The Carter administration's promise to cut unemployment to 4.5 per cent by 1981 and to reduce the rate of inflation to 4 per cent by the end of 1979 was challenged yesterday in two new studies published by the Brookings Institution.

In one economist George L. Perry said that to reach even a level of 5 per cent unemployment by 1981, the economy would have to grow at an unprecedented average of 5.7 per cent for five years, rising over 6 per cent most of the time.

"I'm not saying that it's not do-able," Perry told a press conference, "but it's at the optimistic end of a (possible) range." He said that concerns about inflation could "inhibit policymakers from pursuing such a vigorous course."

Similar doubts about the feasibility of Carter's economic goals, including a balanced budget by fiscal 1981, have been voiced by the Congressional Joint Economic Committee, and in staff studies by the Congressional Budget Office.

The swift expansion during 1961-66 is sometimes cited by the Carter administration as a precedent for the economic thrust needed in the years ahead. But Perry said that the growth rate was only about 5 per cent and that the expansion began - in contrast to the present - in a period without inflation. According to Brookings economist Arthur M. Okun, the sustained growth rates cited as necessary by Perry have not occurred since recovery from the depression of the 1930s.

The administration's announced anti-inflation goal is to lower the rate from what it terms a "basic" 6 per cent currently to 4 per cent by the end of 1979. But new projections issued last Friday by the Office of Management and Budget show a deterioration in prospect.The 1979 consumer inflation rate is projected at 5.9 per cent. It does not fall to 4.3 per cent until 1981.

The new OMB projections show a drop in unemployment to 4.6 per cent by the end of 1981, with economic growth averaging a shade over 5 per cent for the five-year period.

The administration's new economic projections were developed by Council of Economic Advisors chairman Charles I. Schultze, a former Brookings colleague of Perry's.

The second Brookings study, by professor Robert J. Gordon of Northwestern University, is pessimistic analysis of the inflation outlook. He said flatly that the Carter goals of simultaneous reductions in inflation and unemployment were "inconsistent."

Gordan said that the outlook "is rather grim." and that prices would continue to rise at rates of 6 to 7 per cent "for the next several years." If Carter tries to reduce inflation by keeping unemployment high, Gordon said, the rate of inflation might be cut by two points some time around 1985, but at the cost of $1 trillion in lost output.

Perry's study was based on a new look at potential economic performance, which he concluded was substantially higher than the 3.5 per cent annual growth rate seen likely by the final report of former President Ford's economic council.

The Brookings economist estimated potential growth in the gross national product at 3.9 per cent from now through 1981. His report rests heavily on a conclusion that labor productively will rise because the number of younger workers in the labor force will decline in the years ahead.

Among professional economists, the importance of the "potential GNP" concept is that it is supposed to measure the gap between performance and potential.

Perry's study says that the gap is wider than the Ford CEA and some private economists have concluded it leads to his analysis that economic policy will have to be more expansionary than Carter is planning if the rate of unemployment is to be lowered.