The key government index designed to predict turning points in the economy plunged sharply in November, bolstering suggestions that the economy is truly on a recession slide, the Commerce Department reported yesterday.

The department's index of leading economic indicators fell 1.3 percent, following a revised 1.4 percent drop the previous month. The weakness was spread throughout seven of the 10 indicators now available.

The figures came as the Agriculture Department announced separately that farm prices rose a relatively moderate 0.5 percent in December for the second month in a row, bringing them to 8 percent above a year ago.

Meanwhile, the Labor Department reported the layoff rate among factory workers rose 0.2 percentage point in October to 1.3 percent, while the number of strikes and striking workers declined sharply.

The combination of figures was in line with most analysts' assessments that the economy is in or just entering a moderate recession, which is likely to show up in earnest early this year.

William A. Cox, the Commerce Department's deputy chief economist, noted there already has been a steep falloff in both automobile production and housing. If those continue as expected, the downturn will spread, he said.

Perhaps the most significant feature of the leading indicators index this time was the continuing spread of the declines to indicators beyond the financial and stock market sphere, such as building permits.

The 1.4 percent drop recorded for October was revised from an 0.9 percent decline estimated previously. The index generally has been edging downward since its peak this past March. It is not universally regarded as infallible.

The figures nevertheless appeared to jibe with a new survey of corporate purchasing managers which showed that the economy softened visibly in December, with new orders slumping in the face of cutbacks in production.

Charles T. Haffey of Pfizer, Inc., chairman of the group's business survey committee, said there "isn't any question that danger signals are flashing all over the place." Still, some firms continue to see business good ahead.

At the same time, producers of machine tools say they are winding up their best year ever, and they're unusually optimistic about the outlook for 1980, according to the National Machine Tool Builder's Association.

The trade group said that while November orders fell 23 percent from the previous month's level, the total still was in line with those of the first eight months of 1979, and there are no indications that orders will be curtailed soon.

Most economists still believe the economy is continuing robust enough that output will grow a slight 1 to 1.5 percent, at an annual rate, the final three months of 1979, but that declines may be posted in early 1980.

Although the consensus among economists is that a downturn is coming, if it is not already here, the Carter administration is remaining cautious, for fear of exacerbating inflation.

President Carter is said to have decided not to propose a major tax cut as part of the fiscal 1981 budget he will send Congress in late January. However, aides say Carter could change his mind in late spring if conditions change.

The relative slowdown in agricultural prices would appear to point to some further relief for grocery shoppers in coming months. Food prices, as well as energy prices, have risen less rapidly at the retail level in recent weeks .

The Agriculture Department is predicting that retail food prices will rise about 8 percent again in 1980. However, year-ahead predictions such as that depend heavily on variables such as weather and potential crop damage.

The Labor Department's new figures on the layoff rate were matched by companion statistics showing the rate of new hirings down 0.5 percentage point and the rate for quits down 0.1 percentage point.