The government's index of leading economic indicators, which is supposed to foretell economic developments, rose sharply in March, the Commerce Department reported yesterday.

The strong 1.4 per cent increase supports President Carter's contentions that the economy is improving strongly and does not need the stimulus a tax rebate would provide, although undoubtedly some of the blimb was a catchup from the severe cold weather which retarded the economy early this year.

At the same time, the Agriculture Department reported that retail food prices may rise slightly faster this year than it originally had thought.

The department said that its upward estimate is due to the sharp rise in food prices in the first three months of the year, due to the severe cold weather which damaged many crops and interfered with transportation.

In another economic development, the Labor Department reported that first-year wage increases negotiated during the first three months of the year averaged 7.6 per cent, smaller than the 8.4 per cent averaged during the first three months of 1976.

But over the life of collectvie bargaining settlements, wage increases averaged 6.5 per cent a year in contracts negotiated between January and March of this year compared with 6.4 per cent last year.

The Labor Department collects wage data only for bargaining units of 1,000 or more employees. In bargaining units with more than 5,000 members it keeps tracks of wage and benefit settlements, which averaged 8.5 per cent for the first year of the contract in both 1976 and 1977.

Because labor costs account for about 70 per cent of total production costs, increases in the size of settlements would be a source of inflationary pressure in the economy. But yesterday's report suggests that there is no new impetus to inflation from wage settlements, although it does not indicate much of a slowing in labor cost increases either.

The big, 1.4 per cent rise in the leading indicators was the sharpest increase in the index since July, 1975 when it jumped 2.3 per cent.

Courtenay Slater, chief economist for the Department of Commerce, said that while some of the rise represented a rebound from the January-February weather, "the underlying strength is there and it is a reasonably encouraged sign for future growth," according to United Press International.