A Summary of Debraj Ray Ch-8&9. Quick bites for revision!

1. MEASURING POVERTY AND
INEQUALITY
Chapter- 6&8- Debraj Ray

2. What Is Inequality?
Economic inequality is the fundamental
disparity that permits an individual
certain material choices, while denying
another individuals those very same
choices.

4. Criterion for Measuring Inequality
There are 4 criterions for inequality
measurement:
1. Anonymity Principle
2. Population Principle
3. Relative Income Principle
4. The Dalton Principle

5. Anonymity Principle states that it does not matter who
earns the income.
Population Principle states that the absolute population
size does not matter; Proportions of the population that
earns different levels of income matters.
Relative Income Principle states that relative incomes
should matter, not the absolute levels of these incomes.
The Dalton Principle states that in an income distribution,
a regressive transfer will lead to increased inequality.

6. The Lorenz Curve
-Diagrammatic way to depict the distribution of
income in any society
-Horizontal axis depicts cumulative percentages
of population arranged in increasing order of
income; Vertical axis depicts percentage of national
income accruing to any fraction of population
-Slope at any point gives the contribution of the
person at that point to the cumulative share of
national income

7. The Lorenz Curve
Lorenz Curve is always bowed to the right of the line of equality.
The difference between the 45 degree line and the Lorenz curves
depicts the level of inequality. More skewed the curve, greater the
Inequality.

8. Measures of Inequality
There are 5 measures of inequality taken in
consideration-
1.The Range
2.The Kuznets Ratio
3.The Mean Absolute Deviation
4.The Coefficient of Variation
5.The Gini Coefficient

9. The Range
* Given by the difference in the incomes of the
richest and the poorest individuals, divided by the mean.
R= (Ym-Y1)/u,
Where Ym gives the distinct incomes and u is the mean income.
*Crude measure, used when detailed info is missing
*Pays no attention to the incomes falling in b/w the richest
or the poorest on the income scale
* Does not satisfy the Dalton’s Principle.

10. The Kuznets Ratio
Refers to the share of income owned by the poorest
20/40% of the population, or the richest 10%, or more
commonly to the ratio of the shares of income of the richest
X% to the poorest y%
As illustrated in the diagram, Kuznets
Hypothesis says that income inequality
should follow an inverse U-shaped
curve along the development process

11. The Mean Absolute Deviation
* Considers the entire income distribution
* Inequality is proportional to the distance from the mean
income.
Where u stands for mean income and n is the total population
* Insensitive to the Dalton Principle.

12. The Coefficient of Variation
Nothing but the standard deviation divided by the mean,
so that only the relative incomes matter.
•Satisfies all the four principles, including the Dalton Principle
• Lorenz-consistent

13. The Gini Coefficient
* Takes the difference b/w all pairs of incomes &
totals the absolute differences, normalized by dividing
by population squared as well as the mean income.
* Inequality thus is the sum of all pair-wise comparisons
of “two-person inequalities” .
* Satisfies all principles.
* Lorenz consistent

14. What Is Poverty Line?
A critical threshold of income, consumption, or more
generally, access to goods and services below which
individuals are declared to be poor.
It represents a minimum level of “acceptable” economic
participation in a given society at a given point of time.
POVERTY MEASURES-
(i) HEAD COUNT/HEAD COUNT RATIO
(ii) POVERTY GAP RATIO
(iii) INCOME GAP RATIO
(iv) FOSTER-GREER THORBECKE CLASS

15. Head Count Ratio
Represents the number of people below poverty line as
a ratio of the total population.
HCR= HC/n
DRAWBACK: Fails to capture the extent to which individual
income falls below poverty line.
Poverty Gap Ratio
Defined as the ratio of the average of income needed to get
all poor people to the poverty line, divided by the mean
income of the society.
* Not really a measure of poverty itself, but a measure of
resources required to eradicate it.

16. Income Gap Ratio
Depicts the total shortfall of the poor from the poverty
line, divided by the total income required to bring all
the poor people to the poverty line.
•Captures directly the acuteness of poverty, as it
measures it relative to the total income needed to
eradicate poverty
DRAWBACK: Both PGR & IGR only capture the “per-
capita intensity "of poverty. HCR does not suffer from
this problem.

17. Foster-Greer Thorbecke Class
Distributional sensitivity is achieved by raising the poverty
gaps (p-yi) to a power, a.
For a=0, the measure Po is just the head-count ratio.
For a=1, the measure P1 is the Poverty Gap Ratio. As a
increases, larger poverty gaps begin to acquire greater
weight& the measure becomes increasingly sensitive.
For a=2, tells that when
there’s no inequality, poverty can be captured by HCR &
IGR but inequality, given by Cp, raises poverty.