Dynamic Fairness: Mobility, Inequality, and the Distribution of Prospects

This paper clarifies the relationship between dynamic fairness, inequality, and mobility. Suppose agents assess the degree of fairness in a society based on the distribution of expected future income, conditional on current income. Within Markovian environments characterised by stochastically monotone transition rules, in which a globally stable steady-state income distribution exists, we show that the degree of dynamic fairness is jointly determined by inequality and mobility. When mobility is held constant, inequality harms fairness; on the contrary, when inequality is held constant, mobility enhances fairness. Moreover, any particular degree of fairness can be obtained by one of many combinations of inequality and mobility, and trade-offs always exists between any two such pairs. Our results hold true with both the standard Lorenz curve and the generalised Lorenz curve and extend to multi-period settings.