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