Lorenz Curve

What is the 'Lorenz Curve'

The Lorenz curve is the graphical representation of wealth distribution developed by American economist Max Lorenz in 1905. On the graph, a straight diagonal line represents perfect equality of wealth distribution; the Lorenz curve lies beneath it, showing the reality of wealth distribution. The difference between the straight line and the curved line is the amount of inequality of wealth distribution, a figure described by the Gini coefficient.

BREAKING DOWN 'Lorenz Curve'

The Lorenz curve can be used to show what percentage of a nation's residents possess what percentage of that nation's wealth. For example, it might show that the country's poorest 10% possess 2% of the country's wealth.

While the Lorenz curve is most often used to represent economic inequality, it can be used to represent inequality in any system. The further away the curve lines from the baseline, represented by the diagonal, the higher the level of inequality it represents. When related to economics, the Gini coefficient is used the express the inequality with a single figure. The Gini coefficient can be anywhere from 0, representing complete equality, to 1, representing complete inequality.

The Gini Coefficient

The Gini coefficient is calculated based on the discrepancy between the diagonal line and the Lorenz curve, dividing that figure by the total of the wealth held within a particular country. This allows multiple economies to be compared to one another when examining wealth distribution among individual nations.

Tracking the Gini coefficient can demonstrate wealth trends in particular nations over time.

Lorenz Curve, Gini Coefficient and Measuring Inequality

In an economy with perfect equality, noted by a Gini coefficient of 0, 20% of the population would hold 20% of the wealth. As the percentage of the population in consideration rises, so do the amount of wealth held, with a one for one increase.

In a perfectly inequality curve, the Gini coefficient is 1, and the curve represents 100% of a nation's wealth being held by one single person or entity.

More commonly, Lorenz curves bring out information showing some level of inequality, such as 50% of the population only holding 35% of the wealth. The greater the disparity within a nation, the closer the Gini coefficient will be toward 1.

Validity of the Lorenz Curve and Gini Coefficient

The Lorenz curve and Gini coefficient are popular in economics because they allow for negative wealth. If a certain portion of the population has negative wealth, the Lorenz curve can move below the x-axis.

Though this can provide valuable information, it should be used in conjunction with other information and models. It cannot demonstrate the cause of the negative wealth, which may be relevant to the overall economic analysis.