Full text of DOI:10.1111/j.1744-7976.2000.tb00269.x

The Economics of Erosion and Sustainable
Practices: The Case of the Saint-Esprit Watershed
Jean-Christophe Dissart, Laurie Baker and Paul J. Thomassin
Master’s student, assistant professor and associate professor, respectively,
Department of Agricultural Economics, McGill University, Montréal, Québec.
Received September 1998, accepted January 2000
This paper examines the economics of the adoption of sustainable production practices for soil erosion
control. The research was conducted on three case farms within the Saint-Esprit watershed in Quebec
using a two-stage process. The first stage involved the use of GIS (Geographical Information Systems)
to record erosion characteristics (slope, etc.) for these farmers’ fields. This erosion information was then
included as input information in the second stage of the process. Mixed integer linear programming
(MILP) was used to model both individual farms and the watershed. Increasing erosion constraints
were applied to these models to investigate changes in crop production mixes for farms and the water-
shed. A comparison of the results (farms versus watershed) was used to investigate policy questions
concerning an optimal erosion constraint for society. Results generated indicate that farms with higher
net incomes would be advantaged by erosion constraints set at the watershed level, whereas farms with
lower net revenues would be disadvantaged. Thus, trading of pollution permits could be encouraged.
Cet article examine les aspects économiques de l’adoption de pratiques de production durables visant
à réduire l’érosion du sol. La recherche fut effectuée sur trois fermes situées dans le bassin du Saint-
Esprit au Québec, et impliqua un processus à deux étapes. Le premier étape consiste en l’utilisation du
système d’informations géographiques « SIG » afin de noter les caractéristiques de l’érosion (pente,
etc.) dans ces champs agricoles. Ces renseignements servirent de données au sein du deuxième étape.
La méthode de programmation linéaire à nombres entiers mixtes fut employée afin de modéliser les fermes
individuelles, ainsi que le bassin. Ensuite, les contraintes d’érosion furent appliquées sur ces modèles
de manière croissante, et ce afin d’étudier les changements dans le mélange des productions de cultures
pour les fermes et le bassin. Une comparaison des résultats (fermes vs. bassin) fut accomplie pour
examiner les questions de politiques pouvant mener à une contrainte d’érosion optimale pour la société.
Les résultats obtenus démontrent que les fermes ayant des revenus nets élevés seraient avantagées par
des contraintes d’érosion établies au niveau du bassin, tandis que les fermes aux revenus nets plus bas
en seraient désavantagées. En conséquence, l’échange de permis de pollution est recommandé.
INTRODUCTION
Public concern over agriculture’s effect on soil and water resources has created a need to
develop relevant agricultural policies. Policy revisions should recognize both the impacts of
agricultural practices on the environment and the economic consequences to the farm of
adopting practices that are more compatible with resource protection. Although there is wide
disagreement over whether sustainable agriculture is more profitable than conventional agri-
culture, there is anecdotal evidence of successful alternative farming systems (Batie and
Taylor 1989). However, such evidence is not usually sufficiently rigorous to be used for policy
development or legislative purposes, nor does it tend to incite the farming community at large
Canadian Journal of Agricultural Economics 48 (2000) 103–122
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to adopt sustainable alternatives independently of policy or legislation. It is also difficult to
generalize results from one site or region because differences in factors such as type of crop,
soil, weather, topography and others can significantly influence profitability at the individual
farm and larger scale levels, as well as the susceptibility of the resources to degradation.
In this context, case studies based on individual farms and watersheds may provide
information for analysis at a scale relevant to regional policy development. This paper pre-
sents the economic evaluation of a pilot project to reduce soil erosion and improve water
quality at the outlet of the Ruisseau Saint-Esprit watershed in Quebec, Canada. The pilot pro-
ject was requested of the Ministère de l’Agriculture, des Pêcheries et de l’Alimentation du
Québec (MAPAQ) by the Saint-Jacques-de-Montcalm agricultural society. The scientific
partner was McGill University. The project included technical assistance to 29 of the 52 farmers
that had agreed to implement sustainable farming practices. This accounted for approximately
90% of the agricultural area of the watershed. Sustainable practices included reduction of fer-
tilizer applications in corn production, reduced tillage and green manuring for other crop pro-
ductions. Base data included water contamination indicators and sedimentation at the watershed
outlet, as well as farm input and output data. The objective of the economic component of the
project was to assess the costs to individual farm enterprises and to the watershed as a whole,
of implementing soil and water conservation strategies. The analyses reported in this paper
were based on a mixed linear programming (MILP) model, and involved an erosion constraint
using erosion estimates derived from the Universal Soil Loss Equation for Application in Canada
(RUSLEFAC) applied to base data obtained from a Geographical Information System (GIS).
BACKGROUND
The profitability of sustainable versus conventional farming is often a contentious issue.
Individual profitability may result from good management as well as employing fewer pur-
chased inputs. Disparities may result from on- farm unmeasured benefits such as less vulner-
ability to drought, nutrient conservation and better seasonal distribution of inputs (Batie and
Taylor 1989). Other reasons range from the definition of sustainable agriculture to the
assumptions regarding agricultural subsidies and price differentials, the scale of application,
the importance of the farmer’s management ability and the viewpoint from which the eco-
nomic comparison is made (society, farmers or future generations). Finally, most economic
studies of crop production focus exclusively on profitability and neither incorporate environ-
mental criteria nor the dynamic characteristics inherent in alternative systems (Roberts and
Swinton 1996). One exception is the paper by Turvey and Weersink (1991), which explicitly
incorporated an erosion constraint.
Hession and Shanholtz (1988) used a pollution density index derived from the USLE
(Universal Soil Loss Equation) with a GIS to estimate potential sediment loading to streams
from agricultural land. More recent models have tended to provide a better integration of eco-
nomic and environmental dimensions of water quality management (Bockstael et al 1995;
Prato and Wu 1995). This paper combines GIS and optimizing techniques to develop farm-level
and watershed models that can provide insight into distributional questions of erosion control.
CHOICE OF REPRESENTATIVE FARMS
A two-stage process was used to select the farms to be included in the model. Initially, seven
farmers were selected from the 29 participating farmers. This group was reduced to three after
application of the following criteria:

ECONOMICS OF EROSION AND SUSTAINABLE PRACTICES
105
Table 1. Data input on farm size, number of fields, crop net incomes and animal nutrient requirements
for sample farms A, B and C
Farm A
Farm B
Farm C
Hectares (ha)
Number of fields
47.77
15
105,24
85.61
—
633.77
30.26
8
119.13
16
—
—
1,109.89
Conventional barley ($/ha)
Green manure barley ($/ha)
Plowed corn ($/ha)
Reduced-till corn ($/ha)
No-till corn ($/ha)
Plowed soybeans ($/ha)
No-till soybeans ($/ha)
Hay ($/ha)
—
—
843.65
840.84
—
600.32
1,042.10
694.14
543.58
100.76
poultry
—
—
100.76
dairy
311.21
173.65
100.76
swine
ME, DE, CP
Animal production
Estimated nutrientsa
DMI, TDN, NEM,
NEG, NEL, ME,
DE, CP
ME , CP
n
aDMI = dry matter intake; TDN = total digestible nutrients; NEM = net energy for maintenance; NEG
net energy for body gain; NEL = net energy for lactation; ME = metabolizable energy; DE =
digestible energy; CP = crude protein; ME = nitrogen-corrected metabolizable energy.
=
n
•
the reliability of the available economic data
the crops grown and the sustainable practices used
the type of animal husbandry employed
•
•
•
•
farm size
erosion values relative to the rest of the watershed.
Each farm grew corn (conventional and alternative), which is the predominant crop in
the Saint-Esprit area and provides the highest net income. Each farm was also allowed to
grow hay (alfalfa) because it is efficient in abating erosion. The remaining crops (conven-
tional and alternative) were selected according to animal nutrient requirements. Data input on
farming practices, number of fields, farm size and net incomes are listed in Table 1 for the
three farms.
Each of the tested alternative farming practices was designed to reduce soil erosion. One
can distinguish two types of practice: reduced-till or no-till and green manure. Reduced-till
and no-till leave more than 30% of residues on the topsoil after preparation of the seedbed,
and thus reduce erosion. This objective is reached with most tillage practices except plowing.
Green manuring, the practice of plowing down a growing crop, provides organic fertilizer and
reduces the risk of erosion by providing more organic matter to the soil.
THE MODEL
A programming model was chosen to compare the impacts of erosion abatement practices on
the profitability of individual farms with that of the whole watershed. The objective of this

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model is to maximize the sum of field net incomes, derived from crop budgets, subject to
three types of constraints:
•
•
•
singleness of field use
animal nutrient requirements
erosion.
Given the interest in singleness of field use, it was decided that a MILP model run on
1
LINGO would be most suitable for this analysis.
Farmers may purchase nutrients from the Rest of the World (ROW) to satisfy animal
needs. Inputs are purchased from ROW at the same price used to estimate income in crop
budgets. Since soybeans are fed to animals as soybean meal, the extrusion cost was added to
the purchase price. No constraint was imposed on what crops should be grown. An erosion
constraint was applied at the farm and watershed levels to permit comparison of its economic
impact at these levels and to study distributional effects between producers. One model was
built for each of three farms (Farms A, B and C), and a fourth to represent the watershed was
2
defined as the summation of the three others. The four models were built using the same
types of constraints, decision variables and coefficients.
The model used crop budgets and erosion data obtained and/or calculated at the field
level, respecting proprietary boundaries and the cropping plans of the farmers. The unit of
3
analysis replicating the real world in the model was therefore single fields. This is why MILP
was used.
The following assumptions were explicitly made:
•
the crops grown are used on-farm and are grown to satisfy animal nutrient requirements,
unless the particular crop cannot be fed to an animal (i.e., hay to swine and poultry, or sold
to ROW)
•
•
•
•
•
prices remain constant throughout the year both for product sales and purchased inputs
the three farms are assumed to be representative of the Saint-Esprit watershed as a whole4
the watershed is the sum of the three farms in all respects
no new technologies are used on these farms
transportation costs are not explicitly included because exchanges with ROW are extremely
limited.
MATHEMATICAL MODEL
The objective function is written as follows:
Max Σ aXijk – Σ eZRip
(1)
where:
X = a field activity (0/1 variable)
a = the field level net income ($)
i = the farm code
j = the field number
k = the crop/practice code
ZR = crop p sold by ROW (rest of the world) to farm i (real variable)
p = the crop code
e = the purchased input price ($/t).

ECONOMICS OF EROSION AND SUSTAINABLE PRACTICES
107
Constraints
There are three sets of constraints. The first set forces the model to choose only one use out
of five for a given field. There are as many constraints of this type as there are fields for a
given farm model (i.e., 15 for model A, 8 for model B, 16 for model C and 39 for the water-
shed model). This is summarized mathematically as follows:
Σ X = 1 for given i and j
(2)
k
where:
X = a field activity (0/1)
i = the farm code
j = the field number
k = the crop/practice code.
The second set of constraints forces the model to satisfy animal nutrient requirements.
These constraints account for the nutrients provided by crops grown on-farm and by pur-
chased inputs from ROW. The number of constraints of this type depends on the type of animal
production. There are 10 constraints of this type for model A, 5 for model B, 4 for model C
and 19 for the watershed model. This may be mathematically summarized as follows:
Σ bmXijk + Σ d ZR ≥ B
m
(3)
m
ip
where:
X = a field activity (0/1)
i = the farm code
j = the field number
k = the crop/practice code
bm = the field contribution to satisfying animal needs in nutrient m
ZR = crop 1 sold by ROW to farm i (real)
p = the crop code
dm = the crop contribution to satisfying animal needs in nutrient m
Bm = the animal nutrient requirement in element m.
The third set of constraints forces the model to satisfy the erosion constraint. There is
only one constraint of this type for a given model, including the watershed model. This may
be mathematically summarized as follows:
Σ gXijk ≤ C
(4)
where:
X = a field activity (0/1)
i = the farm code
j = the field number
k = the crop/practice code
g = the field contribution to erosion
C = the erosion target.
It should be noted that the models focus on erosion control assuming the number and
species of animal produced on each farm remain unchanged. This again identifies the models
as being short-run in nature.

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DATA AND METHODS
Crop Budgets
Economic data were collected at the farm level for the year 1995, at which time the farmers
had begun on-farm trials of alternative practices. Budgets were created using additional data
from MAPAQ and assuming constant returns to scale. Additional information on the agri-
cultural situation within the watershed was also obtained from project reports. When relevant
costs had been omitted from the producer’s budgets, they were estimated from secondary
sources, e.g., Comité de Références Économiques en Agriculture du Québec (CREAQ 1996,
1994a, 1994b, 1991) budgets. Crops used on the farm were attributed a value equal to the sell-
ing price to ROW. When yields from conventional and alternative farming practices were not
available for a given crop, they were assumed to be the same. Thus, the conventional and
alternative approaches could sometimes be compared only on the basis of costs. Income from
Assurance Stabilisation du Revenu Agricole (ASRA, government revenue insurance program)
was not taken into account.
Crop operation costs were split into labor and fuel costs. Farmers were asked to record
the time taken to perform each crop operation and to note which tractor was used for that
operation, in order to permit inference of labor and fuel costs. Since most alternative farming
practices required special equipment, fixed costs were calculated using a machinery inventory
that recorded the purchase date and value. Although some machinery purchases were subsi-
dized by the project, those items were recorded at their market price in the crop budgets to
5
eliminate bias.
Animal Nutrient Requirements Data
Animal nutrient requirements were estimated from three sources:
•
•
•
herd inventories for Farms A, B and C
Comité de Références Économiques en Agriculture du Québec (CREAQ) data
National Research Council (NRC) data.
Inventories provided data on animal species for a given herd and for the year 1995. “Life
cycles” were derived for the year 1995; that is, the different phases that a given animal species
would go through for that year. Nutrient requirements were then estimated for each animal
species and, consequently, for the whole herd. It should be understood that these estimates
were sometimes based on diets and dietary energy concentrations provided by NRC. Since
crops grown by selected farmers may not be exactly the same, it is acknowledged that values
generated in this fashion may be different from those actually required. However, as stated
by NRC (1994, 61): “From a nutritional point of view, there is no ‘best’ diet formula in terms
of ingredients that are used. Ingredients should, therefore, be selected on the basis of avail-
ability, price and the quality of the nutrients they contain.”
In 1995, Farm A was predominantly a dairy farm (48 cows and 30 heifers), Farm B was
predominantly in swine production (12 gilts, 135 sows, 2,686 piglets and three adult boars)
and Farm C specialized in poultry production (25,530 immature chickens and 25,030 laying
hens). Nutrient requirements for these animal productions are listed in Table 1. The farmers
bought pre-mixed feeds from ROW to satisfy requirements in macro-minerals. It was decided
not to account for these elements explicitly because no data were available on the ability of
the farms to satisfy these requirements themselves. NRC data (1994, 1988a, 1988b) were
used to estimate the nutritional value of the crops grown by Farms A, B and C.

ECONOMICS OF EROSION AND SUSTAINABLE PRACTICES
109
Erosion Data
Erosion is defined as the movement of soil by water, wind and gravity. It occurs in all regions
of Canada under a wide range of land uses and creates problems on and off the farm (Wall
et al 1997). The on-farm impact of topsoil loss is long-term loss of productivity. Off-farm
impacts include: sediment deposits, bacteria from organic matter, nutrients and pesticides in
surface water. This has a negative impact on water quality and an economic consequence on
surface water use (Wall et al 1997). Quantitative methods to predict erosion have not been
developed for specific Canadian conditions; however, the Universal Soil Loss Equation (USLE)
is a field scale model developed in the United States. There has been limited use of USLE in
Canada because the information required to determine soil erosion rates has not been avail-
able (Wall et al 1997). The Revised USLE (RUSLE) was developed for interim use until the
development of a new generation of soil erosion process models. The RUSLE For
Application in Canada (RUSLEFAC) has been prepared to provide information pertinent to
Canadian conditions.
The purpose of the RUSLEFAC is “to predict the long-term average annual rate of soil
erosion for various land management practices in association with an area’s rainfall pattern,
specified soil type and topography” (Wall et al 1997, 1.4). “There are several general condi-
tions, unique to any site, which affect erosion by water. These are: climate; soil; topography;
vegetation or crop; land use practices. Each of the conditions is represented by a different factor
in the USLE or RUSLE” (Wall et al 1997, 1.5), as follows:
A = R * K * L * S * C * P
(5)
where:
A = the estimated potential long-term average annual soil loss (t/ha) per year
6
R = the rainfall and runoff erositivity factor (MJ.mm/ha/h)
K = the soil erodibility factor (t.h/MJ/mm)
L, S = the slope length (in metres) and steepness (dimentionless) factors
7
C = the cropping-management factor (dimensionless)
8
P = the support practice factor (dimensionless).
Erosion values were calculated by a two-stage process tied to the selection of watershed
farmers (Figure 1). Differences between the two sets of erosion values were limited to the L
and S factors only. The first set was calculated using the proposed RUSLEFAC table. Results
showed that the three selected farms were representative of the watershed in terms of erosion.
The analysis also showed that the L and S factor values were biased due to field shapes (long
9
and narrow) and lengths often exceeding the maximum applicable in the formula. A modified
RUSELFAC method was therefore used to obtain more accurate L and S factors for the three
farms.
Data needed to calculate the two sets of erosion values were extracted from a SPANS/GIS
database that was developed for the Saint-Esprit watershed project (Mousavizadeh et al 1995).
Data layers include public domain and site-specific information. The public domain informa-
tion consists of cadaster, hydrography, watershed boundary, road, land use, soil information,
elevation points and topographic contour lines, slope and land ownership. The site-specific
information includes farm plans, soil fertility, fertilizer, manure and pesticide applications and
crop yield data. A specific data set was generated1 from this database to calculate the erosion
factors. A basemap of the watershed was created, featuring areas of the watershed with the fol-
0

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ECONOMICS OF EROSION AND SUSTAINABLE PRACTICES
111
lowing land uses: grains, vegetables and hay. Other land uses (e.g., forest, residential, pasture
and any other unspecified use) were removed. The following data were made available by
overlaying on a sub-field basis: slope percentage, soil texture, soil series, area, field number
and ownership. The tabular data were exported into a spreadsheet format and recombined for
each field.
The R factor was determined by locating the area of interest on the isoerodent map indi-
cating annual R values for Ontario and Quebec (Wall et al 1997). Since the K factor represents
the inherent erodibility of a soil type, a separate K value was determined for the “predomi-
nant” soil series and soil texture for each field on the basis of sub-area field size in the map
unit. Soil erodibility values for common surface textures were used (Wall et al 1997) because
information was limited for this watershed. Generalized C values for Quebec were used (Wall
et al 1997) according to farmers’ crops and tillage practices. The P factor reflects the erosion
control effectiveness of support practices, such as cross slope cultivation, contour farming,
strip cropping and terracing, used to reduce the amount and rate of runoff water (Wall et al
1
997). Since none of these support practices was used in the watershed, P was set equal to 1
in the RUSLEFAC.
For moderately consolidated soil conditions, including row-cropped agricultural land,
with little to moderate cover and where rill and inter-rill erosion processes are of similar
importance, Wall et al (1997) recommended that a table giving L and S factors as a function
of slope length and slope percentage be used. The majority of the fields in the area are long
and narrow in the direction perpendicular to streams (see note 9). The slope length of each
individual field on farms A to C was measured manually on the cadastral map (1:10,000). A
second set of more precise L and S factor values was obtained from the original USLE equa-
tion for a uniform slope, which is based on the slope length of the site, the angle of the slope
and a coefficient related to the ratio of rill to inter-rill erosion describing the nature of the ero-
sion process (Wall et al 1997).
The modified RUSLEFAC calculations showed that Farms A, B and C were represen-
tative of the rest of the watershed in terms of percentages of fields in a given erosion class.
Modified RUSLEFAC calculations for Farms A, B and C yielded the following estimates of
the average erosion value per hectare weighted by field area using corn grain with conven-
tional tillage for comparison: 4.36 t/ha/y for Farm A, 4.11 t/ha/y for Farm B and 4.40 t/ha/y
for Farm C. These values fell in the very low erosion class (< 6 t/ha/y), and soils in this class
had very slight to no erosion potential (Wall et al 1997). However, some individual fields had
erosion values in the low (6–11 t/ha/y, about 17%) to moderate (11–22 t/ha/y, about 2%) erosion
classes. Nevertheless, long-term productivity should be sustainable if average management
practices are used.
RESULTS AND POLICY IMPLICATIONS
The four models described in the previous section were run with two erosion scenarios:
•
•
base case with no erosion constraint
a series of estimates with increasing erosion constraints.
The farm and watershed models were run 20 times, using erosion values ranging from
the lowest to the highest per hectare in increments of 250 kg/ha. The lowest erosion value per
hectare for a given farm was reached when the cropping plan was 100% hay. The cost of com-
plying with the erosion constraint was estimated through changes in net income (the objective
function value).

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Choice variables of interest for the analysis were: erosion per hectare, net income per
hectare, conventional corn hectares (on plowed land), corn hectares produced using alterna-
tive cultivation techniques and hay hectares. Barley was not used at all because it is a supplier
of energy like corn, but provides much lower net incomes for both the conventional and the
alternative practices. Soybean was rarely used because it is usually cheaper to buy soybean/
protein from ROW rather than cultivate it. This held as long as access to higher net income
corn was possible. Percentages of hectares in conventional corn, alternative corn and hay
were calculated for each farm and the watershed in total. The following relationships were
analyzed: net income as a function of erosion, corn and hay hectares as a function of erosion,
and the difference in net income between farm and watershed levels. Finally, results obtained
from simulations of the watershed model were decomposed and recomposed for each farm.
It was therefore possible to study what happens at the farm level when the erosion target value
is set at the watershed level.
Base Case — No Erosion Constraint
The binding constraint in each of the four models was the crude protein requirement. Erosion
was calculated by subtracting the slack value of the constraint from its right-hand side. In the
base case scenario, Farm C had the highest net income ($1,086/ha) and the highest erosion
value (4,751 kg/ha). Farm B values were $700/ha and 4,272 kg/ha, while Farm A had the lowest
income and lowest erosion ($495/ha and 3,806 kg/ha). For the watershed, the model yielded
the following results: $883/ha and 4,448 kg/ha. Conventional corn (i.e., corn on plowed land
for Farms B and C and reduced-till corn for Farm A) was selected on 100% of the farm
hectares for Farms A and B and 94% of Farm C’s hectares.
Objective Function Value as a Function of Erosion
The relationship between net income per hectare and soil erosion value per hectare for the
three individual farm models and for the watershed model is shown in Figure 2. Note that the
shapes of the curves are similar. They are fairly straight up to 2,000 kg/ha and then fall rapidly.
The watershed curve is closer to that for Farm C. This is due to the greater weight in terms
of land area for Farm C (60% of the watershed hectares). The watershed curve intersects that
of Farm C at a soil erosion value of 1,250 kg/ha. Farm A’s curve does not fall as quickly as
the others because it has the lowest erosion values per hectare, and the erosion constraint is
not binding for soil erosion values less than 3,806 kg/ha. Also, Farm A has the smallest dif-
ference between conventional corn and hay net incomes ($533/ha versus $743/ha for Farm B
and $1,009/ha for Farm C). As a consequence, Farm A’s net income per hectare cannot fall
as dramatically as it does for the two other farms when conventional corn is gradually
replaced with lower net income crops.
It was proposed that increasing the erosion constraint would reduce the amount of ero-
sion generated from agricultural production. As can be seen in Table 2, the farm operations
in the watershed could adjust their production decisions to satisfy a policy objective of
decreasing the amount of soil erosion in the watershed. Table 2 shows the estimated decrease
in profits for the erosion constraint analyzed. For example, for an erosion target of 3,250 kg/ha,
(i.e., a reduction in soil loss of 1,501 kg/ha from the baseline solution), the costs are $9/ha to
Farm A, $123/ha to Farm B and $31/ha to Farm C and $23/ha to the watershed as a whole.
Net income becomes negative for erosion values of less than 500 kg/ha, as seen in Figure 2

ECONOMICS OF EROSION AND SUSTAINABLE PRACTICES
113
Figure 2. Net income as a function of erosion
(explanation provided in the next section). Finally, Figure 2 shows that net income curves
become steeper as the erosion constraint increases, indicating that the marginal cost of com-
plying with the environmental constraint increases. The explanation for this increase is the
substitution of alternative corn with hay. Hay is the only crop that can satisfy an increasingly
severe erosion constraint but this results in the lowest net income per hectare. Furthermore,
more animal inputs must be purchased from ROW to fulfil energy and protein needs if hay
replaces corn, thus further reducing net income.
Cropping Patterns as a Function of Erosion
Figure 3 shows the relationship between the percentage of hectares in conventional corn,
alternative corn and hay and erosion for the watershed. It is possible to distinguish two phases
in the cropping pattern evolution as the erosion constraint increases. In the first phase, the pro-
portion of total hectares in conventional corn decreases continuously to zero from about 100%,
the proportion of total hectares in alternative corn increases continuously from zero to about
100%, and the proportion of total hectares in hay is constant and equal to zero. In the second
phase, the proportion of total hectares in conventional corn is constant and equal to zero, the
proportion of total hectares in alternative corn decreases continuously from about 100% to
zero, and the proportion of total hectares in hay increases continuously from zero to 100%.

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Table 2. Costs for farms of reducing erosion, farm and watershed levelsa
Lost profits A Lost profits B Lost profits C
Lost profits Lost profits
FAMb
WMc
FBMb
WM
FCMb
WM
FABCM
d
ABC, WM
e
Erosion
kg/ha)
(
($/ha)
0
($/ha)
0
($/ha)
0
($/ha)
0
($/ha)
0
($/ha)
0
($/ha)
0
($/ha)
0
4
4
3
3
2
2
1
1
7
2
2
751
272
806
250
750
250
750
250
50
0
9
0
2
12
0
7
2
0
13
8
3
19
12
12
11
9
18
33
61
163
338
616
616
16
33
61
189
471
616
616
616
123
167
171
301
539
1122
2010
2010
4
6
15
254
399
930
2010
2010
31
50
75
236
548
1263
2409
n.f.f
31
50
85
111
320
887
2335
n.f.
40
23
60
39
80
68
204
453
1017
1913
n.f.
152
369
828
1869
n.f.
55
38
a
For reasons of conciseness, only half of scenario results are shown.
FAM = Farm A Model; FBM = Farm B Model; FCM = Farm C Model; erosion target value set at the
b
farm level.
c
WM = Watershed Model; erosion target value set at the watershed level.
Weighted average of lost profits per hectare for Farms A, B, C. Values obtained from Farm A Model,
d
Farm B Model and Farm C Model.
e
Weighted average of lost profits per hectare for Farms A, B, C. Values obtained from the Watershed
Model.
f
n.f. = not feasible. The erosion constraint cannot be satisfied even with 100% of the land being allocated
to hay (the crop with lowest erosion value).
The explanation for this change in cropping patterns is as follows. Conventional corn is
chosen in the first phase because it provides the highest net income. Alternative corn gradu-
ally replaces it because it provides the second highest net income while abating soil loss to a
certain extent. Hay is not used because it has the lowest net income. The erosion constraint is
not large enough during this phase to force hay into the solution. In the second phase, alter-
native corn is gradually replaced by hay to satisfy the increasing erosion constraint. At this
point, most if not all animal nutrients are purchased from ROW. In this situation, net incomes
from crop production are decreasing and the costs of purchased inputs are increasing. This
results in a negative net income for the highest erosion constraints.
Watershed versus Farm Scale
Results from the watershed model were decomposed and recomposed at the farm level in
terms of net income, erosion and cropping patterns. This was done to assess the consequences
of imposing target values for erosion at the farm and watershed levels. Figure 4 shows the dif-
ference in net income per hectare for each farm when the erosion target value is set at:
•
•
the watershed level
at the farm level.

ECONOMICS OF EROSION AND SUSTAINABLE PRACTICES
115
Figure 3. Watershed: Corn and hay hectares as a function of erosion
Figure 4. Farms A, B and C: Difference in net income per hectare of watershed model versus individual
farm models

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Three regions can be distinguished. In the first region — 4,751 kg/ha (i.e., maximum
erosion for Farm C) to 3,806 kg/ha (i.e., maximum erosion for Farm A) — there is no major
effect of setting the target erosion at the watershed level. This is evidenced by the fact that
the curves stay close to zero. The second region stretches from 3,806 kg/ha to 2,000 kg/ha.
Here, Farm B’s net income is higher with an erosion target value set at the watershed level
(the curve is above the zero line). In the third region (2,000 kg/ha to 255 kg/ha; i.e., minimum
erosion for Farm C), Farms B and C are better off with the erosion target value set at the
watershed level, whereas Farm A is worse off.
If the difference between the watershed and the individual farm model solutions were
plotted against the percentage of hectares of crops other than hay, the curves would mimic
those in Figure 4. The decision on where to grow hay in the whole watershed drives the
observed differences in net income per hectare. The watershed model results in a higher per-
centage of area cropped to hay in Farm A than does the single model for Farm A. The expla-
nation is as follows.
Net incomes from conventional or alternative corn production increase from Farm A to
Farm C. For Farm A, net income for conventional and alternative corn is $600/ha and
$
$
634/ha, respectively. Net incomes for Farm B are $840/ha and $844/ha, whereas they are
1,042/ha and $1,110/ha for Farm C. The average difference between the watershed and the
individual farm net income per hectare also increases from Farm A to Farm C: –$91/ha for
Farm A, $78/ha for Farm B and $85/ha for Farm C. Since the watershed model maximizes
the sum of Farms A, B, C net incomes, it first chooses to grow conventional corn on each
farm. The model then decides where to grow alternative corn or hay to satisfy the increasing
erosion constraint. The choice is clearly to do that where conventional corn net incomes are
lower, thus minimizing the economic loss of the watershed as a whole. Thus, in a watershed
with an implemented erosion reduction policy and reasonably homogeneous susceptibility to
erosion, farms with higher net incomes will be better off if the erosion target value is set at
the watershed level, while farms with lower net incomes will be worse off.
Sensitivity Analysis
Figures 5, 6, 7 and 8 illustrate the impact of increasing the field level erosion values on the
objective function value (OFV) for the three farm models and the watershed model. The figures
show the abatement cost curve for the original solution for each model. This curve is derived
by solving the appropriate model for each erosion threshold. As the erosion threshold is
decreased, greater efforts must be made to apply abatement measures by the producer. The
erosion values per field reflect the results of solving the RUSLEFAC model for each field.
Thus, the appropriate slope and length of each field was taken into account along with the
prevailing soil type for the field in question.
The abatement cost curves identified in these figures as 2X Solution and 2.5X Solution
were derived as follows. The base case field level erosion values were increased by a factor
of 2 (and then by a factor of 2.5) to approximate different slope, length and soil type scenarios.
The models were then run again using these new erosion estimates to produce data for these
figures.
The models are quite responsive to changes in the RUSLEFAC erosion values set at the
field level. Figure 5 indicates that the original solution resulted in a reduction of $33/ha in the
OFV of Farm A for an erosion constraint of 2250 kg/ha. When the field erosion values were

ECONOMICS OF EROSION AND SUSTAINABLE PRACTICES
117
Figure 5. Abatement cost curves for Farm A
Figure 6. Abatement cost curves for Farm B

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Figure 7. Abatement cost curves for Farm C
Figure 8. Abatement cost curves for watershed

ECONOMICS OF EROSION AND SUSTAINABLE PRACTICES
119
doubled and increased by a factor of 2.5, the OFV dropped by $193/ha and $270/ha, respec-
tively. These reductions in the OFV are 485% and 718% (2.5 times base case). The behavior
for Farm B is similar; however, the reductions are much greater (note difference in y-axis
scale in Figure 6). In percentage terms, Farm C (Figure 7) suffers the greatest percentage
reductions in the OFV/ha, particularly at the higher end of the erosion limit scale (least
restrictive). At lower erosion limits, the reductions in OFV/ha of Farm C were closer to those
of Farm B and the watershed model.
Equity Issues and Policy Implications
Table 2 provides the estimated costs of reducing soil erosion for each farm and for the water-
shed. Thus, if an erosion reduction policy were implemented in the Saint-Esprit watershed
and the erosion target value set at 2,750 kg/ha for each farm, it would cost Farms A, B and C
$18/ha, $167/ha and $50/ha, respectively. If an erosion reduction policy were implemented at
the Saint-Esprit watershed level and the erosion target value set at 2,750 kg/ha for the whole
watershed, it would cost: $33/ha, $6/ha and $50/ha respectively for Farms A, B and C.
For Farm A, the estimated cost of reducing soil erosion with the target set for the water-
shed is always greater than or equal to that set at the farm level. For Farm B, watershed costs
are greater than individual farm costs at 4,272 kg/ha. However, after this, the estimated cost
of reducing soil erosion with the erosion target value set at the farm level is always greater
than or equal to that set at the watershed level. For Farm C, except for a soil erosion value of
2,250 kg/ha, the estimated cost of reducing soil erosion with the erosion target value set at the
farm level is always greater than or equal to that set at the watershed level.
The two right-most columns in Table 2 estimate the opportunity cost per hectare at the
watershed level and a weighted average of the opportunity cost for the three individual farms.
The estimates show that the opportunity cost is lower when the required erosion target is set
at the watershed level. This can be explained by the fact that when an erosion target is set at
the watershed level, the model has more room to maneuver to allocate crops to fields; that is,
it does so in a more efficient (less costly) manner.
Policy makers could implement a standard for erosion or subsidize producers to decrease
erosion. Applied to the watershed, the Quebec Ministry of the Environment could fix a stan-
dard corresponding to a certain level of erosion or soil loss per hectare (e.g., 2,750 kg/ha) for
each farm or for the watershed. Farmers or the watershed as a whole polluting beyond this
standard would be charged a penalty (e.g., lump-sum fine or fines per unit of erosion beyond
that permitted under the standard). On the other hand, once the baseline level of effluents is
established (e.g., 4,751 kg/ha), the Ministry could subsidize each farmer or the watershed as
a whole for reductions in soil loss. This could, however, attract more producers into the water-
shed and increase the total amount of pollution generated (Baumol and Oates1988).
Sergenson (1998) and Bystrom and Bromley (1998) have proposed new policy designs
for nonpoint pollution control for agriculture. Both of these designs attempted to minimize
the transaction costs associated with the pollution control policy. Sergenson (1998) integrat-
ed both voluntary and mandatory aspects into her design. The voluntary aspect is a subsidy
with mandatory controls if specific quality goals are not met. The Bystrom and Bromley
(1998) policy was based on a watershed scale and included a trading scheme that allowed pro-
ducers to trade abatement effort between one another with collective penalties if target levels
were violated.

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CONCLUSION
This study shows that implementing an erosion constraint:
•
•
•
reduces the amount of soil loss generated from agricultural production
forces cropping patterns and farming practices to change
reduces profits.
Also, in a given watershed with comparable average soil losses per hectare across farms,
farms with higher net incomes would be better off if the erosion target value were set at the
watershed level, while farms with lower net incomes would be worse off. If a subsidy or a
regulation approach were used, the least cost approach would be to set the erosion target value
at the watershed level.
A sensitivity analysis was undertaken to estimate the impact on opportunity cost as field
level erosion values are changed with an increasing soil erosion constraint. The abatement
cost curves were quite responsive to changes in field level erosion values as estimated by
RUSLEFAC. This implies that the cost of erosion abatement would be substantially higher
for agricultural lands that were more susceptible to erosion, i.e., steep slope, field length
and/or soil type.
There are several contributions of this study. First, it used data extracted from a GIS
database and recombined at the field level in order to calculate erosion values on a field basis.
Second, it used a modified RUSLEFAC method to calculate erosion values. This was done
because of the Canadian context of the study and the field layout, which was the result of the
former French land use. Third, MILP models were built to study the effect of an increasing
erosion constraint and distributional issues, both at the farm and the watershed levels. Fourth,
animal nutrient requirements are taken into account. Finally, even though a different methodol-
ogy was used, conclusions are comparable with those of other studies. In particular, it is con-
cluded that farmers’ costs increase when forced to comply to more stringent erosion constraints.
This study has several limitations. First, the number of field activities was limited. An
increase in this number would permit one to run models with more conventional and alterna-
tive practices for a given field, more fields for a given farm, and more farms within a given
watershed, allowing for more complex problems and distributional issues. Also, off-farm
benefits of reducing erosion have not been taken into account. Quantitative economic studies
of off-farm benefits of reducing nonpoint source pollution are rather limited, but such studies
could be used by a government agency to set tax rates or subsidy levels or pollution permit
prices. Third, crop sales between producers could be developed. Transportation costs would
have to be taken into account and these potential sources of trade could be studied both from
an economic and an environmental point of view. Finally, the study reports the results of a
short-term analysis. The development of a multiperiod framework, such as presented by
Miranowski (1984), incorporating GIS at the field level would allow producers in the analysis
to make appropriate changes in their production plans over time.
NOTES
1
LINGO version 6.0 by Lindo Systems Inc. Chicago, Illinois. 1999.
This summing of the three farms into the “watershed” model is used to investigate distributional ques-
2
tions. Therefore, the use of the term “watershed” does not imply that all farms in the watershed are rep-
resented by this model. Rather, the model represents an aggegation of three farms (A, B and C) within
the watershed.

ECONOMICS OF EROSION AND SUSTAINABLE PRACTICES
121
3Field size and other physical characteristics of the fields were not allowed to be altered in the study.
Thus, the analysis is short-run in nature.
4
The farms were to a degree self-selected as few of the 29 participating farmers were willing to collect
the economic data. However, the farms used for this economic analysis were reasonably representative
of the watershed farmers involved in the production of the same commodities. The “representativeness”
implies that the species and size (animal units or hectares) of commodities produced on these farms are
typical of other watershed farmers. However, these farmers do not control all of the land in the water-
shed nor do they produce all of the commodities produced in the watershed.
5
Subsidization of the equipment might encourage farmers to use the sustainable technique employing
the equipment whereas they might not have used the technique in the absence of the subsidization. A
group of the farmers involved in the project purchased the equipment using a subsidy from the project.
Thus they were interested in the sustainable technique, but whether the subsidization was required to
“
cement” the choice of technique was not determined.
6
MJ stands for megajoule.
7“
The C factor is used to determine the relative effectiveness of soil and crop management systems in
terms of preventing or reducing soil loss” (Wall et al 1997, 1.32).
8
“The P factor accounts for the erosion control effectiveness of support practices. . . . The P factor
reflects the effect of practices that will reduce the amount and rate of runoff and thus reduce the amount
of erosion” (Wall et al 1997, 1.43).
9
Field shape in Quebec is quite different from that observed in other parts of Canada, e.g., the prairie
provinces. Due to the historic reliance on water transportation, fields tend to be very elongated in
Quebec with the narrow end adjoining the waterway. This design allowed for maximum access to the
waterway by the most people.
1
0Data generated by M. Mousavizadeh, Department of Agricultural and Biosystems Engineering,
McGill University.
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