Directory UMM :Data Elmu:jurnal:A:Agricultural Systems:Vol64.Issue2.May2000:

Agricultural Systems 64 (2000) 83±98
www.elsevier.com/locate/agsy

An ecological and economic analysis of
phosphorus replenishment for Vihiga
Division, western Kenya$
M.J. Soule a,*, K.D. Shepherd b
a
Economic Research Service, USDA, Washington DC 20036-5831, USA
International Centre for Research in Agroforestry (ICRAF), PO Box 30677, Nairobi, Kenya

b

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 economic costs and bene®ts as well as ecological impacts of di€erent 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 di€erent strategies for
phosphorus replenishment with di€erent 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 endowments on low and medium pH soils rather than spread evenly across all soil and farm types.
# 2000 Elsevier Science Ltd. All rights reserved.
Keywords: Soil fertility; Ecological economics; Simulation model; Cost-bene®t analysis; Kenya

$
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.
E-mail address: msoule@ers.usda.gov (M.J. Soule).

0308-521X/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.
PII: S0308-521X(00)00015-9

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M.J. Soule, K.D. Shepherd / Agricultural Systems 64 (2000) 83±98

1. Introduction
Soils de®cient in the major nutrients, nitrogen (N) and phosphorus (P), have been
identi®ed as a major problem a€ecting 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 dominated 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 insucient 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 haÿ1 yearÿ1
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 haÿ1 yearÿ1 (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-su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 e€ects 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 di€erent 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 longrun; 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 di€erent 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 carbon (C) over time as an indicator of long-term soil productivity and resilience
(Young, 1997).
The analysis was carried out for three representative farm types that have been

de®ned for Vihiga Division, based on extensive ®eld work (Crowley et al., 1996;
Shepherd and Soule, 1998). The three farm types di€er in their access to resources

M.J. Soule, K.D. Shepherd / Agricultural Systems 64 (2000) 83±98

85

(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 seasons: 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 production 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, asymbiotic 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.
The economic sub-model (Shepherd and Soule, 1998) used the output grain, milk,
and wood production from the ecological sub-model for calculating various measures
of farm ®nancial return given input and output prices. The model was conceptually

86

M.J. Soule, K.D. Shepherd / Agricultural Systems 64 (2000) 83±98

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 replenishment, 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 di€erences 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, abbreviated HRE, MRE and LRE, respectively), there were large di€erences 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.
From the participatory wealth rankings and cluster analysis of the data from the
soil fertility management surveys, we estimated that about 55% of the farmers in the

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M.J. Soule, K.D. Shepherd / Agricultural Systems 64 (2000) 83±98

Table 1
Principal characteristics of composite low, medium and high resource endowment (LRE, MRE and HRE,
respectively) farms in Vihiga District, western Kenyaa
Variable

Farm size
Local cattle
Grade cattle
Farm area in maize/beans
Farm area in woodlot
Farm area in fodder grass
Farm area in homestead
Crop residues used for fuel
Fertilizer use

Units

ha
number
number
%
%
%
%

%
kg haÿ1 yearÿ1

Farm resource endowment
Low (LRE)

Medium (MRE)

High (HRE)

0.3
0
0
61
0
0
26
50
0

0.8
1
0
60
10
0
19
25
0

1.6
1
2
27
11
38
17
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).

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 representative soil types, based on topsoil pH. We based the three representative 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 2
Values of initial soil parameters for three representative soil types
Soil pH class

Topsoil pH
Soil carbon (%)
Clay fraction (kg kgÿ1)
Labile Pa (mg kgÿ1)
a

Low (4.9±5.7)

Medium (5.7±6.2)

High (6.2±7.0)

5.3
1.2
0.32
3.4

6.0
1.2
0.32
3.4

6.6
1.2
0.32
6.2

The soil survey measured Olsen-P. Labile P was calculated as 2.1+0.55 Olsen-P (mg kgÿ1).

88

M.J. Soule, K.D. Shepherd / Agricultural Systems 64 (2000) 83±98

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 average 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 markets in western Kenya in 1995±96. Small village markets as well as larger, regional
markets were included in the survey. The markets were surveyed at three times during 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 on-farm and onstation research in the area. Some labor data was also derived from unpublished survey 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 application levels of DAP were considered, and a scenario with no P was also evaluated.
The application of P in combination with N was also analyzed. Three sources of N
were considered: urea at three levels (30, 60 and 120 kg N haÿ1), an improved fallow
(IF) of sesbania (sesbania sesban), and biomass transfer (BT) with tithonia (tithonia
diversifolia). IFs involve planting a N-®xing legume or shrub into a fallowed area to
speed up the process of fertility replenishment which happens naturally in fallowed
lands. For biomass transfer, farmers apply the leaves cut from tithonia hedges to
their ®elds for fertility enhancement. The annual amounts of N added in the BT

M.J. Soule, K.D. Shepherd / Agricultural Systems 64 (2000) 83±98

89

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 haÿ1 annual

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 haÿ1 annual

PR, annual, 10 kg P haÿ1
DAP, annual, 25 or 50 kg P haÿ1
a

TSP, triple super phosphate; PR, phosphate rock; DAP, diamonium phosphate.

were small, at about 6 kg N haÿ1 and 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 cropped 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 haÿ1 of crop land in LRE and MRE but
were about 60±85 kg N haÿ1 in HRE. The amounts of P inputs were about 5% of
those values. The application of 30 kg N haÿ1 in 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 approximately 12,000 farm households on 7200 ha, in the Division. Using the distribution

90

M.J. Soule, K.D. Shepherd / Agricultural Systems 64 (2000) 83±98

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 medium 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 percentage 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 managerial 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 di€erent degrees of targeting 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 categorya and 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
LRE, medium pH
LRE, high pH

2603
2127
1870

21.7
17.7
15.6

781
638
561

10.8
8.8
7.7

LRE subtotal

6600

55.0

1980

27.3

MRE farm size=0.8 ha
MRE, low pH
MRE, medium pH
MRE, high pH

1657
1353
1190

13.8
11.3
9.9

1325
1083
952

18.3
14.9
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

12,000

100.0

7260

100.0

Total
a

LRE, MRE, HRE, low, medium, high resource endowment, respectively.

M.J. Soule, K.D. Shepherd / Agricultural Systems 64 (2000) 83±98

91

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 eciency 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 justi®ed by the free trade in agricultural products at a larger regional scale, including
eastern Uganda. However, sensitivity analysis was conducted to account for decreases 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 simulation period. The average maize plus bean yield over the 10-year simulation was 1.3
t haÿ1 for LRE, 1.4 t haÿ1 for MRE and 3.4 t haÿ1 for 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
yearÿ1 for 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).
Milk yields for the local cow were 0.6 kg dayÿ1 in MRE and 1.0 kg dayÿ1 in HRE,
compared with average milk yields for the area reported by Sands (1983) of 1.0 kg
dayÿ1. In HRE, milk yield per lactation day per grade cow was 5.3 kg, which is
comparable to values from district surveys of 5.7 kg (Van der Valk, 1990).

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M.J. Soule, K.D. Shepherd / Agricultural Systems 64 (2000) 83±98

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 a€ected 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 di€erences.
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 fertilizer for a wide range of soil types, given maize/fertilizer 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 haÿ1 of TSP) to smaller annual doses (say 10 kg P haÿ1 of 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
low and
medium
pH

LRE Ð
high pH

MRE Ð
low and
medium
pH

MRE Ð
high pH

HRE Ð
high pH

Current practice
No P, no N
No P, 30 kg N haÿ1
No P, 0.5 of area in IF
No P, BT
TSP, 200 kg P haÿ1, no N
TSP, 100 kg P haÿ1, no N
TSP, 100 kg P haÿ1, 30 kg N haÿ1
TSP, 100 kg P haÿ1, 0.5 of area in IF
TSP, 25 kg P haÿ1 for 5 years, no N
TSP, 10 kg P haÿ1, annual, no N
PR, 200 kg P haÿ1, no N
PR, 100 kg P haÿ1, no N
PR, 100 kg P haÿ1, 30 kg N haÿ1
DAP, 25 kg P haÿ1, annual, no N

1390
1390
ÿ170
610
510
7940
8950
5830
3100
8790
5860
7960
9780
9920
8850

10,800
10,800
6330
3880
9780
8010
10,190
10,460
6500
10,300
10,870
8110
10,240
10,580
11,050

16,770
16,770
12,990
14,120
15,540
35,610
36,190
28,720
20,710
36,040
26,880
35,450
39,750
40,120
36,430

39,510
39,510
28,650
22,700
37,980
35,770
41,290
42,110
29,600
41,560
42,810
36,030
41,400
42,750
43,830

110,470
113,250
97,150
110,100
110,900
99,660
111,300
109,350
115,430
109,900
102,520
99,240
109,860
107,230
110,470

a
LRE, MRE, HRE, low, medium, high resource endowment, respectively. TSP, triple super phosphate; PR, phosphate rock; DAP, diamonium phosphate; IF, improved fallow; BT, biomass transfer.

93

M.J. Soule, K.D. Shepherd / Agricultural Systems 64 (2000) 83±98
Table 6
Selected simulation results, average annual maize/bean yields (kg haÿ1) for 10-year simulationsa
Scenario

LRE Ð
low and
medium
pH

LRE Ð
high pH

MRE Ð
low and
medium
pH

MRE Ð
high pH

HRE Ð
high pH

Current practice
No P, no N
No P, 30 kg N haÿ1
No P, 0.5 of area in IF
No P, BT
TSP, 200 kg P haÿ1, no N
TSP, 100 kg P haÿ1, no N
TSP, 100 kg P haÿ1, 30 kg N haÿ1
TSP, 100 kg P haÿ1, 0.5 of area in IF
TSP, 25 kg P haÿ1 for 5 years, no N
TSP, 10 kg P haÿ1, annual, no N
PR, 200 kg P haÿ1, no N
PR, 100 kg P haÿ1, no N
PR, 100 kg P haÿ1, 30 kg N haÿ1
DAP, 25 kg P haÿ1, annual, no N

1040/230
1040/230
1060/220
850/210
1080/220
1040/860
1040/750
1510/490
940/400
1040/810
1050/670
1040/860
1040/850
1510/830
1390/790

1040/740
1040/740
1530/430
920/360
1100/720
1040/860
1040/860
1510/850
1010/550
1040/860
1040/860
1040/860
1040/860
1510/860
1390/860

1150/240
1150/240
1150/240
1010/230
1170/240
1270/860
1280/700
1680/470
1100/410
1270/780
1270/610
1270/860
1270/840
1750/810
1630/770

1280/680
1280/680
1720/390
1070/380
1320/670
1270/860
1270/860
1750/840
1170/570
1270/860
1270/860
1270/860
1270/860
1750/860
1630/860

2600/820
2160/690
2430/290
2210/420
2190/670
2190/860
2190/860
2750/860
2320/760
2180/830
2600/830
2180/850
2180/830
2740/830
2600/820

a
LRE, MRE, HRE, low, medium, high resource endowment, respectively. TSP, triple super phosphate; PR, phosphate rock; DAP, diamonium phosphate; IF, improved fallow; BT, biomass transfer.

Table 7
Selected simulation results, percentage change in soil organic carbon stock (0±0.15 m) over 10-year
simulationsa
Scenario

LRE Ð
low and
medium
pH

LRE Ð
high pH

MRE Ð
low and
medium
pH

MRE Ð
high pH

HRE Ð
high pH

Current practice
No P, no N
No P, 30 kg N haÿ1
No P, 0.5 of area in IF
No P, BT
TSP, 200 kg P haÿ1, no N
TSP, 100 kg P haÿ1, no N
TSP, 100 kg P haÿ1, 30 kg N haÿ1
TSP, 100 kg P haÿ1, 0.5 of area in IF
TSP, 25 kg P haÿ1 for 5 years, no N
TSP, 10 kg P haÿ1, annual, no N
PR, 200 kg P haÿ1, no N
PR, 100 kg P haÿ1, no N
PR, 100 kg P haÿ1, 30 kg N haÿ1
DAP, 25 kg P haÿ1, annual, no N

ÿ16
ÿ16
ÿ16
ÿ13
ÿ14
ÿ7
ÿ9
ÿ7
ÿ4
ÿ7
ÿ9
ÿ7
ÿ7
ÿ2
ÿ3

ÿ9
ÿ9
ÿ7
ÿ5
ÿ7
ÿ7
ÿ7
ÿ1
5
ÿ7
ÿ7
ÿ7
ÿ7
ÿ1
ÿ3

ÿ12
ÿ12
ÿ12
ÿ9
ÿ11
ÿ3
ÿ4
ÿ3
0
ÿ3
ÿ5
ÿ3
ÿ3
3
2

ÿ4
ÿ4
ÿ3
ÿ1
ÿ3
ÿ3
ÿ3
3
9
ÿ3
ÿ3
ÿ3
ÿ3
4
3

12
8
8
11
8
8
8
13
19
8
12
8
8
13
12

a
LRE, MRE, HRE, low, medium, high resource endowment, respectively. TSP, triple super phosphate; PR, phosphate rock; DAP, diamonium phosphate; IF, improved fallow; BT, biomass transfer.

94

M.J. Soule, K.D. Shepherd / Agricultural Systems 64 (2000) 83±98

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 e€ect 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 current 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 tradeo€s 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 providing 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 haÿ1 of 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.
Three P replenishment scenarios were used to test the e€ect of targeting by farm
type. In scenario 1, the ®eld area of all farms with low or medium pH was covered at
the rate of 100 kg P haÿ1 of TSP. Table 8 shows that this scenario covered 2339 ha
and 7740 LRE or MRE farms. The P replenishment cost KSH 28.9 million (about
$525,000 at an exchange rate of US$1=KSH 55) and earned an NPV of KSH 94.2
million (about $1,713,000) at the discount rate of 20%. The NPV was lower at higher
discount rates and higher at lower discount rates (Table 8). The results discussed

95

M.J. Soule, K.D. Shepherd / Agricultural Systems 64 (2000) 83±98

Table 8
Costs and bene®ts of three regional scenarios for P replenishment (at the rate of 100 kg P haÿ1 in 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%
Discount rate of 20%
Discount rate of 10%
Discount rate of 1%

Million KSH
Million KSH
Million KSH
Million KSH

65.1
94.2
143.5
224.0

44.8
68.2
108.3
174.3

31.1
49.9
81.9
134.7

Incremental maize production
Incremental bean production
Number of farms
Number of hectares

MT
MT

182
1275
7740
2339

131
914
7740
2339

94
546
6221
2339

a
Scenario 1: the ®eld area of all farms with low and medium pH are covered; Scenario 2: the cost of scenario 1 is applied equally across low and medium resource endowment farms; Scenario 3: the cost of scenario
1 is applied equally across all farms (including high resource endowment); KSH denotes Kenya shillings.
During the time of this study (1995±96), the exchange rate was US$=KSH 55.

henceforth are for the 20% discount rate. To illustrate a less targeted policy, scenario 2 considered spending the same amount on replenishment as in scenario 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 haÿ1 of TSP to 200 kg haÿ1 of 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 haÿ1 of TSP proportionately up to the cost of
covering all low and medium pH ®elds with 100 kg P haÿ1 of TSP (the cost of scenario 1) resulted in a regional NPV of KSH 44.1 million (compared to KSH 94.2

96

M.J. Soule, K.D. Shepherd / Agricultural Systems 64 (2000) 83±98

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 signi®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 replenishment 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 e€ective in increasing
bean yields and thus farm returns on farms with low or medium pH soils and associated 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. Applying P to farms with high pH soils either decreased the net return or only increased it
marginally, and it had little e€ect on the change in soil organic C. Therefore, in general, 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). Promotion 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
lower yields or lower prices depresses farm returns.

M.J. Soule, K.D. Shepherd / Agricultural Systems 64 (2000) 83±98

97

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 Foundation Social Science Research Fellowship in Agriculture is gratefully acknowledged.
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