John von Neumann, 1903-1957
Born in Budapest, Hungary in 1903. After simultaneously earning a doctorate
in mathematics from the University of Budapest and a doctorate in
chemistry from the University of Zurich, he joined the faculty of the University
of Berlin in 1927. He moved to Princeton in 1932 where he became the youngest
member of the IAS. During this time, he made important contributions not only to
pure and applied mathematics, but also to physics and, in some ways, philosophy
(esp. in relation to the quantum paradox). He was also active in the Manhattan
Project (the development of the atomic bomb) and was one of President Truman's
advisors on the Atomic Energy Commission. His later work on parallel processes
and networks has earned him the label of the "father of the modern
computer". As Nicholas Kaldor would later write, "He was
unquestionably the nearest thing to a genius I have ever encountered."
This astoundingly creative mathematician has played a rather important role
in post-war economic theory through two essential pieces of work: his 1937 paper
on General Equilibrium and his 1944 book (with Oskar Morgenstern) on Game
Theory.
John von Neumann's famous 1937 paper, initially written under the auspices of
the famous "Vienna Colloquium" and derived from his reading of
Wicksell and Cassel, has been called "the greatest paper in mathematical
economics that was ever written" (E. Roy Weintraub, 1983). It precipitated
what Morishima later called a veritable "von Neumann Revolution" in
general equilibrium, capital and growth theory. He introduced several important
concepts in his 1937 paper, besides the obvious methodological one of
resurrecting "mathematical economics":
To General Equilibrium Theory:
- (1) The concept of "activity analysis" production sets - to be
later extensively employed by Koopmans, Gale, Debreu and others in G.E.
- (2) Linear system of "production of commodities by means of
commodities"/"input-output" as later used and developed by
Leontief and Sraffa.
- (3) price-cost and demand-supply inequalities which accounted for the
Vienna Critique of Walrasian systems and did away with the old method of
"counting equations and unknowns".
- (4) The first use of a (generalization) of Brouwer's fixed- point theorem
to prove the existence of an equilibrium.
- (5) The minimax and maximin solution method.
- (6) The duality of prices and quantities.
- (7) Linear Programming and Complementary Slackness - concepts later
developed by Dantzig, Kantorovich and others.
To Capital and Growth Theory:
- (1) Concept of disaggregated time and capital.
- (2) Linear production system with inequalities and joint production.
- (3) The concept of "balanced" or "steady-state" growth
- later employed with gusto by Harrod, Solow and the entire flow of growth
models since.
- (4) The "Golden Rule" - showing that the rate of interest is
related to the rate of growth rather than the quantity of capital,
anticipating Allais.
- (5) The "Turnpike"/"von Neumann Ray" - later developed
by Hicks, Samuelson, Radner, McKenzie and related to the "optimal
growth theory" of Cass-Koopmans and successors.
John von Neumann's 1944 book with Oskar Morgenstern, Theory of Games and
Economic Behavior was a landmark of twentieth century social science.
Besides single-handedly inventing the entire field of Game Theory (which he
began doing with a famous 1928 article), this book introduced several other
important elements used in other fields of economics:
- (1) The set-theoretic axiomatization of choice theory per se (as later
pursued by Arrow, Debreu, etc.)
- (2) The theory of choice under conditions of risk/uncertainty - in
particular, the development of the "von Neumann-Morgenstern"
utility function.