Chapter 1.4, Problem 21E

Income Inequality The share of aggregate income held by middle-income households in 1970 was $62\%$, whereas that held by upper-income households was $29\%$. The corresponding figures in 2014 were $43\%$ and $49\%$, respectively. The models describing the fall and the rise in the share of the aggregate incomes of these two groups are approximately linear over the period under consideration.

a. Find the mathematical models describing the aggregate income held by each group from 1970 through 2014. (Let t denote the time, in years, with $t=0$ corresponding to 1970.)

b. Find the time when the aggregate income held by upper-income households first exceeded that held by middle-income households.

Source: Pew Research Center.