John von Neumann's contribution to economic science

International Social Science Review, Fall-Winter, 2003 by Maria Joao Cardoso De Pina Cabral

(13) Von Neumann was the youngest member of the faculty at IAS.

(14) Actually, von Neumann's earlier work focused on topics of interest to Hilbert such as set theory, operator theory, and the mathematical foundations of quantum mechanics.

(15) Philip Mirowsky, "What were von Neumann and Morgenstern Trying to Accomplish?" History of Political Economy 24 (1992):117.

(16) Ibid.

(17) Leonard, "From Parlor Games to Social Science," 732.

(18) Macrae, John von Neumann, 253.

(19) Christian Schmidt, "Game Theory and Economics: An Historical Survey," Revue d'Economie Politique 100 (September-October 1990):605.

(20) Leonard, "Creating a Context for Game Theory," 50.

(21) Menger, a professor of mathematics and the son of the famous economist, was one of the three founders of the neoclassical school.

(22) It seems likely that von Neumann just sent the text to the colloquium's organizer. Macrae, John von Neumann, 248.

(23) John von Neumann, "A Model of General Economic Equalibrium," Review of Economic Studies XIII (October 1945):1-9.

(24) Heinz D. Kurz and Neri Salvadori, "Von Neumann Growth Model and the Classical Tradition," European Journal of the History of Economic Thought 1 (Autumn 1993):134.

(25) Nicholas Kaldor, "John von Neumann: A Personal Recollection," in John von Neumann and Modern Economics, eds. Dore, Chakravarty, and Goodwin, 303.

(26) Ibid.

(27) Macrae, John von Neumann, 253. Fixed-point theorems are useful for establishing the existence of solutions to a system of non-linear equations. In economics, fixed point theorems, such as the Brower Fixed Theorem, are often used to guarantee the existence of equilibrium in a wide variety of models of the economy. See Jerry Green and Walter P. Heller, "Mathematical Analysis and Convexity with Applications to Economics," in Handbook of Mathematical Economics, vol. 1, eds. Kenneth Arrow and Michael Intrilligator (New York: North-Holland, 1981):49-50.

(28) Leonard, "Creating a Context for Game Theory," 50.

(29) Macrae, John von Neumann, 253-55.

(30) Ibid., 248.

(31) Leonard, "Creating a Context for Game Theory," 50. Walras' theory refers to the general equalibrium theory developed by the Frenchman Leon Walrus in his Elements of Pure Economics (1874). In the "Walrasian" approach, the fundamental tool of analysis was a system of simultaneous market demand and supply equations. In this context, Walrus' theory was concerned with grand themes such as the existence of an equilibrium solution, the stability of that equalibrium, the incorporation of capital and growth, and the introduction of money.

(32) Leonard, "From Parlor Games to Social Science," 736.

(33) Kurz and Salvadori, "Von Neumann Growth Model and the Classical Tradition," 138.

(34) Ibid.

(35) Ibid., 151.

(36) Ibid., 140.

(37) In support of their position, Kurz and Salvadori argue that there are difficulties in conciliating neoclassical analysis with von Neumann's growth model. They stress that in von Neumann's model: The initial endowment of the economy is not present; the growth rate is determined endogenuously; the direct marginalist connection between prices and quantities is not assumed in contrast to Walras' formula; there is an asymmetry in the theory of distribution that is characteristic of classical analysis; and, it takes into account both circulating and fixed capital. Ibid., 135-37.