A generative model for income and capital inequality

The purpose of this study is to formalize a generative model for income and capital inequality by focusing on the accumulation process of human and network capital. Using this model, we attempt to provide theoretical explanations to three empirical questions. First, why is the relationship between economic growth and income inequality expressed as an inverted U-curve? Second, why does societal relative deprivation increase when economic growth rises (the so-called China puzzle)? Third, why is income inequality stable despite the reduction of human capital inequality? The model assumes that people in a society experience repeatedly random chances of gaining capital interest with a success probability p. People gain additional capital as an interest when they succeed and incur a cost when they fail randomly. We show that the capital distribution approaches a lognormal distribution, and as an output of Cobb-Douglas production function, income distribution is also subject to a lognormal distribution. Analyzing the Gini coefficient and the average income as a function of parameters of the model, we derive the following implications. 1) The inverted U-curve is realized by the expansion of success chance. 2) The China puzzle occurs because the increase of average income and Gini coefficient are simultaneously followed by the expansion of success probability p under the range p ∈ (0,0.5). 3) The income inequality is stable, though human capital inequality decreases because of human and network capital elasticity and network capital diminishes the impact of human capital equalization on income inequality.