Principles of Microeconomics / Unit 14 MIC 1308 worked example, 60 to 90 seconds
Drawing Two Lorenz Curves
The idea
From each year's quintile shares, build cumulative shares by adding each fifth to the total before it; the fifth entry must be one hundred, which checks the arithmetic. Plot each year's five points against twenty, forty, sixty, eighty and one hundred percent of households, with the origin. Compare the two curves: the one lying further below the diagonal is the more unequal year. Say which fifths gained share and which lost.
In practice
Worked example: year one's fifths earn six, eleven, sixteen, twenty-four and forty-three percent; year two's earn four, nine, fifteen, twenty-four and forty-eight. Year one's cumulative shares are six, seventeen, thirty-three, fifty-seven and one hundred; year two's are four, thirteen, twenty-eight, fifty-two and one hundred. At every point but the last, year two's curve lies lower, so year two is more unequal. The bottom three fifths each lost share, the fourth held, and the top fifth gained five points.
Where people slip
Cumulate in order from the bottom; a curve built from the top down is a different object. And two curves can cross, in which case neither year is unambiguously more unequal and a single number like the Gini hides the crossing.
Your place on the trail
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