To reach perfect income equality, factors that determine individual income, such as intelligence, inherited wealth, personalities, and social skills, should be identical for everyone. That is an infeasible ideal. Chae Un Kim and Ji-Won Park propose a more feasible and realistic concept of income equality that could be incorporated in the Gini coefficient, the most widely used measure of inequality, guaranteeing the maximisation of overall social welfare without hampering overall economic efficacy

Kim, Chae Un

Park, Ji-Won

English

LSE Research Online

Chae Un Kim Ji-Won Park June 2nd, 2021Towards a feasible income equality0 comments | 20 sharesEstimated reading time: 3 minutesTo reach perfect income equality, factors that determine individual income, such as intelligence,inherited wealth, personalities, and social skills, should be identical for everyone. That is aninfeasible ideal. Chae Un Kim and Ji-Won Park propose a more feasible and realistic concept ofincome equality that could be incorporated in the Gini coe cient, the most widely used measure ofinequality, guaranteeing the maximisation of overall social welfare without hampering overalleconomic e cacy. Income inequality is well known to negatively affect any economic system, and it has been thesubject of political dispute for the past 100 years or more. Many methods have been proposed tomeasure income inequality quantitatively; of these, the Gini coe cient—which ranges from 0(perfect equality) to 1 (perfect inequality)—is the most widely used measure. Perfect equality isachieved when all members of a given nation or society share the same income level. It’s oftenalleged within political disputes that perfect equality leads to economic ine cacy, and thus to a lessproductive society. Perfect income equality can only be achieved when everyone is identical andequally able to contribute economically. To reach perfect income equality, factors that determineindividual income, such as intelligence, inherited wealth, personalities, and social skills, should beidentical for everyone. However, these conditions cannot be met, even in the Smurfs’ village.Therefore, it’s obvious that the concept of perfect income equality is rather idealistic and practicallyinfeasible in the real world.If a more feasible and realistic concept of income equality can be incorporated in the Ginicoe cient, it can provide a useful guideline for realistic and practical income distribution,guaranteeing the maximization of overall social welfare without hampering overall economice cacy.Figure 1 shows the Lorenz curve for a typical nation. The Lorenz curve illustrates the nationalincome distribution (to the right of the perfect equality line). The perfect equality line cannot be auseful reference for the real world, so we need a more practical and feasible equality line. If it exists,this line provides a valuable reference for government policies (e.g., income taxes) for redistributingincomes and reducing income inequality.Figure 1. The Lorenz curve of a typical nation Feasible income equality is de ned as an optimal income distribution that maximizes total socialwelfare without hindering the sustainable economic growth of a given nation or society. In addition,under a feasible income equality, income must be distributed fairly to individuals by properlyre ecting the realistic factors in uencing their economic contributions. In our study, an optimalincome distribution (i.e., the feasible equality) could be modelled using the sigmoid welfare functionand the Boltzmann income distribution. A sigmoid function is an S-shaped, non-linear function andis used in a wide range of research  elds such as physics and economics. The Boltzmann incomedistribution is adapted from the physical sciences, where the underlying principle is based onentropy maximization and provides the most probable, natural, and unbiased distribution of aphysical system at thermal equilibrium. The concept of most probable in the physical sciences wastranslated into fair in our study.Figure 2. Individual welfare function and total social welfareNotes: a) The non-linear sigmoid function, re ecting more realistic individualwelfare as income increases. With the critical low- and high-income values(L and H), the two constants (µ and α) in the sigmoid function can bedetermined. b) The total social welfare function is maximized at β = β  (theoptimal income distribution).As shown in Figure 2-a, the sigmoid individual welfare function represents the realistic welfare, suchas well-being, happiness, and satisfaction, that a person feels as their income increases. If theirincome is close to zero, welfare value must be at the minimum. Welfare value will increase asincome rises, but not rapidly below the critical low-income value (i.e., the minimum cost of living).Because in this case income is still insu cient to support a basic living standard, welfare valueincreases slowly and gradually. But if income rises above the critical low-income value, people beginto experience some economic freedom. Hence, welfare value will suddenly increase rapidly. Asincome rises further, the degrees of economic freedoms increase and become saturated at a criticallarge su cient income value. At the critical large-income value, the welfare value would also besaturated; afterward, welfare value would again increase only gradually.*As shown in Figure 2-b, the Boltzmann income distribution (Pi) is expressed as an exponentialfunction of the income distribution factor (Ẽi), which is a measure of economic contributions anddepends on factors such as intelligence, personality, and physical and social skills. According to thesingle value (β) in the Boltzmann distribution, the income distribution can represent a wide range ofincome distributions, from perfect equality (β = 0) to perfect inequality (β = ∞). When the Boltzmannincome distribution is inserted into the sigmoid welfare function, the total social welfare functionbecomes a function of the β value and can be maximized at β*. The Boltzmann income distributionwith β* represents the feasible equality (the optimal income distribution).Based on the model, we conducted an empirical analysis of four countries (the US, China, Finland,and South Africa) and demonstrated how optimal income distributions could be evaluated. Figure 3shows the Lorenz curves for the actual and optimal income distributions for each of thosecountries. In all countries, the Lorenz curves for actual income distribution are widely dispersed. Bycontrast, the Lorenz curve for optimal income distribution (the feasible income equality line) liesbetween the diagonal (idealistic perfect equal) and actual income lines. In addition, the shape of thefeasible equality line is very similar for all four countries. This observation is supported by the Ginicoe cient calculations. The Gini coe cients for the actual income distributions are relativelybroadly distributed, whereas those for optimal income distributions are distributed narrowly.Therefore, this result raises the possibility that a universal feasible equality line could be found andapplicable to all countries around the world.Figure 3. Lorenz curves for the actual and the optimal income distributionsfor four countriesNote: The feasible equality lines (blue) are similar for all four countries. The hypothetical feasibleequality line (blue) can serve as a practical guideline for government policies and interventions (redarrow).In conclusion, our results show that the feasible income equality could provide a practical guidelinefor government policies (e.g., income taxes) and interventions for the redistribution of income andwealth. We strongly believe that our work provides direct input for future theoretical and empiricalstudies on reducing income inequality or suggesting government policies, and we anticipate openinga new window to feasible equality in the real world.♣♣♣Notes:• This blog post is based on Getting to a feasible income equality, PLoS ONE 16(3):e0249204 (2021).  • The post expresses the views of its author(s), and do not necessarily represent those of LSE Business Reviewor the London School of Economics. • Featured image by Thomas de LUZE on Unsplash  • When you leave a comment, you’re agreeing to our Comment Policy About the authorPosted In: Economics and FinanceLeave a ReplyYour email address will not be published. Required  elds are marked * NameEmail SiteCommentChae Un Kim is an associate professor in the Department of Physics at UNIST (Ulsan NationalInstitute of Science and Technology) in South Korea.Chae Un KimJi-Won Park is a Ph.D. recipient in regional science at Cornell University.Ji-Won Park

Towards a feasible income equality

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Towards a feasible income equality

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