華氏産業連関理論について(横田禎昭教授退職記念特集)

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概要

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• Loo-keng Hua (1910〜1985) was a famous and world wide known mathematician with a great number of important contributions to number theory, algebra, function theory of several complex variables, partial differential equations, mathematical physics and operations research, optimization etc. He published more than 200 papers and 23 books, 9 of which were translated from Chinese into foreign languages. He also studies of some economic problems, and submitted a new input-output theory. He calls his input-output theory "Mathematical Theory of Globally Optimal Planned Economic Systems". Applying a theorem of non-negative matrix to an economic system, he obtains of growth of the system and the ratio between the sectors of production. Accordingly, he establishes a positive eigenvector method. Hua's input-output method is based a relation of this year and next year to different than Leontief. Hua building-up the positive eigenvector method, and has a important conclusion: if the initial state is not a positive eigenvector, then the economic system will break down sooner or later. When he prove the conclusion, he find his method is better than Brouwer's fixed-point theorem in mathematic. Because, the fixed point of Hua's mapping is unique and interior to the simplex, furthermore no liming cycle can exist. He found a more general model for if each sector has its own rate of change. He also considers the measure of deviation from the positive eigenvector, in distance of vector.

• 島根県立大学の論文
• 2003-03-28

著者

• 張 忠任

  島根県立大学総合政策学部・大学院開発研究科

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