
3 Apr 26-May 2 7 3.1
4 May 3-May 9 7 3.5
5 May 10-May 16 7 3.8
6 May 17-May 23 7 4.3
7 May 24-May 30 7 5.0
8 May 31-Jun 6 7 5.1
9 Jun 7-Jun 13 7 5.1
10 Jun 14-Jun 20 7 4.2
11 Jun 21-Jun 27 7 3.8
12 Jun 28-Jul 4 7 4.8
13 Jul 5-Jul 11 7 5.5
14 Jul 12-Aug 29 49 36.7
15 Aug 30—Sep 12 14 10.3
16 Sep l3-Sep 19 7 4.8
17 Sep 20-Sep 26 7 4.8
18 Sep 27-Oct 10 14 13.9
19 Oct ll-Oct 31 21 10.8
20 Nov l-Nov 21 21 5.1
21 Nov 22-Dec 5 14 1.3
22 Dec 6-Mar 31 116 0.0
23 Apr l-Apr 14 14 4.0

 

(Sources: Rosenberg et al., 1982; Doster et al., 1994; and King, 1995)

215

Table C.3: Yield adjustment and moisture level sets

A. Commercial Corn

A.l Yield adjustment for commercial corn (percent)

 

 

 

 

 

 

 

 

 

Hamempd
Sep 27 Oct 11 Nov 1 Nov 22
Plant Period to to to to
Oct 10 Oct 31 Nov 21 Dec 5
Apr 22-Apr 25 96.0 96.0 93.0 86.0
Apr 26-May 2 100.0 100.0 95.0 90.0
May 3-May 9 96.0 98.0 95.0 90.0
May 10-May 16 91.0 94.0 91.0 86.0
May 17-May 23 0.0 84.0 84.0 81.0
May 24-May 30 0.0 74.0 74.0 71.0
May 3l-Jun 6 0.0 0.0 0.0 55.0
(Source: Black and King, 1995)
A.2 Moisture level (precent)
Hmﬁcripd
Sep 27 Oct 11 Nov 1 Nov 22
Plant Period to to to to
Oct 10 Oct 31 Nov 21 Dec 5
Apr 22-Apr 25 26.0 22.0 19.0 18.0
Apr 26-May 2 28.0 22.0 19.0 18.0
May 3-May 9 26.0 24.0 20.0 19.0
May 10—May 16 28.0 26.0 21.0 19.0
May 17-May 23 0.0 24.0 23.0 20.0
May 24-May 30 0.0 27.0 26.0 22.0
May 31-Jun 6 0.0 0.0 0.0 23.0

 

(Source: Black and King, 1995)

216

B. Soybean yield adjustment (percent)

 

Harvest Period

 

 

 

 

 

 

Sep 20 Sep 27 Oct 11
Plant Period to to to
Sep 26 Oct 10 Oct 31
Apr 26-May 2 98.0 98.0 94.0
May 3-May 9 99.0 99.0 95.5
May 10—May 16 100.0 100.0 97.0
May l7-May 23 99.0 99.0 96.0
May 24-May 30 0.0 95.0 92.0
May 31-Jun 6 0.0 91.0 88.0
Jun 7-Jun 13 0.0 86.0 83.0
(Source: Black and King, 1995)
C. Seed Corn yield adjustment (percent)
HamesLPeripd
Aug 30 Sep 13 Sep 20
Plant Period to to to
Sep 12 Sep 19 Sep 26
Apr 26-May 2 100.0 100.0 100.0
May 3-May 9 0.0 100.0 100.0
May lO-May 16 0.0 0.0 100.0

 

(Source: Miron and King, 1995)

217

 

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220

APPENDIX D

OPTIMAL CROP ENTERPRISES FROM EXPECTED UTILITY
MAXIMIZATION

Table D.l: Optimal mixed of crop enterprises from expected utility maximization
for alternative contract designs under three levels of risk-aversion

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Coeﬁrcrent oi Risk-Aversion (1)
1:0 A=10" A=10“
Strate ies Entegp. Name Acreage Entem. Name Acrgge Emery. Name m
PSEED(M) 500 PSEED(M) 500 PSEED(M) 500
Unrestricted base model PCORN (M) 246 PCORN (M) 350 PCORN (L) 100
BCORN(L) 103 POTATO 850 POTATO 600
SOYBEAN 103
POTATO 746
la. 1 . l BSEED(M) 374 BSEED(M) 374 BSEED(M) 500
Restrict ANL to 35 lblac PSEED(M) 126 PSEED(M) 126 PCORN (L) 73
(Whole farm) BCORN (L) 350 BCORN(L) 350 BCORN(L) 27
SOYBEAN 724 SOYBEAN 724 SOYBEAN 527
POTATO 126 POTATO 126 POTATO 73
la. 1.2 BSEED(M) 483 IBSEED(M) 483 BSEED(L) 47$
Restrict ASNL to 35 Iblac PSEED(M) ‘ l7 PSEED(M) l7 PSEED(M) 25
(Seed corn) PCORN(M) 350 PCORN(L) 350 PCORN(L) 100
SOYBEAN 483 SOYBEAN 483 SOYBEAN 475
POTATO 367 POTATO 367 POTATO 125
a.2 PSEED(L) soo :IPSEEDG.) soo PSEED(L) 500
Restrict N fert. to 107 lblac PCORN (M) 246 PCORN (M) 350 PCORN(L) 100
BCORN(L) 104 POTATO 500 POTATO 600
SOYBEAN 246
POTATO 746
Ia.3 BSEED(M) 500 BSEED(M) 500 BSEED(M) 500
No rotation with potato PCORN (M) 350 PCORN (L) 350 PCORN(L) 100
SOYBEAN 500 SOYBEAN 500 SOYBEAN 600
POTATO 350 POTATO 350 POTATO 100
b. l BSEED(M) 457 PSEED(M) 500 PSEED(M) 500
Charge 10 ¢/Ib on NL> 3O PSEED(M) 43 PCORN (M) 350 PCORN(L) 100
lblac PCORN (M) 350 POTATO 850 POTATO 600
SOYBEAN 43
POTATO 807
b.2 BSEED(M) 457 PSEED(L) 500 PSEED(M) 500
Charge 15 Cllb on N fert. PSEED(L) 43 PCORN (M) 350 PCORN(L) 100
> 901b/ac PCORN (M) 350 POTATO 850 POTATO 600
SOYBEAN 43
POTATO 807
c. l PSEED(L) 500 PSEED(M) 500 PSEED(M) 500
Fixed pay: $253 lac plus BCORN (L) 104 PCORN(M) 350 PCORN(L) 100
var. pay: $3.96 PCORN(M) 246 POTATO 850 POTATO 600
SOYBEAN 104
POTATO 746
c.2 PSEED(L) 500 PSEED(M) 500 PSEED(M) 500
Fixed pay: $230 lac plus BCORN (L) 104 PCORN(M) 350 PCORN(L) 100
var. pay: $3.96 PCORN(M) 246 POTATO 850 POTATO 600
SOYBEAN 104
POTATO 746

 

 

 

 

 

 

(Source: GAMS whole-farm optimization)

221

Table D. 1: Optimal mixed of crop enterprises from expected utility maximization
for alternative contract designs under three levels of risk-aversion (continuous)

 

 

 

 

 

 

 

 

 

 

 

Coerfment o? Rislt-Aversion A)
A=0 A=10‘s A=10“
Strategies Entegp. Name Acreage Entegp. Name Acreage Entem. Egg Acme
PSEED(M) 500 PSEED(M) 500 PSEED(M) 500
Unrestricted base model PCORN (M) 246 PCORN (M) 350 PCORN (L) 100
BCORN (L) 103 POTATO 850 POTATO 600
SOYBEAN 103
POTATO 746 _
ll'. 1 . l SSEED(L) l 15 SSEED(L) l 15 SSEED(L) 115
Restrict Prob(SNLz 35)s 1l2 BSEED(L) 385 BSEED(L) 385 BSEED(L) 385
PCORN(M) 407.5 PCORN(L) 407.5 PCORN(L) 157.5
SOYBEAN 385 SOYBEAN 385 SOYBEAN 385
POTATO 407.5 POTATO 407.5 POTATO 157.5
r. l .2 SSEED(L) 299 SS EED(L) 299 SSEED(L) 299
Restrict Prob(SNL2 35)s BSEED(L) 201 BSEED(L) 201 BSEED(L) 201
1/10 PCORN(M) 454 PCORN(M) 499.5 PCORN(L) 249.5
BCORN(L) 46 SOYBEAN 201 SOYBEAN 201
SOYBEAN 247 POTATO 499.5 POTATO 249.5
POTATO 454
r.2. l PSEED(L) 500 PSEED(L) 500 PSEED(L) 500
Restrict Prob(SNL24O)s 1/2 PCORN (M) . 246 PCORN (M) 350 PCORN(L) 100
BCORN(L) 104 POTATO 500 POTATO 600
SOYBEAN 246
POTATO 746
Ir.2.2 BSEED(M) 500 BSEED(M) 500 BSEED(M) 500
Restrict Prob(SNL2 40):. PCORN (M) 350 PCORN (L) 350 PCORN(L) 100
1/10 SOYBEAN 500 SOYBEAN 500 SOYBEAN 6m
POTATO 350 POTATO 350 POTATO 100

 

 

 

 

 

(Source: GAMS whole-farm optimization)

222

APPENDIX E

PROOF THE EQUIVALENT CONDITION OF A CHANCE CONSTRAINT

To prove probog yo ) _< I/g" implies t - g*8(a,t) 2y0, this study uses the low
partial moment (LPM), presented by Fishbum (1977). A general form of the low

partial moment is deﬁned as:

p<a¢>= f (t-x)“/(x)dx

where t is a risk reference level of income, and a is a positive constant. Let ﬂbe

deﬁned as the positive a" root of Fishburn’s lower partial moment, i.e., .6 = p‘".

9(a,t)= f (t-x)“f(x)dx

l-p6(a,t) l

= f (t—x>:r(x)dx+ f (r—x):/(x)dx
—w l-p9(a,t)

l-p6(a,t)

2 f (t-x)°f/(x)dx

‘W

Because rel-w, t-p6(a,t)], the minimum value of (t-x) equals p6(a:,t). Therefore,

r-p6(a,t)

P(a,t)2 P“P(a,t) f ﬂﬂdx

Therefore, implies:

223
Prob(xs t-p6(a,t))sI/p"
The upper limit can be derived to satisfy this constraint. Let a =1, p=g*; the sufﬁcient

condition to satisfy this constraint is:

xogt-p6(1,t) = t-g*6(1,t) Q.E.D.

The next section proves that L’ - h’ 2 (L .- - L—) p I. 2 0 is sufﬁcient to ensure the constraint
1.,le

Prob(L 2 L ) _< I/h’ (Atwood, Watts, and Helmets, 1988).
ML 21) = M L-L50)
Because it was proven above that the sufﬁcient condition to satisfy the constraint
Prob(xs t-p6(1,t))51/p
is xost-p6(1,t) = t-g*6(1,t), hence, the sufﬁcient condition for M L-Ls0): I/h‘
becomes:

L'- ME (Li-1:)pi20.

L,2L

224

APPENDIX F

GAMS VERSION OF PC-LP WHOLE-FARM PROGRAMMING MODEL

STITLE " Michigan Seed Corn Farm (PCLP a la GAMS) "

*tiiiiﬁﬁki$tttl~ﬁ$

#N'ﬁliiﬁﬂ-

The authors would like to promote the dissemination of this
program through as many channels as possible. However, we
do wish to rain copyright on the program and request
notification of any plans to redistribute the program.

Redistribution and use of this program is permitted provided that
this notice is preserved and that due credit is given to the
Purdue Research Foundation and the authors listed below:

Authors: Craig Dobbins, Martin Etyang, Hayri Onal, Paul V. Preckel
Translations, derivative works, or aggregate works incorporating
this program must be covered under this copyright notice. That
is, you may not produce a derivative work from this program and
impose additional restrictions on its distribution. Exceptions
to this rule may be granted by special permission from the
authors. Please contact the program use coordinator
<preckel@agecon.purdue.edu).

The orginal program developed by Dobbins et al., has been modified by
Mei-Chin Chu. Several changes are made in order to meet

the following goals:

1. The whole-farm planning of a seed corn contracted-grower

2. Chance constraints on contract loss and nitrate leaching reduction
3. Mean-Variance Expected utility of the grower

4. The gross margin of the seed corn processing firm

SOFFSYMLIST
SOFFSYMXREF
option lp=minosS ;

OPTION DECIMALS = 6 ;
OPTION LIMROW 2

I
I

OPTION LIMCOL = O .
OPTION ITERLIM = 100000;
*%%%%%%%%%%%%%% SETS %%%%%%%%%%%%%
SETS
CROP Crops
/CO, SC, BN, PO /
PRODUCT Commodities primary
/CORN, SEED, BEAN, POTATO /
PER Periods

##tl‘tt

ﬁﬁﬁi

/APR3,APRMAY,MAY1,MAY2,MAY3,MAY4,MAYJ,JUN1,JUN2,
JUN3,JUNJLY,JULY,JLYAUG,AUGSEP,SEPl,SEP2,SEPOCT,OCT,NOV,

NOVDEC,APR1,APR2/
The time periods are defined as follows:
APR3 : Apr.22-25; APRMAY: April 26-May 2;
MAYl : May 3-9; MAYZ : May 10-16; MAY3 : May 17-23 ; MAY4 : May24-30;
MAYJ : MAYBl-June 6; JUNl : June 7-13; JUNZ : June 14-20; JUN3: June 21-27;

JUNJLY: June 28-July 4; JULY : July 5-11;JLYAUG:July 12-Aug. 29;
AUGSEP: Aug.30-Sep.12; SEPl : Sep.l3-19; SEPZ : Sep. 20-26;

SEPOCT: Aep.27-Oct.10; OCT : Oct.ll-31;

NOV : Nov.1-21; NOVDEC: Nov.22-Dec.5.

APRl : Apr.l-l4; APRZ : Apr.15-21;

Source: Rod King, Extension Director in St. Joseph County, Michigan

225

state states of nature
/ 1 * 10 /

PPER(PER) Planting periods
/APR3,APRMAY,MAY1,MAY2,MAY3,MAY4,MAYJ,JUNl/

HPER(PER) Harvesting periods
/AUGSEP,SEP1,SEP2,SEPOCT,OCT,NOV,NOVDEC/

PLPER(PER) Plowing periods
/OCT,NOV,NOVDEC,APR1,APR2/

NOPER(PER) Periods when no activities take place

PRAC Production practice (nitrogen fertilizers applied here)
/HIGH, MEDIUM, LOW, NNA/

ITEMS Cost items

/FERTIL,herb,insect,SEED,IRRIG,OTHER/
EQUIP Farm equipment types

/PKS,MOLDB,CHISEL,vrip,DISC,COMB,PLANT,CULT,ROTHOE,ANHY/
EPLOW(Equip) Plowing equipment
/PKS, CHISEL,vrip/
EPREP(Equip) Preparation equipment
/DISC, COMB/
EPLANT(Equip) Planting equipment
/PLANT/
EPOST(Equip) Postplanting equipment
/CULT,ROTHOE,ANHY/ ;

ALIAS (PER,PERIOD,per1,period1), (CROP,PRCROP,cr1,prcl),
(state,states),(product,prodl),(prac,prac1),(hper,hper1);

*%%%%%%%%%%%% RESOURCES .%%%%%%%%%%%%%%%%%%%%%%%%%
SCALAR LANDRHS Land availability (acres) /1200/
HARVESTER Number of combine harvesters /l/

MAXLAND Maximum amount of rented land (acres) /500/
MAXSEED Maximum amount of seed corn contract (acres) /500/
TRACTOR Number of tractors /2/

PARAMETER
DAYS<Per) number of working days by time period
/ APRl 4.0, APRZ 3.0, APR3 1.7, APRMAY 3.1,
MAYl 3.5, MAYZ 3.8, MAY3 4.3, MAY4 5.0,MAYJ 5.1,
JUNl 5.1, JUN2 4.2, JUN3 3.8, JUNJLY 4.8,
JULY 5.5,JLYAUG 36.7, AUGSEP 10.3, SEPl 4.8,SEP2 4.8,
SEPOCT 13.9, OCT 10.8, NOV 5.1, NOVDEC 1.3/

PARAMETER
WORKER(Per) Number of hired workers in each period

/ APRl 2, APRZ 2, APR3 2, APRMAY 2,
MAYl 2, MAYZ 2, MAY3 2, MAY4 2, MAYJ 2,
JUNl 2, JUN2 2, JUN3 4, JUNJLY 4,
JULY 4, JLYAUG 4, AUGSEP 2, SEPl 2, SEPZ 2,
SEPOCT 2, OCT 2, NOV 2, NOVDEC 2/

FARMER(Per) Number of family members available for farm work

/ APRl 1, APRZ 1, APR3 l, APRMAY 1,

MAYl 1, MAYZ 1, MAY3 1, MAY4 l, MAYJ 1,

JUNl 1, JUN2 1, JUN3 l, JUNJLY 1,

JULY 1, JLYAUG 1, AUGSEP 1, SEPl 1, SEPZ l,

SEPOCT 1, OCT 1, NOV 1, NOVDEC 1/

SCALARS

HRSPERDAY Number of net field work hours per day /12/
HRSPERDAYC Number of field hours for combine /lO/
HRSPERDAYP Number of field hours for planter /ll/ ;

PARAMETERS TRACRHS(Per) Tractor power capacity (hrs)
EQUIPRHS(Equip,Per) Farm equipment capacity (hrs)
COMBRHS(Per) Combine harvester capacity (hrs)
MAXHIRE(Per) Maximum amount of hired labor (hrs)

226

OWNLAB(Per) Self employed labor in regions (hrs) ;
EQUIPRHS(Equip,Per) = Days(Per)*hrsperday;
EQUIPRHS('PLANT',PER) = Days(Per)*hrsperdayp;
TRACRHS(Per) TRACTOR*DAYS(Per)*HrsPerday;
COMBRHS(Per) HARVESTER*DAYS(Per)*HrsPerDayc;
OWNLAB(Per) FARMER(Per)*DAYS(Per)*HrsPerDay;
MAXHIRE(Per) WORKER(Per)*DAYS(Per)*HrsPerDay;
*%%%%%%%%%%%%% INPUT REQUIREMENTS & TECHNOLOGY PARAMETERS %%%%%%%%%%%%%%%%

* Tractor times are obtained by inverting the working rates (i.e. l/workrate)
* Source: Doane's Agricultural Report 58 (April 1995).

Parameter POSTLAG(CROP) Time lag between planting and postplanting
/CO 3, SC 3, EN 3, PO O/;

TABLE PLEQUIP(PrCrop,Crop,Equip) plowing equip rates(hrs per acre)

PKS CHISEL vrip MOLDB
CO.CO 0.042 0.0 0 0.120
BN.CO 0.042 0.0953 0 0
PO.CO 0.042 0.0953 0.0951 0
SC.SC 0.042 0.0 O 0.120
BN.SC 0.042 0.0953 0 0
PO.SC 0.042 0.0953 0.0951 0
SC.BN 0.042 0.0953 0 0
CO.BN 0.042 0.0953 0 0
CO.PO 0.042 0.0953 0 0
SC.PO 0.042 0.0953 0 0 ;

parameters PLOWLAB<PrCrop,CROP) Labor requirement for plowing
PLOWTRAC(PrCrop,CROP) Labor requirement for plowing;
PLOWLAB(PrCrop,CROP) = sum(equip,plequip(PrCrop,crop,equip));
PLOWTRAC(PrCrop,CROP) = sum(equip,plequip(PrCrop,crop,equip));

TABLE PrEQUIP(CROP,EQUIP) Preparation equip rates (hrs per acre)

DISC COMB
CO 0.05882 0.042
SC 0.05882 0.042
BN 0.05882 0.042

PO 0 0 ;
parameters PrepLAB(CROP) Labor requirement for plowing
PrepTrac(CROP) Tractor requirement for plowing;
PrepLab(CROP) = prequip(crop,'disc')*0.5+prequip(crop,'comb');
PrepTrac(CROP) = prequip(crop,'disc')*0.5+prequip(crop,'comb');
* PrepLab(CROP) = sum(equip,prequip(crop,equip));
* PrepTrac(CROP) = sum(equip,prequip(crop,equip));

TABLE NFEng(PrCrop,Crop,Prac) Nitrogen fertilizer applied (kgs per hacter)

HIGH MEDIUM LOW NNA
CO.CO 190 170 150 0
BN.CO 150 130 110 O
PO.CO 190 170 150 0
SC.SC 140 130 120 0
BN.SC 100 90 8O 0
PO.SC 140 130 120 0:

Parameters NFER(PrCrop,Crop,Prac) nitrogen fertilizer applied (lbs per acre);
NFER(PrCrop,Crop,Prac)=NFEng(PrCrop,Crop,Prac)/1.12;

parameters PLANTeq(CROP,equip) Planting equipment rates(hrs per acre)
/ CO.plant 0.0787, SC.plant 0.1574, BN.plant 0.0787, PO.plant 0/
PLTLAB(Crop) Planting labor coefficients (hrs per acre)
/ CO 0.11811, SC 0.23438, BN 0.11811, PO 0/
PLTTRAC(Crop) Tractor coeffs. for planting Crop (hrs per acre)

227

/ CO 0.11811, SC 0.23438, BN 0.11811, PO 0/ ;

TABLE POSTEQUIP(PRCROP,CROP,EQUIP) Postplanting equip rates (hrs per acre)

ROTHOE CULT ANHY
CO.CO 0.0270 0.0647 0.0833
BN.CO 0.0270 0.0647 0.0833
PO.CO 0.0270 0.0647 0.0833
SC.SC 0.0270 0.0647 0.0833
BN.SC 0.0270 0.0647 0.0833
PO.SC 0.0270 0.0647 0.0833
CO.BN 0.0270 0.0647 0
SC.BN 0.0270 0.0647 0 ;

parameter PostLab(PrCrop,Crop) labor requirement for post-planting
PostTrac(PrCrop,Crop) tractor requirement for post-planting ;

PostLab(PrCrop,Crop)=sum(equip,postequip(prcrop,CROP,EQUIP));
PostTrac(PrCrop,Crop)=PostLab(prcrop,CROP);

parameter PostTime(Crop) Time period for doing postplanting
/CO 3, SC 3, EN 2, po 0/;

parameters HAVLAB(Crop) Harvesting labor coefficients (hrs per acre)
/ CO 0.4912, SC 0, EN 0.4912, PO 0/
HAVTRAC(Crop) Tractor coefficients for harvest (hrs per acre)
/ CO 0.1961, SC 0, EN 0.1961, PO 0/
COMB(Crop)~ Harvester coefficients (harvesting) hrs per acre
/ CO 0.1961, SC 0, EN 0.1961, PO 0/ ;

* The above figures are inverse of working rates for plowing and chiseling
* Source: Doane's Agricultural Report 58 (April 1995).

TABLE PERCYLD(Crop,Per,Period) Crop yield changes (%) from optimum yields

* Per is planting time, Period is harvest time

AugSep Sepl Sep2 SepOct Oct Nov NovDec
CO.Apr3 0.96 0.96 0.93 0.86
CO.AprMay 1.00 1.00 0.95 0.90
CO.Mayl 0.96 0.98 0 95 0.90
CO.MayZ 0.91 0.94 0.91 0.86
CO.May3 0.84 0.84 0.81
CO.May4 0.74 0.74 0.71
CO.MayJ 0.55
SC.AprMay 1.00 1.00 1.00
SC.Mayl 1.00 1.00
SC.May2 1.00
Bn.AprMay 0.98 0.98 0.94 0 0.
Bn.Mayl 0.99 0.99 0.955 0 0.
Bn.MayZ 1.00 1.00 0.97 0 0.
Bn.May3 0.99 0 99 0.96 0 0.
Bn.May4 0.00 0.95 0.92 0 0.
Bn.MayJ 0.00 0.91 0.88 O 0.
Bn.Jun1 0.00 0 86 0.83 0 0.0

Po.may1 1.00 ;
*Source: Consult with Rod King and Dr. Roy Black (1996).

PERCYLD(Crop,Per,Period)$(NOT PPER(Per))= 0;
PERCYLD(Crop,Per,Period)$(NOT HPER(Period))=0;

PARAMETER FIRSTPLANT<Crop) First planting period for crops ;
FIRSTPLANT(Crop) = 0 ;

LOOP(CROP,
LOOP(PER$(FIRSTPLANTiCrOp) E0 0),
FIRSTPLANT(Crop)=ORD(Per)$(SMAX(PERIOD,PERCYLD(CROP,PER,PERIOD)) GT 0))) ;

PARAMETER LASTPLANT(Crop) Last planting of crops ;
LASTPLANT(Crop) = 0 ;

LOOP(CROP,

LOOP(PER$(ORD(PER)
LASTPLANT(CROP)

TABLE MOIST(Per,Period)

APR3

APRmay

MAYl
MAYZ
MAY3
MAY4
MAYJ

SCALAR

TABLE sYLDl(PRODUCT,PrCrop,Crop,Prac,state) Expected crop yields (kg per
hectare)
1 2 3 4 5
CORN CO.CO.high 7833.5 10518.5 11034.25 12800.5 11930.5
CORN BN.CO.high 7905.25 10517 10966.5 12798.75 11929
CORN PO.CO.high 7833.5 .10519.00 10966.00 12807.75 11929.25
SEED SC.SC.high 4614.00 5257.75 5679.25 5943.25 6069.75
SEED BN.SC.high 4604.00 5250.50 5667.50 5929.75 6060.00
SEED PO.SC.high 4627.75 5250.25 5667.25 5958.25 6060.50
CORN . CO.CO.medium 7762.75 10491.25 10916 12700.5 11921
CORN BN.CO.medium 7823.5 10497.75 10945.5 12766.5 11917
CORN PO.CO.medium 7900.25 10501.50 10927.50 12789.50 11917.50
SEED . SC.SC.medium 4601.75 5225.75 5644.00 5917.75 6058.00
SEED . BN.SC.medium 4615.50 5224.75 5632.00 5896.75 6043.50
SEED PO.SC.medium 4616.00 5218.50 5629.75 5930.00 6044.50
CORN CO.CO.1ow 7712.75 10431.75 10774.5 12526.25 11817.75
CORN BN.CO.low 7762.25 10421.25 10827.50 12631.75 11869.75
CORN PO.CO.low 7837.0 10375.50 10749.75 12623.75 11870.50
SEED . SC.SC.low 4578.50 5176.75 5510.75 5827.25 6029.00
SEED BN.SC.low 4577.00 5189.25 5585.50 5823.00 6016.75
SEED PO.SC.low 4581.50 5177.00 5510.00 5885.50 6021.50
BEAN SC.BN.nna 2686.50 3137.25 3278.50 3331.50 3143.50
BEAN . CO.BN.nna 2682.75 3128.25 3272.00 3321.25 3130.50
POTATO. CO.PO.nna 1.0 1.0 1.0 1.0 1.0
POTATO. SC.PO.nna 1.0 1.0 1.0 1.0 1.0
+
6 7 8 9 10
CORN . CO.CO.high 11747 12347 13476.5 13222.5 13531.51
CORN . BN.CO.high 11749.75 12347.5 13473.25 13262.25 13584.75
CORN PO.CO.high 11747.00 12347.00 13475.75 13112.75 13449.70
SEED SC.SC.high 6336.25 6541.75 6737.75 6845.00 7161.50
SEED BN.SC.high 6344.25 6531.00 6714.50 6830.00 7154.25
SEED PO.SC.high 6338.00 6533.00 6721.50 6827.75 7160.25
CORN CO.CO.medium 11730.25 12338 13338.25 13116.25 13446.25
CORN BN.CO.medium 11740.75 12337.75 13441 13168.25 13489
CORN PO.CO.medium 11908.25 12341.00 13139.00 12998.50 13383.75
SEED SC.SC.medium 6308.50 6529.00 6720.00 6833.00 7140.75
SEED BN.SC.medium 6307.75 6517.75 6684.75 6808.00 7130.75
SEED PO.SC.medium 6314.00 6519.50 6696.75 6803.00 7139.75
CORN CO.CO.low 11687.75 12301.5 12844.5 12920.25 13195
CORN BN.CO.1ow 11688.50 12313.50 13109.00 13029.25 13328.50
CORN PO.CO.low 11737.00 12316.75 12781.25 12713.00 13077.25
SEED SC.SC.low 6264.00 6503.75 6681.00 6799.50 7100.75
SEED BN.SC.low 6268.75 6497.50 6640.50 6771.00 7095.25

MOISTSTAN Dry corn moisture standard

SEPoct

0.

000000

228

PERCYLD(CROP,PER,PERIOD)) BO 0)));
* DISPLAY FIRSTPLANT,LASTPLANT ;

Moisture content Points

OCT

OOOOOOO

N

OOOOOOOO

<

/0.155/;

GE FIRSTPLANT(CROP) AND LASTPLANT(CROP) E0 0),
(ORD(PER)-l)$(SMAX(PERIOD,

(for corn only)

229

SEED . PO.SC.low 6274.50 6501.00 6658.25 6758.00 7109.00

BEAN . SC.BN.nna 3070.75 3172.25 3209.75 3164.00 3196.75

BEAN . CO.BN.nna 3075.25 3168.25 3190.00 3145.00 3192.25

POTATO. CO.PO.nna 1.0 1.0 1.0 1.0 1.0

POTATO. SC.PO.nna 1.0 1.0 1.0 1.0 1.0 ;
parameters

sYLD(PRODUCT,PrCrop,Crop,Prac,state) Converted yield (bushels per acre);
sYLD('corn',PrCrop,Crop,Prac,state)=sYLDl('corn',Prcrop,crop,Prac,state)/62.7l
sYLD('seed',PrCrop,Crop,Prac,state)=0.80*sYLDl('seed',PrCrop,Crop,Prac,state)/

62.71;

* sYLD('corn','co','co',Prac,state)=sYLD('corn','co','co',Prac,state)*0.98;

* sYLD('seed','sc','sc',Prac,state)=sYLD('seed','sc','sc',Prac,state)*0.98;
sYLD('bean',PrCrop,Crop,Prac,state)=sYLD1('bean',PrCrop,Crop,Prac,state)/67.19

sYLD('potato',PrCrop,Crop,Prac,state)=sYLD1('potato',PrCrop,Crop,Prac,state);
display syld;

* The above yields must be the best yields obtained when planting and
* harvesting activities occur at their optimum times.

PARAMETERS
YLD(PRODUCT,PrCrop,Crop,Prac) Average crop yields;
YLD(PRODUCT,PrCrop,Crop,Prac)
= sum(state,sYLD(PRODUCT,PrCrop,Crop,Prac,state))/(card(state));
Display yld;

** MEAN YIELD

PARAMETERS
d1(PRODUCT,PrCrop,Crop,Prac,state) Deviation from average crop yields;
d1(PRODUCT,PrCrop,Crop,Prac,state)
= sYLD(PRODUCT,PrCrop,Crop,Prac,state)-YLD(PRODUCT,PrCrop,Crop,Prac);

** DEVIATION FROM MEAN YIELD

PARAMETERS
vYLD(PRODUCT,PrCrop,Crop,Prac,prodl,prc1,crl,prac1) var-covariance of crop
yields;
vYLD(PRODUCT,PrCrop,Crop,Prac,prod1,prc1,cr1,prac1)
= sum(state,dl(PRODUCT,PrCrop,Crop,Prac,state)*
d1(PRODl,PrC1,Cr1,Prac1,state))/(card(state)-1);
Display vyld;

PARAMETERS
YIELD(PRODUCT,PrCrop,Crop,Prac,Per,HPer) Adjusted crop yields;
YIELD(PRODUCT,PrCrop,Crop,Prac,PPer,HPer)
= YLD(PRODUCT,PrCrop,Crop,Prac)*PERCYLD(Crop,PPer,HPer);

* The above statement adjusts crop yields with respect to planting and
* harvesting dates which are different from optimum dates

TABLE NLS(PRODUCT,PrCrop,Crop,Prac,state)Expected nitrate leaching (kg per ha)

1 2 3 4 5
CORN . CO.CO.high 18.50 17.75 25.25 28.25 25.25
CORN . BN.CO.high 20.75 24.75 27.75 32.00 28.00
CORN . PO.CO.high 55.50 52.25 46.75 57.50 64.00
SEED . SC.SC.high 21.00 22.25 27.25 34.50 32.50
SEED . BN.SC.high 20.75 26.00 27.50 33.25 32.25
SEED . PO.SC.high 53.25 51.75 44.75 56.50 69.75
CORN . CO.CO.medium 15.75 16.00 23.00 25.75 23.25
CORN . BN.CO.medium 18.75 23.50 26.00 30.25 26.75
CORN . PO.CO.medium 52.25 50.00 44.75 55.00 61.00

SEED . SC.SC.medium 18.00 18.75 24.25 30.25 28.75

SEED . BN.SC.medium 19.25 25.25 26.00 32.00 30.50
SEED . PO.SC.medium 52.00 50.00 44.00 54.75 65.50
CORN . CO.CO.low 13.00 14.00 20.25 23.00 20.50
CORN . BN.CO.low 20.25 22.50 24.75 28.75 25.75
CORN . PO.CO.low 49.00 48.50 42.50 52.25 58.25
SEED . SC.SC.low 15.50 17.00 21.50 27.00 25.75
SEED . BN.SC.low 21.75 24.50 25.25 30.50 29.75
SEED . PO.SC.low 51.50 50.25 43.25 54.75 63.50
BEAN . SC.BN.nna 16.25 23.00 24.00 35.25 30.25
BEAN . CO.BN.nna 15.50 21.25 23.25 32.75 29.00
POTATO. CO.PO.nna 89.75 116.00 184.50 184.25 133.25
POTATO. SC.PO.nna 87.25 117.75 186.00 186.75 133.25
+
6 7 8 9 10
CORN . CO.CO.high 20.25 29.25 24.25 25.75 23.25
CORN . BN.CO.high 24.25 30.50 27.00 28.75 27.00
CORN . PO.CO.high 40.75 67.00 71.50 56.25 63.25
SEED . SC.SC.high 20.75 35.50 30.25 31.50 29.50
SEED . BN.SC.high 24.25 32.50 29.50 30.00 30.25
SEED . PO.SC.high 40.50 71.25 72.25 55.75 64.75
CORN . CO.CO.medium 17.75 25.50 21.50 23.25 21.00
CORN . BN.CO.medium 23.50 29.25 25.75 27.50 26.50
CORN . PO.CO.medium 39.50 64.00 68.50 53.50 62.25
SEED . SC.SC.medium 19.75 30.00 26.75 27.00 25.75
SEED . BN.SC.medium 24.00 30.75 28.50 28.75 29.25
SEED . PO.SC.medium 39.25 67.25 68.75 55.00 63.25
CORN . CO.CO.1ow 16.75 23.00 19.25 20.25 18.75
CORN . BN.CO.low 22.75 28.00 25.00 26.25 25.75
CORN . PO.CO.low 38.25 60.25 66.75 51.00 62.00
SEED . SC.SC.low 18.75 26.50 23.50 24.00 23.00
SEED . BN.SC.low 23.50 30.00 27.75 28.50 28.00
SEED . PO.SC.low 39.00 64.25 68.25 53.75 62.00
BEAN . SC.BN.nna 18.00 30.00 28.00 27.50 27.25
BEAN . CO.BN.nna 17.25 29.00 26.75 25.75 26.00
POTATO. CO.PO.nna 82.00 175.25 154.25 108.75 122.50
POTATO. SC.PO.nna 82.50 117.50 149.75 110.00 125.75 ;

* Source: simulation data from DSSAT 3.0

PARAMETERS
NLL(PRODUCT,PrCrop,Crop,Prac,state) crops’ nitrate leaching (lbs per acre);
NLL(PRODUCT,PrCrop,Crop,Prac,state)
= NLS(PRODUCT,PrCrop,Crop,Prac,state)/1.12;
NLL(‘seed',PrCrop,'sc',Prac,state)
= (O.8*NLS('seed',PrCrop,'sc',Prac,state)+
0.2*(29.1248+1.87447*NLS('seed',PrCrop,'sc',Prac,state)))/1.12;
display NLL;

PARAMETERS
NLA(PRODUCT,PrCrop,Crop,Prac) mean nitrate leaching (kg per ha);
NLA(PRODUCT,PrCrop,Crop,Prac)
= sum(state,NLL(PRODUCT,PrCrop,Crop,Prac,state))/(card(state));
NLA(‘seed',PrCrop,'sc',Prac)
= sum(state,NLL('seed‘,PrCrop,'sc',Prac,state))/(card(state));
Display NLA;

*%%%%%%%%%%%%%%%%%%%%%%%% ECONOMIC DATA %%%%%%%%%%%%%%%%%%%%%%%%

PARAMETERS
PRICE(PRODUCT) Commodity market prices (dollars per bushel)
/ CORN 2.40, SEED 5.28, BEAN 6.00, POTATO 235 /
Truck(product) trucking cost (dollars per bushel)
/ corn 0.15, seed 0.08, bean 0.15/

Scalars

231

RENTLAND rental price for land (dollars per acre) /165/
DRYCOST Corn drying cost per pct. moisture ($ per point per bu) /0.025/

* including storage cost
NITCOST Nitrogen cost per pound (dollars) /0.25/
WAGE Market wage (dollars per hour) /7.5/
avgyld hybrid average yield /66.56/
byld plant base yield /190/
alpha variety convert factor /2.0/
beta premium factor /l.1/
RSCMC seed conditioning plus marketing costs over income /0.40/
WPS wholesale price of a 80000 kernel bag seed corn /7l.5/
TABLE COSTS(PrCrop,Crop,Items) Itemized costs by crop

FERTIL herb insect SEED IRRIG OTHER
CO.CO 33.10 20.35 16.30 26.88 24.00 39.49
BN.CO 33.10 20.35 3.25 26.88 24.00 37.99
PO.CO 25.30 20.35 3.25 26.88 24.00 39.67
SC.SC 29.04 20.35 10.75 20.00 24.00 32.42
BN.SC 29.04 20.35 0.00 20.0 24.00 30.92
PO.SC 21.70 20.35 0.00 20.0 24.00 32.60
CO.BN 16.50 26.63 0.00 13.20 0.00 26.16
SC.BN 16.50 26.63 0.00 13.20 0.00 26.16
CO.PO 10.00 0.00 0.00 0.00 28.00 4.32
SC.PO 10.00 0.00 0.00 0.00 28.00 4.32;

**Fertil: P($0.25/1b)+ K($0.13/1b) + Lime($20/ton)

* CO: 30 lbs (P), 120 lbs (K), 0.5 ton (Lime); for PO.CO 60lbs (K)
* SC: 18 lbs (P), 113 lbs (K), 0.5 ton (Lime)

* BN: 50 lbs (K), 0.5 ton (Lime)

* P0: 0.5 ton (Lime)

*

**Seed: Corn: 28 K @$0.96

* Soybean: 6O lbs@$0.22

**Seed corn: $20/A license fee

**Other: variable cost from machinery operation
**Source : 1995 Crops and Livestock Budgets Estimates for Michigan (Nott et al.
1995)

** and Rod King.

PARAMETER
P_HCOST(PrCrop,Crop,Prac) Planting PostPlanting and Harvesting costs ;
P_HCOST(PrCrop,Crop,Prac) = Sum(Items, Costs(PrCrop,Crop,Items))

+ NFER(PrCrop,Crop,Prac)*nitcost;
Display yld,price,p_hcost ;

*%%%%%%%%%%%%%%%%%%%%%% Alternative contract terms %%%%%%%%%%%%%%%%%%%%%
Scalars
** Impose a Restriction **
maxn maximum allowed nitrogen (lbs per acre) /150/
maxnl maximum allowed nitrate leaching for seed corn (lbs@acre) /100/
maanl maximum allowed nitrate leaching for the whole-farm (lbs@acre) /100/
rindex restriction on rotation with potato (one--yes) /0/
** Charge a Fee **

MAXNF nitrogen without user charge (lb@acre) /90/

MAXNLF nitrate leaching without fee (lbs@acre) /30/

nfee user charge on nitrogen use ($ per ac) /O/

nlfee user charge on nitrate leaching ($ per ac) /0/

scale scale that changes the variable payment /1/;
scalars

FIXPAY fixed payment for seed corn contract (dollars per acre) ;
fixpay = (byld - alpha*avgyld)*beta*price("corn")+
price('corn')*alpha*beta*(1-scale)*yld('seed','sc','sc','medium');

scalars
VARPAY variable payment for seed corn contract (dollars per bushel) ;
VARPAY =price('corn')*alpha*beta*scale;

232
Price('seed')=price('corn')*a1pha*beta*scale;

Display fixpay, varpay;

Parameter
Feel(PrCrop,Crop,Prac) financial charge on nitrogen use or nitrate leaching;
Fee1(prcrop,'sc',prac) = max(0,NFER(PrCrop,'sc',Prac)-maxnf)*nfee

+ max(0,NLA('seed',PrCrop,'sc',Prac)-maxnlf)*nlfee;
display feel;

Parameter
rr(PrCrop,Crop,Prac) index of restriction on rotation with potato;
rr(‘po',‘sc',prac)=rindex;

Parameter
Punish(PrCrop,Crop,Prac) Violation of contraint on contracts;
Punish(prcrop,'sc',prac) = max(NFER(PrCrop,'sc',Prac)-maxn,0)*100000
+ rr(prcrop,'sc',prac)*100000;
Parameter

Fee(PrCrop,Crop,Prac) Financial charge on nitrogen use or nitrate leaching;
Fee(PrCrop,'sc',Prac)=Fee1(PrCrop,'sc',Prac)+Punish(PrCrop,'sc',Prac);

*%%%%%%%%%%%% MISCELLANEOUS DATA %%%%%%

Table PracYes(Crop,Prac) Flag parameter for production practices
HIGH MEDIUM LOW NNA

CO 1 l 1 0
SC 1 1 1 0
EN 0 0 O 1
PO 0 0 O 1;
Table RotYes(PrCrop,Crop) Flag parameter for rotation
CO SC BN PO
CO 1 0 1 1
SC 0 l 1 1
EN 1 l O 0
PO 1 1 O 0;
PARAMETER

ACTYES(PRCROP,CROP,PRAC,PER,PERIOD) Flag parameter for planting variables ;

* This parameter shows whether each planting variable (by crop, by time of
* planting and harvesting) is included in the model. 1 means the activity
* is included, else it is not included.

ActYes(PrCrop,Crop,Prac,Per,Period)$(Perchd(Crop,Per,Period)$PPer(Per)
$HPer(Period)$PracYes(Crop,Prac)$RotYes(PrCrop,Crop))=1;
Display ACTYES;

PARAMETER PREPYES(Cr0p,Per) Flag parameter for land preparation;
PREPYES(Cr0p,Per)=l$(ORD(Per) LE LASTPLANT(Crop));

PARAMETER POSTYES(Crop,Per,Period) Flag parameter for postpl activities;
POSTYES(Crop,Per,Period) = 13((ORD(Per) GE FIRSTPLANT(Crop))
AND (ORD(Period) GE ORD(Per)+POSTLAG(Crop))
AND (ORD(Period) LE ORD(Per)+POSTLAG(Crop)+POSTTIME(Crop)-1)
AND (ORD(Per) LE LASTPLANT(Crop)));
POSTYES(CROP,PER,PERIOD)$(NOT POSTLAG(CROP))= 0;
NOPER(PER) = YES ;

NOPER(PER)$PPER(PER) = NO ;
NOPER(PER)$PLPER(PER) = NO ;
NOPER(PER)$HPER(PER) = NO ; .

NOPER(PER)$(ORD(PER) LE
SMAX((CROP),POSTLAG(CROP)+POSTTIME(CROP)+LASTPLANT(CROP)—1)) = NO ;
DISPLAY NOPER,prepyes,postyes ;

233

PARAMETERS
vaLD(PRODUCT,PrCrop,Crop,Prac,PRODl,PrCl,Cr1,Pracl) Adjusted crop yields;
vaLD(PRODUCT,PrCrop,Crop,Prac,PROD1,PrC1,Cr1,Prac1)$(pracYes(Crop,Prac) and
rotYes(prcrop,crop) and pracYes(Crl,Pracl) and rotYes(prcl,cr1))
= price(product)*
vYLD(PRODUCT,PrCrop,Crop,Prac,PRODl,PrCl,Cr1,Prac1)*price(prod1);

*%%%%%%%%%% MODEL %%%%%%%%%%%%
VARIABLE
EU Expected utility funtion (maximize);

POSITIVE VARIABLES

NETREV Expected net revenue

NETGM Expected net gross margin of the processor

TNL Total amount of nitrate leaching from whole
farm

TSNL(crop) Total amount of nitrate leaching from seed corn

TSYLD(crop) Total amount of seed corn yield

PLOW(Prcrop,Crop,Per) Plowing activity after crop

PREP(Crop,Per) Prep done in PERIOD for crop planted per

POST(prcrop,Crop,Per,Period) Postplanting done in period planted per
ACRE(PrCrop,Crop,Prac,Per,Period) Acreage of each cropping activity (acres)

RLAND Rented land (acres)
LABHIRE(Per) Seasonal hired labor (hrs)
yy(product,crop,state) Deviation of seed corn yield
ety(product,crop) Endogeneous target yield level
y(product,crop,state) Deviation of nitrate leaching
‘et(product,crop) Endogeneous target leaching level;

** y & et are transfer columns

PLOW.up(Prcrop,Crop,Per) = 10000 ;

PREP.up(Crop,Per) = 10000 ;

POST.up(prcrop,Crop,Per,Period) = 10000 ;

ACRE.up(PrCrop,Crop,Prac,Per,Period) = 10000 ;

RLAND.up = 10000 ;

LABHIRE.up(Per) = 10000 ;

EQUATIONS
OBJECTIVE Objective function
NETREVE Expected net revenue
GME Gross margin of the processor
TNLE Total nitrate leaching from the whole farm
TSNLE(crop) Total amount of nitrate leaching from seed corn
TSYLDE(crop) Total seed corn yield
LAND Land availability constraints
SEEDL(crop) Seed corn contract availability constraints
PLOWPALL(Crop) Land plowed in the Fall
ROTATE(prCrop,crop) Crop Rotation constraint
LABOR(Per) Total labor use accounting
TRACTR(Per) Tractor power constraints in planting seasons
EQUIPCON(Equip,Per) Farm equipment constraint
PREPPLANT(Crop,Period) Land prepared for planting
PLANTPOST(Crop,Per) Land cultivated after planting
HARVEST(Per) Combine harvester constraint in harvest seasons
HARVPLOW(per,Crop) Harvesting and plowing sequencing constraint
PLOWACRE(Crop,PrCrop) Make number of acres of plowing equal cropping
varsy(product,crop,state) variation of seed corn yield
chancey(product,crop) chanced contraint for seed corn contract loss
vars(product,crop,state) variation of seed corn leaching
chance(product,crop) chanced contraint for seed corn leaching
tsnlup(crop) maximum allowed nitrate leaching
twnlup maximum allowed nitrate leaching;
OBJECTIVE..

EU =E= Sum(Product,Sum((PrCrop,Crop,Prac,Per,HPer)

234

$ActYes(PrCrop,Crop,Prac,Per,HPer),
Yield(Product,PrCrop,Crop,Prac,Per,HPer)*
ACRE(PrCrop,Crop,Prac,Per,HPer)*(Price(Product)-truck(product))))
+sum((prcrop,Prac,pper,hper)$ActYes(PrCrop,'sc',Prac,PPer,HPer),
(fixpay—Fee(PrCrop,'sc',Prac))*acre(prcrop,"sc",Prac,pper,hper))
-Sum((PrCrop,Crop,Prac,Per,HPer)$ActYes(PrCrop,Crop,Prac,Per,HPer),
(P_HCost(prcrop,Crop,Prac)+
DryCost*Max(MOIST(PER,HPER)-MOISTSTAN,0)
*100*Yield("corn",PrCrop,Crop,Prac,Per,HPer))*
ACRE(PrCrop,Crop,Prac,Per,HPer))
-Sum(per,wage*LABHIRE(Per))-rland*rentland
- (0.00005/2)*sum((product,PrCrop,Crop,Prac,Per,HPer),
(ACRE(PrCrop,Crop,Prac,Per,HPer)$ActYes(PrCrop,Crop,Prac,Per,HPer))*
sum((prodl,PrC1,Cr1,Pracl,Per1,HPer1),
(ACRE(PrC1,Cr1,Prac1,Perl,HPer1)$ActYes(PrC1,Cr1,Pracl,Per1,HPer1))*
vaLD(PRODUCT,PrCrop,Crop,Prac,prod1,prcl,cr1,prac1)))

##4##-

* RISK CALCULATION

NETREVE..

NETREV =E= Sum(Product,Sum((PrCrop,Crop,Prac,Per,HPer)
$ActYes(PrCrop,Crop,Prac,Per,HPer),
Yield(Product,PrCrop,Crop,Prac,Per,HPer)*
ACRE(PrCrop,Crop,Prac,Per,HPer)*(Price(Product)-truck(product))))

+sum((prcrop,Prac,pper,hper)$ActYes(PrCrop,'sc',Prac,PPer,HPer),
(fixpay-Fee(PrCrop,'sc',Prac))*acre(prcrop,"sc",Prac,pper,hper))

-Sum((PrCrop,Crop,Prac,Per,HPer)$ActYes(PrCrop,Crop,Prac,Per,HPer),
(P_HCost(prcrop,Crop,Prac)+
DryCost*Max(MOIST(PER,HPER)-MOISTSTAN,O)
*100*Yield("corn",PrCrop,Crop,Prac,Per,HPer))*
ACRE(PrCrop,Crop,Prac,Per,HPer))
-Sum(per,wage*LABHIRE(Per))—rland*rentland;

GME..
NETGM =E= Sum((PrCrop,Prac,Per,HPer)$ActYes(PrCrop,'SC',Prac,Per,HPer),

ACRE(PrCrop,"SC",Prac,Per,HPer)*
((WPS*(1-RSCMC)-VARPAY)*Yield("SEED",PrCrop,'SC',Prac,Per,HPer)-FIXPAY

+Feel(PrCrop,'sc',Prac)));

TNLE..

TNL =E= Sum(Product,Sum((PrCrop,Crop,Prac,Per,HPer)
$ActYes(PrCrop,Crop,Prac,Per,HPer),
NLA(Product,PrCrop,Crop,Prac)*
ACRE(PrCrop,Crop,Prac,Per,HPer)));

TSNLE(‘sc')..

TSNL(‘sc') =E= Sum(Product,Sum((PrCrop,Prac,Per,HPer),
NLA(Product,PrCrop,'sc',Prac)*
ACRE(PrCrop,'sc',Prac,Per,HPer)

$ActYes(PrCrop,'sc',Prac,Per,HPer)));

TSYLDE('sc')..

TSYLD('sc') =E= Sum(Product,Sum((PrCrop,Prac,Per,HPer),
YLD(Product,PrCrop,'sc',Prac)*
ACRE(PrCrop,'sc',Prac,Per,HPer)

$ActYes(PrCrop,'sc',Prac,Per,HPer)));

LAND..

Sum((PrCrop,Crop,Prac,Per,HPer)$ActYes(PrCrop,Crop,Prac,Per,HPer),
ACRE(PrCrop,Crop,Prac,Per,HPer)) =L= LandRhs+r1and;

235

SEEDL("sc")..

Sum((PrCrop,Prac,Per,HPer)$ActYes(PrCrop,'SC',Prac,Per,HPer),
ACRE(PrCrop,"SC",Prac,Per,HPer)) =L= MAXSEED;

ROTATE(PrCrop,Crop)$rotyes(PrCrop,Crop)..

Sum((Prac,Per,Period),ACRE(PrCrop,Crop,Prac,Per,Period)
$ActYes(PrCrop,Crop,Pra c,Per,Period))

=E=Sum((Prac,Per,Period),ACRE(Crop,PrCrop,Prac,Per,Period)
$ActYes(Crop,PrCrop,Pra c,Per,Period));

PLOWFALL(CrOp)..

Sum((Prcrop,PlPer)$rotyes(prcrop,crop),PLOW(Prcrop,Crop,PlPer))
=G=Sum(Per,PREP(Crop,Per)$PREPYES(Crop,Per));

PREPPLANT(Crop,Period)Sprepyes(crop,period)..

Sum(Per$(ORD(Per) LE ORD(Period)),PREP(Crop,Per)$PREPYES(Crop,Per))
=G= Sum(Per$(ORD(Per) LE ORD(Period)),

Sum((PrCrop,Prac,HPer),
ACRE(PrCrop,Crop,Prac,Per,HPer)$ActYes(PrCrop,Crop,Prac,Per,HPer))) ;

PLANTPOST(Crop,Per)$(SMAX((HPer,PrCrop,Prac), ActYes(PrCrop,Crop,Prac,Per,HPer))
AND POSTLAG(CROP))..

Sum(PERIOD$((ORD(PERIOD) GE ORD(PER)+POSTLAG(Crop))

AND(ORD(PERIOD) LE ORD(PER)+POSTLAG(Crop)+POSTTIME(Crop)-1)),

sum(prcrop,POST(prcrop,Crop,Per,Period)
$(POSTYES(Crop,Per,Period)$rotyes(prcro p,crop))))

=E=Sum((PrCrop,Prac,HPer),
ACRE(PrCrop,Crop,Prac,Per,HPer)$ActYes(PrCrop,Crop,Prac,Per,HPer)) ;

HARVPLOW(per,Crop)$PlPer(Per)..

Sum(Period$((ORD(Period) LE ORD(Per))$HPer(Period)),
Sum((PrCrop,Prac,PPer),
ACRE(Crop,PrCrop,Prac,PPer,Period)
$ActYes(Crop,PrCrop,Prac,PPer,Period)))
=G=Sum((Period,PrcrOp)$((0rd(Period) le ord(Per))$PlPer(Period)),
PLOW(Prcrop,Crop,Period)$rotyes(prcrop,crop));

LABOR(Per)$(NOT NOPER(Per))

Sum((PrCrop,Crop,Prac,HPer)$ActYes(PrCrop,Crop,Prac,Per,HPer),
PltLab(Crop)*ACRE(PrCrop,Crop,Prac,Per,HPer))+
Sum((Crop),PREPLAB(Crop)*PREP(Crop,Per)$PREPYES(Crop,Per))
+Sum((prcrop,Crop,Period)$rotyes(prcrop,crop),
Post(prcrop,Crop,Period,Per)*Postlab(prcrop,Crop)
$POSTYES(Crop,Period,Per))
+Sum((Crop,PrCrop)$rotyes(crop,prcrop),
PlowLab(crop,prcrop)*PLOW(Crop,prCr0p,Per)$(PlPer(Per)))+
Sum((PrCrop,Crop,Prac,PPer)$ActYes(PrCrop,Crop,Prac,PPer,Per),
HavLab(Crop)*ACRE(PrCrop,Crop,Prac,PPer,Per))
=L= LABHIRE(Per) + FARMER(PER)*HRSPERDAY*DAYS(PER) ;

TRACTR(Per)$(NOT NOPER(Per))

Sum((PrCrop,Crop,Prac,HPer)$ActYes(PrCrop,Crop,Prac,Per,HPer),
PltTrac(Crop)*ACRE(PrCrop,Crop,Prac,Per,HPer))+
Sum((Crop),PrepTrac(Crop)*PREP(Crop,Per)$PREPYES(Crop,Per))
+Sum((prcrop,Crop,Period),
Post(prcrop,Crop,Period,Per)*PostTrac(prcrop,Crop)SPOSTYES(Crop,Period,Per))
+Sum((Crop,PrCrop),
PlowTrac(crop,prCrop)*PLOW(Crop,PrCrop,Per)$(PlPer(Per)))

236

+ Sum((PrCrop,Crop,Prac,PPer)$ActYes(PrCrop,Cr0p,Prac,PPer,Per),
HavTrac(Crop)*ACRE(PrCrop,Crop,Prac,PPer,Per))
=L= Tractor*HRSPERDAY*DAYS(PER) ;

EQUIPCON(EQUIP,PER).

Sum((Crop)$EPREP(EQUIP),PREQUIP(Crop,Equip)*PREP(Crop,Per)$PREPYES(Crop,Per))
+Sum((Prcrop,Crop,Prac,HPer)$EPLANT(EQUIP),PLANTeq(crop,equip)*
ACRE(PrCrop,Crop,Prac,Per,HPer)$ActYes(PrCrop,Crop,Prac,Per,HPer))
+Sum((Prcrop,Crop)$EPLOW(EQUIP),PLEQUIP(Prcrop,crop,Equip)*
Plow(Prcrop,Crop,Per)$(Plper(Per)))
+Sum((prcrop,Crop,Period)$EPOST(EQUIP),POSTEQUIP(prcrop,CROP,EQUIP)*

POST(prcrop,Crop,Period,Per)$POSTYES(Crop,Period,Per))
=L= (HrsPerDay$(NOT Eplant(Equip))+HrsPerDayP$Eplant(Equip))*DAYS(PER) ;

HARVEST(HPer)..

Sum((PrCrop,Crop,Prac,PPer)$ActYes(PrCrop,Crop,Prac,PPer,HPer),
Comb(Crop)*ACRE(PrCrop,Crop,Prac,PPer,HPer)) =L= Comths(HPer);

PLOWACRE(Crop,PrCrop)$rotyes(prcrop,crop)..
Sum(PlPer,PLOW(prcrop,Crop,PlPer))
=E= sum((Prac,PPer,HPer)$ActYes(PrCrop,Crop,Prac,PPer,HPer),
ACRE(PrCrop,Crop,Prac,PPer,HPer)) ;

varsy("seed”,"sc",state)..

Sum((prcrop,prac,per,HPer),(syld("seed",prcrop,"sc",prac,state)
$(pracYes('sc',prac) and rotyes(prcrop,'sc')))*
ACRE(PrCrop,"SC",Prac,Per,HPer)$ActYes(PrCrop,”sc",Prac,Per,HPer))
-ety("seed",”sc")

+yy("seed","sc",state)

=g= 0;

** the following four equations are used to set up chance constraints
** for contract loss risk and for nitrate leaching abatement _
** Reference: Atwood et al. (Western Journal of Agr. Econ. 1988)

chancey("seed","sc")..

ety("seed","sc")

-lO/5*sum(state yy(" seed", "sc",state)*(1/card(state)))
-70*Sum((prcrop,prac, per, HPer),

ACRE(PrCrop,"SC", Prac, Per, HPer)$ActYes(PrCrop, "s ",Prac,Per,HPer))
=g=0. '

vars("seed","sc",state)..

Sum((prcrop,prac,per,HPer),(45-NLL("seed",prcrop,"sc",prac,state)
$(pracYes(' sc ,prac) and rotyes(prcrop,' sc' )))*
ACRE(PrCrop, "SC", Prac, Per, HPer)$ActYes(PrCrop,"sc",Prac, Per, HPer))
-et("seed", "sc" )
+y("seed", ”sc" ,state)
=9: 0;

chance("seed","sc")..

et("seed","sc")
-5*sum(state,y("seed","sc",state)*(1/card(state)))

tsnlup(‘sc')..
tsn1('sc') =l= sum((prcrop,prac,per,hper),maxnl*
acre(prcrop,'sc',prac,per,hper)$ActYes(PrCrop,"sc",Prac,Per,HPer));
* maximum amount of nitrate leaching from growing seed corn

237

twnlup..
tnl =l= sum((prcrop,crop,prac,per,hper),maanl*
acre(prcrop,crop,prac,per,hper)$ActYes(PrCrop,crop,Prac,Per,HPer));
* maximum amount of nitrate leaching from growing whole-farm operation

LABHIRE.UP(Per) = maxhire(Per);
RLAND.UP = MAXLAND;

MODEL MICHIGAN

/ OBJECTIVE
NETREVE
GME
TNLE
TSNLE
TSYLDE
LAND
SEEDL
PLOWFALL
ROTATE
LABOR
TRACTR
EQUIPCON
PREPPLANT
PLANTPOST
HARVEST
HARVPLOW
PLOWACRE
tsnlup
twnlup
varsy
chancey
vars
chance

/;
* OPTION SOLPRINT = OFF;

SOLVE MICHIGAN MAXIMIZING EU USING NLP;

238

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