Uncertainty and inequality: a relationship between entropy and income distribution in society
Abstract
The paper is aimed to discussing features of a relationship between income inequality and entropy.The analyses is based on the theoretical thesis that income inequality is a factor of uncertainty and instability in society, chaotic behaviour of social-economic system, and it is accompanied with entropy increase. Theil index and Gini coefficient are used as income inequality measures in the analyses,Shannonentropy is chosen as entropy measure.The relationship between income inequality measures and entropy measures, including entropy based on income distribution and entropy based on people distribution are discussed. It is noted that changes of entropy and Gini coefficient can have unlike signs: entropy can increase with both inequality increase and inequality decrease. Entropy maximum takes place for Lorenz curve with Gini coefficient 1/3, a deviation from it leads to entropy decrease. This is illustrated by power-series distribution.The analyses give arguments to conclude the following. If majority of population is located in low-income clusters, inequality increasing can lead to decreasing of uncertainty and rising of controllability of social-economic system. If a government starts an implementing a politic aimed to inequality decreasing, in the beginning it will meet uncertainty and chaos rising. It can be suggested that nonlinear change of entropy accompanying changes in income distribution is a factor which slows dawn a further progress in this direction and blocks economic reforms in developing countries.Key words: entropy, income distribution, Theil index, Gini coefficientReferences
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