Final answer:
The New Deal initiative that paid farmers to reduce production through subsidies was the Agricultural Adjustment Act of 1933. Despite being declared unconstitutional and replaced, similar measures continued to influence American agricultural policies.
Step-by-step explanation:
The New Deal initiative that paid farmers subsidies to take acreage out of production was the Agricultural Adjustment Act (AAA) of 1933. This act sought to stabilize agricultural commodity prices by reducing crop surplus. The government offered direct payments to producers of key commodities, such as wheat and cotton, to decrease their output. Funds for these subsidies were raised through a tax on processors of the agricultural products. Although the original AAA was struck down by the Supreme Court, it was later replaced with the Soil Conservation and Domestic Allotment Act and a second version of the AAA, which continued the practice of paying farmers to limit production to raise prices and provided additional assistance to sharecroppers and tenant farmers.