Lorenz Curves and Index of Income Distribution (Gini Index)

Max Otto Lorenz was a professor at the University of Wisconsin Corrodo Gini was an Italian statistician who first employed Lorenz’ ideas.

When a high percentage of the population receives a low percentage of the total income, there exists income inequalities.

A measure of the income inequalities can be done by defining the Lorenz Curve.

Lorenz Curve

A company has five employees whose incomes are $10,000, $15,000, $25,000, $40,000, and $110,000. The total annual income for the five employees is $200,000 The lowest paid person (which represents 20% of the employees) earns $10,000 which is 5% of the total income.

The two lowest paid employees (which represents 40% of the employees) earn $25,000 together, which is 12.5% of the total income.

The lowest paid 60% of the employees earns $50,000, which is 25% of the total income. The lowest paid 80% of the employees earn $90,000, which is 45% of the total income. And finally, 100% of the employees earn 100% of the total income.

This table summarizes the distribution:

Here is a plot of the information:

A Statistics class can teach the details of finding a function for data. The quick way is to use the TI calculator. Use Stat-Edit to enter the data: Use Stat-Calc-CubicReg to find the function:

So, the Lorenz Curve would be

Equality of income distribution occurs when 10% of the people receive 10% of the income, 20% of the people receive 20% of the income, and so on.

NOW, this is where calculus comes in. The area between the line of equality and the Lorenz curve represents the total amount of income inequality.

In economics, the index of income distribution (or Gini coefficient) is used to illustrate the degree of equity in income distribution. The Gini coefficient is found by taking the ratio of the total amount of income inequality to the absolute inequality. TO

Gini coefficient

The Gini coefficient for this example would be

The Gini coefficient is always a number between 0 and 1. A Gini coefficient closer to 0 indicates a more equitable distribution of income. In 1997, the Gini coefficient for incomes of people in the US was 0.410, while Bolivia was and Italy was