Getting to a feasible income equality

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.

A quantitative method for benchmarking fair income distribution

“…Our benchmark is constructed based on the concepts of procedural justice, distributive justice, and power of authority in the realm of 11 well-known professional sports where the allocations of athlete's salary are the outcomes of fair rules, individual and/or team performance, and luck. While the political economy of what levels of income differences countries would accept as fair remains an unexplored territory (Rogoff, 2012), with the exception of a few studies by Venkatasubramanian (2009Venkatasubramanian ( , 2010Venkatasubramanian ( , 2019 and Venkatasubramanian et al (2015) who propose the use of entropy in statistical mechanics and information theory as a quantitative measure of fairness in income distribution and a study by Park and Kim (2021) who introduce the concept of a feasible income equality that maximizes the total social welfare and show that an optimal income distribution representing the feasible equality could be modeled by using the sigmoid welfare function and the Boltzmann income distribution, to our knowledge, no study has attempted to quantitatively measure fair income distribution across countries using the benchmark that is derived from the statistical relationship between the salary shares of the professional athlete in each quintile and the Gini index for the professional athlete's salary in this way before. Our benchmark also satisfies the no-envy principle of fair allocation introduced by Tinbergen (1930) and the general consensus or the international norm criterion of a meaningful benchmark according to the OHCHR (2012).…”

“…These studies are Venkatasubramanian (2009 , 2010 , 2019) , Venkatasubramanian et al. (2015) , and Park and Kim (2021) . Venkatasubramanian (2009 , 2010 , 2019) and Venkatasubramanian et al.…”

“…While the political economy of what levels of income inequalities that countries would accept as fair remains an uncharted territory (Rogoff, 2012), to our knowledge, there have been very few studies that attempt to quantitatively measure how much inequality in income distribution is fair. These studies are Venkatasubramanian (2009Venkatasubramanian ( , 2010Venkatasubramanian ( , 2019, Venkatasubramanian et al (2015), and Park and Kim (2021). Venkatasubramanian (2009Venkatasubramanian ( , 2010Venkatasubramanian ( , 2019 and Venkatasubramanian et al (2015) develop a benchmark that is based primarily on the concept of maximum entropy in statistical mechanics and information theory, and propose that, in an ideal free market, fair income allocation should follow a log-normal distribution whereas Park and Kim (2021) propose the concept of a feasible income equality that maximizes the total social welfare and demonstrate that an optimal income distribution that represents the feasible equality could be modeled by using the sigmoid welfare function and the Boltzmann income distribution.…”

“…These studies are Venkatasubramanian (2009Venkatasubramanian ( , 2010Venkatasubramanian ( , 2019, Venkatasubramanian et al (2015), and Park and Kim (2021). Venkatasubramanian (2009Venkatasubramanian ( , 2010Venkatasubramanian ( , 2019 and Venkatasubramanian et al (2015) develop a benchmark that is based primarily on the concept of maximum entropy in statistical mechanics and information theory, and propose that, in an ideal free market, fair income allocation should follow a log-normal distribution whereas Park and Kim (2021) propose the concept of a feasible income equality that maximizes the total social welfare and demonstrate that an optimal income distribution that represents the feasible equality could be modeled by using the sigmoid welfare function and the Boltzmann income distribution.…”

Is Tanzania’s economic growth leaving the poor behind? A nonlinear autoregressive distributed lag assessment

“…It is also referred to as the GINI index and it ranges from 0 (0%) to 1 (1%) such that 0 represent perfect equality and 1 perfect inequality. It is noted here that while the GINI index shows the income distribution among the population in a country, it, however, does not show its overall income [47]. Thus, a low-income and high-income country can exhibit the same GINI index for the index is only an indication of wealth distribution, not income level.…”