What would the Gini coefficient be if one person retains all of the income in a country?
A.) 0 B.) −1 C.) 50 D.) 1
The correct answer and explanation is:
The correct answer is D.) 1.
The Gini coefficient is a measure of income inequality within a country or a population. It ranges from 0 to 1, where 0 represents perfect equality (everyone has the same income), and 1 represents perfect inequality (one person has all the income, and everyone else has none).
To understand this concept, think about the Lorenz curve, which is a graphical representation of income distribution. On the x-axis, you plot the cumulative percentage of the population, and on the y-axis, you plot the cumulative percentage of income. If income were distributed perfectly equally, the Lorenz curve would be a straight diagonal line from the bottom-left to the top-right corner. This straight line represents 100% of the population earning 100% of the income equally.
However, when one person in the country holds all of the income, the Lorenz curve becomes a sharp curve that hugs the bottom-left corner almost entirely, and then rises vertically to the top-right corner. In this scenario, the area between the Lorenz curve and the line of perfect equality is maximized.
The Gini coefficient is calculated as the ratio of the area between the Lorenz curve and the line of perfect equality to the total area under the line of perfect equality. The closer the Lorenz curve is to the line of perfect equality, the smaller the Gini coefficient. If one person controls all of the income, the area between the curve and the line of equality is as large as it can possibly be, resulting in a Gini coefficient of 1. This indicates the maximum level of inequality, where one person has all the wealth or income, and the rest have none.
So, in the case where one individual has all the income, the Gini coefficient is 1, indicating extreme income inequality.