# Measurement Of Inequality, Lorenz Curve

The Lorenz Curve

The Lorenz is named after an American Statistician Lorenz who devised it to depict and measure inequalities in the distribution of income. It is used to compare a society’s actual distribution of income among families with an equal distribution.

The Lorenz curve is derived by plotting the cumulative percentage of income recipients on the horizontal axis. Usually, families rather than individuals are represented. On the vertical axis are measured percentages of total national income associated with or received by each percentage of population. It is also cumulated in the same percentages as on the horizontal axis and it is represented in the below given diagrammatic representation.

The point marked 10 on the horizontal axis shows the lowest 10 % of the population, the point marked 25, the lowest 40 % and so on. Similarly, the percentages of income on the vertical axis are also marked in the same manner. Thus both the axes have the same length and equal scales and the entire diagram is enclosed in a square.

If we construct a diagonal line from the origin O and inclining upward from the left to the upper right hand corner D of the square, the curve OD represents complete or perfect equality. At every point on this 45 degree diagonal line, the percentage of income received exactly equals the percentage of income recipients.

For instance, 10 % of population receives 10 % of income, 25 % of population receives 25 % of income and so on. But no nation exposes absolute distribution of income. The lowest 10 % of the population usually gets much less than 10 % of income, whereas the highest 10 % of population gets more than 10 % of income and so on.

This is what the curved line Lorenz curve depicts in the diagram. This curve lies below the 45 degree line of equal income distribution. The area between this 45 degree line of equal income distribution and the Lorenz curve reflects the extent of income inequality. The more unequal the distribution of income, the more curvature there is in the Lorenz curve.

If the entire income of the nation were received by just one percent of population and the 99 percent of the population receives no income, this would be the case of absolute or perfectly inequality. In such a situation, the Lorenz curve would be represented by the co-existence of the bottom horizontal axis and the right hand vertical axis. This is represented in the diagram as the thick line running along the horizontal axis and the right hand side of the vertical line.

Since no nation has either perfect equality or perfect inequality in its income distribution, the Lorenz curve will lie to the right of the 45 degree diagonal line. If the degree of inequality is greater, the Lorenz curve will have more bend and will be closer to the bottom horizontal axis as represented by the dotted curve to the right of the original Lorenz curve in the diagram.

Conversely, if the degree of inequality is less (or there is more equal income distribution), the Lorenz curve will flatten out and move closer to the 45 degree line as represented in the diagram as dotted line to the left of the original Lorenz curve.

Limitations of the Lorenz Curve

1. Not Based on Disposable Income

The Lorenz curve is based on the data relating to money income rather than disposable income. It does not take into consideration personal income taxes, social security deductions, subsidies received by the poor families etc. Moreover, the data are converted to a per capita basis to adjust for differences in average family size within each quantile (5th) or decile (10th) group of the population. As a consequence, smaller families may sometimes be shown better off than large ones with greater incomes.

2. Does not take Life Time Income

The measurement of income inequality with a Lorenz curve shows income distribution only at a given time. It does not take into consideration lifetime income. For instance, the income of a sports man and of a lecturer may be about the same over their lifetimes. But the income of the lecturer may be spread over a number of years say for 40 years whereas that of sports man may be realised in 10 years. Hence, the two incomes are likely to be highly unequal in a given year.

3. Does not consider age Differences

The construction of a Lorenz curve does not consider the ages of the persons, who receives income. The income of a young individual who enters jobs recently those in mid-career and of old people who have retired are not the same. But the Lorenz curve does not distinguish incomes by ages and reflects inequalities across all ages. It is therefore not correct to group the incomes of the people belonging to different age groups for measuring income inequality.

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