Global Journal of Management and Business Research Vol. 10 Issue 1 (Ver 1.0), February 2010 Page 176-183
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 small- land 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,
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
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 ai = 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 seconddegree 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-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 TargetMOTAD 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 non-overlapping 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) =
n
∑cjxj
j=1
(1)
m n
∑ ∑aijxj ≤ bi
i=1 j=1
(2)
Subject to:
T-Yr+-Yr -≤ 0
Σ PrY-r =α
α = (M 0); X, Y > 0
(3)
(4)
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 activity
j; aij =technical requirement of activity j for resource i; bi =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 =
n
∑ (cij- cj) xj
j=1
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 = D{πxS/2(S -1)}½
(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 = S-1∑I (Crj-C j) Xj I
(6)
n
D = 1/n∑Dj
(7)
j=1
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
Source: Field Survey Data 2005/2006
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.
Table 2: Normative farm plans.
ENTERPRISES
NORMATIVE SITUATION
RISK MINIMIZING
PLANS
RETURNS
YAM(Ha)
MZE(Ha)
GNC(Ha)
MZE/GNC(Ha)
RICE(Ha)
GNT(Ha)
CSV (Ha)
CWP (Ha)
MZE/CSV
PLAN TOTAL
CROPPED
AREA
CROPPED
AREA
RISK LEVEL
I
288,793.4
0.4828
(29.44)
___
___
___
____
___
___
___
___
0.4828
(29.44)
1.64
33246
II
296,050
0.4778
(29.13)
___
___
___
0.0632
(3.85)
___
___
___
___
0.5410
(32.99)
1.64
45000
III
311,489.9
0.4671
(28.48)
___
___
___
0.1912
(11.66)
___
___
___
___
0.6583
(40.14)
1.64
70000
IV
330,015.5
0.4541
(27.69)
___
___
___
0.3506
(21.38)
___
___
___
___
0.8047
(49.07)
1.64
100000
V
360,891.4
0.4328
(26.39)
___
___
___
0.6280
(38.29)
___
___
___
___
1.0608
(64.68)
1.64
150000
PROFIT
MAXIMAZING
VI
370,257.4
0.4263
(25.99)
___
___
___
0.7095
(43.26)
___
___
___
___
1.1358
(69.26)
1.64
165167.06
NOTE: Figures in parenthesis represent the percentages of Cultivated Area.
Source: Programming model Output
Table 2 presents normative plans for the small-land scale agriculture in all the zones. This is done by pooling all the resources
together and getting the average of their risk coefficient. The result shows that profit-maximizing plan suggests the
cultivation of both 0.4263-hectare of yam and 0.7096 hectare of rice which gives N370, 257.4 as returns whereas the lowest
risk minimized plans is cultivation of only 0.4828 hectare of yam N288, 793.7 as returns.
X SENSITIVITY ANALYSIS
The sensitivity analysis of the optimal farm planning under uncertainty solution varying the target level was explored using
the risk programming model (see appendix1). It is observed that the lower the target income level the higher the returns and
the lower the risk level. In another word, there is a positive relationship between target income and risk level and a negative
relationship between target level and income. It is observed that generally, in all the zones the highest return (which is of
profit maximizing plans) with the lowest risk level is found in frontier with lowest target (T = N10,000 see appendix 1). For
instance in zone A, the highest returns of N611,011.80 with the lowest risk level of N32,592.11 is found in frontier with the
target of N10,000. Furthermore, in all the risk-minimizing plans, the lowest target has higher returns accompanied with lower
risk level. For example the risk level of N30, 520 gives a return of N566, 683.90 in the frontier with target of N10,000.00
which is higher than all other targets used.
However, it is further observed that this negative relationship between target and returns is associated with an increase in
return which correlates with less risk level. This is more obvious in zone A. This may be due to high amount of available
capital since capital resource only becomes a limiting factor in the last risk minimizing plan and profit maximizing plan. This
is further shown in Figure1-4. Generally, in the other zones, amount of capital is the only limiting resource in all the
normative plans. Hence, the response of the optimal farm planning under risk solution to changes for capital was also
explored by using the sensitivity analysis of the risk-programming model. Figure 1-4 show the efficiency frontier of risk
minimizing plans with increased capital of zone A, B, C, and D respectively.
700000
600000
500000
Original Frontier
Frontier With Increased Capital
Return
Value
400000
300000
200000
100000
29000
31000
33000
35000
37000
39000
41000
43000
45000
Risk Level
FIG. 1: Sensitivity Analysis: Efficiency Frontier of Risk Minimizing Plans with increased capital of Zone A’s Farm.
350,000.00
330,000.00
310,000.00
290,000.00
Return
Value
270,000.00
Original Frontier
Frontier With Increased Capital
250,000.00
230,000.00
210,000.00
190,000.00
170,000.00
150,000.00
25000
27000
29000
31000
33000
35000
37000
39000
41000
Risk Level
FIG. 2: Sensitivity Analysis: Efficiency Frontier of Risk Minimizing Plans with increased capital of Zone B’s Farm.
350000
300000
Return
Value
250000
200000
Original Frontier
Frontier With Increased Capital
150000
100000
50000
0
26000
26500
27000
27500
28000
28500
29000
29500
Risk Level
FIG. 3: Sensitivity Analysis: Efficiency Frontier of Risk Minimizing Plans with increased capital of Zone C’s Farm.
300000
250000
Return
Value
200000
Original Frontier
Frontier With Increased Capital
150000
100000
50000
20500
21000
21500
22000
22500
23000
23500
24000
24500
25000
Risk Level
FIG. 4: Sensitivity Analysis: Efficiency Frontier of Risk Minimizing Plans with increased capital of Zone D’s Farm.
Generally in all the zones, the sensitivity analysis with increased capital shows an extension of the range of risk-return
possibilities available to the decision maker except in zone A where the extension is minimal. It further revealed that an
increase in amount of capital increases the plans‘ returns.
XI CONCLUSION AND RECOMMENDATION
It can be concluded 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, it is recommended that 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. Given
that capital is a limiting resource and the use of credit on the farm reduces risk, a concerted effort should be made by
government to facilitate access of small farmers to small-scale credits. There should be a concerted effort by the farmers,
their societies, government, and private stakeholder to provide better sources of capital in order to increase the agricultural
crop output and returns. The government can stand as guarantor for the farmers who should be organized into Unions or
Cooperatives. There should be a concerted effort by the farmers through their societies, government, and private stakeholder
to provide better infrastructures amenities, health services, and education service at reduced cost to decrease target income
level, which in turn increases returns with a lower risk level.
XII REFERENCE
1) Adubi, A.A.: (2000) “The Economic of Behaviour Nigerian Small Scale Farmer Implication for Food Policy in the 1990s”
Discovery Innovation. 12 (3/4):199-2002
2) Anderson, J. R. (1983) “Forecasting, Uncertainty and Public Project Appraisal” World Bank Working Paper 1983-4, July
1983.
3) Anderson, J. R, Hardakier J. B. and Huirne R.B.M. (1997) Coping with Risk in Agriculture. CAB INTERNATIONAL
Wallingfor U. K.
4) Cacuci, D. G. (2003) In Sensitivity & Uncertainty Analysis, Volume 1: Theory; Chapman & Hall.
5) Cacuci, D. G., Mihaela Ionescu-Bujor and Michael Navon. (2005) Sensitivity And Uncertainty Analysis: Applications to
Large-Scale Systems (Volume II), Chapman & Hall
6) Gittinger, J. P. (1972) Economic Analysis of Agricultural Project. A world Bank Publication, 99-155
7) Hiller, F. S. (1983) “The Derivation of Probabilistic Information For Evaluation of Risky Investments” Management
Science. 9:443-457
8) KWADP (1995-2001) Staff Appraisal Report. Kwara State Agricultural Development Project (1998-2004)
9) LeBel, P. (2003) Risk in Globalization: A Comparative Analysis of African and Asian countries in 7th International
Conference on Global Business and Economic Development. Bangkok. Thailand.
10) Little, I. M. D. and J. A. Mirrlees (1974) Project Appraisal and Development Planning For the Developing Countries.
Heineman London.
11) McCamley, F.P., and Kliebenstein, J. (1987) “Describing and Identifying the Complete Set of Target-MOTAD
Solutions” American Journal of Agricultural Economic 69(3):669-679.
12) Saisana M., Saltelli A and Tarantola S. (2005) “Uncertainty and Sensitivity analysis techniques as tools for the quality
assessment of composite indicators” Journal Royal Statistical Society A, 168 (2), 307-323.
13) Tauer, L. W. (1983) “Target MOTAD” American Journal of Agric Economics. 65:607-610.
14) Ogundari, K. and Ojo, S.O (2007): “Economic Efficiency of small scale Food crop production in Nigeria: A stochastic
frontier Approach” Journal of Social Science, 14(2):123-130.
15) Ukpong, G. E. (1993) “Some Strategies for the Development of Nigeria‘s Agricultural Sector in the 1990s” Economic
and Financial Review. CBN 31(2): 86-90
16) Wikipedia, (2007) Wikipedia, the free encyclopedia. http://en.wikipedia.org/wiki/sensitivityanalysis.,last modified 19:02,
22 may 2007.
17) World Bank (2003): Washington D.C. Mimeo 2003. World Development Indicators 2003 CD-Rom.
18) Young, D. L. (1979) “Risk Preferences of Agricultural Producers Their use in Extension and Research” American
Journal of Agric Economics.61: 1063 -1084.
APPENDIX I
Zone
Target level = N10,000
Risk level
Return( N)
8,157.31
45,064.44
8,500.00
65,194.96
10,000.00
110,352.50
A
26,520.00
482,368.00
30,520.00
566,683.90
32,592.11
611,011.80
10,000.00
103,204.20
11,640.00
148,666.70
12,150.00
157,642.90
B
15,361.10
200,745.40
20,000.00
205,037.30
26,675.20
205,445.20
7,149.50
76,481.53
7,300.00
84,638.11
8,000.00
110,450.60
C
8,565.00
121,477.00
10,000.00
135,164.80
12,331.60
135,164.80
10,000.00
85,273.68
12,000.00
128,122.80
13,000.00
141,297.80
D
16,500.00
176,739.70
17,500.00
185,910.50
18,315.90
191,271.20
Source: Programming output
Target level = N20,000
Risk level
Return( N)
16,314.31
90,195.55
17,000.00
130,389.90
20,000.00
220,705.00
26,520.00
280,074.00
30,520.00
477,357.60
36,542.50
611,011.80
20,000.00
147,594.00
20,300.00
156,778.20
21,000.00
167,338.50
22,000.00
180,760.80
27,767,80
205,055.00
33,689.60
205,445.20
14,628.90
126,568.00
14,800.00
127,568.00
15,500.00
129,779.40
16,500.00
131,812.10
17,500.00
133,884.90
18,149.3
135,164.80
20,000.00
100,758.60
20,721.10
156,766.60
21,041.40
160,240.30
22,800.00
177,198.00
24,000.00
188,203.20
24,334.50
191,271.20
Target level = N30,000
Risk level
Return( N)
24,472.00
135,251.50
26,520.00
238,721.00
30,520.00
343,279.10
35,120.00
454,825.00
40,120.00
567,057.80
42,078.20
611,011.80
30,000.00
170,697.00
31,327.40
196,854.80
32,500.00
202,720.50
35,000.00
205,037.30
39,725,00
205,348.70
41,675.20
205,445.20
23,238.60
131,499.00
23,990.00
134,332.80
24,000.00
134,553.10
24,100.00
134,556.40
24,300.00
134,962.90
24,399.30
135,164.80
30,000.00
161,427.50
30,100.00
176,423.00
30,200.00
178,515.30
30,300.00
180,349.00
30,500.00
184,016.90
30,961.70
191,271.20