An ecological and economic analysis of
phosphorus replenishment for Vihiga
Division, western Kenya
$
M.J. Soule
a,*, K.D. Shepherd
baEconomic Research Service, USDA, Washington DC 20036-5831, USA
bInternational Centre for Research in Agroforestry (ICRAF), PO Box 30677, Nairobi, Kenya
Received 10 December 1999; received in revised form 1 March 2000; accepted 13 March 2000
Abstract
Soil scientists have identi®ed phosphorus de®ciency as a major constraint to improved maize and bean yields in the highland areas of western Kenya. This study evaluated the eco-nomic costs and bene®ts as well as ecological impacts of dierent phosphorus replenishment strategies from both a farm-level and a regional perspective using an economic-ecological simulation model. The study associated soil properties with representative farm types and showed how the impact of soil fertility replenishment depends on initial soil conditions as well as the resource endowment level of the farmer. Two hundred and ten dierent strategies for phosphorus replenishment with dierent sources of phosphorus applied at various levels were analyzed for seven farm types. The farm-level analysis showed that phosphorus replenishment was generally pro®table for farms with low and medium pH (4.9±6.2) soils, but not for farms with high pH (6.2±7.0) soils. A regional analysis showed that bene®ts were higher when phosphorus replenishment was targeted to farmers with low and medium resource endow-ments on low and medium pH soils rather than spread evenly across all soil and farm types.
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Keywords:Soil fertility; Ecological economics; Simulation model; Cost-bene®t analysis; Kenya
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$ The views expressed in this article are those of the authors and do not necessarily represent policies
or views of the US Department of Agriculture, the Rockefeller Foundation or ICRAF.
* Corresponding author. Present address: Economic Research Service, US Department of Agriculture, Resource Economics Division, Room S4171, 1800 M Street NW, Washington, DC 20036-5831, USA. Tel.: +1-202-694-5552; fax: +1-202-694-5775.
1. Introduction
Soils de®cient in the major nutrients, nitrogen (N) and phosphorus (P), have been identi®ed as a major problem aecting crop productivity in much of sub-Saharan Africa (Mokwunye et al., 1996; Sanchez et al., 1997; Smaling et al., 1997). About 36% of the global tropics (1.7 billion ha) and 64% of the humid tropics are domi-nated by highly weathered soils with limited capacity to supply P. In the case of western Kenya, highly weathered soils that were naturally fertile have been degraded over many years through frequent cropping with insucient additions of organic or inorganic fertilizers. Farmers report that yields for the main food crop, maize, have declined over the years, and typical farm yields in the area are about 1.2 T haÿ1yearÿ1 over the two growing seasons (Shepherd et al., 1997). In contrast, experimental trials in the area with N and P additions often reach yields of 4±8 T haÿ1yearÿ1(Jaetzold and Schmidt, 1982).
P replenishment has been proposed as a strategy to quickly overcome the P de®-ciency and increase yields, farm income, household food self-sude®-ciency and soil productivity (Sanchez et al., 1997). P replenishment involves applying P in excess of crop requirements to build up levels of available soil P. This can be achieved rapidly by application of relatively large amounts of P to the soil in one year to immediately increase soil P and give residual eects for many years in the future. Alternatively, soil P can be built up over longer periods with smaller annual applications, but bene®ts will be smaller in the initial years.
The purpose of this research was to evaluate the costs and bene®ts of dierent P replenishment strategies from both a farm-level and a regional perspective for Vihiga Division in western Kenya. The objectives of this study were to evaluate: (1) how the impact of soil fertility replenishment varies with initial soil conditions and the resource endowment level and farm management practices of the farmer; (2) the trade-o between increased short-run economic bene®ts and sustained soil quality in the long-run; and (3) the regional bene®ts of selected P replenishment strategies.
2. Overall approach
Cost±bene®t analysis using the net present value (NPV) criterion was undertaken using a model that was developed for analyzing the economic and ecological impacts of improved soil management practices in the highlands of East Africa (Shepherd and Soule, 1998). The model was used to simulate many dierent P replenishment strategies in combination with possible annual nitrogen sources. Assuming that the farmer's objective is to maximize farm pro®ts, the strategy with the highest NPV is the most preferable. The model was also used to track changes in soil organic car-bon (C) over time as an indicator of long-term soil productivity and resilience (Young, 1997).
(e.g. farm size, cattle on-farm) and their current farming practices (e.g. fertilizer use). Soil conditions also vary across farms, and three soil types, based on low, medium and high levels of pH were analyzed. Finally, the incremental net bene®ts of P replenishment at the farm level were aggregated to the regional level to determine the regional bene®ts of P replenishment and the NPV of a regional investment in P replenishment. The aggregation was based on the number of farms of each type and associated initial soil conditions. Several approaches to targeting P replenishment were analyzed for their impact on aggregate net bene®ts.
2.1. The study area
The highlands of western Kenya represent a zone with high agricultural potential but severe nutrient depletion (Shepherd et al., 1996). There are two cropping sea-sons: the long rains from March to July and the short rains from August to November, with rainfall totaling 1500±1800 mm annually. The landscape is gently undulating, with predominantly Nitisols and Acrisols and Ferralsols (Andriesse and Van der Pouw, 1985). Vihiga Division in Kenya was chosen for this analysis because it is broadly representative of other areas of the East African highlands found in Uganda, Ethiopia, and Madagascar in terms of soils, climate, technology, and pro-duction potential (Braun et al., 1997). In addition, there is a relative abundance of research data from the Vihiga area. Although Vihiga is more densely populated (over 1000 persons kmÿ2) than some of the other highland areas, it does represent what the future may hold for other parts of the highlands as population pressure increases. The Vihiga area has a mixed crop/livestock farming system, described by Shepherd and Soule (1998). Due to high population densities and the sub-division of farms for inheritance, farm sizes tend to be small. Average farm size is 0.6 ha with many farms as small as 0.2 ha (Shepherd and Soule, 1998).
2.2. Farm-level simulation methods
In the ecological sub-model (Shepherd and Soule, 1998), soil C, N and P cycling and P- or N-limited plant production were simulated for one aggregated ®eld compartment which included a maize/bean intercrop, fodder grass, hedges, woodlots and pasture but excluded the homestead area. Typical management practices for each farm type were speci®ed based on ®eld research. The model was operated on an annual time step, and simulations were run for 10 years. Production and nutrient ¯ows for the two cropping seasons within each year were aggregated. Nutrient levels each year were determined by initial soil conditions and organic (crop residues, livestock manure, compost, asym-biotic N ®xation) and inorganic (N and P fertilizers and atmospheric deposition) nutrient additions. N inputs through biological nitrogen ®xation were also included. After nutrient removals through crop harvests, leaching, and erosion, the nutrient status of the soil for the next year was determined.
divided into several enterprises: food crops, fodder grass, shrubs, hedges, trees and dairy. Data were entered for each enterprise using crop budgets, which speci®ed the quantity and value of all inputs and the value of outputs. Farm revenue and farm returns were calculated for the whole farm by aggregating the revenue and returns from all the enterprises. Farm revenue was de®ned as the sum of all farm products times the price of each product. Farm returns were calculated as farm revenue less all costs of production, including family labor valued at its opportunity cost. The opportunity cost of family labor was set equal to the annual average market wage for hired agricultural labor.
Cost±bene®t analysis was used to compare options (Lutz et al., 1994). The NPV of the stream of farm returns was calculated over 10 years using a discount rate of 20%. A 20% discount rate is commonly used by the World Bank for analysis of similar agricultural projects (Lutz et al., 1994; Current et al., 1995). A NPV of zero implies that the investment in P replenishment is earning a return just equal to the discount rate. For the discounted cash ¯ow analysis, a distinction was made between annual fertilizer inputs and investment dressings of fertilizer such as a large application of P made in the ®rst year of the analysis. For annual fertilizer applications, the cost of fertilizer was accounted for in the annual crop enterprise budget. For P replenish-ment, the investment was considered to be made in year zero (the beginning of the ®rst production season) and included the cost of the fertilizer plus transport and labor for application.
2.3. Characteristics of farm types
Data sets were compiled for three representative farm types in Vihiga Division to re¯ect dierences in resource endowments (farm size, cattle owned, etc.) The three composite farm types were developed through participatory research with farmers in the area (Crowley et al., 1996). Wealth ranking (Grandin, 1988; Crowley, 1997) was used to allow farmers in an area to stratify local households into three categories by resource endowment. Representatives of households who had been identi®ed as being either resource high, medium or low were then interviewed in groups with other farmers like themselves in order to create a composite representative farm of each category. The data from the participatory method were veri®ed with data from two random sample surveys of soil fertility management practices (Ohlsson et al., 1998; Crowley and Carter, Soil Fertility Management Survey, unpublished data, TSBF, Nairobi, 1995).
Among the three farm types (high, medium and low resource endowment, abbre-viated HRE, MRE and LRE, respectively), there were large dierences in farm size, quantity and quality of livestock, and soil and plant management (Table 1). For example, the composite LRE farm does not have a woodlot, and thus the family is forced to use crop residues for fuel, thus depriving the soil of the crop residues. By contrast, the HRE farm has a woodlot to provide family fuelwood and is thus able to return crop residues to the ®eld or feed them as fodder to livestock. The LRE farm has no cattle and thus produces no milk and no manure for fertilizer.
area fall within the LRE category, while 35% are MRE and 10% have a HRE (Crowley and Carter, Soil Fertility Management Survey, unpublished data, TSBF, Nairobi, 1995; ICRAF, 1996). The LRE families and many of the MRE families may be generally classi®ed as poor. The high percentage of the rural population living in poverty has been con®rmed by other studies (Narayan and Nyamwaya, 1995).
2.4. Initial soil conditions
The bene®ts of P replenishment will depend on the initial soil conditions on farm as well as on farm management. To run the model for this analysis, it was necessary to specify four initial soil parameters: topsoil pH, soil C, clay fraction and labile P (Table 2). There was as much variability in farm soils as there was in farm resources and management, and we again reduced that variability by de®ning three repre-sentative soil types, based on topsoil pH. We based the three reprerepre-sentative soil types on a survey of topsoil samples (0±0.15 m depth) from cropped ®elds on each of 31 farms in Vihiga District (Shepherd et al., 1996, 1997). There was a fairly even
Table 1
Principal characteristics of composite low, medium and high resource endowment (LRE, MRE and HRE, respectively) farms in Vihiga District, western Kenyaa
Variable Units Farm resource endowment
Low (LRE) Medium (MRE) High (HRE)
Farm size ha 0.3 0.8 1.6
Local cattle number 0 1 1
Grade cattle number 0 0 2
Farm area in maize/beans % 61 60 27 Farm area in woodlot % 0 10 11 Farm area in fodder grass % 0 0 38 Farm area in homestead % 26 19 17 Crop residues used for fuel % 50 25 0 Fertilizer use kg haÿ1yearÿ1 0 0 124
a Source: wealth ranking and group budget interviews conducted by E.L. Crowley and M.J. Soule,
ICRAF; analysis of survey data (Ohlsson, Shepherd and David, unpublished data, Nairobi, ICRAF; Crowley and Carter, Soil Fertility Management Survey, unpublished data, Nairobi, TSBF).
Table 2
Values of initial soil parameters for three representative soil types Soil pH class
Low (4.9±5.7) Medium (5.7±6.2) High (6.2±7.0)
Topsoil pH 5.3 6.0 6.6
Soil carbon (%) 1.2 1.2 1.2 Clay fraction (kg kgÿ1) 0.32 0.32 0.32
distribution of pH values among farms: 35.5% of the farms had low pH (4.9±5.7), 29% of the farms had medium pH (5.7±6.2) and 35.5% had high pH (6.2±7.0). We determined the initial values for the other three soil parameters by taking the aver-age value of each parameter within each pH group. The fraction of the phosphate rock pool that solubilizes each year was varied with pH, with values of 0.47, 0.37, and 0.24 at soil pH values of 5.3, 6.0 and 6.6, respectively.
HRE farmers were assumed to have high pH soils as a result of using high levels of organic and inorganic nutrient inputs for many years, resulting in higher soil fertility (e.g. available soil P levels) than on LRE and MRE farms. The simulated trends in available soil P, using the typical nutrient input levels for HRE farmers, supported this assumption (Shepherd and Soule, 1998).
2.5. Input and output prices
The prices of inputs and outputs were based on a market price survey of 10 mar-kets in western Kenya in 1995±96. Small village marmar-kets as well as larger, regional markets were included in the survey. The markets were surveyed at three times dur-ing the year: pre-harvest when output prices are high, post-harvest when prices are low, and mid-season. Average annual prices across markets were used. Quantities of labor, seed, fertilizer, livestock minerals and concentrates, and other production inputs were based on the ®gures provided in published reports from farm and on-station research in the area. Some labor data was also derived from unpublished sur-vey data (Swinkels, ICRAF, Nairobi, 1992). In particular, since labor is the major input in this farming system, and since larger yields require more labor to harvest and transport, an equation was derived linking labor days per hectare to yield.
2.6. Farm-level simulations
Simulations of the soil fertility strategies applied to the maize/bean intercrop and fodder grass areas on the farm were run for seven combinations of farm type and initial soil conditions (LRE, three pH levels; MRE, three pH levels; and HRE, high pH level only). Three sources of P were considered: triple super phosphate (TSP), phosphate rock (PR) and diamonium phosphate (DAP). Nine application levels of TSP and PR were considered as listed in Table 3. Some of the simulated P applications occurred only in year 1, while others were spread over 5 or 10 years. DAP was the most commonly used source of P in the area at the time, and since it also contains N, its use was considered as an annual application rather than a one-time large dose. Two appli-cation levels of DAP were considered, and a scenario with no P was also evaluated.
were small, at about 6 kg N haÿ1and 0.6 kg P haÿ1, because of the small hedge area per unit crop land. Two scenarios of IF were considered, one with 25% of the crop-ped area under improved fallow each year for 1 year, and the other with 50% of the cropped area under the IF each year for 1 year. The amount of nutrient added by the IF depended on soil N and P supply according to the model dynamics, and varied with farm and soil type. When half of the cropped area was under IF, the average annual N inputs ranged from 25 to 65 kg haÿ1of crop land in LRE and MRE but were about 60±85 kg N haÿ1in HRE. The amounts of P inputs were about 5% of those values. The application of 30 kg N haÿ1in the form of urea in combination with both scenarios of IF and the BT scenario was also considered. Combining all the possible P and N scenarios, 210 simulations were run for each of the seven farm type/initial soil condition cases.
2.7. Regional analysis methods
The regional ®nancial analysis of P replenishment was built up from the farm-level analysis of the seven farm types, following methods of agricultural project analysis (Gittinger, 1982). Farm types were aggregated as follows. Vihiga Division has 8000 ha with an average farm size of 0.6 ha (Republic of Kenya, 1995). We assumed that 10% of the land is not agricultural (roads, urban areas, etc.), which gives approxi-mately 12,000 farm households on 7200 ha, in the Division. Using the distribution
Table 3
P and N strategies simulated
P strategya N strategy
No P No N
TSP, one time, 100, 200 or 250 kg P haÿ1 Urea, annual, 30 kg N haÿ1
TSP, one time, 100, 200 or 250 kg P haÿ1
followed by annual maintenance applications of 25 kg P haÿ1
Urea, annual, 60 kg N haÿ1
TSP, annual for 5 years, 25 or 50 kg P haÿ1 Urea, annual, 120 kg N haÿ1
TSP, annual, 10 kg P haÿ1 Improved fallow with sesbania covering
25 or 50% of the maize/bean area PR, one time, 100, 200 or 250 kg P haÿ1 Improved fallow with sesbania covering
25 or 50% of the maize/bean area; plus urea, 30 kg N haÿ1annual
PR, one time, 100, 200 or 250 kg P haÿ1
followed by annual maintenance application of 25 kg P haÿ1
Biomass transfer with tithonia, 25% of hedge area assumed to be tithonia
PR, annual for 5 years, 25 or 50 kg P haÿ1 Biomass transfer with tithonia, 25% of
hedge area assumed to be tithonia; plus urea, 30 kg N haÿ1annual
PR, annual, 10 kg P haÿ1
DAP, annual, 25 or 50 kg P haÿ1
of farms sizes above, this yields 12,000 farms on 7260 ha, which is within 1% of the reported 7200 farm hectares in Vihiga. To aggregate the seven farm types to the regional level, we ®rst estimated the number of farms that fall into each of the seven categories. From the soil survey data, 35.5% of farms had low pH, 29% had med-ium pH and 35.5% had high pH. The well-managed HRE farms were expected to have high pH, so all HRE farms, or 10% of all farms, were allocated to the high pH category. The LRE and MRE farms were allocated to the high pH category according to their relative weights, as shown in Table 4. Note that the highest per-centage of farms, 21.7%, is in the LRE, low pH category, but that most hectares, 26.7%, are in the HRE, high pH category.
For the aggregation of bene®ts, we ®rst calculated the incremental net bene®t of P replenishment for each farm type for each year. The incremental net bene®t is the annual net bene®t of P replenishment over and above the net returns earned from the current practice. We then aggregated the incremental net bene®t over all farms that are involved in the P replenishment project and calculated the NPV at the regional level. The selection of the discount rate used in calculating the NPV for regional projects of this type is controversial (Arrow et al., 1995). Therefore, the NPVs for a range of discount rates (1, 10, 20 and 30%) were used. Aggregation bias was reduced by the selection of farm types that are based on average farm sizes and that face similar resource constraints and are using similar technology and manage-rial ability (Hazell and Norton, 1986).
The analysis was conducted on the most promising strategy identi®ed from the farm-level simulations. Three scenarios were analyzed with dierent degrees of tar-geting to soil and farm types. Further scenarios were simulated to test the sensitivity of the regional analysis to key assumptions.
Table 4
Number of farms and number of hectares by resource endowment categoryaand pH level
Farm resource endowment and pH category No. of farms % of farms ha % of total ha
LRE farm size=0.3 ha
LRE, low pH 2603 21.7 781 10.8 LRE, medium pH 2127 17.7 638 8.8 LRE, high pH 1870 15.6 561 7.7 LRE subtotal 6600 55.0 1980 27.3
MRE farm size=0.8 ha
MRE, low pH 1657 13.8 1325 18.3 MRE, medium pH 1353 11.3 1083 14.9 MRE, high pH 1190 9.9 952 13.1 MRE subtotal 4200 35.0 3260 46.3
HRE farm size=1.6 ha
HRE, high pH 1200 10.0 1920 26.4 Total 12,000 100.0 7260 100.0
2.8. Some limitations
The simulated results were based on average, annual rainfall and assume that N and P supply, rather than rainfall, was limiting. The simulations did not allow for other factors that may limit yield responses when P and N are applied (e.g. pests and diseases, potassium de®ciency). In practice, crop rotations, application of other limiting nutrients and pest and disease control might be necessary to sustain yields. The model did not simulate increased eciency of uptake of applied P that can occur when small applications of P fertilizer are band or point-placed compared to broadcast. In addition, the model did not allow for changes in farmer behavior, such as changing crop allocations, in response to P replenishment.
P replenishment increases production of maize and beans at the farm and regional levels. This study assumes that the increases in supply would not be large enough to impact local prices beyond usual seasonal price ¯uctuations. This assumption is jus-ti®ed by the free trade in agricultural products at a larger regional scale, including eastern Uganda. However, sensitivity analysis was conducted to account for decrea-ses in farm returns that might be brought about by lower yields or lower prices than forecast in the base scenario.
The cost±bene®t analysis ignored potential externalities of P replenishment, both positive and negative, largely because there was very little information available for determining the existence, magnitude or value of the externalities. For example, it is possible that the P applied could wash o the soil during rains and pollute nearby streams. On the positive side, P replenishment might increase the productivity of other crops, and thereby decrease water run-o, or it might cause farmers to add more high value crops as their household needs for maize and beans are met on smaller land areas.
3. Results and discussion
3.1. Validation of yields
Simulated yields decreased with time in LRE and MRE but increased with time for HRE. However, the changes were less than 10% of their means over the simu-lation period. The average maize plus bean yield over the 10-year simusimu-lation was 1.3 t haÿ1for LRE, 1.4 t haÿ1for MRE and 3.4 t haÿ1for HRE. These yields compare with values from farmer-managed trials in the area (Shepherd et al., 1997) which had total yields (maize + intercrop) of 1.0 t for the 25% quartile yield and 2.9 t haÿ1 yearÿ1for the 75% quartile yield. Simulated yields appear slightly higher than actual yields because the model did not simulate pests and diseases. The grain yields for LRE and MRE were also close to average cereal yields in sub-Saharan Africa (World Bank, 1992).
3.2. Farm-level analysis
NPV, yield and soil organic C results for the seven farm simulations are summarized in Tables 5, 6 and 7. The ®rst row in each table re¯ects the current soil management practice for each farm type. The tables are limited to the 15 strategies which were most pro®table or provided the most information for evaluating the strategies. In addition, results for the low and medium pH farms in the LRE and MRE groups are combined. Since the values for the important soil variables (Table 2) were the same for low and medium pH, the results were the same for LRE, low and medium pH and MRE, low and medium pH, except in the case of PR applications. Since the PR solubility rate decreases as pH increases, the NPV of returns and yields was slightly higher at lower pH, but the change in soil organic C was not aected by pH.
As with all crop simulation models, results must be interpreted with care. Large changes in farm return, yield or soil C are more meaningful than small dierences. In general, any P input on the low and medium pH soils resulted in large increases in the NPV, while fertilizer N decreased the NPV. The lack of pro®tability of N fertili-zer for a wide range of soil types, given maize/fertilifertili-zer price ratios in Kenya, has also been shown by other research (de Jager et al., 1998). Comparing one large dose of P (say 100 kg P haÿ1of TSP) to smaller annual doses (say 10 kg P haÿ1of TSP), we saw that the NPVs and overall average yields were higher for the one dose case. This was because, with annual doses, bean yields increased slowly from year to year, but due to
Table 5
Selected simulation results, net present value (in KSH) of returns per farm for 10-year simulationsa
Scenario LRE Ð
Current practice 1390 10,800 16,770 39,510 110,470 No P, no N 1390 10,800 16,770 39,510 113,250 No P, 30 kg N haÿ1
ÿ170 6330 12,990 28,650 97,150
No P, 0.5 of area in IF 610 3880 14,120 22,700 110,100 No P, BT 510 9780 15,540 37,980 110,900 TSP, 200 kg P haÿ1, no N 7940 8010 35,610 35,770 99,660 a LRE, MRE, HRE, low, medium, high resource endowment, respectively. TSP, triple super
Table 7
Selected simulation results, percentage change in soil organic carbon stock (0±0.15 m) over 10-year simulationsa a LRE, MRE, HRE, low, medium, high resource endowment, respectively. TSP, triple super
phos-phate; PR, phosphate rock; DAP, diamonium phosphos-phate; IF, improved fallow; BT, biomass transfer. Table 6
Selected simulation results, average annual maize/bean yields (kg haÿ1) for 10-year simulationsa
Scenario LRE Ð
Current practice 1040/230 1040/740 1150/240 1280/680 2600/820 No P, no N 1040/230 1040/740 1150/240 1280/680 2160/690 No P, 30 kg N haÿ1 1060/220 1530/430 1150/240 1720/390 2430/290
No P, 0.5 of area in IF 850/210 920/360 1010/230 1070/380 2210/420 No P, BT 1080/220 1100/720 1170/240 1320/670 2190/670 TSP, 200 kg P haÿ1, no N 1040/860 1040/860 1270/860 1270/860 2190/860
TSP, 100 kg P haÿ1, no N 1040/750 1040/860 1280/700 1270/860 2190/860
TSP, 100 kg P haÿ1, 30 kg N haÿ1 1510/490 1510/850 1680/470 1750/840 2750/860
TSP, 100 kg P haÿ1, 0.5 of area in IF 940/400 1010/550 1100/410 1170/570 2320/760
TSP, 25 kg P haÿ1for 5 years, no N 1040/810 1040/860 1270/780 1270/860 2180/830
TSP, 10 kg P haÿ1, annual, no N 1050/670 1040/860 1270/610 1270/860 2600/830
PR, 200 kg P haÿ1, no N 1040/860 1040/860 1270/860 1270/860 2180/850
PR, 100 kg P haÿ1, no N 1040/850 1040/860 1270/840 1270/860 2180/830
PR, 100 kg P haÿ1, 30 kg N haÿ1 1510/830 1510/860 1750/810 1750/860 2740/830
DAP, 25 kg P haÿ1, annual, no N 1390/790 1390/860 1630/770 1630/860 2600/820 a LRE, MRE, HRE, low, medium, high resource endowment, respectively. TSP, triple super
discounting, large yield increases were most valuable in the early years. For the case of high pH soils, applying additional P and/or N had very little eect on the NPV.
The improved farm returns when P is applied were completely due to increases in bean yields (Table 6). Maize yields increased only with applications of both N and P. However, the higher maize yields tended to depress bean yields and thus reduced total farm returns since the price of beans was almost three times that of maize. The decrease in bean yields was caused by additional competition between beans and maize for available P. Adding N increased maize demand for P, whereas beans ®x N biologically.
For changes in soil C (Table 7), we again saw the split between results for low and medium pH soils versus high pH soils. On the low and medium pH soils, the current practice of no inputs and the practice of applying only N, resulted in signi®cant losses of soil C. Any strategy with P inputs resulted in gains or smaller losses in soil organic C than without added P because greater amounts of organic residues were produced and returned to the soil. For the high pH cases, losses of soil organic C were much lower than for the lower pH soils under any strategy, including the cur-rent practice, due to the higher P availability and plant productivity in high pH cases. Current practice for the MRE and HRE farms had lower soil organic C losses than for the LRE farm due to the additions of manure from the cattle present on the MRE and HRE farms.
There were clear tradeos between the goals of improving ®nancial performance in the short-run and improving soil quality in the long-run (Tables 4 and 6). On the low and medium pH soils, applying N without P both depressed returns and decreased soil organic C. Annual applications of DAP performed well both in pro-viding high NPVs and in maintaining levels of soil organic C. P from any source combined with an IF allowed for the largest increases in soil organic C but the lowest NPVs. Applying P with no N resulted in moderate decreases in soil organic C while maintaining some of the highest NPVs.
3.3. Regional analysis
The P replenishment strategy with TSP at the rate of 100 kg haÿ1of P was chosen for the regional analysis, because: (1) it was highly pro®table on low and medium pH soils; and (2) we were more con®dent of the price estimates for TSP than for PR, which was not available on the market. However, since PR was also highly pro®table at the price used in the model (15 Kenya shillings [KSH] kgÿ1), we knew that if PR becomes available at the model price or lower, the results for the regional analysis would be at least as good as those for TSP.
henceforth are for the 20% discount rate. To illustrate a less targeted policy, sce-nario 2 considered spending the same amount on replenishment as in scesce-nario 1 (KSH 28.9 million), but the P was spread proportionately across LRE and MRE farmers with any soil type. In this case, the NPV of the incremental net bene®t decreased 34% from scenario 1, for the same cost. Finally, in the third scenario, the P was not targeted but was spread equally across all farm and soil types, including HRE farms. In this case, for the same cost, the incremental net bene®t NPV dropped by 20% from scenario 2 and by 47% from scenario 1.
Table 8 also shows the incremental maize and bean production for each scenario and the number of farms and hectares covered. In all cases, the same number of hectares was covered since it was applied at a constant rate and at a constant cost. Fewer farms were covered when the larger HRE farms were included in the project. Incremental maize and bean production followed the same trends as the net bene®ts, decreasing from scenario 1 to scenario 3.
3.4. Sensitivity of the regional analysis
Two additional scenarios were chosen for sensitivity analysis. In the ®rst scenario, the rate of application was changed from 100 kg haÿ1of TSP to 200 kg haÿ1of TSP. Doubling the rate of P application reduced the NPV for all farms types (Table 5), and only about one-half the area could be covered at the same cost. Covering low and medium pH soils with 200 kg P haÿ1of TSP proportionately up to the cost of covering all low and medium pH ®elds with 100 kg P haÿ1of TSP (the cost of sce-nario 1) resulted in a regional NPV of KSH 44.1 million (compared to KSH 94.2
Table 8
Costs and bene®ts of three regional scenarios for P replenishment (at the rate of 100 kg P haÿ1in the form
of triple super phosphate) for 10-year simulationsa
Unit Scenario 1 Scenario 2 Scenario 3 Total cost Million KSH 28.9 28.9 28.9
NPV of incremental net benefits
Discount rate of 30% Million KSH 65.1 44.8 31.1 Discount rate of 20% Million KSH 94.2 68.2 49.9 Discount rate of 10% Million KSH 143.5 108.3 81.9 Discount rate of 1% Million KSH 224.0 174.3 134.7 Incremental maize production MT 182 131 94 Incremental bean production MT 1275 914 546 Number of farms 7740 7740 6221 Number of hectares 2339 2339 2339
a Scenario 1: the ®eld area of all farms with low and medium pH are covered; Scenario 2: the cost of
million for 100 kg P haÿ1). Therefore, if the size of the project was limited by cost factors, it was more bene®cial to cover a larger area at the rate of 100 kg of P haÿ1 than to cover a smaller area at the rate of 200 kg P haÿ1. Not only were total net bene®ts higher, but a larger number of farmers would be assisted.
The impressive economic results of P replenishment were largely driven by the signi®cant increases in bean yields. Although bean yield potential in the model had already been set to a moderate level to re¯ect moderate management practices, actual bean yields could be lower due to bean diseases or other factors not modeled. Therefore, in the second scenario, bean yields with P replenishment were reduced by 50%.1 Under this scenario, the NPV of incremental net bene®ts dropped sig-ni®cantly to KSH 11.8 million (about $250,000) from KSH 94.2 million. Bean yields were still about 50% higher for the low and medium pH soils than in the no P case. If bean yields were only 50% of simulated results for scenarios 2 and 3 presented earlier, the NPV would be negative. So, if the bean yields fell short of projections, and if the P was not targeted to P-de®cient soils, a P replenishment project would not be a wise investment. On the other hand, if bean yields fell short, but P replen-ishment was targeted, incremental net bene®ts would be greatly reduced from the base bean yield scenario.
4. Conclusions
This paper analyzed the returns to a multitude of P replenishment strategies for seven combinations of farm and soil types in Vihiga Division of western Kenya. Almost any one of the P strategies, with or without N, were eective in increasing bean yields and thus farm returns on farms with low or medium pH soils and asso-ciated soil characteristics. Applying N with P replenishment generally did not improve the NPV due to the costs of purchasing and applying N relative to the price of the main output, maize. On low and medium pH soils, P replenishment was a pro®table strategy which also improved soil organic C over current practices. Apply-ing P to farms with high pH soils either decreased the net return or only increased it marginally, and it had little eect on the change in soil organic C. Therefore, in gen-eral, there was little incentive for those farms with high pH (35.5% of farms in the soil survey) to switch from current practices to a P replenishment strategy.
The regional analysis of P replenishment re¯ected the farm-level results. Targeting P replenishment to low and medium pH soils resulted in the largest bene®ts at the regional level. Untargeted replenishment reduced bene®ts by 47% (scenario 1 vs. scenario 3). To maximize returns at the regional level, P replenishment would need to be targeted to low and medium pH soils (approximately 65% the land). Promo-tion of alternative crops of higher value than maize that respond to P (e.g. some horticultural crops) and N-®xing crops could also help to maximize returns to P investments.
1 This scenario could also re¯ect the impact of lower prices with or without lower yields, since either
Acknowledgements
The authors thank Dr. Len Reynolds for providing a simulation model of nutrient partitioning through livestock and Dr. Eve Crowley for her contributions in de®ning the three farm types and in the design and execution of economic ®eld data collection. Support for this research from the Rockefeller Foundation and the Rockefeller Foun-dation Social Science Research Fellowship in Agriculture is gratefully acknowledged.
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