Charles F. Roos

Charles Frederick Roos (May 18, 1901 – January 6, 1958) was an American economist who made contributions to mathematical economics. He was one of the founders of the Econometric Society together with American economist Irving Fisher and Norwegian economist Ragnar Frisch in 1930. He served as secretary-treasurer during the first year of the society and was elected as president in 1948. He was director of research of the Cowles Commission from September 1934 to January 1937.

Roos earned a PhD in mathematics from Rice University in 1926, under supervision of Griffith C. Evans. His direct involvement with two key institutions in economic history, both the Econometric Society and the Cowles Commission, place him in a pivotal position in the mathematization of economics in the first half of the 20th century.

Biography Charles Frederick Roos was born in New Orleans, Louisiana on 18 May 1901. He studied mathematics at the Rice Institute, receiving his Bachelor of Arts degree in 1921, his Master of Arts degree in 1924, and, being awarded his PhD in 1926. His main interests were in the calculus of variations, integral equations, and the applications of these to economic theory. His early research was deeply inspired by the work of his thesis advisor Griffith C. Evans who used these same mathematical tools to analyze business cycles, economic equilibrium, and economic competition. During the following years, from 1926 to 1928, Roos continued his academic studies as National Research Fellow at the University of Chicago and Princeton University.

At Princeton, Roos met the Norwegian economist Ragnar Frisch who was travelling there under a grant from the Rockefeller Foundation. They shared a common sentiment that economics should be brought closer to mathematics and to statistics (this would later become known as econometrics) and decided to request support from American economist Irving Fisher, at Yale University, to help organize an association to research such topics. Later that year, both Frisch and Roos met with Fisher to discuss the formation of what would become the Econometric Society.

Following his National Research Fellowship Roos was hired as assistant professor of mathematics at Cornell University. He resigned this position in 1931 to assume a position as permanent secretary at the AAAS where he arranged programs in economics. In the wake of the Great Depression Roos organized a symposium on unemployment. This work was a summary of much his previous research and academic work in dynamic economics and explored many business applications such as in the demand for gasoline, agricultural products, and residential building. The Cowles Commission would later become an important institution in mathematical economics specially associated with Walrasian general-equilibrium theory and general-equilibrium models. Many nobel laureates in economics were associated with the Commission and/or wrote a Cowles Monograph. Some examples include Kenneth Arrow (social choice), Gerard Debreu (general equilibrium), Tjalling Koopmans (activity analysis, linear programming), Lawrence Klein (economic fluctuations), and Harry Markowitz (portfolio selection). The second Cowles Monograph was also written by Roos based on his work at the NRA.

Roos' business interests lead him to New York in 1937, where, a couple years later, he founded the Institute for Applied Econometrics (later renamed to Econometric Institute). The firm worked with big businesses such as General Motors and offered broad forecasting services. Roos' work with automobile industry resulted in the book The Dynamics of Automobile Demand, published in 1939. In the same year, Roos was named a Fellow of the American Statistical Association. He would work as director of the Econometric Institute until his death on January 7, 1956. While the latter part of Roos' career saw a decline in his academic publications he still found ways to keep himself active and even published in a survey article in Econometrica in 1955.

Mathematical economics Charles Roos was one of the first to employ the calculus of variations to economic theory. His work follows closely that of his PhD advisor Griffith Evans and is partly inspired by the works of Vilfredo Pareto, Léon Walras, and Cournot. His main interest was to develop a dynamic theory of economics and he most commonly framed his analysis as a profit maximization problem solved by a firm. Solving this by means of differential calculus determines the optimal amount of production in a given instant of time. Roos' approach, on the other hand, allowed one to determine the optimal amounts of production during an interval of time, allowing for prices to change during this period. His 1925 article A Mathematical Theory of Competition explores this situation under the hypothesis of monopoly and that of a large number of individual producers. In his later work he extends this to a general-equilibrium framework by considering how producers and consumers would converge to market equilibrium over a given interval of time. Most of these contributions were summarized in the first Cowles Monograph Dynamic Economics: Theoretical and Statistical Studies of Demand, Production and Prices'' published in 1934.

List of publications