Mathematics and Economics of Leonid Kantorovich

Por • 29 ene, 2011 • Sección: Economía

S.S. Kutateladze

Abstract: This is a short overview of the contribution of Leonid Kantorovich into the formation of the modern outlook on the interaction between mathematics and economics… In 1935 Kantorovich made his major mathematical discovery—he defined K-spaces, i. e., vector lattices whose every nonempty order bounded subset had an infimum and supremum. The Kantorovich spaces have provided the natural framework fordeveloping the theory of linear inequalities which was a practically uncharted area ofresearch those days. The concept of inequality is obviously relevant to approximate calculations where we are always interested in various estimates of the accuracy of

results. Another challenging source of interest in linear inequalities was the stock of problems of economics. The language of partial comparison is rather natural indealing with what is reasonable and optimal in human behavior when means and opportunities are scarce. Finally, the concept of linear inequality is inseparable fromthe key idea of a convex set. Functional analysis implies the existence of nontrivialcontinuous linear functional over the space under consideration, while the presenceof a functional of this type amounts to the existence of nonempty proper open convex subset of the ambient space. Moreover, each convex set is generically the solution set of an appropriate system of simultaneous linear inequalities…

Cite as: arXiv:1101.0984v1 [math.HO]

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