European Journal of Scientific Research - EuroJournals

European Journal of Scientific Research
ISSN 1450-216X Vol.20 No.2 (2008), pp.291-296
© EuroJournals Publishing, Inc. 2008
http://www.eurojournals.com/ejsr.htm
Mathematical Formulation of Poverty Index
Chandra Putcha
Professor, Department of Civil and Environmental Engineering
California State university, Fullerton, CA 92834, USA
Abstract
There are people with different economic levels in any society in the world. The
economic range will vary from household to household, society to society and from
country to country. The economic level of a household will depend on the income and the
inherent wealth of that family. This implies that once the household income drops below an
acceptable level (depending on the country), then that family can be considered as poor.
Obviously, the definition of “poor” would vary from country to country. A person/family
considered “poor” in a developed country like USA or U.K. may not be poor in an
underdeveloped country. The ideal situation is to eradicate poverty completely. While this
is not possible, the aim should be at least reduce the poverty. For this it is important to first
define the human poverty index or simply poverty index. This paper suggests a simple and
new model different than the existing models. The model is then validated using some of
the data from U.S. Census Bureau (2006) and data from Health & Human Services (2007).
Application of optimization principles to poverty index has also been illustrated.
1. Introduction
As stated earlier, the definition of “poor” is not uniform. It changes from country to country. For a
reasonable comparison, an indicator such as human poverty index or simply poverty index can be used.
The poverty index can be considered as an indicator of the standard of living in a country. It
changes from country to country.
Quantification of poverty index is a complex issue. This is because it is a function of so many
parameters. United Nations has generated a document to define HPI (human poverty index). It is
expressed in terns of three factors P1, P2, and P3 as follows:
HPI = [{1/3} (P1 α + P2 α + P3 α )]1/α (1)
Where, P1 = probability at birth of not surviving to age 40
P2 = adult illiteracy rate
P3 = unweighted average of population without sustainable access to an
improved water source and children under weight for age
α = 3
This formulation, in the opinion of this author doesn’t represent realistically the poverty index.
It misses important factors such as the economy of the household and the family size while it includes
unimportant factors such as illiteracy rate and sustainable access to improved water source and children
under weight.
It can be argued that since literacy is directly connected to the economic level of a household
and hence illiteracy is connected to poverty. On the other hand, it is difficult to justify the connection
of human poverty index to sustainable access to an improved water source.
Similarly, there are some other definitions of poverty index given in the literature (Bhattacharya
et al.,1991; Krishnaswamy, 1990; India, 2003).