Lorenz Curves and Partial Orders

Thomas Kämpke and Franz Josef Radermacher
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Thomas Kämpke: Research Institute for Applied Knowledge Processing (FAW/n)
Franz Josef Radermacher: University of Ulm

Chapter Chapter 4 in Income Modeling and Balancing, 2015, pp 55-82 from Springer

Abstract: 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.

Keywords: Utility Function; Gini Index; Lorenz Curve; Expected Utility Representation; Equity Parameter (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-319-13224-2_4

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DOI: 10.1007/978-3-319-13224-2_4

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