Tjalling Koopmans

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Tjalling Koopmans, 1967

Tjalling Charles Koopmans (August 28, 1910February 26, 1985) was a Dutch-American mathematician and economist, the joint winner with Leonid Kantorovich of the 1975 Nobel Memorial Prize in Economic Sciences.


  • While it was long possible and sometimes tempting for physicists to deny the usefulness of the molecular hypothesis, we economists have the good luck of being some of the ‘molecules’ of economic life ourselves, and of having the possibility through human contacts to study the behavior of other ‘molecules’.
    • Tjalling Koopmans in: Review of economics and statistics, Vol. 31 -(1949), p. 87
  • Econometrics may be defined as the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference.
    • Paul Samuelson, Tjalling Koopmans, and Richard Stone. "Report of the evaluative committee for Econometrica." Econometrica- journal of the Econometric Society. (1954): 141-146.
  • Optimizing responses of economic agents are simultaneously feasible only if the proper prices are already known to them. But these prices must somehow themselves be the result of the same responses.
    • Tjalling C. Koopmans, "Is the Theory of Competitive Equilibrium With It?," The American Economic Review, Vol. 64, No. 2, May 1974; p. 327
  • The early thirties brought what liberal economists called the Great Depression and Marxist economists described as the great crisis of capitalism. It dawned on me that the economic world order was unreliable, unstable, and, most of all, iniquitous. I sought intellectual contacts and friendship with a group of socialist students and also with a small handful of communist-oriented students and unemployed workers.

Three Essays (1957)


Tjalling C. Koopmans. Three essays on the state of economic science. Vol. 21. New York: McGraw-Hill, 1957.

  • [This work urges] a clearer separation, in the construction of economic knowledge, between reasoning and recognition of facts, for the better protection of both.
    • p. viii
  • One can in particular interpret the proposition as a statement conditions under which the simplicity of incentive structure and the economies of information handling characteristic of a competitive market organization can be secured without loss of efficiency of allocation... The price system carries to each producer, resource holder, or consumer a summary of information about the production possibilities, resource availabilities and preferences of all other decision makers. Under the conditions postulated, this summary is all that is needed to keep all decision makers reconciled with a Pareto optimal state once it has been established.
    • p. 53, as cited in: Harold Kincaid, ‎Don Ross (2009) The Oxford Handbook of Philosophy of Economics. p. 128
  • It is worth pointing out that in this particular study our authors have abandoned demand and supply functions as a tool for analysis, even as applied to individuals... [The problem] has been reformulated as one of proving that a number of maximizations of individual goals under interdependent restraints can be simultaneously carried out.
    • p. 60, as cited in: Mitra-Kahn, Benjamin H. "General Equilibrium Theory, its history and its relation (if any) to the Market Economy." (2005).
  • If evolutionary selection is the basis for a belief in profit maximization, 'then we should postulate that basis itself and not the profit maximization which it implies in certain circumstances.
    • p. 140-1
  • One is led to conclude that economics as a scientific discipline is still somewhat hanging in the air.
    • p. 141
  • We look upon economic theory as a sequence of conceptual models that seek to express in simplified form different aspects of an always more complicated reality.
    • p. 142
  • Without recognising indivisibilities — in human person, in residences, plants, equipment, and in transportation — location patterns, down to those of the smallest village, cannot be understood
    • p. 143, as cited in: Peter de Gijsel, ‎Hans Schenk (2006) Multidisciplinary Economics. p. 426
  • Decisions and plans made by others... [can be judged to be] quantitatively at least as important as the primary uncertainty arising from random acts of nature and unpredictable changes in consumers' preferences.
    • p. 163; as cited in: Richard Langlois (1989) Economics as a Process. p. 181
  • The solution of important problems may be delayed because the requisite tools are not perceived. Or the availability of certain tools may lead to an awareness of problems, important or not, that can be solved with their help.
    • p. 170

Concepts of Optimality and Their Uses, 1975


Tjalling C. Koopmans. "Prize Lecture: Concepts of Optimality and Their Uses," Nobel Media AB 2013. Web. 10 Jun 2014. Republished in: Nobel Lectures, Economics 1969-1980, Assar Lindbeck (eds), World Scientific Publishing Co., Singapore, 1992

  • According to a frequently cited definition, economics is the study of “best use of scarce resources.” The definition is incomplete. “Second best” use of resources, and outright wasteful uses, have equal claim to attention. They are the other side of the coin.
    • p. 239: Lead sentence
  • … a rather different class of applications of the idea of best allocation of scarce resources... usually referred to as the theory of optimal economic growth. In most studies of this kind made in the countries with market economies there is not an identifiable client to whom the findings are submitted as policy recommendations. Nor is there an obvious choice of objective function, such as cost minimization or profit maximization in the studies addressed to individual enterprises. The field has more of a speculative character. The models studied usually contain only a few highly aggregated variables. One considers alternative objective functions that incorporate or emphasize various strands of ethical, political, or social thought. These objectives are then tried out to see what future paths of the economy they imply under equally simplified assumptions of technology or resource availability.
    • p. 244
  • The principal customers aimed for are other economists or members of other professions, who are somewhat closer to the making of policy recommendations... The question of the clientèle is even more baffling when the problem concerns growth paths for time spans covering several generations. What can at best be recommended in that case is the signal the present generation gives, the tradition it seeks to strengthen or establish, for succeeding generations to take off from.
    • p. 244, as cited in: Vincent Martinet (2012) Economic Theory and Sustainable Development. p. 90

Quotes about Tjalling Koopmans

  • Linear programming was developed as a discipline in the 1940's, motivated initially by the need to solve complex planning problems in wartime operations. Its development accelerated rapidly in the postwar period as many industries found valuable uses for linear programming. The founders of the subject are generally regarded as George B. Dantzig, who devised the simplex method in 1947, and John von Neumann, who established the theory of duality that same year. The Nobel prize in econonmics was awarded in 1975 to the mathematician Leonid Kantorovich (USSR) and the economist Tjalling Koopmans (USA) for their contributions to the theory of optimal allocation of resources, in which linear programming played a key role. Many industries use linear programming as a standard tool, e.g. to allocate a finite set of resources in an optimal way.
  • Koopmans was also like Kantorovich in generalizing his approach from one sector of the economy to the economy as a whole. Koopmans showed the conditions required for economy-wide efficiency in allocating resources. He also, again like Kantorovich, used his activity analysis techniques to derive efficient criteria for allocating between the present and the future.
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