3.4 Structure of the Decision Module
3.4.2 Rainy-season procedures
the effect of additional credits is regulated by the global-policy parameter called the credit deflating factor, which has values between 0 and 1. In the case of the value 0.5 for this factor, the effect of credit on income is only 50 % as strong as the effect of the previous credit on income. Thus, the income converges against a certain limit, with the number of credits obtained Hnr creditsincreasing. Mathematically, this relationship can be expressed as:
credit(n)Hinc i dry
no credit(n)Hinc i dry −1
·Creditdef =
credit(n+1)Hinc i dry
no credit(n+1)Hinc i dry −1
(3.24)
where i indexes the production line, n denotes the number of credits already obtained, and Creditdef the credit deflating factor. This equation can be transformed such that the income for the n+1thcredit can be calculated:
credit(n+1)Hinc i dry=
=
credit(n)Hinc i dry no credit(n)Hinc i dry−1
·Creditdef+1
·no credit(n+1)Hinc i dry
(3.25)
credit leads to a small shift of labor allocation by a factor that has been derived statistically from the empirical data set. This procedure is equivalent to the dry-season equation, but with rainy-season specific parameters, which were identified using SPSS.
Static phase (Rstatic)
Compared to the dry season, financial resources play a lesser role for cultivation during the rainy season. Therefore, the maximum area Cmax a household is capable of cultivating is modeled as only being dependent on the available labor pool for cultivation. This way, Cmax can be formulated as follows:
Cmax=Hlabor cult rainy/Ilab mean
where Hlabor cult rainyis the available labor for cultivation, and Ilab meanis the empirical mean of labor input for a single patch. Since only patches with the land cover ’cropland’ or ’grass-land’ are suitable for cultivation, patches that are covered by bare land or forest have to be ignored during the routine of Rstatic. Thus, we will denote the set of patches owned by a household covered by either grassland or cropland as Harea. Furthermore, it was observed that a farmer usually prefers to continue cultivating the patches that have been used the year before. The reason for this is that he usually reserves grassland holdings for the feeding of his livestock. Therefore, within this routine, first all patches with the land cover ’cropland’
will be selected until all patches have been cultivated. Then the procedure will start selecting grass patches. The procedure Rstaticcan be summarized as follows:
1. Set Used-Patches 0
2. Calculate the number n of owned patches actually cultivated by the household:
n=min(count(Harea), Cmax)
3. Select n random patches from the set Harea
4. For each of these n patches (with preference of patches covered by cropland) choose its land-use type
5. Set the parameters of labor input and management, dependent on the type of land-use 6. Set Used-Patches Used-Patches+n
Moving phase (Rmoving)
In the moving phase, the household agent searches for new patches within his Landscape Vision, if labor is still available. According to field observations, a farmer usually tries to continue to cultivate plots he already asked for during the last season. Therefore, the moving phase can be separated into two sub-routines: In the first, the household agent will try to continue cultivating the patches he has already acquired; in the second, he will scan his Landscape Vision for new patches, and if he is successful, mark them as being borrowed.
These two procedures can be summarized in the following; LVarea denotes the set of still unused patches within the Landscape Vision suitable for cultivation (i.e. either grassland or cropland) and Hborrthe set of patches borrowed by the household and not yet used by any other household:
1. Calculate the number n of patches actually cultivated by the household:
n=min(count(Hborr), Cmax- Used-Patches) 2. Select n random patches from the set Hborr
3. For each of these n patches choose its land-use type
4. Set the parameters of labor input and management, dependent on the type of land use 5. Set Used-Patches Used-Patches+n
6. Calculate the number n of patches actually cultivated by the household:
n=min(count(LVarea), Cmax- Used-Patches) 7. Select n random patches from the set Harea
8. For each of these n patches (with preference of patches covered by cropland) choose its land-use type
9. Set the parameters of labor input and management, dependent on the type of land-use 10. Set Used-Patches Used-Patches+n
Income generation procedure (Rincome)
Analogous to the dry-season procedure, both cash and gross incomes are calculated. The equivalent equations are as follows:
Hinc live rainy= aliverainy+bliverainy·Hlivestock (3.26)
for cash income of livestock, and
Hinc i rainy=airainy+birainy·Hlab i rainy (3.27)
with i indexing the production lines as in the dry-season procedure, and airainyand birainybeing the respective parameters. Equivalently, the gross income from cultivation Hgross inc cult rainy
is calculated as:
Hgross inc cult rainy= X
all cultivated patches
Pyield-rainy (3.28)
with Pyield rainy being the yield of a single patch, as calculated by the land-use-specific pro-ductivity functions.
Regarding the calculation of cash income from cultivation, a different approach is needed, because the pattern of crop sale is distinct from the dry season. Most of the harvest is not sold, but stored and mainly used for consumption during the months after harvest.
Nevertheless, some of the crops such as rice and groundnuts can be considered as cash crops to a limited extent. This way, the amount of sold harvest is not dependent on the total gross income of cultivation as in the dry season, but merely on the type and amount of cultivated crops. Thus, the function of cash income for this season was designed as follows:
Hcash inc cult rainy=a+X
i
bi·Cult-Areai (3.29)
where Cult-Areai is the total cultivated area of the land-use type i of the household. This way, the amount of cash income reflects the pattern of the choice of cash land-use types and non-cash land-use types. For the rainy season, the impact of the first credit on the different income-generating activities is modeled in the same way as for the dry season, but with the corresponding parameters:
credit(1)Hinc i rainy= no credit(1)Hinc i rainy+·ai·Hlab i rainy (3.30)
where i indexes the type of production line, and ai is the additional income per labor unit generated by the first credit. The income generated by further credits is then calculated using the same algorithm as in the dry season.