Exercise 21.10. Consider the model of subsection 21.6.1 and suppose that initial inequality is given by a uniform distribution with mean human capital of h (0) and support over [h (0) − ψ, h (0) + ψ]. Clearly an increase in ψ corresponds to greater inequality. (1) Show that when h (0) is sufficiently small, an increase in ψ will increase long-run average human capital and income, whereas when h (0) is sufficiently large, an increase in ψ will reduce long run human capital and income. [Hint: use Figure 21.8 or Figure 21.9]. (2) What other types of distributions (instead of uniform) would lead to the same result? (3) Show that the same result generalizes to the model of 21.6.2. (4) On the basis of this result, discuss whether we should expect greater inequality to lead to higher income in poor societies and lower income in rich societies. (If your answer is no, then sketch an environment in which this will not be the case).