Inverse problems in analysis of input-output model in the class of CES functions

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. © 2021 De Gruyter. All rights reserved.