Consumer price, which had been rising at a moderate pace for the last half of 1976, spurted 0.8 per cent in January, the Department of Labor reported yesterday.

The agency said the sharp rise was due mainly to increases in the price of food and items such as property taxes and natural gas.

The January increase was the largest one-month rise since Juy, 1973. Consumer prices rose 0.4 per cent in December and 0.3 per cent in September, October and November.

[WORD ILLEGIBLE] year th overall consumer price increase was 4.8 per cent - the [WORD ILLEGIBLE] rise since 1972, when wage price controls were in effect.

The Labor Department cautioned that even though the January rise in consumer prices was a big one, it does not fully reflect the impact of the weather on overall inflation, especially on foods. Much of the information for the consumer price index was collected before the most severe cold weather struck during the last half of January.

While some government analysts said the increase does not portend another inflationary surge, the January reports is bound to strengthen the Carter administration's case for keeping the size of the stimulus package close to the recommended $15.5 billion level so as not to touch off another round of price increases.

In another development, the Commerce Department reported yesterday that the economy grew at an even slower rate during the final three months of 1976 than the dismal 3 per cent it reported last month.

The agency now estimates that the growth of the real gross national product - the output of goods and services by American citizens after adjustment for inflation - was at an annual rate of 2.4 per cent.

Economists say the economy must grow at a 4 per cent annual rate if it is to create enough jobs to keep the unemployment rat constant.

Most of the downward revision occurred not because consumers and businesses bought less than anticipated - final sales actually were revised upward from 4.8 per cent to an annual rate of 5.5 per cent - but because businesses added fewer goods to their inventories than originally thought.

Maynard Comiez, acting chief economist for the Commerce Department, said the revised report is not discouraging. "We already knew it was not a strong quarter," he said, "and natural gas shortages have forced economists to revise that figure down, perhaps to 4 per cent, and, if the weather gets bad again, perhaps lower.

Industrial production fell 1 per cent in January because of the cold weather and the shortage of natural gas.

Comiez said many of the increases in January were one-shot - such as automobile insurance and property taxes - and that while the cold weather may force other prices up again in the next few months, there is no reason to think that inflation is accelerating again.

He said that government economists still thin the underlying rate of inflation is between 5 and 6 per cent. If consumer prices continued to rise as fast for a year as they did last month, the compound annual rate of inflation would be 10 per cent.

Much of the 0.9 per cent January increase in food prices at grocery stores reflected a big surge in farm product prices in December and January.

The Labor Department cited increases in pork, cereal, bakery products, dairy products, beef, poultry, eggs, fresh vegetables and coffee. The 0.9 per cent rise in January compares with a 0.6 per cent rise in grocery store prices for all of 1976.

Most non-food commodities such as clothing and fuel rose 0.7 per cent, about as much as in December, Gasoline prices fell 0.7 per cent. In recent weeks gasoline prices have turned upward.

The Labor Department said that a third of the 0.9 per cent rise in services prices was accounted for by increases in property taxes and natural gas. Natural gas prices alone rose 2.3 per cent and are 10.6 per cent higher than in September.

The consumer price index, a selection of about 400 goods and services, stood at 175.3 per cent of its 1967 average in January. That means that goods and services which costs $10 in 1967 cost $17.53 last month. The index is not adjusted for seasonal variatio,although all percentage changesare.