John von Neumann's contribution to economic science

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

Introduction

Often described as a genius, John von Neumann made significant contributions in a wide range of fields. His work in mathematical physics won him praise as the primary intellectual influence responsible for the emergence of game theory, digital computing, and cellular automata. Despite the mathematical nature of his scientific interest, von Neumann also made important contributions to economics. His influence on the study of economics has received universal acclaim from prominent economists. Despite disagreeing with von Neumann on crucial questions, Paul Samuelson, a Nobel Laureate in Economics, observed: "the incomparable Johnny von Neumann. He darted briefly into our domain, and it has never been the same since." (1) Richard Stone, another Nobel Laureate in Economics, avers that von Neumann and Oskar Morgenstern's The Theory of Games and Economic Behavior (1944) is " ... the most important textbook since [John Maynard] Keynes' General Theory." (2) E. Roy Weintraub, current President of the History of Economics Society, described von Neumann's "A Model of General Economic Equilibrium" as " ... the greatest paper in mathematical economics that was ever written." (3) Richard Goodwin, a specialist in the study of economic dynamics, echoed Weintraub's praise for von Neumann's work, characterizing "A Model of General Economic Equilibrium," as " ... one of the great seminal works of the century.... " (4) This study seeks to validate such admiration for von Neumann's influence on economic science by analyzing his two major contributions to the study of economics, "The Expanding Economic Model" and The Theory of Games and Economic Behavior.

John von Neumann: The Brilliant Young Mathematician

Janos (5) von Neumann was born on December 28, 1903 into a wealthy Jewish banking family (6) in Budapest, Hungary. He benefited from an elitist education in that 'booming' city. (7) At the age of ten, he was recognized a child prodigy. (8) By the age of seventeen, von Neumann enrolled at the University of Budapest to study mathematics. Between 1921 and 1923 he went to Budapest only to take exams while he attended the University of Berlin to take courses in physics, including statistical mechanics taught by Albert Einstein. (9) In Berlin, he associated with other distinguished Hungarian emigres, including Eugene Wigner, Leo Szilard, and Dennis Gabor, all prominent members of the "Hungarian Phenomenon" which later exerted an enormous impact on American physics and mathematics. (10) At the same time, von Neumann met the mathematician David Hilbert, a major influence on much of his work, at Gottingen. (11) He then attended the Swiss Federal Institute of Technology at Zurich, where he received a degree in Chemical Engineering in 1925. One year later, von Neumann earned a Ph.D. in mathematics with the highest honors from the University of Budapest. (12) After teaching mathematics at Princeton University for a semester in 1930, von Neumann moved permanently to the United States in 1933. He taught near Princeton, as a Professor of Mathematics at the newly formed Institute for Advanced Study (IAS) created by Abraham Flexner alongside such notable scientists and mathematicians as Einstein, Enrico Fermi, Hermann Weyl, and Wigner. (13)

Von Neumann proved to be a brilliant young mathematician. Between 1922 and 1927, he produced eighteen major mathematical articles. Much of his early research can best be described as a response to Hilbert's mathematical program. (14) Sometimes called the "formalist" school of mathematics, (15) this approach was concerned with both the foundations of mathematics and axiomatization of mathematical physics. The attempt to establish various areas of mathematics on a secure axiomatic basis stood at the core of Hilbert's program, and von Neumann's projects were included in it. (16) Both men were interested in demonstrating how mathematics could become a widely applicable tool, even in fields that were, until then, not easy to formalize mathematically. (17) In explaining von Neumann's contributions to economics in this manner, his work reflects a belief in the relevant role mathematics could play in science and society rather than a genuine interest in economic issues.

Von Neumann's Contributions to Economics

Von Neumann made two major contributions to economic science. The first, the General Economic Equilibrium Model, is often referred to as von Neumann's 'Expanding Economic Model' (EEM). (18) The second, The Theory of Games and Economic Behavior (TGEB), von Neumann co-authored with Oskar Morgenstern. In both works, von Neumann applied mathematical theory to economics. (19) He first expressed an interest in studying economics during the 1920s to Nicholas Kaldor and at a seminar in Berlin. His first written works on theoretical economics appeared in the early 1930s. (20) In 1932, while traveling regularly between Berlin and America, von Neumann presented an economic model at a Princeton mathematics seminar. The text, delivered in German, was originally entitled "On Certain Equations of Economics and A Generalization of Brower's Fixed-Point Theorem (translation)." The paper would be published in 1937 as part of the proceedings of Karl Menger's (21) Vienna Colloquium. (22) Two years later, von Neumann sent a copy of his paper to Kaldor, then chair of the editorial committee of the Review of Economic Studies, who believed that it deserved a wider audience. After a delay caused by World War II, von Neumann's work was published in October 1945, entitled "A Model of General Economic Equilibrium." (23)