A Lorenz curve is a graphical representation of the distribution of income or wealth within a population. It is named after the economist Max O. Lorenz who developed the concept in 1905. The curve is often depicted as a graph, with the cumulative percentage of the population on the horizontal axis, and the cumulative percentage of income earned by the population on the vertical axis. The resulting region between the line of perfect equality, where the cumulative percentage of income earned is equal to the cumulative percentage of the population, and the Lorenz curve itself is called the Lorenz area.

A Lorenz curve can be used to measure inequality between members of a population, based on their incomes. If the Lorenz curve is close to the line of perfect equality, this indicates that income is widely distributed amongst all members of the population. However, if the Lorenz curve is far from the line of perfect equality, this indicates that income is concentrated amongst a few individuals within the population. Alternatively, the curve can be used to measure population-level inequality changes over time. Lorenz curves can also be used to compare the degree of inequality between different populations, such as males and females or different countries.

The main component of the Lorenz curve is the Gini coefficient, a statistical measurement of inequality. The Gini coefficient is calculated by dividing the Lorenz area, or the area between the Lorenz curve and the line of perfect equality, by the Lorenz area of the line of perfect equality. Since the Gini coefficient is a measure of how far the Lorenz curve is distanced from the perfect equality line, a higher Gini coefficient indicates higher levels of inequality, while a lower Gini coefficient indicates lower levels of inequality.

Due to its relatively simple graphical explanation, the Lorenz curve has become a standard tool in economics. However, because Lorenz curves are estimates based on empirical data, they may be imperfect measurements of true inequality. Additionally, the calculation of the Gini coefficient is subject to limitations such as neglecting income brackets that do not transfer into the category of ‘richer’ or ‘poorer’, meaning that the actual income distribution may not be reflected by the Lorenz curve.

In summary, a Lorenz curve is a graphical representation of the distribution of income or wealth within a population. It is widely used to measure inequality levels in a population and is the main component of the Gini coefficient, a mathematical representation of inequality. Although it is a widely used tool in economics, the Lorenz curve may be an imperfect measure of true inequality.