Lorenz Curve Intersections

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Can two Lorenz Curves representing different study areas when plotted together on the same axes, ever intersect except at their start and end points?

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Yes of course two Lorenz curves can intersect when plotted on the same axes not counting their start and end points.

See this: Crossing Lorenz Curves. And this: Can two Lorenz curves intersect?

However when Lorenz curves intersect there will be ambiguity when trying to determine which curve represents more inequality (as noted in the links).