Inflation is suddenly turning into a worry for the Federal Reserve, which knows that its credibility as a central bank would be damaged if investors concluded it was not determined to combat the recent rise in prices. It still seems unlikely that the Fed will actually raise rates in an election year when the economy is probably in recession. But the surprisingly strong increases in producer prices for May, reported by the government this week, increased the pressure on the Fed at least to sound tough about inflation. The report showed that, over all, producer prices of finished goods rose 1.4 percent in May, raising the 12-month increase to 7.2 percent. That annual gain is still smaller than the 7.8 percent increase reported in the year through January, a figure that was the highest in a quarter century. Not since September 1981, when a severe recession brought on by a large Fed increase in interest rates was beginning to bring down inflation, has the overall producer price inflation rate been that high. Until recently, the Fed has emphasized the so-called core rate of inflation, which excludes energy and food prices. But in recent speeches, officials have conceded the obvious fact that increases in those prices have been large and serious for many consumers. The core rate is up 3.0 percent over the last 12 months, well below the overall rate but still higher than at any time in the last 16 years. A Duke University/CFO Magazine poll of chief financial officers released this week found that 45 percent of the American executives said their companies had raised prices to offset their higher energy costs. They now expect their own firms to raise prices by 4.1 percent over the next 12 months — twice the rate they forecast nine months ago. As yet, however, the price increases are concentrated in some areas. The accompanying charts show that over the last 12 months, the producer prices of grains soared 64.8 percent, but the producer price for livestock edged up just 1.5 percent. Some farmers are selling off cattle quickly, depressing prices, because they cannot afford to feed them. Some industries that historically had little pricing power may be getting a little such power. Producer prices for motor vehicles are up 1.0 percent, which is better than that segment has done in recent years but is still low. Similarly, apparel prices edged up 0.7 percent, which is also low but better than that industry had done earlier in the decade. Over all, the producer price statistics indicate that inflation rates vary widely, but there are signs that even the businesses where prices have been weakest in recent years are starting to find ways to recover at least some of their higher costs.