Sharp increases in farm prices earlier this year showed up on supermarket shelves in April, helping to drive up the cost of living 0.8 per cent, the Labor Department reported yesterday.

The April increase works out to a compound annual rate of 10 per cent. The administration expressed its concern, but Charles L. Schultze, chairman of he President's Council of Economic Advisers, said he was "encouraged" that recent rises in food prices have not spilled over into other areas.

Grocery store prices surged 1.6 per cent in April, after a 0.6 per cent rise in March and a 2 per cent jump in February. The February rise was concentrated in fruits and vegetables and was caused by the cold January weather that damaged many crops.

By contrast, food price increases in April were widespread. But Robert Crandall, acting director of the Council on Wage and Price Stability, said that the agriculture picture is "good" for the rest of the year and that food prices should moderate.

As usual there were also good-sized increases in energy costs. Fuel oil and coal prices were up 0.9 per cent, and gasoline rose 0.6 per cent in April.

The consumer price index rose 0.6 per cent in March and 1 per cent in February mainly because of the January freeze.

White House press secretary Jody Powell said that while the food price increases in April "were cleary not good," some had been anticipated. He admitted the 1.5 per cent jump in grocery prices "was somewhat larger than we had expected."

Powell said that "there isn't much sign that these large increases are extending to other areas of the economy."

Schultze, at a breakfast meeting with reporters, said the administration still feels of inflation is between 6 er cent and 6.5 per cent, despite recent bad numbers.

Schultze told reporters that the biggest problem the administration faces is continuing to lower the overall unemployment rate - which giving new impetus to inflation. He said the administration hopes to lower the unemployment rate to 4.75 per cent by 1981.

He said that the administration is still working on its anti-inflation program. He said the management labor group headed by AFL-CIO president George Meany and General Electric Co. Chairman Reginald Jones is holding discussions.

He said the administration has set no timeable, but still expects the Meany-Jones, but still expects the Meany-Jones group to come up with some framework to enable business and labor to "work together" to minimize inflationary pressures.

The Labor Department also reported that real spendable earnings - take home pay adjusted for inflation and taxes - fell 0.1 per cent in March.

The department reported yesterday that its consumer price index stood at 179.6 per cent of its 1967 average, which means that a selection of goods and services that cost $10 in 1967 cost $17.96 last month.

The consumer price index is based on a sample of about 400 goods and services bought by consumers. The Labor Department does not adjust the index to account for seasonal variations, but all percentage changes are seasonally adjusted.

The department said that when food and energy index rose 0.6 per cent in April, "about the same as in February and March and less than in January."

Nearly all foods rose. Fresh fruits and vegetables, which soared 8.3 per cent in February because of the freeze and rose 0.3 per cent in March, jumped 1.7 per cent last month.

The department said beef prices "also turned up in April after declining for two months. The upsurge in coffee prices continued. In addition, prices for pork, cereal and backery products, sugar and sweet snad fats and oil products increased more in April than in March."

Non-food commodities, such as apparel and shoes, rose 0.4 per cent, the same as in March and well below the 0.7 per cent increases of January and February.

Services, such as medical care and housing increased 0.3 per cent, "about the same as the average monthly increase in the first three months of the year," the Labor Department said.

Schultze also told reporters that he felt unemployment would fall below 7 per cent this year - it is at 7 per cent now - and could go below 6.7 per cent Alice Rivlin, director of the Congressional Budget Office, predicted Thursday that unemployment has fallen about as far as it will this year and that it would not be "implausible" to predict a slight rise.

Schultze said that during the second three months of 1977 the economy will grow at a faster pace than the 6.4 per cent annual rate of the first quarter. The growth rate will slow somewhat in the third and fourth quarters, but that does not mean more economic stimulus will be needed, he said.