Agricultural and Food Science, Vol. 15 (2006): 351–374. 351 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Vol. 15 (2006): 351–374. © Agricultural and Food Science Manuscript received February 2006 Abatement costs for agricultural nitrogen and   phosphorus loads: a case study of crop farming   in south-western Finland Janne Helin, Marita Laukkanen and Kauko Koikkalainen MTT Agrifood Research Finland, Economic Research, Luutnantintie 13, FI-00410 Helsinki, Finland, e-mail: janne.helin@mtt.fi Designing efficient agri-environmental policies for agricultural nutrient load reductions calls for informa- tion on the costs of emission reduction measures. This study develops an empirical framework for estimat- ing abatement costs for nutrient loading from agricultural land. Nitrogen abatement costs and the phospho- rus load reductions associated with nitrogen abatement are derived for crop farming in south-western Fin- land. The model is used to evaluate the effect of the Common Agricultural Policy reform currently under- way on nutrient abatement costs. Results indicate that an efficiently designed policy aimed at a 50% reduc- tion in agricultural nitrogen load would cost € 48 to € 35 million, or € 3756 to € 2752 per farm. Key-words: water pollution, agriculture, abatement, nitrogen, phosphorus, nutrient load Introduction Excessive concentrations of nutrients that regulate phytoplankton growth cause eutrophication of ma- rine and freshwater ecosystems. The most heavily loaded marine areas in Europe show symptoms of severe eutrophication (see for example Ærtebjerg et al. 2001). The Baltic Sea ecosystem has proved particularly vulnerable to nutrient pollution. Blooms of toxic blue-green algae occur during the warm summer months, and filamentous algae cov- er the seabed in coastal areas. Eutrophication re- sults in significant damages through reduced value of fisheries and recreational activities (e.g. Gren et al. 1997, Söderqvist and Scharin 2000, Sandström et al. 2000, Kosenius 2004). Nutrient loading from land-based sources and the atmosphere builds up nutrient concentrations. The state of eutrophied water ecosystems can be improved by reducing nutrient loads from inland sources, which include agriculture, municipalities and industry. Agricul- ture has been identified as the major source of eu- trophying nutrients in developed countries (see e. g. Shortle and Abler 2001). For example in the Nordic countries, municipal and industrial nutrient 352 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Helin, J. et al. Abatement costs for agricultural nutrient load in SW Finland loads have been reduced significantly during the last few decades, while agricultural nutrient loads remain substantial (HELCOM 2005). Linking nutrient load reductions with the costs of those reductions is essential for informed deci- sion making. Abatement costs are relatively easy to assess in the case of municipal and industrial point-source pollution, whereas quantifying abate- ment costs for agricultural non-point pollution poses a challenge (see e.g. Russel and Shogren 1993). Nutrient removal at municipal and indus- trial sources requires setting up wastewater treat- ment facilities, after which chemical or biological nutrient removal occurs at an approximately con- stant cost. Agricultural abatement instead takes place through changes in agricultural practices and through adopting abatement measures that filter runoff, such as buffer strips and wetlands. Nutrient loading is affected both by agricultural manage- ment practices, such as crop choice, fertilizer use, and tillage, and by environmental factors, such as climate, soil type and field slope. Abatement costs arise from forgoing agricultural profits as a result of constraining agricultural production and alter- ing current agricultural practices for more environ- mentally benign ones. Estimating agricultural abatement costs requires considerable information on nutrient loading and a detailed description of the production technology. The costs of agricultural nutrient load reduc- tions have been addressed in numerous studies. Mattsson and Carlsson (1983) and Johnsson (1993) analyzed the effect of nitrogen fertilization on profits from crop production in Sweden using dis- crete fertilization intervals. Gren et al. (1995) con- structed continuous cost functions for nitrogen and phosphorus fertilization reductions in Denmark, Finland and Sweden from estimated fertilizer de- mand. Schou et al. (2000) applied a spatially dis- aggregated partial equilibrium model of Danish agriculture on nitrogen taxes and nitrate loading. Accounting for the increased knowledge on the re- lationship between agricultural management prac- tices and nutrient losses, Brady (2001) modelled crop yield and nitrogen loss as continuous nonlin- ear functions of fertilization, with different coeffi- cients for each cropping alternative. In addition to fertilization reduction, Brady considered catch crops and delayed tillage as abatement measures. The model was applied to estimate an abatement cost function for crop farming in Southern Swe- den. Berntsen et al. (2003) evaluated the effect of four different nitrogen taxes on nitrate losses and profits on Danish pig farms, while Polman and Thijssen (2002) studied a nitrogen levy for Dutch pig farms. Johansson et al. (2004) derived phos- phorus abatement cost functions for the Sand Creek basin in Minnesota using simulation data to describe the effects of 14 distinct sets of manage- ment practices on nutrient loads and profits. They considered crop rotations, fertilizer application rates and methods, and conservation tillage as abatement measures. Turpin et al. (2005) derived the direct and indirect costs for three sets of agri- cultural management practices using national ac- counting data. Petrolia and Gowda (2006) showed that nutrient management policies should be tar- geted at tile drained land in the Midwest of the United States. Grass buffer strips have been shown to be an effective means to reduce nutrient loads from ar- able land (see e.g. Magette et al. 1987, Dillaha and Inamdar 1997, Patty et al. 1997, Uusi-Kämp- pä et al. 2000, Uusi-Kämppä 2005). Recent re- sults on the effect of tillage on nutrient loads sug- gest that no-till also reduces erosion and particu- late phosphorus losses, although the effect on to- tal phosphorus loss is ambiguous (Puustinen 2004, unpublished results). This paper presents a framework for deriving nitrogen abatement costs that includes reductions in nitrogen fertilization rates, crop selection, buffer strips, and changes in tillage as abatement measures. Furthermore, we account for the interdependence of reductions in nitrogen and phosphorus loads. We use an ap- proach that is similar to Brady (2001) and Johans- son (2004), but extend the model to consider buffer strips and depict both nitrogen and phos- phorus loads as nonlinear functions of fertiliza- tion. We apply the model to derive an abatement cost function for crop production in the Uusimaa and Varsinais-Suomi provinces in south-western Finland. The model is used to evaluate the effect of the current agricultural income support poli- 353 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Vol. 15 (2006): 351–374. cies on the cost of reducing agricultural nutrient loading. The paper is constructed as follows: the second section describes a farm-level profit maximization model that links nitrogen abatement levels and costs. In the third section, we present an empirical framework for linking agricultural management practices and nitrogen and phosphorus loading from agricultural land. The fourth section describes the application, crop farming in south-western Finland. The fifth section presents the results, and the sixth section concludes. Economic model The abatement cost function represents the mini- mum cost of achieving any desired abatement lev- el, where the abatement level is measured as the reduction in kilograms of nutrient discharges from the unconstrained level. Thus, the abatement cost function maps the cost-minimizing choice of abatement effort necessary to achieve any abate- ment target. This section outlines the link between farmers’ production choices and nutrient discharg- es. We consider the case of crop production. We adopt an integrated economic and natural science modelling approach: An economic model of farm- ers’ decision making is combined with a biophysi- cal model predicting the effect of farming practices on crop yield as well as nitrogen and phosphorus discharges. Similarly to Yiridoe and Weersink (1998), Brady (2001) and Johansson et al. (2004), we model abatement effort on the extensive and intensive margins. Extensive margin practices in- clude for example crop selection and tillage meth- od, and intensive margin practices fertilizer appli- cation rates and methods. Formally, we consider the problem of maxi- mizing profits from agricultural production, sub- ject to a constraint on the allowed nitrogen dis- charges. The abatement cost function is obtained through varying the constraint and repeatedly solv- ing the constrained optimization problem. By as- sumption, farmers use a compound fertilizer that contains nitrogen and phosphorus in fixed propor- tions and in the absence of constraints choose fer- tilizer application rates based on yield response to nitrogen application.1 The abatement measures on the extensive margin affect both nitrogen and phosphorus discharges. Consequently, nitrogen and phosphorus discharges cannot be reduced in- phosphorus discharges cannot be reduced in-phosphorus discharges cannot be reduced in- dependently. Given a constraint on the allowable nitrogen discharges, phosphorus discharges are de- termined through the phosphorus content of the compound fertilizer and the adopted abatement measures. Current environmental subsidies are not in- cluded in the analysis. The aim of the study is to determine the minimum cost for achieving any given load reduction target and thus to provide guidelines for designing cost-effective agri-envi- ronmental policy. Including agricultural income subsidies means that the analysis is conducted in a second-best framework, which is not unusual for studies of the agricultural sector (see e.g. Antle and Just 1991). The choice also reflects policies in the European Union (EU) in that the Common Agri- cultural Policy income support is decided upon at the EU level, while individual member countries are responsible for environmental policy design. By assumption, farmers are perfectly competi- tive and risk-neutral. Agricultural profits are a function of the chosen farming practices. Farmers’ objective is to maximize farm profits while com- plying with the load restriction. The choice varia- bles are the land area allocated to each crop and tillage method, the nitrogen fertilization rate given crop and tillage method, and the area allocated to buffer strips. The constrained profit function π ( )NLπ gives farm profits as a function of the al- lowed nitrogen load NL when farming practices are chosen optimally. Agricultural profits in the ab- 1 An interview study of Finnish farmers conducted as a part of the Finnish agri-environmental program evaluation indicated that Finnish cereal producers use predominantly compound fertilizers and choose the fertilizer application rate based on the nitrogen content of the fertilizer mix and yield response to nitrogen application. Phosphorus appli- cation rate follows from the phosphorus content of the compound fertilizer. (Sonja Pyykkönen, Finnish Environ- mental Institute, personal communication). 354 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Helin, J. et al. Abatement costs for agricultural nutrient load in SW Finland sence of abatement are denoted by π *. Formally, the constrained profit function π ( )NLπ is defined by the solution to the following maximization problem: ( ) ( ) ( ){ } , , , , , , , , , , , , , , , 1 1 max , , 1 j k j k j k J K j j k j k N j k j k j k j k B j k j k j k X N B j k X N B p f N p N c s B c B Xπ = =  = − − + − − ∑∑π ( ) ( ) ( ){ }, , , , , , , , , , , , ,, , 1 1 max , , 1 j k j k j k J K j j k j k N j k j k j k j k B j k j k j k X N B j k X N B p f N p N c s B c B Xπ = =  = − − + − − ∑∑ , , , , , , , , , , , , , , , 1 1 max , , 1 j k j k j k J K j j k j k N j k j k j k j k B j k j k j k X N B j k X N B p f N p N c s B c B X , , , , , , , , , , , , , , , 1 1 max , , 1 j k j k j k J K j j k j k N j k j k j k j k B j k j k j k X N B j k X N B p f N p N c s B c B X (1) subject to , , , 1 1 , = = ≤ ∀∑∑ J K ii j k j k j k r X R i (2) 0 ,0 ,, ≥≥ kjkj NX (3) , ,/ jj k j kN P F= (4) , 1 1 J K j k j k B B = = ≤∑∑ (5) ( ), , , , 1 1 , . J K Nj k j k j k j k j k e N B X L = = ≤∑∑ (6) The notation in (1) to (6) is as follows. Sub- script j denotes crop and k tillage method. The op- tions for tillage method depend on the measures suitable for each particular crop. Variable kjX , de- notes the land in hectares allocated to crop j and tillage k, kjN , the per hectare nitrogen application rate, and kjB , the proportion of land left unculti- vated as buffer zone. In the profit expression, jp denotes the average price per kilogram for crop j minus yield dependent production costs, ( )kjkj Nf ,, crop yield as a function of nitrogen application for crop j and tillage k, kjs , area based subsidies (ex- cluding environmental subsidies), kjc , per hectare production costs, Np cost of applying a kilogram of nitrogen fertilizer, and kjBc ,, cost of establish- ing and maintaining buffers. The per hectare pro- duction costs include labour, fuel, machinery (op- erating cost), pesticides and herbicides that are used on average to till, sow and harvest a hectare of crop j using tillage k. In constraint (2), , ,i j kr rep- resents the amount of resource i required to farm one hectare of crop j using tillage k, and iR is the total quantity of resource i available. Resources may include for example labour, land and machin- ery. The constraint states that the amount of re- source i used in production may not exceed the total quantity of resource i available. Constraint (3) ensures that land allocated to each crop and tillage as well as fertilizer application rates are nonnega- tive. In constraint (4), jF represents the ratio of nitrogen and phosphorus in the compound ferti- lizer for crop j: given the nitrogen fertilization rate kjN , , the phosphorus fertilization rate ,j kP is de- fined through (4). In constraint (5), B denotes the maximum land area that is suitable for buffer strips, that is, land that is adjacent to watercourses and has potential to reduce nutrient transport. Av- erage nitrogen discharge for crop j and tillage k is given by ( )kjkjkj BNe ,,, , . Finally, constraint (6) implements the constraint that nitrogen discharges may not exceed NL . Solving the constrained optimization problem in (1) to (6) for all possible values of the maximum allowable nitrogen load NL yields the abatement costs as a function of NL . The analytical solution to the problem is presented in Appendix 1. The abatement cost associated with a nitrogen load re- striction NL is the difference between the maxi- mum profits from farming in the absence of load restrictions, π*, and the maximum profits subject to the load constraint NL , denoted by π( )NLπ . Thus, the abatement cost function can be written as ( ) ( )N NC L Lp p*= - p* – p( ) ( )N NC L Lp p*= - . (7) Given the nitrogen fertilizer application rate, crop and tillage choice, and share of buffer strips associated with each level of the nitrogen load constraint NL , the loads of dissolved reactive phosphorus (DRP) and particulate phosphorus (PP) are determined by the ratio of nitrogen and phosphorus in the compound fertilizer in (4), and by phosphorus loss functions which will be de- scribed in the third section below. Reducing nitro- 355 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Vol. 15 (2006): 351–374. gen fertilization below the level that is optimal without load constraints will reduce agricultural profits. The effect of buffer strips, reduced tillage or no-till on profits cannot be determined a priori, as reduced yields are accompanied with cost sav- ings that may outweigh the effect of reduced yield on profits (see e.g. Lankoski et al. 2006). Empirical specifications for crop  yield and nutrient loss functions Crop yield Per hectare crop yield is modelled as a function of nitrogen fertilization. Following Lehtonen (2001), the yield function for turnip rape, silage and sugar- beet is assumed to have the quadratic form 2 , , , , , , ,( ) ,j k j k j k j k j k j k j kf N a b N c N= + + (8) where , ,( )j k j kf N is crop yield and ,j kN is nitrogen application rate, both in kg per hectare. Lehtonen (2001) estimated the parameters in (8) for conven- tional tillage. The crop yield parameters for re- duced tillage and no-till were obtained by adjust- ing the crop yield for conventional technology in Lehtonen (2001) by yield coefficients reduced till- age and no-till reported in Ekman (2000). The crop yield function for spring wheat, bar- ley, oats and winter wheat is assumed to follow the Mitcherlich form , , , , , ,( ) (1 ) j k j kq N j k j k j k j kf N m l e −= − (9) where , ,, j k j km l and ,j kq are parameters. The pa- rameter values corresponding to spring wheat, bar- ley and oats were obtained from Uusitalo and Eriksson (2004). For each tillage method k, the pa- rameters for winter wheat are otherwise the same as for spring wheat, but parameter ,j km has been adjusted as follows: for a given fertilization rate the yield for winter wheat is 1.05 times that for spring wheat. The 5% difference in yields corre- sponds to the average yield difference on Finnish profitability bookeeping farms in years 1995–2003 (a rotating panel of approximately 1000 farms in- cluded each year). The crop yield functions in (8) and (9) can be interpreted as average yield re- sponses to nitrogen fertilizer application. Both the quadratic form and the Mitcherlich form are com- monly used in crop response analyses (see e.g. Bock and Sikora 1990, Cerrato and Blackmer 1990, Frank et al. 1990, Bäckman et al. 1997). Nitrogen load Nitrogen discharges are determined by the concen- tration of mineral nitrogen in the soil and the quan- tity of water percolating through the soil. The choice of agricultural practices affects both soil ni- trogen concentration and percolation. Nitrogen fertilization increases soil nitrogen concentration and has a direct impact on nitrogen loading (see e.g. Simmelsgaard 1991, Randall and Mulla 1991, Randall et al. 1997, Simmelsgaard and Djurhuus 1998). Nitrogen discharges can be controlled through the fertilizer application rate and crop choice. Nitrogen losses can also be reduced by leaving buffer strips (see e.g. Uusi-Kämppä and Yläranta 1992, Uusi-Kämppä and Yläranta 1996, Uusi-Kämppä and Kilpinen 2000). Tillage has been shown to have only a minor effect on nitrogen loss for a given fertilization rate (see Randall and Mulla 2001, Puustinen 2004 unpublished results). We next describe the effect of fertilizer appli- cation rate and crop choice on average nitrogen discharge per hectare. Following Simmelsgaard (1991) and Simmelsgaard and Djurhus (1998), we and Djurhus (1998), we calculate per hectare nitrogen loss through ( ) ( ), , , , ,exp 0.71 / 1j k j k j k j k j ke N N Nφ  = −  φ ( ) ( ), , , , ,exp 0.71 / 1j k j k j k j k j ke N N Nφ  = −  . (10) Parameter φ ,j kφ captures the average nitrogen loss for crop j and tillage k in kilograms per hec- tare and is specific to land characteristics (slope, soil type etc.) and drainage system.2 Term 2 Crop selection, tillage and fertilization rate are choice variables in our model while land characteristics and 356 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Helin, J. et al. Abatement costs for agricultural nutrient load in SW Finland ( ), ,exp 0.71 / 1j k j kN N −  measures the intensity of the actual fertilization rate kjN , relative to a refer- ence rate kjN , , with , ,0.5 / 1.5j k j kN N≤ ≤ . Buffer strips reduce nutrient losses via two channels: nutrient uptake by buffer strips and re- duction in the amount of fertilizer applied. Nutri- ent uptake only affects surface losses. Denoting the proportions of nitrogen losses via surface run- off and drainage water by s n and d n , per hectare nitrogen loss in the presence of buffer strips can be written as ( ) { }0.2, , , , , , ,, (1 ) exp 0.71 (1 ) / 1jkj k j k j k s j k d j k j k j ke N B n B n B N Nφ   = − + − −    ( ) { }0.2, , , , , , ,, (1 ) exp 0.71 (1 ) / 1jkj k j k j k s j k d j k j k j ke N B n B n B N Nφ   = − + − −   φj,k ( ) { }0.2, , , , , , ,, (1 ) exp 0.71 (1 ) / 1jkj k j k j k s j k d j k j k j ke N B n B n B N Nφ   = − + − −    ( ) { }0.2, , , , , , ,, (1 ) exp 0.71 (1 ) / 1jkj k j k j k s j k d j k j k j ke N B n B n B N Nφ   = − + − −    (11) The term 0.2 , (1 ) s j k n B− gives nitrogen uptake by buffer strips, and kjB , denotes the share of land allocated to buffer strips. The second term on the right hand side of (11) accounts for the reduction in fertilizer applied. The parameterization in (11) follows Lankoski et al. (2006), who calibrated the model to data from Finnish experimental studies on grass buffer strips (Uusi-Kämppä and Yläranta 1992, Uusi-Kämppä and Yläranta 1996, Uusi- Kämppä and Kilpinen 2000). Given the per hectare nitrogen losses in (11), the total nitrogen loss, denoted by NL , is ( ), , , , 1 1 , . J K N j k j k j k j k j k L e N B X = = = ∑∑ (12) Phosphorus load Phosphorus is transported from agricultural land to surface water in two forms: (i) dissolved reactive drainage system are assumed to be given. Petrolia and Gowda (2006) considered plugging artificial drainage as an abatement policy but found reducing fertilization rates and retiring land to be more profitable measures. Sim- melsgaard and Djurhus studied the effect of fertilization intensity on nitrogen loss from tile drained sandy-loam soil, while the predominant soil type in south-western Fin- land is clay. Section 4 reports how the φj,k have been ad- justed to describe conditions in the study region. phosphorus (DRP) and (ii) particulate phosphorus (PP). Discharges of both DRP and PP are affected by the fertilizer application rate, crop choice, and tillage method. No-till and reduced tillage are emerging as effective ways to reduce erosion and total phosphorus loading (see e.g. Soileau et al. 1994, Stonehouse 1997, Puustinen 2004 unpub- lished results, Puustinen et al. 2005). Buffer strips have also been shown to reduce phosphorus load- ing (Uusi-Kämppä and Yläranta 1992, Uusi- Kämppä and Yläranta 1996, Uusi-Kämppä and Kilpinen 2000). Phosphorus loss is modelled be- low following Lankoski et al. (2006), who used results from Finnish studies on grass buffer strips (Uusi-Kämppä and Kilpinen 2000) and DRP loss- es (Uusitalo and Jansson 2002), and long-term fer- tilizer trials (Saarela et al. 1995, Saarela et al. 2003) to construct phosphorus loss functions. The losses of dissolved reactive phosphorus and particulate phosphorus in kilograms per hec- tare are given by ( ) ( ) ( )( )1.3 4, , , , , , , ,, 1 2 0.01 1 1.5 10DRP j k j k j k j k s d j k j k j kz P B B drp drp B Pσ θ −  = − + + − − ⋅    ⋅ σ( ) ( ) ( )( )1.3 4, , , , , , , ,, 1 2 0.01 1 1.5 10DRP j k j k j k j k s d j k j k j kz P B B drp drp B Pσ θ −  = − + + − − ⋅    (θ ( ) ( ) ( )( ) 1.3 4 , , , , , , , ,, 1 2 0.01 1 1.5 10DRP j k j k j k j k s d j k j k j kz P B B drp drp B Pσ θ −  = − + + − − ⋅     , (13) ( ) ( ) ( ) ( ){ }0.3 6, , , , ,, 1 250 ln 0 01 1 150 10PP j k j k j k j k s d j,k j,k j,kz P B B pp pp . B P −= − + + − − ⋅ . (14) ( ) ( ) ⋅( ) ( ) ( ) ( ){ }0.3 6, , , , ,, 1 250 ln 0 01 1 150 10PP j k j k j k j k s d j,k j,k j,kz P B B pp pp . B P −= − + + − − ⋅ . (14) ( ) ( ) . (14) The terms ( )1.3,1 j kB− and ( )0.3,1 j kB− capture phos- phorus uptake by buffer strips. The proportions of DRP loss via surface flow and drainage water are denoted by s drp and d drp , and the proportions of PP loss via surface flow and drainage water by s pp and d pp . Parameter σ kj ,σ (mm) describes the im- pact of crop choice j and tillage k on DRP loss, summarizing the effects on total runoff and its DRP content; θ (mg l-1) is the soil phosphorus sta- tus3, kjP , the phosphorus fertilizer application rate (kg ha-1); and kj ,Δ (kg ha-1) summarizes the impact of crop j and tillage k on erosion and the PP con- 3 The parameterization obtains when soil phosphorus status θ is between 9 and 13 mg l-1. 357 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Vol. 15 (2006): 351–374. tent of eroded soil. Fertilizer is not applied on the buffer strip area kjB , . The total losses of dissolved reactive phospho- rus and particulate phosphorus are ( ), , , , , 1 1 , J K DRP DRP j k j k j k j k j k L z P B X = = = ∑∑ (15) ( ), , , , , 1 1 , . J K PP PP j k j k j k j k j k L z P B X = = = ∑∑ (16) Agriculture in Southern Finland We utilize data from the Uusimaa and Varsinais- Suomi provinces in Southern Finland to estimate the abatement cost function. Agricultural loading from southern Finland constitutes the largest an- thropogenic nutrient source in the Finnish coastal waters of the Gulf of Finland, which is the most eutrophied sub-basin of the Baltic Sea. The shal- low coastal waters are particularly prone to eu- trophication, and toxic algae blooms frequently occur during the warm summer months. The Hel- sinki Commission has called for more effort to re- duce the nutrient loads to the Baltic Sea, especially from agriculture (HELCOM). In Finland, agricul- tural nutrient abatement is the single most impor- tant investment under the Water Protection Target Programme (HELCOM 2003). The main objective of Finnish Agro-Environmental Subsidy Pro- gramme is the reduction of nutrient loads to water- ways (Turtola and Lemola 2004). Besides the Bal- tic Sea, these priorities relate to the majority of Finnish lakes, which are shallow and hence vul- nerable to nutrient pollution. Despite past efforts to reduce nutrient loads from arable land, the nutri- ent levels have not been decreasing (Ekholm et al. 2004, Räike and Granlund 2004, Granlund et al. 2005). Figure 1 depicts the study area. Economic data pertain to the regional economic and employment development centers in the Uusimaa and Varsinais- Suomi provinces, while the ecological data come from the catchment area that approximately cor- responds to the two provinces. The area of culti- vated agricultural land in the region was 481 500 hectares in 2003, which represents approximately 20% of cultivated land in Finland. The average farm size in 2003 was 38 ha. Agriculture in the re- gion is predominantly crop farming – only 19% of the 12 632 farms in operation in 2003 were en- gaged in animal production. The crops that took up the highest percentage of cultivated land in 2003 were barley (24%), spring wheat (22%), and oats (13%). Other commonly grown crops were turnip rape (6%), winter wheat (5%), silage (5%), and sugar beet (3%). (Yearbook of farm statistics 2004). Average yields for the crops are shown in Table 1. We included these seven crops and green fallow as land use choices in our model. Both malt- ing barley and feed barley are grown in the study region. The share of malting barley was 55% in 2003 (TIKE 2004). Unfortunately distinct yield functions are not available for feed and malting barley and thus they cannot be considered as dis- tinct crops in our model. As we are concerned with crop farms, we proceed from the assumption that the representative farm plants malting barley which has a higher price. The climate is seasonal and the thermal growing season lasts for 160–190 days.–190 days.190 days. The predominant soil type is clay (vertic and dys- tric cambisols and haplic podzols) (Lilja et al. 2006). In 2003, conventional tillage (i.e. mold- board plowing in the autumn) was predominant. About 74 and 77% of the total cultivated land in the region is drained with subsurface drains (Finn- ish Field Drainage Center 2002). The average field slope (measured 30 meters from river/drain bank) in Finland is 188cm/100m (Puustinen et al. 1994). We analyze the farming decisions at the level of a single representative farm, and scale up the farm to represent the entire region. We consider farming decisions where the time horizon is one year. The area of land allocated to different crops is restricted by farm size, 38 hectares.4 By assump- 4 We proceed from the assumption that the amount of total agricultural land in the region is fixed. As the CAP subsidy system does not grant subsidy rights to fields cleared after 2003, it is unlikely that the agricultural land will be expanded notably. Retiring agricultural land through conversion into forest is a long term decision that 358 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Helin, J. et al. Abatement costs for agricultural nutrient load in SW Finland 0 450 900 1 350 1 800225 Kilometers Value High : 100 Low : 0 % of arable land 0 50 10025 Kilometers Research Area Catchment borders Fig. 1. Baltic Sea drainage basin and the research area. tion, labor is not constrained, and machinery can be rented, so that all technologies (conventional, reduced tillage, and no-till) are available. Nutrient discharges can be reduced through changes in crop selection, reduced tillage and no-till, through es- tablishing buffer strips, and through reducing fer- tilization. We next describe how the parameters describing the representative farm were obtained. The agricultural commodity prices and fertil- izer prices are the annual averages for 2003 (Table 1). As part of malting barley yield generally does not meet the quality requirement for malting and is sold as fodder, we use a weighted average of feed and malting barley prices. The weight of malting barley was 80%, which corresponds to the yield share meeting the quality requirements for malting barley in 2003 (TIKE 2004). The yield parameters under the current CAP policy entails losing subsidy rights. Our model is not able to account for such irreversible in- vestments. The assumption that total area of agricultural land is fixed implies that the size of the representative farm is fixed. In reality a single farm can rent land and is not necessarily bound by such constraint. are shown in Tables 2 and 3 and the costs in Table 4. The per hectare costs include fuel and labor costs, machinery, plant protectants, and harvest, while grain drying costs are yield dependent. Fixed costs of capital are not included in the analysis. The model calculations are based on the use of compound fertilizers that contain nitrogen and phosphorus in a fixed ratio. We considered fertil- izer mixes that are predominant in the production of each crop type in Finland. The nutrient ratios are given in Table 5. Buffer strips that are at the maximum 3 meters wide are eligible for the EU Common Agricultural Policy (CAP) area subsidies. The buffer strip po- tential was estimated based on GIS data of field edges next to water ways and main ditches ob- tained from The Information Centre of the Minis- try of Agriculture and Forestry. The upper limit of buffer strip area was 0.58% or 0.22 ha for a 38 ha farm. Further buffer capacity can be obtained by adoption of wider buffer zones, which are not en- titled to CAP subsidies but do receive EU Less Fa- vored Area (LFA) payments. The regional environ- mental administration has estimated that 1–3% of–3% of3% of 359 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Vol. 15 (2006): 351–374. Table 1. Commodity and fertilizer prices, EUR kg-1 a and average yield in the region, kg ha-1 a. Commodity Prices Yield Spring wheat 0.127 3536 Barley 0.130 3488 Oats 0.099 3442 Winter wheat 0.127 3365 Turnip rape 0.260 1246 Silage 0.034 14 449 Sugar beet 0.054 31 701 Fertilizers b Spring cereal composite fertilizer 1.20 Winter cereal composite fertilizer 1.10 Root vegetable composite fertilizer 1.56 a Yearbook of farm statistics 2004. b The fertilizer price was computed as the price of one kg of nitrogen assuming that a fertilizer mix appropriate for each crop type is applied. Spring cereal mix is applied to spring wheat, barley, oats, and turnip rape. Winter cereal mix is applied to winter wheat, and root vegetable mix to sugar beet. Table 2. Crop yield parameters for Mitcherlich forma. Crop Conventional tillage Chisel plough No-till m k b m k b m k b Spring wheat 4871.0 0.7623 0.0104 4747.2 0.7623 0.0104 3937.3 0.7623 0.0104 Barley 5309.6 0.8280 0.0168 5421.2 0.8280 0.0168 5105.1 0.8280 0.0168 Oats 5659.1 0.7075 0.0197 5677.0 0.7075 0.0197 5368.4 0.7075 0.0197 Winter wheat 5114.55 0.7623 0.0104 4984.56 0.7623 0.0104 4134.17 0.7623 0.0104 aFrom Uusitalo and Eriksson (2004). Winter wheat yield parameters for each tillage method were obtained by increasing parameter m for spring wheat by 5%, which corresponds to the average yield difference between spring wheat and winter wheat on Finnish farm accounting data network farms in years 1995–2003. Table 3. Crop yield parameters quadratic forma. Crop Conventional tillage Chisel plough No-till a b c a b c a b c Turnip rape 1096.1 9.82 –0.0354 1052.26 9.82 –0.0354 986.49 9.82 –0.0354 Silage 1182.9 24.24 –0.0394 Not applicable Sugarbeet 23630.0 53.21 –0.083 a For conventional technology, the parameters are from Lehtonen (2001). The parameters for chisel plough and no- till have been obtained by adjusting the crop yield parameters in Lehtonen (2001) by yield coefficients for chisel plough and no-till reported in Ekman (2000). the arable land area would benefit from such buffer zones (Penttilä 2003). Accordingly, the upper limit for buffer zones was set at 3%, which corresponds to 1.14 ha for a 38 ha farm. Parameters ϕj,k, σj,k and Δj,k in the functions de- scribing the losses of nitrogen, dissolved reactive phosphorus and particulate phosphorus (equations 10 to 16) were calibrated as follows: given the pre- dominant agricultural practices in 2003 (land al- location, fertilizer application, buffers, and tillage), parameters ϕj,k, σj,k and Δj,k were set at values for which the nutrient losses predicted by equations (12), (15) and (16) equaled the observed loads in 2003, whereby the relative nutrient losses pro- duced by the different crops were held fixed. For nitrogen, the relative loads for the different crops were based on field experiments in South-Western Finland (Tapio Salo, MTT Agrifood Research Fin- land, personal communication). For phosphorus, the relative loads were based on simulations from the IceCream model (Tattari et al. 2001). Land al- 360 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Helin, J. et al. Abatement costs for agricultural nutrient load in SW Finland Table 4. Crop production fixed costs, EUR ha-1 a. Crop Conventional tillage Chisel plough No-till Capital cost Operation cost Capital cost Operation cost Capital cost Operation cost Spring wheat 323 113 320 113 314 109 Winter wheat 323 113 320 113 314 109 Barley 323 113 320 113 314 109 Oats 323 113 320 113 314 109 Turnip rape 323 113 320 113 314 109 Silage 235 148 n.a. n.a. n.a. n.a. Sugar beet 384 327 n.a. n.a. n.a. n.a. Green fallow 109 68 108 68 91 40 Buffer zone 109 133 108 133 91 105 Grain drying costs, EUR kg-1 b Spring wheat, winter wheat, barley, oats 0.01 for all tillage practices a Calculated for the representative farm (38 ha) using Pentti (2003) and Enroth (2004). The buffer zone costs consist of the fixed costs of fallow, and a cost of 65 EUR ha-1 a-1 for removing plant residue at the end of the growing season. b From http://www.maaseutukeskus.fi/julkaisut/s_julkaisut.htm Table 5. Ratio of phosphorus and nitrogen in the fertilizer mix applicable to each cropa. Crop Ratio Spring wheat 0.15 Barley 0.15 Oats 0.15 Winter wheat 0.12 Turnip rape 0.15 Silage 0.14 Sugar beet 0.11 Green fallow n. a. a From http://www.maaseutukeskus.fi/julkaisut/s_ julkaisut.htm. location was set equal to the one observed in 2003; tillage was conventional; and fertilizer use was set equal to levels recommended by the Finnish envi- ronmental subsidy program in 2003 (Table 7)5. Soil phosphorus status θ was fixed at 10.6 mg l-1, 5 Farmers participating in the Finnish environmental subsidy program are required not to exceed the recom- mended nitrogen fertilization rates reported in Table 7. which is the average for Finnish Farm Accountan- cy Data Network farms situated in southern and south-western Finland (Myyrä et al. 2003). The proportions of nutrient loss incurring through sur- face flow were set at 0.5, 0.7 and 0.7 for nitrogen, dissolved reactive phosphorus, and particulate phosphorus, respectively, which correspond to av- erage values in Turtola and Paajanen 1995. The calibrated parameters are presented in Table 6.6 About 98% farms in Finland participated in the program in 2003 (Ministry of Agriculture and Forestry 2004). 6 An approach more in line with the economic param- eterization of the model would have been to use average parameter values obtained in field experiments in Finland and average soil characteristics in the region. Unfortunate- ly this approach provided a poor approximation in our study: predicted losses for the study region as a whole were only about 40–50% of the observed nutrient loads in 2003. The discrepancy is probably due to a large part of the actual nutrient losses originating from a small propor- tion of agricultural land that has a very high nutrient loss potential relative to the average nutrient loss potential. As our representative farm model and the available data do not allow accounting for such high risk areas, calibrating the parameter values was deemed to be an approach yield- 361 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Vol. 15 (2006): 351–374. Table 6. Technology- and crop specific impacts on nutrient lossesa. Crop Conventional tillage Chisel plough No-till ϕ (kg ha-1) σ (mm) Δ (kg ha-1) ϕ (kg ha-1) σ (mm) Δ (kg ha-1) ϕ (kg ha-1) σ (mm) Δ (kg ha-1) Spring wheat 24 326 235 24 357 101 24 349 140 Winter wheat 21 355 226 21 355 221 21 363 223 Barley 21 316 220 20 342 86 21 322 125 Oats 12 323 224 12 347 90 13 347 129 Turnip rape 26 329 244 24 357 110 25 340 149 Silage 13 630 58 n.a. n.a. n.a. n.a. n.a. n.a. Sugar beet 19 362 294 n.a. n.a. n.a. n.a. n.a. n.a. Green fallow 12 197 9 12 197 9 12 197 9 a Calibrated so that the nitrogen and phosphorus loads predicted by the loss functions (11) to (13) correspond to observed loads when land allocation is as in 2003, and fertilizer use conforms to current environmental regulations. Table 7. Recommended nitrogen fertilization dose. Crop Fertilization dose, kg ha-1 a Spring wheat 100 Barley 90 Oats 90 Winter wheat 120 Turnip rape 100 Silage 180 Sugar beet 120 Green fallow 0 a The amounts of nitrogen recommended by the Finnish Agri-Environmental support program. Source: Valtioneu- voston asetus luonnonhaittakorvauksista ja maatalouden ympäristötuesta 29.6.2000/644. Available on the Internet: http://www.finlex.fi/fi/laki/smur/2000/20000644. Agricultural policy in terms of area based in- come subsidies is taken as given. The EU Com- mon Agricultural Policy provides farmers with di- rect subsidy payments for crops planted. A reform of the system is currently underway. According to the European Commission, the CAP reform agreed upon in June 2003 is geared towards consumers and taxpayers and linked to the respect of environ- ing more accurate predictions for the study region as a whole. mental, food safety and animal welfare standard (European Commission 2005). The reform levels the CAP hectare subsidy for different crop types and fallow. In Finland, the reform comes into force in 2006. In order to examine how the reform af- fects the cost of agricultural nutrient abatement, we considered two subsidy regimes: the one that prevailed in 2003 and the subsidy regime in place after the reform. In what follows we refer to the two subsidy regimes as BASE 2003 and CAP 2006. In order to eliminate the effects of year-to- year fluctuation, in both scenarios the commodity prices and costs were held at their 2003 levels. The level of subsidies for 2006 is based on the esti- subsidies for 2006 is based on the esti-subsidies for 2006 is based on the esti- mates of the Ministry of Agriculture and Forestry (2006). The subsidies under the two CAP systems are displayed in Tables 8 and 9. Finally, Table 10 summarizes the EU regulatory constraints on pro- duction. To solve the constrained optimization problem in (1) to (6) the model was translated into the Gen- eral Algebraic Modelling System (GAMS) lan- guage (Brooke and Kendrick 1998). The resulting nonlinear mathematical program was solved using the CONOPT3 optimization algorithm (see Drud 2004). We proceeded by first computing the un- constrained maximum profits π * and the associated nitrogen load *NL . Using the unconstrained solu- tion as the baseline, the model was then solved for a series of tightening abatement targets ranging 362 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Helin, J. et al. Abatement costs for agricultural nutrient load in SW Finland Table 8. Subsidies in 2003, EUR ha-1 a. Crop CAP payments LFA support National support Total subsidies A B A B A B A B Spring wheat 279 230 150 200 105 105 534 535 Winter wheat 279 230 150 200 105 105 534 535 Barleyb 279 230 150 200 84 84 513 514 Oats 279 230 150 200 9 9 438 488 Silage 214 176 150 200 0 0 364 376 Turnip rape 279 203 150 200 143 143 572 546 Sugar beet 0 0 150 200 202 202 352 402 Fallow 214 176 150 200 0 0 364 414 Buffer, width 3 to 15 m 0 0 150 200 0 0 150 200 Buffer, width below 3 m Same as main crop a Niemi and Ahlstedt (2003). b The national support for malting barley. The national support for feed barley was 9 EUR ha-1. Table 9. Subsidies in 2006, EUR ha-1. Crop CAP paymentsa LFA supportb National supportc Total subsidies A B A B A B A B Spring wheat 290 240 170 220 105 105 565 565 Winter wheat 290 240 170 220 105 105 565 565 Barley 290 240 170 220 84 84 544 544 Oats 240 190 170 220 6 6 416 416 Silage 240 190 170 220 0 0 410 410 Turnip rape 290 240 170 220 129 129 589 589 Sugar beet 240 190 170 220 129 129 539 539 Fallow 240 190 170 220 0 0 410 410 Buffer, width 3 to 15 m 0 0 170 220 0 0 170 220 Buffer, width below 3 m Same as main crop a Estimate for single farm payment combined with the crop specific production subsidy (Ministry of Agriculture and Forestry 2006). b Least favoured area (LFA) subsidy and its national increment (Ministry of Agriculture and Forestry 2006). c National support (Ministry of Agriculture and Forestry 2006). from 0 to 60% of the unconstrained nitrogen load * NL . Each one of the 1,..., 30h = iterations reduced the allowed load by a further 2%. The allowable nitrogen load ,N hL associated with abatement tar- get ,N hA is * , ,N h N N hL L A= − and the abatement cost ck = π *– π( ),k N hc Lπ π∗= − . A quadratic abatement cost func- tion C(AN) = b( ) 2N NC A Ab= (17) was fitted to the resulting abatement target and cost pairs. Appending an additive error term to equation (17) gives rise to the linear regression model ch = b 2 ,h N h hc Ab e= + eh. We interpret the error terms eh as deviations of the abatement cost generated 363 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Vol. 15 (2006): 351–374. by the mathematical program from the quadratic model and assume them to have mean zero. As theAs the values of the explanatory variable are non-sto- chastic, ordinary least squares (OLS) estimation then provides an unbiased estimate of the param- an unbiased estimate of the param- eter b. Results We assessed abatement costs under the 2003 CAP subsidy regime and under the reformed CAP sys- tem adopted in 2006. Figures 2a and 2b display the simulated abatement costs and the estimated abate- ment cost functions together with their 95% confi- dence intervals. The estimated abatement cost pa- rameters are b2003 = 1.86 for the BASE 2003 sys- tem and b2006 = 1.47 for the CAP 2006 regime. The corresponding t-values, 27.95 for b2003 and 37.44 for b2006, are well above the critical value, and both parameters are significant at the 1% level. The 95% confidence interval for b2003 is 1.73 to 1.99, and for b2006 1.39 to 1.55. In both estimations R2 exhibits a high value (0.96 for BASE 2003 and 0.98 for CAP 2006), indicating a good fit to the model. The unconstrained nitrogen loads were 10 116 tn and 9740 tn per annum for BASE 2003 for CAP 2006, respectively, and the unconstrained phosphorus loads 350 and 356 tn per annum. The average phosphorus load reduction associated with a given nitrogen load reduction was AP = 0.0058AN Table 10. Resource and EU regulatory constraints. Resource EU regulatory constraint Total land on representative farm 38 ha Maximum turnip rape area (agronomic constraint) 9.5 ha Maximum fallow (EU regulatory constraint) 19 ha Minimum fallow (EU regulatory constraint) 3.8 ha Maximum sugarbeet area (from Finland’s sugar quota) 0.5 ha Maximum buffer strip area 0.22 ha Maximum buffer zone area 1.14 ha BASE 2003 0 10 20 30 40 50 60 70 80 90 0 1000 2000 3000 4000 5000 6000 7000 Cost in EUR (millions) CAP 2006 0 10 20 30 40 50 60 70 80 90 0 1000 2000 3000 4000 5000 6000 7000 BASE 2003 (simulated cost) BASE 2003 (predicted cost) CAP 2006 (simulated cost) CAP 2006 (predicted cost) N load reduction (tn) 95% confidence interval for predicted cost Fig. 2. Predicted (OLS) and simulated costs for the research area. 364 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Helin, J. et al. Abatement costs for agricultural nutrient load in SW Finland for BASE 2003, and AP = 0.0071AN for CAP 2006. Given the 50% uniform load reduction target that the Helsinki Convention has set for Finnish agriculture, we computed the cost of reducing ni- trogen loading in the study region by 50%. The resulting total abatement costs are € 47.6 million under BASE 2003, and the average abatement costs € 9.4 per kg or € 99 per ha. The cost to a typical farm in southern Finland would be € 3756, which equals 49% of the environmental subsidies received by the typical farm in the region in 2003. The reduction in phosphorus loading associated with the 50% reduction in nitrogen loading would a mere 2%. Under the CAP 2006 regime the total cost of a 50% reduction in nitrogen loading would be € 34.9 million (€ 7.2 per kg, € 72 per ha or € 2752 for the typical farm) and the associated re- duction in phosphorus loading again only 2%. Gren et al. 1995 found the abatement cost range for Finnish agriculture to be € 6–24 per kg–24 per kg24 per kg of nitrogen and € 24–662 per kg of phosphorus.–662 per kg of phosphorus.662 per kg of phosphorus. The abatement costs were estimated based on fer- tilizer demand, using catch crops, energy forests and green fallow as abatement measures. Finnish data were used to derive the fertilizer demand in Finnish study region while the costs of abatement measures were assumed to be the same as in the Swedish Bothian Bay catchment. The lowest cost abatement measure in their study was the reduc- tion of fertilizer inputs. Our model allows for buf- fer strips, which reduces the costs compared to those obtained by Gren et al. As several model as- sumptions differ in the two studies, the results can only be compared roughly. The same caveat ap- plies to comparing our results to those in Brady (2001, 2003). Nevertheless, our results support Hart and Brady (2002), who found that significant reductions in nitrogen losses can be obtained at a relatively small decrease in gross profits. Figure 3 illustrates the effect of load restric- tions on farm profits.7 As one would expect, profits decrease when the load restriction is tightened. Here the CAP reform reduces profits relative to the 7 We considered variable profits. Thus fixed costs on capital were not included in the analysis. BASE 2003 level for most load restrictions.8 The EU and national subsidies form a significant share of farm profits, which smoothes the effect of tight- er load restrictions. Fixed costs and subsidies af- fect the allocation of land between different crops, but do not affect the choice of fertilizer application rate or the width of buffer strip once the crop choice has been made. Figures 4a and 4b depict the effect of load constraints on crop choice under the two subsidy regimes. As the load constraint is tightened, a larger share of land is allocated to green fallow under both subsidy regimes. The de- coupling of subsidies from crop type in CAP 2006 favors turnip rape and silage relative to the BASE 2003 system. As the amount of available land is constant by assumption, a part of barley produc- tion is replaced by turnip rape. The area under bar- ley is further decreased and replaced by silage as the load constraint is tightened. By assumption, the region retains its grain production emphasis and animal husbandry remains at its 2003 level, which limits silage production. The area allocated 8 The Finnish government has agreed to compensate farmers for the loss of CAP subsidies following the 2006 reform, but the level of compensation remains undecided (as of 2 Aug 2006). Hence the compensation has not been included here. 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 N load reduction % € /a BASE 2003 CAP 2006 Fig. 3. Profits of the representative farm as a function of nitrogen load constraint. 365 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Vol. 15 (2006): 351–374. BASE 2003 0 10 20 30 40 50 60 70 80 90 100 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 % of arable land area CAP 2006 0 10 20 30 40 50 60 70 80 90 100 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 green fallow N load reduction % barley turnip rape silage sugar beet Fig. 4. Representative farm’s allocation of land between different crop types as a function of nitrogen load constraint. to the most profitable crop, sugar beet, is con- strained by the EU sugar quota. The constraint is binding for both subsidy regimes and for all load restrictions considered. Brady (2001, 2003) obtained a broader selec- tion of crops than the one suggested by our model. He also found more changes in the land cultivation practices. The broader scope of crop choices may be due to the larger number of hectare constraints in Brady’s study. Adding modelling constraints is a trade-off between the description of the farmers’ adaptation possibilities and a more detailed de- scription of current farming practices. Further- more, the possibility of establishing buffer strips, not considered in Brady (2003), provides farmers with an alternative way to reduce the nutrient load. Here, load restrictions decrease yield levels. Figures 5a and 5b depict yields as a percentage of the levels produced by the unconstrained solution. Fertilization levels are presented in Figures 6a and 6b. The decline in yields is explained by reduced fertilization. The yield curves level as converting land to green fallow becomes more profitable than further reductions in fertilizer use. Fertilizer use is reduced notably to meet tightening load con- straints. For sugar beet and turnip rape fertilization is cut by up to 100%, while fertilization of barley is reduced by up to 60% and that of silage by up to 30%. 9 The use of buffer strips as an abatement mea- sure is illustrated in Figure 7. The maximum buffer area eligible for CAP hectare subsidies was 0.5% of arable land in the region, whereas the maximum buffer potential estimated to yield environmental benefits was 3%. Under both subsidy regimes, the buffer area exceeds the area eligible for CAP sup- port when nitrogen loads are restricted moderately. The strictest abatement targets are met by increas- ing the share of green fallow, which results in a decrease in the buffer area. This is logical as green fallow is eligible to CAP subsidies, while buffer zones are not. Buffer zones are established mainly on area in barley. 9 The positive constant terms in the sugar beet and tur- nip rape yield functions make farming the crops profitable even at zero fertilization. While yield levels are likely to remain positive, the yield response function may be inac- curate at zero fertilization. 366 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Helin, J. et al. Abatement costs for agricultural nutrient load in SW Finland barley turnip rape silage sugar beet BASE 2003 30 40 50 60 70 80 90 100 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 % of unconstrained yield CAP 2006 30 40 50 60 70 80 90 100 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 N load reduction % barley turnip rape silage sugar beet BASE 2003 0 20 40 60 80 100 120 140 160 180 200 220 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 kg/ha CAP 2006 0 20 40 60 80 100 120 140 160 180 200 220 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 N load reduction % Fig. 5. Effects of nitrogen abatement on total yields: the constrained yield as a percentage of the yield in the unconstrained optimum. Fig. 6. Fertilization levels as a function of nitrogen load constraint. As can be seen from Figures 4–7, a combina-–7, a combina-7, a combina- tion of different abatement measures is used to achieve least cost abatement. Moderate load re- strictions are met by reducing fertilization and in- troducing buffer strips. Large load reductions are obtained through decreasing fertilization further and through conversion to green fallow. Switching of tillage method did not occur.10 The level of LFA 10 Both the tillage method and crop choice were sensi- tive to the initial values provided to the optimization algo- rithm. Variables with an initial level of zero are undesirable 367 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Vol. 15 (2006): 351–374. 0 0.5 1 1.5 2 2.5 3 3.5 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 N load reduction % % of arable land BASE 2003 CAP 2006 Fig. 7. Buffer area as a function of the nitrogen load. support and CAP payments to fallow increase in the CAP 2006 system relative to the BASE 2003 regime. As buffer zones exceeding the width of 3 m do not receive CAP support but are eligible for LFA payments, the opportunity cost of buffer zones is smaller in the CAP 2006 system. Fallow is also subsidized more, and abatement through set- ting land aside as green fallow is not as expensive as in the BASE 2003 scenario. These differences explain the smaller overall abatement costs in the CAP 2006 scenario. Reductions in nitrogen load lead to only mod- est reductions in phosphorus loads. Under the CAP 2006 regime, the phosphorus load actually increas- es at NL = 9200 tn, which corresponds to a 6% re- 6% re-6% re- duction in the allowed nitrogen load. The increase follows from part of barley production being re- placed by silage, which produces markedly higher loss of dissolved reactive phosphorus than the oth- er crops considered here (Table 6). The small for non-linear optimization, as they appear to have no ef- fect on the profit function (Drud 2004). This effect ham- pers the switch between the tillage practices, which do not have large dissimilarities in the parameter values. Assign- ing arbitrary initial values instead of the values obtained from the previous iteration leads to solutions which are local optima but produce lower profits, although tillage method switching occurs frequently. changes in the phosphorus load are also explained by the impact of soil phosphorus status on the load. In addition to current farming practices, both dis- solved reactive phosphorus and particulate phos- phorus loads are affected by the soil phosphorus status (equations 14 and 15) which cannot be de- creased by farmers in the short run. Our results indicate a higher average cost of phosphorus abate- ment than Gren et al. (1995) who, however, did not, did not account for the effect of soil phosphorus status on phosphorus loads. Above we discussed the costs of nutrient abate- ment under two alternative agricultural policy re- gimes. Finnish agriculture is currently facing a downward trend in crop prices and an upward trend in input prices (Niemi and Ahlstedt 2004). To illustrate the effect of these trends in key economic variables on the abatement costs we studied two alternative parameterizations: one where the crop prices were reduced by 10% and one where nitro- gen fertilizer prices increased by 50%. The main results for each policy regime are reported in Table 11. The full set of results is available from the au- thors upon request. The shares of sugar beet and turnip rape were relatively consistent at different prices, but the shares of other crops, tillage, fertil- izer use and buffer strip width varied. Barley was replaced by winter wheat when the prices of all crops were decreased by 10%, and when the nitro- 0 50 100 150 200 250 300 350 400 0 2000 4000 6000 8000 10000 12000 N Load tn/a P Load tn/a BASE 2003 CAP 2006 Fig. 8. Phosphorus load for the region as a function of ni- trogen load. 368 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Helin, J. et al. Abatement costs for agricultural nutrient load in SW Finland gen price was increased and the allowed load re- duced by more than 40%. The effects of the pa- rameter changes on the unconstrained nitrogen loads and abatement costs are as one would ex- pect: a decrease in crop prices or an increase in fertilizer prices decrease the unconstrained nitro- gen load. A 10% increase in crop prices had little or no effect on the cost of halving the nitrogen load from the associated unconstrained nitrogen load. A marked increase of 50% in the nitrogen price re- sulted in a 15 to 20% increase in the cost of halv- ing the nitrogen load. We also tested the sensitivity of the profit op- tima found by the optimization algorithm to the initial levels of the key variables. The crop choice and the tillage method were sensitive to the initial values of hectares and nitrogen fertilization used in the optimization, while the maximum profit levels were not affected significantly. The sensitivity is due to non-linearities in the production and load functions. The choice of plausible initial values and bounds for variables is a normal part of non- linear optimization problems. Initial levels for land were allocated based on the current regional distri- bution of crops (Yearbook of farm statistics 2003). Fertilizer use was initialized at the unconstrained profit maximizing level. For each consequent itera- tion on the load constraint, the variable values from the previous iteration were used as starting values. This produced relatively smooth yield and profit curves. Discussion and conclusions We studied the costs of agricultural nutrient abate- ment for crop farming in south-western Finland. Our study area covered approximately 21% of the Finnish arable lands. Compared to previous stud- ies we considered an extensive selection of crops and farming technologies and described them by nonlinear functional forms estimated from a large set of empirical data. We also modelled the loads of two nutrients simultaneously, where many stud- ies have focused on a single nutrient and neglected the effect of reduction measures on the other. The modelling framework described here can be ap- plied to other regions, and the results can be used in empirical studies and decision support systems tackling with optimal nutrient abatement. Empirical modelling of agricultural loads and abatement costs is a challenging task. Data re- quirements are vast. Whereas economic data are relatively easy to obtain and applicable to the en- tire region, data on crop yield and nutrient loads are specific to crop and the characteristics of each parcel of land, most notably the slope and soil type. Furthermore, weather affects both the farm yields and nutrient loads. For tractability, we ab- stracted from heterogeneity in land and farmer characteristics, and from uncertainty pertaining to weather conditions. We focused on crop farming, which is predominant in the study region, and con- Table 11. Main results of the sensitivity analysis. BASE 2003 CAP 2006 2003 commodity and fertilizer prices 10% decrease in crop prices 50% increase in nitrogen price 2003 commodity and fertilizer prices 10% decrease in crop prices 50% increase in nitrogen price Estimated coefficient 1.86 1.92 2.57 1.47 1.69 2.18 R2 0.96 0.97 0.97 0.98 0.99 0.98 Unconstrained nitrogen load (tn) 10116 9593 8380 9740 8576 7989 Costs of 50 % reduction in N-load € kg-1 9.4 9.2 10.8 7.2 7.2 8.7 369 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Vol. 15 (2006): 351–374. sidered farming decisions where the time horizon is one year. The long run effect of nitrogen load restrictions or other water protection measures on phosphorus loss is likely to be larger than the one predicted by our short run model. Assessing the long run impacts would require a dynamic model tracking changes in soil phosphorus status, which merits full attention in a separate future study. We also assumed that machinery can be rented and hence that farmers do not face capacity constraints, and that labor is not constrained. These assump- tions are reasonable in that contractor services are widely available in Finland and crop production is not particularly labor intensive. By the Le Chate- lier principle (Samuelson 1983), the abatement costs would be at least as large as those suggested by our analysis if machinery or labor constraints were added. The effect of relaxing the assumption of fixed area of agricultural land would be the op- posite: the abatement costs would be at most as large as those obtained here. The land allocation produced by the model un- der the BASE 2003 regime differs from the ob- served land allocation in 2003 even when nutrient loads are not restricted. The discrepancy follows from the modelling choice of no heterogeneity in soil quality and farmer skills, whereby barley be- comes the most profitable cereal for the represent- ative farm and replaces all other cereals. While ac- counting for heterogeneity would be an important extension, one can argue that the land allocation produced by our model is a reasonable approxima- tion. As in the 2003 observed land allocation, most land is in cereal production, and barley is the pre- dominant crop. Abstracting from heterogeneity of soil types and other environmental factors may, however, overestimate the abatement costs (for an empirical example see Johansson 2004). Large scale animal farms produce a challenge for agri- cultural nutrient abatement, and the abatement costs may also be somewhat over or underestimat- ed due to leaving manure management and animal farms outside the analysis. Nevertheless, our re- sults on crop farming are of a similar magnitude with previous Danish and Dutch studies on abate- ment costs in pig farming (Berntsen et al. 2003, Polman and Thijssen 2002). Catch crops could also provide a low cost abatement alternative (Gren et al. 1995), but they have not been common in Finland and no empirical data are available on their effect on nutrient loading in the study region. Hence, catch crops were not considered in this study. The differences in the results pertaining to the BASE 2003 and CAP 2006 regimes support the findings by Hofreither 2003 and Serra et al. 2004 that decoupling agricultural subsidies from pro- duction reduces the environmental impacts of agri- culture. Wier et al. (2002) on the contrary found that the EU Agenda 2000 reform, which involved reductions in price support and compensations in the form of hectare support, had almost no effects on the environment. In our analysis the latest CAP reform, adopted in Finland in 2006, led to slight decreases in farmers’ variable profits, the uncon- strained nitrogen load, and abatement costs. The results are also in line with Lehtonen et al. (2006), according to whom significant reductions in nutri- ent loading would require radical policy changes. All in all, our results support changes in the design and implementation of further agri-environmental nutrient policies in Finland. Efficiency and en- forcement issues should be taken seriously, as our analysis suggests that load reductions could be ob- tained without excessive costs or marked income transfers from taxpayers to farmers. Acknowledgements. The authors would like thank Tapio Salo and Sirkka Tattari for providing the data on the effect of crop choice and tillage method on nitrogen and phos- phorus loading. The authors are also indebted to Petri Ekholm, Anni Huhtala, Jussi Lankoski, Markku Puusti- nen, Antti Räike and Risto Uusitalo for insightful com- ments and useful discussions over the course of this study. The authors are solely responsible for all remaining er- rors. 370 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Appendix 1. Solution to the constrained optimization problem. The optimization problem defined in equations (1) to (6) is solved using nonlinear programming. The Lagrange function is specified as 20 The optimization problem defined in equations (1) to (6) is solved using nonlinear programming. The Lagrange function is specified as ( ){ } ( ) , , , , , , , , , , 1 1 , , , , , , , 1 1 1 1 1 , 1 1 (1 ) , . J K j j k j k N j k j k j k j k B j k j k j k j k I J K J K i Ni i j k j k j k j k j k j k i j k j k J K j k j k p f N p N c s B c B X R r X L e N B X B B μ λ η = = = = = = = = = = − − + − − + − + − + − L (A1) The Kuhn-Tucker conditions for the problem in (A1) are ( ) ( ) , , , , , , , , , , , , , , , , 1 (1 ) , 0 , ( 0 if 0) j j k j k N j k j k j k j k B j k j k j k I i j k j k j k j k j k i p f N p N c s B c B X r e N B j k Xμ λ = ∂ = − − + − − ∂ − − ≤ ∀ = > L (A2) ( ) ( ), , , , , , , , , , , , , (1 ) 0 , ( 0 if 0) j k j k j k j k j k j N j k j k j k j k j k j k j k f N e N B p p B X X j k N N N N λ ∂ ∂∂ = − − − ≤ ∀ ∂ ∂ ∂ = > L (A3) ( ){ } ( ) , , , , , , , , , , , , , , , , 0 , ( 0 if 0) j j k j k N j k j k j k B j k j k j k j k j k j k j k j k j k p f N p N c s c X B e N B X j k B B λ η ∂ = − − − + − ∂ ∂ − − ≤ ∀ = > ∂ L (A4) , , , 1 1 0 ( 0 if 0) J K i i j k j k i j ki R r X i μ μ = = ∂ = − ≥ ∀ = > ∂ L (A5) ( ), , , , 1 1 , 0 ( 0 if 0) J K N j k j k j k j k j k L e N B X λ λ = = ∂ = − ≥ = > ∂ L (A6) , 1 1 0 ( 0 if 0) J K j k j k B B η η = = ∂ = − ≥ = > ∂ L (A7) In addition, kjX , and kjN , have to satisfy the non-negativity constraints in (3). The solution to the problem in (A1) consists of the values of kjX , , kjN , , and kjB , and the associated Lagrange multipliers that satisfy the Kuhn-Tucker conditions in (A2) to (A7). The Lagrange multipliers iμ express the shadow price of the resource constraints Ri. The multiplier (A1) The Kuhn-Tucker conditions for the problem in (A1) are 20 The optimization problem defined in equations (1) to (6) is solved using nonlinear programming. The Lagrange function is specified as ( ){ } ( ) , , , , , , , , , , 1 1 , , , , , , , 1 1 1 1 1 , 1 1 (1 ) , . J K j j k j k N j k j k j k j k B j k j k j k j k I J K J K i Ni i j k j k j k j k j k j k i j k j k J K j k j k p f N p N c s B c B X R r X L e N B X B B μ λ η = = = = = = = = = = − − + − − + − + − + − L (A1) The Kuhn-Tucker conditions for the problem in (A1) are ( ) ( ) , , , , , , , , , , , , , , , , 1 (1 ) , 0 , ( 0 if 0) j j k j k N j k j k j k j k B j k j k j k I i j k j k j k j k j k i p f N p N c s B c B X r e N B j k Xμ λ = ∂ = − − + − − ∂ − − ≤ ∀ = > L (A2) ( ) ( ), , , , , , , , , , , , , (1 ) 0 , ( 0 if 0) j k j k j k j k j k j N j k j k j k j k j k j k j k f N e N B p p B X X j k N N N N λ ∂ ∂∂ = − − − ≤ ∀ ∂ ∂ ∂ = > L (A3) ( ){ } ( ) , , , , , , , , , , , , , , , , 0 , ( 0 if 0) j j k j k N j k j k j k B j k j k j k j k j k j k j k j k j k p f N p N c s c X B e N B X j k B B λ η ∂ = − − − + − ∂ ∂ − − ≤ ∀ = > ∂ L (A4) , , , 1 1 0 ( 0 if 0) J K i i j k j k i j ki R r X i μ μ = = ∂ = − ≥ ∀ = > ∂ L (A5) ( ), , , , 1 1 , 0 ( 0 if 0) J K N j k j k j k j k j k L e N B X λ λ = = ∂ = − ≥ = > ∂ L (A6) , 1 1 0 ( 0 if 0) J K j k j k B B η η = = ∂ = − ≥ = > ∂ L (A7) In addition, kjX , and kjN , have to satisfy the non-negativity constraints in (3). The solution to the problem in (A1) consists of the values of kjX , , kjN , , and kjB , and the associated Lagrange multipliers that satisfy the Kuhn-Tucker conditions in (A2) to (A7). The Lagrange multipliers iμ express the shadow price of the resource constraints Ri. The multiplier (A2) 20 The optimization problem defined in equations (1) to (6) is solved using nonlinear programming. The Lagrange function is specified as ( ){ } ( ) , , , , , , , , , , 1 1 , , , , , , , 1 1 1 1 1 , 1 1 (1 ) , . J K j j k j k N j k j k j k j k B j k j k j k j k I J K J K i Ni i j k j k j k j k j k j k i j k j k J K j k j k p f N p N c s B c B X R r X L e N B X B B μ λ η = = = = = = = = = = − − + − − + − + − + − L (A1) The Kuhn-Tucker conditions for the problem in (A1) are ( ) ( ) , , , , , , , , , , , , , , , , 1 (1 ) , 0 , ( 0 if 0) j j k j k N j k j k j k j k B j k j k j k I i j k j k j k j k j k i p f N p N c s B c B X r e N B j k Xμ λ = ∂ = − − + − − ∂ − − ≤ ∀ = > L (A2) ( ) ( ), , , , , , , , , , , , , (1 ) 0 , ( 0 if 0) j k j k j k j k j k j N j k j k j k j k j k j k j k f N e N B p p B X X j k N N N N λ ∂ ∂∂ = − − − ≤ ∀ ∂ ∂ ∂ = > L (A3) ( ){ } ( ) , , , , , , , , , , , , , , , , 0 , ( 0 if 0) j j k j k N j k j k j k B j k j k j k j k j k j k j k j k j k p f N p N c s c X B e N B X j k B B λ η ∂ = − − − + − ∂ ∂ − − ≤ ∀ = > ∂ L (A4) , , , 1 1 0 ( 0 if 0) J K i i j k j k i j ki R r X i μ μ = = ∂ = − ≥ ∀ = > ∂ L (A5) ( ), , , , 1 1 , 0 ( 0 if 0) J K N j k j k j k j k j k L e N B X λ λ = = ∂ = − ≥ = > ∂ L (A6) , 1 1 0 ( 0 if 0) J K j k j k B B η η = = ∂ = − ≥ = > ∂ L (A7) In addition, kjX , and kjN , have to satisfy the non-negativity constraints in (3). The solution to the problem in (A1) consists of the values of kjX , , kjN , , and kjB , and the associated Lagrange multipliers that satisfy the Kuhn-Tucker conditions in (A2) to (A7). The Lagrange multipliers iμ express the shadow price of the resource constraints Ri. The multiplier (A3) 20 The optimization problem defined in equations (1) to (6) is solved using nonlinear programming. The Lagrange function is specified as ( ){ } ( ) , , , , , , , , , , 1 1 , , , , , , , 1 1 1 1 1 , 1 1 (1 ) , . J K j j k j k N j k j k j k j k B j k j k j k j k I J K J K i Ni i j k j k j k j k j k j k i j k j k J K j k j k p f N p N c s B c B X R r X L e N B X B B μ λ η = = = = = = = = = = − − + − − + − + − + − L (A1) The Kuhn-Tucker conditions for the problem in (A1) are ( ) ( ) , , , , , , , , , , , , , , , , 1 (1 ) , 0 , ( 0 if 0) j j k j k N j k j k j k j k B j k j k j k I i j k j k j k j k j k i p f N p N c s B c B X r e N B j k Xμ λ = ∂ = − − + − − ∂ − − ≤ ∀ = > L (A2) ( ) ( ), , , , , , , , , , , , , (1 ) 0 , ( 0 if 0) j k j k j k j k j k j N j k j k j k j k j k j k j k f N e N B p p B X X j k N N N N λ ∂ ∂∂ = − − − ≤ ∀ ∂ ∂ ∂ = > L (A3) ( ){ } ( ) , , , , , , , , , , , , , , , , 0 , ( 0 if 0) j j k j k N j k j k j k B j k j k j k j k j k j k j k j k j k p f N p N c s c X B e N B X j k B B λ η ∂ = − − − + − ∂ ∂ − − ≤ ∀ = > ∂ L (A4) , , , 1 1 0 ( 0 if 0) J K i i j k j k i j ki R r X i μ μ = = ∂ = − ≥ ∀ = > ∂ L (A5) ( ), , , , 1 1 , 0 ( 0 if 0) J K N j k j k j k j k j k L e N B X λ λ = = ∂ = − ≥ = > ∂ L (A6) , 1 1 0 ( 0 if 0) J K j k j k B B η η = = ∂ = − ≥ = > ∂ L (A7) In addition, kjX , and kjN , have to satisfy the non-negativity constraints in (3). The solution to the problem in (A1) consists of the values of kjX , , kjN , , and kjB , and the associated Lagrange multipliers that satisfy the Kuhn-Tucker conditions in (A2) to (A7). The Lagrange multipliers iμ express the shadow price of the resource constraints Ri. The multiplier (A4) 20 The optimization problem defined in equations (1) to (6) is solved using nonlinear programming. The Lagrange function is specified as ( ){ } ( ) , , , , , , , , , , 1 1 , , , , , , , 1 1 1 1 1 , 1 1 (1 ) , . J K j j k j k N j k j k j k j k B j k j k j k j k I J K J K i Ni i j k j k j k j k j k j k i j k j k J K j k j k p f N p N c s B c B X R r X L e N B X B B μ λ η = = = = = = = = = = − − + − − + − + − + − L (A1) The Kuhn-Tucker conditions for the problem in (A1) are ( ) ( ) , , , , , , , , , , , , , , , , 1 (1 ) , 0 , ( 0 if 0) j j k j k N j k j k j k j k B j k j k j k I i j k j k j k j k j k i p f N p N c s B c B X r e N B j k Xμ λ = ∂ = − − + − − ∂ − − ≤ ∀ = > L (A2) ( ) ( ), , , , , , , , , , , , , (1 ) 0 , ( 0 if 0) j k j k j k j k j k j N j k j k j k j k j k j k j k f N e N B p p B X X j k N N N N λ ∂ ∂∂ = − − − ≤ ∀ ∂ ∂ ∂ = > L (A3) ( ){ } ( ) , , , , , , , , , , , , , , , , 0 , ( 0 if 0) j j k j k N j k j k j k B j k j k j k j k j k j k j k j k j k p f N p N c s c X B e N B X j k B B λ η ∂ = − − − + − ∂ ∂ − − ≤ ∀ = > ∂ L (A4) , , , 1 1 0 ( 0 if 0) J K i i j k j k i j ki R r X i μ μ = = ∂ = − ≥ ∀ = > ∂ L (A5) ( ), , , , 1 1 , 0 ( 0 if 0) J K N j k j k j k j k j k L e N B X λ λ = = ∂ = − ≥ = > ∂ L (A6) , 1 1 0 ( 0 if 0) J K j k j k B B η η = = ∂ = − ≥ = > ∂ L (A7) In addition, kjX , and kjN , have to satisfy the non-negativity constraints in (3). The solution to the problem in (A1) consists of the values of kjX , , kjN , , and kjB , and the associated Lagrange multipliers that satisfy the Kuhn-Tucker conditions in (A2) to (A7). The Lagrange multipliers iμ express the shadow price of the resource constraints Ri. The multiplier (A5) 20 The optimization problem defined in equations (1) to (6) is solved using nonlinear programming. The Lagrange function is specified as ( ){ } ( ) , , , , , , , , , , 1 1 , , , , , , , 1 1 1 1 1 , 1 1 (1 ) , . J K j j k j k N j k j k j k j k B j k j k j k j k I J K J K i Ni i j k j k j k j k j k j k i j k j k J K j k j k p f N p N c s B c B X R r X L e N B X B B μ λ η = = = = = = = = = = − − + − − + − + − + − L (A1) The Kuhn-Tucker conditions for the problem in (A1) are ( ) ( ) , , , , , , , , , , , , , , , , 1 (1 ) , 0 , ( 0 if 0) j j k j k N j k j k j k j k B j k j k j k I i j k j k j k j k j k i p f N p N c s B c B X r e N B j k Xμ λ = ∂ = − − + − − ∂ − − ≤ ∀ = > L (A2) ( ) ( ), , , , , , , , , , , , , (1 ) 0 , ( 0 if 0) j k j k j k j k j k j N j k j k j k j k j k j k j k f N e N B p p B X X j k N N N N λ ∂ ∂∂ = − − − ≤ ∀ ∂ ∂ ∂ = > L (A3) ( ){ } ( ) , , , , , , , , , , , , , , , , 0 , ( 0 if 0) j j k j k N j k j k j k B j k j k j k j k j k j k j k j k j k p f N p N c s c X B e N B X j k B B λ η ∂ = − − − + − ∂ ∂ − − ≤ ∀ = > ∂ L (A4) , , , 1 1 0 ( 0 if 0) J K i i j k j k i j ki R r X i μ μ = = ∂ = − ≥ ∀ = > ∂ L (A5) ( ), , , , 1 1 , 0 ( 0 if 0) J K N j k j k j k j k j k L e N B X λ λ = = ∂ = − ≥ = > ∂ L (A6) , 1 1 0 ( 0 if 0) J K j k j k B B η η = = ∂ = − ≥ = > ∂ L (A7) In addition, kjX , and kjN , have to satisfy the non-negativity constraints in (3). The solution to the problem in (A1) consists of the values of kjX , , kjN , , and kjB , and the associated Lagrange multipliers that satisfy the Kuhn-Tucker conditions in (A2) to (A7). The Lagrange multipliers iμ express the shadow price of the resource constraints Ri. The multiplier (A6) 20 The optimization problem defined in equations (1) to (6) is solved using nonlinear programming. The Lagrange function is specified as ( ){ } ( ) , , , , , , , , , , 1 1 , , , , , , , 1 1 1 1 1 , 1 1 (1 ) , . J K j j k j k N j k j k j k j k B j k j k j k j k I J K J K i Ni i j k j k j k j k j k j k i j k j k J K j k j k p f N p N c s B c B X R r X L e N B X B B μ λ η = = = = = = = = = = − − + − − + − + − + − L (A1) The Kuhn-Tucker conditions for the problem in (A1) are ( ) ( ) , , , , , , , , , , , , , , , , 1 (1 ) , 0 , ( 0 if 0) j j k j k N j k j k j k j k B j k j k j k I i j k j k j k j k j k i p f N p N c s B c B X r e N B j k Xμ λ = ∂ = − − + − − ∂ − − ≤ ∀ = > L (A2) ( ) ( ), , , , , , , , , , , , , (1 ) 0 , ( 0 if 0) j k j k j k j k j k j N j k j k j k j k j k j k j k f N e N B p p B X X j k N N N N λ ∂ ∂∂ = − − − ≤ ∀ ∂ ∂ ∂ = > L (A3) ( ){ } ( ) , , , , , , , , , , , , , , , , 0 , ( 0 if 0) j j k j k N j k j k j k B j k j k j k j k j k j k j k j k j k p f N p N c s c X B e N B X j k B B λ η ∂ = − − − + − ∂ ∂ − − ≤ ∀ = > ∂ L (A4) , , , 1 1 0 ( 0 if 0) J K i i j k j k i j ki R r X i μ μ = = ∂ = − ≥ ∀ = > ∂ L (A5) ( ), , , , 1 1 , 0 ( 0 if 0) J K N j k j k j k j k j k L e N B X λ λ = = ∂ = − ≥ = > ∂ L (A6) , 1 1 0 ( 0 if 0) J K j k j k B B η η = = ∂ = − ≥ = > ∂ L (A7) In addition, kjX , and kjN , have to satisfy the non-negativity constraints in (3). The solution to the problem in (A1) consists of the values of kjX , , kjN , , and kjB , and the associated Lagrange multipliers that satisfy the Kuhn-Tucker conditions in (A2) to (A7). The Lagrange multipliers iμ express the shadow price of the resource constraints Ri. The multiplier (A7) In addition, kjX , and kjN , have to satisfy the non-negativity constraints in (3). The solution to the problem in (A1) consists of the values of kjX , , kjN , , and kjB , and the associated Lagrange multipliers that satisfy the Kuhn-Tucker conditions in (A2) to (A7). The Lagrange multipliers µi express the shadow price of the resource constraints Ri. The multiplier λ represents the shadow cost of the restriction on nitro- gen discharges: the value of λ shows how much farm profits will fall if the load restriction is tightened by an additional kilogram. That is, the marginal cost of reducing agricultural nitrogen discharges is embedded in λ. The multiplier η gives the shadow value of buffer strips. 371 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Vol. 15 (2006): 351–374. Ærtebjerg G, Carstensen, J., Dahl, K., Hansen, J., Rygg, B., Sørensen, K., Severinsen, G., Nygaard, K., Schrimpf, W., Schiller, C., Druon, J.N., & Casartelli, S., 2001. Eu- trophication in Europe’s coastal waters. European En- vironmental Agency. Topic report no. 7/2001. Cited 16.8.2006. Updated 18.10.2001. Available on the Inter- net: http://reports.eea.europa.eu/topic_report_2001_7/ en/Topic_Report_7_2001. pdf Antle, J.M. & Just, R.E. 1991. Effects of commodity program structure on resource use and the environment. In: Bockstael, N. & Just, R.E. (eds.). Commodity and re- source policies in agricultural systems. New York: Springer Verlag. p. 97–128. Bäckman, S., Vermeulen, S. & Taavitsainen, V. 1997. Long- term fertilizer field trials: comparison of three mathe- matical response models. Agricultural and Food Sci- ence in Finland 6: 151–160. Baltic Sea GIS 1993. Arc shape files. Norway, UNEP:Grid/ Arendal. Cited 16 Aug 2006. Updated 1 Aug 2006. Available on the Internet: http://www.grida.no/baltic/ Baumol, W. & Oates, W. 1988. The theory of environmental policy. Cambridge, UK: Cambridge University Press. 297 p. Berntsen, J., Petersen, B.M., Jacobsen, B.H., Olesen, J.E. & Hutchings N.J. 2003. Evaluating nitrogen taxation scenarios using the dynamic whole farm simulation model FASSET. Agricultural Systems 76: 817–839. Bock, B. & Sikora, F. 1990. Modified quadratic/plateau mod- el for describing plant responses to fertilizer. Soil Sci- ence Society of America Journal 54: 1784–1789. Brady, M. 2001. Baltic Sea nitrogen agricultural abatement and ecosystem adaptation models. Uppsala: Swedish University of Agricultural Sciences. 15 p. Brady, M. 2003. Managing agriculture and water quality four essays on the control of large-scale nitrogen pollution. Uppsala: Swedish University of Agricultural Sciences. Cited 16.8.2006. Updated 4.4.2003. Available on the Internet: http://diss-epsilon.slu.se/archive/00000217/ 01/ejfulltext.pdf Brooke, A., Kendrick, D., Meeraus, A., Raman, R. & Rosen- thal. R. 1998. GAMS user’s guide. Washington:GAMS Development Corporation. 169 p. Cerrato, M. & Blackmer, A. 1990. Comparison of models for describing corn yield response to nitrogen fertilizer. Agronomy Journal 82: 138–143. Dillaha, T. & Inamdar, S. 1997. Buffer zones as sediment traps or source. In: Haycock, N. et al. (eds.). Buffer zones: their processes and potential in water protec- tion. Harpenden: Quest Environmental. p. 33–42. Drud, A. 2004. Conopt user manual. Denmark: Arki Con- sulting and Development. 44 p. Ekholm, P. & Krogerus, K. 2003. Determining algal-avail- able phosphorus of differing origin: routine phospho- rus analyses vs. algal assays. Hydrobiologia 492: 29–42. Ekholm, P., Virtainen, J. & Mitikka, S. 2004. Maatalouden ravinnekuormitus ja sen vesistövaikutukset – arviointi seuranta-aineistojen perusteella, Järvien vedenlaatu. In: Turtola, E. & Lemola, R. (eds.). Maatalouden ympä- ristötuen seuranta MYTVAS 2. Agrifood Research Re- ports 59. Jokioinen, Finland: MTT Agrifood Research Finland. p. 84–176. Ekman, S. 2000. Tillage system selection: a mathematical programming model incorporating weather variability. Journal of Agricultural �ngineering Researchtural �ngineering Research 77: 267– 276. Enroth, A. 2004. Mallilaskelmia maataloudesta 2004. ProAg- ria Maaseutukeskusten Liiton julkaisuja nro 1008. 45 p. European Commission 2005. Agriculture and rural develop- ment – CAP reform. Cited 16 Aug 2006. Updated 26 Jun 2003. http://europa.eu.int/comm/agriculture/capre- form/index_en.htm Finnish Field Drainage Center 2002. Salaojituksen tavoite- ohjelma 2020. Updated 1 Jan 2003. Cited 16 Aug 2006.Updated 1 Jan 2003. Cited 16 Aug 2006. Available on the Internet: http://www.salaojakeskus.fi/ pdf/tavoiteohjelma.pdf (in Finnish). Frank, M., Beattie, B. & Embleton, M. 1990. A comparison of alternative crop response models. American Journal of Agricultural �conomics 72: 597–603. Granlund, K., Raike, A., Ekholm P., Rankinen, K. & Reko- lainen, S. 2005. Assessment of water protection targets for agricultural nutrient loading in Finland. Journal of Hydrology 304: 251–260. Gren, I.M., Söderqvist, T. & Wulff, F. 1997. Nutrient reduc- tions to the Baltic Sea: Ecology, costs and benefits. Journal of �nvironmental Management 51: 123–143. Gren, I.-M., Elofsson, K. & Jannke, P. 1995. Costs of nutri- ent reductions to the Baltic Sea. �nvironmental and Resource �conomics 10: 341–362. Hart, R. & Brady, M. 2002. Nitrogen in the Baltic Sea – pol- icy implications of stock effects. Journal of �nvironmen- tal Management 66: 91–103. Hofreihter, M.F., Schmidt, E. & Sinabell F. 2004. Phasing out environmentally harmful subsidies: �ffects of the CAP 2003 reform. American Agricultural Economics Asso- ciation Annual Meeting, Denver, Colorado, 1–4 July 2004. 20 p. HELCOM 2003. The review of more specific targets to reach the goal set up in the 1988/1998 Ministerial Dec- larations regarding nutrients. Helsinki Commission – Baltic Marine Environment Protection Commission. 15 p. HELCOM 2005. Nutrient pollution to the Baltic Sea in 2000. Baltic Sea �nvironment Proceedings 100. 16 p. Johansson, R.C., Gowda, P.H., Mulla, D. & Dalzell, B. 2004. Metamodelling phosphorus best management practic- es for policy use: a frontier approach. Agricultural �co- nomics 30: 63–74. Kosenius, A.-K. 2004. �stimating the benefit from algal bloom reduction – an application of contingent valua- tion method. Master’s thesis, Department of economics and management, Environmental economics, Univer- sity of Helsinki. 65 p. Lankoski, J., Ollikainen, M. & Uusitalo, P. 2006. No-till tech-No-till tech- nology: benefits to farmers and the environment? The- oretical analysis and application to Finnish agriculture. References 372 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Helin, J. et al. Abatement costs for agricultural nutrient load in SW Finland �uropean Review of Agricultural �conomics 33: 193– 221. Larsson, U., Elmgren, R. & Wulff, F. 1985. Eutrophication and the Baltic Sea. Ambio 14: 9–14. Lehtonen, H. 2001. Principles, structure and application of dynamic regional sector model of Finnish agriculture. Helsinki: Agrifood Research Finland. 264 p. Lehtonen, H., Bärlund, I., Tattari, S. & Hilden M. 2006. Com- bining dynamic economic analysis and environmental impact modelling: Addressing uncertainty and com- plexity of agricultural development. �nvironmental Mo- delling & Software. 22: 710–718. Lilja, H., Uusitalo, R., Yli-Halla, M., Nevalainen, R., Väänä- nen, T. & Tamminen. P. 2006. Finnish soil database.Finnish soil database. MTT:n selvityksiä 114. Jokioinen, Finland: Agrifood Re- search Finland. 54 p. Magette, W. 1998. Factors affecting losses of nutrients from agricultural systems and delivery to water resources. In: Carton, O. (ed.), Draft guidelines for nutrient use in- tensive agricultural enterprises. Teagasc, Johnstown Castle, Wexford, Ireland. p. 6–31. Mattsson, C. & Carlsson, N. 1983. Plant nutrients in agricul- ture. Part 2. Studies of the profitability of nitrogen fertili- zation at farm level. Report 214. Upsala: Swedish Uni- versity of Agricultural Sciences. 74 p. The Ministry of Agriculture and Forestry 2006a. Hakuopas 2006. Helsinki: The Ministry of Agriculture and Forestry. 131 p. The Ministry of Agriculture and Forestry 2006b. �telä-Suo- men kansallisen tuen, pohjoisen tuen, ympäristötuen, kansallisen lisäosan ja perunantuotannon kansallisen tuen tukitasot vuonna 2006. Helsinki: The Ministry ofHelsinki: The Ministry of Agriculture and Forestry. 3 p. The Ministry of Agriculture and Forestry 2004. Horisontaa-Horisontaa- lisen maaseudun kehittämisohjelman väliarviointi: Man- ner-Suomi. Maa- ja metsätalousministeriön julkaisuja Helsinki: The Ministry of Agriculture and Forestry. 272 p. The Ministry of Environment 1998. Water Protection Tar- gets to 2005. The Finnish �nvironment 226. Helsinki: The Ministry of Environment. 82 p. Myyrä, S., Ketola, E., Yli-halla, M. & Pietola, K. 2005. LandLand improvements under land tenure insecurity: the case of pH and phosphate in Finland. Land �conomics 81: 557–569. Niemi, J. & Ahlstedt, J. (eds.). 2003. Finnish agriculture and rural industries 2003. Helsinki: MTT Agrifood Research Finland. 94 p. Niemi, J. & Ahlstedt, J. (eds.). 2005. Finnish agriculture andFinnish agriculture and rural industries 2005. Helsinki: MTT Agrifood Research Finland. 94 p. Patty, L., Réal, B. & Gril, J. 1997. The use of grassed buffer strips to remove pesticides, nitrate and soluble phos- phorus compounds from runoff water. Pesticide Scien- ce 49: 243–251. Pentti, S. 2003. Konetyön kustannukset ja tilastolliset ura- kointihinnat. Työtehoseuran maataloustiedote 7/2003. 12 p. Penttilä, S. 2003. Suojavyöhykkeiden ja maisemanhoidon yleissuunnitelma Uudenmaan ympäristökeskuksen alueella. Uudenmaan ympäristökeskus. Moniste 133. 40 p. Petrolia, D.R. & Prasanna H.G. 2006. Missing the boat: Mid- west farm drainage and Gulf of Mexico Hypoxia. Re- view of Agricultural �conomics 28: 240–253. Polman, N. & Thijssen, G. 2002. Combining results of differ- ent models: the case of a levy on the Dutch nitrogen surplus. Agricultural �conomics 27: 41–49. Puustinen, M., Koskiaho, J. & Peltonen, K. 2005. In��uenceIn��uence of cultivation methods on suspended solids and phos- phorus concentrations in surface runoff on clayey sloped fields in boreal climate. Agriculture, �cosystems & �nvironment 105: 565–579.105: 565–579. Puustinen, M., Merilä, E., Palko, J. & Seuna, P. 1994. Kuiva- tustila, viljelykäytäntö ja vesistökuormitukseen vaikut- tavat ominaisuudet Suomen pelloilla. Vesi- ja ympäris- töhallituksen julkaisuja 198. 130 p. Räike, A., Granlund, K. & Ekholm, P. 2004. MaataloudenMaatalouden ravinnekuormitus ja sen vesistövaikutukset – arviointi seuranta-aineistojen perusteella, ravinnekuormitus. In: Turtola, E. & Lemola, R. (eds.). Maatalouden ympäris- tötuen seuranta MYTVAS 2. Agrifood Research Re-Agrifood Research Re- ports 59. Jokioinen, Finland: MTT Agrifood Research Finland. p. 97–176. Randall, G.W., Huggins, D.R., Russelle, M.P., Fuchs, D.J., Nelson, W.W. & Anderson, J.L. 1997. Nitrate losses through subsurface tile drainage in Conservation re- serve program, alalfa, and row crop systems. Journal of �nvironmental Quality 26: 1240–1247. Randall, G.W. & Mulla, D.J. 2001. Nitrate nitrogen in surface waters as in��uenced by climatic conditions and agricul- tural practices. Journal �nvironmental Quality 30: 337– 344. Saarela, I., Järvi, A., Hakkola, H. & Rinne, K. 1995. Fosfori- lannoituksen porraskokeet 1977–1994. Vuosittain an- netun fosforimäärän vaikutus maan viljavuuteen ja pel-imäärän vaikutus maan viljavuuteen ja pel- tokasvien satoon monivuotisissa kenttäkokeissa. (Summary: Phosphorus fertilizer trials, 1977–1994: ef- fects of the rate of annual phosphorus application on soil fertility and yields of fields crops in long-term field experiments). Agricultural Research Centre of Finland, Tiedote 16/95. 94 p. Saarela, I., Järvi, A., Hakkola, H. & Rinne, K. 2003. Phos- phorus status of diverse soils in Finland as in��uenced by long-term P fertilisation. I. Native and previously ap- plied P at 24 experimental sites. Agricultural and Food Science in Finland 12: 117–132. Samuelson, P. 1983. Foundations of economic analysis. Enlarged Edition. USA: Harvard University Press. 353 p. Sandström, M., Scharin, H. & Söderqvist, T. 2000. Seaside recreation in the Stockholm archipelago: travel patterns and costs. Beijer Discussion Paper, Series No. 129. 20 p. Schou, J.S., Skop, E. & Jensen, J.D. 2000. Integrated agri- environmental modelling: A cost-effectiveness analysis of two nitrogen tax instruments in the Vejle Fjord water- shed, Denmark. Journal of �nvironmental Manage- ment 58: 199–212. Serra, T., Zilberman, D., Goodwin, B.K. & Hyvönen, K. 2004. Replacement of price support measures by direct pay- ments in agricultural policies. Does this benefit the en- vironment? The effects of the post 1992 CAP on pest control in the �U. American Agricultural Economics As- 373 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Vol. 15 (2006): 351–374. sociation Annual Meeting, Denver, Colorado, 1–4 July 2004. 28 p. Shortle, J.S. & Abler, D.G. 2001. �nvironmental policies for agricultural pollution control. Wallingford: CABI Publish- ing. 240 p. Simmelsgaard, S.E. & Djurhuus, J. 1998. An empirical mod-An empirical mod- el for estimating nitrate leaching as affected by crop type and the long-term fertilizer rate. Soil Use and Man- agement 14: 37–43. Simmelsgaard, S.E. 1991. Estimation of nitrogen leakage functions – nitrogen leakage as a function of nitrogen applications for different crops on sandy and clay soils. In: Rude, S. (ed.). Kavelstofgödning i landbruget – be- hov og udvasking nu og i fremtiden. Summary: Nitro- gen fertilizers in Danish agriculture – present and fu- ture application and leaching. Copenhagen. Institute of Agricultural �conomics Report 62. p. 135–150. Söderqvist, T. & Scahrin, H. 2000. The regional willingness to pay for a reduced eutrophication in the Stockholm archipelago. Beijer Discussion Paper, Series No. 128. 23 p. Soileau, J.M., Touchton, J.T., Hajek, B.F. & Baglio, J.V. 1994. Sediment, nitrogen & phosphorus runoff with conven- tional- and conservation tillage cotton in a small water- shed. Journal of Soil & Water Conservation 48: 449– 457. Stonehouse, D.P. 1997. Socio-economics of alternative till- age systems. Soil & Tillage Research 43: 109–130. Tattari, S., Bärlund, I., Rekolainen, S., Posch, M., Siimes, K., Tuhkanen, H.R. & Yli-Halla, M. 2001. Modeling sedi- ment yield and phosphorus transport in Finnish clayey soils. Transactions of the American Society of Agricul- tural �ngineers 44: 297–307. TIKE 2004. Agricultural statistical bulletin 1/2004. Helsinki: The Information Centre of the Ministry of Agriculture and Forestry. 19 p. Turpin, N., Bontems, P., Rotillon, G., Barlund, I., Kaljonen, M., Tattari, S., Feichtinger, F., Strauss, P., Haverkamp, R. & Garnier, M. 2005. AgriBMPWater: systems ap-AgriBMPWater: systems ap- proach to environmentally acceptable farming. �nviron- mental Modelling & Software 20: 187–196. Turtola, E. & Lemola, R. (eds.). 2004. Maatalouden ym-2004. Maatalouden ym- päristötuen seuranta MYTVAS. Agrifood Research Re- ports 59. Jokioinen, Finland: Agrifood Research Fin- land. 169 p. Turtola, E. & Paajanen, A. 1995. In��uence of improved sub- surface drainage on phosphorus losses and nitrogen leaching from a heavy clay soil. Agricultural Water Man- agement 28: 295–310. Uusi-Kämppä, J. 2005. Phosphorus purification in buffer zones in cold climates. In: Mander, U. et al. (eds.). Riparian buffer zones in agricultural watersheds. �co- logical �ngineering 24, 5: 491–502. Uusi-Kämppä, J., Braskerud, B., Jansson, H., Syversen, N. & Uusitalo, R. 2000. Buffer zones and constructed wet-Buffer zones and constructed wet- lands as filters for agricultural phosphorus. Journal of �nvironmental Quality 29: 151–158. Uusi-Kämppä, J. & Kilpinen, M. 2000. Suojakaistat ravinne- kuormituksen vähentäjänä. Maatalouden tutkimuskes- kuksen julkaisuja Sarja A 83. Jokioinen, Finland: Agri- cultural Research Centre of Finland. 49 p. + 2 app. Uusi-Kämppä, J. & Yläranta, T. 1992. Reduction of sedi- ment, phosphorus and nitrogen transport on vegetated buffer strips. Agricultural Science in Finland 1: 569– 575. Uusi-Kämppä, J. & Yläranta. T. 1996. Effect of buffer strip on controlling erosion and nutrient losses in Southern Fin- land. In: Mulamoottil, G. et al. (eds.). Wetlands: environ- mental gradients, boundaries and buffers. Boca Raton: CRC Press/Lewis Publishers. p. 221–235. Uusitalo, P. & Eriksson, C. 2004. Viljanviljelyn perusmuok-Viljanviljelyn perusmuok- kausmenetelmien taloudellisuusvertailu. Abstract: The. Abstract: The effect of tillage method on crop yield. Agrifood Re- search Reports 60. Jokioinen, Finland: MTT Agrifood Research Finland. 48 p. Uusitalo, R. & Jansson, H. 2002. Dissolved reactive phos- phorus in runoff assessed by soil extraction with an acetate buffer. Agricultural and Food Science in Finland 11: 343–353. Uusitalo, R., Turtola, E., Puustinen, M., Paasonen-Kivekäs, M. & Uusi Kämppä, J. 2003. Contribution of particulateContribution of particulate phosphorus to runoff phosphorus bioavailability. Jour- nal of �nvironmental Quality 32: 2007–2016. Wier, M., Andersen, J.M., Jensen, J.D. & Jensen, T.C. 2002. The EU’s Agenda 2000 reform for the agricultural sec- tor: environmental and economic effects in Denmark. �cological �conomics 41: 345–359. Yearbook of farm statistics 2004. Official statistics of Fin- land. Helsinki: Information Centre of the Ministry of Ag- riculture and Forestry. 268 p. Yiridoe, E. & Weersink, A. 1998, Marginal abatement costs of reducing groundwater-N pollution with intensive and extensive farm management choices. Agricultural and Resource �conomics Review 27: 169–185. 374 A G R I C U L T U R A L   A N D   F O O D   S C I E N C E Helin, J. et al. Abatement costs for agricultural nutrient load in SW Finland SELOSTUS Malli selvittää typpikuormituksen vähentämisen kustannukset Janne Helin, Marita Laukkanen ja Kauko Koikkalainen MTT Taloustutkimus Tehokkaan maatalouden ympäristöpolitiikan suunnitte- luun vaaditaan tietoa ravinnekuormituksen vähentämi- sen kustannuksista. Tässä tutkimuksessa kehitettiin em- piirinen malli, jonka avulla kyetään arvioimaan maata- lousmaan ravinnekuormituksen vähentämisestä aiheutu- via kustannuksia. Mallilla voidaan selvittää typpikuor- mituksen vähentämisen ja siitä johtuvan fosforikuormi- tuksen pienenemisen kustannukset Etelä-Suomessa. Tutkimuksessa analysoidaan Euroopan Unionin yhtei- sen maatalouspolitiikan vaikutuksia ravinnekuormituk- sen vähentämisen kustannuksiin sekä uuden että edeltä- vän tukijärjestelmän valossa. Tulokset osoittavat, että tehokkaalla politiikalla typpikuormituksen vähentämi- nen puoleen tulisi maksamaan 48–35 miljoonaa euroa, eli 3756–2752 euroa tilaa kohden. Abatement costs for agricultural nitrogen andphosphorus loads: a case study of crop farmingin south-western Finland Introduction Economic model Empirical specifications for crop yield and nutrient loss functions Agriculture in Southern Finland Results Discussion and conclusions References SELOSTUS