Chapter 11.4, Problem 92AYU

Economic Mobility The relative income of a child (low, medium, or high) generally depends on the relative income of the child's parents. The matrix $P$, given by is called a left stochastic transition matrix. For example, the entry $P_{21}=0.5$ means that $50\%$ of the children of low-relative-income parents will transition to the medium level of income. The diagonal entry $P_{ii}$ represents the percent of children who remain in the same income level as their parents. Assuming that the transition matrix is valid from one generation to the next, compute and interpret $P^2$.

Source: Understanding Mobility in America, April 2006