# Lorenz curve

The Lorenz curve is a graphic representation of the inequality in the distribution of income existing in a certain 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 is placed on the Y axis.

Therefore, at the point we always find that 0% of the population has 0% of the income and at the point that 100% of the population has 100% of the income, as is logical.

## Lorenz curve and ideal situation

Understanding this, we can understand that the closer the curve is to the line that joins the with the, (red line), the better the income will be distributed, the aforementioned line being the most egalitarian distribution possible, in which all the citizens of a population will have exactly the same income.

In the same way, the greater the area that remains between the aforementioned 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 of the three Lorenz curves

Let's go back to the graph shown at the beginning. We are going to comment on several points:

• On 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 come to the conclusion that in that territory, 60% of the population owns approximately 40% of the income.

Additionally, 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 is to the red line, the more egalitarian is the distribution of income in a territory.

Everything mentioned can be calculated mathematically through the Gini index, since there is a relationship between the Lorenz Curve and the Gini index.

Economic inequality

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