European Journal of Scientific Research - EuroJournals

Mathematical Formulation of Poverty Index 292
For example, Gini coefficient has been suggested by Bhattacharya et al. (1991) connecting the
mean income and population size.
It is given as follows:
G(y) = 1 + (1/n) – (2/n z) ∑ i=1 n (n+1-i) yi
Where, G (y) = Gini coefficient
z = mean income
n = population size
But, none of these models existing in the literature catch the essence of poverty index for
families of different sizes. Some of the work reported literature in this respect connects the poverty
level to the prices of the commodities like sugar and rice.
It is to be noted that these are indirect parameters that effect the poverty level.
Further, the equation suggested by United Nations is a non-linear equation not very easy to use.
Hence a need for new formulation of poverty index.
2. Description of new model
PI = k f/e (3)
Where, PI = poverty index
e = economic level (family income)
f = family size
k = constant of proportionality
The above relation is based on the inherent realistic assumption that PI is inversely proportional
to economy level (e) or family income and directly proportional to the family size (f).
Derivation of the formula for new model is given below:
PI α 1/e (4)
PI α f
From the above, one can write the following equalities:
(5)
PI = k1/e (6)
PI = k2 f
Combining the above two equations,
(7)
PI = k f/e (8)
Where, k = k1 k2
(9)
In here k1 and k2 are the constant of proportionalities connected with family income (e) and
family size (f). k is the combined constant of proportionality.
It is to be noted that Eq.8 is the same equation as Eq.3.
The constant of proportionalities can be evaluated based on the actual data. The data for family
size and median family income can be either in terms of median or mean value.
It can be said that this is a simple but realistic approach to calculate the poverty index. It is to
be noted that eq.2 for calculation of poverty index is simple to use even though non-linear in nature.
(2)