Design of a Tax or Charge Scheme for Pesticides

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ANNEX C8: The Farm Resource Allocation Model

Outline

This annex describes the farm-level model developed at the University of Newcastle upon Tyne for pesticide policy evaluation, covering its principal components, the data used and the optimal farm plans generated under different pesticide policy scenarios. The model used for the DETR research was based on one developed for a related pesticide policy evaluation project in 1997, full details of which are given in Falconer (1997). All model structures contain five elements: a description of producers' economic behaviour (i.e., the decision rules, such as profit maximisation and possibly risk aversion); a description of the production functions available; definition of the resource endowments; specification of the market environment in which the producer operates; and specification of the policy environment (for example, levels of agricultural support and, in this instance, the pesticide taxation scenarios). GAMS software (General Algebraic Modelling System, Brooke et al. 1992) was used to solve the model. The results presented here contribute to knowledge in the field through giving an indication of the possible farm-level effects of sample policy scenarios based on banded and unbanded pesticide taxation for a case-study arable business in Eastern England.

Methodology

An empirical policy evaluation model, based on an existing model but tailored specifically to the requirements of the DETR project brief, is presented and applied here to assess alternative economic incentive instruments to address pesticide usage concerns. Policy evaluation methodology has been developing for some years now to examine and compare the consequences of alternative instruments by which to achieve pesticide reductions, and especially reductions of the most hazardous chemicals; see for example, Oskam et al. (1992) and Falconer (1997). This research represents, as far as we are aware, the first time that banded pesticide taxation has been evaluated. Uniform pesticide taxation has been assessed by several authors, particularly Oskam et al. (1992) and Bauer et al. (1995). Falconer (1997) assessed both uniform charges and levies, and levies differentiated according to environmental hazard scores allocated to each chemical. This work takes the previous research further, particularly through the evaluation of differentiated ad valorem taxation.

In this study, a farm-level optimisation model was used as a case-study to illustrate the potential effects of different economic-incentive-based policy options. The farm-level nature of this evaluation also complements the macro-level work completed by ECOTEC (using pesticide demand elasticities and data on the aggregate-level chemical usage for different crops). The choice of a farm-level model from the broad range of potentially-appropriate policy evaluation models (such as econometric approaches based on historical production) can be justified since it can handle details of crop selection and crop management in a way which more aggregated models cannot, so there is scope to explore the consequences of policy implementation in a more in-depth way. Pesticide contamination arises directly from individual decisions (whether or not to use chemicals, or to use particular chemicals, and the most appropriate levels of usage), hence policies need to impact upon these decisions if they are to be effective in reducing environmental problems. Thus work at the level of the individual farm is appropriate, and especially work involving the modelling of production decisions and the outcomes of these with regard to crop protection and pesticide usage. Interest lay in the potential direction, and magnitude, of farm-level crop production practice and cropland allocation changes resulting from policy implementation, and the consequent effects in terms of pesticide use, and in terms of some notion of environmental burden. The results provide some idea of the potential consequences of policy implementation and thus a starting point for policy analysis and decision-making.

Programming approaches permit the examination of what farmers might produce under different economic scenarios, and in particular, permit examination through disaggregation of production and production processes to facilitate the analysis of the relative merits of alternative technological options under different scenarios. The optimisation basis of mathematical programming is more efficient than production-practice budgeting comparisons; there is scope to include new production practices, in addition to existing ones; and the optimisation approach is also attractive in that it is based on rigorous economic theory. Central to the analysis is examination of the quantity and mix of commodities which farmers could produce, and how. There are several necessary elements to any production planning model, as follows. A set of production activities is specified, in terms of their input-output relationships, and linked to relative prices. This set is then searched-across to find the combination of activities that maximises the objective function subject to constraints on resource use (see Hazell & Norton 1986). Optimality is assessed by reference to the law of equi-marginal returns. Programming allows system analysis, in which all the factors relevant to resource allocation are taken into account, rather than merely evaluating activities' values independently of the farm production system. Linear programming (LP) is probably the most common and widely-used method of mathematical programming. It has a number of attractive features, such as its direct relationship to production-economic theory, and its 'engineering' basis which allows the specifics of production and resource use to be taken into account, to the degree to which data is available. It is also relatively easy to adjust input and output parameter values to represent different economic scenarios.

The Empirical Model

Production possibilities are presented within the LP framework as a set of input-output parameters. National standards data could be used to estimate the parameters of interest, but are generally not of sufficient precision: regional or farm type characteristics would be masked by the high level of aggregation. A preferred approach is to estimate parameter values from locally observed commercial production data (although such data are generally available in an aggregated form means) and, for example, do not reflect differences across land classes or for different intensity levels), or from experimental data (trials) for new practices¹.

The model was calibrated using data from the 1996/7 Eastern Counties Farm Business Survey Report (Murphy 1998), i.e., for the 1996 harvest year. This was the most recent year for which published data for the region was available. The chosen case-study region is very important in terms of national arable production, and is also characterised by relatively intense pesticide usage, with a well-perceived pesticide contamination problem. It is very difficult to link to use of hazardous chemicals in any given area to the occurrence of environmental quality changes; however, it is reasonable to assume that the risks related to pesticide use will be highest in areas where pesticides are most intensively used (although the environmental effects are likely to vary considerably with the specific environmental circumstances). The harvest year was one of mixed and variable weather conditions, with excellent drilling conditions in the autumn, an exceptionally cold December, low temperatures and little rain until the spring, and a very dry spring although the drought eased in July. The year marked the end of the three-year transition period of compensated price reductions for cereals, oilseeds and protein crops, and the beginning of many downward revaluations of the green pound² which caused farm-gate prices to decline unexpectedly for practically all products (Murphy 1998).

The models were calibrated for mainly-cereals farms, excluding sugar beet and potatoes, of 0-400 hectares in East Anglia. The total rotational area of the farm was set at 250 hectares, which is fairly typical for the case-study region and farm type. Additional information on field operations was supplied by field experts. Standard cultivations costs were obtained from the Central Association of Agricultural Valuers' handbook. Discussions with field experts in the Department of Land Economy, University of Cambridge also provided information on operations, the timings of these and other aspects of arable cropping relevant to the Eastern region. Nix (1993) was also used in calibrating the model (notably with regard to labour availability).

The Objective Function
The objective function was assumed to be maximisation of management and investment income (MII)³. The riskiness of different activities, and the influence of this on the optimal farm-plan, was not considered in the model given the constraints of data and time. However, it is widely acknowledged that risk is probably an important factor in crop protection decision-making, and is certainly a very important factor with regard to the adoption of low-pesticide input practices, which are widely perceived to be more risky than their conventional counterparts (for which variability over previous years could be estimated from published data). Assessment of farm responses under different policy scenarios given an assumption of risk aversion is an important area for further work.

Cropping Activities
The aim was to model a specialist cereal business: such businesses account for around 65% of the agricultural area in East Anglia. Livestock activities were omitted from the model, although in the longer term these could offer alternative activities to farmers faced with pesticide usage (arable production) constraints. The farm was assumed to have a degree of inertia, i.e. farmers would not change from arable to livestock activities in the short-to-medium term (other arable activities would be more likely). A number of different production practices, varying with regard to their pesticide inputs, were defined for each crop enterprise to provide a variety of points on the production function⁴.

Attention was focused on agricultural enterprises that are potentially profitable for a large number of farmers, especially ones that currently (or could potentially) occupy large areas of land in the catchment or region. Minor and cash crops were excluded (notably potatoes and sugar beet⁵), although this may have resulted in some degree of over-prediction of the cereal area. The model included twelve crops, based on those combinable crops commonly grown in the region: winter and spring crops of wheat (including second and third winter wheats) (ww, sw, ww2, ww3), barley (wb,sb), oilseed rape (wosr, sosr) and field beans (wfb, sfb), combinable peas (peas) and set-aside (seta). No distinction was made between the production of milling, malting and feed grain. Crop by-products such as straw, were not included; in the Eastern Counties, this generally provides little (if any) revenue, and is usually incorporated rather than baled (Murphy, University of Cambridge, pers.comm.).

The simplification of arable production to the dominant enterprises can be justified on the basis that the interest lies in the finer details of production of these, for example, the alternative management practices or input combinations possible and the effects of these on gross margins (see below). Organic production was excluded because of its different underlying philosophy, and a shortage still of relevant data for a large enough sample of farms. Non-agricultural enterprises were also ignored in this model on the grounds that these would significantly increase complexity while not adding to the analytical power of the model for policy evaluation. Such alternative enterprises are also thought to be relatively small contributors to farm income for commercial specialist cereal businesses, although they may be important for other types (such as small mixed family farms). The model spans the short-term only, so significant movement out of arable production would not be expected, although it might be a long-term response.

Pesticide Inputs
Taxes might stimulate a change in the whole mode of production so modelling different types of systems is likely to be useful: in particular, attention would ideally have been given in the model to rotations and the potential for (and consequences of) changes in these^6,7 . However, insufficient data was available at the time of the study; this is another area for future work. Farmers may also wish to change practices gradually, as knowledge and experience accumulate. An important question, therefore, was the degree to which current arable production practices can be rendered less environmentally risky by pesticide usage adjustments, rather than by whole-system change.

Understanding the input substitution possibilities is central for analysis of policy based on reduction of the usage of particular contaminating inputs, and policy impacts should differ depending on the compliance options available to producers. For example, a vast set of near perfect pesticide product substitutes would result in trivial impacts on farm incomes following a ban on one of them; a smaller set would cause a ban to have a much more adverse effect. A preliminary step is therefore to determine the potential array of alternative cropping practices available (see Falconer (1997) for a detailed review, although the applicability of any given practice or technique will depend on site-specifics), before assessing what changes if any should be made in the organisation of the farm to maximise profits.

The inclusion of as many different functional forms for crop production as possible is important to the degree of realism of the model, as LP operates by substituting activities rather than inputs in the face of relative price changes. Thus, sufficient alternative activities must be included to adequately represent shifts along the production possibility frontier for any given crop (for example, by representing various chemical input intensities). The range of cropping variants will affect the accuracy of measurement of the effects of different policy instruments on farm organisation. There is a very wide range of approaches to crop production and protection: for example, within the sphere of chemical control alone, hundreds of different combinations are possible, depending on the crop and its condition, the pest problem, weather and soil types (Box 1 shows the components which would ideally be included in a farm model, although the data required to do this are simply insufficient).

A significant challenge in this research was the number of knowledge and data gaps with regard to the empirical relationships between pesticide inputs and crop outputs. For example, in contrast to nitrogenous fertilisers, pesticides cannot be reduced to a homogenous input with an empirically well-documented response function. Furthermore, it is unlikely that farmers practising low-pesticide-input production will not also adjust their seed, fertiliser and field operations choices. For example, crop varieties bred for disease resistance rather than yield may be selected, and the choice of rotation becomes critical. Although different crop production practices were specified by ECOTEC with regard to pesticide inputs (Table 1 shows the number of packages modelled for each crop), other parameters such as seed, fertiliser inputs and yield were assumed to remain constant, in the absence of any information with regard to the likely directions and magnitudes of changes. The crop production alternatives were also assumed to require identical field operations. These assumptions are reasonable, given the constraints of data, and given that the pesticide packages were carefully selected to be fairly comparable alternatives within the vast range of possible packages that might be applied within 'current commercial practice'. However, it is important to remember that different pesticide doses, perhaps with different methods of applications, may give different yields and gross margins; add to this the range of production conditions on individual farms, and 'typical' strategies are soon seen to be only rough approximations to the scenario for any one farm.

Each pesticide package was costed individually, on the basis of data from the pesticide use survey, and where this was not available, from distributors. Although pesticide prices related to the current year, and the other financial data used to calibrate the model related to 1996/7, the relatively low inflation over the period meant that prices were sufficiently close across the years to be reasonable approximations. More importantly, the relative chemical prices would be unaffected by indexation by one year, leaving the model cropping solutions unchanged.

TABLE 1: NUMBER OF CROP PRODUCTION FUNCTIONS INCLUDED IN THE MODEL
	Number of pesticide input 'packages' entered into the model
ww	12
sw	6
wb	4
sb	4
wosr	8
sosr	4
wfb	4
sfb	4
peas	4
set-aside	1

BOX 1: PRODUCTION FUNCTION VARIABLES

1. Decision Variables in Crop Production: crop variety rotation, use of set-aside in management sowing date method of crop establishment, seed-bed preparations level of nitrogen, timing of applications, type and quality sprays: type, mix, timing, sequences, degree of control to be achieved other crop protection strategies e.g. mechanical weeding other field management practices e.g. headlands, pesticide exclusion strips, beetle banks type of machinery owned / hired, operations contracted out 2. Exogenous Variables: soil weather input-output prices restrictions e.g. on pesticide use, on rotation (set-aside requirements for arable area payment eligibility) management skill of the farmer

Crop Activity Gross Margin Components;
Average seed and fertiliser costs were obtained for each crop from regional data for specialist cereal farms (Murphy 1998). Yields for first, second and third wheats were estimated using an assumption of a 15% yield reduction for second wheats compared with first wheats, and a 23% reduction for third wheats (following Nix 1993). Arable Area Payments available under the reformed Common Agricultural Policy were also included. Different crop activities vary in the resources used, notably machinery costs, so to improve the comparability of different activities, cultivations costs, based on standard estimates, were subtracted from the gross margin per hectare for each crop. Extra 'crop management' costs were taken into account too, through additional crop-walking and soil-sampling expenses.

Rotational Constraints:
These were developed through discussion with field experts and were included in the model to ensure adherence to principles of good husbandry in the choice of crop combination:

1. the area of first winter wheats cannot exceed the area of non-wheat crops
2. second winter wheat must not exceed the area of first winter wheat
3. third winter wheat must not exceed the area of second winter wheat
4. the total cropped area must not exceed the total rotational area (250 hectares)
5. the area of oilseeds must not exceed 20% of the total rotational area
6. the area of pulse crops (field beans and peas) must not exceed 20% of the total rotational area
7. WOSR can only follow winter barley and set-aside, due to a need to drill OSR early
8. set-aside was constrained to be 10% of the total rotational area; the farm was assumed to participate in the arable area payments scheme

Labour Availability For Field Operations:
Twelve month-long periods were defined and the regular available working hours per permanent, full-time worker were taken from Nix (1993), with field workability adjusted down for heavy soil. Monthly overtime availability for field work per permanent, full-time worker was also calculated (two workers were assumed to be employed). Casual labour was also available to remove any labour availability constraint. Permanent workers' costs, the costs of over-time and casual labour, when used, were included in the objective function.

Field Operations Requirements and Costs, Work Rates and Timing:
Field operations (stubble cultivations, drilling, harvesting etc.) were defined for each crop, and standard estimates for their costs were included in each activity's gross margin. Most costs were assumed to be the same regardless of the crop and field conditions, although implements vary greatly depending on their precise type and age, and wear-and-tear varies according to the exact operation, for example, harvesting peas in sub-optimal conditions results in a greater real cost in machinery terms than harvesting wheat under good conditions. However, to keep the model to a reasonable size a number of simplifying assumptions had to be made. Contractors were assumed not to be used. Work rates for 'typical operations' were based on standard estimates, and verified with field experts and available data from Cereals Survey farm data. Operations were allocated to each crop for each month. A distinction was drawn between field operations requiring a tractor and harvesting operations using a combine. Winter wheat was assumed to be ploughed one year in three. Apart from harvesting, work rates were assumed to be the same for all crops, although in reality of course they are likely to vary, according to crop type, conditions and a number of other factors. Approximate timings of each operation on each crop were based on the basis of consultation with field experts and on the monthly break-down for arable activities (premium farms) given in Nix (1993): these rates were calculated to include morning preparation time, travelling to and from field, minor breakdowns and other stoppages, and cleaning time. They relate broadly to averages over the whole season on medium and medium-to-heavy land; in practice, rates vary of course according to topography, lay-out and the natural features of the particular farm. Total field operations time for each month per hectare of each crop was then calculated.

Timing is very important for resource constraints (such as labour and machinery availability) and for output coefficients (for example, timing affects the return to agro-chemical inputs). Ideally, the variability in weather conditions would be taken into account; these affect the number of workable days and the types of field operations possible; crop growth, weeds and disease development; the efficacy of control strategies, both chemical and non-chemical; and resulting yields and gross margins. However, including the timeliness of activities in the model is complicated by the stochasticity of these conditions: it is practically impossible to take account of the crop growth stage in a simple LP model, although this is very important for crop protection strategies and timing in practice. Field operations were allocated to each month on the basis of 'typical' timings.

Total potential field working time is limited not only by the labour available (both permanent and casual), but also by machine availability; additional labour can only be useful if there are machines available for it to use. It was assumed that fieldwork was limited more by soil and weather conditions than by daylight, as tractor headlights can be used. Thus total machine availability in each month was based on an 18 hour day (to take into account factors such as dew), times a percentage (from Nix 1993) to reflect field workability in each month. Harvesting does not require a tractor but a combine, so field-working time for crop harvest was constrained separately; total potential machine hours were calculated on the same basis as for other field-work. Thus the sum of field-work time needed in each month for all crops must not exceed the total field-work labour time available (including casual labour) for the total machinery time for field-work available. However, in reality, different operations may well face extra constraints too (for example, it is possible to plough when it is windy but not to spray).

Working Capital:
Cash-flow was assumed to be balanced quarterly with an overdraft facility, up to a limit of £45,000. Cash deficits or surpluses were carried-over from the one quarter to the next. Following Oglethorpe (1996), it was assumed that there would be no transfer of cash deficit or surplus from the fourth quarter to the first one: the feasible solution was constrained to generate enough working capital to pay back all overdraft deficits incurred over the four quarters. It was assumed that cultivations and labour costs were funded on an annual basis, rather than from the current account, and therefore did not enter the cash-flow constraint. A further cash-flow assumption was that crops were sold immediately on harvest, even though they might not in fact by sold until later in the year⁸ . The long-term debt and financial structure of the farm was ignored; renting and leasing of land, and hiring-out of labour was also excluded: the model was intended to represent the short term only. However, such aspects of the farm business might be important as characteristics of longer-term farm-plan change in the light of policy implementation. The imputed rental costs of land were not considered explicitly, as in the short-term these would probably be similar across all the policy scenarios modelled here.

Fixed costs:
While farm management accounting procedures traditionally treat all machinery costs as 'fixed', clearly some of these are 'variable' in the sense of varying directly with enterprise size (e.g., fuel, depreciation, repairs); others are more 'lumpy' (e.g. insurance) and are not easily handled in LP models which deal only with linearly variable costs and returns. The approach taken here was to allocate only 'truly' variable costs for each enterprise and deduce these from the activity gross margin; fixed costs such as rent, full-time labour and other overheads would then be subtracted from the objective function as a later stage. The objective function therefore maximised the management and investment income, taking account of cultivations and harvesting costs, casual labour costs, spray tax or levy payments (under policy scenarios), crop-walking and soil-sampling. Fixed costs were then estimated and subtracted on a flat-rate basis, per hectare of the total rotational area.

Caveats:
There are of course limitations to the necessarily simplified nature of production modelling, and caution must be exercised when interpreting model outputs. The principle caveats are listed below:

• the model is static
• it relates to the short-term only, i.e., the period within which resource constraints are fixed
• no new technologies included (new chemicals, low-pesticide input farming techniques etc)
• no swing away from 'current commercial practice' in the near future
• limited range of pesticide input practices, given limitations on the size of the model
• assumption of constant yields despite different pesticide inputs
• assumption of technical efficiency and profit maximisation as the single business objective (risk neutrality)
• no diversification into other activities (both agricultural, such as livestock production) and non-agricultural)
• perfect divisibility of activities and resources (e.g., fractions of fields can be grown of different crops)
• proportionality of activity levels (for example, no economies of scale)
• single-valued expectations, i.e. deterministic modelling

A very important caveat relates to the linearity in the model structure. It is necessary to specify discrete production activities, i.e., specific points on the production function, for each crop, rather than continuous production functions. This has the effect that the optimal plan may not change immediately when the gross margin for a 'basic' activity (i.e., one included in the optimal farm plan) increases or decreases relative to the rest. Changes in relative gross margins (more precisely, relative marginal value products) must be sufficiently large for the iso-profit line to swing around to touch another (model-specified) point on the production possibility frontier. This limitation highlights the importance of a range of activities for different crops: as activities enter the plan discretely rather than continuously, unless a wide range of activities are included, input substitutions may be masked by product substitutions. For example, winter oilseed rape may be substituted for winter wheat following pesticide input taxation, when in reality, it is more likely that winter wheat would continue to be grown but using different chemicals. An implication is that changes in the farm-level supply function for different crops will be stepped, compared to the smooth continuous curves of economic theory.

Another limitation relates to the degree of freedom given in the model to shifts between enterprises following changes in the economic context of production. There is no allowance for the gradual development of the farm plan, risking the generation of extreme solutions: for example, sweeping changes in enterprise mix may be made to achieve trivial improvements in overall profit. It is important to recognition, when interpreting the model output, that the real-world passes through transitional phases, and that some aspects of change might take much longer to achieve than others is very important. The socio-economic element of farming systems is also an area for further consideration, given increasing recognition now of the importance of individual decision-makers' attitudes. Modelling attitudes is at present severely constrained by the available knowledge and understanding.

Despite the caveats indicated above, linear programming still provides a useful approach: its chief advantage is the application of economic principles, through simplified⁹ but carefully specified and calibrated farm models. This allows economic policy problems, and policy evaluation, to be approached logically and can permit useful analysis of farm production under different scenarios.

Results

Principle interest lies in the changes triggered by policy implementation of different specifications in both the cropland allocation and the crop production practices selected as optimal in each particular economic scenario.

Given the environmental context of this research, it is particularly important to examine any qualitative changes in pesticide usage, in addition to quantitative change. For example, we would expect banded taxation to shift usage towards pesticides in lower tax bands; unbanded taxation may achieve this to a lesser degree if at all, depending on the correlation between product price and the tax band based on ecological hazard criteria (see Falconer 1997 for further discussion on this). It was decided to present any usage changes with regard to the bands in which individual pesticide active ingredients lay, rather than with regard to the hazard scores on which the banding was based, given the spurious precision which the latter approach would imply.

The cost increases for the pesticide inputs for each crop production activity were calculated separately for each policy scenario using a series of EXCEL spreadsheets. The resulting prices were then fed into the farm policy evaluation model. The results of optimising farm production in the model are presented below for 12 policy scenarios (2 groups of 6), i.e.,

1. Unbanded taxation, using three bases (per dose, per kilogram of active ingredient and an ad valorem tax), for high and low tax scenarios, and
2. Banded taxation (i.e. taxation differentiated across pesticides according to their type and notional environmental hazard, using the same three bases (per dose, per kilogram of active ingredient and an ad valorem tax), for high and low tax scenarios

Validation was based on the average ('typical') land uses for mainly-cereals farms in the Eastern Counties, from published farm-level data (Murphy 1998) (see Table 2). Most Farm Business Survey farms grew some other crops apart from cereals, oilseed rape and pulses, particularly root-crops, linseed, forage and grass. Table 3 shows the cropland allocation given by the model under all of the scenarios evaluated. The model output considered satisfactory with empirically-observed observations: the wheat and barley areas were within what might be expected, although winter barley was perhaps slightly high (to compensate for the absence of spring cereals); the total cereals area matched the published estimates quite well. Oilseed rape was high, but this was explained by the fact that no other break crops were grown. Results are unlikely to match reality perfectly given the assumptions inherent in the structure of the model. The existing model was therefore accepted as the basis of the policy evaluation exercise. The LP models could have been further refined to better represent reality, but nevertheless, considering the data and the resources available, the models were considered capable of generating useful information for evaluating and comparing different policy instruments.

TABLE 2: EASTERN COUNTIES SURVEY CROPLAND ALLOCATION RESULTS
	% of total rotational area
	all mainly cereals farms	Top 10 Mainly Cereals Farms	Mainly Cereals Farms excluding sugar beet and potato growers
average size, hectares	263.3	309.1	258.8
winter wheat	47.8	53.4	52.6
spring wheat	0.0	0.0	0.1
spring barley	2.7	0.9	1.1
winter barley	10.9	8.9	8.8
all cereals	62.2	63.2	63.5
field beans	3.2	1.9	4.1
field peas	2.2	0.5	2.8
oilseed rape	7.9	13.7	9.7
potatoes	0.2	0.0	0.0
sugar beet	3.4	3.1	0.0
set-aside	3.2	9.0	9.9

Source: Murphy (1998).

The financial results in terms of farm management and investment income (MII) per hectare compare favourably with mean levels for mainly cereals farms in the Eastern Counties Farm Business Survey (Murphy 1998). While the MII achieved did not reach the levels of the Top 10 mainly cereals farms in the region (£479.2/hectare), it was above the average level achieved (£219.7 / hectare for all mainly-cereal farms, and £216.0/hectare for all mainly-cereal farms excluding potato and sugar beet growers), primarily because of the narrower mix of enterprises operated by the model farm compared to the survey farms. The levels achieved can be considered as reasonable 'ball-park' figures for efficiently-managed farms of this type, in the Eastern region of the UK.

TABLE 3: CROP LAND ALLOCATION, AS A PERCENTAGE OF THE TOTAL ROTATIONAL AREA
	% of total rotational area
first winter wheat	50
second winter wheat	10
winter barley	10
winter oilseed rape	20
set-aside	10

The MII figures given are the post-tax levels, i.e., the predicted actual cash MII after any applicable pesticide taxes or charges have been paid. These figures will this vary from the 'economic' MII net of tax payments (i.e., representing the opportunity cost of production on the farm). The economic MII under the policy scenarios examined in this study did not vary much, as the crop land allocations and production practices did not vary greatly. That is, production was very similar under all of the scenarios considered; the main change related to farm income only. The financial effects of implementation of the example policy scenarios are given in Table C4.

TABLE 4: FINANCIAL RESULTS
	Farm Management & Investment Income
	£	as % of base level
Base scenario ('policy-off')	86435.8	100.0
BANDED TAX
dose levy, low rate	82635.8	95.6
kg levy, low rate	83923.3	97.1
ad valorem tax, low rate	81975.8	94.8
dose levy, low rate	74153.3	85.8
kg levy, low rate	78060.8	85.8
ad valorem tax, low rate	76668.3	88.7
UNBANDED TAX
dose levy, low rate	82370.8	95.3
kg levy, low rate	83808.3	97.0
ad valorem tax, low rate	82530.8	95.5
dose levy, high rate	74630.8	86.3
kg levy, high rate	78328.3	90.6
ad valorem tax, high rate	71803.3	83.1

For the given policy scenarios, no switching between crop enterprises was observed, although a small number of changes in the pesticides used on some crops were observed under some scenarios (see Table 5 for a summary of pesticide usage by crop). These results are partly related to the model design, i.e., the necessity of inclusion of different crop activities in the programme as discrete activities, rather than as discrete production functions, and partly related to the relative prices assumed in the model, i.e., as indicated by earlier studies (such as Falconer 1997 and Oskam et al. 1992), pesticide usage is relatively inelastic so relatively large levies or percentage price increases would be necessary to achieve much effect in terms of pesticide usage reduction or change.

TABLE 5: SUMMARY OF FARM OPTIMISATION RESULTS: PESTICIDE PACKAGES SELECTED AS OPTIMAL UNDER EACH SCENARIO
	Chemicals used on each crop
	first winter wheat	second winter wheat	winter barley	winter-sown oilseed rape
Base	i	I	c	e
BANDED TAX
dose levy, low rate	i	I	c	b
kg levy, low rate	i	I	c	a
ad valorem tax, low rate	i	I	c	a
dose levy, low rate	i	I	c	b
kg levy, low rate	i	I	c	a
ad valorem tax, low rate	i	I	c	f
UNBANDED TAX
dose levy, low rate	i	I	c	e
kg levy, low rate	i	I	c	e
ad valorem tax, low rate
dose levy, low rate	i	I	c	f
kg levy, low rate	i	I	c	e
ad valorem tax, low rate	i	I	c	e

NB: the same pesticide inputs were assumed to be used on all hectares of the crop grown on the farm, although in reality, sprays may differ across fields depending on the situation-specific conditions.

The results indicate very little chemical switching from the base-case pesticide usage scenario; only the sprays used on the oilseed rape varied, as shown in Table 6. Table 7 shows the chemicals used on the cereals crops.

TABLE 6: PESTICIDES APPLIED TO OILSEED RAPE
	Package a	Package b	Package e	Package f
Chemicals applied	1. cypermethrin 2. carbendazim/ flusilazole 3. tebuconazole 4. metazachlor 5. propyzamide 6. fluazifop-p-butyl	1. lambda-cyhalothrin 2. carbendazim-flusilazole 3. tebuconazole 4. metazachlor 5. fluazifop-p-butyl	1. cypermethrin 2. carbendazim /flusilazole 3. tebuconazole 4. metazachlor 5. propaquizafop 6. diquat	1. lambda-cyhalothrin 2. carbendazim/ flusilazole 3. tebuconazole metazachlor 4. propaquizafop 5. diquat

TABLE 7 : PESTICIDES APPLIED TO WHEAT AND BARLEY IN THE MODEL SOLUTIONS
	winter wheat	winter barley
Chemicals applied	1. chlorothalonil 2. fenpropidin 3. epoxiconazole 4. fenpropimorph 5. cypermethrin 6. isoproturon 7. diflufenican/isoproturon	1. cypermethrin 2. isoproturon 3. diflufenican/isoproturon 4. carbendazim 5. prochloraz

It is interesting to examine the close alternatives to the selected pesticide input packages, with regard to per-hectare marginal productivity. An advantage of the GAMS programme is that it automatically provided calculations of the marginal value products (shadow prices) for each activity under every scenario for which the model is run (saving extra sensitivity analysis computations to answer 'what if' questions about marginal changes to resource constraints). The shadow prices represent the increase in the objective function (farm MII) that would be observed if that activity was forced into the farm plan. They can also be interpreted as the amount by which the marginal return to the activity would have to increase for the activity to enter the plan. Table 8 shows the alternative pesticide strategies that might have been employed in each situation for each crop.

TABLE 8: ALTERNATIVE PESTICIDE INPUT PACKAGE MARGINAL VALUE PRODUCTS
	close alternative packages	(see Appendix for details)	package marginal value product (£/ha.)
Base	winter wheat winter barley winter oilseed	g,e,h a,b,d a,b,f	-3.6, -8.5, -25.2 -2.8, -23.7, -20.8 -3.2, -10.9, -7.7
BANDED TAX
dose levy, low rate	winter wheat winter barley winter oilseed	g,e a a,b,f	-3.0, -8.4 -5.4 -0.8, -2.3, -1.5
kg levy, low rate	winter wheat winter barley winter oilseed	g,e a a,b,f	-5.5, -9.2 -5.0 -1.8, -9.3, -7.5
ad valorem tax, low rate	winter wheat winter barley winter oilseed	g,e a,d a,b	-4.7, -11.1 -3.7, -27.1 -1.3, -11.4
dose levy, high rate	winter wheat winter barley winter oilseed	g,e d,a b,a,e	-1.7, -8.0 -26.6, -11.6 -0.2, -13.4, -13.3
kg levy, high rate	winter wheat winter barley winter oilseed	g,e a,b f,a,b	-9.8, -10.5 -10.3, -23.8 -7.1, -3.6, -10.6
ad valorem tax, high rate	winter wheat winter barley winter oilseed	g,e a a,b,f	-7.3, -17.2 -5.6 -2.1, -17.6, -15.5
UNBANDED TAX
dose levy, low rate	winter wheat winter barley winter oilseed	e,g a a,f	-7.6, -22.0 -12.0 -27.1, -6.4
kg levy, low rate	winter wheat winter barley winter oilseed	e,k a,d b,e,f	-13.5, -28.6 -19.4, -26.6 -6.0, -5.9, -12.0
ad valorem tax, low rate	winter wheat winter barley winter oilseed	g,e a	-21.5, -26.5 -8.8
dose levy, high rate	winter wheat winter barley winter oilseed	g,e a,d,f f,a,e	-9.1, -8.3 -5.6, -25.0 -1.2, -2.7, -3.9
kg levy, high rate	winter wheat winter barley winter oilseed	g,e a,d b,e,f	-13.1, -10.0 -7.7, -22.5 -7.2, -1.0, -8.3
ad valorem tax, high rate	winter wheat winter barley winter oilseed	g,e a b,e	-9.0, -14.0 -4.6 -12.6, -4.5

Interpretation of the Results and Analysis / Implications

Surprisingly few changes were observed in the cropland allocations and in the production practices selected as optimal under the different policy scenarios. The results imply that the levels of taxes and levies considered were simply too low to change the relative marginal value products of the activities. Previous research also found that high levels of taxation were required to trigger change in the optimal plan, for example, ad valorem taxation of over 100% of the current price, and a uniform per-dose levey of around £20, and a per-kilogram of active ingredient levy of around £15 (Falconer 1997).

The only changes in pesticide use were those in winter oilseed rape where the banded instrument caused a shift out of package e and into other packages. What the packages imply, in terms of use of active ingredients, is shown in Table 9. Making judgements about which is best and which is worst is not completely straightforward, but almost certainly, package b is he environmentally best outcome (according to the hazard ranking scheme) and package e is the worst. Deciding between packages a and f is less straightforward.

TABLE 9 : KILOGRAMS OF ACTIVE INGREDIENT IN WINTER OILSEED RAPE PESTICIDE PACKAGES
	a	a relative to e	b	b relative to e	e	f	f relative to e
kg a.i. in Band 1	0.56	+0.560	0.56	+0.560	0	0	0
kg a.i. in Band 2	0.16	0	0.16	0	0.16	0.16	0
kg a.i. in Band 3	0.896	-0.390	0.896	-0.390	1.286	1.286	0
kg a.i. in Band 4	0.048	0	0.012	-0.036	0.048	0.012	0.036
kg a.i. in Band 5	0		0		0	0

At the lower tax rate, the package shift is from e to a for the per kg and ad valorem cases, and from e to b for the per dose case. At the higher rate, the switch is from e to a, b and f for the banded per dose, per kg and ad valorem taxes, respectively. In this case, therefore, the banded per dose tax generates the best outcome in environmental terms. It does, however, have the most significant impact on farm MII. The banded per kg and ad valorem taxes generate the same outcome at low rates of price increase, but differ at higher rates. It is difficult to decide which performs better given the difficulty in trading off different weights of active ingredient in the different hazard bands.

A comment on the longer-term economic impacts of pesticide price increases must be made. The modelling presented here relates to the short-term only, and the potential for switching between different crops grown according to current commercial practice. However, there has been, for some years now, a developing interest in 'integrated farming' and the use of approaches such as careful choice of crop rotation to reduce agro-chemical inputs while maintaining production and profit levels. So far, trials of these new, integrated approaches have been confined largely to government-sponsored experimental farms, and the results have benefited from the expertise of management available. It is still to be seen whether commercial farms could achieve the same degree of success using these approaches. It is highly likely that commercial practice will evolve in the future in the direction of integrated crop management, and consequently, the longer-term pesticide usage reduction impacts of pesticide price increases might be expected to be greater, with less adverse income effects. A fuller assessment of the impacts is impossible, given the inability to predict change in terms of both the farming techniques themselves, and the wider agricultural economic environment.

The model results for MII might be considered to give a 'floor' to the potential income changes following pesticide price increases (as would be expected to happen following the implementation of a tax or levy, for example) for a typical arable farm in East Anglia. However, much depends on farm- and farmer-specific factors affecting adjustment in the face of pesticide price increases; the are enormous challenges to predicting adjustments given how little we know about farmer behaviour with regard to pesticide usage; this is a highly complex area. The model MII prediction is the highest that would be obtained by such a farm if it was perfectly efficient. However, if it is likely that there are other possible cropping and production adjustments in existence that have not been considered here, and that might be lower-cost than those included in the model, the results may in fact over-state the income changes following policy implementation. There is good reason to believe that this is indeed the case given the growing interest amongst commercial arable producers in 'integrated crop management' approaches indicated by an ADAS survey in 1996/7. However, at present, interest per se does not equate to up-take. Many farmers might consider that they have little room to manoeuvre in terms of their crop protection practices; the problem is that while there may be few options in terms of marginal changes to current systems, far greater improvements might be achieved through broader changes to production practices, in terms of strategies as well as tactics. The problem is the heightened riskiness that producers could potentially expose themselves too through making more radical changes; there is a clear need for far greater levels of extension and expert-support for producers willing to consider such changes in the interests of the environment.

The effect on management and investment income (MII) was to reduce it by 2.9-5.2% under 30% price increases, and 9.4-16.9% under 100% price increases. These reductions are smaller than the changes in net farm income arrived at through use of farm business data (if anything, given that MII makes a deduction for labour of the farmer and spouse, one would have expected the reductions in MII to be greater than those for net farm income above)¹⁰. The ad valorem tax appears to have the greatest impact, and the per kg tax usually has the smallest impact. However, further work is needed, particularly with the inclusion of a greater range of pesticides in the model, to check the generalisability of this result.

The significance of these results is as follows:

• the tax causes no switches in enterprises on the type of farm modelled; and
• in no case did the tax prompt switching from less hazardous to more hazardous packages. On the contrary, in the only instances of switching between packages, all the switches were environmentally positive. All the banded instruments triggered hazard-reduction changes in pesticide use. However, only one unbanded instrument encouraged such change.

References

Bauer S, Hoppe U, Hummelsheim S (1995): Decision Support System for Controlling Pesticide Use in Hessen. Proceedings, Workshop on Pesticides, August 1995, Wageningen.
Brooke A, Kendrick D & Meeraus A (1992): General Algebraic Modelling System (GAMS): A User's Guide. Release 2.05. (GAMS Corporation, Washington DC).
Falconer KE (1995): Environmental Contamination and Pesticides: Farm Decision-Making and Policy. Unpublished M.Phil thesis, University of Cambridge.
Falconer KE (1997): Environmental Policy and the Use of Agricultural Pesticides. Ph.D. thesis, University of Cambridge.
Hazell PBR & Norton G (1982): Mathematical Programming for Economic Analysis in Agriculture. MacMillan: London.
Murphy M (1998): Report on Farming in the Eastern Counties of England 1996/7. Department of Land Economy, University of Cambridge.
Nix J (1993): Farm Management Handbook. Wye College, University of London.
Oglethorpe D (1996): Farm-Level Land use and Environmental Management Decisions: A Modelling Approach to the Analysis of Policy Change. Ph.D. thesis, University of Newcastle.
Oskam A, van Zeijts H, Thijssen GJ, Wossink GAA & Vijftigschild R (1992): Pesticide Use and Pesticide Policy in the Netherlands. Wageningen Economic Studies 26, Wageningen Agricultural University.
Tiffin R & Renwick A (1996): Estimates of Production Response in the UK Cereal Sector Using Non-Parametric Methods. European Review of Agricultural Economics 23(2): 179-196.

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¹ ADAS farms such as Boxworth and Rosemaund are one source of such data, and have the advantage of being reasonably comparable with commercial farms as alternative management practices are carried out at field level, alongside commercially produced crops. However, experimental data have limitations: they relate to a limited time period, the management costs are hidden and results are location specific.

² " The green money bonanza has now run its course for UK farmers. The results for the harvest year 1997 are likely to reveal even more clearly the results of farming in a less-protected market and farm incomes are expected to fall by up to a further 50% to about £150 per hectare" (ibid., p6).

³ Tiffin & Renwick (1996) considered that the production on the sample farms used in their study was consistent with an assumption of variable profit maximisation as an important short-term objective. Interviews with farmers carried out in 1995 suggested that decisions were made on the basis of 'normal' expectations of pest infestations, i.e. profit maximisation (Falconer 1995).

⁴ A caveat is that an LP model can only pick from the range of activities it is presented with, and the identification of a pragmatic subset of activities to model is relatively subjective, especially for new technologies.

⁵ These are significantly more complex in terms of crop protection, require different machinery (lifters etc) and are grown on a relatively small area of the total regional crop area.

⁶ An assumption of LP is activity additivity (independence): margins are constant, regardless of the proportions of crops grown. However, there may be yield penalties for some sequences of crops: rotational effects are particularly important to the cultivation of low-pesticide input crops and the performance of each. Field trials generally have been designed to investigate whole rotations, and the effects of these is clearly an area for further development of the model once more data has been gathered.

⁷ Falconer (1997) calibrated the farm-level policy evaluation model for two production scenarios, one representing current commercial crop production and one representing a more 'progressive' farm, with the same range of cropping activities but with a number of different agro-chemical regimes. The aim was to improve the modelling approach by including, for each crop, variants ranging from the intensive to the ecological production system, to represent a discrete set of production alternatives per crop.

⁸ Output markets were assumed to perfect, i.e., storage costs and lost interest would exactly equal the premium gained by selling later in the year, so the timing of sale is unimportant with respect to net revenues.

⁹ It is possible to make a number of refinements to the basic programming model, for example, to overcome assumptions such as perfect divisibility of resources, single objective maximisation and proportionality; see further Falconer (1997).

¹⁰ One reason for this could be that the optimisation process in the model is such that it will always choose the lowest price package of pesticides for a given enterprise. The survey will include farmers whose ratio of output:pesticide use varies considerably (see Fig.4 for a diagrammatic representation of user performance on large cereal farms in the Eastern Counties.

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Published 29 April 2000

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