# Lorenz Curve: Measure of Inequality-Graphical Representation of Gini՚s Coefficient YouTube Lecture Handouts

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# Title: Lorenz Curve

## Measure of Inequality

- A Lorenz curve is a graphical representation income/wealth inequality developed by American economist Max Lorenz in 1905. The graph plots percentiles of the population on the horizontal axis according to income or wealth. It plots cumulative income or wealth on the vertical axis, so that an x-value of 45 and a y-value of 14.2 would mean that the bottom 45 % of the population controls 14.2 % of the total income or wealth while perfect society will mean 45 % population earns 45 % income – line of perfect equality
- The extent to which the curve sags below a straight diagonal line indicates the degree of inequality of distribution

- Area lying between line of perfect equality and observed Lorenz curve as a percent of the area between line of perfect equality and perfect inequality is Gini coefficient. In the figure for Lorenz curve this is given as .
- Gini coefficient increases with increasing dip in Lorenz curve
- Area lies between line of perfect equality and Lorenz curve and depicts inequality. Area below Lorenz curve is depicted by . Therefore, Gini coefficient is
- Lorenz Asymmetry Coefficient (LAC) measures the asymmetry of the Lorenz curve. Gini՚s coefficient measures inequality in the society, LAC measures which size or wealth classes contribute most to the population՚s total inequality. If the LAC is less than 1, the inequality is primarily due to the relatively many small or poor individuals. If the LAC is greater than 1, the inequality is primarily due to the few largest or wealthiest individuals. Thus, LAC adds more meaning to Gini՚s coefficient.

## Properties of Lorenz Curve

- Starts at 0,0 and ends at 1,1
- Continuous function for probability distribution
- If measured variable cannot take negative values (like wealth, education etc.) , Lorenz curve:
- Can՚t go above line of perfect equality
- Can՚t go below line of perfect inequality
- Is always increasing and convex
- If mean of the probability distribution is zero or infinite, Lorenz curve is not defined.

## Limitations of Lorenz Curve

- Person՚s Income
- Compare 2 curves & intersect
- Person՚s income changes throughout life and this is not considered under Lorenz curve. That is, it ignores life cycle effects.
- If 2 Lorenz curves are compared and the 2 curves intersect, it is difficult to determine which distribution has higher inequality

✍ Manishika