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Tjalling Koopmans,
Physicist and Economist

Tjalling (challing) Charles Koopmans, a Dutch-American economist, won the Nobel Prize in economics in 1975, but he started his intellectual career as a physicist. There is a Koopmans' Theorem in quantum mechanics which is still an important result used today in physics. He characterized this theorem to lay people as being about a way to compute the energy required to ionize the atoms of alkali metals (sodium, potassium, etc.) but it is more general than this application.

Tjalling Koopmans' family came from Freisland to the town of   's Graveland, near Hilversum. Tjalling, the third son, was born in 1910. He entered the University of Utrect at age 17 and studied mathematics. Although young Tjalling Koopmans had a definite talent for mathematics he found pure mathematics unfullfilling and began to read in other fields, such as the philosophy of science. At one time considered becoming a psychiatrist.

He wanted a field that dealt with the real world but utilized the mathematics that he had learned. He decided in 1930 to become a thoretical physicist and completed a master's degree in physics at the University of Utrecht in 1933. He entered a doctoral program at the University of Leiden and completed this graduate work in 1936. Under the guidance of Kramers, the leading theoretical physicist of the Netherlands, Tjalling Koopmans published in 1934 the article that contained what later became known as Koopmans' Theorem.

Even while he was gaining his training in physics Tjalling Koopmans was developing an interest in economics, particularly mathematical economics although his first reading was in Marx. He became acquainted with Jan Tinbergen while still at the University of Utrecht and joined the circle of students who met with Tinbergen once a week for a lecture and discussion. His doctoral dissertation was not in physics but a topic in mathematical statistics which was applicable to the newly born field of econometrics. Nevertheless Kramers served as his thesis adviser and his dissertation was presented to the Faculty of Mathematical and Physical Sciences in 1936. Also in 1936, shortly before the award of his doctorate, he married the very beautiful Truus Wanningen, an economist whom tutored in mathematics.

After graduation Tjalling Koopmans lectured for about two years at the School of Economics in Rotterdam. Afterwards he worked on business cycle modeling for the League of Nations in Geneva. Thereafter World War II began and the Koopmans family moved to the United States. It was then that Tjalling Koopmans began work on methods for allocating shipments between sources and destinations such that total cost would be minimized. This is called the transportation problem, a special case of what subsequently became known as linear programming.

After World War II Tjalling Koopmans joined the Cowles Commission for Research in Economics in in Chicago. The Cowles Commission had been funded by Alfred Cowles III who lived in Colorado Springs because of his tuberculosis. It was created to develop methods which combined economic theory, mathematical modeling and statistics and was instrumental in the development of econometrics as a field of study. After a few years in Colorado Springs the staff of the Cowles Commission moved it to the University of Chicago where it was when Tjalling Koopmans joinedit. But Chicago was only a temporary sojourn. Problems with the urban environment around the campus of the University led to another move to Yale University in New Haven, Connecticut. Along the way the name was changed from Cowles Commission to the Cowles Foundation for Research in Economics. Tjalling Koopmans, along with other members of the Cowles Foundation including James Tobin, accepted appointments to the faculty of Yale. Tjalling Koopmans remained with Yale and the Cowles Foundation the rest of his academic career, serving for a period as the director of the Cowles Foundation. Tjalling Koopmans died in 1985 at age 75 after a brief illness.

This page deals only with a minor but elegant formulation of Koopmans. He published a volume entitled, Three Essays on the State of Economics. The first was a simple presentation of general equilibrium theory. In that essay he examined the question of how one could construct the joint production possibilities set for two economies when one knows the production possibilities sets for those two economies. Suppose the production possibilities sets are those given below for economies involving the production of only two goods, X and Y. If (x1, y1) and (x2, y2) are two production combinations from the production possibilities sets of 1 and 2, respectively, then (x1+2, y1+y2) is a feasible production combination in their joint production possibilities set. The vector addition of the two feasible production combinations is given below.

This construction indicates the essential role of maximization in establishing efficiency. One can consider the production possibilities set for an economy being the sum of the production possibilities sets of the firms in the economy. Unless the firms are maximizing profit with respect to a common set of prices it is unlikely that the economy will achieve economic efficiency.

One can imagine systematically adding together different combinations, but no matter what set of points was constructed there would be the nagging doubt as to whether the total production possibilities set had been delineated. Koopmans provided an elegant way to map out the joint production possilibies set. One simply chooses a set of prices ((p1, p1) and maximizes the value of production on each of the production possibilities sets, as is shown in the graph below. The maximization will lead to efficient production combinations and the sum of outputs will be an efficient combination on the joint production possibility curve. By letting the relative prices sweep through all possible values from zero to positive infinity the entire set of efficient production combinations for the joint production possibilities set will be mapped out.

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