endogenous transport coefficients: implications for improving water quality from multi-contaminants...

Environmental and Resource Economics14: 269–296, 1999.© 1999Kluwer Academic Publishers. Printed in the Netherlands.

269

Endogenous Transport CoefficientsImplications for Improving Water Quality from Multi-Contaminants in anAgricultural Watershed

ANASTASIA M. LINTNER1 and ALFONS WEERSINK21Department of Economics, Memorial University, St. Johns, Newfoundland, A1C 5S7, Canada([email protected]);2Department of Agricultural Economics and Business, Universityof Guelph, Guelph, Ontario, N1G 2W1, Canada

Accepted 10 July 1998

Abstract. The effectiveness of imperfect pollution control instruments is examined for a diffusesource, multi-contaminant problem in which the transport coefficients for sediment-bound residualsare endogenous. Similar evaluations fix the percentage of sediment deposited and optimize eitherfor a single firm managing the whole watershed or on a firm by firm basis. This study shows thatignoring the dependence of the transport coefficients on intervening land uses creates a positiveexternality. The filtering potential of activities conducted by firms close to the receptor permits firmsfurther away to undertake more profitable but erosive practices. Optimizing management choices,and consequently endogenizing the transport coefficients, for all firms simultaneously removes theexternality. An empirical application combines hydrological simulation models with an economicoptimization model for nutrient pollution of surface and ground water within an agricultural water-shed. Although firms are homogeneous in abatement costs, differences in spatial location leaveuniform instruments unable to achieve the water quality goal efficiently. An ambient tax/subsidyscheme can achieve the water quality goal efficiently but the informational requirements will beexcessive in most situations where the transport mechanisms for residuals are dependent upon thepractices of independent decision making units.

Key words: transport coefficients, multiple pollutants

JEL classification: Q2

I. Introduction

Nutrients, such as nitrogen and phosphorus, are applied by agricultural producersto enhance plant growth. However, costs in terms of on-farm productivity reduction(Briggs and Bos 1990) and off-farm water pollution (Pearce et al. 1985; PLUARG1978) can result if soil and/or the applied nutrients are lost through erosion andwater infiltration. Nutrient water pollution can cause a number of health problems,upset ecosystem integrity and reduce recreational values. The health effects fromexcess nitrates include infantile methemoglobinemia or blue baby syndrome andstomach cancer in adults (Health and Welfare Canada 1980; Hanley 1990). Inaddition, excess nutrients can cause the growth of blue green algae which producestoxins that are harmful to humans if ingested (Fuller and Flemming 1990). A

270 ANASTASIA M. LINTNER AND ALFONS WEERSINK

nutrient imbalance can affect the food web dynamic by upsetting the photoplanktoncommunity (IJC 1991) and cause excess algae growth which depletes the dissolvedoxygen as it decays (Environment Canada 1987). These ecosystem impacts mayalso influence the recreational enjoyment of the environment. A reduction inoxygen from eutrophication can decrease the stock of valued fish species such astrout and increase the stock of other species which require little oxygen such assludge worms and carp (Environment Canada 1987).

Agriculture is the major diffuse source contributor of nutrients in the waters ofthe Great Lakes Basin (GLWQB 1989). Phosphorus (P) was the key nutrient inthe eutrophication of Lake Erie in the late 1960s and 1970s (Environment Canada1987). Concern over P levels in the Basin led to the implementation of programssuch as the Soil and Water Environmental Enhancement Program (SWEEP) andTillage 2000 which encouraged farmers to change to less erosive farming practicesin order to reduce the amount of P runoff into the Great Lakes (Stonehouse andBohl 1990). The suggested switch to conservation tillage from conventional tillagepractices has several implications for water quality in an agricultural watershed.First, conservation tillage reduces the amount of sediment eroded from a given fieldand allows for the interception or filtering of sediment-bound nutrients carried onto the field from neighbouring locations through surface runoff. Previous studiesexamining the transport of pollutants to surface water simplify the delivery mech-anism. Transport coefficients are assumed fixed or the watershed is treated as asingle farm unit under the control of a social planner (Braden et al. 1990). Ifthe existence of actual farm units and decision makers is not incorporated intothe analysis, then the interdependency of individual farm decisions and emissionsfor the entire watershed may be ignored. However, the dependency of transportcoefficients on intervening land uses with multiple decision making units creates apositive externality for firms located further away from the damage point that mayinfluence the optimal set of practices and policy instruments. In addition, environ-mental policy instruments such as Segerson’s (1988) ambient scheme cannot beevaluated without individual farm units in the model.

Another implication of the switch to conservation tillage is the associated rise ingroundwater nitrogen (N) concentration which has indeed risen in the Great LakesBasin. Tillage stimulates mineralization and nitrification while slowing denitrifi-cation thereby reducing N leaching into the groundwater but it leaves the surfacemore susceptible to erosion and runoff (OECD 1986). Reducing tillage results ingreater infiltration (Bedient and Huber 1992; Kachanoski and Rudra 1992). Indeed,the level of nitrates has risen and this emphasizes the need to consider poten-tial tradeoffs in pollutants when examining how water quality objectives may beefficiently attained. Despite the observed trade-offs among nutrient pollutants fromagriculture and the joint effect these pollutants can have on water quality, previousstudies have generally focused on only one type of pollution at a time. For example,the nitrogen problem was studied by Fernandez-Santos et al. (1993), Johnson etal. (1991), Moxey and White (1994), Pan and Hodge (1994), and Helfand and

ENDOGENOUS TRANSPORT COEFFICIENTS 271

House (1995) and the soil erosion and/or sediment-bound phosphorus problem wasstudied by Braden et al. (1989, 1991), Bouzaher et al. (1990). Teague et al. (1995)develop an environmental risk index for both pesticides and nitrates and examinethe effects on farm income from a reduction in these indices but do not look at alter-native instruments for achieving the environmental objectives. Kramer et al. (1984)used a model to account for both sediment and sediment-bound phosphorus as wellas soluble nitrogen but “no attention was made to model the delivery mechanismfor agricultural nonpoint source pollution” (p. 843).

The purpose of this paper is to evaluate pollution control instruments aimedat simultaneously controlling the concentrations of surface and ground waternutrients given sediment-bound transport coefficients between decision makingunits that are dependent on intervening land uses. The multi-contaminant water-shed management problem presented in this paper for an agricultural watershedin Ontario determines the cost-effective farming and abatement activities whileattempting to meet water quality objectives for two types of nutrient pollution;the concentration of phosphorus in surface water while ensuring no potential foreutrophication (the P:N ratio) and the groundwater concentration of nitrogen. Thepaper begins with a theoretical model that demonstrates the existence of a positiveexternality created for farms within the watershed by the filtering activities of farmscloser to the receptor. An empirical model examines the impact of the externalityon the efficient outcome and the minimum abatement costs of four input and ambi-ent based regulatory instruments; i) a mandatory switch in farming practices, ii)a ceiling on nitrogen fertilizer applications, iii) a uniform nitrogen fertilizer tax,and iv) an ambient tax/subsidy scheme. The modeling of actual firms within awatershed, as opposed to the field-specific approach of previous studies, permitswhat is believed to be the first empirical examination of the system of taxes andsubsidies based on a threshold ambient concentration proposed by Segerson (1988)in order to address a diffuse source pollution problem.

II. Theoretical Model

A. PRIVATE DECISION PROBLEM

To illustrate the impact of filtering by downstream activities and the potential trade-offs associated with multi-pollutants, assume there is a single strip ofF farmseach with a single field in a watershed. Farm location is denoted byj. Distance towatershed outlet increases with the value ofj so that for example Farm 1 is closerto the outlet than Farm 2. Each farm has a choice ofA activities with area devotedto activity i by farm j denoted byXij . Net returns to activityi are given byπi andare assumed to be the same for each farm. Increases in the value ofi indicate anincrease in profitability (π1 < π2 < . . .< πA). Without any regulations, each farmj will use all available area (Xj ) in the most profitable activity. Thus,XA1 = X1,XA2 = X2, . . . , XAF = XF and Xij = 0, i = 1, 2, . . . ,A-1, j = 1, 2, . . . ,F. Whendetermining these optimal decisions for their own operation, the individual farms


do not consider the impact of the pollutants generated from their activities sincethe farmer does not have to pay for the damages done by the nutrients depositedinto the water body. The generation and transport of these residuals is described inthe next section.

B. TRANSPORT AND FILTERING OF RESIDUALS

Farms generate two types of residuals as a result of their production activities; oneleaches into the groundwater and the other is deposited into a surface water body.For activity i, emission rates for the groundwater and surface water pollutants arerespectively denoted byegi andesi . Each are assumed to depend only on the type ofactivity conducted at a given farm and not on farm location. Thus, the total amountof leachate generated by farms within the watershed will be

∑Ai=1

∑Fj=1egiXij

which in the case of no regulations will be∑F

j=1egAXAj . It is assumed that theemission rates for the groundwater pollutant are inversely related to profitabilityimplying eg1 > eg2 > . . .> egA. For example, conventional tillage practices tendto be more profitable and lead to little infiltration of nutrients.

Total amount of surface pollutant produced by farmj is∑A

i=1esiXij but onlya percentage of this total will be deposited at the watershed outlet into the waterbody. Typically, the percentage of sediment-bound emissions transported from agiven farm is assumed to be set exogenously. This percentage of total sedimentdeposited at the outlet from farmj depends on the management practice chosenand is denoted here astij (0< tij < 1). It is assumed both the emission rate of thesurface pollutant and the percentage moving from the farm to the watershed outletdecrease with the value for an activity and thus are positively related to profitability(es1 < es2 < . . .< esA andt1j < t2j < . . .< tAj ). For example, the generally moreprofitable conventional tillage results in more soil erosion than conservation tillageand also permits more of the total eroded material to be transported from the farm.

The amount of sediment transported from a given farm into the waterbody notonly depends on the location of the farm and the production activities taking placeon that farm but also on the activities of farms between it and the outlet andthe size of those farms. Rather than being fixed, the dependence of the transportcoefficient on intervening land uses is incorporated into the model by denotingthe percentage filtered from farmj by farm j − k that is k farms closer to thewaterbody asfj−k(X1,j−k, . . . , XA,j−k. It is assumed that the percentage filteredfor the same activity will be the same in different downstream farms of equal size(∂fj−1/∂Xi,j−1|X1,j−1=c = ∂fj−2/∂Xi,j−2|Xi,j−2=c) and more filtering occurs in a givenfield from activities with lower surface pollutant emission rates (∂fj−k/∂Xi,j−k >∂fj−k/∂Xi+1,j−k). The total percentage filtered by downstream farms must be lessthan or equal to one thereby preventing residuals being removed from the surfacewater body through agricultural activities (0≤∑j−1

k=1fj−k(X1,j−k, . . . ,XA,j−k)≤ 1).Incorporating the filtering activities of downstream farms directly into the

model makes the transport coefficient endogenous rather than exogenous. Implic-


itly embedded in the fixed transport coefficient (tij ) are assumptions related to thesize and activities of farms closer to the outlet. For example, it may be thattijassumes all downstream farms use the same management practicei, tij = 1 −∑j−1

k=1fj−k(Xi,j−k). The percentage transported from farms further away from thereceptor will be greater than those close despite all farms using the same practicebecause of the number of farms available to filter. Another common formulationis to assume the least erosive land use on the farm closest to the outlet while allother farms use the same activity,tij = 1−∑j−1

k=2fj−k(Xi,j−k) − f1(X1,1). Ignoringthe dependency of the transport coefficients on intervening land uses when evalu-ating the optimal management choices for independent farms to meet water qualityobjectives can create a potential externality as illustrated below.

C. SOCIAL DECISION PROBLEM

The socially optimal level of leachate and surface pollutant is where the marginalabatement cost is equal to the marginal damage of those residuals. The privatedecisions of producers result in pollutant levels which are greater than the sociallyoptimal since the farmers do not have to pay for any associated environmentaldamages. The negative externaility thereby created can be addressed by inducingfarmers to change from their current practices (activity A) to one which reduces theresiduals to the socially optimal levels. This practice can be determined by solvingthe follwing social decision problem where the objective of the regulator is to maxi-mize watershed profits through the choice of management activities on each farmwhile meeting water quality objectives for the two residuals. These environmentalobjectives are met through the imposition of restrictions to the socially optimallevel of soluble residuals moving into groundwater,G, and sediment-bound pollu-tants moving into surface water,S. This problem with a fixed transport coefficientcan be formally stated as;

ζ(X,µ,λ) = MaxX,µ,λ

{∑Ai=1

∑Fj=1 πiXij +

∑Fj=1µj (Xj −

∑Ai=1Xij )+ λG(G−

∑Ai=1

∑Fj=1 egiXij )

+λS(S −∑Ai=1

∑Fj=1 tij esiXij )} (1)

and with a transport coefficient dependent on intervening land uses as;

ζ(X,µ,λ) = MaxX,µ,λ

{∑Ai=1

∑Fj=1 πiXij +

∑Fj=1µj (Xj −

∑Ai=1Xij )+ λG(G−

∑Ai=1

∑Fj=1 egiXij )

+λS(S −∑Ai=1

∑Fj=1((1−

∑j−1k=1 fj−k (X1,j−k, . . . , XA,j−k))esiXij ))} (1′)

whereζ is the Lagrangean function,µj is the marginal value of an extra unit ofland to farmj, andλ is the marginal reduction in watershed profits associated witha decrease in the level of allowable pollutant, either soluble (G) or sediment-bound(S). It is assumed that some of the total emission level of sediment is depositedinto the waterbody so that the associated constraint on filtering activities of down-


stream farms is non-binding for simplicity. The resulting Kuhn-Tucker first orderconditions for the management choices are thus;

{πi − µj − λGegi − λS tij esi }Xij = 0. (2)

{πi − µj − λGegi − λS [(1−

∑j−1k=1 fj−k(·))esi −

∂fj (·)∂Xij

(∑Ai=1

∑Fk=1 esiXij+k )]

}Xij = 0. (2′)

In the private decision problem with no regulations on the pollutants, watershedprofits are maximized by growing the most profitable activity (A) on each farm asdescribed previously. The shadow price for an extra unit of land is the net return toactivity A (µj = πA). In addition, the marginal abatement cost of controlling eitheremission type is zero (λG = λS = 0).

If the only environmental regulation binding was on the soluble pollutant, thenall farms would still be using the same management practice (A) given the earlierassumption that relative profitability is inversely related to the leachate emissionrate. For the optimal activity, the difference between per unit area net returnsand costs of meeting the standard will be maximized. These per unit area costsare the marginal abatement cost or reduction in watershed profits from tighten-ing the groundwater quality objective (λG) multiplied by the emission rate of theactivity (eg). Under the present assumptions, the returns to an extra unit of landor the difference between net farm returns and abatement costs for the optimalactivity will be maximized through the choice of practiceA (µj = πA − λGegA).Taxing leachate emissions atλG would generate funds to compensate to coverenvironmental damages and thereby address the externality.

Fixed Transport Coefficients

If the binding environmental regulation was on the sediment-bound pollutant, thenall farms would not likely use the same practice. The per unit area costs of theenvironmental regulation without filtering explicitly considered areλStijesi . Whilethe marginal abatement cost and emission rate for a given activity are the sameacross farms, the transport coefficient (tij ) varies depending on farm location andthus so will abatement costs. Costs of meeting the water quality objective will begreater for farms closer to the waterbody (farms will lower values ofj and thushigher values oftij ). Therefore, those farms should more likely adopt practices thatreduce soil erosion rates (practices with lower values ofi) despite having lower netfarm returns. In contrast, farms further away from the watershed outlet are morelikely to use more erosive but more profitable activities since a smaller proportionof the sediment is transported to the damage point. The actual mix of activities foreach farm depends on relative profitability and emission rates for the practices andfarm location. The socially optimal practice for each farmj maximizes the differ-ence between net returns and abatement costs (µj = πj − λStijegi). The resultingactivity that addresses the externality can be induced through forcing the farm toadopt that practice or through a selection of a Pigouvian tax on surface emissions.


Differing abatement cost functions between farms according to distance is the basison which targeting erosion efforts has been promoted.

Endogenous Transport Coefficients

While previous studies have accounted for proximity to the waterbody in determin-ing the socially optimal management practice for each farm, the externality effectfor interior farms from the filtering potential of activities conducted on interveningfarms has not been incorporated. The dependence of the first order conditions forXij (2′) on management choices in other fields requires the FOCs for all fields tobe solved simultaneously. Per unit area cost of meeting the sediment water qualityobjective which accounts for filtering is

fj−k(·))esi − ∂fj(·)∂Xij

(

A∑i=1

F∑k=1

esiXij+k)]. (3)

The first component (1− ∑j−1k=1fj−k(·)) represents the percentage of the emis-

sion rate that is deposited into the waterbody by all farms from 1 toj − 1that are downstream from farmj. The greater the number of downstream farmsthe greater the reduction in cost for meeting the sediment objective and thusthe more likely the farms will adopt more erosive but profitable practices. Thesecond component represents the change in the filtering rate from farmj due to itschoice of management practice (∂fj (·)

∂Xij) on total emissions from all upstream farms

(∑A

i=1

∑Fk=1esiXij+k). The closer the farm is to the waterbody and thus the larger

the total emissions available to filter, the greater will be the reduction in socialabatement costs from changing to a less erosive practice. Whether adoption of aless erosive practice occurs depends on relative net farm returns and the differencein abatement costs with a fixed transport coefficient (λS tijesi) and the costs withendogenously determined transport as given by (3). The externality resulting fromexplicitly recognizing the filtering activities of downstream farms also allows forthe possibility of more erosive practices by upstream farms.

The value of the externality associated with filtering can be illustrated in thecase of two farms, Farms 1 and 2. The marginal value of land for these two farmsare respectively;

µ1 = πi − λGegi − λS{esi − ∂f1(Xi1)

∂Xi1(

A∑i=1

esiXi2)

}(4)

µ2 = πi − λGegi − λS{(1− f1(Xi1))esi} (4′)

The optimal solutions for each farm with a fixed transport coefficient will be theactivity that maximizes the difference between the net returns to an activity and theabatement costs of meeting the environmental constraints which will beπi − λGegi− λSesi for Farm 1 andπi − λGegi − λSti2esi for Farm 2. The solution for Farm


2 under the assumption of exogenous transport coefficients requires taking Farm1’s actions as given. For example, Farm 2 could assume that Farm 1 chooses themost profitable activity which meets the water quality objective on sediment-boundpollution. If this is activityA− 2, then the assumed transport coefficient from Farm2 using the same activity istA−2,2 = 1− f1(XA−2,1). The resulting private solutionfor Farm 2 is assumed to be a more erosive but profitable activity,A− 1. The totalamount of sediment (esA−2XA−2,1 + esA−1tA−1,2XA−1,2) eroded does not exceed thestandard.

The socially optimal solution, however, considers the positive externalitycreated by Farm 1’s filtering activity to the owner of Farm 2. The marginal value ofland to Farm 1 is increased by the amount that abatement costs are reduced to Farm2 by Farm 1’s choice. These abatement costs consist of the marginal abatement cost(λS) and the amount of Farm 2’s sediment pollutant reduced by Farm 1’s filtering( ∂f1(Xi1)

∂Xi1(∑A

i=1esiXi2)). Consideration of the filtering in the simultaneous solutionof the two first order conditions, will increase the marginal returns to land in thewatershed. For example, if the socially optimal practices areA− 3 for Farm 1 andA for Farm 2, then

[πA−3− λGegA−3 − λS{esA−3 − ∂f1(XA−3,1)

∂XA−3,1(esA,2XA,2)

}] +

[πA − λGegA − λS{(1− f1(XA−3,1))esA}] >[πA−2− λGegA−2 − λS

{esA−2 − ∂f1(XA−2,1)

∂XA−2,1(esA−1,2XA−1,2)

}] +

[πA−1− λGegA−1 − λS{(1− f1(XA−2,1))esA−1}]The difference represents the value of the filtering externality.

In summary, three scenarios have been presented. The first is the private deci-sion problem in which each individual farm maximizes net returns by adoptingthe most profitable management activity (A). There are two socially optimal solu-tions considered. One assumes the only externality is associated with the damagescaused by the pollutants and assumes a fixed transport coefficient for the sediment-bound pollutant. The optimal activity for each farm is the one that maximizessocial returns which is net returns less abatement costs of meeting the water qualitystandard. In the case where the private solution results in sediment-bound pollutiongreater than the socially optimal (S), the social net returns per land area for activityj is µj = πj − λStijegi . The final scenario considers the environmental damagesplus the positive externality from the filtering potential of activities conducted byfarms close to the waterbody. Endogenizing the transport coefficient into the socialdecision model explicitly recognizes the filtering activities of downstream farmswhich allows upstream farms to use more erosive but profitable practices therebyincreasing total returns for the watershed.

The existence of multi-contaminants is also incorporated into the model. It hasbeen assumed here that practices which generate high sediment levels produce the


lowest emissions of soluble pollutants. The trade-off between pollutants is typicalfor nutrients used in agricultural production which are transported with surfacewater and groundwater through runoff and infiltration respectively. Conventionaltillage mixes or inverts all of the topsoil whereas conservation tillage leaves protec-tive amounts of crop residue on the soil surface. The rougher surface due tothese residues allows less water to runoff thereby reducing soil erosion. Whilesediment-bound surface emissions maybe reduced with conservation tillage, solu-ble emissions into the groundwater may increase due to the larger soil poresassociated with conservation tillage. The optimal management choice for a givenfarm as determined by the FOC’s given by (2) or (2′) will depend on the restrictionlevels for the residuals, and the emission rates and profitability of each activity.

III. Empirical Model

The theoretical model is empirically estimated for an agricultural watershed inwhich the surface pathway is not linear and there are distinct independent deci-sion makers controlling possibly multiple fields. The objective of the regulatorremains to maximize watershed profits while meeting water quality objectives forboth sediment-bound and soluble pollutants. The concentration of surface P (whilemaintaining an appropriate P:N ratio) and the concentration of groundwater N arecontrolled. The surface water constraint is complicated by the fact that there is bothsoluble and sediment-bound N moving into surface water. Soluble P emissions arenegligible and are ignored in the analysis (Frere et al. 1980). Concentrations of thenutrient pollutants in the surface water and groundwater are jointly determined bywater volumes, emissions, transport mechanisms, and pollutant pathways. Thesepathways are not linear in reality and a hydrological simulation model is necessaryto estimate the both the transport coefficients and emission levels. Formally, theproblem is represented as:

MaxX

∑Ai=1

∑Fj=1πiXij (5a)

subject toXij ≥ 0∀ i, j (5b)∑Ai=1Xij = Xj∀j (5c)

Xlj = Xmj = Xnj∀j, and crops l, m, n in rotation i (5d)∑Ai=1

∑Fj=1 espi tj0(Xi1,...,Xij−1)Xij∑Ai=1

∑Fj=1 riXij+RO

∗ 100≤ SP (5e)

∑Ai=1

∑Fj=1 es

′ni tj0(Xi1,...,Xij−1)Xij+(∑Ai=1

∑Fi=1 egniXij+NSO)∑A

i=1∑Fj=1 riXij+RO

∗ 100≤ ¯SN (5f)

∑Ai=1

∑Fj=1 egniXij∑A

i=1∑Fj=1 diXij+IO

∗ 100≤ GN (5g)


Nonnegativity, land availability, and rotational conditions are represented by theconstraints 5b, 5c and 5d respectively. These constraints together with the objectivemake up the profit maximizing problem for the entire watershed when pollutionemissions are not controlled. This is the private decision problem or base model.

The social decision model involves maximizing watershed profits while ensur-ing the water quality objectives are met. The environmental considerations areincorporated by adding constraints on residual levels to the base model throughequations 5e, 5f, and 5g.1 Constraint 5e requires that the average concentrationof surface water phosphorus, which is equal to total loadings divided by thetotal volume of runoff, be less than or equal to some levelSP (mg/L). Since thetotal amount of nutrients transported and water volume depend on the number ofhectares chosen for each activity, this constraint along with 5f and 5g are non-linear. Total loadings are determined by taking emissions from each field andcalculating the amount which will reach the watershed outlet. The emission rateof sediment-bound P from activityi (kg/ha) is denoted byespi . The percentageof these emissions from fieldj that reaches the outlet (O) is given by the transfercoefficient tjO . The transport mechanism depends on activities chosen for fieldsdownstream from fieldj starting from the adjoining fieldj − 1 to the field closestto the water outlet 1. The transport pathway is not generally linear so the transportcoefficient is written as a general function of intervening land activities ratherthan explicitly defining the filtering process as in the theoretical model. Volumeof runoff is determined using runoff depth from activityi (ri) multiplied by areafor all fields engaged ini and then adding runoff from other areas in the watershed,such as bush and roadways (RO).2

The second environmental constraint (5f) ensures that nitrogen concentrationin surface water does not exceed some specified concentration,SN. Concentrationis calculated in a similar fashion to that of P discussed above except that solubleemissions of N must be accounted for.3 The first term in parenthesis of total surfaceN loadings represents emissions of sediment-bound N. This level is found by takingemissions from each activity (esni ), multiplied by area allocated to that activity andthen the transport mechanism is used to determine the amount reaching the outlet.The second term in the numerator represents soluble N emissions. Total solubleN load for surface water is determined by adding up emissions from each activity(es’ni ) and each field plus any other soluble emissions (NSO). The soluble load isin solution in the runoff water and is therefore completely transported to the outletwithout any deposition. Runoff volume is calculated using the same method asfor P.

The final constraint, 5g, provides a condition for groundwater nitrogen concen-tration,GN. The numerator sums the total soluble N load moving further into thesoil which depends on the emissions of soluble ground pollutant from activityi(egni ). The denominator calculates the volume of infiltration water as the sum ofthe depth of water infiltrating soil for each activity (di) multiplied by the area


for each of the activities and each of the fields.4 Infiltration from the bushes,farmsteads, and the road must be also accounted for (IO).

TheF fields in the social planner model are not generally owned and operatedby F individuals. Rather, an individual producer manages a set of fields. The multi-contaminant model just developed can be extended to account for this situation bysetting uph objective functions whereh is the number of farm operators (h ≤ F).Each operator chooses the activities for fields only under her control independentof the activities of others. The designation of the decision making units is importantin the presence of endogenous transport coefficients. With the interdependency ofland uses, the optimal choices must be chosen simultaneously or an externality iscreated for upstream farms as demonstrated earlier. The effect will be internalizedif all fields in the watershed are under the control of a single farm operator.

IV. Data

The multi-contaminant pollutant control model with endogenous transport coeffi-cients is applied to an Ontario agricultural watershed to determine the effectivenessof policy instruments for achieving multiple environmental objectives. The nextsection describes the information used to implement the model.

A. STUDY AREA

The watershed used in this study is a sub-watershed of the Lake St. Clair drainagebasin located in Maidstone Township, Essex County, Ontario. This 280 hectarewatershed was chosen for the Pilot Watershed Study by Agriculture Canada toexamine the effects of alternative farming practices on soil erosion and phosphoruscontamination (Agriculture Canada 1990). The 15 farms partly contained withinthe boundary of the watershed happen to possess identical physical characteristics(slope, soil type, etc.) in all aspects except distance to watershed outlet. The soil isa poorly drained Brookston clay loam (Agriculture Canada 1990). The watershedis further divided into 65 fields among these 15 farms. The division of farms, fieldsand field size along with the direction of water flow throughout the watershed isillustrated in Figure 1.

B. MANAGEMENT SYSTEMS

Agricultural activities of the watershed are exclusively cash cropping, withsoybean, corn, and wheat grown on 56, 14 and 10 percent, respectively, of thewatershed over the period 1989 to 1991 (Deloitte and Touche 1992a). Five three-year crop rotations based on actual rotations employed over the life of the PilotWatershed Study are evaluated; i) continuous corn (CCC), (ii) corn followed bytwo years of soybean (CSS), (iii) corn-soybean-wheat (CSW), (iv) wheat followedby two years of soybean (WSS), and (v) an alfalfa hay pasture (HHH) (see column


Figure 1. Farm boundaries, field boundaries, and water flow direction for Maidstone Water-shed.

3, Table I). These rotations are grown using either conventional tillage (CT) or no-till (NT) (see column 5, Table I). In addition, two nitrogen fertilization levels areassumed for corn (see column 6, Table I). The first is the actual average N applica-tion (A) of approximately 133 kg/ha given in the Pilot Watershed Study (Deloitteand Touche 1992b). The second is the privately-efficient use (M) defined where themarginal value product of nitrogen is equal to its cost. Yield response curves fromBeauchamp et al. (1987) were used in determining the marginal product. The Mlevels on corn were less than the A levels for the CSS rotations but were higher onother rotations with more corn. Actual average applications of fertilizer were usedwhere possible for the remaining crops, otherwise suggested applications given bythe Ontario Ministry of Agriculture and Food (1988) were used (both are denotedA).

A total of 35 farming activities representing a combination of crop withina particular rotation and the tillage practice and fertilizer application used areidentified. Together these annual activities define 15 farm management practiceswhich are a specific combination of crop rotation (5), tillage method (2), and cornfertilization level (2).5 The relationship between activities and farm managementpractice required for the rotation constraints is given in Table I. Suppose the farmerchooses to grow one hectare of conventionally tilled corn followed by two yearsof soybeans (CSS-CT-M, or management practice 6 in Table I). Over the three


year rotation, a choice of farm management practice 6 will require a hectare ofconventionally tilled corn in the first year, and one hectare of conventionally tilledsoybeans in each of the second and third years. As such, the model requires thatfor one hectare of the CSS-CT rotation there will be one-third of a hectare of cornand two-thirds of a hectare of soybeans.

Yield, output price, and input cost for each farming activity are based onactual farm data gathered in the Pilot Watershed Study (Agriculture Canada 1990;Deloitte and Touche 1992a, b) or, if the necessary information was not gath-ered, from provincial sources (OMAF 1988, 1992). Table I lists the subsequentnet revenues for each annual activity (column 7) and for each farm managementpractice averaged over three years (column 8). Corn is the most profitable activityprovided it is in a rotation with another crop. The most profitable farm managementpractice is corn followed by two years of soybeans. Soybeans allow for higher cornyield and a lower cost than other rotations which include corn. The least profitablefarm management practice is continuous corn under conventional tillage.

C. EMISSIONS AND TRANSPORT

Field characteristics, rainfall, and farm management practices are all used in thehydrological simulation model to determine the level of emissions and their trans-port generated under alternative conditions. The Agricultural Non-Point SourcePollution (AGNPS) model was chosen for its ability to determine surface andground water implications for many different pollutants, including nitrogen andphosphorus, at the same time (Young et al. 1994). Emissions of soluble N availableto leach into the groundwater is determined through AGNPS using the Chemi-cals, Runoff and Erosion Agricultural Management Systems algorithm (Frere et al.1980). Infiltration and runoff volumes resulting from the different farm manage-ment practices are calculated using the Soil Conservation Service Curve Numbermethod (Bedient and Huber 1992). The transport mechanism for sediment-boundpollution is determined using the soil deposition output from the AGNPS model.The pathways indicate the direction of the movement of the pollutants to thewatershed outlet from each of the fields (Figure 1). The transport mechanismdetermines, for each farm management practice chosen, the amount of pollutantsfrom any given field which reach the outlet given the farming activities chosen“downstream”. Water volumes, emissions, transport mechanism, and pollutantpathways all jointly determine the pollution concentrations in the surface waterand groundwater.

The hydrological simulation is carried out for a single storm. Details on stormduration, intensity, and total rainfall are found in Hogg and Carr (1985). Pollu-tant pathways are determined using topographic maps and the Pilot WatershedStudy (Agriculture Canada 1990; Energy Mines and Resources 1986). Other para-meters required to run the AGNPS model are found using: Bedient and Huber

282A

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Table I. Farm management practices and pollutant parameters.

Practice Activity Rotation Crop Tillage Fertil Annual 3 yr avg Emissions (kg/ha) Runoff Infilt.

(i) profits profits Surface Ground (mm) (r) (mm) (d)

($/ha) ($/ha) Sed P (esp) Sed N (esn) Sol N (es’n) Sol N (egn)

1 1 CCC C CT A 93.33 93.33 1.01 2.03 1.09 2.48 47 35

2 2 CCC C CT M 59.32 59.32 1.01 2.03 1.23 2.88 47 35

3 3 CCC C NT A 137.25 137.25 0.30 0.61 0.64 4.67 32 50

4 4 CCC C NT M 103.49 103.49 0.30 0.61 0.73 5.42 32 50

5 5 CSS C CT A 214.19 172.61 1.20 2.39 1.09 2.48 47 35

6 CSS S CT A 151.83 0.95 1.91 0.08 0.06 38 44

7 CSS S CT A 151.83 1.12 2.24 0.08 0.06 38 44

6 8 CSS C CT M 214.8 5 172.84 1.20 2.39 0.95 2.17 47 35

9 CSS S CT A 151.8 3 0.95 1.91 0.08 0.06 38 44

10 CSS S CT A 151.8 3 1.12 2.24 0.08 0.06 38 44

7 11 CSS C NT A 253.1 0 144.70 0.57 1.13 0.64 4.67 32 50

12 CSS S NT A 90.50 0.54 1.07 0.06 0.08 25 57

13 CSS S NT A 90.50 0.52 1.02 0.06 0.08 25 57

8 14 CSS C NT M 255.9 0 145.63 0.57 1.13 0.57 4.08 32 50

15 CSS S NT A 90.50 0.54 1.07 0.06 0.08 25 57

16 CSS S NT A 90.50 0.52 1.02 0.06 0.08 25 57

9 17 CSW C CT A 204.2 6 161.53 1.01 2.03 1.09 2.48 47 35

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Table I. Continued.

Practice Activity Rotation Crop Tillage Fertil Annual 3 yr avg Emissions (kg/ha) Runoff Infilt.

(i) profits profits Surface Ground (mm) (r) (mm) (d)

($/ha) ($/ha) Sed P (esp) Sed N (esn) Sol N (es’n) Sol N (egn)

18 CSW S CT A 151.8 3 0.95 1.91 0.08 0.06 38 44

19 CSW W CT A 128.5 0 0.63 1.26 0.42 1.52 39 43

10 20 CSW C CT M 223.4 3 167.92 1.01 2.03 1.39 3.24 47 35

21 CSW S CT A 151.8 3 0.95 1.91 0.08 0.06 38 44

22 CSW W CT A 128.5 0 0.63 1.26 0.42 1.52 39 43

11 23 CSW C NT A 244.2 8 154.87 0.56 1.11 0.64 4.67 32 50

24 CSW S NT A 90.50 0.54 1.07 0.06 0.08 25 57

25 CSW W NT A 129.8 2 0.37 0.74 0.30 3.20 27 55

12 26 CSW C NT M 264.6 9 161.67 0.56 1.11 0.82 6.11 32 50

27 CSW S NT A 90.50 0.54 1.07 0.06 0.08 25 57

28 CSW W NT A 129.8 2 0.37 0.74 0.30 3.20 27 55

13 29 WSS W CT A 128.5 0 144.05 0.63 1.26 0.42 1.52 39 43

30 WSS S CT A 151.8 3 0.79 1.57 0.08 0.06 38 44

31 WSS S CT A 151.8 3 1.12 2.24 0.08 0.06 38 44

14 32 WSS W NT A 129.8 2 103.61 0.37 0.74 0.30 3.20 27 55

33 WSS S NT A 90.50 0.49 0.99 0.06 0.08 25 57

34 WSS S NT A 90.50 0.52 1.02 0.06 0.08 25 57

15 35 HHH H NT A 70.99 70.99 0.59 1.18 0.08 0.06 38 44

– – Bush – – – 0.00 0.00 0.21 0.10 0.20 0.00 24 58

– – Farm – – – 0.00 0.00 0.00 0.00 0.00 0.00 40 42

Notes: Crops in rotation are corn (C), soybeans (S), wheat (W), and hay (H). Tillage choices are either conventional tillage (CT)or no-till (NT). Corn fertilization levels (Fertil) are either efficient (M) or actual use (A).


(1992), Frere et al. (1980), Joy (1994), National Engineering Handbook (1972),Wischmeier and Smith (1978), and Young et al. (1987, 1994).

Sediment-bound emissions of nitrogen (esn) and phosphorus (esp) are listed foreach activity in Table I (columns 9 and 10). Sediment-bound emissions for bothpollutants are highest for corn in the corn-soy-soy rotations under conventionaltillage (activities 5 and 8). The second year of soybeans in the same rotation withconventional tillage emits the second highest amount of sediment-bound pollutants.A switch from conventional tillage to no-till reduces sediment-bound emissions ofboth N and P. Emissions of soluble N (es’n) moving to surface water (column 11Table I) are highest for corn under conventional tillage. Again, a switch to no-tillreduces emissions to the surface water. Soluble groundwater nitrogen emissions(egn) are highest for no-till corn activities (column 12 Table I). In contrast to solu-ble N moving to surface water, a switch from conventional tillage to no-till willincrease emissions of soluble N moving to the groundwater. In general, a move-ment to no-till farming will decrease runoff and increase infiltration as indicatedby the levels of runoff (r) and infiltration (d) (columns 13 and 14 Table I).

Transport of sediment-bound emissions to the watershed outlet depends uponthe activities chosen on all fields which are in a pathway to the outlet. The transportcoefficients are from the field to the neighbouring field rather than to the outlet asin the theoretical model due to the nonlinearity and the large number of possiblecombinations of intervening farms and their management choices. The transportmechanism is demonstrated with the following example. Sediment travels fromfield 1 across field 2, field 3, the farmstead and out of the watershed (see Figure 1).Suppose that on field 1, practice 6 is used which will result in sediment-boundphosphorus emissions of 6.18 kg.6 These emissions move to field 2. Activitieschosen for field 2 generate emissions from that field and also influence the extentthat the emissions received from field 1 proceed toward the watershed outlet orsurface water. If the same practice is grown on field 2, about 80% of the originalemissions from field 1, 5.01 kg, will also leave this field and move to field 3.7 Theseemissions will continue to travel across the farmstead and out the watershed withthe extent of deposition depending upon the activities chosen in fields along theway.

V. Results

a. PRIVATE DECISION PROBLEM

The profit maximization solution for the entire watershed when pollution emissionsare not controlled is for all farms to grow a rotation of corn followed by two yearsof soybean using conventional tillage with the efficient nitrogen use on corn (farmmanagement practice 6). Average profits for the entire watershed over the threeyears are $47,129.10 per year and each farm will annually earn per hectare averageprofits of $172.84. Average emissions, runoff, and infiltration per hectare are alsothe same for every farm. These values, combined with the transport mechanism,


determine the concentrations of pollutants in surface and ground water. At theoutlet of the watershed, the phosphorus concentration is 0.8 milligrams of phos-phorus per litre (mgP/L) with yearly concentrations ranging from 0.67 mgP/L in theyear corn is grown to 1.28 mgP/L in the second year of soybeans due to the highererosivity of the latter crop. Nitrogen concentrations are 2.4 and 1.7 milligrams ofnitrogen per litre (mgN/L) in the surface and ground waters respectively. Yearlyconcentrations in the surface water are 3.30 mgN/L when corn is grown, 2.36mgN/L in the first soybean year, and increasing up to 2.77 mgN/L when the secondsoybean crop is planted.8 In this case, the erosivity of the soybean crop is counter-balanced by the low soluble N emissions associated with soybeans. GroundwaterN concentrations are much higher when corn is grown in the rotation (5.31 mgN/Lvs. 0.16 mgN/L for soybeans) due to the high application levels of N fertilizer usedfor corn.

The only pollutant concentration for which a standard presently exists inOntario that has any regulatory basis is soluble N in groundwater. The solubleN concentration (1.7 mgN/L) estimated for the watershed is below the drinkingwater quality guideline of 10 mgN/L. The surface water phosphorus concentrationof 0.8 mgP/L would indicate a potential eutrophication problem since the surfaceP concentration is greater than 0.01 mgP/L (p. 342, Mengel and Kirkby 1987).However, the emissions which reach the Belle River will depend upon whether ornot the land use between the watershed and the river serves to further reduce orto enhance the transportation of emissions. For example, if farmland between thewatershed outlet and the Belle River is under no-till, emissions originating fromthe watershed may be reduced to a negligible amount. Although these issues areimportant to the amount of pollution reaching the Belle River, and eventually LakeSt. Clair, for the purposes of this paper the surface water quality is considered atthe watershed outlet.

B. SOCIAL DECISION PROBLEM

Since water quality objectives are only violated with respect to the level ofphosphorus in surface water, the cost-effective allocation of farming activities isdetermined for reducing the P concentration, while at the same time maintainingthe nitrogen water quality objectives that the surface N concentration be no morethat ten times the P concentration and that watershed groundwater concentrationof N be no more than 10 mgN/L. The optimal allocation of farming and abatementactivities is determined where the marginal benefit of abatement is equal to themarginal abatement cost (Field and Olewiler 1995; Tietenberg 1992). Since themarginal benefits of P abatement are unknown and a P concentration level less thanthe eutrophication threshold of 0.01 mgP/L cannot be achieved with any farmingactivities, the “optimal level” of abatement is assessed by arbitrarily setting thewater quality goal at a surface water P concentration of 0.64 mgP/L which repre-


sents a 20% reduction in the concentration while at the same time maintaining theestablished nitrogen surface and ground water quality objectives.

The cost effective solution to this environmental goal requires only Farms 2 and4, which are closest to the outlet (Figure 1), to change from their base solutionpractice of growing a corn-soy-soy rotation under conventional tillage. These twofarms each switch one field to conventionally tilled corn-soy-wheat (managementpractice 10) and one field to no-till corn-soy-wheat (management practice 12)(Table II). Initial restrictions on P prompt a change in the last crop grown in therotation due to the lower emissions of sediment-bound pollutants and lower trans-port coefficients associated with growing wheat as compared to soybeans. Furtherconstraints on P from this initial restriction up to the 20% desired reduction causeno-till continuous corn to be grown on one field by the affected two farms. Whilethe change in activities for Farms 2 and 4 do reduce loadings directly and therebyserve to dilute the overall P concentration, the major reason for the runoff reductionfrom the watershed is that their activities act as a filter that reduces the transportof surface pollutants from other farms. Other farms in the watershed could thusbe considered as free riders unless they compensate Farms 2 and 4 for bringingthe watershed into compliance. However, their position in the watershed results inthose farms having larger marginal benefits from a given pollutant reduction thanother farms. Consequently, the cost-effective policy would target Farms 2 and 4.

Annual watershed profits are reduced by $113.15 to $47,015.95 or $172.42/ha.9

Profits of Farms 2 and 4 are reduced by 1.5% and 3.3% respectively relative tothe base solution. The shadow value of this 20% reduction in P concentration is$1,415.90 per mg/L which can be used as the marginal abatement cost for thepurpose of setting emission taxes.10 Despite the restrictions on the P concentra-tions, water quality objectives on nitrogen concentrations are still met. Surfacewater N concentration of 2.2 mgN/L fell due to the switch in management practicesbut groundwater N concentration rose from 1.8 mgN/L on both affected farmsto 2.9 mgN/L on Farm 2 and 4.1 mgN/L on Farm 4. The result illustrates thetrade-off between nutrient pollutant levels which motivated development of themulti-contaminant model. Other empirical examples may lead to situations whereall excess nutrient levels exceed optimal levels.

Externality of Filtering by Intervening Land Uses

The socially optimal set of farming practices requires only two farms to deviatefrom their profit maximizing choices. The result not only illustrates the efficiencyof targeting but also the positive externality created by the filtering activities offarms closer to the outlet for farms further away. As illustrated in the theoreticalmodel, the value of the externality for a given farm depends on its location and theassumptions it makes regarding practices conducted by intervening farms.

Location affects the value of the externality in two ways. First, is its impact onthe farms for which there is an inter-relationship. For example, any eroded sedimentfrom Farm 1 travels only onto fields operated by Farm 2 (Figure 1) and therefore

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Table II. Effects of instruments on farm management practices, profit and water quality.

Farm management practice (% of watershed area) Farm profit Water quality

Instrument CSS-CT CSW-CT CSW-NT WSS-CT HHH before tax Surface Surface Ground

(6) (10) (12) (13) (15) ($/ha) P (mg/L) N (mg/L) N (mg/L)

Base 1.00 172.84 0.80 2.4 1.7

Cost-effective abatement 0.94 0.04 0.02 172.42 0.64 2.2 1.9

Mandatory wwitch to 1.00 161.67 0.43a 2.2 5.5

no-till

N ceiling

(0 kgN/ha) 1.00 70.99 0.64 1.5 0.1

(29 kgN/ha) 1.00 144.05 0.75 2.0 1.2

Ambient tax/subsidy 0.94 0.04 0.02 172.42 0.64 2.2 1.9

($1415.9/mg P/L)

Note – Dollar values and concentrations are averaged over the duration of a rotation (3 years)Practices: CSS = corn-soy-soy, CSW = corn-soy-wheat, WSS = wheat-soy-soy, HHH = continuous hay, CT = conven-tional tillage, NT = no-till, (.) = farm management practice from Table I.a Instrument exceeds P goal by 33%


receives no direct value from the filtering activities of Farm 4. The opposite is truefor Farm 6. Second, is the impact on the number of intervening farms and the valueof the externality from each. Farm 4 (Field 5) is the direct outlet for any sedimentfrom both Farms 6 and 12 but the importance of Farm 4’s choices for this field aremore important to Farm 6 than Farm 12 which is further away from the outlet andhas several other farms which act to filter eroded soil.

The value to the watershed of the filtering externality by intervening farmsalso depends on the assumptions made by other farms regarding the activities ofintervening farms and thus the transport coefficients. A number of combinationsfor each farm and management practice are possible so to simplify the illustration,consider only Farms 4 and 6. If Farm 6 assumed that Farm 4 would not change fromits private profit maximizing solution (CSS under conventional tillage), the envi-ronmental constraint on sediment loading could be met if Farm 6 went to a CSWrotation under conventional tillage. Farm 6 would suffer a per hectare loss of $5.02(172.94–167.92). However, if Farm 6 assumed that Farm 4 would either replace thesecond soybean crop with wheat or switch to no-till (which in both cases increasesits filtering potential), Farm 6 could maintain its profit maximizing solution. Thevalue of the filtering externality is limited by the small change required to meetthe phosphorus constraint. Further restrictions on sediment loading would increasethe number of activities between the two farms that would meet the constraint andthereby also increase both the externality value and possible number of values.

C. EVALUATION OF CONTROL INSTRUMENTS

The socially optimal instrument would achieve the environmental goal(s) at leastcost. The cost effective solution above involves field specific standards on emissionlevels of individual firms (performance base).11 However, field-specific stan-dards or taxes on relatively homogeneous farms may be administratively difficultfor the regulator to implement and politically infeasible. Uniform instrumentson emissions12 may then be an alternative but both firm-specific and uniformperformance-based instruments require emissions to be observable. Emissionscould be estimated with the type of physical simulation used in this study. However,current models are costly to apply regularly due to data needs and cannot providesufficiently accurate estimates of the complex fate and transport process to with-stand legal challenges. Without the ability to measure or proxy the instruments at areasonable cost, the regulator may need to resort to input-based or ambient-basedinstruments.

Since the cost effective abatement cannot be attained with any policy instru-ment under present technology, the environmental objectives can only be met withimperfect regulatory instruments. The cost of these instruments relative to the leastcost solution depends upon the degree of heterogeneity in marginal abatement costsamong firms which are a function of the transport coefficients. These costs areevaluated for 4 second-best control instruments; i) a mandatory switch in farming


practices, ii) a ceiling on nitrogen fertilizer applications, iii) a uniform nitrogenfertilizer tax, and iv) an ambient tax/subsidy scheme. Efficiency in meeting thewater quality objectives is determined by comparing the outcome of the behavior ofindividual farms to the cost-effective allocation of abatement. Note that efficiencyin abatement cost minimization of the instruments relative to the cost-effectiveallocation is independent of whether of not the specific water quality goal wasdetermined to be efficient in the first place. Not all instruments are able to achievethe desired water quality goal for P. In those cases, a comparison will be made interms of the total cost to the farmers of the instrument and how close the P concen-tration is to the desired concentration. In the cases that do achieve the desired goalfor the P concentration, the policies may have varying impacts on the other waterquality measures as well as potential differences in efficiency. Because the dollarvalues of the damages caused by the different pollutants are not known, the impactof the instrument on other water quality measures is merely noted. Each of theinstruments is discussed in turn. All results are summarized in Table II.

Mandatory Switch to No-Till

The regulator could require a mandatory switch to no-till practices in an effortto reduce erosion and subsequently surface water concentrations of the nutrientpollutants. Imposing such a best management practice would be relatively easy toobserve with a trip in a small plane over the watershed or through the use of satelliteremote sensing. In response to the regulation on tillage, the entire watershed wouldswitch to no-till corn-soy-wheat (practice 12) since this is the most profitable no-till practice. Groundwater N concentrations increase to 5.5 mgN/L (which is stilllower than the drinking water guideline) since more nitrogen is applied with wheatnow included in rotation and more is infiltrating the soil with the use of no-till.Annual watershed profits are reduced to $161.67/ha/yr which is a 6.5% decreasefrom the cost effective solution.13

Limits on Fertilizer Applied

Since the cost-effective outcome induces a reduction in surface water N concentra-tions along with the change in the P concentration, perhaps it is possible to achievethe desired water quality goals using controls based on N fertilizer applications.Because corn yield response to nitrogen is the same for both tillage practices, thedesired reduction in loadings has to occur through a change in crop choice ratherthan through a switch from conventional tillage to no-till. The only means by whichthe surface water P concentration of the cost-effective solution can be met is byentirely restricting N fertilizer use. All nutrient emissions will be lowered as theoptimal solution is for the entire watershed to be planted in hay. Since profits willbe reduced by 59%, this instrument is inefficient and overly effective.


Fertilizer Tax

A nitrogen fertilizer tax of 300% would induce the same outcome as the ceiling ofzero kg N/ha. The crop rotation with the next lowest fertilizer requirements is thewheat-soy-soy rotation. Imposing a restriction either equal to the amount of N usedor that this rotation be grown results in a decrease in profits of 17% if convention-ally tilled. While the N emissions are reduced, the surface water concentration ofP is increased relative to the cost-effective solution.

Ambient Tax/Subsidy Scheme

Rather than use a design based instrument, an alternative is to base an incentiveon the environmental quality of the resource receiving the pollutant, such as awater body. Following Holmstrom’s (1982) work on incentive structures for labour,Segerson (1988) proposed a system for non-point source pollution that rewardsfarmers for environmental quality above a given standard and penalizes them forsubstandard levels of the ambient residual concentration. Since individual emis-sions are unobservable, the compensation or liability for each polluter dependsupon the aggregate emissions from the entire group of polluters affecting the waterbody. When faced with such a program, farmers have the incentive to reduceresidual levels to lower their tax liability if the ambient concentration of the pollu-tant exceeds the standard or increase their subsidy payment if the concentrationis less than the standard. Segerson (1988) demonstrated that when many firmscontribute to the ambient concentration, the tax/subsidy on ambient concentrationsabove/below a threshold level should be equal to the full marginal damage for allfarms. Such an incentive will lead to a situation where the marginal taxes received,when only the tax is applied, will be larger than the marginal damage of theconcentration which must be done to avoid free-riding when individual emissionsare unobservable.

The diffuse nature of the sediment-bound pollution in this paper lends itselfto the application of the ambient tax suggested by Segerson. Full informationon transport coefficients is required for such a program to be implemented. Withendogenous transport coefficients, the informational requirements and potential forstrategic games among decision making units would exacerbate the informationproblems associated with this ambient scheme. In this paper, however, the costeffective solution requires two farms to change behaviour relative to the base solu-tion and thus only these farms need to be considered explicitly. Farms 2 and 4will choose the socially optimal practices if a tax/subsidy is set at $1415.90 permgP/L which is the shadow value of a 20% reduction in P loading (the value of themarginal damages at the cost effective solution). If the other farms in the watershedcontinue to engage in their base profit maximizing choice (conventionally tilledcorn-soy-soy), Farm 2 will choose to change practices to that of the regulator’scost-effective solution. Given the high cost of ambient concentration, Farm 2’sprofit maximizing choice is to change practices regardless of the practices chosen


by other farmers. Farm 2 will change to the regulator’s cost-effective solution evenif Farm 4 engages in the regulator’s cost-effective activities which will be Farm 4’sprofit maximizing choice as predicted by Segerson. Thus, the efficient solution isreached. Note that if the marginal damage value was shared among the 15 farmsin the watershed, the tax would be $94.39 per mgP/L (1415.90/15)14 and no farmswould change their behavior from the base model.

If an ambient tax only is applied, all farms share in paying the total tax which is15 times the marginal damage and is no longer a balanced budget (Segerson 1988).The same result, however, can be achieved with the tax/subsidy scheme that paysthe marginal damage ($1415.90 per mgP/L) under the threshold of 0.64 mg P/Land charges the same over the threshold. The profit maximizing choice for Farms2 and 4 will exactly meet the threshold and no taxes (nor subsidies) will be paid.Farmers would prefer the ambient tax to a firm-specific emission tax, if feasible,since no taxes are actually paid. However, farmers lose profit by modifying theirbehaviour and so are not indifferent to the policy.

The major advantage of the incentive scheme on ambient concentration is that itis directly correlated with the environmental health of the resource concerned andit does not require continual monitoring of emissions. Cabe and Herriges (1992),however, point out several drawbacks. The most significant problem is the need todetermine both the correlation between an individual farmer’s management prac-tices and the ambient concentrations on which the farmer is taxed or subsidizedand the farmer’s beliefs about that transport system. This instrument transfersthe burden of information from the planner to the farmers. This burden is exces-sive when the transport mechanism is dependent upon other farms’ managementchoices. The regulator needs to observe only the ambient concentration and applythe tax/subsidy to every farmer equally whereas the farmers now need to have fullinformation about other farmers’ activities and thus the transport mechanism. Withmany agricultural residuals, the correlation between practices and ambient concen-trations is low because of the large number of contributors to the pollution problemand the long lag time between the polluting activity and the delivery of pollutantsto the monitoring station. The transaction costs to farmers of obtaining informationon the pollutant delivery mechanism could be greater than the cost for the regulatordoing the same thing and thus change the relative cost-effectiveness of the policy.Given the increased informational requirements to producers on a process that isnot known with certainty, costly abatement activities are unlikely to be adopted byproducers until the charge is raised high enough that it may ultimately force themto shut down. The limitations suggest the ambient charge/subsidy is best suited toenvironmental problems in small watersheds with relatively homogeneous farmssolely contributing to the problem, readily monitored water quality, and relativelyshort lags between polluting activities and pollutant delivery.


VI. Conclusions

A multi-contaminant management model of an actual Ontario watershed wasdeveloped to examine the cost-effective farming and abatement activities whilemeeting water quality objectives for four types of nutrient pollution; sediment-bound and soluble nitrogen and sediment-bound phosphorus in surface water alongwith soluble nitrogen in groundwater. Water quality depends on a number ofpollutant parameters and the model permits the examination of means to achieveenvironmental objectives while recognizing the potential trade-offs that affectquality. Not only is more than one type of pollution considered but the actual farmsin the watershed are recognized rather than treating the watershed a single unit withdiffering fields. The emissions originating from any particular farm which reachthe receptor are dependent upon the abatement activities of the farmer and theabatement activities of other farmers within the watershed. The interdependence ofemissions will lead to a more complicated efficiency condition for incentive controlinstruments since a farm’s transport coefficients are no longer fixed values.

Four control instruments were evaluated in terms of their cost efficiency andeffectiveness in meeting the environmental objectives. In the actual watershedexamined only a proposed standard on surface water phosphorus was violatedwhile the water quality constraints on nitrate concentrations were not binding.Although the farms in the watershed examined are nearly homogeneous, thefarms are heterogeneous in terms of abatement for surface water nutrients. Theinterdependence of emissions created a situation where the cost efficient solu-tion involved only two farms changing their behavior to meet the desired waterquality goals. The only instrument which achieved the same pattern of farming andabatement activities as the cost-effective allocation and achieve the desired waterquality goals was the ambient tax scheme which had not been previously testedin an empirical application. Provided the marginal damages can be estimated, thetax/subsidy scheme would be preferred over a firm-specific emission instrumentby the farmers due to the smaller impact on profitability and by the regulatorbecause of the relative ease of enforcement. However, the transfer of informationalrequirements on other farm activities and transport mechanism from the planner tothe farmer may lead farmers to prefer another less efficient instrument.

The hydrological simulation used in this model is based on a single storm whichoccurs at the same time in each of the three years. When the uncertainty in rainfallis taken into account in the creation of nutrient pollution, the most severe stormswill lead to the greatest concentrations of nutrient pollution. If the instrument isset sufficiently high to ensure that the cost-effective concentrations of pollutionare met in the worst case storm event, the concentrations in other less severeevents will be much lower than the desired concentrations. This will put a hugefinancial burden on the firms involved and lead to “over regulation” in all but themost severe (and least probable) case. Baumol and Oates (1988) suggest a two partinstrument of a standard and a penalty which will only be applied if the standard


is violated. Segerson (1988) also suggests that the combination tax/subsidy forambient concentrations is effective in the face of this type of uncertainty. Theseinstruments could quite easily be tested empirically in the framework of the multi-contaminant model developed in this paper. In addition, accounting for stochasticemissions and thus damages may influence the cost-effective abatement activitiesfor each firm (Shortle 1990).

Uncertainty in the timing, duration, and intensity of rainfall will not only influ-ence the concentrations of pollutants but also the yields that farmers will realize.Risk averse behavior may cause reactions to control instruments to differ particu-larly if no-till and other practices used in the optimal solution have more variabilitythan conventional tilled counterparts. Along the same lines, farm managementpractices could be extended to include more farm choices, giving farmers moreflexibility and perhaps decreasing the inefficiency of some of the control instru-ments. With or without these extensions, the model developed in this paper can beapplied to other economic problems where the joint outcome of individual actionsare interdependent in creating an outcome that the regulator desires to control.

Notes

1. Each of the environmental constraints restricts mean emissions from a storm event. Expecteddamage costs from these emissions are assumed to be linearly related to emissons. Cost-effectiveness of the evaluated policies could change depending on the relationship betweenemissions and damage costs.

2. The runoff from a storm is measured by depth in mm. This value multiplied by area is used todetermine the volume of runoff.

3. It is assumed that soluble N goes into the runoff water and then is completely transported withrunoff into the surface water.

4. Depth is used here, as in hydrology, for the amount of infiltration in millimetres. It is not meantto describe the distance down into the soil that the water moves.

5. Fifteen rather 20 (5∗2∗2) farm management practices are defined since the pasture rotationinvolves only one tillage choice and it along with the wheat-soy-soy rotation do not includecorn and subsequently have one fertilization level.

6. (1.2 kg/ha∗5.67 ha + 0.95 kg/ha∗5.67 ha + 1.12 kg/ha∗5.67 ha)/3 = 6.18.7. There is a transport coefficient for each activity on each field which is multiplied by the extent of

soluble emissions to determine the extent of pollutants that move on to the watershed outlet, e.g.2.268 kg∗0.69 + 1.7955 kg∗0.88 + 2.1168 kg∗0.88 = 5.01 kg. In total there are 2,275 coefficients.The complete list of transport coefficients is available from the authors upon request.

8. The model has been set up to determine the average profitability and average concentrations fora static model of a three year rotation. As such, the reported average concentration of nutrientswill not equal the average of the actual nutrient concentrations from each year of the rotation(determined from the hydrological model for a specific year) due to rounding errors.

9. Reduction in P concentrations can be attained for relatively small changes in overall watershedprofitability. However, the loss in profit from the environmental restrictions are borne largely bydownstream farms, such as Farms 2 and 4. A 10% (60%) reduction in P concentrations at theoutlet requires a switch of farming activities on only 3% (29%) of the watershed. Many farmsnot near the watershed outlet need not change farming practices at all. As the fields around thewatershed outlet change cropping choice and tillage practice, the amount of sediment-boundpollution which reaches the pollution receptor from farms further away also declines.


10. A constant marginal benefit of phosphorus abatement of $1415.90 per mgP/L would result inthe same 20% reduction in P concentrations at the outlet. The cost-effective level of abatement(0.80–0.64), would cost $113.15 for abatement and provide $226.54 in benefits ($1415.90 permg P/L∗0.16 mg P/L). The net benefits would thus be $113.39 ($226.54–$113.15).

11. A firm-specific tax of $18.62/kgP on Farms 2 and 4 only will induce those farms to changefrom the base practice 6 to growing the corn-soy-wheat rotation using no-till (practice 12) ontheir entire farms. This corner solution is the result of the risk neutrality and lumpy abatementtechnology assumptions made in the modeling of individual farm management decisions.

12. Water quality objectives can also be met if all firms are imposed with a 22% reduction in Pemissions. The uniform reduction in emissions requires that all but Farm 4 must lower emissionsrelative to the firm-specific standard. The reduction is achieved by all farms switching 40% oftheir area to the no-till corn-soy-wheat rotation (practice 12). Profits for each farm and for thewatershed decrease by 2.6% relative to the base solution.

13. Abatement activity for the mandatory switch to no-till is the same as with the uniform P emis-sions tax. However, actions are observable and farmers pay no taxes so the reduction in profitsis 6.5% as opposed to 11.7% with the uniform emission tax.

14. The $1,415 value is the shadow price of the ambient concentration and not the marginal value ofthe pollution damages unless the 20% P reduction represents the economically efficient ambientstandard.

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