Lorenz Curves and Partial Orders

  • Thomas Kämpke
  • Franz Josef Radermacher
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 679)


A partial order for Lorenz curves results from one Lorenz curve lying consistently below the other Lorenz curve. This Lorenz order is shown to be equivalent to majorization of vectors in case the Lorenz curves belong to finite discrete distributions. For arbitrary distributions with equal expectations the Lorenz order is equivalent to the convex stochastic order. This quite known relation is explicitly verified.

Also, a formula for expected utility is given in terms of Lorenz densities. This expected utility representation admits the equivalence between a distribution having a finite variance and having a Lorenz density that is square integrable. Via so-called consumption-inequality functions it will be shown that maximizing utility of consumption does, typically, not lead to maximum consumption, but to underconsumption.


Utility Function Gini Index Lorenz Curve Expected Utility Representation Equity Parameter 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Thomas Kämpke
    • 1
  • Franz Josef Radermacher
    • 2
  1. 1.Research Institute for Applied Knowledge Processing (FAW/n)UlmGermany
  2. 2.Department of Computer ScienceUniversity of UlmUlmGermany

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