Economics of Variable Rate Lime - 2001

Ing. Agr. Rodolfo Bongiovanni
National Institute for Agricultural Technology (INTA), Manfredi, Córdoba, Argentina
 
J. Lowenberg-DeBoer
Department of Agricultural Economics, Purdue University, West Lafayette, Indiana

ABSTRACT

In Indiana, variable rate application (VRA) of lime is often considered a good place to start site-specific management (SSM). This is because soil pH is one of the most variable of manageable soil characteristics in the state, the availability of essential nutrients is closely related to soil pH, and because spreaders can be retrofitted relatively inexpensively to do VRA. The objective of this study is to evaluate the profitability of VRA for lime as a stand-alone activity. The methodology involves a spreadsheet model using corn and soybean pH response functions estimated with small plot data. The overall results indicate increased annual returns to corn and soybean production with site-specific pH management strategies. On average, SSM with agronomic recommendations provides an increased annual return of $7.24 per hectare (ha) (+1.78%). SSM with the economic decision rule provides an average increase in annual return of $19.55 ha-1 (+4.82%). Information strategy, which uses site-specific information to determine the economically optimal uniform rate of lime, provides an average increase in annual return of $14.38 ha-1 (+3.54%).

Soil acidity is commonly indicated by soil pH, a measure of hydronium ion activity in a soil suspension. Acidity may be created by a removal of bases by harvested crops, leaching, and an acid residual that is left in the soil from nitrogen fertilizers, and it has long been recognized as one reason soils become unproductive. Liming to correct soil acidity has been practiced for centuries, but during the last several years, limestone use has tended to decrease while crop yield and nitrogen fertilizer use have increased markedly (Frank, 1994).

Soil variability within farm fields has long been recognized by soil scientists as well as farmers, and soil pH is one of the soil characteristics with the highest spatial variability (Cline, 1944). Lime used to correct soil pH is an important cost for Indiana farmers. The per unit cost is low relative to other fertilizers, but the application rates are comparatively high. Lime application is measured in tons, instead of the kilograms (kg) used for nitrogen (N), phosphorus (P) and potash (K). Uniform rates can leave underlimed areas or apply lime to portions of the field where the soil pH is satisfactory. Unlike some other fertilizers, lime can produce a negative effect on crop response if it is applied in excess. Most crops require some lime if pH falls below 5.0, most require no lime if pH is 7.0 or higher. If pH exceeds 7.5, the soil becomes too basic, probably affecting nutrient availability, plant nutrient uptake, and microorganism activity. Moreover, soil pH will potentially affect herbicide choice, herbicide damage and performance (Childs et al., 1997).

From an economic point of view, lime is a crop-production input that provides certain benefits at a cost. If liming increases crop yield (or reduces the requirements for other inputs) and if the value of the increased yield (savings in the cost of other inputs) exceeds the cost of lime, then liming is profitable. A farmer who wants to maximize the net returns will increase his lime rate as long as the value of the benefits exceed the cost of the lime (Hall, 1983).

How much lime will pay for itself at any specific location? Answering that question requires knowledge of how crop yields respond to lime applications. In this study, yield-response functions are fitted to field-plot data from controlled lime rate experiments reported in the literature.

Beyond the determination of optimal lime rates, this study addresses the decision to adopt site-specific management (SSM). Variable rate application (VRA) of lime is often considered a good place to start SSM, since pH is one of the most variable of manageable soil characteristics and affects the availability of plant nutrients. Most lime spreaders can be retrofitted relatively inexpensively to do VRA. Theoretically, this practice should allow growers to manage field variability while improving profitability.

If fields were uniform, there would be no need for SSM. Since fields contain a complex of soils and landscapes, and because of variability of previous management, extensive spatial variability in soil properties and crop productivity is the norm rather than the exception in most fields (Mulla and Schepers, 1997). With such extensive variations, potential exists for adoption of SSM.

There are no published economic evaluations of SSM of lime. Most existing studies of the economics of SSM focus on VRA of N, P, and K because this was the first SSM technology that was technically feasible (Lowenberg-DeBoer and Swinton, 1997). Published studies on the economics of precision farming report mixed results. Farmers and agribusinesses are currently beginning to invest on SSM for lime and there is an urgent need for information on the profitability of the practice to guide decisions.

Different SSM strategies can be implemented, but only two SSM strategies and one intermediate approach will be considered here. First, SSM using agronomic recommendations (SSM-Agronomic). This approach grid samples the field, and applies the recommended rate of lime to the individual grid cells using the agronomic recommendation rules, e.g., Tri-State Fertilizer Recommendations (Vitosh et al., 1995). Lime requirement (LR) for agronomic recommendations was calculated to reach a desired pH level, according to the present lime indexes. These rules are based mainly on yield optimization. The economic reasoning underlying the recommendations is not made explicit, but rates are somewhat less than what would be required to maximize physical yield, perhaps on recognition that the cost of the lime needed to obtain the least few kilograms of grain would be greater than the value of the extra production. Based on research, actual yield response to lime is less than normally recommended. The recommendations are meant to cover variability inherent across fields, known to commonly occur (Mengel, 2000). The SSM-Agronomic strategy is the most common current practice for those beginning precision farming. Under this framework, quasi-fixed costs due to soil sampling and VRA are constant if a given technique or input is used, but zero if that technique or input is not used.

Second, SSM with the economic rule (SSM-Economic) is considered. This approach is similar to SSM-Agronomic, but uses the economic rule, marginal value product equal to marginal factor cost (MVP=MFC), to determine the recommended rate of lime to the individual grid cell. This strategy calculates a rate of lime that maximizes net present value (NPV) over a four-year period. NPV is maximized when the marginal response to one unit of lime equals the number of units of output that must be sold to pay for that unit of lime. SSM with the economic rule is considered because it is the approach recommended in the production economics literature and as a test of the sensitivity of the SSM adoption choice to the lime rate decision rule.

Third, an "information strategy" is examined. The information strategy considered here uses site-specific information to determine the economically optimal uniform rate of lime. Information strategies are considered because some farmers have grid soil information and they do not have access to variable rate equipment; and also because they have been found potential profitable in management of P and K (Schnitkey et al., 1996). In this case the VRA fee drops out of the profit equation, but the cost of gathering site-specific information is still incurred. It differs from WFM in the sense that the information strategy approach averages the individual marginal products, while the WFM profit maximization condition uses the marginal product of an average response function (Lowenberg-DeBoer and Boehlje, 1996). The choice between full adoption with both intensive data collection and variable rate application boils down to whether the value of the yield increase with full adoption, plus the input cost savings is greater than the quasi-fixed cost of variable rate application. Intensive data collection and analysis costs are incurred in both the full and partial adoption scenarios and thus are not a factor in the technology choice between these two options.

To evaluate profitability, the three SSM strategies are compared to the whole field management (WFM) strategy, considered here as the baseline case. WFM makes a composite soil test, resulting in an average pH for the field and a single rate for lime application, using the agronomic recommendation rule (e.g., Vitosh et al., 1995). This is the most common current practice in the Midwestern United States. The option of doing nothing is also reported for comparison purposes as the control case.

The main objective of this research is to evaluate the profitability of custom-operated VRA for lime as a stand-alone activity, using data for Indiana farms that produce grain in a corn-soybean rotation. The term "profitable", as defined by Lowenberg-DeBoer and Swinton (1997), means that switching to SSM yields higher NPV of returns than WFM.

The specific objectives are to determine (1) if SSM is profitable using agronomic recommendations for lime rates, compared to WFM; (2) to determine if SSM is profitable using the economic rule (MVP=MFC) for lime rates, compared to WFM; (3) to determine if the information strategy presents any advantage over VRA and (4) to compare profitability with 0.4-ha and 1-ha soil sampling systems.

The general hypothesis is that site-specific soil pH correction maximizes NPV over a four-year soil sampling cycle, and that a 1-ha grid is more profitable than a 0.4-ha grid for SSM with current technology. A secondary hypothesis is that the information strategy is a profitable alternative for farmers who lack access to VRA equipment or who just want to minimize costs.

The methodology involves a spreadsheet simulation model using corn and soybean pH response functions estimated with experimental data. The ideal data for this study would be results from long-term field trials in several locations comparing SSM and WFM for lime. Unfortunately, such data is not available and many farmers and agribusiness people need to make decisions about SSM for lime before such results could be collected. Simulation is a way to use available data to provide preliminary results. Bongiovanni (1998) gives a complete description and other aspects of the methodology.

The planning period for the simulation is four years, a typical soil sampling cycle and consistent with a decision to maintain an adequate pH level. In multiperiod cases it is useful to cast the problem in terms of maximizing net present value (NPV). NPV allows for the time preferences of decision-makers that often value returns in the future differently from current returns. For a four year corn-soybean rotation, the objective function is the NPV of returns:

where:

V = Net present value (NPV) of returns above variable costs, for the 4-year term, in $ ha^-1.
i = 1,…n: number of management zones
A_i = Area in ha per management zone
P_corn = Price of corn
P_soy = Price of soybean
P_l = Cost of lime
Y_{t corn} = Yield of corn in year t, where t= 1, 3. Corn production function is equation (4)
Y_{t soy} = Yield of soybean in year t, where t= 2, 4. Soybean production function is equation (5)
d = Discount rate
C_t = Variable cost of production (where t= 1, 2, 3, 4), multiplied by (1+d), because variable costs are assumed to be paid at the beginning of the season.

LR = Lime requirement (tons ha^-1) which in SSM-Economic is 

PH_t = pH in year t, where t= 0, 1, 2, 3, 4. (Lime is applied at time 0, but pH changes every year with cropping and fertilizer application. In order to calculate yields, the production function requires a pH value for each year).

Bs_i = Base saturation, defined by Black (1993) as:

CEC = Cation exchange capacity

Equation (1) represents the NPV of returns above variable costs (e.g. hired labor, fertilizer, seed, chemicals, machinery repairs, fuel, dryer fuel, interest, storage, crop insurance and miscellaneous), taken from Doster et al. (1998). Because returns to lime vary from year to year, returns are summarized for communication purposes in dollars per hectare per year ($ ha^-1 year^-1), using the annualization formula:

Annualized Value =   (2)

Crop response to pH is a complex phenomenon dependent on soil characteristics and other factors. Because of its complexity and its long term nature, few researchers have attempted to estimate pH response functions and no such functions have been published for Indiana conditions. To allow an initial evaluation of SSM profitability for lime, a general corn and soybean response function was estimated with data pooled over several locations in the U.S. and Canada.

Agronomic evidence indicates that corn and soybean response to pH should exhibit (a) decreasing marginal returns to lime application (Woodruff et al., 1987) and (b) a yield plateau beginning somewhere below pH 7.0 (Adams, 1969). A quadratic response and plateau (QRP) function was chosen because it fits the biological response and because it is widely used in the agricultural literature (Mengel et al., 1987; Gotway Crawford et al., 1997).

Mathematically, the QRP can be expressed as:

    (3)

where X is the input level and X^* is some specified value of X. The parameters are restricted, so that the curve and its first derivative are continuous at X^*.

The form of the initial diminishing returns portion of the yield response is unknown, so the quadratic can be thought of as a Taylor series approximation of that unknown function. The QRP can be estimated with ordinary least squares (OLS) using the grafted polynomial technique (Fuller, 1969), which imposes constraints on the coefficient estimates to insure smooth, continuous functions to the first derivative. Each constraint is used to determine one coefficient. The QRP estimation requires two constraints, leaving one independent variable in the estimation. In this case, the independent variable in the transformed data was (X*-X)² for pH less than X* and zero otherwise. The estimated coefficient was b, the linear portion of the response. The quadratic coefficient can be recovered from the constraint (c=-b/2X*). The join point is estimated selecting the X* value for which the regression of the transformed data has the highest R². The regression results for the transformed data with one independent variable are reported in Table 1.

Because available pH response data did not include yields at high pH levels, the estimated response function did not include the negative effects of high pH. This is because soil pH would have to be higher than 7.5 for crop yields to decrease in most soils. These negative effects were modeled using a weed science rule of thumb of a 1% decline in yields for each one tenth (0.1) increase in pH over 7.5 (Jordan, 1997).

Published data from controlled experiments were compiled from experiment stations in Alabama, Delaware, Florida, Georgia, Illinois, Indiana, Iowa, Kentucky, Minnesota, Mississippi, Missouri, Nebraska, Ohio, Ontario, Pennsylvania, South Carolina, Virginia and Wisconsin. The data are for corn and soybeans. Data from experimental plots were sought for at least two variables: soil pH and crop yield. Bongiovanni (1998) gives the data and sources.

Experimental data are converted and reported as relative yields (percentage of maximum), following the methodology used by McLean and Brown (1984). This methodology allows the pooling of data from diverse areas and various sources without significant bias. The next step was to convert the relative yields reported in the tables to representative yields for Indiana. The values for representative yields were taken from Doster et al. (1998), corresponding to average yields of 8315 kg ha^-1 for corn and 2849 kg ha^-1 for soybeans. These averages are the yield values used to convert the estimated relative yields to absolute yields.

In terms of relative yields, the pH response function for corn is:

Relative Yield  (4)

According to the estimated regression, corn yield increases to a pH of 6.8 and then approaches a plateau with a relative yield of 97.96% (8145 kg ha^-1). The reason why the plateau level is reached at 97.96% (and not at 100% of relative yield), is because the regression estimates average response with error in both directions. This means that there are observations above and below the OLS estimator. Regression comparative statistics are shown in Table 1.

The estimated production function in terms of relative yields is:

Relative Yield  (5)

According to the estimated regression, soybean yield increases to a pH of 6.8 and then approaches a plateau with a relative yield of 95% (2706 kg ha^-1). Regression comparative statistics are shown in Table 1.

Table 1: Estimated corn and soybean production function coefficients and associated t-ratios (in parentheses).

*, ** Denote significant at the 0.05 and 0.01 levels of significance, respectively.
⁺ Where X = (6.8 – pH)² if pH 6.8 and X = 0 otherwise

Field soil test data to test this simulation model were taken from three sources: (1) the Ph.D. thesis of Karr (1988), which examined six fields in southwestern Indiana, sampled on a 0.04-ha grid; (2) data from seven fields of Purdue’s Davis Farm (Top-Soil Testing Service, 1994), sampled on a 1-ha grid; and (3) data provided by Lynn Harvest Land Co-op, from nine fields sampled on a 1-ha grid. Lynn, Indiana is located in the east central part of the state. For the Karr fields the 0.04 ha cells were grouped into roughly square 1-ha and 0.4-ha grids for the analysis. The soil sample for the 0.04-ha cell nearest to the center of the 1-ha or 0.4-ha grid was used to represent that grid.

Quantities of lime applied per strategy for the three locations (i.e., Karr, Purdue’s Davis Farm and Lynn Coop) are shown in Table 2.

Table 2. Quantities of lime applied per strategy for the three locations.

Lime requirement (LR) for agronomic recommendations was calculated with the method from Watson and Brown (1997), who provide a table with the lime required to reach a desired pH level, according to the present lime indexes. This table is the same used by Vitosh et al. (1995). Thus, LR was estimated for each grid with a spreadsheet equation, based on the original pH soil test (pH₀).

LR for economic recommendations was calculated using marginal analysis, which states that when the value of the increased yield from added lime equals the cost of applying one additional unit, profit is maximized; or when marginal value product equals marginal factor cost (MVP = MFC). In this case the MVP is the NPV of marginal returns over the four-year planning period.

To calculate LR for a four-year period, lime carryover was estimated through the change in pH. According to Mengel (1997), there are two major factors which cause pH to drop. One is the removal of calcium and magnesium through cropping and the other is N fertilizer application and N transformation processes in the soil that add hydronium ions (H⁺), which must be neutralized. Other factors include leaching of base-forming cations, acid deposition, and nitrification of organic N. In other words, with normal cropping, the decrease in soil pH is a function of crop uptake, of nitrogen acidification, and of the buffering capacity of the soil. Using the values given by the Potash and Phosphate Institute (1997), total lime consumption was estimated as 0.78 tons ha^-1 year^-1 for corn and 0.34 tons ha^-1 year^-1 for soybeans, or as stated by Mengel (1997): 2.24 tons ha^-1 of lime every four years in a corn-soybean rotation.

Having this value of lime consumption, change in pH was estimated for each individual grid cell by modifying the equation from Black (1993):

    (6)

where:

pH_t = pH in year t resulting from lime application in year 1, (t=1,2,3,4)
Bs = pH buffering capacity of soils
LA = lime applied in year 1
LC_z = lime consumed in the previous period of time considered

A few general assumptions are necessary to complete the study.

1. All other production factors are constant. The only factor considered in determining yields is the pH of the soil.

2. Soil testing and applications are done by custom operators the fall preceding the first crop season. A simplifying assumption is that all pH corrections occur the first year. Recommendations over 9 tons per hectare are assumed to be split between fall and spring preceding the first crop.

3. LR assumes the use of agricultural limestone with a neutralizing value of 90%, which is incorporated in the first 0.2 meters of soil with conventional tillage (Vitosh et al., 1995).

4. The applicator is capable of delivering the required rates with VRA. For simplicity, rates are varied by grid of 0.4 or 1 hectares. No interpolated maps are used. Use of interpolated maps would add a confounding variable. Lime rates and hence returns are sensitive to the interpolation method (e.g., inverse distance, krigging), but no one knows which interpolation method maximizes returns. In addition, interpolation would be a problem on small fields with only a few grids.

5. Inflation is not considered in this study. Therefore, all the values are given in real terms. The discount rate used is 10 %.

6. Corn price: $0.10236 kg^-1 and soybean price: $0.23332 kg^-1 (Doster et al., 1998).

7. Cost of agricultural lime (90% neutralizing value): $24.26 per metric ton, including transportation (Delphi Limestone, 1997).

8. Conventional lime spreading $7.41 per ha; extra cost of lime spreading with VRA: $7.41 per ha over conventional spreading cost; cost of soil sampling: $2.47 per ha and cost of soil analysis: $5.50 each (Swaim, 1997).

9. Other costs of production were taken from Doster et al. (1998) and interpolated for the estimated yields within each grid.

To observe the effects of the five strategies for the three locations (i.e., Karr, Purdue’s Davis Farm and Lynn Coop), mean results for all fields are shown in Figure 1. These results represent the case in which the farmer has no previous information on the pH of the fields tested. For instance, this may be the case when a producer rents or buys land. In many cases, farmers have some information about pH and need for lime because of cropping practices and the elapsed time since the last lime application. In those cases they can concentrate on fields that they suspect need lime.

 Figure 1: Overall Mean Annual Returns by Strategy for All Fields

For the baseline case, the most profitable option is SSM-Economic, which gives a 4.82% improvement in return above variable cost or $19.55 ha^-1 year^-1 more than WFM. SSM-Agronomic is the third most profitable option, with a 1.78% improvement in return above variable cost or $7.24 ha^-1 year^-1 more than WFM. WFM provides economic benefits over the option of doing nothing. Information Strategy is less profitable than SSM with the economic rule, but more profitable than SSM Agronomic. Information strategy returns $14.38 (3.54%) more than the base case of WFM. It is also $7.14 ha^-1 year^-1 (1.73%) higher than SSM-Agronomic, although it is $5.16 ha^-1 year^-1 (1.21%) lower than SSM-Economic.

If only fields where lime was applied are considered, the benefits of the SSM strategies are higher. For Karr data, 3/6 fields need lime for all strategies. For Lynn Coop data, with WFM, 4/9 fields need lime; with SSM, all fields needs lime; and with the information strategy, 8/9 fields need some lime. For Davis Farm data, with WFM, 4/7 fields need lime; with SSM, all fields need some lime; and with information strategy, 6/7 fields need lime. The higher benefits that would be obtained from sampling and testing only the fields needing lime, could be achieved only by the farmer who has previous information about his fields and can focus only on those fields that probably need lime.

The most profitable option when only fields needing lime are considered is SSM-Economic, which gives a 5.80% improvement in return above variable cost or $23.45 ha^-1 year^-1. SSM-Agronomic is the third most profitable, with 2.60% improvement or $10.53 ha^-1 year^-1 more than WFM. The benefit of the information strategy is slightly higher than in the all fields case: $16.06 ha^-1 year^-1 (3.97%) higher than the base case of WFM.

To observe the change in variability in pH and yields, the spatial standard deviation for each field was estimated. Mean initial pH and mean pH of year four were compared for each strategy and data set. For yield, corn was chosen as the reference crop, and yield without lime application was compared to yield of the third year under each strategy.

On average, all site-specific strategies tend to decrease estimated spatial variability in yields. The decrease in the standard deviation of the yield was 132.32 kg ha^-1 for the information strategy and 178.72 kg ha^-1 for both SSM strategies, while the WFM standard deviation decreased by 55.81 kg ha^-1. This decrease in yield variability may be linked to a decrease in the variability of returns with site-specific management, as reported by Lowenberg-DeBoer and Aghib (1997).

As shown by Figure 1, strategies can be ranked with respect to profitability in descending order: (1) SSM-Economic, (2) Information, (3) SSM-Agronomic, (4) WFM,. (5) Do nothing. When locations are considered individually, SSM-Economic also ranks first, although the ranking for the other strategies differs (Table 3). For Karr data (1-ha grids), the ranking is (1) SSM-Economic, (2) SSM-Agronomic, (3) Information, (4) WFM, (5) Do nothing. For Karr data (0.4-ha grids), the ranking is (1) SSM-Economic, (2) Information, (3), WFM, (4) SSM-Agronomic, (5) Do nothing. For Davis Farm data, the ranking is (1) SSM-Economic, (2) Information, (3), Do nothing, (4) WFM. (SSM-Agronomic was not available in this data set). For Lynn data, the ranking is (1) SSM-Economic, (2) Information, (3), SSM-Agronomic, (4) Do nothing, (5) WFM.

Table 3. Mean Annual Returns by Strategy for All Locations.

Karr data set was used as the basis for a sensitivity analysis for 0.4-ha grids, because it is the only data set sampled at 0.04-ha. With 0.4-ha grids four fields out of six require some lime. Results are presented with respect to WFM with a 1-ha grid (Figure 2).

Figure 2: Comparative Annual Returns of Soil Sampling Grid Size for All Fields in Karr Data.

The 0.4-ha grid does not show economic benefits over the 1-ha grid, because of the cost involved on sampling at a higher intensity. All site-specific strategies show lower returns for 0.4-ha grids than for 1-ha grids. With 0.4-ha grids, only the SSM-economic strategy shows a modest increase in returns over WFM. The information strategy has almost exactly the same return as WFM, because benefits of fine tuning the lime rate are almost exactly offset by the cost of 0.4-ha sampling.

Given uncertainty about appropriate VRA fees, one sensitivity test of particular interest is the effect of fee increases. The baseline assumption is a $7.41 ha^-1 additional fee for VRA. Complete sensitivity testing results are given in Bongiovanni (1998).

With a $14.83 ha^-1 charge for VRA, the most profitable option continues to be SSM-Economic, which the highest return above variable cost over time: $424.02 ha^-1 year^-1, $1.11 below the annual return with the assumed $7.41 ha^-1 extra cost of VRA (Figure 3).

Figure 3: Comparative Annual Returns of Increasing the Charge for VRA

The decrease in the annual return is less than with the $7.41 ha^-1 VRA cost because the fee is spread over the four years of the soil sampling cycle. SSM Agronomic and SSM Economic do not fall by the same amount because SSM Economic applies lime to more grids than SSM Agronomic. The information strategy is the second best choice, with a difference of only $4.05 with respect to SSM-Economic, down from the $5.16 of difference with VRA at $7.41. The higher the extra cost of VRA, the greater the advantage of information strategy. At a VRA fee of $27.68 ha^-1, the information strategy becomes the most profitable option.

To test sensitivity of results to commodity prices, results were recalculated at the minimum and maximum prices reported in the period 1970-1996 by the Indiana Agricultural Statistics Service (1996). The minimum corn and soybean prices were reported in October 1986. They were $0.05472 kg^-1 and $0.16865 kg^-1, respectively. The maximum corn price is $0.16968 kg^-1 in April 1995 and the maximum soybean price is $0.32885 kg^-1 in July 1987.

With a decrease in the market price of commodities (i.e., at the new price of $0.05472 kg^-1 for corn and $0.16865 kg^-1 for soybean), the most profitable option is still SSM with the economic rule, which gives a 9.48% average improvement in returns, or $12.48 ha^-1 year^-1 more, compared to WFM. Information strategy is the second best choice, with a 9.41% improvement in returns, or $12.40 ha^-1 year^-1 more than WFM. SSM-Agronomic is the third best choice, with a 3.29% improvement in returns, or $4.35 ha^-1 year^-1 more than WFM.

With an increase in the market price of commodities (i.e., at the new price of $0.16968 kg^-1 for corn and $0.32885 kg^-1 for soybean), the most profitable option is still SSM with the economic rule, which gives a 3.72% average increase in returns, or $29.65 ha^-1 year^-1 more than WFM. Information strategy is the second best choice, with a 3.11% improvement in returns, or $24.78 ha^-1 year^-1 more than WFM. SSM-Agronomic is the third best choice, with a 1.43% improvement in returns, or $11.39 ha^-1 year^-1 more than WFM.

GENERAL CONCLUSIONS

The baseline results indicate that with either the SSM agronomic recommendations or the economic optimization, VRA of lime is profitable as a stand-alone technology. The overall results indicate that SSM-Agronomic provides an increased annual return of $7.24 ha^-1 (+1.78%) over WFM. SSM-Economic provides an increased annual return of $19.55 ha^-1 (+4.82%) over WFM. The information strategy provides an increased annual return of $14.38 ha^-1 (+3.54%) over WFM, which lies between SSM-Economic and SSM-Agronomic. Because of the extra cost of sampling, returns are higher on a 1-ha grid than on a 0.4-ha grid. SSM-Economic ranks as the most profitable production strategy in all locations.

Sensitivity testing indicates that SSM and information strategies for lime are more profitable than WFM over a wide range of prices and conditions. Doubling the cost of VRA services did not change the ranking. Information strategy becomes the most profitable option at a VRA charge of $27.68 ha^-1 over the uniform rate fee. Estimates indicate that spatial variability of yield decreases with SSM and information strategies.

Given the experience in this study, the priority research needs in the area of SSM for lime include: cheaper methods for testing spatial variability of soil pH, improved understanding of crop response to lime and site-specific field testing of the agronomics and economics of variable rate lime. Accurate sensors for soil pH will be developed eventually, but until that time we will rely on soil sampling. Grid size and alignment of the sample points for grid sampling are important questions. Guided sampling designs using soil type, topography, remote sensing and other information also need to be considered.

The results of this study depend to a large degree on the reliability of the crop response functions estimated with sparse data collected under a wide range of conditions. This reliability is barely adequate for a first approximation study and inadequate to capture the specifics of the range of conditions under which lime might be used. Improved lime response models are needed that include the effect of soil characteristics as well as interactions with other nutrients and management practices. The long run benefit of such improved models would be decision support systems that would help producers improve productivity and profitability.

Our model uses soil data from three sources: Karr, Davis Farm and Lynn Coop. While Karr data uses 0.04-ha cells to account for the undetected variability of the larger grids, Davis Farm and Lynn data may have some weakness associated with the use of the cell technique, as opposed to interpolation methods.

Simulation studies can only do so much. They are useful in providing timely answers to urgent questions. They do not replace gathering and analyzing field data. Yield monitors and other precision farming technology have made it easier and cheaper for farmers and researchers to collect that field data. On-farm trials are needed to verify the economics of SSM of lime and to fine tune lime requirement estimates for site-specific conditions.

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FOOTNOTES