Lorenz curve

In economics, the Lorenz curve is a graphical representation of the distribution of income or of wealth. It was developed by Max O. Lorenz in 1905 for representing inequality of the wealth distribution. The curve is a graph showing the proportion of overall income or wealth assumed by the bottom x% of the people, although this is not rigorously true for a finite population (see below). It is often used to represent income distribution, where it shows for the bottom x% of households, what percentage (y%) of the total income they have. The percentage of households is plotted on the x-axis, the percentage of income on the y-axis. It can also be used to show distribution of assets. In such use, many economists consider it to be a measure of social inequality. The concept is useful in describing inequality among the size of individuals in ecology and in studies of biodiversity, where the cumulative proportion of species is plotted against the cumulative proportion of individuals. It is also useful in business modeling: e.g., in consumer finance, to measure the actual percentage y% of delinquencies attributable to the x% of people with worst risk scores. Data from 2005. Points on the Lorenz curve represent statements such as, "the bottom 20% of all households have 10% of the total income." A perfectly equal income distribution would be one in which every person has the same income. In this case, the bottom N% of society would always have N% of the income. This can be depicted by the straight line y = x; called the "line of perfect equality." By contrast, a perfectly unequal distribution would be one in which one person has all the income and everyone else has none. In that case, the curve would be at y = 0% for all x < 100%, and y = 100% when x = 100%. This curve is called the "line of perfect inequality." The Gini coefficient is the ratio of the area between the line of perfect equality and the observed Lorenz curve to the area between the line of perfect equality and the line of perfect inequality.