The Lorenz curve is a simple graphical representation of inequality. It represents the way a variable is distributed proportionally to a set of units. The Lorenz curve is often used by economists to describe social inequality, but it has also been appropriated by other fields. It was invented in 1905 by Max Lorenz.
Plotting a Lorenz curve requires a two-dimensional graph. Both axes represent percentages, and are thus numbered from zero to 100 or zero to one. The x-axis usually represents a population of individuals. The y-axis describes some resource or feature which the individuals on the x-axis have in different degrees. The individuals on the x-axis are ranked according to the variable on the y-axis.
The result is a curve lying somewhere between a straight diagonal line and a ninety-degree angle. The straight diagonal line represents the most possible equality. It has a slope of one; it always has the same value for x and y. The implication of this line is that members of the population do not differ according to the variable on the y-axis. The opposite condition, complete inequality, has a slope of zero until it reaches the end of the x-axis, at which point it becomes abruptly vertical. This condition suggests that only one member of the population has any of the resource or property on the y-axis. All curves in between represent intermediate inequality.
The most common use of the Lorenz curve is in economics. The x-axis represents households and the y-axis corresponds to their income. Lines on this graph correspond to ideas like "the poorest 40% of households earn 15% of the total income." The further away the curve is from a straight diagonal line, the worse the inequality. Because it is two dimensional, the graph represents more than just the amount of inequality. It can show where in a population the lines of inequality are drawn. It can also represent inequality as gradual or severe.
Economists use a number called the Gini coefficient to summarize the inequality represented by the Lorenz curve. The Gini coefficient is calculated by dividing the area between the actual curve and the line of perfect equality by the total area of the triangle beneath the line. The Gini coefficient can fall anywhere between zero and one, moving from complete equality to complete inequality. Performing this calculation for economies in the real world yields a range of results, with Northern Europe at the bottom and Africa and South America at the top.
