Final answer:
The collection of less personal income tax revenue as the economy declines into recession exemplifies how a progressive income tax system acts as an automatic stabilizer for the economy by moderating fluctuations in economic activity.
Step-by-step explanation:
As the economy declines into recession, the collection of personal income tax revenues automatically falls because individuals and businesses are earning less income. This phenomenon illustrates how a progressive income tax system serves as an automatic stabilizer for the economy. During recessions, the automatic reduction in tax revenues and increase in government spending on welfare and unemployment benefits help to inject money into the economy, thereby stabilizing aggregate demand. Conversely, during economic booms, tax revenues increase, and government spending on social support decreases, which helps to cool down the economy and prevent it from overheating.