A brief study on the measures of income distribution for both analytic and quantitative purposes in terms of size distribution and functional distribution. The study includes discussion on following concepts- Lorenz Curve Gini Coefficient Absolute Poverty Foster Greer Thorbecke Measure

1. POVERTY
AND
MEASURE OF
INEQUALITY

2. INTRODUCTION
Poverty is general scarcity or dearth, or the state of one who lacks a certain amount of
material possessions or money. Absolute poverty or destitution refers to the
deprivation of basic human needs, which commonly includes food, water, sanitation,
clothing, shelter, health care and education. Relative poverty is defined contextually
as economic inequality in the location or society in which people live.
After the industrial revolution, mass production in factories made production goods
increasingly less expensive and more accessible. Of more importance is the
modernization of agriculture, to provide enough yields to feed the population. The
supply of basic needs can be restricted by constraints on government services such as
corruption, tax avoidance, debt and loan conditionality's and by the brain drain of health
care and educational professionals. Strategies of increasing income to make basic
needs more affordable typically include welfare, economic freedoms, and providing
financial services.
Poverty reduction is a major goal and issue for many international organizations such
as the United Nations and the World Bank. The World Bank estimated 1.29 billion
people were living in absolute poverty in 2008. Of these, about 400 million people in
absolute poverty lived in India. Extreme poverty is a global challenge; it is observed in
all parts of the world, including developed economies; UNICEF estimates half the
world's children (or 1.1 billion) live in poverty.
MEASURING INEQUALITY
There are two measures of income distribution for both analytic and quantitave
purposes:
01. The personal or size distribution of income
02. The functional or distributative factor share distribution of income
Size Distributions
Personal or size distribution of income deals with the individual persons or households
and the total income they receive. The way of income received is not considered. How
much is earned irrespective of the sources from where it is derived matters. The
geographical and occupational sources are neglected.

3.  Quantiles and Deciles
a. The statisticians arrange all individuals by ascending personal incomes and
divide the total population into distinct groups or sizes.
b. Divide the population into successive quintiles or deciles according to ascending
income levels and then determine the proportion of N.I received by each income
group
c. Common measure of income inequality is the ratio of incomes received by the
top 20% and bottom 40% of the population.

4.  LorenzCurve
 The Lorenz curve is a graphical representation of the cumulative
distribution function of the empirical probability distribution of wealth, and
was developed by Max O. Lorenz in 1905 for representing inequality of the
wealth distribution.
 The curve is a graph showing the proportion of the distribution assumed
by the bottom y% of the values, although this is not rigorously true for a
finite population (see below). It is often used to
represent income distribution, where it shows for the bottom x% of
households, what percentage y% of the total income they have.
The percentage of households is plotted on the x-axis, the percentage of
income on the y-axis. It can also be used to show distribution of assets. In
such use, many economists consider it to be a measure of social
inequality.
 The concept is useful in describing inequality among the size of individuals
in ecology, and in studies of biodiversity, where cumulative proportion of
species is plotted against cumulative proportion of individuals. It is also
useful in business modeling: e.g., in consumer finance, to measure the
actual delinquency Y% of the X% of people with worst predicted risk
scores.
 They show the actual quantitative relationship between the percentage of
income recipients and the percentage of total income they received
during a time period (year).They also depict the variance of the size
distribution of income from perfect equality .

5. The more the lorenz curve is away from the diagnol, the greater the degree of
inequality represented. The extreme case of perfect inequality( where a erson
receives all the national income while everybody else receives nothing would be
represented by congruence of Lorenz Curve with bottom horizontal and right
hand vertical axes. The greater the degree of inequality , the greater the bend
and the closer to the bottom horizontal axis the Lorenz Curve will be.
 Gini Coefficient
 The Gini coefficient ,also known as the Gini index or Gini ratiois
a measure of statistical dispersion intended to represent the income
distribution of a nation's residents. It was developed by
the Italian statistician and sociologist Corrado Gini and published in his
1912 paper "Variability and Mutability.
 The Gini coefficient measures the inequality among values of a frequency
distribution. A Gini coefficient of zero expresses perfect equality, where all

6. values are the same (for example, where everyone has the same income).
A Gini coefficient of one (or 100%) expresses maximal inequality among
values, for example where only one person has all the income. However,
a value greater than one may occur if some persons have negative
income or wealth. For larger groups, values close to or above 1 are very
unlikely in practice.
 Gini coefficient is commonly used as a measure
of inequality of income or wealth. For OECD countries, in the late 2000s,
considering the effect of taxes and transfer payments, the income Gini
coefficient ranged between 0.24 to 0.49, with Slovenia the lowest
and Chile the highest. The countries in Africa had the highest pre-tax Gini
coefficients in 2008–2009, with South Africa the world's highest at 0.7. The
global income inequality Gini coefficient in 2005, for all human beings
taken together, has been estimated to be between 0.61 and 0.68 by
various sources.
 Gini coefficient is among other measures which satisfy four highly
desirable properties : the anonymity, scale independence, population
independence, and transfer principles.
 Principle of anonymity means that our measure of inequality must not
depend on who has a higher income.
Scale Independence Scale means that our measure of inequality shouldn't
depend on size of our economy or the way we measure its income.
Population Independence Principle states that measure of inequality
should not be based on number of income recipients.
Coefficient of variation is a measure of dispersion which is the sample
standard deviation divided by sample mean .

7. Functional Distribution
Functional distribution of income is a theory explaining how income is divided
between different groups involved in the production process, specifically, the
income earned by the "owners" of various factors or steps in production; namely
land, labor , capital. This income is determined by the supply and demand for
the end goods produced by each of them.
Basically, like the departments of a large firm that makes potato chips, there is
going to be a department that processes the potatoes, another department that
peels them, another that slices them, another that fries the slices, another that
salts them, and another that packages them. Each department has individual
costs, such as labor, materials, and overhead, and they share the overall fixed
costs. The profits then are needed to pay for each departments individual costs

8. We assume that there are only two factors of production: capital, which is a fixed (given)
factor, and labor, which is the only variable factor. Under competitive market
assumptions, the demand for labor will be determined by labor’s marginal product (i.e.,
additional workers will be hired up to the point where the value of their marginal product
equals their real wage). But in accordance with the principle of diminishing marginal
products, this demand for labor will be a declining function of the numbers employed.
Such a negatively sloped labor demand curve is shown by line DL in the figure above.
With a traditional neoclassical upward-sloping labor supply curve SL, the equilibrium
wage will be equal to WE and the equilibrium level of employment will be LE. Total
national output (which equals total national income) will be represented by the area
0RELE. This national income will be distributed in two shares: 0WEELE going to workers
in the form of wages and WERE remaining as capitalist profits (the return to owners of
capital). Hence in a competitive market economy with constant-returns-to-scale
production functions (a doubling of all inputs doubles output), factor prices are
determined by factor supply and demand curves, and factor shares always combine to
exhaust the total national product. Income is distributed by function— laborers are paid
wages, owners of land receive rents, and capitalists obtain profits. It is a neat and
logical theory in that each and every factor gets paid only in accordance with what it
contributes to national output, no more and no less. This model of income distribution is
at the core of the Lewis theory of modern-sector growth based on the reinvestment of
rising capitalist profits.
Unfortunately, the relevance of the functional theory is greatly diminished by its failure to
take into account the important role and influence of nonmarket forces such as power in
determining these factor prices—for example, the role of collective bargaining between
employers and trade unions in the setting of modern-sector wage rates and the power
of monopolists and wealthy landowners to manipulate prices on capital, land, and output
to their own personal advantage.

9.  Absolute Poverty
Absolute poverty refers to the ability of the person or family to get the basic
necessities of life, such as shelter, food, clean water, clothes, medicine. It is
measured based upon the ability to purchase or otherwise garner these things
regardless of the relative wealth in the neighborhood, province, country, or world.
Relative poverty refers to the purchasing power a person or family has relative to
the people in the same society. For example, a family living in a very small but
clean house, who must walk or ride a bus to travel, who can get enough food to
maintain normal weight and activity, but no more than that, and who can buy
decent clothes, but only if they are used, would be considered to be fairly well off
in many African countries, but would be living in relative poverty if they resided in
San Francisco, or Tokyo. The idea of relative poverty is politically charged, since it
can be used to argue for a change in political and social structure by showing the
large disparity in wealth, and using the emotionally loaded word "poverty" to
describe people who, in real terms, may live quite well. If absolute poverty were
the scale, than very few people in the Western world could be considered to live in
poverty, because almost everyone there has access to safe water, plenty of food,
decent clothing, etc.
Absolute poverty is sometimes measured by the number, or “headcount,” H, of
those whose incomes fall below the absolute poverty line, Yp. When the
headcount is taken as a fraction of the total population, N, we define the
headcount index, H/N. The poverty line is set at a level that remains constant in
real terms so that we can chart our progress on an absolute level over time. The
idea is to set this level at a standard below which we would consider a person to
live in “absolute human misery,” such that the person’s health is in jeopardy.
 Poverty Gap measures the total amount of income necessary to raise
everyone who is below the poverty line up to that line. The extent to which
teh incomes of the poor lie below teh poverty line is shown by Total Income
Shortfall, or total poverty gap(TPG) which is defined as
TPG=∑( Yp - Yi)

10.  The Foster-Greer-ThorbeckeMeasure
We are also often interested in the degree of income inequality among the poor,
such as the Gini coefficient among those who are poor, Gp, or alternatively, the
coefficient of variation (CV) of incomes among the poor, CVp. One reason that the
Gini or CV among the poor can be important is that the impact on poverty of
economic shocks can differ greatly, depending on the level and distribution of
resources among the poor. For example, if the price of rice rises, as it did in 1998
in Indonesia, low-income rice producers, who sell a little of their rice on local
markets and whose incomes are slightly below the absolute poverty line, may find
that this price rise increases their incomes to bring them out of absolute poverty.
On the other hand, for those with too little land to be able to sell any of the rice
they grow and who are net buyers of rice on markets, this price increase can

11. greatly worsen their poverty. Thus the most desirable measures of poverty would
also be sensitive to the distribution of income among the poor. A well-known
poverty index that in certain forms satisfies all four criteria is the Foster-Greer-
Thorbecke (FGT) index, often called the Pα class of poverty measures. The Pα
index is given by