# Lorenz Curve  ## Lorenz Curve Definition

Lorenz Curve, named after American Economist Max O. Lorenz, is a graphical representation of an model.  The curve is a while taking the population percentile on the X-axis and Cumulative wealth on the Y-axis. Complementing this graph would be a diagonal line at 45 angle from the origin (meeting point of the X & Y axis) indicating the perfect income or wealth distribution among the population.

Below this straight diagonal line would be this actual distribution Lorenz curve and the area enclosed between the line and this curve is the actual measurement of inequality. The area between the two lines expressed as a ratio to the area under the straight line gives a representation of the inequality and is called the (developed by the Italian statistician Corrado Gini in the year 1912).

### Example of Lorenz Curve

Following is the example to understand the Lorenz curve with the help of a graph.

Let us consider an economy with the following population and income statistics:

And for the line of perfect equality, let us consider this table:

Let us now see how a graph for this data actually looks:

For eg:
Source: Lorenz Curve (wallstreetmojo.com)

As we can see, there are two lines in the graph of the Lorenz curve, the curved red line, and the straight black line. The black line represents the fictional line called the line of equality i.e. the ideal graph when income or wealth is equally distributed amongst the population. The red curve, the Lorenz curve, which we have been discussing, represents the actual distribution of wealth among the population.

Hence, we can say that the Lorenz curve is the graphical method of studying dispersion. Gini Coefficient, also known as the Gini Index, can be computed as follows. Let us assume in the graph area between the Lorenz Curve and the line is represented by A1 and the line below the curve is represented by A2. So,

Gini Coefficient = A1/ (A1+ A2)

Gini Coefficient lies between 0 and 1; 0 being the instance where there is perfect equality and 1 being the instance where there is perfect inequality. The higher the area enclosed between the two lines represents higher inequality in the economy.

• The Lorenz curve is the Visual Indicator and
• The Gini Coefficient is the Mathematical Indicator.

Income inequality is a pressing issue across the world. So, what are the reasons for inequality in an economy?

• Corruption
• Education
• Tax
• Gender differences
• Culture
• Race and Cast discriminations
• The difference in preferences of leisure and risks.

Reasons for income inequality

• The distribution of economic characteristics across the population should be considered.
• Analyzing how the differences give rise to different outcomes in terms of income.
• A country may have a high degree of inequality because of –
• The great disparity in these characteristics across the population.
• These characteristics generate huge effects on the amount of income a person earns.

### Uses of the Lorenz Curve

• It can be used to show the effectiveness of a government policy to help redistribute income. The impact of a particular policy introduced can be shown with the help of the Lorenz curve, how the curve has moved closer to the perfect equality line post-implementation of that policy.
• It is one of the simplest representations of inequality.
• It is most useful in comparing the variability of two or more distributions.
• It shows the distribution of wealth of a country among different percentages of the population with the help of a graph which helps many businesses in establishing their target bases.
• It helps in business modeling.
• It can be used majorly while taking specific measures to develop the weaker sections in the economy.

### Limitations

• This might not always be rigorously true for a finite level of population.
• The equality measure shown may be misleading.
• When two Lorenz curves are being compared and such two curves intersect, it is not possible to ascertain which distribution represented by the curves display more inequality.
• The variation of income over the lifecycle of an individual is ignored by the Lorenz Curve while determining the inequality.

### Conclusion

To conclude by summarizing what we have learned, Introduced more than 100 years ago, the Lorenz curve provides an innate and complete understanding of the income distribution and provides the basis for inequality measurements through the Gini Index.

The curve defines the relationship between the cumulative portions of income as received by the cumulative population when the income-earning population is arranged in ascending order.

The extent to which the curve bulges downward below the straight diagonal line called the line of equality indicates the degree of inequality of distribution. This implies the curve will always be bowed downwards until there exists inequality in the economy.

Though considered to be the simplest among all other measures of inequalities, the graph can be misleading and might not always produce accurate results.

### Recommended Articles

This has been a guide to what is the Lorenz Curve and its definition. Here we learn how the Lorenz curve measures inequality with the help of examples and its limitations. You can learn more about economics from the following articles –