Optimal normalized structure of demand and value added in a productive leontief model¹

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• 作者：P. I. Stetsyuk and L. B. Koshlai
• 关键词：Leontief matrix ; static Leontief model ; extremum quadratic problem ; eigenvalues and eigenvectors
• 刊名：Cybernetics and Systems Analysis
• 出版时间：September 2010
• 出版年：2010
• 期刊代码：16_10600396
• 类别：mt
• 卷：46
• 期：5
• 页码：729-736
• 数据来源：sp

摘要

The problem of finding normalized vectors of demand and value added in a productive Leontief model is solved. These vectors maximize the national income. It is shown that if the Leontief matrix is productive and indecomposable, then an optimal normalized structure is determined by positive components of the eigenvectors that correspond to maximum eigenvalues of some symmetric matrices. The results of test calculations for a seven-branch matrix are presented.