Abstract
Income inequality is known to have negative impacts on an economic system, thus has been debated for a hundred years past or more. Numerous ideas have been proposed to quantify income inequality, and the Gini coefficient is a prevalent index. However, the concept of perfect equality in the Gini coefficient is rather idealistic and cannot provide realistic guidance on whether government interventions are needed to adjust income inequality. In this paper, we first propose the concept of a more realistic and 'feasible' income equality that maximizes total social welfare. Then we show that an optimal income distribution representing the feasible equality could be modeled using the sigmoid welfare function and the Boltzmann income distribution. Finally, we carry out an empirical analysis of four countries and demonstrate how optimal income distributions could be evaluated. Our results show that the feasible income equality could be used as a practical guideline for government policies and interventions.
Highlights
Income inequality is an enduring focus of inquiry in the social sciences [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
We demonstrated that an optimal income distribution representing feasible income equality could be modeled using the sigmoid welfare function and the Boltzmann income distribution
In the empirical data analysis, we showed how the optimal income distribution could be evaluated in the four countries
Summary
Income inequality is an enduring focus of inquiry in the social sciences [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. Various ways have been proposed to quantitatively measure income inequality such as Atkinson’s index, Gini coefficient, Hoover index, Theil index, and generalized entropy index [1, 19,20,21,22,23,24,25,26,27,28]. The Gini coefficient is a prevalent index, representing income inequality within a nation or any other group of people with a single number [23, 29, 30]. The Gini coefficient can be used to show whether the present income distribution is made more equal than it was in the past or whether less-developed countries are characterized by greater inequality than developed countries. The Gini coefficient shows if government interventions such as taxes can lead to greater equality in the income or wealth distribution
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