Lorenz Curve

For those interested in distribution of income in a society, the Lorenz curve is a must-know. Why? It puts a ton of information that would otherwise be hard to figure out into simple, graphical form.

The Lorenz curve is also the precursor to the Gini coefficient, another important metric in the income distribution space.

To understand the Lorenz curve, we first need to understand the graph it’s on. The x-axis graphs the cumulative share of people’s income. For instance, the first tick on the x-axis is the poorest 10% of earners, while the ninth tick is the bottom 90% of earners (see the “cumulative” in action?). On the y-axis, we have the cumulative share of income earned. The graph has a diagonal line with an upward slope of one. The Lorenz curve always falls somewhere on or below this diagonal line.

In a perfectly equal society, our Lorenz curve is on the diagonal line: the line of income equality. In graphical terms, that means the bottom 10% of the population has 10% of the income, the bottom 90% of the population has 90% of the income, etc. As the Lorenz curve starts to sag, we see increasing inequality of income distribution. For instance, perhaps the bottom 10% of people have 1% of the society’s income, and the bottom 90% of earners have 50% of the society’s income. The saggier the curve, the less equally distributed income is.

See: Gini Index to learn how to turn the Lorenz curve into one number, allowing you to easily compare inequality of income between different nations.