Economic Theory in the Mathematical Mode

I. If a symbolic date were to be chosen for the birth of mathematical economics, our profession, in rare unanimous agreement, would select 1838, the year in which Augustin Cournot published his Recherches sur les Principes Mathématiques de la Théorie des Richesses. Students of the history of economic analysis could point out contributions made to mathematical economics as early as the beginning of the eighteenth century. They could also point out Johann Heinrich von Thünen’s Der isolierte Staat, 1826, a prototypical example of the use of mathematical reasoning in economic theory with little mathematical formalism. But Cournot stands out as the first great builder of mathematical models explaining economic phenomena. Among his successors in the nineteenth century and the early twentieth century, the highest prominence will be given in this lecture to Léon Walras (1834-1910), the founder of the mathematical theory of general economic equilibrium, to Francis Y. Edgeworth (18451926), and to Vilfredo Pareto (1848-1923). All three lived long enough into the twentieth century to have increased, for all Nobel Laureates, the value of the economics prize, had it, like the other prizes, been initiated in 1901. If 1838 is the symbolic birthdate of mathematical economics, 1944 is the symbolic beginning of its contemporary period. In that year, John von Neumann and Oskar Morgenstern published the first edition of the Theory of Games and Economic Behavior, an event that announced a profound and extensive transformation of economic theory. In the following decade, powerful intellectual stimuli also came from many other directions. In addition to von Neumann and Morgenstern’s book, Wassily Leontiefs input-output analysis, Paul Samuelson’s Foundations of Economic Analysis, Tjalling Koopmans’ activity analysis of production, and George Dantzig’s simplex algorithm were frequent topics of discussion, notably at the Cowles Commission when I joined it on June 1, 1950. To become associated at that time with a strongly interactive group which provided the optimal environment for the type of research that I wanted to do was an exceptional privilege. One leading motivation for that research was the study of the theory of