Public finance theory, in which he is particularly known for his work on determining the optimal allocation of resources in the presence of both public goods and private goods.
He was also the author of an influential economics textbook, Economics, first published in 1948, and revised regularly for the following fifty years.
Stanislaw Ulam once challenged Samuelson to name one theory in all of the social sciences which is both true and nontrivial. Several years later, Samuelson responded with David Ricardo's theory of Comparative advantage.
Along with Kenneth Arrow, he is considered one of the founders of modern neoclassical economics. The following is an excerpt from the reasons for awarding Samuelson the Nobel Prize:
Generally speaking, Samuelson's contribution has been that, more than any other contemporary economist, he has contributed to raising the general analytical and methodological level in economic science. He has in fact simply rewritten considerable parts of economic theory. He has also shown the fundamental unity of both the problems and analytical techniques in economics, partly by a systematic application of the methodology of maximization for a broad set of problems. This means that Samuelson's contributions range over a large number of different fields.
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