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Lorenz Curves and Partial Orders

In: Income Modeling and Balancing

Author

Listed:
  • Thomas Kämpke

    (Research Institute for Applied Knowledge Processing (FAW/n))

  • Franz Josef Radermacher

    (University of Ulm)

Abstract

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.

Suggested Citation

  • Thomas Kämpke & Franz Josef Radermacher, 2015. "Lorenz Curves and Partial Orders," Lecture Notes in Economics and Mathematical Systems, in: Income Modeling and Balancing, edition 127, chapter 0, pages 55-82, Springer.
    • Handle: RePEc:spr:lnechp:978-3-319-13224-2_4
    DOI: 10.1007/978-3-319-13224-2_4
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