# Hurwicz, Leonid

# Hurwicz, Leonid *1917-*

Leonid Hurwicz is among the leading mathematical economists of his generation. He utilized game theory, mathematical programming, dynamical systems, and topology, among many other fields of mathematics, contributing to the development of those fields and to their application to economic theory and policy. Hurwicz was born in Moscow to Polish Jewish parents in the year of the Russian Revolution. His parents therefore moved with him to Warsaw in 1918. Hurwicz shared the educational experience of all Jewish boys in Warsaw, likely attending a gymnasium, or high school, with further education in a yeshiva. He entered the University of Warsaw in 1933, graduating in 1938 with a degree in law, having concentrated in political economy. In 1938 Hurwicz traveled to Britain to study at the London School of Economics and Political Science under neo-Austrian economists Lionel Robbins (1898–1984) and Friedrich Hayek (1899–1992). Importantly for his subsequent career, a recent member of the faculty was Polish socialist refugee Oskar Lange (1904–1965), who had left the University of Krakow in 1935. In 1939 Hurwicz studied at the Postgraduate Institute of International Studies in Geneva, where he attended a seminar conducted by Jewish Austrian economist Ludwig von Mises (1881–1973).

At the suggestion of Lange, Hurwicz migrated to the United States in 1940. He went to Chicago, which had a large Polish immigrant population, and studied for two years at the University of Chicago, where Lange was on the economics faculty. In 1941, while a student at Chicago, Hurwicz also studied at Harvard University under Wassily Leontief (1906–1999), whom he met at the Cowles Commission conference in Colorado Springs in 1940.

In January 1942 Hurwicz was recruited to the staff of the Cowles Commission by research director Theodore O. Yntema (1900–1985). In this position, Hurwicz assisted Lange in statistical testing of business-cycle theories, and worked with Yntema and Joel Dean (1906–1979) as executive director of the project on wartime price controls of the Committee on Price Determination of the Price Conference of the National Bureau of Economic Research (NBER). He would remain on the commission staff until 1961.

In 1941 Hurwicz secured a research and teaching fellowship at the Massachusetts Institute of Technology. The following year, he taught mathematics and statistics to members of the U.S. Army Signal Corps at the Illinois Institute of Technology. Simultaneously, and continuing to 1944, he was hired as a faculty member of the Institute of Meteorology at the University of Chicago and an instructor of statistics in the Economics Department. He was awarded a Guggenheim Fellowship for the 1945–1946 period. From 1946 to 1949 he served as associate professor of economics at Iowa State University in Ames. From 1949 to 1951 Hurwicz served as professor of economics at the University of Illinois. He then became professor of economics and mathematics at the University of Minnesota Graduate School of Business, a position he retained until retiring around 1987.

In the 1940s and early 1950s Hurwicz presented several papers to professional associations in mathematics, statistics, and economics, and he published papers in the journals of these associations and in a book published by the Cowles Commission. Most of these papers were on statistics. His focus shifted to game theory in 1953, then in 1955 he began to focus explicitly on economics, publishing articles on resource allocation, including a review of Leontief’s book on input-output analysis. In 1956 Hurwicz and Kenneth Arrow began a long collaboration that would continue beyond the 1970s. In 1958 Hurwicz and Arrow published an article on the stability of equilibrium in a general equilibrium system. Hurwicz’s first book was published in 1958, when he was forty-one years old. It was a joint effort with Arrow and Hirofumi Uzawa.

In 1955 Hurwicz published a Cowles Commission discussion paper titled “Decentralized Resource Allocation,” in which he initiated his research on economic information theory. In this paper, he was stimulated by Hayek’s polemic with the socialists on the feasibility of calculating equilibrium prices and quantities in the absence of a market, due to the absence at the center of decentralized price information. Hurwicz’s 1955 paper developed from the argument by Hayek and Mises that only a decentralized (i.e., market) system could manage a modern economy. His subsequent writings in this area represent extensions of this argument in different mathematical directions. Arrow and Hurwicz later observed that the Hayek-Mises position implied that information was not a costless resource, but that a perfectly competitive market minimized this cost.

Because solving a system of linear equations is simpler than solving a system of nonlinear equations, most macroeconomic models are specified as linear models. Hurwicz was a leader in research on estimating the parameters of the nonlinear model. The parameters were the prices at which demand equaled supply in each of hundreds of industries. His motivation for this research was not only theoretical, but stemmed from his work in the 1940s at the Cowles Commission, where he directed the program to study empirically, as well as theoretically, the wartime price-controls program, the nearest that the United States has ever come to comprehensive central economic planning.

Given a system of differential equations, several questions may be posed: Does a solution to the system exist? Is any given solution, once found, a stable solution? And what mathematical tools can be used to answer the first two questions? Hurwicz did not contribute to the literature on the existence problem. Between 1958 and 1960, he and Arrow published four articles and one book on the stability issue. In these publications, they attempted to extend the stability conditions for a single market to the general equilibrium case of multiple markets. Arrow and Hurwicz developed an analysis that economist Don Patinkin (1922–1995) called “stability in the large,” defined as “the conditions that make it possible for the Walrasian *tâtonnement* to bring the economy to an equilibrium from any point whatsoever.” They simplified this task by reducing the economy to a two-good economy (Hurwicz and Arrow 1958, p. 522). A recent answer to the third question is phase diagrams, which assist in solving systems of differential equations. Hurwicz did not use this technique in any publications through the 1970s.

Hurwicz’s work in linear and nonlinear programming was done largely in the 1950s with Arrow. Most of this research focused on the development of the gradient method of finding a solution to the programming problem of optimizing a function under constraints. The gradient method was intended to solve concave functions, rather than linear functions. The project found that the gradient method was inferior to the simplex method, an algorithm developed by George Dantzig (1914–2005). This was so despite the fact that the simplex method had been developed to solve linear functions.

Hurwicz is considered the father of information theory in economics. He showed clearly that information and its distribution within economic institutions was critical to decision making in resource allocation. This work provided additional theoretical underpinnings for transfer pricing in state enterprises and large complex private corporations.

**SEE ALSO** *Cumulative Causation; Difference Equations; Differential Equations; Information, Economics of; Nonlinear Regression; Phase Diagrams; Programming, Linear and Nonlinear; Stability in Economics; Transfer Pricing*

## BIBLIOGRAPHY

### PRIMARY WORKS

Arrow, Kenneth, and Leonid Hurwicz, eds. 1977. *Studies in Resource Allocation Processes*. New York: Cambridge University Press.

Chipman, John S., Leonid Hurwicz, Marcel K. Richter, and Hugo S. Sonnenschein, eds. 1971. *Preferences, Utility, and Demand: A Minnesota Symposium*. New York: Harcourt.

Hurwicz, Leonid. 1955. Decentralized Resource Allocation. Cowles Commission Discussion Paper No. 2112.

Hurwicz, Leonid. 1973. The Design of Mechanisms for Resource Allocation: Richard T. Ely Lecture. *American Economic Review: Papers and Proceedings of the Eighty-fifth Annual Meeting of the American Economic Association* 63 (2): 1–30.

Hurwicz, Leonid, and Kenneth Arrow. 1958. On the Stability of the Competitive Equilibrium, I. *Econometrica* 26 (4): 522–553.

Hurwicz, Leonid, Kenneth Arrow, and Hirofumi Uzawa. 1958. *Studies in Linear and Non-Linear Programming*. Stanford, CA: Stanford University Press.

Hurwicz, Leonid, and Stanley Reiter. 2006. *Designing Economic Mechanisms*. New York: Cambridge University Press.

Hurwicz, Leonid, David Schmeidler, and Hugo Sonnenschein, eds. 1985. *Social Goals and Social Organization: Essays in Memory of Elisha Pazner*. Cambridge, U.K.: Cambridge University Press.

### SECONDARY WORKS

Chipman, John, Daniel McFadden, and Marcel K. Richter, eds. 1988. *Preferences, Uncertainty, and Optimality: Essays in Honor of Leonid Hurwicz*. Boulder, CO: Westview.

Graves, Theodore, Roy Radner, and Stanley Reiter, eds. 1987. *Information, Incentives, and Economic Mechanisms: Essays in Honor of Leonid Hurwicz*. Minneapolis: University of Minnesota Press.

*Julian Ellison*

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