1

Evaluating input-based and stock-based tax incentives to reduce and

reallocate phosphor application across farm types in Denmark

Abstract

A non-linear agricultural optimisation model for a water catchment area is constructed and used to

analyse the effect on agricultural soil-P accumulation from implementation of two tax systems.

Regulation of P in the agricultural sector is central to reduce the risk of damaging aquatic eco-

system. The two systems considered are: a P surplus tax, which depend on soil P stock, and a tax on

mineral-fertilizer P. Analysis shows, that the two tax systems creates different incentives for the

utilisation of P between farm types as they address the application of P in different ways. A P

surplus tax addresses all P sources at the farm, including the soil P content, whereas a mineral-

fertilizer P tax addresses only the fertilizer input. Taking the temporal and spatial dynamics of a

catchment area into account, this paper focuses on how the two economic instruments can be used

to improve the interactions between livestock and arable farmers to improve utilization of P within

the catchment area. The analysis extends previous research on agricultural P regulation by

differentiating between farm types, by including P stock based taxes and by analyzing the effect

over time of implementing different P taxes with respect to soil P accumulation.

Keywords: Phosphorus pollution, soil P accumulation, nitrogen, phosphorus dynamics, farm types

2

1 Introduction

Nutrients such as phosphorus (P) and nitrogen (N) are essential for profitable arable and livestock-

based agriculture as well as for the functioning of natural ecosystems. However, application of P in

excess of crop requirements can lead to its accumulation in the soil. Leaching of P from eroded soils

or through run-off and drainage water from cultivated fields can in turn damage aquatic ecosystems

by fuelling excessive algae growth and accelerating eutrophication of lakes and streams (Sharpley

et al., 2003; Ekholm et al., 2005; Maguire et al., 2009; Sharpley et al., 2009). Once a water body has

undergone eutrophication, returning the system to a healthy state can be both difficult and

expensive, and since P is stored in sediment, is a slow and lengthy process. Eutrophication will

influence ecosystem functions and reduce the benefits from other uses and ecosystem services, e.g.

fishing, recreation, industry and drinking water, of the aquatic resource (Carpenter et al., 1998;

Bateman et al., 2011; Athiainen et al., 2013).

Accumulation of P in the soil in excess of crop requirements is a growing environmental problem

(OECD, 2008), which is partially caused by the intensive application of animal manure to

agricultural fields. In Europe and the U.S., application rates for animal manure have been based on

crop requirements of N in order to minimize nitrate losses. In most cases this has led to an

accumulation of P in the soil, since P application exceeds crop requirements when manure is

applied on the basis of optimal N application (Sharpley et al., 2009). P accumulation over time has

now led to increased P run-off in many areas of Europe and North America, and research

emphasizes that soil fertility on many farms is at a level where, for optimal P fertilization, the

quantity of P applied can be equal to or less than that of crop removal (Withers et al., 2001;

Sharpley et al., 2003; Sharpley et al, 2009).

In the U.S., nonpoint pollution control is pursued through voluntary programs originating from the

Clean Water Act of 1987. Programs such as the farm bill are established to motivate farmers via

incentive payments to apply best management practices in nutrient and manure management (EPA,

2003; Baylis et al., 2008). However, in 2006 the Environmental Protection Agency (EPA) found

that 42% of U.S. stream miles were in poor biological condition (compared to only 28% found in

good condition). N and P from run-off were amongst the most widespread stressors (EPA, 2010). In

the EU, the European Water Framework Directive requires that all inland and coastal waters be in a

3

healthy ecological state by 2015, obtained through the implementation of cost-effective reductions

of nutrient loads in the water, including P from agriculture (The European Parliament and the

Council, 2000).

In Denmark the overall surplus application of agricultural P (measured as the difference between

application rates and crop removal) has declined with almost 75% from the years 1986/1987 to

2010/11 (Vinther and Olsen 2012). This reduction of P surplus can be explained mainly by the

Danish fixed-quota system for N application, which has indirectly introduced an upper limit for P

surplus application (Maguire et al., 2009). In addition, a number of measures have been

implemented specifically to reduce P pollution to comply with the Danish implementation of the

Water Framework Directive and the requirements of the Danish Aquatic Action Plans (Børgesen et

al., 2009). But existing regulations do not give farmers, and especially livestock farmers, incentives

to reduce the application of P surplus further or to take P in the soil into account in their fertilizer

planning. This, together with the fact that soil P reserves are only utilized slowly (Meals, 2008;

Sharpley et al., 2009), has ensured that the agricultural contribution of P to surface waters has

remained constant since the 1980s (Maguire et al., 2009).

Several papers have focused on the problem of P leaching and on management measures to reduce

loss of P surplus to the aquatic environment. Part of the literature couples complex biological

dynamic P-models with different P management systems and analyzes the consequent effects on

soil and aquatic environments, e.g. Vatn et al. (2006), and Meals et al. (2008). Meals et al. evaluate

soil P development over a time horizon of 80 years with management strategies such as thresholds

for P application based on soil P levels, and erosion control. However, none of these papers address

how farmers respond to developments in soil P over time and most do not consider how the

different management systems could be implemented and at what economic cost. Analysing soil P

development over time is valuable for understanding both the long-term effects of measures for

reducing P loss and policy intervention. But if P policies are to be evaluated dynamic modelling of

soil P has to be linked to behavioural agricultural modelling. In the present work, dynamic

modelling of soil P directly – through its influence on optimal P application levels - influences the

optimal decisions of a farmer even within a one-period profit-maximisation behavioural framework.

4

In the literature, a number of simple deterministic P models are coupled with farm economics to

analyse the economic and environmental effects of implementing different regulatory systems.

However, common for a large part of the regulatory policies suggested in this literature is that soil P

is not taken into account. This means that only application levels of P determine rates of P losses

(e.g. Schnitkey and Miranda, 1993; Weersink et al., 2004; Malmaeus and Karlsson, 2010). If P

policies are to be evaluated properly, soil P dynamics must be understood and taken into account

because soil P plays a key role in crop nutrition. Soil P is part of the P fertilization planning for all

arable farms, because all P inputs have an economic value. In contrast, most livestock-based farms

produce manure P in excess of crop requirements and therefore assign low or no values to their

slack P resources on the margin. Some research does take soil P into account when evaluating

different P policies and their effect on P losses (e.g. Goetz and Zilberman, 2000; Westra and Olson,

2001; Helin et al., 2006). However, if the analysis of soil P accumulation is not carried out over

time, but only evaluated in one-period models, results do not reflect how soil P accumulates in

relation to P policies or how farmers should adjust P applications.

Iho and Laukkanen (2012) extend their previous work (Iho, 2007; Iho and Laukkanen, 2009) by

building a detailed bio-economic model taking soil P dynamics over time into account. Losses of P

into waterways are assumed to be directly dependent on soil P, which in turn depend on fertilizer

application rates. They find that P policies should be based on motivating farmers to plan their P

fertilization in response to soil P levels and, importantly, they find that the reduction of soil P

reserves, particularly in fields with high soil P values, should follow a dynamic pathway rather than

determined through a fixed fertilizer application rate. They conclude that as long as farmers know

the role of P in crop nutrition and how soil P accumulates in response to P applications over time,

the social welfare produced by the privately optimal depletion path can be very close to that of the

socially optimal path. However, these results cannot be applied to the livestock sector where

incentives that are effective in the arable sector may not work because of differences in the shadow

value of applying P and the availability of manure P. Differentiating analyses between farm types is

important in order to elucidate differences required in farm management practices and differentiate

environmental policies accordingly.

The variability in soil P levels across Danish fields (Pedersen, 2003) implies differences in P-

management incentives across different farm types, in particular livestock and arable farmers.

5

Taking the temporal and spatial dynamics of a catchment area into account, this paper focuses on

how economic instruments can be used to improve the interactions between livestock and arable

farmers to improve utilization of P within the catchment area. Two instruments are considered: a P

surplus tax, which depend on soil P stock, and a tax on mineral-fertilizer P. It is hypothesised that

these two instruments will create different incentives for the utilisation of P between farms as they

address the application of P in different ways. A P surplus tax addresses all P sources at the farm,

including the soil P content, whereas a mineral-fertilizer P tax addresses only the fertilizer input

(albeit that the tax is also an incentive to utilise P more effectively from all sources because of the

shadow-price of the other P sources (Hansen and Hansen, 2012)).

A non-linear agricultural optimisation model for a water catchment area is constructed and used to

analyse the effect of these tax systems. Focus is given to differences between farm types, to the

effect that soil P accumulation over time has on farmers’ decision making, and to the

implementation costs of the two tax systems. The analysis extends previous research on agricultural

P regulation by differentiating between farm types, by including P stock based taxes and by

analyzing the effect over time of implementing different P taxes with respect to soil P accumulation.

Furthermore, economic costs are compared between farm types.

6

2 The Model Setup

To model the private farm-level choice of optimal fertilization, it is assumed that farmers will

maximize profit from arable crop production on their own land. Livestock production, and profit

from this production, is considered fixed and is therefore not part of the optimization in our model.

Of course, in the long run a tax on P emissions from livestock production might reduce livestock

levels marginally. However, livestock production involve large sunk costs from investments in

buildings which are not likely to be adjusted in the short run due to the taxes tested here, in

particular not, as we shall see, the overall costs of the taxes are not major, yet large enough to cause

improved efficiency in and reduced P application. Reduction of the livestock units as a measure to

reduce the P-problem is not considered separately in our analysis. Thus, here crop and livestock

productions are linked by the application of manure from cattle and pig farms to crops as a

fertilizer. Arable farmers can buy manure and use it as a substitute for mineral fertilizer1, and cattle

producers are restricted to producing a share of their own feed units2. Farms are classified into three

types: arable, pig and cattle.

The full model including the aggregate objective function for the individual farmers and all the

main co-state equations and restrictions are shown in equations (1)-(8) and carefully explained

below.

∏ ∑

(1)

(

)

)

(

)

(2)

∑

∑

(3)

(4)

1 In Denmark, sludge and sewage are used as alternative fertilizers to supplement manure and mineral fertilizers.

However they comprise a small percentage of total fertilizer volume and are not included in the current model. 2 The share is calculated from farm statistics (Gravholt, 2004). Grains for feed are not used in the present model so the

limitation is only for other feed crops and is restricted to 11%. Feed restrictions are included in the model to keep a

realistic distribution of crops for the case study area.

7

(5)

( )

(6)

∑ ⁄ ∑ (7)

(8)

Profit, Π, is maximized at each time period t and is the aggregated profit for all fields owned and

cultivated by the farmer, where gives the cultivated area in hectares. Baseline prices are

taken from 2003, projected over time for N and P mineral fertilizers3. Each farmer grows a mix of

crops4 (j types of crops, j = 1–12) in his fields (i, i = 1,...,I) with different soil types (m = 1, 2, clay

or sandy soils). Farm profit is modelled from revenue from growing crops for sale ( )

and from receiving subsides ( )5. Costs include those from using energy, machinery,

chemicals and other resources in crop production, given in DKK per hectare ( ), and costs of N

(

) and P (

) in mineral fertilizers, given as the price of mineral fertilizer in

DKK/kg multiplied by the amount of mineral fertilizer applied in kg/ha. Farmers also incur costs in

buying manure (or receive payment for selling manure) (

), given in DKK/kg manure

bought or sold multiplied by the amount of manure traded in kg. The price of manure in any period t

is determined endogenous by the model as the equilibrium price that balances demand and supply

of manure, and it changes every year (adjusting to increasing mineral fertilizer prices and taxes,

changing soil-P levels and crop patterns). In addition to the cost of manure, farmers have

application costs and transportation costs. The cost of transporting manure to or from the trading

station is dependent on the distance and the amount of manure traded, ( ) where p

F is

the cost of transporting manure, given in DKK/kg per meter transported, and r is the distance in

3 Baseline prices (and distribution of farm types and amount of livestock units, LU) are taken from 2003 because the

current model is going to be part of a larger model complex where other data are only available for that year. The

increase in mineral fertilizer prices between years is estimated as the real price increase between mineral fertilizers and

crops. The percentage increase is calculated as 3.21% for both N and P based on price developments for the most

common single-mineral fertilizers bought in Denmark (Plantedirektoratet, 2004) and price developments for agricultural

crop products (Statistic Denmark, 2013). All other prices in the model are held constant over time. 4 See Appendix section 7.1for the different crop types included.

5 The hectare payment from the EU Common Agricultural Policy, given in DKK/ha.

8

meters. To reduce model complexity, transport costs are modelled on transportation to and from a

trading station (e.g. a biogas plant). This way of estimating transport costs is similar to the function

applied in Schnitkey and Miranda (1993) where the transport function is built upon both the

distance from the livestock farm to some fixed point, and the manure application rate at that point.

In the present model, application costs are lowest for the application of mineral fertilizers,

, and highest for the application of manure, , where and is

given in DKK/kg of fertilizer applied6. Approximately 75% of N in pig manure is utilized by crops

and only 70% in cattle manure. This is taken into account in the costs of transporting manure.

The relation between yield y for any specific crop j and the application of N follow the general

response function7 described in equation (2), where gives the crop yield in 100 kg per hectare

when no N is applied and

gives crop yield when N is applied in the given amount from

mineral fertilizer and manure. Application of N is also restricted in line with Danish legislation as

given in equation (3). Here N must only be applied at a maximum level (

) given for each

crop type in kg per hectare depending on the soil type (Plantedirektoratet, 2002). The restriction in

N use is given as a total restriction for N application across all fields at a given farm.

Equation (4) is a restriction on minimum P application at a given field. The P application is

modelled as a minimum restriction because farmers add P to the soil to maintain the total amount of

crop-available P in the soil at a level that can sustain viable crop production8. Farmers are then

obliged to apply P from mineral fertilizer or manure at an amount of , estimated in (5).

is estimated from guidelines given by the Danish Knowledge Center of Agriculture given

in table 1. These guidelines are based upon the soil P level (measured at the start of the year, Pt-1)

and average measured values for P removal by crops at harvest ( ) measured in kg/ha and

6 See Section 5 for a discussion of other differences between the application of manure and mineral fertilizers that are

not considered in this model. See Feinerman and Komen (2005) for a modelling approach of arable farmers’ incentives

to substitute mineral fertilizer with animal manure. 7 The response function is estimated from data from Danish field trials (Pedersen, 2003).

8 Soil P plays a dominant role in crop P nutrition. This is exemplified by the fact that more than 80% of the P taken up

by crops originates from soil-bound P, while less than 20% originates from the manure or mineral fertilizer applied

immediately before the growing season. Farmers therefore add P to the soil to maintain the total amount of P in the soil

at a level that can sustain viable crop production (see Hansen et al. (2010) for a brief explanation or Rubæk et al.

(2005)). Phosphorus response functions are available in the literature to use equivalent to the N response function.

However, such data was not available from Danish field trials and for all different crop types included in the current

model.

9

multiplied by a factor ( ) adjusting the application level to the content of P in the soil (

) (see table 1). In keeping with Danish and European law, there is no upper

limit for application of P9, i.e. farmers are allowed to apply P in excess of crop requirements.

Table 1: Minimum P application levels based on guidelines from the Danish Knowledge Centre for

Agriculture (Rubæk et al., 2005).

Phosphorus level in the soil ( ) Phosphorus application levels,

Less than 2 1.4 ~ 40% more P than removed by plants

2 to less then 3 1.2 ~ 20% more P than removed by plants

3 to less than 5 1.0 ~ P corresponding to average plant uptake

5 to less than 6 0.5 ~ 50% of plant uptake

6 to less than 7 0.25 ~ 25% of plant uptake

7 and above 0.0 ~ In the short run, no application of P

Development in soil P over time is described by equation (6) based on Ekholm et al. (2005)10

. The

soil P level in year t ( ) is dependent on the soil P level in year 0 ( )11

, P surplus applied

(measured as the difference between applications in year t and the estimated based on

soil P in year t-1), and the number of years from year 0 (Y). The factor corresponds to the

specific P application levels given in table 1 multiplied by a calibrating factor that adjusts the model

in Ekholm et al. (2005) to Danish guidelines for P application such that equilibrium is obtained at a

soil P level of 4 mg/L12

.

9 Due to Danish and European law, P application is restricted in specially defined vulnerable areas (European

Commission, 2012). This is not taken onto account in our modelling framework. 10

Data used in Ekholm et al. (2005) is primarily based on field trials from Saarela et al. (1995). The experiment was

carried out over 10–15 years thus limiting equation (6) to a range of 10–15 years. In the current model P0j therefore

changes every 12 years (years 2015 and 2027). The estimated relationship in Ekholm et al. is based upon six principle

soil types in Finland. The equation would change if it were based on Danish soil types and Danish weather conditions.

In addition, the soil test value in Ekholm et al. is extracted from acidic ammonium acetate buffer where the soil P values

used for P0j in the current model are extracted using the Olsen-P method (see Pierzynski et al., 2009 for a description of

the different soil P tests). 11

Denmark does not produce databases of measured soil P levels at the field level. However, the distribution of soil P

values for different regions of Denmark is published annually by the Danish Knowledge Centre for Agriculture. The

distribution for the island Funen, where the Odense Fjord catchment is placed, is used in this model as the P0j value in

equation (6), and distributed to all fields in the case study area by Monte Carlo simulation. The simulation is not

restricted to other variables. 12

Due to the Danish guidelines for optimal P fertilization, a soil P level between 3 and 5 mg/L is optimal. In the current

model a soil P level of 4 mg/L is chosen as the absolute optimal level where soil P is in equilibrium. However, another

level could have been chosen, which would increase or decrease the number of farmers who apply P in excess of crop

requirements in the no trade scenario. Also, see Appendix section 7.2 for a detailed description of the soil P equation.

10

Each farmer’s crop choice for each field in a given year is restricted as in equation (7) to avoid

unrealistic corner solutions. The total area of each crop the farmer is allowed to grow (∑ ) is

equal to the observed maximum percentage grown in different farm types in the area in 2003

( ) multiplied by the total farm area. A few crop types are slightly more

restricted.

Equation (8) ensures positive levels of yield, fertilizer applications and soil P values and that the

size of each field is constant over time.

The mathematical problem is rather large due to the number of fields, farmers and crop decision. It

was programmed in general algebraic modelling language (GAMS) and solved with the solver

Conopt (Drud 1985). We note some important aspects of this model, which implies some

limitations: First of all, the profit function is a one-period model, where farmers myopically

maximize profit in time t based on yearly prices and the soil P level at the start of the season. The P

level changes from one period to the next but farmer behaviour is assumed to be myopic, only

taking the soil P level given in the current year into account. Ideally, a dynamic optimization model

factoring in future soil-P levels, tax effects and P-prices would be favorable, but practically

infeasible in connection with the detailed real spatial aspects, which we focus on here. Based on the

literature investigating related regulation issues, we conjecture, however, that if the planning period

the farmer optimizes over is the entire planning horizon over 30 years, the taxes imposed could be

lower to bring about the same effect, at least in the initial period (Goetz and Keusch 2005).

2.1 Modelling regulation scenarios

The idea of a P surplus tax is to establish a deposit–refund system for P pollution, much like the

deposit–refund systems that have been established for returnable bottles (c.f. Hansen and Hansen,

2012). The P surplus tax is calculated as the payment for the P content in inputs minus the

corresponding payment for the P content in outputs. Farmers then have an incentive to avoid P

losses in the production. Because the P-surplus is dependent on soil-P, this tax indirectly also relate

to the management of the P-stock in the soil. The tax on mineral-fertilizer P is a more simple input

tax. The surplus tax and the input tax will lead to different incentives and allocation of tax burden

costs between livestock and arable farms. The mineral-fertilizer-P tax will be a cost for arable

farmers, who have no available substitutes, whereas the livestock farmers will suddenly get a price

11

for their manure. On the other hand, the P surplus tax will lead to higher costs for livestock farmers

since all P sources in the livestock production process, including soil P, will be taxed. In both tax

systems there is an incentive for livestock farmers to sell manure P to arable farmers. However, for

these two instruments, heterogeneity of the soil P content between farms will influence the

distribution of costs between farms as well as the incentives to utilize P in the soil and in manure.

In the model, the tax rate for both scenarios is set at 50% of the price of mineral-fertilizer P. A

sensitivity analysis is carried out with tax levels set at 10% and 150% of the mineral-fertilizer price.

The nominal tax increases over time as the fertilizer price increases.

3 Case study area and data

3.1 Farm and catchment area data

The case study area covers 15,273 hectares of field land corresponding to 21% of the agricultural

land13

in the Odense Fjord catchment in Denmark, see figure 1. The data comprises of 3,993 fields

cultivated by 258 farmers.

Figure 1: Case study area

13

See Appendix section 7.3 for a description of the selection process of the fields included in the case study.

12

Information on livestock and crop production for all farms in Denmark is obtained from two Danish

agricultural databases: the Central Livestock Register and the General Agricultural Register. Input

costs such as those for agro-chemicals, contractors, energy, and labour are derived from Statistic

Denmark (Statistic Denmark, 2004).

Arable, pig and cattle farms comprise 81% of the farms in the Odense Fjord catchment (and 72%

percent in Denmark overall). The three farm types14

are all included in the case study and a brief

description of them is given in table 2.

Table 2: Farm statistics

Number of

farms Area (hectares)

Manure P

produced (tons)

Manure N

produced (tons)

Cattle farms 79 (31%) 4,180 (27%) 84 344

Arable farms 113 (44%) 5,505 (36%) 0 0

Pig farms 66 (26%) 5,588 (37%) 153 435

Total 258 15,273 237 779

Table 2 shows that pig farmers cultivate 37% of the study area, more than 5,500 hectares and on

average produce 27 kg P from manure per hectare. This corresponds to 5 kg of P in excess of that

which is, on average, removed by crops on their lands. Cattle farmers on average produce 20 kg P

from manure per hectare, which on average corresponds to crops requirements. Arable farmers do

not produce manure P, but import from outside to compensate for removals. This means, that there

is a very good possibility to reallocate excess manure P between farm types and fields.

3.2 Modelled application rates of mineral fertilizers and manure

The quantity of manure traded in the marketplace, and the quantity of mineral fertilizer and manure

that farmers actually apply on a field-by-field basis, are not available in any database. Estimates

were therefore made of mineral fertilizer and manure inputs for all farm types to provide a value of

the P surplus produced in the case study area. Using the model described in the model section and

in the absence of manure trade, average application rates of N and P in mineral fertilizer and

14

Arable farms are defined as farms with fewer than two livestock units of any kind of animal. Pig and cattle farms are

defined as farms where pigs or cattle respectively constitute more than two thirds of the LU on the farm. Other

combinations of livestock production are removed from the data. Analysis of farm typologies to identify groups of

farms creating differential pressures on the environment has also been carried out by, e.g., Cuttler et al. (2007) and

Fezzi et al. (2008).

13

manure are estimated for all farm types. The results are given in Table 3. The P and N norms are

also estimated based on the predicted crop distribution in the case study area and soil type

variability.

Table 3: Predicted average quantities and norms of fertilizers applied to farms within the case study

area for 2003.

Manure P

(kg/ha)

Manure N

(kg/ha)

Mineral-

fertilizer P

(kg/ha)

Mineral-

fertilizer N

(kg/ha)

P norm

(kg/ha)

N norm

(kg/ha)

Cattle farms 20 (1-35) 82 (5-121) 4 (0-22) 51 (0-141) 21 (12-26) 136 (92-147)

Arable farms 0 (0-2) 0 (0-6) 23 (10-28) 119 (91-143) 23 (10-28) 120 (93-143)

Pig farms 27 (1-47) 78 (2-119) 4 (0-22) 45 (0-122) 22 (15-27) 123 (103-141)

Average values are not weighted values. The distribution shown assumes no manure is traded in the marketplace and

fertilizer is evenly distributed on fields. Values in brackets are minimum and maximum values.

Because arable farmers do not produce any manure, only mineral fertilizers are applied to their

fields at an average rate of 23 kg P/ha and 119 kg N/ha. Some of this applied mineral fertilizer

could be substituted with animal manure reallocated from (especially) pig farms, where manure P is

applied in excess of crop requirements at an average of 5 kg/ha (sometimes up to 20 kg P/ha).

However, farmers already do trade manure to some extend and some of the surplus manure P may

already be reallocated to arable farm fields. How the full potential of trade may affect the

distribution of fertilizers between fields is modelled in section 4 below.

4 Results

We simulated developments in N and P applications from manure and mineral fertilizer and

developments in the levels of P surplus applications and developments in soil P levels solving the

problem (1)-(8) over 30 years from 2003–2033 for all farms in the case study area. Three trade-

including scenarios are modelled: i) a baseline scenario where farmers trade manure and no

regulation is implemented besides the restrictions on N and P as described in equations (3) – (5); ii)

implementation of a P surplus tax; and iii) implementation of a tax on mineral-fertilizer P.

Comparing results from these three scenarios with a restricted scenario iv) without a market for

trading manure enables the value of voluntary and incentive-enhanced trade of manure to be shown.

Figure 2 shows the development in average soil P values over time for the baseline scenario

compared to when farmers apply all their manure onto their own fields (no trade). Two sensitivity

14

analyses based on the baseline scenario are also shown where the price increase in mineral

fertilizers is changed15

.

Figure 2: Developments in average soil P values across all fields and over time for the baseline

scenario, a no-trade scenario and two sensitivity analyses.

As can be seen from Figure 2, average soil P values increase over time from an average P0,i value

slightly above 3. In the model, farmers are obliged to apply a minimum amount of P to their fields

(cf. equation (4) and Table 1), depending on soil P and removals. All soil P values then develop

until the equilibrium level of 4 mg/L is obtained, where the amount of P removed by harvest equals

the minimum allowable application level. This is the case for arable farms where the annual P

application rate is chosen mainly to control P reserves in the soil (c.f. Hansen et al. (2010) and Iho

and Laukkanen (2012)). When livestock farmers apply all the manure they produce to their own

fields (“no trade” legend in Figure 2), P is applied in excess of crop requirements (see table 3) and

the total P stock therefore increase over time in the case study area. The average soil P values still

increase over time when manure is traded (“Baseline” in Figure 2), but the value of trade becomes

apparent when comparing the baseline scenario with the no-trade scenario.

15

The price of mineral fertilizers increases by 3.2% for both mineral-fertilizer N and P. In the two sensitivity analyses

the price increase is reduced to 0.32% (10% of the price increase used) and increased to 4.8% (150% of the price

increase used).

3

3.2

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Ave

rage

so

il P

val

ue

s, m

g/L

No trade

Baseline

Sensitivity analysis, low increase

Sensitivity analysis, high increase

15

Increasing prices of mineral fertilizers over time increase the shadow price of the P content in

manure and the incentive to switch between manure P and mineral-fertilizer P. However, the

substitution between mineral fertilizers and manure is slow, because livestock farmers do not have

N in excess of crops requirements16

, and therefore most of the manure-N sold must be substituted

with mineral-fertilizer N. The equilibrium price for selling manure is therefore close to the mineral-

fertilizer N price minus transport costs and saved application costs. In compliance hereof, analysis

of the baseline scenario shows that only 1.2% of all P applied in the case study area in 2003 is from

manure traded in the marketplace, increasing to 9.1% in 2033. However, if the price increase was

only 0.32% annually (“Low increase” in Figure 2), average soil P values would increase over time

to above the equilibrium level of 4 mg/L. On the other hand, if the price increase was 4.8% (“High

increase” in Figure 2), enforcing farmers incentives to utilize P more efficiently, the increase in

average soil P values would significantly slow down.

Now, the interesting point is to see how the average soil P values develop in fields with a high P0i

value (i.e. soil P values above 4 mg/L in the initial period). These fields are the most vulnerable in

terms of P losses and therefore those where it is most efficient to reduce the soil P content. Figures

3A–C show the development of average soil P values over time for fields with high P0i values. The

development in soil P is shown for three scenarios: i) where there is no regulation but trade is

possible (baseline); ii) with the mineral-fertilizer P tax; and iii) with the P surplus tax where, for

both tax scenarios, the tax rate is 50% of the mineral-fertilizer P price.

Figure 3: Development in average soil P values over time for fields with P0j > 4 mg/L, split by farm

type. A) Baseline; B) Mineral-fertilizer P tax; C) P surplus tax.

16

In compliance with Danish and European law, cattle farmers are restricted to producing a maximum of 1.7 LU/ha and

pig farmers to 1.4 LU/ha.

16

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For arable farms, soil P values decrease rapidly towards the equilibrium value of 4 mg/L17

. In our

model, arable farmers do not apply P in excess of crops requirements as this is costly, thus they

utilize soil P very efficiently18

. Therefore, independently of the instrument implemented, or lack

thereof, soil P on arable farms decreases at the same rate, as can be seen in figures 3A–C. When no

instrument is implemented (baseline), the soil P level on pig farms increases since the shadow price

of P in manure is not high enough to motivate pig farmers to trade their entire P surplus. So even

though pig farmers do trade manure and thus reduce the quantity of P surplus they apply to the soil,

the overall P surplus stays at a high level (Figure 4A). This is because P surplus is defined as the

difference between applied P and the Pminimum

value, and the latter decreases with high soil P levels

(see table 1). Because of the higher N/P ratio in cattle manure, cattle farmers apply less P in surplus

17

The curves in figure 3 and 4 are bumped. This is because of the non-continuity between years as the Pminimm

(equation

5 in the methodology section) defining minimum application limits and the P surplus is modelled at intervals thus

making the equations jump between years, see table 1. 18

The reason they have soils with higher P-values than 4 is due in part to natural high content in some clay soils as well

as earlier farm livestock systems on the same land.

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17

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Pigs - Baseline

of crop requirements than pig farmers do. The average soil P level therefore remains stabile as the

decreased P application level through trade is just outbalanced by the decrease in the Pminimum

value.

Implementing a tax motivates both pig and cattle farmers to trade more manure. Under the mineral-

fertilizer P tax scenario the percentage of P from traded manure compared to the total P applied

increases from 2% in 2003 to 20.4% in 2033. Under the P surplus tax scenario the percentage

increases from 4.6% in 2003 to 16.8% in 203319

. Figures 3B and, especially, 3C make it apparent

that with enhanced incentives, manure is reallocated more evenly between farms as soil P at both

pig and cattle farms decreases towards equilibrium, following the pattern for arable farms. Figures

4A–C show the development in the average P surplus applied on pig and cattle farms. Arable farms

are omitted as their P surplus application is zero.

Figure 4: Development in average P surpluses over time for pig and cattle farms. A) Mineral-

fertilizer-P tax compared to the baseline; B) P surplus tax compared to the baseline.

When no economic instrument is implemented (baseline) the P surplus stays high, exceeding crop

requirements by 40 kg/ha for pig farms in 2033, and by 9 kg/ha for cattle farms (see Figures 4A and

B). Application of either economic instrument motivates farmers to increase trading manure and so

significantly reduce the P surplus. However, the tax on P surplus reduces the P surplus on pig farms

faster than the tax on mineral-fertilizer P: a surplus of zero was attained by 2027 for the former

compared to 2034 for the latter. For cattle farms both instruments create the same outcome: the P

surplus reaches zero in 2032. However, soil P values in figures 3A–C show that neither of the farm

types, independent of the instrument implemented, reaches the average equilibrium soil P value of 4

19

See Appendix section 7.4 for an illustration of how the manure market develops over time.

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18

mg/L on their high soil-P soils. This is because soil P is only utilized slowly over time even if no

additional P is applied (see eq. (6) in the methodology section).

This shows how important it is to study the effects of P regulation over time. If effects in the

environment are to be obtained within a short period, reducing the level of P surplus application

alone might not be sufficient. However, the analysis shows that if no regulation is implemented by

2033 2,858 ha (~ 19%) of the cultivated area has soil P values above 5. This is reduced to 1,786 ha

(~ 12 %) with the mineral-fertilizer P tax and to 1,224 ha (~ 8%) with the P surplus tax. Thus, the

vulnerable areas at risk of P leaching are more than halved under the P surplus tax scenario

compared to the scenario with no enhanced incentives to manage P.

Table 4: Predicted application rates of N and P across farms and for the three scenarios in 2033.

Farm/scenario Mineral-fertilizer P Mineral-fertilizer N Manure P Manure N Total P

(Kg/ha) (Kg/ha) (Kg/ha) (Kg/ha) (Kg/ha)

Cattle – baseline 5 19 18 75 23

Cattle – fertilizer 5 23 17 68 21

Cattle – surplus 5 23 17 70 22

Arable – baseline 20 68 5 16 25

Arable – fertilizer 15 54 10 32 24

Arable – surplus 16 56 8 28 25

Pigs – baseline 3 22 24 68 27

Pigs – fertilizer 2 29 20 57 22

Pigs – surplus 2 27 21 61 24

*Average values are not weighted values.

Table 4 shows the difference in manure application between farms and across the three intervention

scenarios. For cattle farms, application of manure P decreases from 18 kg/ha to 17 kg/ha when

either of the tax scenarios is introduced. For pig farms, application of manure P is reduced from 24

kg/ha to 20 kg/ha under the mineral-fertilizer P tax scenario and to 21 kg/ha under the P surplus tax

scenario. However, we saw from figures 4A and 4B that the P surplus on pig farms was reduced

faster under the P surplus tax than under the mineral-fertilizer P tax. Table 4 also shows that the

application of mineral-fertilizer P is reduced on pig farms by 1 kg/ha under either of the two tax

scenarios, while on arable farms it is reduced by 5 and 4 kg/ha under the mineral-fertilizer P and P

surplus taxes respectively. So implementing either a tax on mineral-fertilizer P or a tax on all P

inputs in the agricultural sector, including soil P creates incentives amongst farmers to reallocate

manure between farm types and thereby reduce the application of mineral-fertilizer P. The total

19

application of P is slightly higher with the P surplus tax, but the distribution of soil P becomes

sustainable faster.

In total for the case study area, the application of mineral-fertilizer P in 2003 was 167 tons. Table 5

shows that the total mineral-fertilizer P applied in the case study area is reduced by 23 tons when

comparing the no-trade scenario of 2003 with the baseline scenario of 2033. With the mineral-

fertilizer P tax the reduction is 58 tons in total (i.e. 35% reduction) and with the P surplus tax the

reduction is 46 tons (i.e. 28% reduction). These are significant reductions.

Table 5: Total predicted N and P application rates for the case study area for 2033 and the predicted

no-trade scenario rates for 2003.

Mineral-fertilizer

P (ton)

Total P

(ton)

P surplus

(ton)

Mineral- fertilizer

N (ton)

Total N

(ton)

No trade (2003) 167 405 66 1121 1.900

Baseline (2033) 144 380 61 580 1.359

Fertilizer tax (2033) 109 342 4 559 1.340

P surplus tax (2033) 121 358 0 557 1.346

Decreasing the P surplus to zero in both tax scenarios and for all three farm types, as shown in

figures 4A and 4B, not only occurred through reductions in total P applications but also occurred

through reallocation of manure to fields with low soil P levels. From Table 5 it is seen that total P

application is reduced by 63 tons with the mineral-fertilizer P tax and by 47 ton with the P surplus

tax. Some of the reduction in P surplus occurred through changed crop rotation patterns. The

mineral-fertilizer P tax in particular influence arable farmers and compared to the baseline scenario,

we find that winter rape and spring barley were substituted with winter barley, winter wheat and rye

because these are much less P-demanding than the two former crops. Implementing the P surplus

tax does not change the crop rotation pattern significantly at arable farms. Pig farmers do also

substitute high P-demanding crops with low P-demanding crops under the mineral-fertilizer tax, but

implementing the P surplus tax motivates pig farmers to increase the cultivation of high P-

demanding crops. This is because cultivation of high P-demanding crops as beets and whole crops

allows the farmers to apply more P on their fields and thereby reducing their P surplus, i.e. reduce

the tax payment. Cattle farmers are motivated a bit differently than the other two farm types, as they

are obliged to produce a percentage of their need for feed crops. Implementing the P surplus tax

motivates cattle farmers to substitute especially their production of pasture with corn and whole

20

crop production, because the last mentioned require more P than pasture does. The mineral-fertilizer

P tax does not change the crop pattern significantly at cattle farms. Over time the fields with low

soil P levels will reach the equilibrium value of 4 mg/L and the possibility for dumping P surpluses

on fields with low soil P levels will be exhausted, forcing farmers to trade more manure.

As a sensitivity analysis, the tax level in both the mineral-fertilizer P tax scenario and the P surplus

tax scenario is changed to 10% and 150% of the mineral-fertilizer P price. Implementing the 150%

mineral-fertilizer P tax reduces the P surplus to zero by 2015 for both cattle and pig farms, while

implementing the 150% P surplus tax reduces the P surplus for pig farms to zero by 2004 and for

cattle farms by 2013. The amount of manure sold increases rapidly because of rapidly increasing tax

levels, but because manure can be reallocated between fields with different soil P values, this is

more cost-effective than selling more manure in the marketplace. With a tax of 10% (for either type

of tax) farmers are not motivated significantly more than if no instruments were implemented20

.

For all scenarios, arable farmers purchase manure N which therefore reduces the application of

mineral-fertilizer N. But application of mineral-fertilizer N increases on livestock farms. This is

because pig and cattle farmers substitute all traded manure N with mineral-fertilizer N (as

legislation states that they cannot produce manure N in excess of crop requirements). However, in

total, the application of mineral-fertilizer N is reduced by 562 tons under the mineral-fertilizer P tax

and by 564 tons under the P surplus tax (see Table 5), corresponding to around 25 % of total N

application. This is significant amounts which is a positive externality derived from the P regulation

incentives.

Under the MINAS system in the Netherlands, any P surplus at the farm level exceeding a levy-free

rate of 8.7 kg/ha and year was taxed at €20.60/kg (Oenema, 2004), corresponding to DKK149/kg.

In the current model, the tax rate in both scenarios increases from only DKK16 per kg in 2003 to

DKK42 per kg. This is much less than under the MINAS system but, in the current model, the

whole P surplus is taxed. Weersink et al. (2004) also evaluate a tax on P surplus. They find that a

tax up to $1.62 per kg (DKK10 per kg) reduces the P surplus to zero as producers obtain more land

on which to apply manure. If no land is available a tax of $34 per kg (DKK207 per kg) drives P

surpluses down to zero and reduces the herd size by 34% and farm returns by approximately 30%.

20

See Appendix section 7.6 for an illustration of how average soil P values and P surpluses develop over time under a

10% and 150% tax scenario.

21

However, the study does not take into account that manure can be allocated to other farm types

thereby decreasing the need for more land and/or a reduction in herd size. Furthermore, soil P is not

considered, which excludes the possibility of depositing manure on fields with low soil P levels.

However, both studies agree that farm returns are heavily reduced. In the current study farm profit

is also reduced but the extent and the distribution of the reduction depends on the instrument used.

Figure 5 shows developments in farm profits over time for the two tax scenarios.

Figure 5: Developments in average profit over time across farms and for the two scenarios. Average

values are not weighted values.

In our baseline model, mineral P is assumed to increase in real prices over time, due to the global P

resource restrictions and global demand drivers. This is a main factor driving the development of

farm profits over time, as increased P-costs drive down profits in particular for arable farmers that

depend entirely on P-import. Implementing a tax on mineral-fertilizer P drives the manure price

further upwards21

as arable farmers have no substitute for mineral fertilizer and therefore demand

more manure the higher the alternative price. The manure price under the P surplus tax scenario is,

on the other hand, lower, as all P resources (including soil P) in livestock production are taxed and

21

See Appendix section 7.5 for an illustration of how the manure price develops over time.

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22

therefore livestock farmers are willing to trade manure at lower prices. The price of substituting

mineral fertilizer with manure therefore changes farm profit over time and between the three

scenarios. Pig farms are, in this model, the farm type with the largest profits (figure 5). This is

because pig farmers have the largest production of manure P and therefore have a substitute for

mineral fertilizer as its price increases, which they can sell in the marketplace. Cattle farmers also

produce manure P but, due to the lower P content in manure, they have a lower surplus to substitute

for mineral-fertilizer P and less to sell in the marketplace. Furthermore, cattle farmers are restricted

to growing 11% of their feed for which they receive no income. Arable farmers’ profits decline

proportional to the increase in mineral-fertilizer P prices. However, comparing the two tax

scenarios, arable farmers’ profits decline most under the mineral-fertilizer P tax scenario and pig

farmers’ profits decline most under the P surplus tax scenario. However, livestock farmers profit is

not reduced in significantly amounts and the overall tax might therefore not reduce the livestock

unit as argued in section 2.

5 Concluding Discussion

This paper analysed and assessed the effectiveness of two economic instruments to reduce P surplus

applications, improve P-resource management and avert environmentally hazardous P build-up in

agricultural soils. Detailed data were generated to mimic farmers’ responses to regulation in the

area of the Odense Fjord catchment in Denmark. A tax on P applied in excess of crop requirements,

and a tax on mineral-fertilizer P were compared with a baseline scenario with no intervening

regulation. Farms with livestock typically produce P in excess of crop needs. Those farmers fertilize

their crops with reference to N levels in manure and do not take into account that P is concomitantly

applied in excess of crop needs.

Analysing the effects of the two different instruments over time showed that manure P can be

reallocated better between farm types to reduce pressure on the environment. A non-linear

programming farm model was used to model and estimate farm profit from growing crops subject

to restrictions on P and N application levels, soil P levels, P surplus, feed-crop production and crop

rotation pattern. P accumulated in the soil, measured as soil P values for each field in a farm, was

used as a measure of the effect of the interventions on the environment over time.

23

Results showed that if no incentive enhancing policy interventions are implemented, average soil P

values in soils with a high P content will continue to increase over time on livestock farms..

However, as the price of mineral fertilizer increases over time, the shadow price of manure P

increases and manure is naturally reallocated between farm types. Nevertheless, this market price

pressure was not enough to reallocate significant parts of the P surpluses between fields and farm

types. As all P surplus application is costly, on arable farms P is applied according to crop

requirements whilst taking soil P into account. The soil P content is therefore reduced over time to

an equilibrium level of 4 mg/L.

Implementing a tax on all P inputs including soil P through the P surplus tax motivates livestock

farmers to sell manure to avoid paying taxes. On pig and cattle farms P surpluses are reduced to

zero by 2027 and 2032 respectively. Because of the lower content of P in cattle manure, it is more

expensive for cattle farmers to sell manure as more N per kg of manure P needs to be substituted

with expensive mineral-fertilizer N. The P surplus tax constitutes a more effective incentive to

induce livestock farmers to improve the utilisation of manure P than the mineral-fertilizer P tax.

Implementing a tax on mineral-fertilizer P motivates arable farmers to substitute mineral fertilizers

with manure and in this way slowly reduces the P surplus on both cattle and pig farms. The mineral-

fertilizer P tax increases the shadow price of manure reducing profit on arable farms, i.e. arable

farmers pay a high price for utilizing mineral-fertilizer P. This is contrary to the P surplus tax where

the shadow price of manure P decreases because livestock farmers are forced to get rid of expensive

P surpluses. Both taxes can therefore be seen to regulate two problems: that of environmental P

pollution, and that of exploiting mineral-fertilizer P, a non-renewable resource.

However, even though P surpluses are reduced under both of the tax scenarios, the average soil P

values for high P-content soils do not, in the case study area, reach the equilibrium level of 4 mg/L

within 30 years. Whether this will be the case in other areas depends upon the distribution of farm

types and on the acreage of high P-content soils. The present study shows, however, that exploiting

P in the soil efficiently only slowly reduces the problem of high P-content soils. A positive

externality derived from both tax scenarios, is that a considerable decrease in the use of mineral-

fertilizer N is obtained. At livestock farms the application of mineral-fertilizer N increases because

most sold manure-N is substituted with mineral-fertilizer N. However, arable farmers purchase

manure N which therefore reduces the application of mineral-fertilizer N.

24

The system of taxing either P surpluses or mineral-fertilizer P can be a useful tool in areas where

livestock density is not too high, or in other words, where arable farmers demand for P can induce

improved P-management through trade.. Reallocation can be costly for farmers because of high

transport costs, e.g. in Holland, the MINAS system became expensive for livestock farmers to

comply with because of high livestock densities (Oenema and Berentsen, 2005). However, this does

not disqualify manure reallocation as a very efficient tool for overcoming the P surplus problem, but

rather puts focus on the possibilities for the establishment of cooperatives as being a cost-efficient

means of trading manure. This would lower the shadow price of manure and make it more attractive

to farmers to trade, even without regulation. Nevertheless, implementing a tax on P surplus or a tax

on mineral-fertilizer P should not be seen as a first best tool for overcoming the P pollution

problem, but as an efficient core element in an optimal regulatory policy.

Caveats and possible extensions

Research shows that critical source areas contribute to more than 80% of the P lost to a watershed

(Carpenter et al., 1998; Sharpley et al., 2009), meaning that some regions need more attention than

general taxes as those analyzed here can offer. Spatial variables such as slope towards and distance

from the water body, soil characteristics and the condition of the surface water can be important

variables in choosing the most efficient measure to reduce P losses. The model of this paper did not

contain any spatial variables at field level and a damage function was not defined.

The current model did not take into account that arable farmers for other reasons can be rather

reluctant to use manure as a substitute for mineral fertilizers. Feinerman and Komen (2005) develop

a model to gain insight into the decision-making process of an average Dutch arable farmer when

choosing between mineral fertilizer and manure. Several factors prevent farmers from substituting

mineral fertilizers with manure including the lack of homogeneity of the manure, technical

limitations on applying manure uniformly and without damaging the top soil, and the unidentified

mineral content of manure. Taking this into account would lower the price of manure (or even force

livestock farmers to pay other farmers to take their manure) and therefore slow down the process of

reallocation. Both taxes analysed in this article should then be higher to reach the same level of

reallocation. The acceptability of manure by arable farmers is therefore a crucial point in

developing future policy to avoid decreases in livestock production and to promote reallocate of

manure between farmers.

25

In our model, we have also assumed full compliance and hence costless monitoring of P-surpluses.

The monitoring costs of ensuring that farmers do not apply P in excess of crop requirements at the

field level are of course a major further obstacle. However, regulation as designed here is based

upon measurable soil P values per field, and the authority’s ability to measure them. This could, for

example, be carried out every five years after taxes are calculated from reported crop rotations and

P application levels at the farm level – information available from existing accounts of nutrients

imports for fodder and fertilizer. Farmers would therefore not be motivated to commit fraud as even

higher taxes would be imposed five years later. Thus, the existing regulation and information

collection offer quite some opportunities for handling issues of asymmetric information and moral

hazard.

Further caveats include also the myopic optimization assumptions made. We cannot rule out that a

full information inter-temporal optimization would have provided slightly different results (e.g.

livestock farmers would perhaps have been willing to sell slightly more manure earlier – at a lower

price – to reduce their future soil-P and P-surpluses and hence future higher taxes driven up by P

price increases), but we find it most likely that the overall findings are fairly robust to these

modifications. Finally, our model did not allow for changes in livestock levels and hence P-manure

production in our case area. However, the analysis showed that the total tax did not change

livestock farmers profit significantly and might not in the case study area impact on costs in a

degree that motivates livestock farmers to reduce their livestock units.

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7 Appendix: Data calibration and modelling

7.1 Crop types

In the Odense Fjord catchment 81 different crops were grown in 2003. Most of these crops (36

different crops) constitute a very little share of the total area (15 %, of which the 12 % is contract

crops as potatoes and sugar beets, 1 % is crop out of rotation as Christmas tree production and

fallow, 1% is different vegetables and 1 % is other crops not defined). Because of insufficient data,

these crop types are left out from data. The remaining 45 crops are aggregated into 12 groups given

below in table 6. Due to missing data it has not been possible to distinguish between winter wheat

and buckwheat, between grains for feed and for sale or to distinguish between different types of

grass, peas or between different whole crops. The aggregation is done with guidelines from

experts22

.

Table 6: Aggregated crop types

Crop type Crops in the category

Spring barley Spring barley, spring wheat and oat

Winter barley Winter barley

Winter wheat Winter wheat, buckwheat and other winter grains

Rye Rye and triticale

22

Correspondence with senior researcher Jens Petersen, Institute for Bioscience, University of Aarhus, Email:

jepe@dmu.dk.

32

Corn Corn for animal feed

Winter whole crop Whole crops of winter barley, winter wheat, rye and triticale

Spring whole crop Whole crops of spring barley, spring wheat, oat, other spring grains, other spring sown grains,

other spring whole crops, whole crops of peas and alfalfa

Spring rapes Spring rapes

Winter rapes Winter rapes

Peas Peas for animal feed, horse bean, lupine, other leguminous plants and organic grown

leguminous plants

Beets for feed Beets for animal feed, and marrow-stem kale

Pasture 14 different kind of grass, e.g. harvest grass first, second, third and fifth year, and pasture first,

second, third, fourth and fifth year,

From the 12 crop types, barley, wheat, rye and rapes are solely sale crops. Corn, whole crops, peas

and beets are feed crops in the cattle production sector, while they are sale crops in the pig and

arable production sector. Pasture is solely for feed and is not a sale crop in any of the three sectors.

7.2 Soil P equation

Phosphorus surplus is estimated from the standard given in table 1 (in the methodology section)

which is based upon table values of crop removal. As estimates for P removals is used guidelines

given from Danish law on P-uptake. These guidelines are given in kg/ha for all crop types on fine

sand soils not irrigated with a “normal content of P” (i.e. soil P = 4 mg/L, measured by the Olsen-P

method) and where N is applied due to the given N-norm. The values for P-uptake are used for both

sand and clay soils in the model and for all application levels of N. This is of cause an

approximation of P uptake as P removal changes due to N application and yield.

As estimate for the baseline soil P value (P0j) in equation (6) is used values given from the Danish

Knowledge Centre for Agriculture who publish soil P value distributions for different parts of

Denmark on a yearly basis. This distribution is further distributed to the fields in the data by use of

Monte Carlo simulation. In table 7 is given the percentage for the area Funen (where the case area is

placed) and the obtained distribution for the case study area.

Table 7: Distribution of measured P0j in the case study area

P0j Percentage of fields in Funen within

the given range

Number of fields in the case area

within the given range

0.0 - 0.9 0 0

33

1.0 - 1.9 13 493

2.0 - 2.9 29 1141

3.0 - 3.9 27 1061

4.0 - 4.9 17 680

5.0 - 5.9 8 316

6.0 - 6.9 3 135

7.0 - 7.9 2 81

8,0 -8,9 1 45

9,0 - 10 0 0

>10 1 41

Number of soil samples taken from August 1st. 2002 to July 31st. 2003 in Funen: 4.475

Source: Pedersen (2003).

From table 7 it can be seen, that most part of the fields is given soil P numbers which is quite low (<

3) or at the level where P only should be applied according to crop uptake (3 - 4). However, quite a

few fields (15 %) should not be applied any P at all or at least only a percentage of plant removal (5

to above 10).

The correlation between the soil P value and P surplus is given in equation 6 in the methodology

section and taken from Ekholm et al. (2005). However, the equation used in the current article is

adjusted so that an equilibrium soil P value is obtained at soil P equal to 4. In equation (9) is given

the original equation in Ekholm et al. (2005):

( ) (9)

Where PBal

is the P balance application being positive for surplus applications and negative for

applications less than crop uptake.

From the equation can be seen that the relationship between soil P in the first period (P0j) and soil P

in the next period (Ptj) is: (Ptj)/ (P0j) = 0.9816, meaning that for a P surplus of 0, soil P is declining

over time i.e. no equilibrium value for soil P exist. If fields with a soil P value of 4 only needs

applications corresponding to P removal to be in equilibrium (due to Danish guidelines), the

equation has to be adjusted. This changes the soil P in (9) to equation (10):

34

( )

(10)

Where correspond to 1.4, 1.2, 1, 0.5 and 0.25 respectively (taken from table 1 in the methodology

section). In this way, the relation between Ptj and P0j becomes: (Ptj)/ (P0j) =1 for = 1 (i.e. soil P =

4). Phosphorus surplus is then given as the difference between P applied minus the P minimum

norm plus .

7.3 Geographical selection of case study area

Data in the case study only covers 68 percent of the agricultural area in the Odense fjord catchment.

258 farms of the in total 1,425 farms in the catchment are analyzed. Reducing the number of farms

to less than 25% is because of computer capacity and possibilities in the program GAMS using

Conopt as solver.

Because trade is modelled as trade to and from a trade station, farms around an existing Danish

biogas plant (Fangel Biogas) are chosen. The average distance for farms delivering and buying

degassed manure to and from the biogas plant located in Fangel is 6.5 km. To obtain this average all

farms within 10.5 km of the biogas plant is included in data. Of these farms, are farmers cultivating

less than 10 hectares (in Denmark 10 hectares are the limit for full taxation) removed from data.

The reason for removing these small farms is that they are motivated differently in their production

choices compared to larger farms where profit maximization is the main motivation factor. Also,

cultivating less than 10 hectares makes it difficult for cattle farmers to comply with the model

restrictions on feed production. Of the remaining farms only farms defined as cattle farms, pig

farms and arable farms are taken into account. Other combinations of livestock are removed as e.g

farmers having poultry, sheeps, goats or mink as their main production. The removed farms are

farms very different from the three considered categories and might not be addressed by the policy

measures analysed in this article. A few more farms are excluded from data as they have no

registrated KMS coordinates, which is needed to calculated the distances from farm to trade station

and to map the farms and their fields. A few is removed as they are registrated as living in other

parts of Denmark (e.g. in Copenhagen). This gives 258 farms which is the final data for further

estimation and modelling.

35

7.4 Manure market development

In figure 6 is shown how the manure market develops over time as illustrated by the amount of

manure traded at the market in ton.

Figure 6: Manure market volume development: Sold manure in kg for the three scenarios

7.5 Manure price development

In figure 7 is shown how the manure price develop over time under the three scenarios.

Implementing the mineral-fertilizer P tax drive the manure price upwards, compared to the price

under the baseline scenario. While implementing the P surplus tax reduces the manure price. To

compare is shown the price development in mineral-fertilizer N, and it is seen that the manure price

follows this path.

Figure 7: Manure price development in DKK/kg N in manure for the three scenarios

0

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Figure 8A Cattle - Fertilizer tax (150 %)

Pigs - Fertilizer tax (150 %)

Cattle - Baseline

Pigs - Baseline

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Figure 8C

Cattle - Fertilizer tax (10%)

Pigs - Fertilizer tax (10 %)

Cattle - Baseline

Pigs - Baseline

7.6 Sensitivity analysis

In figure 8A-D we show the development in average soil P values for fields with P0j > 4. Only

developments at cattle and pig farms are shown. The 10% and 150% tax is compared to the baseline

scenario.

Figure 8: Development in average soil P values over time for fields with P0j > 4 mg/L for A) 150%

mineral-fertilizer P tax, B) 150% P surplus tax, C) 10% mineral-fertilizer P tax and D) 10% P

surplus tax.

4.7

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Figure 8B Cattle - Surplus tax (150 %)

Pigs - Surplus tax (150 %)

Cattle - Baseline

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38

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Cattle - Baseline

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Figure 9C

Cattle - Fertilizer tax (10%)

Pigs - Fertilizer tax (10 %)

Cattle - Baseline

Pigs - Baseline

In figure 9A-D is shown development in average P surplus values over time. Developments are

shown for both tax scenarios but only split on cattle and pig farms. The 10% and 150% tax is

compared to the baseline scenario.

Figure 9: Development in average P surplus values over time A) 150% mineral-fertilizer P tax, B)

150% P surplus tax, C) 10% mineral-fertilizer P tax and D) 10% P surplus tax.

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