Lorenz Curve
What is Lorenz Curve?
The Lorenz curve is a graphical representation of income or wealth distribution within a population, comparing actual distribution to perfect equality.
It plots cumulative percentages of income against cumulative percentages of households, with perfect equality shown as a 45-degree line. The further the curve is from this line, the greater the inequality. It is used to visualize the extent of income disparity in a society.
Lorenz Curve: a worked example
Rank households poorest to richest and split them into fifths. Say the bottom fifth earns 5 percent of income, the next 10, then 15, then 25, and the top fifth 45. Cumulate as you move across: 5, then 5 + 10 = 15, then 15 + 15 = 30, then 30 + 25 = 55, then 55 + 45 = 100. The plotted points are (20, 5), (40, 15), (60, 30), (80, 55) and (100, 100). Perfect equality would put the fourth point at (80, 80), so the actual curve sags 80 - 55 = 25 percentage points below the line right there.
The mistake students make with lorenz curve
The usual wreck is plotting each fifth's own share straight from the table instead of cumulating, which produces points like (80, 25) and a curve that wanders up and down and never reaches the top right corner. Every Lorenz curve starts at (0, 0), ends at (100, 100) and only rises, because adding another group can never subtract income. The error is natural, since the data arrives as separate shares. Cumulate first, plot second.
Lorenz Curve questions
How do you draw a Lorenz curve from a table of quintile shares?
Drawing a Lorenz curve takes three steps. Order the groups from lowest income to highest, add the shares as you move across so each point shows the total held by everyone up to that group, then plot cumulative population on the horizontal axis against cumulative income on the vertical. Join the points from the origin to the top right corner and compare with the 45 degree line.
Why is the Lorenz curve bowed below the line of equality?
The Lorenz curve bows below the equality line because households are ranked poorest first, so the bottom 40 percent can never hold more than 40 percent of income. Each step to the right adds a richer group than the last, which makes the curve steepen as it goes. It lies flat on the line only when every household earns exactly the same amount.
What does it mean when two Lorenz curves cross?
Crossing Lorenz curves mean neither distribution is unambiguously more equal than the other. One country may treat its poorest fifth better while the other has a less dominant top fifth, so the ranking depends on which part of the distribution you care about. A single summary number hides that disagreement, and comparing quintile shares directly tells you more.
Related terms
Common comparisons
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