Final answer:
The textbook attributes the decline in within-family inequality to changes in family structures, like the emergence of single-parent households and dual-income high-earner couples, as well as growing wage inequality.
Step-by-step explanation:
According to the textbook, factors such as the changing shape of American households and the greater inequality of wages are important factors in explaining the decline in the amount of within-family inequality over the past 50 years. For instance, the growth of single-parent families, typically with lower income, and the increase of two-career high-earner couples, who earn more, contribute significantly to this phenomemon. Additionally, the trend towards 'winner take all' labor markets, where the wage gap between high and low earners widens, plays a crucial role in the overall rise in inequality of household income.