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Lorenz Curve

What is the Lorenz curve?

A Lorenz curve is a type of graph that shows how unequal the distribution of income or wealth is in a population. It was invented by Max Lorenz, an American economist, in 1905. The graph has the population percentage on the horizontal axis, ordered by their income or wealth level, and the cumulative percentage of income or wealth on the vertical axis.

Lorenz Curve Explained

The Lorenz curve shows how income or wealth is distributed among a population. It plots the cumulative percentage of people on the x-axis and the cumulative percentage of income or wealth on the y-axis. The straight diagonal line represents perfect equality, where everyone has the same share of income or wealth. The curved line represents the actual distribution, which is usually unequal. The more the curved line deviates from the straight line, the more unequal the distribution is.

The area between the straight and curved lines is used to calculate the Gini coefficient, a numerical measure of inequality. The Gini coefficient ranges from 0 to 1, where 0 equals perfect equality, and 1 equals perfect inequality. The Gini coefficient equals the area ratio between the straight and curved lines to the total area under the straight line.

The Lorenz curve is based on empirical data, such as tax returns or surveys, that may not cover the whole population or may be subject to errors. Therefore, the Lorenz curve is an estimate that depends on how well the data fits a continuous function. Different methods of fitting a function may result in different shapes of the Lorenz curve and different values of the Gini coefficient. Thus, the Lorenz curve may not accurately reflect the true income or wealth distribution