Richness (or Affluence) measures provide another approach for understanding income concentration. Unlike inequality measures, that are sensitive to the changes over the entire income distribution, richness measures are restricted to the top incomes.
In that sense, they work like “inverted” poverty measures: while the poverty focus axiom states that poverty measures should be insensitive to changes in the incomes of the non-poor, the richness focus axiom states that richness measures should remain unaltered by changes in the incomes of the non-rich.
Also like poverty measures, richness measures also rely on a “richness threshold”: those above that threshold are regarded as rich, while those below are regarded as non-rich.14 Not necessarily, but including the poor Like for poverty measurement, these richness thresholds can be somewhat arbitrary; Medeiros (2006Medeiros, Marcelo. 2006. “The Rich and the Poor: The Construction of an Affluence Line from the Poverty Line.” Social Indicators Research 78 (1): 1–18. https://doi.org/10.1007/s11205-005-7156-1.) provide a nice review of proposed richness thresholds and also propose one possible approach with practical and theoretical grounds.
Peichl, Schaefer, and Scheicher (2010Peichl, Andreas, Thilo Schaefer, and Christoph Scheicher. 2010. “Measuring Richness and Poverty: A micro data application to Europe and Germany.” Review of Income and Wealth 56 (3): 597–619. https://doi.org/https://doi.org/10.1111/j.1475-4991.2010.00404.x.) presented an axiomatic study of richness measures. They classify richness measures in two types depending on the effect of income transfers among the rich. A concave measure follows the concave transfer axiom (T1): the measure should increase when a progressive transfer occurs among two rich individuals. On the other hand, a convex measure follows the convex transfer axiom (T2): the measure should decrease when a progressive transfer occurs among two rich individuals.
The reasoning behind the concave transfer axiom is that such progressive transfer would make the income distribution among the rich more internally homogeneous. By clustering the incomes and assets of the rich away from the rest of society, the distribution of income becomes more polarized. On the other hand, the convex transfer axiom means that a progressive transfer among rich individuals reduces inequality among them, so the convex inequality measure should register a reduction. In a sense, concave measures are related to the income polarization approach, meaning that increases in income polarization among the rich should increase the value of the richness measure, while convex measures are related to the income inequality approach, meaning that a reduction in inequality among the rich should also result in a reduction of a convex richness measure.