Lorenz Curve – Measuring Inequality

Lorenz Curve is the "Rich vs Poor" graph! It shows how unequally wealth (or anything else) is distributed. 💰

What is Lorenz Curve?

[!NOTE] Definition: A cumulative percentage curve used to measure the inequality of distribution of wealth, income, or profits.

Developed by: Max O. Lorenz (1905).

Construction Steps 🛠️

Data: Income of 5 people.

1. Convert to Cumulative Frequencies:
   • Calculate Cumulative % of Persons (X).
   • Calculate Cumulative % of Income (Y).
2. Draw Line of Equal Distribution:
   • A diagonal straight line from (0,0) to (100,100).
   • This represents Perfect Equality (10% people have 10% income).
3. Plot the Curve:
   • Plot the actual Cumulative % points.
   • Join them with a smooth curve.

Interpretation 🧐

• Line of Equal Distribution: Perfect Equality.
• Lorenz Curve: The actual distribution.
• Gap: The area between the Line and the Curve shows the extent of inequality.
  • Small Gap: Low Inequality (Good).
  • Large Gap: High Inequality (Bad).

Uses 🌟

1. Wealth Distribution: To see gap between rich and poor.
2. Business: To see if sales are concentrated in few products.
3. Comparison: Compare inequality of two countries.

Summary

• Lorenz Curve measures Inequality.
• Diagonal Line = Perfect Equality.
• Further the curve, greater the inequality.
• Gini Coefficient is the numerical measure of this area (0 to 1).

The Bottom Line: If the curve touches the diagonal, everyone is equal. If it hugs the axes, one person owns everything! 🌍