A retired chairman of the economics faculty at the University of Chicago and a West Indian native who teaches at Princeton University were awarded the Nobel Prize for economic science yesterday, in honor of their pioneering work in probing the problems of poor and rural countries.

Named by Sweden's Royal Academy of Sciences to share equally the $190,000 prize were Theodore W. Schultz, who has been a professor emeritus at Chicago since 1972, and Sir W. Arthur Lewis, born at Castries on the island of St. Lucia and currently the James Madison professor of political economy at Princeton.

Schultz, 77, grew up on a farm near Aberdeen, S.D., and devoted his life to agricultural economic issues -- initially American farm crises during the Depression era and subsequently the difficulty of feeding people in developing countries.

A frequent critic of U. S. government policies, Schultz has described Washington as "indifferent or antagonistic to agricultural development" in favor of the "myth" that industrialization is the sole key to economic expansion.

Lewis, 64, was trained as a classical English economist, having moved to Britain from the West Indies when he was 18. He worked initially on economic-growth research and developed the "Lewis model," an economic theory that describes how traditional societies make the economic transition to modern nations, beginning with an abundance of cheap labor from rural areas but litle capital.

In more recent years, Lewis returned to the Caribbean area to head the Universities of the West Indies and Guyana and to serve as first president of the Caribbean Development Bank from 1970 to 1973. He has been an outspoken critic of industrial countries for their lack of attention to the needs of mostly rural, developing nations.

"Characteristic of them both is their interests in problems of economic policy," the Swedish Academy said. "Both are deeply concerned about the need and poverty in the world and engaged in finding ways out of underdevelopment."

The awards were made at a time when worldwide inflation and possible recession are expected to result in severe pressure on poor nations during the early 1980s.

Schultz, educated at South Dakota colleges and the University of Wisconsin, has authored about a dozen books, mostly on agriculture and education. After 13 years at Iowa State College, Schultz joined the Chicago faculty in 1943 and headed the economics department there from 1946 to 1961.

The Swedish Academy noted specifically that in addition to developing a critique of industrialization policies for poor nations, Schultz was the first researcher to show how an investment in education can increase productivity in agriculture as well as an entire economy.

"I think it's a very nice time for a prize that recognizes this subject because it's a political issue now as well as an economic one . . . My colleague, Ted Schultz, and I have worked together for a long time on such things as education," Lewis said yesterday, when told of the awards. Schultz gave credit for his share of the Nobel to graduate students over the years. "My debt to them is tremendous," he said.

Schultz denounced agricultural subsidy programs and concluded that Third World countries would be able to feed themselves if politicians did not interfere, according to an assessment by a Nobel committee member, Asar Lindbeck.

The work of Schultz on the U. S. economy also showed that for a long time there has been a considerably higher yield on "human capital" than on actual money invested.

Cited by the academy as Schultz's "most trailblazing book" was "Transforming Traditional Agriculture," published in 1964.

Lewis, now a British citizen, was educated at the University of Manchester and the London School of Economics. He joined the Princeton faculty in 1963 -- the same year he was knighted by Queen Elizabeth Ii for serving as president of the University of the West Indies.

His major work was published as "The Theory of Economic Growth" in 1955, and he has written a dozen other major books on West Africa and general development of poor nations.

Described by nobel economics laureate Paul Samuelson as "one of the leading economists in the world," Lewis was the first of his profession to begin fundamental research on whether economic growth -- particularly in certain "underdeveloped" areas -- is really a desirable social objective.

He found there are painful costs to rapid urbanization and industrialization but concluded that growth banishes famine, lessens infant mortality, eliminates disease and provides more goods as well as time for mental pursuits.

Lewis also has specialized in studying the economic role of women in poor nations.

Discussing the problems of blacks in this country, Lewis has observed: "The black problem is that while we are 11 percent of the population, we have only 2 percent of the jobs at the top, 4 percent of the jobs in the middle, and are forced into 16 percent of the jobs at the bottom . . . The measure of whether we are winning our battle is in how many of us rise to the middle and the top."

Lewis currently is serving on an advisory council for national economic policy of the NAACP. The chairman of that panel, Washington economist and former Federal Reserve Board governor Andrew Brimmer, said yesterday that Lewis has "made substantial contributions . . . not only theory but application of theory to policy."

According to Brimmer, Lewis "has not been content to live and work in the academic community . . . his preoccupations and concerns have been greatly influenced by his origins in the West Indies and his concern for the problem of economic development involving countries with surplus labor."