Lorenz Curve

The Lorenz curve is a graphic representation of the inequality in the distribution of existing income in a given territory (usually a country). In it, the accumulated population (P) expressed as a percentage is placed on the X axis and the accumulated income (Q) expressed as a percentage on the Y axis.

Therefore, at point (0,0) we always find that 0% of the population has 0% of the income and at point (1,1) that 100% of the population has 100% of the income rent, of course.

Lorenz curve and ideal situation

With this in mind, we can understand that the closer the curve of the line is that joins (0,0) with (1,1), (red line), the better the income will be distributed, the said line being the most equal distribution possible, in which all citizens of a population will have exactly the same income.

In the same way, the greater the area between the said straight line and the curve, the greater the existing inequality, the population represented by the blue line has a more equal distribution than that represented by the green line).

Explanation and the three Lorenz curves

Let’s go back to the graph shown at the beginning. Let’s comment on several points:

  • In the green curve when observing point 3: At that point, we can say that 60% of the population owns 20% of the income
  • In the blue curve when observing point 2: At this point, we would conclude that in that territory, 60% of the population owns approximately 40% of the income.

Additionally, by making a comparison we would understand that the territory represented by the blue line has a more equal or equitable distribution of income than that represented by the green curve, since as I have already mentioned, the closer the curve of the red line is, the more Equal is the distribution of income in a territory.

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