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A Markov Chain Process Approach of Table Egg
Production in Ibadan Metropolis, Oyo State, Nigeria.
Oladele Osanyinlusi1, Ayodeji Ogundeji, Adetola Adeoti
Nigerian Institute of Social and Economic Research (NISER)1 , Department of Agricultural Economics, University of Ibadan, Nigeria.
Correspondence: Oladele Osanyinlusi. Email address: osandele17@gmail.com. Phone:+2348067002496
Introduction
Poultry business is done on the purpose of meat or egg production with the focus of
making profit. Recently, there has been increase in the price of poultry feeds which
accounts for 60 to 70 per cent of total running cost of production thereby has the
capacity to impact on the level of profit (Nmadu et al., 2014). For them to remain in
business against this harsh economic condition, there is a need for the egg-producers
to find a way in reducing the cost of feeding without hampering the productivity of
their birds. The egg-feed price ratio, which is the number of eggs required to purchase
a kilogram of feed, is an efficient management tool to classify egg production into
favourable, marginal and knockout states (Jadhav and Siddiqui, 2010).
Materials and Methods
Study area: Ibadan metropolis area.
Type and source of data: Primary data collected with the aid of a well-structured
questionnaire complemented with key informant interview.
Sampling procedure: A three-or multi-stage sampling procedure was employed. 116
respondents were used for the analysis.
Method of data analysis: Descriptive statistics and Markov Chain Process Analysis
Model Specification: For period t, the Markov Chain finite stochastic process for this
situation can be represented as:
𝑋𝑋𝑡𝑡 =
𝐹𝐹, 𝑖𝑖𝑖𝑖 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓
𝑀𝑀, 𝑖𝑖𝑖𝑖 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚
𝐾𝐾, 𝑖𝑖𝑖𝑖 𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘
, 𝑡𝑡 = 1, 2, … , 𝑇𝑇
Where: 𝑋𝑋𝑡𝑡 =
𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑜𝑜𝑜𝑜 𝑎𝑎 𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘 𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘 𝑜𝑜𝑜𝑜 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑖𝑖 𝑖𝑖 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝 𝑡𝑡
𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑜𝑜𝑜𝑜 𝑎𝑎𝑎𝑎 𝑒𝑒𝑒𝑒𝑒𝑒 𝑖𝑖 𝑖𝑖 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝 𝑡𝑡
Let the ratio, denoted as Xt, be categorized as Favourable (F) when 2 ˂ Xt ≤ 3, Marginal (M) when 4≤Xt
<5, and Knockout (K) when Xt ≥ 5.
Objectives
To examine the socio-economic characteristics of the egg-producers
To examine and predict the business states of egg production in Ibadan metropolis
Results and Discussion
Transition Matrix And Vector Of Initial Probabilities
The vector of initial probabilities (P(0)) which is the starting probability
of egg farmers being in any of these three business states at the
beginning period is; P(0) = {0.0259, 0.6207, 0.3534}. This implies that,
on the average, 2.6%, 62.1% and 35.3% of poultry egg farmers are
currently in the favourable, marginal and knockout state respectively.










=
4286.05714.00
3608.06083.00309.0
25.075.00
K
M
F
P
KMF
Absolute (unconditional) and n-step transition (conditional) probabilities
P(1) = {0.0192, 0.5989, 0.3819}
This reveals that after a production year, the number of egg farmers would have reduced to 1.9% and 59.7% for
favourable and marginal states respectively but increased to 38.2% for knockout state.
Steady-state Probabilities
The steady-state absolute probabilities of poultry egg farmers are computed as:
𝜋𝜋𝐽𝐽 = 0.0184, 0.5967, 0.3848
These probabilities stipulate that, in the long run, 1.84%, 59.67% and 38.48% of the poultry egg farmers will be in
the favourable, marginal and knockout states respectively.
Steady-state Probabilities
The steady-state absolute probabilities of poultry egg farmers are computed as:
𝜋𝜋𝐽𝐽 = 0.0184, 0.5967, 0.3848
These probabilities stipulate that, in the long run, 1.84%, 59.67% and 38.48% of the poultry egg farmers will be in
the favourable, marginal and knockout states respectively.
Figure 1: Limiting state transition probabilities of table egg production
Business States Of Table Egg Production Under Feed Cost Optimization
P(0) = {0.2845, 0.6897, 0.0259}----Initial transition probabilities
This implies that, on the average, 28.4% , 68.9% and 2.6%, of the poultry
egg farmers are currently in the favourable, marginal, and knockout states
respectively when linear programming technique was applied in the feed
formulation.
P(1) = {0.2776, 0.7011, 0.0213}----- After a production year
This implies that after a year, on the average, 27.7% , 70.1% and 2.1%, of
the poultry egg farmers would be in the favourable, marginal, and knockout
states respectively under the feed cost optimisation.
Mean Return Times of Ergodic Chains
The expected number of transitions before the system
returns to a state j for the first time. The mean first
return times are computed as:
𝜇𝜇11 = 3.59
𝜇𝜇12 = 1.43
𝜇𝜇13 = 46.16
It will take approximately 4 years to return to a
favourable state, 1 year to return to a marginal state, and
46 years to return to a knockout state under feed cost
optimisation
Table 1: Social Economic Characteristics of the Table Egg Producers
Variables Frequency Percentage
Age
< 30
30-39
40-49
50-59
≥ 60
Total
Mean = 45.2; Std= 9.64
6
29
39
34
8
116
5.2
25.0
33.6
29.3
6.9
100.0
Gender
Male
Female
Total
97
19
116
83.6
16.4
100.0
Educational status
Primary
Secondary
Tertiary
Total
Mean=13; std =4.72
18
47
51
116
15.5
40.5
44.0
100.0
Year of poultry experience
1-3
4-6
7-9
≥ 10
Total
Mean=6.3; std=2.71
19
44
37
16
116
16.4
37.9
31.9
13.8
100.0
Housing system
Deep litter
Battery Cage
Total
44
72
116
37.9
62.1
100
Initial stock type
Day-old-chicks (DOC)
Point-of-lay (POL)
Total
83
33
116
71.6
28.4
100.0
Stock size
< 1,000
1,000 - 4,999
≥ 5,000
Total
Mean=2,837; std=1,877.33
33
61
22
116
28.4
52.6
19.0
100.0
Mean Return Times of Ergodic
Chains
The expected number of transitions before
the system returns to a state j for the first
time. The mean first return times are
computed as:
𝜇𝜇11 = 54.19
𝜇𝜇12 = 1.68
𝜇𝜇13 = 2.59
It will take approximately 54 years to return
to a favourable state, 2 years to return to a
marginal state, and 3 years to return to a
knockout state.
Steady-state Probabilities
under Feed Cost Optimisation
The steady-state absolute probabilities of
poultry egg farmers are computed as:
𝜋𝜋𝐽𝐽 = 0.2778, 0.7005, 0.0217
These probabilities stipulate that, in the long run using
feed optimisation technique, 27.8%, 70.1% and 2.2%
of the poultry egg farmers would be in the favourable,
marginal and knockout states respectively.
Conclusion and Recommendation
An average poultry egg farmer in this area stands a
higher chance of remaining in unfavourable state or
being forced out of the business due to high cost of feed.
The bulk of the table egg producers are operating at the
marginal state. However, an application of linear
programming technique to feed cost reduced the
chances of being in unfavourable business state(s).
Hence, linear programming approach was recommended
to reducing the proportion of egg producers in both
marginal and knockout states.
Figure 2: Limiting state transition probabilities of table egg production under feed cost
optimization
References
Nmadu, J. N., Ogidan, I. O. and Omolehin, R. A. (2014).
Profitability and Resource Use Efficiency of Poultry Egg
Production in Abuja, Nigeria. Kasetsart J. (Social Sciences)
35:134 – 146.
Jadhav, N. V., and Siddiqui, M. F. (2010). Handbook of poultry
production and management. Second Edition. Jaypee Brothers
Medical Publishers (P) Ltd., New Delhi, India. Pp. 1-4; 125-
145.
Source: Field Survey, 2017