Global Journal of Management and Business Research Vol. 10 Issue 1 (Ver 1.0), Febuary 2010 P a g e 176
Sensitivity and Uncertainty Analysis:
Applications to Small-land Scale Agriculture
Systems in Nigeria
*Ayinde,
O. E, Ayinde K; Omotesho O.A. and Muhammad-Lawal. A
Department of Agric – Economics and Farm Management
University of Ilorin, P.M.B.1515, Ilorin, Nigeria.
*E- mail: opeayinde@yahoo.com
Abstract- Sensitivity and uncertainty analysis is useful in providing information about local and global change tendency of
the management of enterprise mixtures to the choice of target return level. Hence, the study examines the sensitivity and
uncertainty analysis in small-land scale agriculture in Nigeria. The study used both primary and secondary data (time
series). A structured questionnaire was employed to obtain information from the five hundred (500) randomly selected
small-land scale farmers in central part of Nigeria. Descriptive statistics and Target-MOTAD (Minimization of Total
Absolute Deviation) model were used to analyze the data. The result reveals the normative plans for the small-land scale
agriculture system in Nigeria. The sensitivity analysis reveals that there is a positive relationship between capital and
returns and negative relationship exists between risk level and returns in small-land scale agriculture systems. Hence,
policies and programmes that increase returns and reduce risk level should be put in place in order to shape the small
land scale agriculture system.
Keywords- Small-land scale, sensitivity, Nigeria, Target-MOTAD model
I INTRODUCTION
Nigeria is blessed with various climatic zones, enormous resources and the potentials of producing, processing,
marketing and exporting of different output and commodities from agriculture (Babafada 2003). Agriculture is an
indispensable real sector in Nigerian economy. The roles of agriculture remain significant in the Nigerian economy
despite the strategic importance of the oil sector. Agriculture provides primary means of employment in Nigeria
(Ogundari and Ojo, 2007), and accounts for more than one-third of total Gross Domestic Product (GDP) (World
Bank, 2003). Nigerian agriculture is characterized by: a multitude of small land scale agriculture systems scattered
over wide expanse of land area, with smallholding ranging from 0.05 to 3.0 hectares per farmland, rudimentary farm
systems, low capitalization, and low yield per hectare (Ogundari and Ojo, 2007).
Nigeria agriculture has for decades depended largely on these small-scale landholders farmers, in spite of the
existence of urban agriculture. This set of small land scale holders representing over 90% of the farming populace,
cultivate produce as much as 85% of the total agricultural
production and 87% of export crops (Adubi, 2000). More so, these small-land scale farmers will continue to
constitute the backbone of Nigeria agriculture for the next twenty-five years. Despite the importance of the smallland scale farmers, they still operate largely under risk and uncertainty and are inadequately equipped against risk
and uncertainties (Adubi, 2000).
Risk and Uncertainty may result from one or a combination of four factors which may be endogenous or exogenous
(Anderson, Hardakier and Huirne 1997). These factors include prices or markets, production inputs, farm outputs
and institutional factors. Invariably, these result into the different types of risk and uncertainty faced by farmers.
Production risk could emanate from the unpredictable nature of the weather and uncertainty about the performance
of crops or livestock. Price or market risk comes from imperfect knowledge about prices of farm inputs and outputs
at the time that a farmer takes decisions. Financial risk may result from unexpected risk in interest rates on borrowed
funds, and the possible lack of availability of loan finance when required. While institutional risks emanate from the
instabilities in government and its policies, and socio-legal uncertainty within which the farmer operates. The
international environment also creates uncertainties because of unpredictability. For examples, the merging of
Eastern and Western Europe definitely had an effect in the world market; so also was the outcome of Europe‘ 92 on
commodities. In addition, Globalization has caused the East Asian countries to enjoy remarkable increases in per
capita income but sub-Saharan African countries have had effect of low rates of economic performance (LeBel,
2003). And World Trade Organization, although creates free trade, has results into high inequality internationally
and within the countries.
Given this setting of the small-land scale agriculture in uncertainty, their aforementioned importance and with the
expectation that developing countries such as Nigeria is expected to experience increase in economic growth,
Nigerian governments have over time tried several strategies and introduced numerous policies and programmes
aimed at shaping the Nigeria agriculture production, increasing the level, grade and varieties of their export crops.
These policies and programmes include Agricultural Credit Guarantee Scheme, Operation Feed the Nation, Green
Revolution, River Basin Development Authorities, National Accelerated Food Production Programme, Guaranteed
Minimum Price Scheme, Marketing Board System,
P a g e |177 Vol. 10 Issue 1 (Ver 1.0), January2010 Global Journal of Management and Business
Research
Agricultural Development Projects (ADPs), etc. However, the success of all the various agricultural programmes has
been minimal (Ukpong, 1993). This is may be because the factors at which the small land scale agriculture is
responsive are still yet to be considered in the various programmes. This couple with the fact that this small-scale
agriculture is more expose to risk and uncertainty than other segment of economy may cause the results of the
various programme been minimal in its impact on agricultural and economics growth. Hence a need to understand
the factors that can result into the small land scale agriculture stability on the efficiency frontier through a sensitivity
and uncertainty analysis. Therefore, the study examines the farm plan(s) that would adequately provide the smallscale farmers with improved income under uncertainty and explores the sensitivity and uncertainty analysis that will
consequently raise the efficiency of the small-land scale agriculture in Nigeria. This study will not only help policy
planners but it will also provide useful information to small-scale land agriculture especially on farm size plan,
budgets and returns to investments. It will also offer suggestions on how risk efficiency in small-scale agriculture
could be improved such that it would have greater impact on agricultural and economic growth.
II THEORETICAL AND EMPIRICAL
FRAMEWORK IN UNCERTAINTY ANALYSIS
The concept of uncertainty in any application depends on the behavioral decision model employed. The popular
Bernoullian (1738) expected utility criterion utilizes an objective function that is a function of all the statistical
properties of the outcome of risky actions ai, (i = l - - - - - n) available to the decision makers. In practice, it is
popular among empiricists to assume that the underlying utility function is quadratic and that profits are normally
distributed yielding the simpler function of mean and variance only (Young 1979).Thus, Max (E U) of a i = f (μa,
σ2ai) – (1) With equation (1), variance or standard deviation or coefficient of variation is clearly the appropriate
―measure of uncertainty and risk‖.
Different sets of risk concepts are implied by various non-Bernoullian decision models. For example, the
―minimax‖ model would identify the maximum loss of an action (regardless of how remote the probability of its
occurrence) as a measure of riskness of an action. The lexicographic ―safety first‖ model identifies the probability
(α) that random net income (Y) will fall below some critical or disaster levels (d) as risk, i.e. Pr (Y < d) =α (2) There
are many criteria in decision making under risk and uncertainty. These are Wald‘s Maximin, Maximax, Huriwicz
Laplace, Salvage Minimum Regrets, and Excess Benefit.
Wald‘s maximin criterion is associated with strategy, which maximizes its minimum while maximax criterion is
associated with strategy which gives the highest possible outcome. Hurwicz criterion is a hybrid of the maximin and
maximax criteria. It considers the weighted average of the minimum and maximum payoffs under each of the
strategies. Savage Minimum Regret criterion aims at selecting a strategy, which minimizes the opportunity cost of
marking decision. The Excess Benefit is associated with subtraction of the minimum element from original matrix
and applying the maximin criterion to it.
Laplace criterion assumes that each state of nature is equally likely to occur. Equal probabilities are, therefore
assigned to the various states of nature and the decision maker selects that strategy which gives the highest expected
income. This study employed programming model developed from the laplace criterion model with modification
given to the Lexicographic ―safety first‖ principle. This study utilized a programming model called target-MOTAD
model under safety – first principle.
III TARGET MOTAD MODEL
This study employs the linear programming model called Target-MOTAD (Minimization of Total Absolute
Deviation) programming developed by Tauer, (1983). There are other risk programming such as Mean-Gini model
which has been criticized based on the fact that some stochastically efficient solutions that would be preferred by
strong risk-averse decision makers may be excluded from the efficient set and its tableau is much larger than that for
Target MOTAD and direct maximization of expected utility and utility-efficient which are non- non-linear
programming models and are superior to linear programming model. However, they are not widely used as they
have been criticized because they can only be applied when an individual decision maker exists who is risk averse
and whose utility function is available. Moreover, they are not applicable to a group of farmers considered in this
study (Anderson et al 1997). The Target MOTAD model is superior to other programming model under risk because
it is computational efficient and generates solutions that meet the second-degree stochastic dominance (SSD) test
(Tauer, 1983).
IV SENSITIVITY ANALYSIS
Sensitivity analysis is the study of how the variation in the output of a model (numerical or otherwise) can be
approached qualitatively or quantitatively to different sources of variation (Wikipedia 2007). Sensitivity analysis can
be used to determine model resemblance with the process under study, quality of model definition, factors that
mostly contribute to the output variability, region in the space of input factors for which the space of factors for use
in a subsequent calibration study, and interaction between factors (Wikipedia, 2007). It is in fact described as been
useful in providing information about local and global sensitivity of the enterprise mixture(s) to the choice of target
return level (McCamley and Kliebenstein, 1987)
Sensitivity analysis is popular in financial application, risk analysis, signal processing, neutral network, and model-
Global Journal of Management and Business Research Vol. 10 Issue 1 (Ver 1.0), Febuary 2010 P a g e |
178
based policy assessment studies and any area where models are developed (Saisana et al, 2005). The conventional
methodology to account for risk and uncertainty in project appraisal analysis adopted by Gittinger, 1972, and little
and Mirrlees, 1974. However, sensitivity analysis based on this method is surely inadequate because it is based on
the subjective judgment about possible increments in project costs of otherwise reduction in project benefits. Hiller
(1983), developed a project appraisal model for estimating the probability distribution of present value (PV) by
using expected value E(PV). He relied on the Central Limit Theorem for approximately normal distribution of PV.
By estimating the mean and variance of PV, the decision makers can evaluate the risk consequences of a particular
investment. This model, however, is criticized for statistical dependencies and potential correlations of covariance.
Stochastic simulation model was also used for evaluating uncertainty in project appraisal (Anderson, 1983). Monte
Carlo sampling technique for estimating distribution of PV and internal rate of return (IRR) was also examined by
Reutlinger, 1970. This approach as developed and applied by Reutlinger is based on identifying the most applied
critical components of the project and simulating the probability of IRR under different assumptions underlying the
critical components. However the most common sensitivity analysis is sampling-based. A sampling-based
sensitivity is one in which the model is executed repeatedly for combinations of values sampled from the
distribution (assumed known) of the input factors (Cacuci, 2003, Cacuci, Mihaela and Navon, 2005). In general
sampling-based method performed the sensitivity analysis jointly with uncertainty analysis by executing the model
repeatedly for combination of factor values with some probability distribution (Cacuci, 2003).The steps involved are
as follows: Specify the target function and select the input of interest; assign a distribution function to the selected
factors; generate a matrix of inputs with that distribution(s) through an appropriate design; Evaluate the model and
compute the distribution of the target function; and select a method for assessing the influence or relative importance
of ach input factor on the target function. Risk programming models such as Target-MOTAD used in this study
perform a sampled–based sensitivity analysis. Hence the study employed The Target-MOTAD in perform the
sensitivity analysis.
V METHODOLOGY
The study was carried out in Kwara state of Nigeria. The state lies in the central part of Nigeria. It comprises of
sixteen (16) Local Governments with a population of about 1.8 million (1991 census). It has a total land size of
3682500 hectares (F0S, 1995). Agriculture is major occupation in the state with over 70 percent of the population
being farmers and majority of the farmers in the state are into small land scale agriculture. The climatic pattern,
vegetation and the fertile soil make the state suitable for the cultivation of a wide range of food and tree crops. The
major food crops planted are Cassava, Yam, Maize, Rice, Soyabeans, Cowpea, Guinea-corn and millet. The sixteen
Local Government Areas have been divided into four zones by the Kwara State Agricultural Development Project
(KWADP) in consonance with ecological characteristics and cultural practices (KWADP 1998).
VI SAMPLING DESIGN
The population for this study consists of small scale farming households of Kwara state of Nigeria. A three - stage
stratified random sampling technique was utilized to select the sample for the study. In the first stage, the nonoverlapping four zones divided by the KWADP as Zone A, Zone B, Zone C and Zone D zone were utilized. In the
second stage, half of the blocks in each zone were randomly selected. While in the third stage, proportion allocation
technique was utilized to distribute a sample size of 500 into each zone using proportion allocation technique.
Consequently, a random sample of 64 respondents was taken from zone A, 128 from Zone B, 132 from Zone C and
176 from Zone D based on the farming household population‘s proportion of the zones.
VII SOURCE AND METHOD OF DATA COLLECTION
Both primary and secondary data were collected for this study. The primary data were collected during the 2006
production year through a survey with the aid of interview schedule administered to the heads of the selected
farming household heads with the assistance of well trained enumerators. Input-output data were collected on
individual farms. The secondary data were collected from the yearly agronomic field records of KWADP to
determine the past performance of crops. A seven-year (1999-2005) record was synthesized for all crops. Other
information was obtained from the records of the National Bureau of Statistics, journals and relevant texts to
supplement the primary data.
VIII ANALYTICAL TECHNIQUE
The study employed Target MOTAD Model and Sensitivity analysis for it analysis. Mathematically, the model is
stated as Max E (Z) = (1) Subject to: (2) T-Yr+-Yr -≤ 0 (3) Σ PrY-r =α (4) α = (M 0); X, Y > 0
Where E (Z)=expected returns of the plan or solution to the plan in C j; cj =expected returns of activity j; Xj = level of
Global Journal of Management and Business Research Vol. 10 Issue 1 (Ver 1.0), Febuary 2010 P a g e |
178 based policy assessment studies and any area where models are developed (Saisana et al, 2005). The
conventional methodology to account for risk and uncertainty in project appraisal analysis adopted by Gittinger,
1972, and little and Mirrlees, 1974. However, sensitivity analysis based on this method is surely inadequate because
it is based on the subjective judgment about possible increments in project costs of otherwise reduction in project
benefits. Hiller (1983), developed a project appraisal model for estimating the probability distribution of present
value (PV) by using expected value E(PV). He relied on the Central Limit Theorem for approximately normal
distribution of PV. By estimating the mean and variance of PV, the decision makers can evaluate the risk
consequences of a particular investment. This model, however, is criticized for statistical dependencies and potential
correlations of covariance.
Stochastic simulation model was also used for evaluating uncertainty in project appraisal (Anderson, 1983). Monte
Carlo sampling technique for estimating distribution of PV and internal rate of return (IRR) was also examined by
Reutlinger, 1970. This approach as developed and applied by Reutlinger is based on identifying the most applied
critical components of the project and simulating the probability of IRR under different assumptions underlying the
critical components. However the most common sensitivity analysis is sampling-based. A sampling-based
sensitivity is one in which the model is executed repeatedly for combinations of values sampled from the
distribution (assumed known) of the input factors (Cacuci, 2003, Cacuci, Mihaela and Navon, 2005). In general
sampling-based method performed the sensitivity analysis jointly with uncertainty analysis by executing the model
repeatedly for combination of factor values with some probability distribution (Cacuci, 2003).The steps involved are
as follows: Specify the target function and select the input of interest; assign a distribution function to the selected
factors; generate a matrix of inputs with that distribution(s) through an appropriate design; Evaluate the model and
compute the distribution of the target function; and select a method for assessing the influence or relative importance
of ach input factor on the target function. Risk programming models such as Target-MOTAD used in this study
perform a sampled–based sensitivity analysis. Hence the study employed The Target-MOTAD in perform the
sensitivity analysis.
V METHODOLOGY
The study was carried out in Kwara state of Nigeria. The state lies in the central part of Nigeria. It comprises of
sixteen (16) Local Governments with a population of about 1.8 million (1991 census). It has a total land size of
3682500 hectares (F0S, 1995). Agriculture is major occupation in the state with over 70 percent of the population
being farmers and majority of the farmers in the state are into small land scale agriculture. The climatic pattern,
vegetation and the fertile soil make the state suitable for the cultivation of a wide range of food and tree crops. The
major food crops planted are Cassava, Yam, Maize, Rice, Soyabeans, Cowpea, Guinea-corn and millet. The sixteen
Local Government Areas have been divided into four zones by the Kwara State Agricultural Development Project
(KWADP) in consonance with ecological characteristics and cultural practices (KWADP 1998).
VI SAMPLING DESIGN
The population for this study consists of small scale farming households of Kwara state of Nigeria. A three - stage
stratified random sampling technique was utilized to select the sample for the study. In the first stage, the nonoverlapping four zones divided by the KWADP as Zone A, Zone B, Zone C and Zone D zone were utilized. In the
second stage, half of the blocks in each zone were randomly selected. While in the third stage, proportion allocation
technique was utilized to distribute a sample size of 500 into each zone using proportion allocation technique.
Consequently, a random sample of 64 respondents was taken from zone A, 128 from Zone B, 132 from Zone C and
176 from Zone D based on the farming household population‘s proportion of the zones.
VII SOURCE AND METHOD OF DATA COLLECTION
Both primary and secondary data were collected for this study. The primary data were collected during the 2006
production year through a survey with the aid of interview schedule administered to the heads of the selected
farming household heads with the assistance of well trained enumerators. Input-output data were collected on
individual farms. The secondary data were collected from the yearly agronomic field records of KWADP to
determine the past performance of crops. A seven-year (1999-2005) record was synthesized for all crops. Other
information was obtained from the records of the National Bureau of Statistics, journals and relevant texts to
supplement the primary data.
VIII ANALYTICAL TECHNIQUE
The study employed Target MOTAD Model and Sensitivity analysis for it analysis. Mathematically, the model is
stated as Max E (Z) = (1) Subject to: (2) T-Yr+-Yr -≤ 0 (3) Σ PrY-r =α (4) α = (M 0); X, Y > 0
Where E (Z)=expected returns of the plan or solution to the plan in C j; cj =expected returns of activity j; Xj = level of
P a g e |177 Vol. 10 Issue 1 (Ver 1.0), January2010 Global Journal of Management and Business
Research Agricultural Development Projects (ADPs), etc. However, the success of all the various agricultural
programmes has been minimal (Ukpong, 1993). This is may be because the factors at which the small land scale
agriculture is responsive are still yet to be considered in the various programmes. This couple with the fact that this
small-scale agriculture is more expose to risk and uncertainty than other segment of economy may cause the results
of the various programme been minimal in its impact on agricultural and economics growth. Hence a need to
understand the factors that can result into the small land scale agriculture stability on the efficiency frontier through
a sensitivity and uncertainty analysis. Therefore, the study examines the farm plan(s) that would adequately provide
the small-scale farmers with improved income under uncertainty and explores the sensitivity and uncertainty
analysis that will consequently raise the efficiency of the small-land scale agriculture in Nigeria. This study will not
only help policy planners but it will also provide useful information to small-scale land agriculture especially on
farm size plan, budgets and returns to investments. It will also offer suggestions on how risk efficiency in smallscale agriculture could be improved such that it would have greater impact on agricultural and economic growth.
II THEORETICAL AND EMPIRICAL
FRAMEWORK IN UNCERTAINTY ANALYSIS
The concept of uncertainty in any application depends on the behavioral decision model employed. The popular
Bernoullian (1738) expected utility criterion utilizes an objective function that is a function of all the statistical
properties of the outcome of risky actions ai, (i = l - - - - - n) available to the decision makers. In practice, it is
popular among empiricists to assume that the underlying utility function is quadratic and that profits are normally
distributed yielding the simpler function of mean and variance only (Young 1979).Thus, Max (E U) of a i = f (μa,
σ2ai) – (1) With equation (1), variance or standard deviation or coefficient of variation is clearly the appropriate
―measure of uncertainty and risk‖.
Different sets of risk concepts are implied by various non-Bernoullian decision models. For example, the
―minimax‖ model would identify the maximum loss of an action (regardless of how remote the probability of its
occurrence) as a measure of riskness of an action. The lexicographic ―safety first‖ model identifies the probability
(α) that random net income (Y) will fall below some critical or disaster levels (d) as risk, i.e. Pr (Y < d) =α (2) There
are many criteria in decision making under risk and uncertainty. These are Wald‘s Maximin, Maximax, Huriwicz
Laplace, Salvage Minimum Regrets, and Excess Benefit.
Wald‘s maximin criterion is associated with strategy, which maximizes its minimum while maximax criterion is
associated with strategy which gives the highest possible outcome. Hurwicz criterion is a hybrid of the maximin and
maximax criteria. It considers the weighted average of the minimum and maximum payoffs under each of the
strategies. Savage Minimum Regret criterion aims at selecting a strategy, which minimizes the opportunity cost of
marking decision. The Excess Benefit is associated with subtraction of the minimum element from original matrix
and applying the maximin criterion to it.
Laplace criterion assumes that each state of nature is equally likely to occur. Equal probabilities are, therefore
assigned to the various states of nature and the decision maker selects that strategy which gives the highest expected
income. This study employed programming model developed from the laplace criterion model with modification
given to the Lexicographic ―safety first‖ principle. This study utilized a programming model called target-MOTAD
model under safety – first principle.
III TARGET MOTAD MODEL
This study employs the linear programming model called Target-MOTAD (Minimization of Total Absolute
Deviation) programming developed by Tauer, (1983). There are other risk programming such as Mean-Gini model
which has been criticized based on the fact that some stochastically efficient solutions that would be preferred by
strong risk-averse decision makers may be excluded from the efficient set and its tableau is much larger than that for
Target MOTAD and direct maximization of expected utility and utility-efficient which are non- non-linear
programming models and are superior to linear programming model. However, they are not widely used as they
have been criticized because they can only be applied when an individual decision maker exists who is risk averse
and whose utility function is available. Moreover, they are not applicable to a group of farmers considered in this
study (Anderson et al 1997). The Target MOTAD model is superior to other programming model under risk because
it is computational efficient and generates solutions that meet the second-degree stochastic dominance (SSD) test
(Tauer, 1983).
IV SENSITIVITY ANALYSIS
Sensitivity analysis is the study of how the variation in the output of a model (numerical or otherwise) can be
approached qualitatively or quantitatively to different sources of variation (Wikipedia 2007). Sensitivity analysis can
be used to determine model resemblance with the process under study, quality of model definition, factors that
mostly contribute to the output variability, region in the space of input factors for which the space of factors for use
in a subsequent calibration study, and interaction between factors (Wikipedia, 2007). It is in fact described as been
useful in providing information about local and global sensitivity of the enterprise mixture(s) to the choice of target
return level (McCamley and Kliebenstein, 1987)
Sensitivity analysis is popular in financial application, risk analysis, signal processing, neutral network, and model-
Global Journal of Management and Business Research Vol. 10 Issue 1 (Ver 1.0), Febuary 2010 P a g e |
178
based policy assessment studies and any area where models are developed (Saisana et al, 2005). The conventional
methodology to account for risk and uncertainty in project appraisal analysis adopted by Gittinger, 1972, and little
and Mirrlees, 1974. However, sensitivity analysis based on this method is surely inadequate because it is based on
the subjective judgment about possible increments in project costs of otherwise reduction in project benefits. Hiller
(1983), developed a project appraisal model for estimating the probability distribution of present value (PV) by
using expected value E(PV). He relied on the Central Limit Theorem for approximately normal distribution of PV.
By estimating the mean and variance of PV, the decision makers can evaluate the risk consequences of a particular
investment. This model, however, is criticized for statistical dependencies and potential correlations of covariance.
Stochastic simulation model was also used for evaluating uncertainty in project appraisal (Anderson, 1983). Monte
Carlo sampling technique for estimating distribution of PV and internal rate of return (IRR) was also examined by
Reutlinger, 1970. This approach as developed and applied by Reutlinger is based on identifying the most applied
critical components of the project and simulating the probability of IRR under different assumptions underlying the
critical components. However the most common sensitivity analysis is sampling-based. A sampling-based
sensitivity is one in which the model is executed repeatedly for combinations of values sampled from the
distribution (assumed known) of the input factors (Cacuci, 2003, Cacuci, Mihaela and Navon, 2005). In general
sampling-based method performed the sensitivity analysis jointly with uncertainty analysis by executing the model
repeatedly for combination of factor values with some probability distribution (Cacuci, 2003).The steps involved are
as follows: Specify the target function and select the input of interest; assign a distribution function to the selected
factors; generate a matrix of inputs with that distribution(s) through an appropriate design; Evaluate the model and
compute the distribution of the target function; and select a method for assessing the influence or relative importance
of ach input factor on the target function. Risk programming models such as Target-MOTAD used in this study
perform a sampled–based sensitivity analysis. Hence the study employed The Target-MOTAD in perform the
sensitivity analysis.
V METHODOLOGY
The study was carried out in Kwara state of Nigeria. The state lies in the central part of Nigeria. It comprises of
sixteen (16) Local Governments with a population of about 1.8 million (1991 census). It has a total land size of
3682500 hectares (F0S, 1995). Agriculture is major occupation in the state with over 70 percent of the population
being farmers and majority of the farmers in the state are into small land scale agriculture. The climatic pattern,
vegetation and the fertile soil make the state suitable for the cultivation of a wide range of food and tree crops. The
major food crops planted are Cassava, Yam, Maize, Rice, Soyabeans, Cowpea, Guinea-corn and millet. The sixteen
Local Government Areas have been divided into four zones by the Kwara State Agricultural Development Project
(KWADP) in consonance with ecological characteristics and cultural practices (KWADP 1998).
VI SAMPLING DESIGN
The population for this study consists of small scale farming households of Kwara state of Nigeria. A three - stage
stratified random sampling technique was utilized to select the sample for the study. In the first stage, the nonoverlapping four zones divided by the KWADP as Zone A, Zone B, Zone C and Zone D zone were utilized. In the
second stage, half of the blocks in each zone were randomly selected. While in the third stage, proportion allocation
technique was utilized to distribute a sample size of 500 into each zone using proportion allocation technique.
Consequently, a random sample of 64 respondents was taken from zone A, 128 from Zone B, 132 from Zone C and
176 from Zone D based on the farming household population‘s proportion of the zones.
VII SOURCE AND METHOD OF DATA COLLECTION
Both primary and secondary data were collected for this study. The primary data were collected during the 2006
production year through a survey with the aid of interview schedule administered to the heads of the selected
farming household heads with the assistance of well trained enumerators. Input-output data were collected on
individual farms. The secondary data were collected from the yearly agronomic field records of KWADP to
determine the past performance of crops. A seven-year (1999-2005) record was synthesized for all crops. Other
information was obtained from the records of the National Bureau of Statistics, journals and relevant texts to
supplement the primary data.
VIII ANALYTICAL TECHNIQUE
The study employed Target MOTAD Model and Sensitivity analysis for it analysis. Mathematically, the model is
stated as Max E (Z) = (1) Subject to: (2) T-Yr+-Yr -≤ 0 (3) Σ PrY-r =α (4) α = (M 0); X, Y > 0
Where E (Z)=expected returns of the plan or solution to the plan in C j; cj =expected returns of activity j; Xj = level of
P a g e |179 Vol. 10 Issue 1 (Ver 1.0), January2010 Global Journal of Management and Business
Research
activity j; aij =technical requirement of activity j for resource i; b i =level of resource i; T = target level of returns in
naira (it was derived from mean absolute deviation); Crj=returns of activity j for state of nature or observation r (N);
Y+= deviation above expected returns; Y- = deviation below expected returns; Pr = probability that state of nature or
observation r will occur; α = a constant parameterized from M to 0; i =1, ----------, m; j = 1,----, n. Yr =
m = number of constraints or resource equation; r = number of state of nature or observation; M = large number
(represents the maximum total absolute deviation of return of the model). Points on the risk efficiency frontier are
obtained by arbitrarily decreasing the value (y) parametrically. Along the efficiency frontier, the Target-MOTAD
model minimizes the mean absolute deviation (MAD) for any given expected gross margins. Essentially, this
minimizes the standard deviation of returns to the farm measured by the estimator. Std Deviation =- (5) Where, S =
number of states of nature; D = estimated mean absolute deviation of return to the farm. The mean absolute
deviation (MAD) or D for an activity (j) and for the whole farm over all states of nature (years) is estimated
respectively as Follows; Dj = (6) D =(7)
All variables are as defined earlier in this risk model; magnitude of standard deviation allows the model to determine
a set of efficient farm plans along the E-V efficiency frontier. Furthermore, sensitivity analysis was carried out using
the Target MOTAD programming model.
IX RESULTS AND DISCUSSION
Table 1: Availability of Different Resources for the Small Scale Farms
RESOURCES
(a)
Average
Cultivated Area (Ha)
(b)
Average
Available
Labor
(Mondays/Ha/
Growing Season).
(
c)
Capital
(N/Ha/Growing
Season)
(d) Minimum Food
Requirements (MJ)
(e) Target Level(N)
ZONE A
2.49
ZONE B
4.4687
ZONE C
3.6154
ZONE D
2.8I68
300.00
380.00
214.82
270.54
71,038.46
60,331.3
37907.69
41,442.1
145.908
118.944
92.484
144.569
32,416.22
27,767.78
36,795.80
43,576.1
The framework for this study is based on incorporating such stochastic elements to evaluate the planning process in
a risky agriculture environment. This study assumed that risk in returns arises from price and yield factors. In the
risk model, the farmer decides between possible crop combinations on the basis of expected returns and the absolute
deviation of returns for each crop from its expected value. Table 1 presents the resource position of small land scale
crops farms.
The result of the risk programming model gives the normative plans. The normative plans are divided into risk
minimizing plans and profit maximizing plan. The profit maximizing plans for all the zones are only profit
responsive, they are therefore likely to be selected by a risk neutral decision maker. The plan has the highest risk
expected returns and hence the highest risk. Any risk level higher than that of the profit-maximizing plan‘s risk level
will give no different plan. Also any risk level lower than that of the lowest risk minimized plan will result in no
feasible solution. Hence the lowest risk minimizing plan and profit-maximizing plan fall on both extremes and
therefore forms the risk efficiency frontier.
Global Journal of Management and Business Research Vol. 10 Issue 1 (Ver 1.0), Febuary 2010 P a g e |
180 Table 2: Normative farm plans.
ENTERPRISES
NORMATIVE SITUATION
PROFIT MAXIM-AZING
RISK MINIMIZING
PLANS
RETURNS
YAM(Ha)
I
288,793.4
0.4828 (29.44)
II
296,050
0.4778 (29.13)
III
311,489.9
0.4671 (28.48)
IV
330,015.5
0.4541 (27.69)
V
360,891.4
0.4328 (26.39)
VI
370,257.4
0.4263 (25.99)
MZE(Ha)
GNC(Ha)
MZE/GNC(Ha)
___
___
___
___
___
___
___
___
___
___
___
___
___
___
___
___
___
___
RICE(Ha)
____
0.0632 (3.85)
0.1912 (11.66)
0.3506 (21.38)
0.6280 (38.29)
0.7095 (43.26)
GNT(Ha)
CSV (Ha)
CWP (Ha)
MZE/CSV
PLAN
TOTAL
CROPPED AREA
CROPPED AREA
RISK LEVEL
___
___
___
___
0.4828 (29.44)
___
___
___
___
0.5410 (32.99)
___
___
___
___
0.6583 (40.14)
___
___
___
___
0.8047 (49.07)
___
___
___
___
1.0608 (64.68)
___
___
___
___
1.1358 (69.26)
1.64
33246
1.64
45000
1.64
70000
1.64
100000
1.64
150000
1.64
165167.06