Lorenz curve


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Lorenz Curve

A graph showing what percentage of a population possesses a certain percentage of a thing. For example, a Lorenz curve may show that the top five percent of the people in a country control 40% of the wealth. While it may be used in ecology as well as some other fields, it is frequently used in economics to represent social inequality. It was developed in 1905.

Lorenz curve

see CONCENTRATION MEASURES.
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Similar to an Edgeworth Box, Max Lorenz created the Lorenz Curve in 1905 in order to show the percentage of income (the y-axis in Figure 1) held by a certain percentage of the population (the x-axis in Figure 1).
This article extends the Lorenz curve and Gini index by ordering insurance risks; the ordering variable is a risk-based score relative to price, known as a relativity.
If all employers had the same low-wage density, the Lorenz curve would be a 45-degree '/'-shaped line.
For this purpose, the focus is on poverty measures which can be fully characterised in terms of the poverty line, the mean income of the distribution, and the Lorenz curve representing the structure of relative income inequalities.
For instance, Restuccia and Rogerson (2008) use the 2000 establishment size distribution and Greenwood, Sanchez, and Wang (2008) use the Lorenz curve for the distribution of employment by establishment size for 1974.
If each journal had the same number of citations, the Lorenz Curve would simply be the diagonal line running from the bottom left hand corner to the upper right hand corner; this would be the representation corresponding to complete equality.
The 45-degree line represents equal income distribution across the population and the larger the distance of the Lorenz curve to the equal distribution line the greater is income inequality.
Clearly in this situation the Lorenz curve and, therefore, the Gini coefficient remain fixed.
The authors write, "The Lorenz curve for earnings lies below the Lorenz curve for income in the bottom part of the distribution, and these roles are reversed after approximately the 87th percentile.
Figure 1 compares the Lorenz curve for earnings across the five countries.
If the cumulative percentage of a population is graphed from the poorest to the richest along the horizontal axis, and the cumulative percentage of income received by the bottom x percent of the population up the vertical axis, one obtains the Lorenz curve which, typically, has a convex-from-below shape.
where u is the average income and [Sigma](yj) is the value of the Lorenz curve.