**Paul Samuelson Equilibrium Stability Definition**

Another path was somewhat less formal, mathematically, but was still highly formal relative to Marshallian economics. This work had a major influence on the economics presented in economic texts.

Of the many economists involved in this formalization, Paul Samuelson is probably the best known. Born in 1915, Samuelson began graduate economics studies at Harvard in 1935 after acquiring a strong undergraduate background in mathematics. There he proceeded to publish significant articles applying mathematics to both micro- and macroeconomic theory. He received his Ph.D. in 1941 at the age of twenty-six, and by the time he was thirty-two had become a full professor at the Massachusetts Institute of Technology and the first recipient of the American Economic Association's John Bates Clark Award, which is given to economists under forty years of age who have made significant professional contributions. Samuelson later became the first American to receive the Nobel Prize in economics.

The sources of Samuelson's intellectual inspiration were Cournot, Jevons, Walras, Pareto, Edgeworth, and Fisher, all of whom contributed piecemeal applications of mathematics to economic theory. Using his mathematical background, Samuelson extended their work and helped to lay the mathematical foundations of modern economic theory. Like Edgeworth, he had harsh words for Alfred Marshall, whose ambiguities, he said, "paralyzed the best brains in the Anglo-Saxon branch of our profession for three decades." He went on to say: I have come to feel that Marshall's dictum that "it seems doubtful whether any one spends his time well in reading lengthy translations of economic doctrines into mathematics, that have not been done by himself" should be exactly reversed. The laborious literary working over of essentially simple mathematical concepts such as is characteristic of much of modern economic theory is not only unrewarding from the standpoint of advancing science, but involves as well mental gymnastics of a peculiarly depraved type.

The direction Samuelson's contribution to economic theory would take is evident in his Ph.D. dissertation, completed in 1941 and published in 1947 as Foundations of Economic Analysis. A subtitle, "The Operational Significance of Economic Theory," was eliminated in the published edition, and the statement "Mathematics Is a Language" was added to its title page. The book undertakes to analyze mathematically the foundations of modern micro- and macro-economic theory. In the introductory chapter, Samuelson explains that his purpose is to work out the implications for economic theory of the following statement: "The existence of analogies between central features of various theories implies the existence of a general theory which underlies the particular theories and unifies them with respect to those essential features."

Equilibrium and Stability, Equilibrium Definition and Analysis

According to Samuelson, the theoretical structure that underlies and unifies the individual elements of micro- and macroeconomic theory rests on two very general hypotheses concerning the conditions, first, of equilibrium and second, of its stability. For problems of comparative statics, the conditions of equilibrium can be placed in the familiar maximization framework in which much of the previous work in microeconomic theory had been done. Samuelson illustrates the unity of this approach by working through the firm's minimization of costs and maximization of profits, the consumer's maximization of satisfaction, and welfare theory. Whereas previous economists had paid less attention to dynamic analysis, Samuelson demonstrates that once the dynamic properties of a system are specified, its stability can be assessed. Equilibrium and stability conditions thus emerge as the two-part structure underlying economic theory.

Although Samuelson's Foundations and his subsequent work have dealt almost exclusively with mathematical economic theory, he is sensitive to the relationship between mathematical economics and the process of economic research. He consistently attempts to formulate operationally meaningful, not merely elegant, theorems—in other words, to provide testable hypotheses useful in economic research. "By a meaningful theorem," he says, "I mean simply a hypothesis about empirical data which could conceivably be refuted, if only under ideal conditions."