FOR SOLVED PREVIOUS PAPERS OF INDIAN ECONOMIC SERVICE KINDLY CONTACT US ON OUR WHATSAPP NUMBER 9009368238
FOR SOLVED PREVIOUS PAPERS OF ISS KINDLY CONTACT US ON OUR WHATSAPP NUMBER 9009368238
FOR BOOK CATALOGUE
CLICK ON WHATSAPP CATALOGUE LINK https://wa.me/c/919009368238
Measurement of Income Inequality
1. Introduction
📌 Income inequality refers to the unequal distribution of income among individuals or households in an economy.
📌 Measuring income inequality is crucial for understanding economic disparities, poverty, and policy effectiveness.
📌 Several statistical methods are used to quantify inequality, including the Gini coefficient, Lorenz curve, Theil index, Atkinson index, and Palma ratio.
✔ Example: Countries like Norway and Sweden have low income inequality, while South Africa and Brazil have high income inequality.
2. Major Measures of Income Inequality
🔹 (1) Lorenz Curve
✔ A graphical representation of income distribution.
✔ X-axis: Cumulative percentage of the population (from poorest to richest).
✔ Y-axis: Cumulative percentage of total income.
✔ The closer the Lorenz curve is to the diagonal (line of equality), the more equal the income distribution.
✔ Example:
- A perfectly equal society would have a 45-degree diagonal line.
- A highly unequal society would have a steeply curved Lorenz line.
✔ Graphical Representation:
📈 Lorenz Curve → Shows how far income distribution deviates from perfect equality.
🔹 (2) Gini Coefficient
✔ One of the most commonly used measures of income inequality.
✔ Ranges from 0 to 1:
- 0 = Perfect equality (everyone has the same income).
- 1 = Perfect inequality (one person has all the income, others have none).
✔ Formula:
G=AA+BG = \frac{A}{A + B}
where:
- AA = Area between line of equality and Lorenz curve
- BB = Area under the Lorenz curve
✔ Example Gini Coefficients of Countries:
- Denmark (low inequality) → 0.25
- USA (moderate inequality) → 0.41
- South Africa (high inequality) → 0.63
📌 Limitations of Gini Coefficient:
❌ Doesn’t show how income is distributed among different classes.
❌ Two different societies can have the same Gini but different wealth distributions.
🔹 (3) Theil Index
✔ A measure from information theory, capturing inequality in income distribution.
✔ More sensitive to differences at the top of the income distribution than Gini.
✔ Formula: T=∑i=1nxixˉln(xixˉ)T = \sum_{i=1}^{n} \frac{x_i}{\bar{x}} \ln \left( \frac{x_i}{\bar{x}} \right)
where:
- xix_i = income of person ii
- xˉ\bar{x} = mean income
✔ Interpretation:
- 0 → Perfect equality.
- Higher values → Greater inequality.
✔ Advantage:
- Theil index allows for decomposition → It can measure inequality within and between different groups (e.g., rural vs. urban).
📌 Limitation: Complex to calculate compared to the Gini coefficient.
🔹 (4) Atkinson Index
✔ Adjusts for social preferences for equality.
✔ More sensitive to changes in income at the bottom of the distribution (useful for poverty studies).
✔ Formula includes an inequality aversion parameter ϵ\epsilon: A=1−(1n∑i=1n(xixˉ)1−ϵ)11−ϵA = 1 – \left( \frac{1}{n} \sum_{i=1}^{n} \left( \frac{x_i}{\bar{x}} \right)^{1-\epsilon} \right)^{\frac{1}{1-\epsilon}}
where:
- ϵ\epsilon = parameter for inequality aversion (higher values mean more weight on reducing poverty).
✔ Example:
- High Atkinson index → Society values equality more, and policies should focus on the poor.
📌 Limitation:
❌ Requires selecting ϵ\epsilon, which can be subjective.
🔹 (5) Palma Ratio
✔ Measures the ratio of income between the richest 10% and the poorest 40%.
✔ Formula: P = \frac{\text{Income of top 10%}}{\text{Income of bottom 40%}}
✔ Example:
- If the top 10% earn 50% of total income and the bottom 40% earn 10%, the Palma ratio is:
P=5010=5P = \frac{50}{10} = 5
✔ Interpretation:
- Lower Palma Ratio (close to 1) → More equal income distribution.
- Higher Palma Ratio (>5) → High inequality.
✔ Advantage:
- Focuses on both rich and poor, ignoring the middle class (which remains stable in most economies).
📌 Limitation:
❌ Ignores the middle-income group, which may be important in some economies.
3. Comparing Income Inequality Measures
| Measure | Key Feature | Strength | Weakness |
|---|---|---|---|
| Lorenz Curve | Graphical | Easy to interpret | No numerical value |
| Gini Coefficient | Widely used | Simple, comparable | Doesn’t show income distribution |
| Theil Index | Sensitive to high earners | Can separate inequality by groups | Complex formula |
| Atkinson Index | Adjusts for inequality aversion | Focuses on poverty reduction | Requires choosing ϵ\epsilon |
| Palma Ratio | Focuses on top 10% vs. bottom 40% | Easy to understand | Ignores middle class |
4. Policy Implications of Income Inequality Measurement
📌 Governments and policymakers use these measures to design economic policies such as:
✅ Progressive Taxation → Higher taxes on the rich to reduce inequality.
✅ Minimum Wage Laws → Ensuring fair wages for low-income workers.
✅ Social Welfare Programs → Healthcare, education, and unemployment benefits.
✅ Universal Basic Income (UBI) → Providing a minimum income for all citizens.
✅ Reducing Corporate Monopolies → Encouraging fair wages and competition.
✔ Example: Scandinavian countries (like Sweden and Norway) have low Gini coefficients because of high social spending and progressive taxation.
5. Conclusion
✔ Income inequality measurement is crucial for economic policy and social welfare.
✔ Gini coefficient is the most widely used but has limitations.
✔ Lorenz curve, Theil index, Atkinson index, and Palma ratio provide additional insights.
✔ Policymakers use these tools to design tax systems, minimum wage laws, and social programs to reduce inequality.