Title Page
 Results and discussion

Group Title: Staff paper - University of Florida. Food and Resource Economics Dept. - SP 03-6
Title: Economic assessment of constraints to the adoption of improved fallows in Zimbabwe using linear programming models
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Permanent Link: http://ufdc.ufl.edu/UF00053830/00001
 Material Information
Title: Economic assessment of constraints to the adoption of improved fallows in Zimbabwe using linear programming models
Series Title: Staff paper
Physical Description: 16 p. : ; 28 cm.
Language: English
Creator: Mudhara, M
Hildebrand, Peter E
University of Florida -- Food and Resource Economics Dept
Publisher: University of Florida, Institute of Food and Agricultural Sciences, Food and Resource Economics Department
Place of Publication: Gainesville Fla
Publication Date: 2002
Subject: Soil fertility -- Zimbabwe   ( lcsh )
Agriculture -- Zimbabwe   ( lcsh )
Economic conditions -- Zimbabwe   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
Bibliography: Includes bibliographical references (p. 11-12).
Statement of Responsibility: by M. Mudhara and P. Hildebrand.
General Note: Cover title.
General Note: "October 2003."
Funding: Florida Historical Agriculture and Rural Life
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Bibliographic ID: UF00053830
Volume ID: VID00001
Source Institution: Marston Science Library, George A. Smathers Libraries, University of Florida
Holding Location: Florida Agricultural Experiment Station, Florida Cooperative Extension Service, Florida Department of Agriculture and Consumer Services, and the Engineering and Industrial Experiment Station; Institute for Food and Agricultural Services (IFAS), University of Florida
Rights Management: All rights reserved, Board of Trustees of the University of Florida
Resource Identifier: aleph - 002983127
oclc - 53245848
notis - APM4938

Table of Contents
    Title Page
        Title Page
        Page 1
        Page 2
        Page 3
    Results and discussion
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
Full Text

SP 03-6


Institute of Food and Agricultural Sciences
Food and Resource Economics Department
Gainesville, Florida 32611


M. Mudhara and P. Hildebrand

Staff Paper SP 03-6

October 2003



Abstract. A study was undertaken to assess the potential of resource-poor farmers adopting improved
fallow technologies tested on-station in Zimbabwe. The technologies had not been extended to farmers. A
questionnaire survey was administered on 105 randomly selected households in Mangwende Communal
Area (CA), in the northeastern part of Zimbabwe (Southern Africa). A five-year LP model, reflecting the
livelihood system of the smallholder farmers, was constructed. The model was validated to ensure that it
reflected farmers' livelihood strategies. The results indicated that household welfare would be improved
following adoption of the improved fallows. Critical determinants of the level of adoption were
household composition, size of the arable land owned by the farmers and the differentiation of activities
conducted on the farm by gender and level of cash remittances. The model can be employed to determine
the effect of change in available household labor or sources of non-farming income, as might result from
HIV/AIDS, on the welfare of the household.


For the past three decades, poverty alleviation and food security have been the
preoccupations of development practitioners in sub-Saharan Africa (SSA). One
cause of low crop productivity and hence food insecurity has been low soil fertility.
Use of improved fallows is one of the interventions proposed for improving soil
fertility in a sustainable manner.
Leaving fields fallow to regenerate soil fertility has been a traditional
practice in Zimbabwe, as in the rest of SSA. The practice is being abandoned due to
the increase in population pressure. In an attempt to boost agricultural production,
some governments embarked on programmes to promote the use of chemical
fertilizers. In Zimbabwe, widespread promotion of chemical fertilizers was
undertaken after independence in 1980. Between 1980 and 1991, fertilizer prices
under the direct control of the government were set at levels considered affordable
to farmers to increase fertilizer demand. Free fertilizer was distributed to
smallholder farmers in 1980, 1986, 1992 and various years after 1992 to boost their
demand of fertilizer and cushion them from the drought effects. In 2002 and 2003,
fertilizer was allocated as input loans. The free handouts were insufficient to meet
farmers' requirements. While the government tried to increase fertilizer
consumption, it also controlled producer prices, leading to a squeeze on profit

T.H.E. Editor(s) (ed), Book title, 1-6.
2003 KluwerAcademic Publishers. Printed in the Netherlands.


Research on viable agroforestry technologies for the smallholder farmers
has been intensified (e.g., Swinkels 1997; Buresh and Cooper 1999; Franzel 1999;
Kwesiga et al. 1999; Keil 2001; Franzel et al. 2002; Place et al. 2002; Pisanelli et al.
2002). This has mostly been in response to the escalating fertilizer prices and the
declining production levels in the sector. Available literature shows that this
complex technology presents a challenge for assessing its adoption by farmers,
particularly when the assessment is done ex ante. Most studies have evaluated the
adoption of the technologies ex post (Franzel 1999; Kwesiga et al. 1999).
Since 1992, ICRAF and Department of Research and Specialist Services
(DR&SS) conducted research on soil fertility management using improved fallow
agroforestry technologies at Domboshawa Training Centre and Makoholi
Experiment Station. Technical analysis was indicating that the proposed
interventions increased maize yields (Dzowela 1992; Dzowela 1993; Mafongoya
and Dzowela 1998; Mafongoya and Dzowela 1999). However, the technologies had
not been evaluated in the context of the whole farm, i.e., in relation to all activities
that compete for limited resources at the household level, given the multiple
objectives. Rohrbach (1998) noted that a technology needs to be more profitable
than alternative investment opportunities for the farm as a whole. As such, the
potential of the adoption of the technologies was unknown, so that extension could
not identify the targets for the various facets of the complex technologies. Partly for
this reason, the technologies had not been extended to smallholder farmers.
This chapter presents the use a linear programming (LP) model for
simulating the livelihoods of smallholder farmers and assessing the potential
adoption of improved fallows in Mangwende Communal Area of Zimbabwe. In
addition, the chapter also discusses how the model was used for determining the
potential of households of different resource levels to adopt technologies for
improving soil fertility. The likely impacts of the technologies on the livelihoods of
households that adopt them under different scenarios were assessed.


2.1. Characterization ofResearch Site

The survey for this study was conducted in Mangwende Communal Area (CA),
lying between 17 22' and 170 56' S and between 310 31' and 320 09' E, in
Mashonaland East Province of Zimbabwe. The CA lies in the north east of the
country, some 90 km from Harare, the capital city of Zimbabwe. It has annual
rainfall between 800 and 950 mm, the bulk of which falls between the end of
October and the end of March. The predominant soil in the area is derived from
granite parent materials. Therefore, the soils have low inherent fertility and require
high levels of external inputs to improve fertility.
The smallholder farmers of Mangwende CA are typical of other
smallholder farmers. They have limited resource levels, multiple activities and poor
access to services, such as extension. Fertilizer purchases are decreasing over time,
suggesting that the farmers' lifeline of farming is threatened and food insecurity


exists in some years. The farming system is complex, with households relying on
various activities to sustain their livelihoods given their limited resources.
Crop production is the major activity for the farm households in
Mangwende CA. Surplus crops are marketed. Maize, the dominant subsistence and
cash crop, occupies approximately 70 percent of the cultivated area. Other major
crops are groundnuts and sunflower. Vegetable gardens are widespread, producing a
variety of vegetables for consumption and cash. Maize planting is staggered to
ensure that farmers spread out the requirements of labour and to minimize the risk of
total crop failure. Cattle are kept as a financial back up and for providing draft
power. They are the dominant livestock and about half of the farmers own cattle.
Households also depend on members who do not live on the farm for cash
remittances and non-cash support.
The following define the level of resources on the farm:
number of members in the household;
the age and gender of the head of the household;
size of the farm,
amount of fertilizer purchased in any year or amount of unmanaged fallow
land; and
number of cattle owned (and the accompanying access to cattle manure).
Resource levels vary across households. Technologies are likely to be suitable to
varying degrees to the households with different resources. Nevertheless, some
similarities exist across households, e.g., maize was the major cash and food crop in
the area, and every household planted some. In addition, all households practice dry-
land farming.
Some households experience food shortages during the year. While farmers were
aware of the secondary benefits of some crops, such as soil fertility enrichment, they
only planted crops for food and cash. This points to the need for new technologies to
satisfy the farmers' food and cash requirements. Technologies should not make
households more food insecure or short of cash requirements.

2.2 Data Collection

Both primary and secondary data sources were utilized. For primary data, three
wards were randomly selected from the 28 in the CA. Lists of the names of
households in each village in the selected wards were compiled from the village lists
kept by village heads. A household was defined as people who shared the same
kitchen Thirty-five households were selected randomly from each ward, to give a
sample size of 105 households. Trained enumerators administered the
questionnaires. In addition to the questionnaires, farmer focus group discussions
were conducted to address contextual issues.
Data on technical coefficients for improved fallows were obtained from
published results of experiments conducted in the area by the FSRU and by ICRAF-
Zimbabwe at Domboshawa Training Center.


2.3. The Household LP Model

A five-year LP model was constructed using the Premium Solver Plus V3.5 for
Excel to reflect the livelihood system of the smallholder farmers. Details of the
theoretical formulation of the model and its construct are presented in Appendix 1.
The model was run for each of the sample households. Household specific
parameters from the questionnaire survey and technical coefficients from group
interviews were used for each respective household. The objective function in the
models was to maximize discretionary household income from farm and non-
farming activities, subject to various constraints reflecting household characteristics,
such as food security, household composition, draft power ownership, available
arable land.
To ensure that the model reflected the farmers' livelihood strategies, the
model was validated in two stages. The first stage of validation, conducted in the
research area, involved discussions of the results of computer simulations of a sub-
sample of the sampled farmers. Fertilizer prices were varied to see the model's
prediction of how households were likely to respond. The responses that the model
predicted were also discussed with the farmers. Farmers' suggestions on the model
were incorporated. Farmers agreed that the model simulated their livelihoods well,
especially in its ability to identify resources that were limiting in their farming
In the second stage of validation, the levels of activities reported by the
farmers during the questionnaire survey were compared to the model results. The
second validation was done after running the model on all households. Comparison
was conducted on two variables, i.e., the area planted to maize and the area under
unmanaged fallow. Maize was important for validation because it was the major
staple and cash crop. In addition, maize was the crop for which the potential for
adoption of improved fallow technologies was to be evaluated in the study. The new
technologies compete for land with crops or replace the land under unmanaged
fallow. The difference in the size of unmanaged fallow in the model and reported by
farmers during interviews had to be insignificant. Therefore, the unmanaged fallow
area was used for validation. After validation of the models, activities for improved
fallows were included in the LP models to assess whether the new technologies had
a potential to be adopted, ceteris paribus.


Smallholder farmers have limited resources and multiple objectives (Netting, 1993;
Hildebrand, 1986; Ellis, 1992). However, this common characteristic can be
mistaken to imply that the farmers are homogeneous. The survey results show
household diversity in various respects, e.g., resource levels across households,
composition of the household and the activities they conduct. Resource levels dictate


the ability of households to exploit opportunities that different technological
innovations offer.
The diversity between households makes the development of technologies
compatible to different household types difficult. When models are used for
matching technologies to different household types, extension programs can then
target farmers with specific attributes. A household LP model sensitive to the
diverse characteristics of households can be used for matching households and
technologies. Use of such LP models should increase the efficiency and productivity
of extension services.

4.1. Agroforestry Improved Fallow Technologies

Agroforestry improved fallow technologies are complex with several components
that have different developmental cycles, and multiple interactions. Therefore, when
assessing the potential adoption of such technologies, the objectives and resources of
farmers must be considered. Since all activities conducted on the farm compete for
household resources, an evaluation of potential adoption of improved fallow
technologies also has to consider their contribution to households in comparison to
alternative activities. To achieve this, improved fallow technologies carried out in
research station experiments were incorporated in validated household LP models.
Options of improved fallows of one, two and three-year durations introduced into
the household LP model are presented in Table 1.

Table 1. Options of improvedfallows introduced into the household LP model

Year in One year fallow Two year fallow Three year
Model fallow
1.1 1.2 1.3 1.4 2.1 2.2 3.1
1 F_ F F
2 MZ F F F F
F = Year when fallow is in the field; MZ = A maize crop year is in the field.
Fallow notation: Fallow (.k) is aj year fallow, planted in year, where = 1,2,3 and k= 1,2,.., 5.

For better establishment, Sesbania sesban has to be planted from seedlings,
which is recommended and is the approach used in the model. This is in contrast to
the method where the multi-purpose trees (MPTs) are seeded directly into the soil.
At the end of the fallow period, trees in the improved fallow plots are cut down and
pruned before ox-drawn ploughs incorporate the biomass. Data on labour
requirements and yields were recorded during experimentation The distribution of


the yields that farmers reported was skewed to the left of the mean yield realized on
the experiment station. Therefore, yields realized on experimental plots were
reduced by 40% to'bring them to the same level as the yields that farmers are likely
to realize in their own fields (CIMMYT, 1988). Figure 1 shows that experimental
yields are higher than farmers' yields. In the figure, A (2.0 Mg ha') is the average
maize yield realized by farmers in 2001, B (3.50 Mg ha") is the average maize yield
following pigeon pea, and C (4.50 Mg ha-') is the average maize yield following
Sesbania sesban. In 1994/95, maize yields on plots grown continuously with maize
on station were 2.71 Mg ha-1 for no fertilizer and 3.3 Mg ha'' when 38 kg ha"' of
nitrogen was applied.



S0.1 -


0 1 2 3 4 5 6
Maize yields (Mg/ha)

Figure 1. Probability distribution of farmers' maize yields

(compared to station

4.2 Potential Adoption ofSesbania sesban Improved Fallow
Results of the LP model indicate that households would adopt Sesbania
sesban improved fallow under two scenarios, i.e., when it is the only technology
available or when it is available at the same time as pigeon pea but without a market
for pigeon pea seed. At the time of the study, pigeon pea seeds were not marketed in
Zimbabwe. Over the five years that the model spanned, households adopt fallows of
different duration. The highest number of households adopts improved fallows in the
first year, tailing off over time.
In the first year, 81% of the households adopt 1-year improved fallows,
51% adopt the 2-year improved fallow and 59% adopt the 3-year improved fallow.
In the second year 12% adopt 1-year improved fallow and 5% adopt 2-year


improved fallow. In the third year, 48% of the households adopt 1-year fallow while
16% adopt 1-year fallow in the fourth year. The area planted to different improved
allows over the first four years of the household LP model is presented in Table 2.
One-year Sesbania sesban fallow planted is an average of 0.55 ha, occupying an
average of 63% of the area under improved fallow in the first year. One-year fallow
planted in the first year is planted to maize during the second and third years.
Farmers then plant 0.24 ha of one-year fallow in the third year. The fallow is planted
with maize in the fourth and fifth years.

Table 1. Formatting instructions

Fallow duration Year

2nd 3rd 4th
Area (ha)
1-year 0.55 0.04 0.24 0.04
2-year 0.08 0.08 0 0
3-year 0.25 0.25 0.25 0

According to the LP model results, a three-year fallow is also planted in
the first year and then planted with maize in the fourth and fifth years. In the first
year, the 3-year fallow occupies 28% of the land under improved fallow. In the
second year very little improved fallow is planted, so that the 3-year Sesbania
sesban improved fallow carried over from the first year is the dominant fallow,
occupying 68% of the area under Sesbania sesban improved fallow. The 3-year
Sesbania sesban improved fallow constitutes 51% of the area under Sesbania sesban
fallow in the third year, with the other area being occupied by the 1-year fallow
planted in year three. On aggregate, households plant 1.2 ha of Sesbania sesban
improved fallow in the first four years of the model.
Figure 2 shows the fertility management of maize over time, after the
introduction of Sesbania sesban improved fallow. It compares the maize area
planted on land fertilized using the conventional means, i.e., chemical fertilizers and
cattle manure, on one hand, and on Sesbania sesban improved fallows, on the other.
On average, from the second to the fifth year, maize on improved fallow occupies
0.6 ha, which is 60% of the maize area, out of an average farm size of 2.6 ha.
After the introduction of Sesbania sesban improved fallow, income for
discretionary spending for non-owners of draft power increases significantly (p =
0.009) from Z$17,500 to Z$19,400, a 10% increase. The income for discretionary
spending for draft power owners increases from Z$24,400 to Z$24,800 after the
introduction ofSesbania sesban improved fallow. This 2% increase, however, is not
statistically significant (p = 0.6). Therefore, although the income of households
without draft power remains lower than that for owners of draft power, introduction


of Sesbania sesban improved fallow is more beneficial to non-owners of draft power
than owners.
After the introduction of Sesbania sesban improved fallow, income is
statistically significantly different between households with one to four members
working fulltime on the farm (p = 0.0001). The average annual income for
discretionary spending for households with one member working fulltime on the
farm, after the adoption of improved fallows, is Z$18,000. The income for
households with two, three and four members working fulltime on the farm is
Z$20,000, Z$29,000 and Z$32,000 per annum, respectively. However, only
households with one member working fulltime on the farm experience a significant
(p = 0.03) increase in their income for discretionary spending from the introduction
of Sesbania sesban improved fallow into the system. Therefore, although Sesbania
sesban improved fallow can be widely adopted, only households with one member
working fulltime on the farm benefit in terms of income for discretionary spending.
De facto FHHs have the least number of members working on the farm. However,
their income remains the lowest across different numbers of household members
working fulltime on the farm. Households with larger farms are able to adopt more
improved fallows compared to those with smaller farms (Table 3).

0.6 -

0.4 -



3 4


S Fertilizer and Manure Sesbania s. allows ---- Maize without fallow

Figure 2. Maize area under different soil fertility options over time when Sesbania sesban
improved fallow is available.


Fifty-three percent of the households in the sample differentiated labour by gender.
Differentiating labour by gender implies that male labour has specified tasks it
carries out, which are different from those for female labour. More households that
differentiate labour by gender are limited by labour than those that do not. When
labour is limiting, households are less able to adopt improved fallows, as they have
less labour available for conducting work on the improved fallows. Households that
differentiate labour by gender plant 270 m2 less Sesbania sesban improved fallow
than those that do not. Differentiation of labour by gender is an inhibitor to the
adoption of Sesbania sesban improved fallow.

Table 3. Area wider Sesbania sesban improved fallows adopted by ownership of draft power
and farm size.

Range of Owners of Non-owners Significance
farm sizes draft power of draft level of
(ha) power differences

Less than 0.73 1.15(0.65) 0.022
2.5 ha (0.59)"
1.33(0.71) 0.150
Greater than 1.70(0.78)
2.5 ha

Significance 0.001 0.480
level of
'In brackets are Standard Deviations

Draft power owners plant 200 m2 less Sesbania sesban improved fallow for
each additional bag of fertilizer they have. The results suggest that Sesbania sesban
fallows substitute for fertilizers and cattle manure. When farmers have access to
fertilizers, their use of Sesbania sesban fallow is reduced. However, the amount of
fertilizers that non-owners of draft power have does not affect the area of Sesbania
sesban improved fallows they plant. Non-owners of draft power do not have access
to cattle manure and are more in need of Sesbania sesban improved fallow.
Households headed by different gender did not differ in the area under
Sesbania sesban improved fallow.
No market outlets for pigeon pea seed currently exist in the communal
areas of Zimbabwe. Early adopters of pigeon pea fallows will not be able to market
the pigeon pea seeds. However, it is anticipated that, over time, the market outlets
might develop as entrepreneurs realize that quantities viable for marketing could be
available. Initially, the government might have to purchase the seed as a way of
promoting the use of pigeon pea improved fallow. The government might have to


guarantee the price at Z$2,500/Mg as a start. This would motivate farmers to adopt
an average of 0.2 ha of pigeon pea improved fallows.



annual 12
area(ha) ----------------

Pigeon pea
0. \ Area (ha)

0.6 - Sesbania
/ sesban Area
0.4 / (ba)

0 2 4 6 0
Price of pigeon pea seed (ZS'000'kg)

Figure 3. Average area planted to Sesbania sesban and pigeon pea fallows over 5
years at different pigeon pea seed prices.


When both Sesbania sesban and pigeon pea improved fallows were offered to
farmers at the same time, a market for pigeon pea seeds was needed for farmers to
adopt pigeon pea improved fallow. The adoption of improved fallows buffered
income for discretionary spending from the negative effects of fertilizer price
increases. Income did not change significantly due to changes in fertilizer prices
following the adoption of improved fallows and green manure.
Several recommendations can be drawn from the study. The results from
this study show that under the current economic and social circumstances facing
smallholder farm households in Zimbabwe, there is potential for improved fallow
technologies being adopted. Given the high rate of inflation in Zimbabwe (estimated
to be 400% per annum) and the absence of a mechanism to subsidize chemical
fertilizer, fertilizer prices are going to continue rising. Study findings suggest that
the percentage of adopters and the area under fallows could also increase. Therefore,
these technologies should be extended to smallholder farmers.


The study shows that, LP models are developed to simulate the behaviour
of smallholder farmers. They can also be used to determine the farmers' potential
adoption of technologies and for assessing the impact of such technologies of the
welfare of the households, measured in various ways. In addition the impact of
various policies, e.g., low fertilizer prices or availability of markets, could also be
determined. In the same light, the model can be employed to determine the effect of
change in available household labor or sources of non-farming income, as might
result from HIV/AIDS, on the welfare of the household.
However, it should be borne in mind that the model results represent the
long-term position in the adoption of the technologies, i.e., when farmers have full
information about technologies and at peak adoption. This is likely to take time to be
achieved. The model does not determine how long the adoption process takes
before reaching peak adoption The duration of adoption will depend on how the
technologies are extended to farmers. In this respect, an efficient extension
organization will hasten the adoption process. Nevertheless, the households that
adopt the technologies and the area they adopt, in the long run, were determined in
the model.


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The objective of the model is to maximize the sum of annual discretionary cash over
five years. Some of the cash is transferred from the previous quarter, c-l, after
taking account of the expenditure in current quarter, c. The sources that contribute to
cash vary in each quarter. Some non-farming activities, such as poultry production
and beer brewing, bring in cash each quarter income of the year. Other activities like
selling crops only bring cash in one quarter of the year. Some cash is transferred to
the next quarter to meet the future expenses.

The model had the following activities:
Maize, groundnuts, Bambara nuts, finger millet, sunflower, cotton, sweet
potatoes, soyabeans, horticulture, hired out labour, hired in labour, vending,
poultry production, beer brewing and selling, construction of houses,
making peanut butter, molding bricks for sale, purchase maize to meet own
food requirements, managing cattle manure.

The mathematical for of the model is as follows:

Maximize: Z = jX

Subject to: a.X < b, for all i

xj 0


Land: The household allocates its land to different crops. All crops, except
groundnuts, can be planted early or late. Early planted crops are planted in the first
quarter. Late planted crops are planted in the second quarter. Groundnuts are only
planted early, in the first quarter. In addition, manure can be applied to the land.
Maize is planted on the land with manure. Land constraint stipulates that the area
under crops in a given year cannot exceed the arable land that the household

Garden Area. The area planted to maize in the garden cannot exceed the size of the
garden. In the garden, cattle manure or chemical fertilizers can be used solely, or in
combination as with field maize.
Garden maize is planted in the third quarter. Therefore, its cycle spans two years,
i.e., planted in the third quarter of year t and harvested in the second quarter of the
following year, t+l. Garden area planted in year t, is transferred into the next season.
Similarly, garden area planted in year, t-1 i.e., GMZ(t-l) is only harvested in year t.
Area of maize planted in the garden in year t, i.e., GMZ(t) is transferred into the
following year, t+l. Similarly, garden area planted in the preceding year (t-l) is
transferred into current year (t). Land with manure is distinguished from land
without manure.
Manure area planted to maize in year t is replanted to maize in the following year,
t+l. The area under manure in year t-1 is the same as the area planted to the same
plots in the second season.
The area applied with manure in year t-1, is planted to field maize or
garden maize in year t.
The area under maize in season t equals the area planted to maize on
residual manure in the following year.

Generating manure area. Manure area generated in year t equals all the manure
area transferred to the following year, i.e., (t+l).

Labour: Activities are conducted at different times of the year, so the opportunity
cost of labour also varies within the year. Some households differentiate labour by
gender, while others do not. In food deficit households, labour might also be
expended in working for food. Working for food can take place throughout the year,
depending on when the household seeks to bridge up the food deficit. The
differentiation and tiring of labour use are reflected in the model.

Beginning Cash: This variable is the cash used for farming from the beginning to the
end of the season obtained from sources such as sales of the previous year's crop,
remittances, and non-farming activities. Use of credit has been declining over the
years. Credit was used by 6% and 26% of the sample farmers in 2000 and 1990,
respectively. In 2000, credit was only available for groundnut inputs.
Households start the year or quarter with a stock of cash. This is cash
carried over from the previous year or quarter. Exogenous cash is injected into the


Where: Z = objective function,
Aj=jd production activity of the farm, e.g. Maize, cotton, cattle,
cj = forecast gross margin of j,
aij = the amount of input i pope4d to operate activity j on a unit of a
resource, e.g., a hectare of land;
bi = available supply of the resource i.

An LP model is organized as a tableau (Figure 2-1). The taplau consists of
inputs, activities, constraints and the objective function. The input section has a list
of the inputs needed for all activities. All the inputs listed are not necessarily used by
all activities. Activities are represented as columns. They account for the different
production techniques through the input-output coefficients. For each activity, the
coefficients are linear and constant. In the tableau, the constraints vector, often
called the right hand side (RHS), consists of the resources available to the farmer or
the constraints to be met. There is also an objective function to be r~ximized or
minimized in the model.
LP models can handle multiple crop activities. Effects of changes in
decisions on the various crops cap be determined (Singh and Jarlakiram, 1986).
Consumption requirements can be incorporated in the model as constraints. This
makes LP models ideal for smallholder farmers who have to meet food security
requirements. Separate activities compete for scarce resources in the model.

Activity Levels Net Revenue
Inputs Crop activities: Input-output Constraints
List of inputs Coefficients Resources
needed for all all or available to the
activities. Not ai farmer,
all activities or Also consumption
require all the requirements.
inputs A(i+)j
The coefficients indicate the
amount a of an input i needed to
operate activity on a unit, e.g.,
unit of land.
The coefficients are linear and

Figure 2-1. Structural Form of the LP model (Adaptedfrom Timmer et al, 1983)

The constraints in the models are as follows: The constraints are represented by the
mathematical representation: a,.Xj < b,. In essence, each constraint states that

the use of the resources in each of the activities, Xj, which the household could
undertake, cannot exceed the resources that the household possesses.


system through remittances from employed members staying away from home. The
household also needs to pay for the expenditure they incur during that quarter.
At the end of the season, any surplus is transferred to the income at the end
of the quarter. Expenditure in each crop depends on the stage of development of the
crop. For example, early-planted maize is top-dressed at a different time from that of
the late-planted crop. Crops under different levels of management also require
different financial resources, e.g., maize produced using chemical fertilizer alone
requires expenditure for basal fertilizer at planting. This is not required in maize
produced using a combination of cattle manure and chemical fertilizer.

Crop accounting: Maize transferred from years t-1 should be equal to maize for
consumption and maize transferred to the next quarter. Maize is also brought in from
harvests from garden plots in the second quarter and from the field crop in the third
quarter. The same applies to groundnuts and bambaranuts, only that they are not
produced in gardens. Maize is used as an input in beer production while groundnuts
are used in making peanut butter during the third and fourth quarters. Cash crops
like sunflower and cotton are produced and sold on the market without transferring
them from one quarter to another.

Maximum on non-farming activities: The limits on the level of non-farm activities
that households could engage in were determined from survey data. Without placing
limits, the model would have allowed some households to exceed the stipulated
limits, which would have been unrealistic since such a scenario would result in over
supply on the markets. Farmers avoid over supply. For example for beer brewing,
they indicated that they took turns to ensure that the person selling in any day was
guaranteed of buyers.

Consumption Requirements: Typically, semi-commercial smallholder farm
households store some food for consumption by their membership. The quantity of
the staple food crops that each household stores every season was obtained during
the survey. Maize requirements for subsistence were expressed as a regression
equation. This was to allow variations in household composition during sensitivity
analysis to be captured through the consumption regression model.
Maize for subsistence requirements is met from maize transferred to
consumption from the proceeding quarter, plus maize obtained by working on other
people's farms. A minimum level of subsistence requirements has to be met in each
Bambara nuts are transferred directly from third quarter with 4% losses
during storage and processing.
Area planted to groundnuts in year t has to be less than equal to the
maximum area that farmers can plant to groundnuts.
Households owned few cattle. Therefore, a limited area could be applied to
manure each year. An average area is used in the model.


The income generated in quarter c bf year t has to be greater than or equal
to the income required to meet the cash requirements of the household in that

M. Mudhara, University of Zimbabwe, Zimbabwe and P. Hildebrand, University of
Florida, USA

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