The Department of Agriculture, confirming what the farm-supply industry has predicted for months, reported yesterday that the federal crop reduction program could cut seed, fertilizer and pesticide use by 15 percent and add as much as 3 percent to farm-related unemployment.

The department's economic research service said that farmers' decisions to withhold as much as 82 million acres from planting this year under the payment-in-kind (PIK) program will have an adverse impact throughout the supply industry.

Although the USDA provided no dollar figures, it forecast these results from reduced plantings of wheat, corn, sorghum, rice and cotton:

* Shorter work weeks, layoffs and job elimination in agriculture-related industries, resulting from lessened activity, will affect about one-twentieth of 1 percent of total U.S. employment or roughly 50,000 workers.

* The demand for seed, fertilizer and pesticide and the need for repairs will decline between 12 and 15 percent, while fuel use will drop from 8 to 10 percent.

* Machinery purchases could be down as little as 2 to 3 percent, because historically machine sales rise as farm income grows.

* Food prices in 1983 should not be measurably affected, although they may increase in the second half of 1984 because of tighter meat supplies, resulting from higher costs to farmers of feed grains.

* Farm production expenses will decline 2 to 4 percent from the $144 billion estimated for last year. This would be the first decline since 1953, the USDA said.

The report, a summary of a larger study that will be released next week, said that the land diversion program's most direct effect on farm income will come from production expense savings rather than higher cash receipts.

"Although grain prices will improve, crop cash receipts are forecast to decline from 1982's preliminary estimate of $75 billion, possibly to $64-68 billion," the report said. "This decline will be due in large part to PIK's impact on marketings, prices and loan activity."

Under PIK, participants will receive surplus federal commodities in exchange for idling portions of their cropland. The idea is to increase sagging farm prices, reduce surpluses and cut federal budget outlays on agricultural support programs.

The USDA also reported yesterday that prices paid to farmers for crops and livestock scored their third straight monthly rise in March, up slightly from a year ago. The department offered no explanation for the increase, but prices strengthened throughout the winter in anticipation of the crop-reduction plan.