President Carter got a preelection shot-in-the-arm yesterday as the Labor Department reported that the unemployment rate edged down from 7.6 to 7.5 percent last month, while producer prices fell 0.2 percent -- their first decline in 4 1/2 years.

The reports, the last in both categories scheduled to be released before the Nov. 4 election, were a double dose of good political news for Carter, whose economic record has been a major issue in his fight with Republican candidate Ronald Reagan for the presidency.

The White House, seizing on the favorable reports, issued a statement calling the new figures "gratifying." It said the statistics showed Carter's economic policies "are working and will provide the basis for a healthy and noninflationary recovery."

However, government and private economists warned that the good news in yesterday's figures may prove short-lived, and that both the employment picture and inflation rate could worsen in coming weeks as a result of soaring interest rates and sharply rising food prices.

Meanwhile Carter drew some brickbats about his latest criticism of the Federal Reserve Board, as Fed chairman Paul A. Volcker defended the board's policies and Republican economists charged the credit-easing that Carter was advocating would bring on more inflation. [Details of Page c1.]

The dip in the jobless rate was the second in a row for the politically sensitive indicator. The unemployment rate peaked at 7.8 percent in July after rising from the 6 percent range early this spring.

However, Carter still faces high unemployment rates in several politically critical states. The jobless rate in Michigan, for example, jumped to 12.7 percent over the month, while those for New York and California were 7.1 percent and 6.9 percent respectively.

The decline in producer prices -- the first since May 1976 -- followed increases of 1.5 percent in August and 1.7 percent in July. Producer prices have surged at an annual rate of 12.6 percent over the first nine months of the year. The figure previously was known as the wholesale price index. Although the price relief last month was welcomed by economists, analysts cautioned that the September report was skewed by some special factors, and warned that producer prices could rise sharply again when the October figures are compiled.

The Bureau of Labor Statistics said almost two-thirds of the price slow-down in September stemmed from an 0.2 percent decrease in food prices, which had risen sharply in previous months and may go up further this autumn, if Agriculture Department forecasts are correct.

The remainder came mostly from a recorded decline in auto prices -- the result of end-of-model-year descounts by car dealers eager to unload their 1980 stocks. Prices of 1981 models, due to show up in the October index, are scheduled to increase sharply.

Producers' prices for other items ready for shipment to retailers rose 0.7 percent over the month -- about the same as they did in August. At the same time, however, energy prices actually declined 0.4 percent -- contrasting with unusually sharp increases recorded earlier this year.

Despite the caveats, government economists were optimistic about the figures. Commissioner on Labor Statistics Janet L. Norwood said the statistics show there "clearly was . . . improvement" in September -- both in the job situation and on the inflation front.

Norwood, however, declined to predict how the September decline in wholesale prices might affect the consumer price index, which is scheduled to be released Oct. 24 -- the last major government economic statistic to be published before the November election.

Analysts said the Oct. 24 figure could be bloated by the rise in home mortgage interest rates, which normally do not show up in the index until several months after they are set by bankers and savings-and-loan institution executives.

The September report, which is based on mortgage commitments made in July and August, benefitted from the relatively low rates that were prevalent then. Interest rates however, have begun rising sharply again in recent months. These could show up in the October figures.

The improvement in the jobless rate was concentrated primarily among women, teen-agers, white workers and blue-collar workers. The jobless rate for blacks leaped 0.6 of a percentage point over the month to 14.2 percent -- more than double the 6.5 percent rate for whites.

The number of jobs in the economy rose by 200,000, with sharp rebounds in the construction and service sectors. The length of the average workweek also rose by one-tenth of an hour to 35.2 hours. The number of persons out of work fell to 7.8 million.

The last unemployment figure before the election is considered important politically for any incumbent president. A worrisome jump in the jobless rate this time in 1976 was said to have contributed to President Ford's defeat. Ironically, the unemployment rate declined after the election.

Although the jobless rate usually continues to rise after a recession has hit bottom, the figure has edged down this time, in part because the number of persons looking for work has remained stable. In 1976, the labor force was hit with a large influx of teen-agers and women.

The September increase brought the overall producer price index to [WORD ILLEGIBLE] percent of its 1967 average. That means it took $248.90 to buy the same goods [WORD ILLEGIBLE] wholesale last month that cost $100 just 13 years ago. The index now stands 12.8 percent above its level of a year ago.