Led by rising food prices, the nation's inflation rate jumped sharply last month, the government reported yesterday.Producer prices for finished goods went up by 1.7 percent in July, equivalent to an annual rate of almost 22 1/2 percent.

The rise was the biggest for a single month since November 1974, just after President Ford lifted the last phase of wage and price controls. And the news came as the Federal Reserve Board announced that the nation's money supply increased a record amount last week.

The administration did not try to play down the importance of yesterday's bad inflation news. Charles Schultze, chairman of the Council of Economic Advisers, said the rise showed that "inflation is still a major national problem and cannot be ignored."

But he said, "We still expect the rate of increase in the overall consumer price index to slow significantly in the next few months, even taking into account the implications of the food price rises."

Both administration and private economists are predicting a slowdown in inflation in the second half of the year.

Changes in producer prices usually feed through to the shops after a time lag, but they are not an exact guide to what will happen to consumer prices.

The Fed's announcement was further bad news for the administration because rapid rises in the money supply are widely regarded as fueling inflation. Also, if the Fed attempts to rein in the money supply, that effort would likely lead to higher interest rates.

However, the Fed warned that "special caution" should be taken in interpreting week-to-week changes in the money figures.

Schultze also said that yesterday's price figures "underline the importance of what the president and the administration said at the convention: any economic program must be fashioned in the context of worrying, and continuing to worry, about inflation."

The president is expected to make a major statement on economic and industrial policy soon. Sources say tax cuts for industry and probably for individuals will be included.

At its convention in New York this week the Democratic Party adopted several key economic planks supported by the president's rival for the nomination, Sen. Edward M. Kennedy (D-Mass.). One of these calls for a $12 billion jobs program to be implemented as soon as possible to fight the recession. The president avoided pledging support for this measure, while endorsing the general aim of reducing unemployment.

But the main emphasis in the administration's planning on the policy statement has been toward helping industry revive, rather than toward creating jobs. Officials are also extremely wary of proposing measures that could be inflationary.

The timing of the president's statement is uncertain. Schultze said that there were still a "lot of consultations to do," with Capitol Hill and other groups.

He did not specify whether the other groups included Kennedy and his advisers.

Martin Anderson, a top economic adviser to Republican presidential nominee Ronald Reagan, yesterday characterized the producer price increase as a "testament to the failure of Mr. Carter's economic policies."

A 3.8 percent leap in food prices was the major reason for the overall rise in the finished goods index last month.But while this had been anticipated, there was a more surprising rise in prices charged for some durable goods, particularly autos and trucks.

"It's the large increase outside of food that's worrisome," Schultze said. He admitted that the rise in nonfood prices was larger than he had thought, although the food price increase was no surprise.

"What was really out of line was cars and trucks," he said. Price increases in these two categories accounted for one-fifth of the overall rise, and for almost all of the increases in prices other than food.

An acceleration in the price of capital equipment, which industry buys, from 0.9 percent in June to 1.3 percent last month, was entirely due to higher truck prices, the Bureau of Labor Statistics said.

Courtenay M. Slater, chief economist at the Commerce Department, agreed that the increase in nonfood prices was unexpectedly large. She said she hoped it would prove "a temporary aberration," and warned against putting too much weight on one month's figures.

She said the U.S. auto industry is competing in a world market of "intense competition," and manufacturers would be well advised to keep prices down if they can.

She said that the food price rise was a result of the recent very hot and dry weather and a rebounding of farm incomes from a very low level.

The drought has been a major factor in pushing up prices for both meat and grain. Farmers had already begun cutting back production of broilers and some meat, to push up prices, and the trend toward higher food prices was then accelerated by the bad weather.

However, over the last year food prices have gone up by 6.5 percent, much less than the rate of inflation. Next year food prices are likely to contribute to a worsening in inflation, rather than helping to hold down the price level as they have in the past 12 months, according to analyst Joel Popkin.

A separate report released by the Federal reserve Board yesterday confirmed that the recession is starting to ease. Industry continued to cut back production last month, but the fall in output was much less than in each of the previous three months.

Industrial production dropped by an estimated 1.6 percent in July, compared with 2.3, 2.6 and 2.3 percent declines in April, May and June, respectively, the Fed reported.

It said that the auto industry had begun to pick up, with a 9 percent increase in auto assemblies in the month to an annual rate of 6.4 million units.

Outside the auto industry, economic output continued to decline last month. Production of business equipment was down by 1.4 percent in the month, after large cutbacks in the preceding three months.

Consumer goods production was down by 1.1 percent in July, about the same as in June. The Fed said that, excluding cars, output of home goods and consumer nondurable goods showed further sharp declines in July.

The steel and auto industries, which were hit first in the recession, are showing signs of recovery. U.S. Steel yesterday announced that it is rehiring about one-third of the 10,000 workers it had laid off.