Figure 2.4a: The Lorenz Curve and Gini Coefficient for Wealth Ownership
Figure 2.4a illustrates how to approximate the Gini coefficient for a given wealth distribution, such as land ownership. The calculation is based on the ratio of Area A (the space between the Lorenz curve and the perfect equality line) to the total area of the triangle under the 45-degree line, denoted as (A + B). This method provides a geometric estimate of inequality based on the Lorenz curve.
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Gini Coefficient Formula (Based on Lorenz Curve Areas)
Figure 2.4b: Gini Coefficients from Various Lorenz Curves
Figure E2.1: Calculating the Gini Coefficient from a Lorenz Curve Diagram
Causal Link Between Lorenz Curve Area and Gini Coefficient
An economist is comparing income distribution in two countries. A graph shows a 45-degree line representing perfect equality. Country A's income distribution is represented by a curve that bows significantly away from this 45-degree line, creating a large area between the curve and the line. Country B's income distribution is represented by a curve that lies much closer to the 45-degree line, creating a very small area between its curve and the line. Based on this information, what can be concluded about the Gini coefficients of the two countries?
Analyzing Policy Impact on Income Inequality
If a new government policy causes the area between the 45-degree line of perfect equality and a country's Lorenz curve to become smaller, this indicates that the country's Gini coefficient has increased.
Calculating Inequality from a Distribution Graph
Evaluating Inequality with Crossing Distribution Curves
Figure 2.4a: The Lorenz Curve and Gini Coefficient for Wealth Ownership
Figure 2.4a: The Lorenz Curve and Gini Coefficient for Wealth Ownership
A country's income distribution is represented graphically. The area between the line of perfect equality and the curve representing the actual income distribution (defined as Area A) is calculated to be 0.18. The total triangular area under the line of perfect equality (defined as the sum of Area A and Area B) is 0.5. Based on these values, what is the Gini coefficient for this country?
Comparative Inequality Analysis
Analyzing Changes in Income Distribution
Consider a society's income distribution represented graphically. If a policy change causes the area between the line of perfect equality and the curve of actual distribution (Area A) to increase, while the area under the curve of actual distribution (Area B) remains constant, the calculated measure of income inequality will necessarily increase.