Problem

A small startup has five employees with annual salaries of $30,000, $40,000, $50,000, $60,000 and $70,000. Use the Gini Index to measure the income inequality among the employees.

Solution

Step 1 :Step 1: First, we need to calculate the average income. It is given by the formula \[ \bar{x} = \frac{\sum_{i=1}^{n} x_i}{n} \], where \(x_i\) are the incomes and \(n\) is the number of employees.

Step 2 :Step 2: Next, we calculate the cumulative incomes and cumulative percentages of both incomes and population.

Step 3 :Step 3: Then, we calculate the area A between the line of perfect equality (a diagonal) and the Lorenz curve (the actual distribution).

Step 4 :Step 4: We also calculate the area B under the Lorenz curve.

Step 5 :Step 5: Finally, the Gini Index is given by \[ G = \frac{A}{A+B} \] or equivalently \[ G = 1 - \frac{2B}{A+B} \].

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Source: https://solvelyapp.com/problems/V18VulLDQC/

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