The article proposes a modification of the approach to the analysis of inter-industry balance. Instead of linear models of inter-industry balance, based on the hypothesis of W. Leontief about the constancy of the cost standards of production factors, the article studies nonlinear models. For the case of production functions with constant elasticity of substitution (CES) an algorithm for solving the inverse problem is proposed, which allows to identify the model of nonlinear inter-industry balance based on the data of the symmetric input-output table. Based on the Young transform and Fennel duality, with the help of this model, we develop a technology for analyzing inter-industry relationships. The technology has been tested on the data of economic statistics of Russia.

中文翻译：

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CES函数类的输入输出模型分析中的反问题

本文提出了一种行业间平衡分析方法的改进。本文基于W. Leontief关于生产要素成本标准不变的假设，而不是行业间平衡的线性模型，而是研究非线性模型。对于具有恒定替代弹性（CES）的生产函数，提出了一种求解逆问题的算法，该算法可以根据对称输入输出表的数据来识别非线性行业间余额模型。基于Young变换和Fennel对偶，在此模型的帮助下，我们开发了一种用于分析行业间关系的技术。该技术已经过俄罗斯经济统计数据的测试。