mathematics

Tjalling Koopmans

Tjalling Koopmans is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Tjalling Koopmans rather than just read about it. In short: Tjalling Charles Koopmans (August 28, 1910 – February 26, 1985) was a Dutch-American mathematician and economist. He was the joint winner with Leonid Kantorovich of the 1975 Nobel Memorial Prize in Economic Sciences for his work on the theory of the optimum allocation of resources.

Key takeaways

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Reproduce the core statement of Tjalling Koopmans from memory before moving on to harder problems.

Reference excerpt

Tjalling Charles Koopmans (August 28, 1910 – February 26, 1985) was a Dutch-American mathematician and economist. He was the joint winner with Leonid Kantorovich of the 1975 Nobel Memorial Prize in Economic Sciences for his work on the theory of the optimum allocation of resources. Koopmans showed that on the basis of certain efficiency criteria, it is possible to make important deductions concerning optimum price systems.

Biography

Koopmans was born in 's-Graveland, Netherlands. He began his university education at the Utrecht University at seventeen, specializing in mathematics. Three years later, in 1930, he switched to theoretical physics. In 1933, he met Jan Tinbergen, the winner of the 1969 Nobel Memorial Prize in Economics and moved to Amsterdam to study mathematical economics under him. In addition to mathematical economics, Koopmans extended his explorations to econometrics and statistics. In 1936, he graduated from Leiden University with a PhD, under the direction of Hendrik Kramers. The title of the thesis was "Linear regression analysis of economic time series". He also worked for the Economic and Financial Organization of the League of Nations. Koopmans moved to the United States in 1940. There, he worked for a while for a government body in Washington, D.C., where he published on the economics of transportation focusing on optimal routing, then moved to Chicago where he joined a research body, the Cowles Commission for Research in Economics, affiliated with the University of Chicago. In 1946, he became a naturalized citizen of the United States, and in 1948, director of the Cowles Commission. Also in 1948, he was elected as a Fellow of the American Statistical Association. In 1950, he became a corresponding member of the Royal Netherlands Academy of Arts and Sciences. Rising hostile opposition to the Cowles Commission by the department of economics at University of Chicago during the 1950s led Koopmans to convince the Cowles family to move it to Yale University in 1955 (where it was renamed the Cowles Foundation). He continued to publish, on the economics of optimal growth and activity analysis. Koopmans's early works on the Hartree-Fock theory of atomic and molecular structure are associated with the Koopmans' theorem, which is very well known in quantum chemistry. Koopmans was awarded his Nobel memorial prize (jointly with Leonid Kantorovich) for his contributions to the field of resource allocation, specifically the theory of optimal use of resources. The work for which the prize was awarded focused on activity analysis, the study of interactions between the inputs and outputs of production, and their relationship to economic efficiency and prices. Finally, the importance of the article by Koopmans (1942) deriving the distribution of the serial correlation coefficient was recognized by John von Neumann, and it later influenced the optimal tests for a unit root by John Denis Sargan and Alok Bhargava (Sargan and Bhargava, 1983).

Family and name Tjalling Charles Koopmans was a son of Sjoerd Koopmans and Wytske van der Zee; his middle name Charles was probably derived from his patronymic "Sjoerds". One of Sjoerd Koopmans's sisters, Gatske Koopmans, and her husband Symon van der Meer were the paternal grandparents of Nobel Prize winner Simon van der Meer. Tjalling Koopmans and Simon van der Meer were therefore first cousins once removed. Tjalling had two brothers, one of whom was theologian Rev. Dr Jan Koopmans, who in 1940, early during the German occupation of the Netherlands, wrote the widely distributed pamphlet "Bijna te laat" ("Almost too late", 30,000 copies), warning about the future of the Jews under the Nazi regime. In 1945, towards the end of the war, he witnessed an execution of hostages in Amsterdam from behind a window and was mortally wounded by a stray bullet. Koopmans married Truus Wanningen in October 1936. The couple had three children – a son, Henry, and two daughters, Anne and Helen.

Selected works Koopmans, Tjalling C. (March 1942). "Serial correlation and quadratic forms in normal variables". Annals of Mathematical Statistics. 13 (1). Institute of Mathematical Statistics: 14–33. doi:10.1214/aoms/1177731639. JSTOR 2236158. Koopmans, Tjalling C.; Montias, J.M. (1971). On the Description and Comparison of Economic Systems (Cowles Foundation Paper 357). Koopmans, Tjalling C. (December 11, 1975). Nobel Memorial Lecture: Concepts of optimality and their uses (PDF). Koopmans, Tjalling C.; Debreu, Gérard (December 1982). "Additively decomposed quasiconvex functions" (PDF). Mathematical Programming. 24 (1). Springer: 1–38. doi:10.1007/BF01585092. S2CID 206799604.

Further reading Hughes Hallett, Andrew J. (1989). "Econometrics and the Theory of Economic Policy: The Tinbergen–Theil Contributions 40 Years On". Oxford Economic Papers. 41 (1): 189–214. doi:10.1093/oxfordjournals.oep.a041892. JSTOR 2663189. Sargan, J. D.; Bhargava, Alok (1983). "Testing residuals from least squares regressions for being generated by the Gaussian random walk". Econometrica. 51 (1): 153–174. doi:10.2307/1912252. JSTOR 1912252.

See also Linear programming Transportation theory (mathematics) Koopmans' Theorem (in quantum chemistry)

References

External links

Tjalling Koopmans on Nobelprize.org Scarf, Herbert E., "Tjalling Charles Koopmans: August 28, 1910 – February 26, 1985", National Academy of Science IDEAS/RePEc Tjalling Koopmans at the Mathematics Genealogy Project Henderson, David R., ed. (2008). "Tjalling Charles Koopmans (1940– )". The Concise Encyclopedia of Economics. Library of Economics and Liberty (2nd ed.). Liberty Fund. p. 552. ISBN 978-0865976665. Biography of Tjalling Koopmans from the Institute for Operations Research and the Management Sciences Tjalling Charles Koopmans Papers (MS 1439). Manuscripts and Archives, Yale University Library.

Illustrations

Worked examples

Example 1 — a first encounter with Tjalling Koopmans

Start with the simplest possible case. Write down what Tjalling Koopmans claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Tjalling Koopmans before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Tjalling Koopmans ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Tjalling Koopmans

In research: Tjalling Koopmans appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Tjalling Koopmans in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Tjalling Koopmans is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1910 births, 1985 deaths, 20th-century American economists, so understanding it makes those chapters shorter.
In everyday life: Look for Tjalling Koopmans outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Tjalling Koopmans in 20 minutes

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Frequently asked questions

What is Tjalling Koopmans in simple terms?

Why does Tjalling Koopmans matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Tjalling Koopmans?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Tjalling Koopmans.