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The productivity of American workers increased a moderate 1.6 percent last year, just under half as fast as in 1992 when it grew at the steepest pace in two decades.

But the Labor Department report released Tuesday showed productivity rising at a brisk 4.2 percent seasonally adjusted annual rate in the final three months, even better than the 4 percent jump from July through September.

The department said the annual increase in productivity-defined as output per number of hours worked-was the third straight, including a revised gain of 3.1 percent in 1992 and 1.1 percent in 1991.

Economists maintain that increased productivity is essential for improved living standards and to make American products more competitive in global markets.

Unit labor costs rose 1.9 percent in 1993, down from 2 percent a year earlier.

But the improvement in productivity is coming at the expense of American jobs as many companies restructure and shrink their work forces in efforts to increase long-term efficiency.

Manufacturing productivity jumped 5.3 percent in 1993, up from a 4.3 percent advance in 1992. That included an 8.2 percent jump at factories that make long-lasting goods such as automobiles and appliances.

In another report Tuesday, the National Association of Realtors said prices of existing homes were up 3.4 percent in the fourth quarter, compared with a year earlier.

All regions posted gains: 4 percent in the Midwest, 3.6 percent in the South, 1.7 percent in the Northeast and 0.8 percent in the West. Prices ranged from $360,000 in Honolulu to $52,500 in Waterloo-Cedar Falls, Iowa.

“All the factors are there-low rates, an improving economy, an ample supply of housing and willing consumers,” said Realtors President Robert H. Elrod. “The timing has been perfect for both buyers and sellers.”

Seventy-eight of the markets had increases larger than the nation as a whole.