INTRODUCTION
Since independence, tea production in Kenya has increased from 18,000 to 220,000
metric tons with smallholder subsector rising from 1.7 to 59% (Nyangito
and Kimura, 1999a). At a macro level, tea has made a substantial impact
on Kenya’s economy by employing over 3 million individuals (Gesimba
et al., 2005) and contributing to foreign exchange. In fact, Kenya
is the fourth major black tea producer in the world market and also ranks second
after Sri Lanka in tea exports. Kenya’s tea plays a very important role
in blending with others (Nyangito and Kimura, 1999b) to
improve their quality. Compared with other export crops, tea has maintained
an upward trend. However, the contribution of tea at the micro level has been
declining, especially among smallholders. This is despite the fact that smallscale
tea production accounts for 65% of the total area under tea production and about
62% of production (Nyangito, 2000). This decline may be
attributed to decline in the world market and diminishing demand in most of
the main traditional markets. Since, the late 90s to date, earnings from tea
production have not been lucrative and farmers are unable to fulfil their family
needs as compared to the period following the introduction of the crop in Kenya
and the late 1980’s to early 1990’s when tea farmers earned much higher
than other farmers in the neighbouring regions and other parts of the country.
Due to earlier attractive tea prices, they planted large parcels of their land
with tea and left little for food crop and other activities. They therefore
relied on the market purchase of food. With fluctuation of tea prices and increased
production costs, tea smallholders are now faced with double tragedylow income
and low food availability. Getting alternative sources of income has been a
challenge for these farmers as they have limited land, capital and water resourcesall
which are required to increase agricultural production and increase their family
income. Some have tried to venture into offfarm activities. However, these
opportunities are also limited. There are no large scale farms to work in and
those farmers who offer casual labour are few and do not pay enough to enable
the labourers to adequately support their families.
The study focus is small scale tea producers who are facing declining
living standards and economical struggle despite the fact that tea is
a major foreign earner for the country. Farmers are no longer able to
meet their basic needs and many youths are moving to urban regions to
search for better paying jobs. This study aimed at identifying and testing
strategies that could be implemented to enhance family income.
MATERIALS AND METHODS
The analysis presented in this study relate to data collected in the tea growing
zones of Murarandia location, Murang’a District in the year 2005, within
a larger framework of a Ph.D research. To select families for the family survey,
a list of tea buying centres was obtained from Githambo tea processing factory,
the only tea factory in the region. All smallholder tea producers in Kenya have
accounts in factories through which they sell their produce. After tea is harvested
from the farm, it is taken to the buying centre where it is sorted to ensure
only quality leaf is delivered to the factory for further processing and also
weighed to determine the amount each farmer has. Eight buying centres under
the jurisdiction of Githambo tea factory were randomly selected. The names of
all families delivering tea through the eight buying centres were listed alphabetically
and systematic random sampling was applied to select 60 families. After data
collection and preliminary analysis of family resources, the tea families were
found not to be homogenous based on their family and land sizes. These two factors
determine the class or group a family can be identified with in terms of their
living standards or welfare. Like in many agricultural areas in sub Sahara Africa,
land size in this region determines the potential or limitation of production
in a family while family size determines requirement of food and sometimes,
accessibility of other needs such as education and health. Therefore, variables
that explained family and/or land size were used to classify the sample into
two homogenous groups, namely the resource rich and resource poor, using hierarchical
cluster analysis in SPSS. To identify variables for the analysis, a correlation
analysis was first done. As Marz (1990) indicates, those
variables which show high correlations, r > 0.5, with one or more other variables
disturbs the classification process. Therefore, the variables selected for the
analysis showed a weak correlation. Using SPSS, average linkage procedure in
combination with cosine distance measure were selected to carry out the analysis.
Descriptive statistical analysis of resources, crop and livestock production
activities, offfarm and consumption activities and other aspects of living
standards of the families were then done to provide an understanding of
the farming systems and hence formulate a strategy to improve their income.
The analysis indicated that fluctuation of tea prices was a major problem
in the region. A strategy of changing the tea prices was therefore formulated.
The hypothesis was that increasing tea prices may increase family income.
Ten year dynamic models were applied to measure the impact of the strategy
on family income. Averages calculated from descriptive analysis were used
as statistics in the models. Modelling entails allocation of limited family
resources to activities which compete for these resources and provide
different contributions to the family objectives. Decision making about
resource use in a year has an effect on resource use in other years because
farm resources change over time thus the need for dynamic models. Every
year or every period in the model applied in this study was linked by
a single objective. First and foremost, basic models of the two groups
created through hierarchical cluster analysis were designed. The basic
model of each group describes the farming system of the group through
technical coefficients, resource constraints and a set of activities based
on the results of the survey and therefore represent reality. Monte Carlo
simulation was then used to randomly create future prices that were applied
in testing the strategy of changes in tea prices. After implementation
of the strategy, that is, replacing the survey tea prices with the future
prices, the models were run again. The results of the model were calculated
using the XA professional programme. To assess the impact of the strategy,
two procedures were followed:
• 
Application of the dynamic models of each group for
a period of 10 years assuming only the current trend for the entire
period (without a new strategy) 
• 
Application of the dynamic models with a modified scenario
(with strategies) and then the results were compared 
The difference between both outcomes may be regarded as the impact of
the tested strategy on the living standards of the farmers.
FLUCTUATION AND FUTURE STRATEGY
Smallholders sell their produce through factories located in their regions.
The prices of tea from each of these factories vary depending on various
factors, the major one being the quality of tea leaves. Tea prices in
Kenya have been fluctuating over the years. In all smallholder factories
in the country, farmers are paid monthly according to the amount of tea
(green leaf) they deliver. They are also paid a second time (commonly
known as bonus) which may be once a year or distributed twice a year.
In Githambo tea factory, the price of one kilo of tea leaf per month increased
from Ksh 6 in 1999/2000 to Ksh 9 in 2003/04. Bonus decreased from Kshs
23.38 to 12.05 during the same period. Therefore, a strategy of changing
tea prices would be appropriate in improving family income and living
standards of the smallholders.

Fig. 1: 
Strategy and scenario tested for the future impact analysis
on family income of smallholder tea producers in Murarandia Location,
Murang’a district, Kenya, 2005 
This strategy was selected based on farming systems and living standard
analysis of the smallholder tea farmers in the region. These analysis
identified fluctuation of tea prices as a major problem affecting tea
farmers. This is because it leads to variation of family income prompting
farmers to continuously adjust their way of life. If a family does not
have another source of income, these changes may be more devastating.
Children may drop out of school, diseases may go untreated, family may
incur debts and food ration may reduce among other problems. The scenario
describes how the strategy was tested. This was done by simulating old
tea prices to create future prices and then observe the impact of the
new prices on family income. When creating the new prices, the trend displayed
by the old prices was assumed. Other factors were also assumed to be constant.
The problem, scenario and strategy tested are shown in Fig.
1 .
Due to the high income contribution of tea to farming families, it was
hypothesized that fluctuation of its prices could have a negative effect
on the stability of farm income and consequently family income of the
families. The fluctuations of tea prices over ten years were simulated
using the MonteCarlo method and the effects on the stability of family
income and of the tea production area were estimated using a onesample
ttest. Data to simulate tea prices was for 12 years.
DYNAMIC MODELS
Models provide the link between economic theory and data on one hand and practical
appreciation of problems on the other hand (Hazell and Norton,
1986). Limited productive resources have necessitated individual families
to make decisions (Hazell and Norton, 1986) on farm, offfarm
and household sectors (Grueninger, 2001) which impact
on living standards of the farming families. Different actions on this sectors
lead to different levels of realization of family objectives. The families are
therefore faced with a decision making problem between alternative levels of
objective realization (Wallace and Moss, 2001). The modelling
of family decisions therefore aims at determining the optimal family resource
allocation by determining what is feasible with given knowledge and limited
access to resources (Akinsanmi, 2005). This entails allocation
of limited family resources to activities which compete for these resources
and provide different contributions to the family objectives.
The rationale of modelling is based on the idea that any phenomenon or process
can be simplified by leaving out of the picture any aspects or variables that
are not of interest to the modeller, while still portraying something meaningful
about the real phenomenon or process (Katwijukye, 2005).
An attempt is made to investigate the implications for resource management and
their use on the sustainable living standard development of the farmers by applying
a family model premised on programming techniques.
Decision making about resource use in a year will have an effect on resource
use in other years because farm resources change over time. Every year
or every period in the model applied in this study was linked by a single
objective. The general structure of the dynamic linear programming model
has the following mathematical form:
Subject to
all i = 1 to m and all t = 1 to y 
all j = 1 to n and all t = 1 to y 
Where:
Z 
= 
Objective function (family income) 
X_{jt} 
= 
Level of activity j in period t 
P_{jt} 
= 
Price of per unit of the j output activity in period t 
C_{jt} 
= 
Cost per unit of j input activity in period t 
y 
= 
No. of periods 
n 
= 
No. of possible activities 
m 
= 
No. of resources and constraints 
a_{ijt} 
= 
Technical coefficient (amount of ith input required to produce one
unit of jth activity in period t) 
b_{it} 
= 
Amount of ith resource available in period t 
The objective function was to maximize the family income subject to family
resource availability and other constraints. The family income was maximized
through maximization of value of crop and livestock products and offfarm
income and minimization of production costs. The components of the objective
functions were the variable costs of crop and livestock production per
unit of land or livestock unit excluding hired labour costs, the average
sales prices of crops and livestock products, household consumption, food
purchase, average offfarm wage rate and interest from formal and informal
credit. To achieve its objectives, a family must perform activities by
using the available resources. These includes farm, family and offfarm
activities such as crop production (allocation of each crop), livestock
production, selling activities, purchasing of inputs and food, labour
used for offfarm activities and hiring of outside labour. The model was
subject to resource constraints, the needs of the farm, family and activities
that were fixed or have certain minimum or maximum values.
A oneyear basic model was used to build the dynamic model for a period
of ten years which were linked by a single objective. This is because
production plans for one season will have an effect on the following seasons
especially in food crop production. The same effect is found in perennial
crops whereby effect of one year transcends on the subsequent years. The
dynamic model consisted of different periods. For every period, the requirements
differ in terms of capital, labour needs and crop yield levels. The technical
coefficients in some cases were assumed to be the same in each period
but in other cases they were different between periods. The dynamic models
were built in such a way that it was possible to transfer surplus cash
from period 1 to 2, from period 2 to 3 up to period 10.
Modelling a system requires a certain level of abstraction and simplification
of reality, which is expressed in a matrix of main activities and constraints
(Katwijukye, 2005). Obtaining model results identical
to reality therefore requires complete knowledge and information about farmers’
behaviour and decisionmaking (PapeChristiansen, 2001).
To test how realistic the basic model is and how suitable it will be for future
strategy testing, validation is necessary (Praneetvatakul,
1996). A good model should present results, that is, farm, offfarm, family
incomes and resource use, that are close to reality (Regassa,
2002) and which behaves in its main components like the real system (Marz,
1990). Despite the fact that the basic models were designed as close to
reality as possible, a gap between the basic model and reality still exists
due to the complexity of the real world (Kitchaicharoen, 2003).
The mathematical basic model gives results through optimal use and integration
of resources in farm and family. It is assumed that the model quality can be
accepted if the model results are close to reality. This will not be identical,
since reality does not show perfect knowledge and immediate decisions. Validation
was done through (1) comparison of farm, offfarm and family income (2) comparison
of resource use (land and labour), allocated and enterprise combination.
Table 1 shows that the model predicted higher farm,
offfarm and family incomes. The model allocated land used for food crop
production to kale, cabbage and potato production. Other food crops which
deemed not to contribute significantly to family income were not included.
For example, other than kale and cabbage, there were other vegetables
such as solanum sp. and Amaranthus sp. grown but only for
home consumption and sometimes as wild. Other animals other than cows
were found in the farms such as chicken and goats. The farmers however
did not keep enough to be considered in the model. As for goats, one could
find only one or two which were kept for Christmas or other family gatherings.
The other explanation of the big difference between model results and
survey data is that the model allocated the existing land under food crops
plus noncultivated land to food crop production in the model.
Table 1: 
Comparison of farm, offfarm and family incomes between
the basic model and survey among tea smallholders in Murarandia Location,
Murang’a District, Kenya, 2005 

Diff (%): Differences between survey and model results
in percentage 
Table 2: 
Comparison of farm, offfarm and family incomes between
the basic models and survey among resource rich and resource poor
tea smallholders in Murarandia Location, Murang’a District, Kenya,
2005 

Diff (%): Differences between survey and model results
in percentage, RR: Resource Rich, RP: Resource Poor 
Table 3: 
Comparison of enterprise combinations between the basic
models and survey incomes, Murarandia Location, Murang’a District,
Kenya, 2005 

NA: Not Applicable, Diff (%): Differences between survey
and model results in percentage 
Therefore,
the land under food crop production in the model was higher than the land
under food crop production in reality. All the land that do not have cash
crop was considered as land that a farmer could grow food. For example,
some tea farmers have not cultivated close to the river but there is a
possibility that in the future, farmers might grow vegetables in this
land. Because of this reason, farm income was higher than reality and
this also increases family income.
Analysis between the RR and RP tea smallholders indicate a higher difference
between the model and survey incomes (Table 2) among
the resource rich. The resource rich also have more uncultivated land
which was allocated to food production by the model. The optimal model
results indicate variable land sizes were optimized to grow different
crops (Table 3).
The model of all farmers has allocated significantly more land to cabbage
production as compared to survey results. The model has allocated similar
land to tea production because there was no competition of tea land with
another crop. The number of dairy cows was the same in both the model
and the survey results. There was also no competition of resources with
other livestock. Among the resource rich, the model did not allocate any
land to kale production but allocated most land to cabbage production.
Among the resource poor, results of kale production were not highly significant,
similar as what was observed among all farmers. The model also allocates
only 0.002 ha of land to potato production as compared to 0.02 ha in survey
results. This was due to high production costs of potatoes.
The model allowed for hiring of labour especially during the peak period of
tea harvesting and during preparation and planting of food crops. The dual value
from the model indicated that increasing land under tea production by 1 ha would
increase earnings by Kshs 8,319.21 while increasing land under food crop production
by 1 ha would increase earnings by Kshs 50,967.11. This indicates the importance
of improving food crop production in the tea zone. The differences in the use
of family resources between the model and survey results may be explained by
the risk behaviours of the farmers. Farmers may prefer farm plans that provide
a satisfactory level of security even if it means sacrificing income on average.
The risk behaviours therefore create a gap between the model results and real
practices (Sattarasart, 1999). The model assumes a perfect
environment but the real practices are met by risks and uncertainties. Based
on the results of farm, offfarm and family income, as well as resource use
and a combination of farm enterprises, the basic model of all farmers, RR and
RP farmers presents enough approximation to the actual farmers’ practices.
The basic models have therefore been used as a basis of constructing the multiperiodic
models.
MONTE CARLO SIMULATION
Simulation is a numerical technique for conducting experiments which involves
certain types of mathematical and logical models that describe the behaviour
of a system over extended periods of real time (Naylor et
al., 1966). Monte Carlo is a simulation method which is defined as a
stochastic technique that involves using random numbers (Hammersley
and Handscomb, 1964; Gujarati, 1995; Wittwer,
2004) and probability statistics to solve or investigate problems. To call
something a Monte Carlo experiment, all that is needed is to use random numbers
to examine some problem (Pecherska and Merkuryev, 2005).
The random variables are defined as stochastic variates which are uniformly
distributed (Marz, 1987).

Fig. 2: 
Fluctuation in average prices of tea in the last 12
year, Murarandia location, Murang’a District 
The inputs are randomly generated
from probability distributions and so the aim is to choose a distribution for
the inputs that most closely matches the existing data, or best represents the
current state of knowledge (Wittwer, 2004). A typical
Monte Carlo simulation calculates the model hundreds or thousands of times,
each time using different randomlyselected values (Wittwer,
2004). The principle behind Monte Carlo therefore, is that the behaviour
of a statistic in random samples can be assessed by the empirical process of
actually drawing lots of random samples and observing this behaviour (Mooney,
1997). This aims at creating an artificial world which resembles the real
world (Kitchaicharoen, 2003).
Marz (1990) applied Monte Carlo method to simulate a
set of correlated crop yieldprice data while Kitchaicharoen
(2003) simulated a set of lychee prices from historical data of lychee price
over 13 years. The same concept was applied in this study. Data obtained from
the main tea factory in the study area provided the basis for specifying the
parameters (mean and standard deviation) of a normal distribution of tea prices
over time. The data includes prices paid to the farmers monthly (first payments)
and bonus (second payment) for the year 1994 to 2005. Figure 2
shows fluctuation of tea prices in the past 12 years. Figure 2
used averages of first payments and second payments.
The simplest methods to simulate and test random series are based on the assumption
of normal distribution of the data (Marz, 1987). In this
study, price distributions over time are statistically normal. Following Kitchaicharoen,
2003, the procedures (Fig. 3) of the Monte Carlo simulations
were as follows:
• 
Analysis of the distribution of the historical data
of tea prices, that is, mean and standard deviation of the distribution
of tea prices 
• 
The parameters from the first step were used to generate random
tea prices that follow the same distribution as the historical data. For
each model run, a new set of random variates of the stochastic variables
are generated (Marz, 1987) 
• 
The simulated tea prices were then entered in the dynamic
model 
• 
The dynamic model was run and the results of each run
recorded 
• 
The second to fourth steps were repeated 100 times to
obtain the probability distribution almost similar to historical data 
RANDOM NUMBERS GENERATION AND SIMULATION
As described earlier, historical fluctuation of tea prices in the study area
were used as a basis for specifying the mean and standard deviation of a normal
distribution of tea prices. The historical tea prices were tested for distribution
and were found to be normally distributed and the average of 12 years was 10.3
Kshs kg^{1}, with a standard deviation of 2.47 Kshs kg^{1}.
These parameters were used to generate random observations which follow the
same distribution (Marz, 1987). The tea prices over time
were randomly generated using the random number generation tool in Microsoft
Excel 2000. To generate the random number, the number of variables and number
of random numbers required were specified. In this study, the variables required
were 100 because the model was run 100 times. The number of random numbers required
was 10 since the model used was a 10 year dynamic model. Therefore, one random
variable was entered for each year, from 1 to 10 year. What were also required
to generate the random numbers were the parameters and in this case it was the
mean (10.3) and SD (2.47) generated from the historical data. The results generated
were saved because the computer clock was used as the random seed and regenerating
random numbers a different time would give different results. A random seed
is a number used to set the starting point for generating a series of random
numbers. It ensures that later rerun of the same analysis at any time produces
similar results.
The average price of the simulated tea prices over all ten years and
all 100 tenyear iterations was estimated at 10.25 Kshs kg^{1},
with a standard deviation of 2.44 Kshs kg^{1}. This average price
and standard deviation differ from the average historical prices and the
standard deviation by 0.85 and 1%, respectively. A tenyear simulation
of the model with the random tea prices for each of the ten years comprises
one run of the model. The tenyear simulation run was repeated 100 times
to allow estimation of a probability distribution for family income. The
average annual family income over all ten years and all 100 runs of all
tea farmers and also the two different groups in the tea zone (resource
rich and resource poor) was estimated and compared to the average annual
family income over ten year under a constant tea price. A statistical
ttest was performed to test the significance difference between the average
annual family income under simulated prices and the average annual family
income under the constant price.
RESULTS OF SIMULATION AND IMPACT OF THE STRATEGY ON FAMILY INCOME
Impact of strategy on family income of all tea farmers: Average
annual family income under simulated prices after every 20 years was compared
with average annual family income under constant prices. The results indicated
that after one run, the difference between the average annual family incomes
under constant prices and simulated prices was high (14.19%) as compared
to 60 runs which was only 0.18%. This point out that the more runs that
are done, the closer the average annual family income under simulated
prices is to the average annual family income under constant prices (Table
4). This indicates that in simulation models generating more random
variables to solve a problem gives more effective results and which are
close to reality. After the 80 runs, the difference was positive and higher
than average annual family income under constant price.
Table 4: 
Comparison of average annual family income between the
constant prices and simulated prices scenarios in the tea zone, Murarandia
Location, Murang’a District, Kenya, 2005 

Average family income under constant price = Kshs 136,
360.81, *Percentage differences between average family income under
simulated prices and average family income under constant prices 
Table 5: 
A ttest to demonstrate the significance difference
between the average annual family income under simulated tea prices
and average annual family income under constant tea price, Murarandia
Location, Murang’a District, Kenya, 2005 

Test value = 136,360.81 
This indicates
that the data generated (average annual family income under simulated
prices) was following normal distribution trend. If more runs were done
above 100 and the data generated was positioned in a graph, it would produce
a normal shaped distribution.
Results also show that the average annual family income under the simulated
prices (Mean = 135741.20; SD = 10479.44) was less than the average annual
family income of Kshs 136,360.81 under determined constant price. This
was about 0.45% less than the average annual family income under the constant
price of Kshs 10 kg^{1}. However, a onesample ttest (Table
5) shows that the difference between the two incomes was not significant:
t (99) = 0.59; p = 0.56 (twotailed). The 95% confidence interval of
the difference was (2,698.96; 1,459.74). The fact that pvalue was high
indicate that fluctuation in the tea prices has low effect on the stability
of family income of the whole sample of tea farmers. The low standard
deviation in percentage of the average annual family income under the
simulated prices (7.72 %) also indicates stability of family income among
the tea farmers.
The histogram (Fig. 4) shows the distribution of the
average annual family income over the 10 year simulation and after rerunning
the model 100 times. N represents 100 different average annual family
incomes, each representing an average of the family incomes calculated
from running a 10 year dynamic model. The frequency represents the number
of runs or how many average annual family income lie within a particular
point.

Fig. 4: 
Distribution of the average annual family incomes of
tea farmers under the simulated tea prices, in Murarandia location,
Murang’a District 
If added up together, they will total to N = 100. The histogram
indicates as mentioned above that the data generated lies along a normal
distribution. This is because the data used to generate the random variables
was also normally distributed. Since this also follows a normal trend,
it is unlikely that errors were made during the calculation of the average
annual family income under simulated prices. The histogram also indicates
that the probability that the expected average annual family income under
simulated prices is equal or above 136,360.81 (average annual family income
under constant price) was 47.6% among the tea farmers in the study area.
This was calculated using the following equation of zscores.
Where:
X 
= 
Average family income under constant price 

= 
Average family income under simulated prices 
s 
= 
Standard deviation of family income under simulated prices 
X = 136,360.81;
= 135,741.20; s = 10,479.44. Z score was calculated as 0.06.
This value in the table of standard normal distribution was 0.47608.
One may therefore expect the average of all first years in 100 runs to
reflect the average annual family income for the year 2006 (information
from the factory in the study area confirmed that the average price paid
to the farmer in the year 2006 was 12.44% higher than average price paid
in the year 2005), the average of all second years to reflect the average
family income for the year 2007 and so on. Figure 5
shows the average annual family incomes for the ten years in the dynamic
model after 100 runs.

Fig. 5: 
Distribution of the average annual family incomes under
simulated tea prices for 10 years after 100 runs in Murarandia location,
Murang’a District 
Table 6: 
Comparison of average family income between the constant
prices and simulated prices scenarios among the resource rich in the
tea zone, Murarandia Location, Murang’a District, Kenya, 2005 

NB: Average family income under constant price = Kshs
199,998.70, *Percentage differences between average family income
under simulated prices and average family income under constant prices 
The average for the first years of the 100 runs was calculated and this
was repeated for the second to the tenth year. The graph indicates that
the average annual family income may increase for the years 2006 and 2007
and then reduce drastically in the year 2008 and then shoot up again in
2009. This may probably be due changes in market forces that affect the
prices. The other reason would be climatic changes that may reduce the
yields of green leaf harvested thus lowering the average annual family
income.
Impact of strategy on family income of resource rich tea farmers:
Similar to all farmers situation, the average family income under
simulated prices after every 20 years was compared with average family
income under constant prices. The results indicate that after one run,
the difference between the average family incomes under constant prices
and simulated prices was high (14.46%) as compared to 50 runs which was
only 0.50% (Table 6). The direction of the difference
changed at 60 runs to positive and was at peak at 80 runs. Similar to
the whole zone analysis, the trend of a normal distribution was also observed
among the Resource Rich tea farmers.
Results show that the average annual family income under the simulated
prices (mean = 200,375.45; SD = 16,428.51) was greater than the average
annual family income of Kshs 199,998.70 under determined constant price.
Table 7: 
A ttest to demonstrate the significance difference
between the average annual family income under simulated tea prices
and average annual family income under constant tea price, among the
resource rich tea farmers, Murarandia Location, Murang’a District,
Kenya, 2005 

Test value = 199,998.70 

Fig. 6: 
Distribution of the average annual family income of
resource rich tea farmers under the simulated tea prices, in Murarandia
location, Murang’a District, Kenya, 2005 
This was about 0.19% higher than the average annual family income under
the constant price of Kshs 10 kg^{1}. However, a onesample ttest
(Table 7) shows that the difference between the two
incomes was not significant: t (99) = 0.23; p = 0.819 (twotailed). The
95% confidence interval of the difference was (2,883.00; 3,636.55). The
fact that pvalue was high indicate that fluctuation in the tea prices
has low effect on the stability of family income of the resource rich
tea farmers. The low standard deviation in percentage of the average annual
family income under the simulated prices (8.20%) also indicates stability
of family income in this group.
The histogram (Fig. 6) shows the distribution of the
average annual family income over the 10 year simulation and after rerunning
the model 100 times. The frequency represents the number of runs or how
many average annual family income lie within a particular point. Similar
to the observation among all tea farmers, the histogram indicates that
the data generated lies along a normal distribution. The probability that
the farm families will get an average annual income in the range from
Kshs 200,375.45 to 216,803.96, that is, between the mean and a value one
standard deviation above the mean, was approximately 38%.
Table 8: 
Comparison of average family income between the constant
prices and simulated prices scenarios among the resource poor in the
tea zone, Murarandia Location, Murang’a District, Kenya, 2005 

NB: Average family income under constant price = Kshs
95,598.69, *Percentage differences between average family income under
simulated prices and average family income under constant prices 
Table 9: 
A ttest to demonstrate the significance difference
between the average annual family income under simulated tea prices
and average annual family income under constant tea price, among the
Resource Poor, Murarandia Location, Murang’a District, Kenya,
2005 

Test value = 95,598.69 
Impact of strategy on family income of resource poor tea farmers:
Average family income under simulated prices after every 20 years was
also compared with average family income under constant prices. The results
indicate that after one run, the difference between the average family
incomes under constant prices and simulated prices was high (12.17%)
as compared to 40 runs which was only 0.10% (Table 8).
The direction also changes as observed in earlier analysis but after 60
runs. The peak was after 80 runs which then start to reduce at 100 runs.
The trend of a normal distribution was also valid and one can expect a
normal curve after more runs above 100.
Results show that the average annual family income under the simulated prices
(mean = 96,032.62; SD = 6,439.62) was greater than the average annual family
income of Kshs 95,598.69 under determined constant price. This was about 0.45%
higher than the average annual family income under the constant price of Kshs
10 per kilogram. However, a onesample ttest (Table 9) shows
that the difference between the two incomes was not significant: t (99) = 0.67;
p = 0.50 (twotailed). The 95% confidence interval of the difference was (843.83;
1,711.69). The fact that pvalue was high indicate that fluctuation in the tea
prices has low effect on the stability of family income of resource poor tea
farmers. The low standard deviation in percentage of the average annual family
income under the simulated prices (6.71%) also indicates stability of family
income among the resource poor tea farmers.
The histogram (Fig. 7) shows the distribution of the
average annual family income over the 10 year simulation and after rerunning
the model 100 times.

Fig. 7: 
Distribution of the average annual family income of
Resource Poor tea farmers under the simulated tea prices, in Murarandia
location, Murang’a District, Kenya, 2005 
The probability that the expected average annual
family income under simulated prices is equal or above 95,598.69 (the
average annual family income under the constant price) was 47% among the
resource poor tea farmers. At the same time, the probability that the
farm families will get an average annual income in the range from Kshs
96,032.62 to 102,472.25, that is, between the mean and a value one standard
deviation above the mean, was approximately 38%. The results indicate
that among the whole sample of tea farmers and also among the resource
rich and the resource poor, fluctuation of tea prices has low effect on
average family income. However, variation was higher among the resource
rich as compared to the resource poor. This was because they had more
land under tea production and were less diversified with other crops.
CONCLUSION
Results indicated that the difference in average annual family income
with simulated prices and with constant prices was not large. This indicates
that prices of tea in the study area were fairly stable and the effect
of prices changes to average annual family income and resource use was
not significant. Other factors which may or may not be related to tea
production may affect the average annual family income and resources.
This may include lack of good husbandrypoor plucking styles, not utilising
the recommended fertilizer, intense sorting of harvested green leaf in
the buying centres etc.
ACKNOWLEDGMENTS
The authors are indeed grateful to DAAD for the fellowship to collect
data, analyse and write up this research work. We also thank the staff
of University of Hohenheim, Institute 490 C for their support and the
farmers who willingly participated in the research.