The Lorenz curve is a graphical representation of inequality, often used in economics to show income distribution. It was invented in 1905 by Max Lorenz and is represented on a two-dimensional graph with the x-axis representing individuals and the y-axis representing a resource or characteristic. The Gini coefficient is used to summarize the inequality represented by the Lorenz curve.
The Lorenz curve is a simple graphical representation of the inequality. Represents how a variable is distributed proportionally over 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 aces represent percentages and are therefore 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 characteristic that individuals on the x-axis have to varying degrees. Individuals on the x-axis are ranked by the variable on the y-axis.
The result is a curve that is somewhere between a straight diagonal line and a ninety degree angle. The straight diagonal line represents the closest possible equality. It has a slope of one; always has the same value for x and y. The implication of this line is that population members do not differ on 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 goes sharply vertical. This condition suggests that only one member of the population has any of the resources or properties on the y-axis. All intermediate curves represent an 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. The lines in this graph correspond to ideas such as “the bottom 40% of households earn 15% of total income”. The farther the curve is from a straight diagonal line, the worse the inequality. Because it is two-dimensional, the graph represents much more than just inequality. It can show where in a population inequality lines 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 under the line. The Gini coefficient can fall anywhere between zero and one, going from complete equality to complete inequality. Running this calculation for real-world economies produces a variety of results, with Northern Europe at the bottom and Africa and South America at the top.
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