With beef out in front, the cost of living rose 0.8 percent in March, a 10 percent rate of inflation if sustained and compounded for a year, the Labor Department said yesterday.

This cost-of-living announcement was followed by two other pieces of news suggesting that the high rate of inflation will continue and may even worsen in the months ahead.

The Agriculture Department said farm prices rose 4 percent in April, an indication of further price increases in grocery stores in summer.

And General Motors announced it will raise the prices of its cars about $63 apiece, or 1.1 per cent, the first increase since it introduced the 1978 models last September. GM said rising production costs were the reason.

The bad news was tempered in one respect. The Labor Department said prices locally rose only about half as fast as nationally in the last two months. Over the long haul, however, local and national prices rise pretty much in tandem.

The March rise in prices was greater than the rise in wage rates.The purchasing power of an average hour's work fell 0.2 percent, the Labor Department calculated. The buying power of an hour's work is now 1.4 per cent above a year ago.

Food prices increased 1.3 percent in March and have risen at an annual rate of 15.8 percent the first three months of this year. Administration economists said they were concerned that inflation seemed to be accelerating in other areas, too, including clothing, energy and the cost of owning or renting a home.

Beef prices have been the major force pushing up farm prices this year, although pork, fruits and some grains are increasing rapidly too. Beef has been rising at an annual rate of 42.4 percent during the last three months and beef prices are 13.3 percent higher than a year ago. Americans eat more beef than all other meats combined.

The recent surge in inflation caught the administration off guard. President Carter had been more concerned about unemployment during his first year in office, and joblessness has declined markedly since early last year.

Earlier this month the president announced a voluntary program to combat inflation, asking business and labor to moderate their price and wage demands enough this year to reduce the underlying rate of inflation by a half percentage point. Administration officials said the underlying rate is about 6 percent - roughly the difference between increases in wages and fringe benefits and the rise in worker productiviy.

White House spokesman Rex Granum said it is "too early to conclude that we've seen a fundamental worsening in the inflation outlooks as a result of yesterday's 0.8 percent rise in consumer prices, although he conceded that the president is "of course disappointed."

Carter's top economic adviser Charles L. Schultze, chairman of the Council of Economic Advisers, said the increase "underlines the necessity of getting something done." Speaking to reporters after addressing the Eastern Economic Association here, he said the sacrifices the president's anti-inflation program asks are not that much.

Robert Strauss, the president's top inflation fighter, described as "responsible" the 1.1 percent General Motors price increase and said he found "reassuring" the company's statement that it would meet the presidential's goal of raising prices less this year that last.

Food prices behaved moderately formost of the latter half of 1977, but the recent increases in meat and other prices this year left food prices 8.1 percent higher in March 1978 than in March 1977 while overall retail prices were 6.5 percent higher.

The consumer price index stood at 189.8 percent of its 1967 average, which means that a selection of goods and services that cost $10 in 1967 cost $18.98 last month. The index is based on a survey of prices of goods and services thought to represent the purchases of the average urban consumer, who accounts for 80 percent of the population.

Housing costs rose 1 percent in March after rising 0.6 percent in February. The Labor Department said fuels, utilities and furnishings went up more in March than in February. Gas and electricity prices rose 1.4 percent.

Clothing prices, which fell 1 percent in February, rose 1 percent in March. Medical care prices rose 0.6 percent, after increasing 0.8 percent in January and February.

More than half of the Washington cost-of-living increase during February and March was attributed to prices for food and beverages. However, after a 2.2 percent jumps in local supermarket price during February, the March gain was 0.5 percent - less than half the national average increase of 1.2 percent.

For the two months, prices for grocery store food rose 2.7 percent and food in restaurants was up 1.4 percent.

For the two months, prices for grocery store food rose 2.7 percent and food a restaurants was up 1.4 percent.

In the past two months area housing costs, which accounts for 47 percent of a family budget, rose 0.3 percent because of higher bills for rent, furnishings and electricity.