  With a new deprivation (or poverty) function, in this paper, we theoretically
study the changes in poverty with respect to the `global' mean and variance of
the income distribution using Indian survey data. We show that when the income
obeys a log-normal distribution, a rising mean income generally indicates a
reduction in poverty while an increase in the variance of the income
distribution increases poverty. This altruistic view for a developing economy,
however, is not tenable anymore once the poverty index is found to follow a
pareto distribution. Here although a rising mean income indicates a reduction
in poverty, due to the presence of an inflexion point in the poverty function,
there is a critical value of the variance below which poverty decreases with
increasing variance while beyond this value, poverty undergoes a steep increase
followed by a decrease with respect to higher variance. Following these
results, we make quantitative predictions to correlate a developing with a
developed economy.
