economic evaluation of topsoil loss in spring wheat production in the northern great plains, usa
TRANSCRIPT
ELSEVIER Soil & Tillage Research 37 (1996) 95- 112
soil& Tikge Research
Economic evaluation of topsoil loss in spring wheat production in the northern Great Plains, USA ’
Jeffery R. Williams ay * , Donald L. Tanaka b a Department of Agricultural Economics, Waters Hall, Kansas State University, Manhattan, KS 66506-4011.
USA
b US Department of Agriculture- Agricultural Research Service, Northern Great Plains Soil and Water Research Laboratory, Mandan, ND, USA
Received 27 June 1994; accepted 28 November 1995
Abstract
Relationships among topsoil removal treatments and additions of nitrogen and phosphorus fertilizer on dryland spring wheat yields in a wheat-fallow rotation were used to determine the on-site effects of topsoil loss and fertilizer applications on net returns and to estimate the value of soil. Yields estimated from a production function and corresponding net returns for spring wheat under alternative soil loss levels and fertilization rates were examined. A numerical optimization routine was used to determine the most efficient levels of fertilizer applications for farm managers at various levels of soil loss. The value of soil in spring wheat production was derived by estimating the accumulated discounted values of production from land without soil loss versus land with soil loss over various planning horizons. Production function estimates indicated that, when all variables were at their mean values and soil loss was varied, the first centimeter of soil loss reduced wheat yield from 1719 kg ha- ’ to 1709 kg ha- ‘, whereas the last centimeter of loss reduced yield from 1362 kg ha-’ to 133 1 kg ha-‘. Each additional centimeter of soil loss increased the yield loss. The economic analysis indicates that the optimum amount of N and P that should be applied increases with each increment of soil loss. Fertilizer reduces yield loss to some extent, but net returns continue to decline as soil loss increases. This result confirms that N and P fertilizers are imperfect economic substitutes for soil. Estimated soil values are a function of the farm manager’s planning horizon and the natural soil erosion rate. If erosion is occurring at a rate of 44.8 Mg ha- ’ year- ‘, the value of soil ranges from $59.33 ha- ’ for a planning horizon of
* Corresponding author. Tel.: (913) 532 4491; Fax.: (913) 532 6925; e-mail: [email protected]. ’ Kansas Agricultural Experiment Station Contribution No. 95-539-J.
0167-1987/96/$15.00 0 1996 Elsevier Science B.V. All rights reserved SSDI 0167-1987(95)01003-3
96 J.R. Williams, D.L. Tanaka/Soil & Tillage Research 37 (1996) 95-112
20 years to $305.48 ha-’ for a planning horizon of 68 years. The equivalent level annuity values of these estimates are $3.99 ha-’ year-’ and $10.58 ha-’ year-‘, respectively.
Keywords: Soil erosion; Fertilizer; Topsoil value; Spring wheat
1. Introduction
Topsoil loss and the subtle changes that it causes in soil properties can reduce crop productivity and create soil management problems (Tanaka and Aase, 1989). The rate of topsoil loss also can affect yields and the resulting net returns from crop production. Topsoil loss also influences net returns because of attempts of producers to compensate for it by applying fertilizers. Use of improved cultivars, better weed control, and applications of commercial fertilizers have been shown to offset the effects of soil loss and increase yields (Krauss and Allmaras, 1982). However, Young et al. (1985) report that, although net positive impacts of technological improvements have more than offset the negative yield impact of topsoil loss, some production loss has resulted from soil erosion. The proper measure of yield impact is the reduction in potential yield, i.e. the yield that could be achieved with reduced erosion.
Crop residue management for soil erosion control is critical during the spring wheat fallow period (Allmaras et al., 1994). Soil erosion control in the northern Great Plains for the spring wheat-fallow system is critical during early spring after the soil thaws and before spring wheat produces enough controlling roughness along the soil surface. As much as 90% of the surface residue present after harvest can be lost during the fallow period. For conventional fallow methods, most of the residue is horizontal on the soil surface and not very effective in controlling wind erosion. Wind erosion is the most serious erosion problem but has minimal, negative, off-site damage. Most of the soil is moved to adjacent field edges or fence rows.
Studies such as those by Larson et al. (1983) and Pierce et al. (1988) have attempted to estimate the accumulated yield reductions that would occur from soil erosion over a specified planning horizon. Both Klemme (1985) and Williams (1988) derived the annualized present values generated by various rates of annual percentage losses in yield of corn from soil erosion as a way of determining the additional production costs that would be acceptable in changing from conventional-tillage to no-tillage systems. These studies did not account for the loss of potential yield. Walker (1982) developed an erosion damage function to evaluate reduced-tillage for wheat in the Idaho/Washington Palouse area. The author found that erosion was economically rational on some deep soils, because the reduction in yields from the loss of the first layer of soil was small. Williams et al. (1993) found that risk-averse managers would not be willing to make an expenditure to control erosion to prevent 6.35 cm of soil loss over a 20-year period. The maximum amount they would be willing to spend was $12.84 ha-’ at the beginning of a 23-year period to prevent a second 6.35 cm of soil from eroding over that period.
The analysis performed in this study addresses not only yield loss in spring wheat-fallow rotation from erosion, but also the compensation for this potential yield loss with fertilizers. An economic evaluation was used to determine the effects on net returns of spring wheat for various combinations of instantaneous soil loss and fertilizer
J.R. Williams. D.L. Tanaka /Soil & Tillage Research 37 (1996) 95-I 12 97
application rates on an important northern Great Plains soil. The value of soil loss caused by erosion without the masked effects of technological progress over time then was estimated. The objectives were to determine: (a) the most efficient fertilizer application rates for each level of soil loss, (b) the net returns from fertilizing with the optimal amount of nitrogen (N) and phosphorous (P) at each soil loss level, and (c) the value of the eroded soil. The derived value of soil reported in this study is equivalent to the private annualized present value (equivalent level annuity) that dryland spring wheat-fallow producers could incur to reduce soil erosion in the northern Great Plains.
2. Procedures
Yields estimated from a production function and corresponding net returns for spring wheat after fallow under alternative soil loss levels and fertilization rates were exam- ined. A numerical optimization routine was used to determine the most efficient levels of fertilizer applications for farm managers at various levels of soil loss. The value of soil in spring wheat production was derived by estimating the accumulated discounted values of production from land without soil loss versus land with soil loss over various planning horizons.
2.1. Yields
The source of yield data used in the estimation of the production function is a study conducted near Sidney, Montana, from 1982 through 1989 (Tanaka and Aase, 1989). The study was initiated in the spring of 1982 on a Williams loam (fine-loamy mixed, Typic Argiborolls). Soil was removed mechanically using a small paddle scraper to 0.00, 6.35, 12.70, and 19.05 cm depths co~esponding to no soil removal, half of the Ap horizon, all of the Ap horizon, and all of the Ap horizon plus half of the BWf horizon, respectively. Soil removal treatments were whole plots (15 by 48 m). Three levels each of N (0, 33.6, and 67.2 kg ha-’ ) and P (0, 20.2, and 40.3 kg ha-’ ) fertilizers (subplots, 5 by 16 m) were used in a complete factorial arrangement. Fertilizers were broadcast to each soil removal treatment during each crop year and incorporated with a disk immediately prior to seeding spring wheat. Three replications of the split-plot experi- mental design were seeded to spring wheat after fallow, and three replications were fallowed in alternate years.
Topsoil removal is a means of gaining much needed information on the influences of erosion with all soil fo~ation factors equal. While this method as described in Tanaka and Aase (1989) may be artificial, it does agree with other methods. Topsoil removal and landscape positions studies such as one by Bauer and Black (1994) have resulted in similar crop responses. Both studies were conducted on a similar soil (Williams loan, fine-loamy, mixed, Typic Argiboroll). The resuIts of the two studies were very similar and the topsoil removal study was designed to minimize the possibility of water and soil movement from plot to plot.
Choosing soils on the landscape to represent varying of degrees of erosion may not be a good indicator of erosion in the northern Great Plains. A critical assumption has to be made that all soil formation factors are equal. This is not true. In the virgin state, the
98 J.R. Williams, D. L. Tanaka /Soil & Tillage Research 37 (I 996) 95-1 I2
topography greatly influences the climatic forces of soil formation. Therefore, soils in some positions on the landscape did not develop as thick of an A horizon or as mature of a soil profile. The difference in soil thickness on the landscape is not entirely due to soil erosion, but is confounded with the soil formation factors.
Assumptions in soil removal studies also need to be made. One assumption is that compaction and traffic during the removal phase did not influence some of the physicai soil properties. Data suggests that little or no change in physical properties occurred in the study by Tanaka and Aase (1989) which this study is based on. Another assumption is that natural soil erosion and topsoil removal result in similar crop responses. Topsoil removal results in a situation that could approach the worse case scenario in the first year or two because of the lack of sorting and mixing that occurs in natural erosion.
From the results of studies conducted in the northern Great Plains, it would appear that soil removal and landscape position techniques, while both make assumptions, produce similar crop responses in long-term studies.
One crop was planted and harvested on each plot every 2 years. Fertilizer was applied just before wheat was drilled in late April. Chemicals for weed control were applied after seedling emergence in early June. Wheat was harvested in August of each year. The land remained in fallow for 21 months following harvest. Stubble-mulch fallow was used, and tillage consisted of sweep tillage in late May of the following year. This operation was followed by two or three rod-weeder operations to control weeds.
lonely precipitation and potential evapotranspiration data were obtained. The growing-season precipitation and evapotranspiration data were included as variables in the production function to capture the impacts of growing-season climate on yield,
2.2. Production function
A quadratic production function was estimated using the field study data and data on annual weather variation. The function was defined as:
+j3,sPRiPi+&PRiNi+&6PRiET;+ei (1)
where: Y = kilograms per hectare of spring wheat produced, N = kilograms per hectare of N fertilizer, P = kilograms per hectare of P fertilizer, E = centimeters per hectare erosion or soil loss, PR = centimeters of precipitation during primary growing season (April through July), E’Z’ = centimeters of potential eva~~~spiration during primary growing season, e = error term, and /3 = parameters to be estimated. The model was estimated using ordinary least squares techniques. This functional
form was chosen because it is a conceptually satisfactory representation of yield-input
J. R. Williams, D. L. Tanaka /Soil & Tillage Research 37 (I 996) 95-l I2 99
relationships. The quadratic form allows for a positive yield when all or one of the independent variables are zero. This functional form also allows marginal products from added inputs to increase, decrease, or not change. Thus, the function can demonstrate increasing total product over a range, a peak output, and also decreasing total output over a range.
2.3. Net returns
Once the production function was estimated, annual per-hectare net returns over variable costs (net returns to land, overhead, risk, and management) per hectare for wheat in the US government commodity program were estimated using Eq. (2) which is the net return function.
When farm operators decide to participate in the US farm commodity program, they elect to forgo the potential income from crop production on set-aside hectares in exchange for minimum price protection (target price) on an established average crop yield (program yield). Participating farmers receive a deficiency payment per unit of program yield, based on the difference between the legislatively set target price and the market price or the legislatively set loan price (whichever difference is smaller). If the market price exceeds the target price, no deficiency payments are received. The maximum per unit deficiency payment, the target price minus the loan price, occurs when the market price falls below the loan price. The deficiency payment received is in addition to the income received from the sale of the crop produced. The deficiency payment per unit of measure is multiplied by the farm’s program yield for the specific program crop to determine the deficiency payment per hectare. Farmers also must remove an additional 15% of their commodity program based hectares from deficiency payment eligibility. These hectares are called the ‘normal’ flex hectares. On flex hectares, farmers may grow any crop (except fruit and vegetables), but the hectares are ineligible to receive deficiency payments. In short, crops on flex hectares provide returns similar to crops not employing the commodity program. Additional detail concerning the government program is available in Williams and Barnaby (1994).
Eq. (2) reports how net returns from wheat are calculated in this study using the government program provisions.
NR=[((max{P,,L) *Y)-(P;N)-(P;P)-PRODC-HARVC)*PA]
+ [(ma,{ O,( TP - max{ NPW,L})} * Y,) . (PA - FA)] - (SC. SA)
-(SFC.SFA), (2) where:
NR = net returns ($ ha-‘); P,,, = local market price of wheat ($ kg-i); L = national average commodity program loan rate for wheat ($ kg-‘); Y = estimated kilograms per hectare of wheat from the production function in Eq. (1); P, = price of N fertilizer ($ kg-‘); N = optimum rate of N fertilizer at a specific soil loss level (kg ha- * );
100 J.R. Williams, D.L. Tanaka/Soil & Tillage Research 37 (1996) 95-112
Pp = price of P fertilizer ($ kg-’ ); P = optimum rate of P fertilizer at a specific soil loss level (kg ha- ’ ); PRODC = all other variable production costs that are not functions of N and P input levels and output level Y ($ ha- ’ ); HARVC = harvest cost on planted hectares ($ ha- ’ ); PA = planted hectares as a percent of total base hectares including planted, fallow, and set-aside hectares (%); TP = commodity-program wheat target price ($ kg-’ ); NPW = national average wheat price, which is equivalent to P, in this study ($ kg-‘); Yp = commodity program wheat yield (kg ha-’ ); FA = flex hectare requirement as a percentage of total hectares including planted, fallow, and set-aside hectares (%); SC = maintenance cost on set-aside hectares ($ ha-’ ); SA = set-aside requirement as a percent of total hectares including planted, fallow, and set-aside hectares (%); SFC = maintenance costs on fallow hectares ($ ha-’ ); and SFA = fallowed hectares as a percentage of total hectares including planted, fallow, and set-aside hectares (%).
2.4. Soil value
Once net returns were estimated for each level of soil loss, the value of soil was determined. This value was determined by estimating the present value of the differ- ences among the net return with no soil loss and net returns under increasing amounts of soil loss. This value was calculated for planning horizons from l-68 years and is described in Eq. (3). The 68-year time period is the time required to loose 19.05 cm of soil at a rate of 44.8 Mg ha-’ year-‘.
(3)
where: PVS, = present value of soil to year i in planning horizon ($ ha-‘); i = years in planning horizon; n = last year in planning horizon; r = real discount rate, where r = ((1 + n)/( 1 + i)) - 1 and n is a nominal interest rate and i is the inflation rate; NRC, = real net return in year i from treatment with conservation (no soil loss), and NRE, = real net return in year i from treatment with uncontrolled erosion. In the analysis, NRC, was held constant under the assumption that all soil is
conserved under a conservation plan. The value of NRC, was the net return from no soil loss. The value of NREi declined gradually over time from the net return under no soil loss to the value of the highest net return possible under each respective soil loss increment. Specific values of NRC, and NREi are reported in the results section. Because constant real prices and input costs per unit are used, it is appropriate to discount and annualize with a real discount rate.
J.R. Williams, D.L. Tanaka/Soil & Tillage Research 37 (1996) 95-112 101
Once the present value of soil was estimated, the annual amount that could be spent by the farm manager to prevent soil erosion also was reported. This value was the equivalent level annuity of PVSi and was calculated using Eq. (4).
A,=PVS,*[r*(l +r)“/(l ++ l] (4)
where Ai = annualized value of soil equivalent to the amount that could be spent each year
to conserve soil to year i ($ ha-’ ). All other variables are as defined in Eq. (3). The value of PVS, and, therefore, the
value of A, change as the planning horizon lengthens for a given discount rate.
3. Economic data
The 8 years of yield data from the 36 treatments, combined with the soil removal levels, fertilizer applications, and measures of precipitation and evapotranspiration, were used to estimate the quadratic production function. Once the production function was estimated, net returns over variable cost per hectare were estimated using Eq. (2). A brief explanation of the prices and estimates of variable costs used in the calculation of the net returns follows.
Wheat prices used in the analysis were the &year (1982-89) market prices for the Sidney, Montana area. These 8 years of prices were adjusted to 1990 dollars using the US Department of Agriculture index of crop prices received by farmers and averaged for use in Eq. (2). The loan rate, target price, and hectare reduction requirement for the 1992 commodity program were used. The program yield used in Eq. (2) for estimating the net return of each treatment was the estimated yield for the optimum level of N and P at each respective soil loss level. The target price and loan rate used for wheat were $.147 kg-’ and $.081 kg-‘, respectively. The hectare reduction requirement (set-aside) used for wheat was 5%. The analysis was based on per-hectare costs and returns including fallow costs. For this reason, the planted hectare costs of spring wheat were weighted by 0.475 (380 ha planted for each 800 ha), and the per-hectare costs of set-aside and fallow hectares were weighted by 0.025 and 0.50; respectively (20 set-aside ha and 400 fallow ha in each 800 total ha). The required flex hectares used for wheat was 15%. It was assumed that wheat was planted on the flex hectares, although deficiency payments were not received on these hectares. This was a typical management practice. Therefore, market returns were weighted by 0.475, and those from deficiency payments were weighted by 0.40.
The input levels for labor and machinery were based on Montana State University Cooperative Extension budgets for conventional-tillage spring wheat (Johnson et al., 1986). Labor costs were estimated using an input level of 0.86 h ha-’ for planted hectares and 0.79 h ha-’ for set-aside and fallow hectares. Set-aside hectares were assumed to be in fallow. A labor charge of $6 h-’ was used. The seeding rate was 2.47 kg ha-‘. Seed costs were $16.05 per planted hectare. Chemical costs were based upon application rates of 3.5 1 ha-’ of Diclofop ((I)-2-(4-(2,4-dechlorophenoxy) phenoxy) propanic acid) and 2.3 1 ha-’ of bromoxynil (3,5-dibromo-4-hydroxybenzonitrile). Total
102 J.R. Williams, D.L. Tanaka/Soil & Tillage Research 37(1996195-I12
chemical costs were $65.83 per planted hectare. Equipment and machinery expenses including depreciation were equal to $25.61 ha-’ for planted hectares and $18.11 ha-’ for set-aside and fallow hectares. Refer to Johnson et al. (1986) for a more detailed explanation of the cost estimates.
The remainder of the variable input costs, those that vary by treatment, are explained below. Fertilizer costs were estimated using the kilograms per hectare of N and P applied. The g-year average prices of ammonium nitrate (34-O-O) and triple superphos- phate (20% P) were used. Average costs were $.55 kg-i for N and $1.20 kg-’ for P. All fertilizer was assumed to be applied at planting. A charge of $.22 100 kg-’ was used to estimate the hauling expense. Interest on one-half of the variable input cost was charged at a nominal rate of 12%.
4. Results and discussion
4.1. Production function
Table 1 shows the values of the parameter estimates for the quadratic production function. The regression performed with the quadratic model provided a good fit for the data considered (adjusted R2 = 0.794). Most of the parameter estimates are statistically
Table 1
Parameter estimates for the quadratic production function for spring wheat yields in terms of topsoil removal
and fertilizer applications
Variable Regression T-statistic Variable
coefficient mean
Intercept 680.3268 14.53 l
Nitrogen (N)
N-squared (N*) Phosphorus ( P)
f-squared (P’) Erosion (El
E-squared ( E* 1 Precipitation ( PR)
PR-squared ( PR* ) Evapotranspiration (ET)
ET-squared (ET* ) E-N interaction (EN)
E- P interaction (EP) N-P interaction (NT’) PR- E interaction (PRE) PR - P interaction (PRP)
PR- N interaction (PRN) PR - ET interaction ( PRET)
- 0.0859 - o.ooo5
0.0438
- 0.0023 0.5502
- 0.0089
- 46.0837 0.5458
- 27.4333
0.2591 0.0014 0.0050 0.0009
- 0.0729 0.0084 0.0108 1.1122
-3.22 * 33.60 -1.70 ** 1881.60
0.99 20.16 -2.93 * 677.38
5.46 * 9.52 -2.41 * 141.13
- 17.14 * 11.38 18.06 * 146.48
-11.69 * 29.63
8.21 * 883.99 1.83 * * 320.04
3.90 * 192.02 2.75 * 677.38
- 14.25 l 108.41 3.79 l 229.45 8.19 * 382.41
17.16 * 333.91
l Significant at the 0.05 level. l * Significant at the 0.10 level. F value = 196.49; Adj R* = 0.794; number of observations = 864.
J.R. Williams. D.L. Tanaka/Soil & Tillage Research 37 (1996) 95-112 103
I_: , , , , , ,‘\::::: 0 2 4 6 8 10 12 14 16 18 :
Centimeters of Erosion
D
-+ N=O kg/ha -x- N=33.6 kg/ha -8- N=67.2 kg/ha
Fig. I. Wheat yield as a function of erosion at three N application rates.
significant at the 0.05 level. Individual parameter estimates and their signs are not directly interpretable, because they show the partial effects on yield of the variable they represent. Several variables make up the effect of a change in a single input level on yield.
Fig. 1 illustrates the impact of soil loss and N on yield when all other independent variables in Eq. (1) are at their mean values. The first centimeter of soil loss reduces yield by 10 kg ha-‘, whereas the last centimeter of soil loss reduces yield by 31 kg ha-’ when N application is 33.6 kg ha-‘.
The level of N fertilizer applied also has some impact on yield and is a substitute for soil. Without any soil loss, the yield at 0 kg ha-’ of N applied is 1653 kg ha-‘. Production function estimates indicate the same yield can be obtained at 5.42 cm of soil loss with 33.6 kg of N, or at 9.44 cm of soil loss with 67.2 kg of N (Fig. 1). At 8.89 cm of soil loss and no N fertilizer, the yield is 1499 kg ha-‘. The same yield can be achieved at 13.14 cm of soil loss and 33.6 kg ha-’ of N or at 16.66 cm of soil loss and 67.2 kg ha-’ of N applied (Fig. 1).
4.2. Economic combination of fertilizers
Although examining the physical relationship between soil erosion, N fertilizer application and yield is interesting, the analysis would be incomplete without an examination of the economic variables. Eq. (1) and Eq. (2) were used in an iterative process to determine the combination of controllable inputs that maximizes the net return and also to determine the incremental value of soil. A computer algorithm was
104 J.R. Williams, D.L. Tanaka /Soil & Tillage Research 37 II 996) 95-I 12
Table 2
Optimum levels of N and P applications, resulting yields and net returns at different soil loss levels
Soil loss a N P Yields Net return (cm) (kg ha- ’ 1 (kg ha-‘) (kg ha-‘) 6 ha-‘)
0.00 0.00 1.22 1.27 0.00 2.61
2.54 0.00 4.00 3.81 0.00 5.38 5.08 0.00 6.76 6.35 0.00 8.15 7.62 0.00 9.53 8.89 0.00 10.92
10.16 2.31 12.76 11.43 6.24 14.93
12.70 10.17 17.09 13.97 14.10 19.26 15.24 18.04 21.43
16.51 21.97 23.60 17.78 25.90 25.75
19.05 29.84 27.93
1580
1569 1556 1541
1526
1509
1471
1463
1465
1466 1467
1467
1466 1465
1463
36.63
35.01 33.29
31.49 29.59
27.61 25.52
23.37
21.09 18.82
16.47
14.13 11.71
9.26 6.80
4.28
a Each I .27-cm increment corresponds to a 0.5 inch soil loss.
used with EGq. (2) to determine which combination of N and P input levels maximize net returns at each level of soil loss. This was done by specifying the soil loss level and holding all other variables with the exception of N and P and those influenced by N and P at their mean values.
Although application of marginal value concepts found in economic theory can be used to dete~ine the optimal levels of erosion and fertilizer application mathematically when all output prices and input prices including the price of erosion are known, direct numerical methods were employed in this study to determine the optimal level of fertilizers to apply at various rates of erosion because the price or value of erosion is unknown. Then this information was used to derive the value of soil. The optimizer component of the electronic spreadsheet Quat~o Pro version 4.0 was used to iteratively determine the optimal levels of N and P at different soil loss levels.
Table 2 indicates that the economically optimal combination of N and P to use with zero soil loss is 0.00 kg ha-’ of N and 1.22 kg ha -’ of P. With each level of soil loss, the economically optimum amounts of N and P generally increase. An application of N is not economical until the amount of soil loss is 10.16 cm. Under the optimum economic combination of N and P, the first 2.54 cm of soil loss reduces yield by 24 kg ha-’ and the last 2.54 cm of soil loss reduces yield by 3 kg ha-‘. As soil loss accumulates and more N and P are applied in an attempt to compensate for it, net returns continue to decline, This indicates that, economically, N and P are imperfect substitutes for soil.
4.3. Net returns from fertilizing
The net return from fertilizing with the optimal amounts of N and P was determined at each level of soil loss. These results illustrate the importance of N and P rates from
J.R. Williams, l?.L. Tanaka/Sail & Tiifage Research 37 (1996) 95-112 105
Table 3 Net returns from feltilizing with the optimum amount of N and P at increasing levels of soil loss
Soil loss a Return from N Return from P km) $ kg-’ $ha-’ $kg-’ $ ha-’
0.00 - 0.013 0.02 1.27 0.027 0.07 2.54 - 0.041 0.17 3.81 - 0.056 0.30 5.08 - 0.070 0.48 6.35 - 0.085 0.69 7.62 0.100 0.97 8.89 0.113 1.22
10.16 0.005 0.01 0.134 1.72 11.43 0.013 0.08 0.153 2.26 12.70 0.022 0.22 0.173 2.87 13.97 0.03 1 0.43 0.200 3.85 15.24 0.039 0.70 0.223 4.77 16.51 0.048 1.05 0.245 5.78 17.78 0.056 1.45 0.268 6.89 19.05 0.065 1.93 0.290 8.10
a Each 1.27-cm increment corresponds to a 0.5 inch soil loss.
an economic perspective. Once the optimum combination of N and P was determined, the change in net return that would be received without one of the fertilizers being used (either N or P) was determined for each level of soil loss. The difference between the net return at the optimum combination of N and P and the net return without N but with P at its optimum level is determined. The results are reported in Table 3, Columns 2 and 3. The returns from using the optimal rate of N range from approximately $0.005 kg-’ to $0.065 kg-’ as soil loss increases from 10.16 to 19.05 cm. The return from N fertilizer becomes positive after almost 10.16 cm of soil has been lost, because no N is applied from an economic optimization perspective until this amount of soil has been lost. In other words, N costs more than it produces in value to that point. Its return then increases as additional soil is lost. The same procedure was used to determined the net return from fertilizing with P. The results are reported in Columns 4 and 5 of Table 3. The net returns range from approximately $0.013 kg-’ to $0.29 kg-‘. Returns from fertilizing with P increase for each level of soil loss.
4.4. Soil value
The value of soil was determined by comparing the difference in net returns from land where no soil was lost to the net returns from land that had soil loss. Table 2 reports the estimates derived from Eq. (1) and Eq. (2). The results indicate that the lower the level of soil loss, the higher the net return will be. The differences in net return (Column 5) between each pair of the first three successive 1.27 cm levels of soil removal are $1.62 ha-‘, $1.72 ha-‘, and $1.80 ha-‘. The amount continues to increase as soil removal increases. These differences are the values of yield lost from soil
Tabl
e 4
Pres
ent
and
annu
alize
d va
lues
of
so
il fo
r op
timum
N
and
P in
puts
Year
Cu
mula
tive
Opt
imum
N
Opt
imum
P
Yiel
d
soil
loss
(&
ha-‘)
(kg
ha
-‘)
(kg
ha-
’ )
(cm
ha
- ’ 1
0 1 2 3 4 5 6 7 8 9 10
I! 12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
0.00
0 0.
3175
0.63
50
0.95
25
I .27
00
1.58
75
1.90
50
2.22
2s
2.54
00
2.85
75
3.17
50
3.49
25
3.81
00
4.12
75
4.44
50
4.76
25
5.08
00
5.39
75
5.71
50
6.03
25
6.35
00
4.62
6 1
6.90
22
7.17
83
7.45
43
7.73
04
8.00
65
8.28
26
8.55
87
0.00
I .22
15
80
Net
retu
rn
with
out
cons
erva
tion
6 ha
-‘)
Net
retu
rn
with
co
nser
vatio
n a
6 ha
- ‘1
E
Diffe
renc
e Pr
esen
t An
nuity
@
ha-
‘1
value
Ye
ar
value
Ye
ar
1 to
II
I to
n
($
ha-‘)
6
ha-
‘1
c,
0.00
1.
57
1578
0.00
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108 J.R. Williams, D.L. Tanaka/Soil & Tillage Research 37f1996) 95-112
removal. If soil were lost instantaneously in 1.27 cm increments, these differences would be equal to the incremental value of soil. In other words, a comparison of no soil removal to higher soil removal (erosion) indicates the maximum amount a manager would be willing to spend ($ ha-’ year-‘) on soil conservation measures to prevent the increment of soil loss. The additional (marginal) value of soil for each of the soil increments is represented by the differences previously reported if soil were lost instantaneously. However, soil loss is gradual and not instantaneous. Therefore, the effects on yield and net return are gradual.
The amount a manager will be willing to invest in the current time period for soil erosion control depends upon the rate of erosion, the time value of money (real discount rate), and the planning horizon. Given the information in Table 2, a farmer faces a choice of conserving all soil and obtaining a net return of $36.63 ha-’ minus annualized conservation costs or of letting soil erode and obtaining a return of $35.01 ha-’ at a time when 1.27 cm has eroded or a return of $33.29 ha-’ when 2.54 cm has eroded. The Soil Conservation Service (SCS) estimates actual soil erosion during the 1980s in eastern Montana to be 33.6 to 44.8 Mg ha-’ year-’ for the Williams soil. The four 6.35cm soil-removal treatments in the experiment from which the data were obtained to estimate the production function are equivalent to 0, 896, 1926, and 3046 Mg ha-‘, accounting for differences in bulk density. The difference between no soil removal and 6.35 cm of soil loss is 896 Mg ha-‘. If soil in this wheat growing region is eroding at 44.8 Mg ha-’ year-’ without control, it would take 20 years to loose 896 Mg ha-’ and an additional 23 years to loose an additional 6.35 cm or 1030 Mg ha-‘. If the erosion occurs in a uniform pattern, approximately 0.3175 cm of soil will be lost each year in the first 20-year period, and 0.2761 cm each year over the next 23 years.
The optimal input combinations of N and P applications for each level of gradual soil loss and the resulting net return for an erosion rate of 44.8 Mg ha-’ year-’ are presented in Table 4. The value of soil lost in the first year discounted with a real rate of 3% is $0.37 ha-’ (Table 4, Column 9). This is equal to the discounted difference between variable NRC,, the net return with conservation of $36.63 ha-’ (Column 7) and the variable NRE,, the net return without conservation of $36.24 ha-’ (Column 6). This can be interpreted as the maximum amount a manager will be willing to pay in net return (give up per hectare) to continue to use a treatment with more erosion (soil loss)
instead of one with less under a l-year planning horizon. Column 9 of Table 4 reports the present value of soil as a function of the manager’s planning horizon from 1 to 68 years (every fifth year after the thirtieth year is presented to conserve space). If the manager’s planning horizon is 20 years, the present value of soil saved over 20 years would be $59.33 ha-‘. In other words, a manager would be willing to invest $59.33 ha-’ at the present time to prevent a soil loss of 896 Mg ha-‘, if the planning horizon is 20 years. This $59.33 in present value is equivalent to annually investing $3.99 ha-’ (Table 4, Column 10) to prevent erosion from occurring. If the manager has a planning horizon greater than 20 years, the present value of the investment and annuity will be more. If the planning horizon is 50 years, then up to $221.03 ha-’ could be invested. Fig. 2 shows the net present values of soil for the l- to 68-year planning horizons, for erosion rates of 44.8 Mg ha-’ year-’ and 33.6 Mg ha-’ year-‘.
Although, no unique real interest rate is available to use in such an analysis, average real discount rates in the United States have historically been approximately 3%. In the
J.R. Williams, D.L. Tanaku /Soil & Tillage Research 37 (1996) 95-112 109
- 33.6 Mglhafyr - 44.6 Mgbe/yr
Fig. 2. Present values of soil for two erosion rates by planning horizon.
early 198Os, real rates were much higher and have recently declined to levels closer to the historical average. The greater the real interest rate, the more reluctant a manager will be to invest in soil conservation because investment costs will be high relative to discounted returns. The lower interest rates become relative to returns, the more likely it is that investments in soil conservation will be made. For example, at real interest rates of 1% and 5%, the net present values of soil with a 20-year planning horizon and an original erosion rate of 44.8 Mg ha-’ year- ’ would be $78.62 ha-’ and $45.42 ha-‘, respectively, instead of $59.33 ha-’ at a 3% rate. The higher the price of wheat relative to production costs, the greater the value of soil will become and the more likely an erosion-control investment will occur.
5. Conclusions
The net return ($ ha-’ > criterion indicates that a manager will prefer to have the lowest level of soil erosion and apply a small amount of P fertilizer when erosion control is costless. Soil erosion prevention, however, is not without cost. Managers must make expenditures, if they wish to control soil erosion. Results of this study indicate that managers may make expenditures for erosion control, but the amount depends upon their planning horizon, uncontrolled erosion rate, and discount rate. If erosion is occurring at a rate of 44.8 Mg ha-’ year-’ and the planning horizon is 20 years, the net present value of soil conserved is equal to $59.33 ha-‘, given a real discount rate of 3%. If managers have planning horizons and investment alternatives for soil erosion control
110 J.R. Williams, D.L. Tanaka /Soil & Tillage Research 37 (1996) 9.5-112
that last longer than 20 years, the dollar amount of the investment increases. If a manager’s planning horizon and effective investment life for soil erosion control are 40 years, the present value of the investment is equal to $167.19/ha, and the annuity value is $7.23 ha-’ year-‘.
The equivalent level annuity values for the investment with I- to 68-year planning horizons ranges from $.39 to $10.58 ha-’ year-‘. The cost of using reduced-tillage systems to reduce soil erosion instead of conventional-tillage in a spring wheat-fallow rotation in eastern Montana (Major Land Resource Area 58A) ranges from $11.06 ha-’ for minimum-tillage to $26.11 ha- ’ for no-tillage. These costs represent the reduction in returns (weighted according to the same method reported in Eq. (2)) caused by changing from a conventional-tillage system to reduced-tillage system with constant yields, as reported by Johnson et al. (1986). Therefore, based on net returns, the likelihood that a manager would undertake soil conservation strategies by adopting reduced-tillage is small. The decision may be different, if greater conservation of soil moisture and other factors besides soil depth increase yields with reduced-tillage systems. These increased yields would result in more revenue to offset the cost of soil conse~ation.
Society may desire to base conservation policy decisions on a planning horizon that takes into account needs of future generations rather than only the time span (planning horizon) of the farm manager. Policy makers may choose to subsidize the cost of erosion control, because as this study demonstrates, productivity and, therefore, economic value are lost over an extended planning horizon. However, the current manager may be willing to make an investment that corresponds to a longer planning horizon (one longer than the manager’s own), if the value of soil conserved beyond the manager’s planning horizon can be capitalized into the value of land when it is transferred to the next farm manager. This would make a larger investment in soil conservation by the farm manager more likely. However, this decision will be cons~ained by the effective life of the soil conservation investment. The longer the effective life, for the dollars invested, the more likely it is that investment will take place. Again, the higher the net return from wheat production, the higher the value becomes for each increment of soil that potentially could be lost.
Benefits of controlling erosion to reduce the external or off-site costs of erosion are not considered. Off-site damage from soil erosion could be considerable in some areas, but in the case of wind erosion, off-site deposition of soil is usually very slow and subtle. The greatest economic impact from soil erosion in the northern Great Plains is from the loss of crop productivity, with minimal off-site impact.
Soil erosion and the decision to allow soil erosion or reduce the rate of erosion is a dynamic process. Therefore, a farm manager faces at least an annual decision of determining whether it is economical to allow erosion to occur without conservation or to make an investment to reduce the rate of erosion. If the managers planning horizon is constant in each subsequent year the economic incentive to conserve soil should increase because of the cumulative effect of soil loss on yield. This assumption may be valid if the current manager considers future generations in the decision framework. In other words, the economic benefit of soil conservation increases as soil loss accumulates as long as the managers planning horizon does not shorten. If the managers planning horizon grows shorter by a year in each subsequent year, then an evaluation of the
J.R. Williams. D.L. Tanaka /Soil & Tillage Research 37 (1996) 95-112 111
discounted stream of net returns from soil conservation in each subsequent year is required. This study does not consider the optimal time to undertake soil conservation practices, but could be used as a starting point for such analysis with some additional assumptions and research data concerning longer term expected yields. Saliba (1985) provides a review of studies which have attempted to address the dynamic decision making process largely using conceptual models. However, these modeIs do not address the trade-off between inputs such as fertilizer and soil erosion as this study does.
In addition to soil depth and productivity impacts in each subsequent year, production costs, commodity prices, institutional constraints, and technology vary and influence the soil conservation decision. Our analysis does not consider all of these variables in a dynamic decision process. It is limited to dete~ining the present value of soil given constant technology, prices, costs, and institutional constraints. For example, our static analysis did not consider the impact of improved technology (such as improved tillage practices) that may act as a complementary input with soil. If new crop production technology develops in such a way that soil becomes an even stronger complement in the production process, the value of soil would increase and this would encourage the use of more erosion control practices. Therefore, the vatue of the soil reported here would be too low. However, if crop production technology develops over time such that it is a stronger substitute for soil, the value of soil would decrease and also decrease the incentive for erosion control. Under these circumstances, the soil values estimated in the study would be too high. Further research that examines tillage and rotationa strategies under various soil loss increments as well as different price and cost structures would be useful. However, data does not exist to examine the entire dynamic decision process with accuracy.
References
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