Gini Coefficient Formula (Based on Lorenz Curve Areas)
The Gini coefficient can be calculated geometrically from a Lorenz curve diagram. It is the ratio of the area between the line of perfect equality and the Lorenz curve (designated as area A) to the total area of the triangle formed under the line of perfect equality (designated as area A + B). The formula is:
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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
Learn After
A nation implements a series of economic policies that result in a more equal distribution of income among its population. When visualizing this change on a standard income distribution diagram, what is the resulting effect on the geometric areas used to calculate the primary measure of inequality, which is defined as the ratio of the area between the line of perfect equality and the income distribution curve (Area A) to the total area under the line of perfect equality (Area A + B)?
Calculating the Gini Coefficient from Geometric Areas
Comparative Income Inequality Analysis
In a diagram representing a country's income distribution, if the area between the line of perfect equality and the income distribution curve (Area A) is exactly equal to the area under the income distribution curve (Area B), then the resulting Gini coefficient is 1.0, indicating perfect inequality.
In a standard diagram used to measure income inequality, the total triangular area under the line of perfect equality is always 0.5. If a country's Gini coefficient is calculated to be 0.3, the numerical value of the area between the line of perfect equality and the country's income distribution curve is ____.
In a standard diagram used to visualize income distribution, match each geometric component or calculation with its corresponding description.
Two countries are analyzed using identical diagrams that plot the cumulative percentage of the population against the cumulative percentage of income. In these diagrams, the area between the line of perfect equality and the country's income distribution curve is labeled 'Area A', and the area under the income distribution curve is labeled 'Area B'. The total area under the line of perfect equality is the sum of these two areas (A + B).
- For Country X, Area A is 0.15.
- For Country Y, Area B is 0.20.
Based on this information and the standard formula where the inequality measure is the ratio A / (A + B), which statement is correct?
Evaluating a Policy Claim on Income Inequality
Calculating Lorenz Curve Area from Gini Coefficient and Area B
In a standard diagram used to visualize income distribution, the area between the line of perfect equality and the income distribution curve is labeled 'Area A', and the area under the income distribution curve is labeled 'Area B'. If Area B is equal to zero, this represents a state of perfect equality, and the corresponding inequality coefficient, calculated as A / (A + B), would be 0.