CHICAGO  Faced with strong worldwide food demand and the accompanying higher prices, American farmers are beginning to respond to the signals of the market. In a new government report, farmers said they would make significant cuts in corn acreage this year in favor of soybeans.

If they carry through with their intentions, the resulting additional soybean oil could help alleviate global shortages of cooking oil that have led to sharply higher prices, hitting poor countries hard.

But a smaller corn harvest would most likely raise prices for that crop, which could also increase the prices Americans pay for meat. Most corn is used as animal feed.Higher corn prices may also compound the difficulties of companies that use corn to produce ethanol as a motor fuel. Despite government mandates for the use of ethanol, those companies are struggling. They expanded so rapidly in recent years that an oversupply of ethanol depressed prices, even as the cost of their main feedstock  corn  was rising.

The release Monday morning of the Agriculture Department’s report on farmers’ plans, based on interviews with growers during the first two weeks of March, caused the price of corn in the commodities markets to rise past $6 a bushel for the first time, before falling back. Soybean prices, meanwhile, fell 70 cents to $10.89 on expectations of a greater supply.