Lorenz Curve and Gini Coefficient: Videos & Practice Problems

The Lorenz curve is a graphical representation used to illustrate income inequality within an economy. It plots the cumulative percentage of households on the horizontal axis against the cumulative percentage of income on the vertical axis. The population is divided into quintiles (five groups of 20% each), starting from the poorest to the richest. The curve shows how much income each cumulative percentage of households earns. A perfectly equal income distribution would be represented by a straight diagonal line, where, for example, 20% of households earn 20% of the income. The Lorenz curve typically bows below this line, indicating inequality, as lower quintiles earn less than their proportional share of income. The further the curve is from the line of equality, the greater the income inequality in the economy.

The Gini coefficient is a numerical measure of income inequality derived from the Lorenz curve. It is calculated using the formula $\frac{A}{A}$, where $A$ is the area between the Lorenz curve and the line of perfect equality, and $B$ is the area under the Lorenz curve. A Gini coefficient of 0 indicates perfect equality, meaning everyone has the same income, while a coefficient of 1 represents complete inequality, where one household earns all the income. Values between 0 and 1 show varying degrees of inequality. This coefficient allows economists to compare income distribution across different countries or time periods effectively.

The line of perfect equality on the Lorenz curve graph represents a hypothetical situation where income is distributed equally among all households. It is a straight diagonal line from the origin (0,0) to the point (100%, 100%), indicating that, for example, 20% of households earn exactly 20% of the total income, 40% earn 40%, and so on. This line serves as a benchmark to compare actual income distributions. The Lorenz curve lies below this line when there is income inequality, with the distance between the two lines reflecting the degree of inequality. The closer the Lorenz curve is to the line of perfect equality, the more equal the income distribution.

Complete inequality on the Lorenz curve is represented by a curve that lies along the horizontal axis until the very end, then jumps vertically to 100% income at 100% of households. This means that all income is earned by a single household, while the rest earn nothing. Graphically, the curve hugs the bottom and right edges of the graph, showing that the poorest 99% of households have zero income, and the richest 1% has all the income. This extreme case is the opposite of the line of perfect equality and corresponds to a Gini coefficient of 1, indicating maximum income inequality.

The population is divided into quintiles, or five equal groups of 20% each, when plotting the Lorenz curve to simplify the analysis of income distribution. This division allows economists to examine how income is distributed across different segments of the population, from the poorest 20% to the richest 20%. By calculating the cumulative income earned by each quintile, the Lorenz curve can be constructed to show the share of total income held by each group. Using quintiles provides a clear and manageable way to visualize and compare income inequality within an economy.

Understanding the Lorenz curve and Gini coefficient helps policymakers assess the level of income inequality in an economy, which is crucial for designing effective macroeconomic policies. High income inequality, indicated by a Lorenz curve far from the line of equality and a high Gini coefficient, can lead to reduced aggregate demand because lower-income households typically spend a higher proportion of their income. This can slow economic growth and increase social tensions. Policymakers can use this information to implement redistributive policies, such as progressive taxation or social welfare programs, to promote a more equitable income distribution, enhance economic stability, and foster inclusive growth.