Final answer:
The labor-force participation rate declines when a person leaves their job to be a stay-at-home parent since they cease to be part of the workforce. The unemployment rate does not change because they are not actively seeking employment.
Step-by-step explanation:
When a person quits their job to become a stay-at-home parent, the labor-force participation rate decreases or falls, and the unemployment rate remains unaffected.
The labor-force participation rate reflects the percentage of the working-age population that is working or actively seeking work. When an employed person becomes a stay-at-home parent, they exit the labor force entirely, thereby decreasing the labor-force participation rate because they are neither working nor looking for work. In contrast, the unemployment rate measures the portion of people in the labor force who are actively seeking work but cannot find it. Since the person is not looking for work, they do not count as unemployed.
Therefore, when employed individuals are reclassified as stay-at-home parents, it influences the labor force figures differently from when they are classified as unemployed or discouraged workers. The latter statuses still imply some relationship to the job market, whereas choosing to stay at home generally signifies a withdrawal from the labor force.