Comparisons of stationary distributions of linear models

In this note, I compare stationary distributions of the linear model X(n+1) = a(n)X(n) + b(n), where a(n) and b(n) are non-negative random variables. I show that an increase of the variability of a(n) and/or b(n) causes a less equal stationary distribution in terms of Lorenz dominance. The result is useful in studies of wealth and income distributions.