The economy continued to grow at a healthy, job-creating clip in the final three months of last year and administration economists said there is no reason to think things will change, at least until mid-year.

By then, Commerce Department chief economist Courtenay Slater said, the $25 billion tax cut the President will propose this weekend will be needed to keep the economy expanding production and creating jobs.

The Commerce Department said total economic output grew at an annual rate of 4.2 per cent during October, November and December. That is slightly slower than the 5.1 per cent rate recorded in the third quarter.

But demand for goods on the part of consumers and businesses was so strong in the last three months of 1977 that companies will have to boost production sharply to ereplenish depleted inventories.

That should assure a helfty growth rate - between 5 per cent and 6 per cent - for the first several months of the year, and will help pull the unemployment rate below the 6.4 per cent level of December.

Economists say that in general the economy must expand its output of goods and services by an average of 4 per cent a year to create enough jobs to keep the unemployment rate from rising. To eat into the unemployment rate, growth must be in excess of 4 per cent.

Between the end of 1976 and the end of 1977 total output - as measured by the real gross national product rose 5.7 per cent and 4.1 million Americans found jobs. The unemployment rate fell from 7.4 per cent to 6.4 per cent during the year.

Even though the economy did not grow as fast during the final months of 1977 as it did earlier in the year, much of the improvement in the unemployment rate came between October and December.

In part, Slater said, the increased hiring in the final months of the year reflects improved business confidence that the economic recovery will continue. So instead of meeting increased production needs by boosting overtime, employers are hiring more workers.

Secretary of Commerce Juanita Kreps called the 1977 performance of the economy "strong." She noted in a statement, that "Growth of employment set a modern record and the unemployment rate was reduced by a full percentage point."

The real gross national product is the broadest measure of the economy that analysts possess. It is the total of goods and services produced by American citizens during a year.

While real growth slowed to a 4.2 per cent annual rate in the final quarter, final sales to businesses and consumers jumped 6.8 per cent, compared with a 4.4 per cent rise in the third quarter. That led to a sharply lower level of inventory growth, which Commerce's Slater called "a needed correction."

At the start of the third quarter, she said, businesses had too many goods in stock relative to sales. Now it is probably the reverse. Secretary Kreps said this should "help pave the way for continued satisfactory economic growth in the first half of this year."

Business investment grew at an annual rate of 8.4 per cent in the final three months of the year, up from a 3.9 per cent rate in the third quarter. Business investment will have to pick up as well if the economy is to continue to expand.

Inflation, as measured by the so-called GNP deflator, accelerated from a 4.3 per cent annual rate in the third quarter to 6 per cent in the fourth quarter. But Slater said that much of the acceleration was due to the federal pay raise in October and price increases in construction. In the consumer sector, she said, prices rose less than in the third quarter.

Before adjustment for inflation, the gross national product was at a seasonally adjusted rate of $1,965.1 billion in the fourth quarter.In 1972 dollars, to adjust for the effects of inflation, so-called real GNP was at a seasonally adjusted annual rate of $1,361.4 billion.

In another development, two leading economists agreed that the economy needs a tax cut this year, but former chairman of the Council of Economic Advisers Alan Greenspan said the tax cuts should be accompanied by spending decreases.

Testifying before the Senate Budget Committee Greenspan said that business investment is falling short and that a tax cut would help stimulate investment.

Lawrence Klein, a professor at the University of Pennsylvania's Wharton School and a former economic adviser to President Carter, said that the economy needs a tax cut bigger than the $25 billion Carter talks about.

He said the recent sharp improvement in the unemployment rate is "no justification for revising the assessment of need for fiscal (taxing or spending) stimulus."